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| Method | #Param | GenEval↑ | CompBench↑ | DSG↑ | HPSv2↑ |
| SDXL | 2.6B | 0.55 | 0.42 | 0.72 | 27.7 |
| FLUX.1 | 12.0B | 0.66 | 0.47 | 0.73 | 29.2 |
| SD3 | 8.0B | 0.71 | 0.49 | 0.76 | 28.9 |
| OneDiff | 2.8B | 0.65 | 0.44 | 0.68 | 27.5 |
| OmniGen | 3.8B | 0.70 | 0.46 | 0.66 | 27.7 |
| UniVG | 3.7B | 0.70 | 0.48 | 0.75 | 28.2 |
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| CLIP-T↑ | CLIP-I↑ | CLIP-T↑ | CLIP-I↑ |
| InsP2P | 24.5 | 83.7 | 21.9 | 83.4 |
| MGIE | 26.4 | 84.6 | 22.4 | 84.2 |
| EmuEdit | 26.1 | 89.7 | 23.1 | 85.9 |
| OneDiff | 24.8 | 88.5 | 22.0 | 85.5 |
| OmniGen | 25.8 | 86.3 | 23.1 | 82.9 |
| UniVG | 29.5 | 86.3 | 25.9 | 84.7 |
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| ✓ | 0.328 | 28.1 |
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| Time | GPU | Time | GPU |
| OneDiff | 2.8B | 6.3 | 8151 | 10.8 | 9155 |
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| UniVG | 3.7B | 10.4 | 8849 | 10.4 | 8849 |
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diff --git a/2025/UniVerse_ Unleashing the Scene Prior of Video Diffusion Models for Robust Radiance Field Reconstruction/1113cb10-817b-436f-9eb6-a3b052766c61_content_list.json b/2025/UniVerse_ Unleashing the Scene Prior of Video Diffusion Models for Robust Radiance Field Reconstruction/1113cb10-817b-436f-9eb6-a3b052766c61_content_list.json
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+ "type": "text",
+ "text": "UniVerse: Unleashing the Scene Prior of Video Diffusion Models for Robust Radiance Field Reconstruction",
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+ "text": "Jin $\\mathsf{Cao}^{1\\dagger}$ Hongrui $\\mathsf{Wu}^{2\\dagger}$ Ziyong Feng $^3$ Hujun $\\mathsf{Bao}^1$ Xiaowei Zhou $^1$ Sida Peng $^{1*}$",
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+ "text": "$^{1}$ State Key Lab of CAD&CG, Zhejiang University $^{2}$ Tongji University $^{3}$ DeepGlint",
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+ "Figure 1. Given a set of inconsistent multi-view images with inconsistencies such as photometric variation or transient occlusions, as shown in (a), existing robust reconstruction methods often fail to produce a high-quality 3D scene with minimal artifacts and floaters when the views are not dense enough, as illustrated in (b). In contrast, our method first utilizes a Video Diffusion Model to restore all images into a consistent state in (c), and then reconstructs the 3D scene from these restored images, resulting in the high-quality 3D scene in (d). (c) Restored Images"
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+ "text": "This paper tackles the challenge of robust reconstruction, i.e., the task of reconstructing a 3D scene from a set of inconsistent multi-view images. Some recent works have attempted to simultaneously remove image inconsistencies and perform reconstruction by integrating image degradation modeling into neural 3D scene representations. However, these methods rely heavily on dense observations for robustly optimizing model parameters. To address this issue, we propose to decouple robust reconstruction into two subtasks: restoration and reconstruction, which naturally simplifies the optimization process. To this end, we introduce UniVerse, a unified framework for robust reconstruction based on a video diffusion model. Specifically, UniVerse first converts inconsistent images into initial videos,",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "then uses a specially designed video diffusion model to restore them into consistent images, and finally reconstructs the 3D scenes from these restored images. Compared with case-by-case per-view degradation modeling, the diffusion model learns a general scene prior from large-scale data, making it applicable to diverse image inconsistencies. Extensive experiments on both synthetic and real-world datasets demonstrate the strong generalization capability and superior performance of our method in robust reconstruction. Moreover, UniVerse can control the style of the reconstructed 3D scene. The code will be released for the reproducibility.",
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+ "type": "text",
+ "text": "1. Introduction",
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+ {
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+ "text": "Novel view synthesis have long been a high-profile and complicated task in computer graphics, which plays a significant role in many applications like virtual reality (VR) and autonomous driving. Traditional approaches [48, 50]",
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+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "reconstruct 3D scenes based on the point cloud representation and multi-view stereo techniques. However, such methods generally suffer from low rendering quality, thus limiting their applications.",
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+ "text": "In recent years, differentiable rendering-based methods, such as Neural Radiance Fields (NeRF) [2, 3, 38, 40] and 3D Gaussian Splatting (3DGS) [7, 23, 28, 63], have made significant progress in rendering photorealistic novel views. However, these methods assume that all input images are static and captured under consistent conditions. In reality, images are frequently affected by illumination variations caused by changes in camera exposure or environmental lighting, content alterations due to dynamic objects, and motion blur resulting from camera shake. These inconsistencies violate the assumptions of the differentiable-rendering based methods, leading to significant performance degradation [35, 64].",
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+ "text": "To overcome this problem, previous methods propose learnable embeddings [10, 29, 35, 52] to additionally model the viewpoint-specific content for each image and jointly optimize it with the underlying 3D scene representation to minimize the rendering loss. When scene observations are sufficient, these methods can successfully recover the intrinsic scene structure from the inconsistent images. However, their performance tends to degrades significantly as the number of observations decreases. A plausible reason is that they introduce additional learnable parameters into the optimization process, making it more unstable, needing dense observations for optimization.",
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+ "text": "In this paper, we propose UniVerse, a video generative model for robust 3D reconstruction from inconsistent multiview images. Our key idea is to exploit the strong consistent prior of video diffusion models [33, 67] to transform all inconsistent images to a consistent state before performing 3D reconstruction. Specifically, given a set of unstructured multi-view images, we first sort them to obtain a camera trajectory and insert blank images along this trajectory to transform images into a video. To better utilize observations, a multiple-input query transformer is proposed to aggregate information from all input images and generate a global semantic embedding, which is injected into the video diffusion model to help the video restoration. In contrast to previous methods that manually model the degradation in each image, the video diffusion model learns a general consistent scene prior from large-scale data, making it more robust in handling diverse inconsistencies.",
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+ "text": "We apply UniVerse to both synthetic and real-world challenging inconsistent image collections and demonstrate its ability to produce high-fidelity renderings with fewer artifacts and floaters, surpassing previous state-of-the-art methods in terms of PSNR, SSIM, and LPIPS. By selecting a style image, UniVerse can change the style of the generated videos to match that of the style image, thereby alter",
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+ "text": "ing the style of the final reconstructed 3D scene. Even when the input images are very sparse and inconsistent (e.g., only 2 images with occlusions), UniVerse can still restore them into convincing consistent images, which can be applied to other downstream tasks such as generating new views [67] and performing further reconstruction. Overall, these results demonstrate the effectiveness of UniVerse and highlight the potential of decoupling robust reconstruction.",
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+ "text": "The success of diffusion models has also spurred research in diffusion-based video generation [5, 5, 8, 27, 58], which are often fine-tuned from T2I models using extensive video datasets [1, 9, 62] and can generate consistent videos from text [5, 8, 27] or image inputs [5, 58]. Recent advancements [6, 8, 18, 54, 69, 72] further enhance text-to-video generation visual quality through extra temporal layers and curated datasets. The rapid developments of VDMs provoke significant interest in more controllable video generation, enabling controls like RGB images [5, 58, 59], depth [12, 60], trajectory [41, 65], and semantic maps [42]. Recently, some works further explore camera motion control for VDMs to generate controllable 3D-aware videos [5, 20, 39, 57]. Recently, CamCo [61] and CameraCtrl [21] introduced Plücker coordinates [49] in video diffusion models for camera motion control. ViewCrafter [67] and ReconX [33] further use explicit point clouds to achieve more precise 3D-aware camera control. These works achieve great success in generating consistent 3D-aware videos which can be directly used to reconstruct a 3D scene. Observing the strong consistent 3D prior of VDMs and noting that multi-view images are similar to frames extracted from a video captured by a camera trajectory, we take inconsistent multi-view images as conditions and generate a consistent video, and then extract them from the generated video with all images being consistent and static.",
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+ "img_path": "images/8503710c2d2c01e73452bd8405525233c407e3edd396fa8015ecce8ceb47da0e.jpg",
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+ "Inpainting Masks",
+ "Noise"
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+ "Latents",
+ "Figure 2. The flowchart of UniVerse. Given a set of inconsistent images, we first convert them into an initial video. We then use SAM [24] to identify transient occlusions and generate inpainting masks. These masks are used to set the occluded pixels in the initial video to zero. Next, we encode the video into latents using a VAE Encoder. After setting one image as the style image and assigning it style mask, we concatenate the style masks, inpainting masks, latents, and randomly sampled Gaussian noise along the channel dimension and feed them into the U-Net. For each masked input image, we obtain semantic embeddings using the CLIP image encoder and aggregate them via the Multi-input Query Transformer to form a global semantic embedding. This embedding guides the U-Net in the video generation process. Finally, the U-Net output is decoded by the VAE Decoder to produce the restored video, from which we extract the consistent images and reconstruct a high-quality 3D scene. If too many images for the VDM to restore at once, we iteratively restore them in batches as described."
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+ "(c) Video Restoration"
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+ "Query Embeddings"
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+ "image_caption": [
+ "3D scene"
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+ "text": "physical rendering models for diverse lighting conditions. Nevertheless, these methods typically couple the process of restoration and reconstruction and directly perform reconstruction on the inconsistent multi-view images, which requires a large amount of training images to identify and remove all inconsistencies. What's more, they typically use handcraft prior to manually model inconsistency in each image [55]. In contrast, our method emphasizes the effectiveness of restoration before reconstruction, decoupling the task and making it much easier. Meanwhile, the VDM we use learns a general consistent scene prior from large-scale data, thus can be more robust facing various inconsistencies. Recently, SimVS [53] utilized a multi-view diffusion model [16] to turn all images into a consistent state given an image as a reference. However, it retains all inconsistencies of the reference image, such as a moving passenger, thus can fail to reconstruct the static scene, while our method removes all inconsistencies in the images and aims to reconstruct the static scene.",
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+ "type": "text",
+ "text": "3. Method",
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+ "text": "Background. 3D reconstruction aims to recover the 3D structure of a scene from multiple 2D images taken from different viewpoints. While traditional methods like structure-from-motion [48, 50] have been widely used, newer techniques such as NeRF [43] and 3DGS [23] leverage differentiable rendering. Given input images $\\{I_i\\}_{i=1}^K$ and their corresponding poses $\\{P_i\\}_{i=1}^K$ , differentiable rendering aims to find a parameterized function $f_\\theta$ that takes a camera pose as input and outputs the corresponding image.",
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+ "text": "The goal is to optimize the parameters $\\theta$ or the 3D representation to minimize the following loss function:",
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+ "type": "equation",
+ "text": "\n$$\n\\theta = \\arg \\min _ {\\theta} \\sum_ {i = 1} ^ {K} D i f \\left(f _ {\\theta} \\left(P _ {i}\\right), I _ {i}\\right). \\tag {1}\n$$\n",
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+ "text": "Here, $Dif(\\cdot)$ is a differentiable function, such as MSE or L1 loss, used to measure the difference between two images. Once $\\theta$ is obtained, we can render novel views from the 3D scene for any new camera pose $P$ using $f_{\\theta}(P)$ , thereby achieving 3D reconstruction. However, these approaches assume that the images $\\{I_i\\}_{i=1}^K$ are consistent and static. If the assumption isn't hold, the learning of $f_{\\theta}$ fails. To address this, UniVerse uses a VDM to restore all input images to be static and consistent. This ensures that the assumption for Eq. (1) is valid, helping $f_{\\theta}$ to easily learn the 3D scene.",
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+ "text": "Overview. Given $K$ inconsistent multi-view images $\\{I_i\\}_{i=1}^K, I_i \\in \\mathbb{R}^{3 \\times H \\times W}$ , our goal is to restore them into $K$ consistent images. We treat the multi-view images as video frames from the same video. We first sort the images into ordered $K$ images based on their camera poses, as described in Sec. 3.1. Then we use a VDM to restore all these $K$ images into a consistent state. Assuming the VDM can generate $f$ frames at a time, we iteratively restore all images, processing $N \\leq f$ images per iteration. We select one of the first $N$ images as the style image $I_{sty}$ , and turn the first $N$ images into a initial video as described in Sec. 3.1. For all frames in the initial video, we assign them inpainting masks to indicate where to be inpainted and style masks",
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+ {
+ "type": "header",
+ "text": "M: Mask pixels to 0 via the masks generated by SAM",
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+ {
+ "type": "header",
+ "text": ": Element-wise addition : Learnable Query Embeddings",
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+ },
+ {
+ "type": "page_number",
+ "text": "27033",
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+ "type": "text",
+ "text": "to indicate which frame should be taken as the style reference via Segment Anything Model (SAM) [24]. Using the initial video, inpainting masks, and style masks as conditions, we use the VDM to generate a restored video with the same style as the style image, extracting the corresponding $N$ consistent frames. We then remove the corresponding $N$ images from the input unrestored $K$ images since they are already restored, and add the last restored image to the unrestored images as the first image, and set it as style image for the next iteration. We update $K$ to $\\max(K - (N - 1), 1)$ and repeat the process until $K \\leq 1$ , which means all images are restored. Finally, with all restored $K$ images, we use 3D reconstruction methods like NeRFs [43] to reconstruct them and return a 3D representation. We show this process in Fig.2 and Alg. 1 in Supp.",
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+ "type": "text",
+ "text": "3.1. Turning Multi-view Images into Videos",
+ "text_level": 1,
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+ "text": "As discussed, UniVerse first converts the $K$ input multiview images into initial videos. These images are essentially captured by cameras at various poses around a single scene. Assuming all $K$ poses $\\{P_i\\}_{i=1}^K$ lie on a single camera trajectory, continuously sampling new poses (and thus new views) from this trajectory yields a video if the poses are sufficiently dense. This approach hinges on solving two key problems: (I) determining the trajectory and (II) sampling new poses from it. The detailed algorithm is provided in Sec. 7, Alg. 2 and Fig. 10 the Supp.",
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+ "text": "Sorting Multi-view Images for Sparse Trajectory. We use ThreadPose to sort the $K$ input poses $\\{P_i\\}_{i=1}^K$ into an ordered list. We initialize a double linked list with a randomly chosen pose and iteratively add the remaining poses based on their distances to the current head and tail of the list. The distance metric combines rotation and translation differences, weighted to ensure consistent scaling. Finally, we traverse the whole list to construct an ordered set of poses $\\{P_i'\\}_{i=1}^K$ , which defines an implicit camera trajectory.",
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+ "type": "text",
+ "text": "Sample Implicit Dense Views from Trajectory At each iteration, given $N$ ordered poses $\\{P_i^{\\prime}\\}_{i = 1}^{N}$ and the corresponding $N$ inconsistent images $\\{I_i^{\\prime}\\}_{i = 1}^{N}$ , our goal is to create an initial video of $f$ frames that includes all $N$ input images. We achieve this by sampling $f - N$ new poses from the trajectory to generate new views. First, we compute the distances $\\{d_i\\}_{i = 1}^{N - 1}$ between neighboring poses:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nd _ {i} = D _ {P} \\left(P _ {i} ^ {\\prime}, P _ {i + 1} ^ {\\prime}\\right), \\quad i = 1, 2, \\dots , N - 1. \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "Here, $D_P(\\cdot)$ is a function to compute the distance between two poses, which is defined in $\\mathbf{Supp}$ . Next, we assign the number of new poses $n_i$ to be inserted between each pair of neighboring poses $P_{i}^{\\prime}$ and $P_{i + 1}^{\\prime}$ , proportional to the distance $d_{i}$ . After assigning the number of poses, we aim to",
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+ {
+ "type": "text",
+ "text": "sample new poses and new views. However, since the input images are inconsistent, it can be difficult to use methods like conditional VDM generation [21, 61], or building 3D structures like point clouds [67], to explicitly render a new view given an explicit camera pose. Considering VDM's strong 3D prior and frame interpolation ability, we simply insert $n_i$ zero frames into each $I_i'$ , $I_{i+1}'$ neighboring image pair and expect the VDM to inpaint these zero frames into new views. In this way, we turn $N$ ordered images $\\{I_i'\\}_{i=1}^N$ into an $f$ -frame initial video with the first image $I_1'$ and the last image $I_N'$ as the first and last frames.",
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+ "type": "text",
+ "text": "3.2. Conditional VDM for Initial Video Restoration",
+ "text_level": 1,
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+ "text": "Preliminary: Video Diffusion Models. In diffusion-based video generation, Latent Diffusion Models (LDMs) [37] are often employed to reduce computational costs. In LDMs, video data $x \\in \\mathbb{R}^{f \\times 3 \\times H \\times W}$ is encoded into the latent space using a pre-trained VAE encoder frame-by-frame, expressed as $z = \\mathcal{E}(x)$ , $z \\in \\mathbb{R}^{f \\times C \\times h \\times w}$ . The forward and reverse processes are then performed in the latent space. The final generated videos are obtained through the VAE decoder $\\hat{x} = \\mathcal{D}(z)$ . In this work, we build our VDM based on an open-sourced Image-to-Video (I2V) diffusion model DynamiCrafter [58].",
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+ "type": "text",
+ "text": "Initial Video Restoration. As shown in Fig. 2, at a certain iteration, given the input images and the corresponding initial video, inpainting masks, and style masks, we first use the VAE encoder to encode the initial video into latents and downsample both masks to match the shape of the latents. We then concatenate the latents, inpainting masks, style masks, and randomly sampled Gaussian noise along the channel dimension to form the image inputs.",
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+ "type": "text",
+ "text": "To better leverage the I2V VDM's ability to control video generation via text-aligned semantic embeddings [58], we extend the Query Transformer in [58] to a Multiple-input Query Transformer. Considering we have $N$ input images per iteration, we pass them through the CLIP image encoder [44] to obtain $N$ embeddings, which are then injected into the Multiple-input Query Transformer via cross-attention as the value and key. This yields a global semantic embedding to aid in generating 3D-aware videos.",
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+ "type": "text",
+ "text": "With the image inputs and the embedding as conditional inputs, we use the VDM to generate restored latents and decode them using the VAE Decoder to produce the consistent restored video. Finally, we extract the corresponding $N$ frames from the restored $f$ -frame video as the restored images. We discard the other $f - N$ new views, as they can be unreliable without 3D-consistency constraints.",
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+ "type": "text",
+ "text": "Training VDMs for Consistency. As discussed, Universe aims to make input images consistent. The purpose of sampling dense views, as described in Sec. 3.1, is to trans",
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+ {
+ "type": "page_number",
+ "text": "27034",
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+ {
+ "type": "text",
+ "text": "form discrete images into a video to leverage the VDM's prior, rather than generating new views. Directly training the VDM using MSE Loss is inappropriate because the simple MSE loss equally weights making the input $N$ frames consistent and generating $f - N$ new views. Given $2 \\leq N < f$ , we need to adjust the loss weights for each of the $f$ frames to ensure the VDM focuses on making existing images consistent. To this end, we propose a consistency loss $\\mathcal{L}_{con}$ for VDM training. Specifically, assuming the initial video is $\\mathbf{v}^{ini} \\in \\mathbb{R}^{f \\times 3 \\times H \\times W}$ , given the VDM's estimated noise $\\epsilon_{\\theta}$ and the ground truth noise $\\epsilon \\in \\mathbb{R}^{f \\times C \\times h \\times w}$ during training, we first compute the MSE loss frame-by-frame to obtain the loss vector $lv \\in \\mathbb{R}^{f}$ :",
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+ "type": "equation",
+ "text": "\n$$\nl v [ i ] = \\| \\epsilon_ {\\theta} [ i ] - \\epsilon [ i ] \\| _ {2} ^ {2}, \\quad \\text {f o r} i = 1, 2, \\dots , f, \\tag {3}\n$$\n",
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+ "text": "where $[i]$ denotes the $i$ -th frame. We then adjust $lv$ as follows:",
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+ "text": "\n$$\nl v [ i ] = l v [ i ] \\times \\left\\{ \\begin{array}{l l} \\omega_ {c} & \\text {i f} \\mathbf {v} ^ {i n i} [ i ] \\text {i s a n i n p u t i m a g e}, \\\\ \\omega_ {n} & \\text {o t h e r w i s e (i . e . ,} \\mathbf {v} ^ {r o} [ i ] \\text {i s a z e r o f r a m e)}. \\end{array} \\right. \\tag {4}\n$$\n",
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+ "text": "The weights $\\omega_{c}$ and $\\omega_{n}$ are computed as:",
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+ "text": "\n$$\n\\omega_ {c} = \\max \\left(\\frac {N}{f}, \\lambda\\right) / \\frac {N}{f}, \\tag {5}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\omega_ {n} = \\min \\left(\\frac {f - N}{N}, 1 - \\lambda\\right) / \\frac {f - N}{f}. \\tag {6}\n$$\n",
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+ "text": "This ensures that the ratio of the loss weights for making images consistent to generating new views is at least $\\lambda : (1 - \\lambda)$ . In practice, we set $\\lambda$ to a large value like 0.98. Additionally, since our VDM takes initial video, inpainting/style masks as input, we need a special training data construction approach, which we discuss in Sec. 4.1.",
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+ "type": "text",
+ "text": "4. Experiment",
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+ "type": "text",
+ "text": "4.1. Implementation Details",
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+ "text": "VDM Training Details: We employ a progressive training strategy to fine-tune the VDM. Specifically, we fine-tune the $576 \\times 1024$ interpolation VDM from ViewCrafter [67]. In the first stage, we train the VDM at a resolution of $320 \\times 512$ , with the frame length $f$ set to 25. The entire video denoising U-Net is fine-tuned for 14,520 iterations using a learning rate of $5 \\times 10^{-5}$ and a batch size of 8. In the second stage, we continue to fine-tune the video denoising U-Net at a resolution of $576 \\times 1024$ for high-resolution adaptation, with 12,000 iterations on a learning rate of $1 \\times 10^{-5}$ and a mini-batch size of 8. All training is conducted on 8 NVIDIA A100 GPUs.",
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+ "text": "Training Data Construction: Our VDM was trained on the DL3DV dataset [32]. Specifically, we first extract 25",
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+ "type": "text",
+ "text": "frames from the video of DL3DV at a random FPS to simulate the varying levels of density and sparsity in real-world multi-view images. Then we randomly set $n, 0 \\leq n \\leq 23$ of the 25 frames to zeros. Next, for each frame in the 25 frames, we randomly adjust their brightness, sharpness, hue, saturation, and simultaneously add Gaussian noise, motion blur, Gaussian blur, and occlusions to simulate inconsistencies. We use the VOC2007 dataset [13] to generate the occlusions and inpainting masks. In the masks, \"1\" indicates that this pixel needs to be inpainted, while \"0\" indicates the opposite. For zero frames, the inpainting masks are filled with \"1\". In this way, we generate a initial video and corresponding inpainting masks. Finally, we randomly choose a non-zero frame from the initial video as the style image and generate the style masks. Specifically, for the style frame, the mask is all \"1\", while for other frames, the mask is \"0\". We then adjust all frames in the original video to match the style of the style image to obtain the target video. In this way, we generate a training pair. In total, we generate 116,158 video pairs as training data.",
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+ "text": "Inferencing Details: During inference, we adopt the DDIM sampler [51] with classifier-free guidance [22]. We use SegNeXt [19] as the semantic segmentation model to identify transient occlusions in the input images, and then use SAM [24] to segment these occlusions and generate the inpainting masks. Assuming $O$ is the minimum integer such that $\\frac{K - 1}{O} < 25$ , we set the number of images processed at each iteration to $N = \\lfloor \\frac{K - 1}{O} \\rfloor + 1$ . After all images are made consistent, we use ZipNeRF [4] with GLO [35] to reconstruct the 3D scene. All inference is conducted on a single NVIDIA A100 GPU.",
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+ "type": "text",
+ "text": "4.2. Evaluation",
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+ "type": "text",
+ "text": "We aim to evaluate the ability of UniVerse to alleviate the problem mentioned in the Background of Sec. 3, i.e. the problem of inconsistent images. We evaluate our method on both synthetic datasets and real-world datasets and compare it with the latest methods.",
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+ "text": "Dataset: For synthetic datasets, we utilize the NeRF llff dataset [43]. Since all images in this dataset are captured under static, consistent conditions, we randomly adjust their brightness, sharpness, hue, and saturation. We also randomly add Gaussian noise, motion blur, Gaussian blur, and occlusions to simulate inconsistencies. To stress test all methods, we limit the number of images for a single scene to 20-50. For real-world datasets, we use cell phone cameras to collect 7 real-world scenes for evaluation. During capture, in addition to the automatic adjustments by camera programs, we manually change local exposure and ISO settings, and apply random post-processing filters to each view. We show samples of our captured images in Fig. 5.",
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+ "type": "text",
+ "text": "Metrics and Compared Methods: For quantitative comparison, we use PSNR, SSIM [56], and LPIPS [71] as",
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+ "Figure 3. Visual results of novel view synthesis on synthetic datasets, with the corresponding depth map displayed in the bottom left corner."
+ ],
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+ "img_path": "images/a3b8ba0b347dda2478575903ce94e708258814957201e9bf428c4ff3b02adf3f.jpg",
+ "image_caption": [
+ "Figure 4. Visual results of novel view synthesis on real datasets, with the corresponding depth map displayed in the bottom left corner."
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+ "image_caption": [
+ "Figure 5. Samples of our captured images."
+ ],
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+ "text": "metrics to assess the performance of our method. Meanwhile, we calculate a per-channel affine transformation to align the output color tints with the ground truth tints (Affine-aligned sRGB) [55]. We also present rendered images generated from the same pose as the input view for visual inspection. To demonstrate the superiority of our method, we compare it against the following meth-",
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+ "img_path": "images/6b13122a9b37953f3e34c61de650c89404280166ebda3ad5c79e2aa5456c2c43.jpg",
+ "table_caption": [
+ "Table 1. The quantitative results in novel view synthesis on synthetic datasets. The best and second-best results are highlighted."
+ ],
+ "table_footnote": [],
+ "table_body": " | sRGB | Affine-aligned sRGB |
| PSNR ↑ | SSIM ↑ | LPIPS ↓ | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| ZipNeRF | 11.52 | 0.2327 | 0.6930 | 14.53 | 0.3548 | 0.6297 |
| ZipNeRF w/GLO | 14.53 | 0.4667 | 0.4394 | 18.58 | 0.5297 | 0.4123 |
| Bilarf | 16.06 | 0.4814 | 0.4489 | 17.68 | 0.5062 | 0.4317 |
| WildGaussians | 13.75 | 0.3972 | 0.6430 | 15.45 | 0.4476 | 0.6244 |
| Ours | 18.09 | 0.5789 | 0.3015 | 20.12 | 0.5926 | 0.2979 |
",
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+ "type": "text",
+ "text": "ods: ZipNeRF [4], ZipNeRF W/GLO [35], Bilarf [55], and WildGaussians [26].",
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+ "text": "Results: We present the average quantitative results in Tab. 1 and Tab. 2, and the qualitative visual results in Fig. 3 and Fig. 4. Both tables show that UniVerse achieves the best metric values under both settings. Moreover, the figures demonstrate that our method provides the most visually",
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+ "table_caption": [
+ "Table 2. The quantitative results in novel view synthesis on real-world datasets. The best and second-best results are highlighted."
+ ],
+ "table_footnote": [],
+ "table_body": " | sRGB | Affine-aligned sRGB |
| PSNR ↑ | SSIM ↑ | LPIPS ↓ | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| ZipNeRF | 13.31 | 0.5222 | 0.4310 | 16.38 | 0.5490 | 0.4328 |
| ZipNeRF w/GLO | 16.14 | 0.5668 | 0.3095 | 20.67 | 0.5907 | 0.3125 |
| Bilarf | 15.46 | 0.5459 | 0.3323 | 18.84 | 0.6055 | 0.3169 |
| WildGaussians | 15.05 | 0.4246 | 0.5046 | 17.39 | 0.5747 | 0.4493 |
| Ours | 19.65 | 0.6511 | 0.2532 | 22.91 | 0.6998 | 0.2132 |
",
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+ {
+ "type": "text",
+ "text": "pleasing results with fewer artifacts and floaters. In contrast, other compared methods often produce novel views with noticeable artifacts and a significant number of floaters due to unstable optimization and the lack of dense observations, thereby highlighting the superiority of our approach.",
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+ "text": "4.3. Abalation Study",
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+ "text": "The Effect of the Design of Turning Images into Videos: As discussed, transforming multi-view images into videos is crucial for unleashing the consistent 3D prior of VDMs. To validate this, we tested the following settings for image restoration and reconstruction: (a) Directly stacking unordered images as the initial video. (b) Sorting images using ThreadPose and stacking them as the initial video. (c) Inserting zero frames (implicit views) into unordered images to form the initial video. (d) Inserting zero frames into ordered images, as described in Sec. 3.1. The results in Tab. 3 show that only our design fully exploits the 3D prior of VDMs, demonstrating its rationality.",
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+ "table_caption": [
+ "Table 3. Results on novel view synthesis with different image to video settings."
+ ],
+ "table_footnote": [],
+ "table_body": "| Setting | ThreadPose | zero frames | PSNR | SSIM |
| (a) (directly stack) | X | X | 15.32 | 0.4598 |
| (b) (w/ ThreadPose) | ✓ | X | 17.29 | 0.5876 |
| (c) (w/ zero frames) | X | ✓ | 18.25 | 0.6067 |
| (d) (ours) | ✓ | ✓ | 20.71 | 0.7708 |
",
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+ "text": "The Effect of our VDM Design: We introduce four new designs for VDMs in this work: the Multi-input Query Transformer (MiQT), style mask, inpainting mask, and consistent loss. We validate each design as follows:",
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+ "(1) Multi-input Query Transformer (MiQT): To assess MiQT's impact, we retrained a model using a single-input QT and compared its robust reconstruction performance with ours. The results in Tab. 4 show MiQT's superiority over QT. This highlights the importance of global semantic information in leveraging VDMs' prior, thereby justifying our design.",
+ "(2) Inpainting Mask: We retrained a VDM without inpainting masks, forcing it to decide which pixels to inpaint. Using a subset of the NeRF-on-the-go dataset [46] contain"
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+ "table_caption": [
+ "Table 4. Results on novel view synthesis with different Query Transformer (QT) settings."
+ ],
+ "table_footnote": [],
+ "table_body": "| Setting | PSNR | SSIM | LPIPS | Setting | PSNR | SSIM | LPIPS |
| QT | 16.80 | 0.4157 | 0.5015 | MiQT | 17.42 | 0.4511 | 0.4549 |
",
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+ "text": "ing only occlusions as inconsistencies, we found that the VDM failed to inpaint all masked pixels (Fig. 8). Thus, inpainting masks are essential for UniVerse.",
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+ "(3) Style Mask: Figure 9 compares results with and without the style mask. Without it, output image tone is uncontrollable despite consistent input tones. Style masks are thus crucial for controlling image appearance and reconstructed 3D scene style.",
+ "(4) Consistent Loss: As elaborated in Sec. 3.2, employing the Consistent Loss is pivotal for directing the VDM to prioritize image consistency. The comparative training outcomes presented in Tab. 5 underscore the superior performance of the Consistent Loss over the regular MSE. This superiority indicates that the Consistent Loss effectively enables the VDM to more adeptly eliminate inconsistencies, thereby substantiating the efficacy of our design approach."
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+ "table_caption": [
+ "Table 5. Results on novel view synthesis with different training loss function settings."
+ ],
+ "table_footnote": [],
+ "table_body": "| Setting | PSNR | SSIM | LPIPS | Setting | PSNR | SSIM | LPIPS |
| MSE | 16.19 | 0.3788 | 0.5340 | Consistent | 17.42 | 0.4511 | 0.4549 |
",
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+ "text": "4.4. Further Applications of UniVerse",
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+ "text": "Controlling the Style of Reconstructed 3D Scene: The style of the restored images, and consequently the reconstructed 3D scenes, is determined by the style image. By changing the style image, we can alter the style of the entire reconstructed 3D scene, as shown in Fig. 6.",
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+ "text": "Robust Reconstruction on Sparse Images: UniVerse focuses on making images consistent rather than generating new views. Thus, even after restoring very sparse input images to a consistent state, reconstruction may still fail due to insufficient views. This issue can be easily resolved by using a generative novel view synthesis model like ViewCrafter [67]. As shown in Fig. 7, given 2 inconsistent input images, ViewCrafter [67] synthesizes distorted novel views with strange occlusions. After the images are restored via UniVerse, the novel views synthesized by ViewCrafter become consistent. In other words, as a restoration model, UniVerse can serve as a pre-processor for other models, enabling robust reconstruction.",
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+ "Figure 6. Controlling the style of reconstructed 3D scene by switching style image."
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+ "Synthesized Novel Views"
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+ "Restore images"
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+ "image_caption": [
+ "Figure 7. Novel views synthesized via ViewCrafter [67]. First line: ViewCrafter synthesizes inconsistent and distorted views from inconsistent images. Second line: After the images are restored by UniVerse, the generated views become consistent.",
+ "Input Image"
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+ "image_caption": [
+ "Figure 8. Visualization of results w/o and w/ inpainting masks.",
+ "Input Image",
+ "Figure 9. Visualization of results w/o and w/ style masks."
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+ "w/o Style Mask"
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+ "w/StyleMask"
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+ "text": "5. Conclusion & Limitation",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "This paper proposes UniVerse, a unified robust reconstruction framework that converts inconsistent multi-view im",
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+ "type": "text",
+ "text": "ages into initial videos and leverages Video Diffusion Models to restore them into consistent images. By decoupling robust reconstruction into two subtasks (i.e. restoration and reconstruction), UniVerse overcomes the limitations of existing approaches that require very dense observations to reconstruct inconsistent images, achieving state-of-the-art performance on both synthetic and real-world datasets. Moreover, we explore UniVerse's ability to control the style of the reconstructed 3D scene by switching the reference image and its potential for reconstructing very sparse inconsistent observations by applying novel view generation models after restoration. We believe our work offers new insights of decoupling robust reconstruction and restoring images using models with 3D priors to the community.",
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+ "text": "Limitations: UniVerse requires synthesizing videos with inconsistencies as training data to fine-tune the VDM for adaptation to a restoration model. While some inconsistencies, like lighting, may be hard to synthesize, [53] have shown tremendous promise for inconsistency synthesis via generative models.",
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+ "text": "27038",
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+ "type": "text",
+ "text": "6. Acknowledgment",
+ "text_level": 1,
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+ {
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+ "text": "This work was partially supported by the National Key R&D Program of China (No. 2024YFB2809102), NSFC (No. 62402427, NO. U24B20154), Zhejiang Provincial Natural Science Foundation of China (No. LR25F020003), DeepGlint, Zhejiang University Education Foundation Qizhen Scholar Foundation, and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University.",
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+ {
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+ "text": "References",
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+ ],
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+ },
+ {
+ "type": "list",
+ "sub_type": "ref_text",
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+ "content": "reconstruct 3D scenes based on the point cloud representation and multi-view stereo techniques. However, such methods generally suffer from low rendering quality, thus limiting their applications."
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+ "content": "In this paper, we propose UniVerse, a video generative model for robust 3D reconstruction from inconsistent multiview images. Our key idea is to exploit the strong consistent prior of video diffusion models [33, 67] to transform all inconsistent images to a consistent state before performing 3D reconstruction. Specifically, given a set of unstructured multi-view images, we first sort them to obtain a camera trajectory and insert blank images along this trajectory to transform images into a video. To better utilize observations, a multiple-input query transformer is proposed to aggregate information from all input images and generate a global semantic embedding, which is injected into the video diffusion model to help the video restoration. In contrast to previous methods that manually model the degradation in each image, the video diffusion model learns a general consistent scene prior from large-scale data, making it more robust in handling diverse inconsistencies."
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+ "content": "The success of diffusion models has also spurred research in diffusion-based video generation [5, 5, 8, 27, 58], which are often fine-tuned from T2I models using extensive video datasets [1, 9, 62] and can generate consistent videos from text [5, 8, 27] or image inputs [5, 58]. Recent advancements [6, 8, 18, 54, 69, 72] further enhance text-to-video generation visual quality through extra temporal layers and curated datasets. The rapid developments of VDMs provoke significant interest in more controllable video generation, enabling controls like RGB images [5, 58, 59], depth [12, 60], trajectory [41, 65], and semantic maps [42]. Recently, some works further explore camera motion control for VDMs to generate controllable 3D-aware videos [5, 20, 39, 57]. Recently, CamCo [61] and CameraCtrl [21] introduced Plücker coordinates [49] in video diffusion models for camera motion control. ViewCrafter [67] and ReconX [33] further use explicit point clouds to achieve more precise 3D-aware camera control. These works achieve great success in generating consistent 3D-aware videos which can be directly used to reconstruct a 3D scene. Observing the strong consistent 3D prior of VDMs and noting that multi-view images are similar to frames extracted from a video captured by a camera trajectory, we take inconsistent multi-view images as conditions and generate a consistent video, and then extract them from the generated video with all images being consistent and static."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.2. Robust 3D Reconstruction"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.705,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Reconstructing a 3D scene from a set of 2D images is a long-standing problem in computer vision. Modern approaches, such as NeRF-based methods [15, 17, 40, 45, 66] and 3DGS-based methods [14, 23, 34, 68], have achieved great success and demonstrated expressive reconstruction quality. However, these methods all assume that the input images are captured in a static scene. Their performance declines significantly when reconstructing from unconstrained inconsistent photo collections. To address this challenging in-the-wild task, several attempts [10, 26, 29, 35, 36, 47, 64] have been made to handle appearance variation and transient occlusions. Other works [30, 31] focus on scenes with time-varying appearances, while methods [11, 25, 70] use"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "27032"
+ }
+ ],
+ [
+ {
+ "type": "header",
+ "bbox": [
+ 0.104,
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+ ],
+ "angle": 0,
+ "content": "M: Mask pixels to 0 via the masks generated by SAM"
+ },
+ {
+ "type": "header",
+ "bbox": [
+ 0.379,
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+ ],
+ "angle": 0,
+ "content": ": Element-wise addition : Learnable Query Embeddings"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.144,
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+ 0.115
+ ],
+ "angle": 0,
+ "content": "(a) Initial Video Construction"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.098,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ 0.269,
+ 0.205,
+ 0.28
+ ],
+ "angle": 0,
+ "content": "Input Images"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ 0.126,
+ 0.344,
+ 0.264
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Initial Video"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(b) Condition Preparation"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Inpainting Masks"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.36,
+ 0.184,
+ 0.385,
+ 0.21
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.429,
+ 0.218,
+ 0.459,
+ 0.226
+ ],
+ "angle": 0,
+ "content": "Noise"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.361,
+ 0.232,
+ 0.385,
+ 0.265
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.399,
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+ 0.488,
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.423,
+ 0.271,
+ 0.462,
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+ ],
+ "angle": 0,
+ "content": "Latents"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "(c) Video Restoration"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Query Embeddings"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.683,
+ 0.104,
+ 0.899,
+ 0.27
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3D scene"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 2. The flowchart of UniVerse. Given a set of inconsistent images, we first convert them into an initial video. We then use SAM [24] to identify transient occlusions and generate inpainting masks. These masks are used to set the occluded pixels in the initial video to zero. Next, we encode the video into latents using a VAE Encoder. After setting one image as the style image and assigning it style mask, we concatenate the style masks, inpainting masks, latents, and randomly sampled Gaussian noise along the channel dimension and feed them into the U-Net. For each masked input image, we obtain semantic embeddings using the CLIP image encoder and aggregate them via the Multi-input Query Transformer to form a global semantic embedding. This embedding guides the U-Net in the video generation process. Finally, the U-Net output is decoded by the VAE Decoder to produce the restored video, from which we extract the consistent images and reconstruct a high-quality 3D scene. If too many images for the VDM to restore at once, we iteratively restore them in batches as described."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.435,
+ 0.486,
+ 0.722
+ ],
+ "angle": 0,
+ "content": "physical rendering models for diverse lighting conditions. Nevertheless, these methods typically couple the process of restoration and reconstruction and directly perform reconstruction on the inconsistent multi-view images, which requires a large amount of training images to identify and remove all inconsistencies. What's more, they typically use handcraft prior to manually model inconsistency in each image [55]. In contrast, our method emphasizes the effectiveness of restoration before reconstruction, decoupling the task and making it much easier. Meanwhile, the VDM we use learns a general consistent scene prior from large-scale data, thus can be more robust facing various inconsistencies. Recently, SimVS [53] utilized a multi-view diffusion model [16] to turn all images into a consistent state given an image as a reference. However, it retains all inconsistencies of the reference image, such as a moving passenger, thus can fail to reconstruct the static scene, while our method removes all inconsistencies in the images and aims to reconstruct the static scene."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.739,
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+ ],
+ "angle": 0,
+ "content": "3. Method"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.765,
+ 0.485,
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+ ],
+ "angle": 0,
+ "content": "Background. 3D reconstruction aims to recover the 3D structure of a scene from multiple 2D images taken from different viewpoints. While traditional methods like structure-from-motion [48, 50] have been widely used, newer techniques such as NeRF [43] and 3DGS [23] leverage differentiable rendering. Given input images \\(\\{I_i\\}_{i=1}^K\\) and their corresponding poses \\(\\{P_i\\}_{i=1}^K\\), differentiable rendering aims to find a parameterized function \\(f_\\theta\\) that takes a camera pose as input and outputs the corresponding image."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.435,
+ 0.907,
+ 0.467
+ ],
+ "angle": 0,
+ "content": "The goal is to optimize the parameters \\(\\theta\\) or the 3D representation to minimize the following loss function:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.596,
+ 0.478,
+ 0.907,
+ 0.52
+ ],
+ "angle": 0,
+ "content": "\\[\n\\theta = \\arg \\min _ {\\theta} \\sum_ {i = 1} ^ {K} D i f \\left(f _ {\\theta} \\left(P _ {i}\\right), I _ {i}\\right). \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.531,
+ 0.907,
+ 0.685
+ ],
+ "angle": 0,
+ "content": "Here, \\(Dif(\\cdot)\\) is a differentiable function, such as MSE or L1 loss, used to measure the difference between two images. Once \\(\\theta\\) is obtained, we can render novel views from the 3D scene for any new camera pose \\(P\\) using \\(f_{\\theta}(P)\\), thereby achieving 3D reconstruction. However, these approaches assume that the images \\(\\{I_i\\}_{i=1}^K\\) are consistent and static. If the assumption isn't hold, the learning of \\(f_{\\theta}\\) fails. To address this, UniVerse uses a VDM to restore all input images to be static and consistent. This ensures that the assumption for Eq. (1) is valid, helping \\(f_{\\theta}\\) to easily learn the 3D scene."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.704,
+ 0.909,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "Overview. Given \\(K\\) inconsistent multi-view images \\(\\{I_i\\}_{i=1}^K, I_i \\in \\mathbb{R}^{3 \\times H \\times W}\\), our goal is to restore them into \\(K\\) consistent images. We treat the multi-view images as video frames from the same video. We first sort the images into ordered \\(K\\) images based on their camera poses, as described in Sec. 3.1. Then we use a VDM to restore all these \\(K\\) images into a consistent state. Assuming the VDM can generate \\(f\\) frames at a time, we iteratively restore all images, processing \\(N \\leq f\\) images per iteration. We select one of the first \\(N\\) images as the style image \\(I_{sty}\\), and turn the first \\(N\\) images into a initial video as described in Sec. 3.1. For all frames in the initial video, we assign them inpainting masks to indicate where to be inpainted and style masks"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
+ 0.945,
+ 0.519,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "27033"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.482,
+ 0.318
+ ],
+ "angle": 0,
+ "content": "to indicate which frame should be taken as the style reference via Segment Anything Model (SAM) [24]. Using the initial video, inpainting masks, and style masks as conditions, we use the VDM to generate a restored video with the same style as the style image, extracting the corresponding \\(N\\) consistent frames. We then remove the corresponding \\(N\\) images from the input unrestored \\(K\\) images since they are already restored, and add the last restored image to the unrestored images as the first image, and set it as style image for the next iteration. We update \\(K\\) to \\(\\max(K - (N - 1), 1)\\) and repeat the process until \\(K \\leq 1\\), which means all images are restored. Finally, with all restored \\(K\\) images, we use 3D reconstruction methods like NeRFs [43] to reconstruct them and return a 3D representation. We show this process in Fig.2 and Alg. 1 in Supp."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.328,
+ 0.427,
+ 0.344
+ ],
+ "angle": 0,
+ "content": "3.1. Turning Multi-view Images into Videos"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.351,
+ 0.483,
+ 0.502
+ ],
+ "angle": 0,
+ "content": "As discussed, UniVerse first converts the \\(K\\) input multiview images into initial videos. These images are essentially captured by cameras at various poses around a single scene. Assuming all \\(K\\) poses \\(\\{P_i\\}_{i=1}^K\\) lie on a single camera trajectory, continuously sampling new poses (and thus new views) from this trajectory yields a video if the poses are sufficiently dense. This approach hinges on solving two key problems: (I) determining the trajectory and (II) sampling new poses from it. The detailed algorithm is provided in Sec. 7, Alg. 2 and Fig. 10 the Supp."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.522,
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+ ],
+ "angle": 0,
+ "content": "Sorting Multi-view Images for Sparse Trajectory. We use ThreadPose to sort the \\(K\\) input poses \\(\\{P_i\\}_{i=1}^K\\) into an ordered list. We initialize a double linked list with a randomly chosen pose and iteratively add the remaining poses based on their distances to the current head and tail of the list. The distance metric combines rotation and translation differences, weighted to ensure consistent scaling. Finally, we traverse the whole list to construct an ordered set of poses \\(\\{P_i'\\}_{i=1}^K\\), which defines an implicit camera trajectory."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.678,
+ 0.483,
+ 0.786
+ ],
+ "angle": 0,
+ "content": "Sample Implicit Dense Views from Trajectory At each iteration, given \\(N\\) ordered poses \\(\\{P_i^{\\prime}\\}_{i = 1}^{N}\\) and the corresponding \\(N\\) inconsistent images \\(\\{I_i^{\\prime}\\}_{i = 1}^{N}\\), our goal is to create an initial video of \\(f\\) frames that includes all \\(N\\) input images. We achieve this by sampling \\(f - N\\) new poses from the trajectory to generate new views. First, we compute the distances \\(\\{d_i\\}_{i = 1}^{N - 1}\\) between neighboring poses:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.14,
+ 0.796,
+ 0.483,
+ 0.814
+ ],
+ "angle": 0,
+ "content": "\\[\nd _ {i} = D _ {P} \\left(P _ {i} ^ {\\prime}, P _ {i + 1} ^ {\\prime}\\right), \\quad i = 1, 2, \\dots , N - 1. \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.825,
+ 0.483,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Here, \\(D_P(\\cdot)\\) is a function to compute the distance between two poses, which is defined in \\(\\mathbf{Supp}\\). Next, we assign the number of new poses \\(n_i\\) to be inserted between each pair of neighboring poses \\(P_{i}^{\\prime}\\) and \\(P_{i + 1}^{\\prime}\\), proportional to the distance \\(d_{i}\\). After assigning the number of poses, we aim to"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.259
+ ],
+ "angle": 0,
+ "content": "sample new poses and new views. However, since the input images are inconsistent, it can be difficult to use methods like conditional VDM generation [21, 61], or building 3D structures like point clouds [67], to explicitly render a new view given an explicit camera pose. Considering VDM's strong 3D prior and frame interpolation ability, we simply insert \\( n_i \\) zero frames into each \\( I_i' \\), \\( I_{i+1}' \\) neighboring image pair and expect the VDM to inpaint these zero frames into new views. In this way, we turn \\( N \\) ordered images \\( \\{I_i'\\}_{i=1}^N \\) into an \\( f \\)-frame initial video with the first image \\( I_1' \\) and the last image \\( I_N' \\) as the first and last frames."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.268,
+ 0.905,
+ 0.283
+ ],
+ "angle": 0,
+ "content": "3.2. Conditional VDM for Initial Video Restoration"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.289,
+ 0.907,
+ 0.456
+ ],
+ "angle": 0,
+ "content": "Preliminary: Video Diffusion Models. In diffusion-based video generation, Latent Diffusion Models (LDMs) [37] are often employed to reduce computational costs. In LDMs, video data \\( x \\in \\mathbb{R}^{f \\times 3 \\times H \\times W} \\) is encoded into the latent space using a pre-trained VAE encoder frame-by-frame, expressed as \\( z = \\mathcal{E}(x) \\), \\( z \\in \\mathbb{R}^{f \\times C \\times h \\times w} \\). The forward and reverse processes are then performed in the latent space. The final generated videos are obtained through the VAE decoder \\( \\hat{x} = \\mathcal{D}(z) \\). In this work, we build our VDM based on an open-sourced Image-to-Video (I2V) diffusion model DynamiCrafter [58]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.475,
+ 0.905,
+ 0.595
+ ],
+ "angle": 0,
+ "content": "Initial Video Restoration. As shown in Fig. 2, at a certain iteration, given the input images and the corresponding initial video, inpainting masks, and style masks, we first use the VAE encoder to encode the initial video into latents and downsample both masks to match the shape of the latents. We then concatenate the latents, inpainting masks, style masks, and randomly sampled Gaussian noise along the channel dimension to form the image inputs."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.596,
+ 0.906,
+ 0.731
+ ],
+ "angle": 0,
+ "content": "To better leverage the I2V VDM's ability to control video generation via text-aligned semantic embeddings [58], we extend the Query Transformer in [58] to a Multiple-input Query Transformer. Considering we have \\(N\\) input images per iteration, we pass them through the CLIP image encoder [44] to obtain \\(N\\) embeddings, which are then injected into the Multiple-input Query Transformer via cross-attention as the value and key. This yields a global semantic embedding to aid in generating 3D-aware videos."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.732,
+ 0.906,
+ 0.837
+ ],
+ "angle": 0,
+ "content": "With the image inputs and the embedding as conditional inputs, we use the VDM to generate restored latents and decode them using the VAE Decoder to produce the consistent restored video. Finally, we extract the corresponding \\(N\\) frames from the restored \\(f\\)-frame video as the restored images. We discard the other \\(f - N\\) new views, as they can be unreliable without 3D-consistency constraints."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.856,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Training VDMs for Consistency. As discussed, Universe aims to make input images consistent. The purpose of sampling dense views, as described in Sec. 3.1, is to trans"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
+ 0.945,
+ 0.521,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "27034"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.485,
+ 0.288
+ ],
+ "angle": 0,
+ "content": "form discrete images into a video to leverage the VDM's prior, rather than generating new views. Directly training the VDM using MSE Loss is inappropriate because the simple MSE loss equally weights making the input \\(N\\) frames consistent and generating \\(f - N\\) new views. Given \\(2 \\leq N < f\\), we need to adjust the loss weights for each of the \\(f\\) frames to ensure the VDM focuses on making existing images consistent. To this end, we propose a consistency loss \\(\\mathcal{L}_{con}\\) for VDM training. Specifically, assuming the initial video is \\(\\mathbf{v}^{ini} \\in \\mathbb{R}^{f \\times 3 \\times H \\times W}\\), given the VDM's estimated noise \\(\\epsilon_{\\theta}\\) and the ground truth noise \\(\\epsilon \\in \\mathbb{R}^{f \\times C \\times h \\times w}\\) during training, we first compute the MSE loss frame-by-frame to obtain the loss vector \\(lv \\in \\mathbb{R}^{f}\\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.138,
+ 0.314,
+ 0.483,
+ 0.332
+ ],
+ "angle": 0,
+ "content": "\\[\nl v [ i ] = \\| \\epsilon_ {\\theta} [ i ] - \\epsilon [ i ] \\| _ {2} ^ {2}, \\quad \\text {f o r} i = 1, 2, \\dots , f, \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.342,
+ 0.483,
+ 0.371
+ ],
+ "angle": 0,
+ "content": "where \\([i]\\) denotes the \\(i\\)-th frame. We then adjust \\(lv\\) as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.09,
+ 0.38,
+ 0.484,
+ 0.432
+ ],
+ "angle": 0,
+ "content": "\\[\nl v [ i ] = l v [ i ] \\times \\left\\{ \\begin{array}{l l} \\omega_ {c} & \\text {i f} \\mathbf {v} ^ {i n i} [ i ] \\text {i s a n i n p u t i m a g e}, \\\\ \\omega_ {n} & \\text {o t h e r w i s e (i . e . ,} \\mathbf {v} ^ {r o} [ i ] \\text {i s a z e r o f r a m e)}. \\end{array} \\right. \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.433,
+ 0.363,
+ 0.449
+ ],
+ "angle": 0,
+ "content": "The weights \\(\\omega_{c}\\) and \\(\\omega_{n}\\) are computed as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.2,
+ 0.458,
+ 0.483,
+ 0.492
+ ],
+ "angle": 0,
+ "content": "\\[\n\\omega_ {c} = \\max \\left(\\frac {N}{f}, \\lambda\\right) / \\frac {N}{f}, \\tag {5}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.157,
+ 0.501,
+ 0.483,
+ 0.535
+ ],
+ "angle": 0,
+ "content": "\\[\n\\omega_ {n} = \\min \\left(\\frac {f - N}{N}, 1 - \\lambda\\right) / \\frac {f - N}{f}. \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.54,
+ 0.484,
+ 0.63
+ ],
+ "angle": 0,
+ "content": "This ensures that the ratio of the loss weights for making images consistent to generating new views is at least \\(\\lambda : (1 - \\lambda)\\). In practice, we set \\(\\lambda\\) to a large value like 0.98. Additionally, since our VDM takes initial video, inpainting/style masks as input, we need a special training data construction approach, which we discuss in Sec. 4.1."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.216,
+ 0.66
+ ],
+ "angle": 0,
+ "content": "4. Experiment"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "4.1. Implementation Details"
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+ "type": "text",
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+ "content": "VDM Training Details: We employ a progressive training strategy to fine-tune the VDM. Specifically, we fine-tune the \\(576 \\times 1024\\) interpolation VDM from ViewCrafter [67]. In the first stage, we train the VDM at a resolution of \\(320 \\times 512\\), with the frame length \\(f\\) set to 25. The entire video denoising U-Net is fine-tuned for 14,520 iterations using a learning rate of \\(5 \\times 10^{-5}\\) and a batch size of 8. In the second stage, we continue to fine-tune the video denoising U-Net at a resolution of \\(576 \\times 1024\\) for high-resolution adaptation, with 12,000 iterations on a learning rate of \\(1 \\times 10^{-5}\\) and a mini-batch size of 8. All training is conducted on 8 NVIDIA A100 GPUs."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "Training Data Construction: Our VDM was trained on the DL3DV dataset [32]. Specifically, we first extract 25"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "frames from the video of DL3DV at a random FPS to simulate the varying levels of density and sparsity in real-world multi-view images. Then we randomly set \\( n, 0 \\leq n \\leq 23 \\) of the 25 frames to zeros. Next, for each frame in the 25 frames, we randomly adjust their brightness, sharpness, hue, saturation, and simultaneously add Gaussian noise, motion blur, Gaussian blur, and occlusions to simulate inconsistencies. We use the VOC2007 dataset [13] to generate the occlusions and inpainting masks. In the masks, \"1\" indicates that this pixel needs to be inpainted, while \"0\" indicates the opposite. For zero frames, the inpainting masks are filled with \"1\". In this way, we generate a initial video and corresponding inpainting masks. Finally, we randomly choose a non-zero frame from the initial video as the style image and generate the style masks. Specifically, for the style frame, the mask is all \"1\", while for other frames, the mask is \"0\". We then adjust all frames in the original video to match the style of the style image to obtain the target video. In this way, we generate a training pair. In total, we generate 116,158 video pairs as training data."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Inferencing Details: During inference, we adopt the DDIM sampler [51] with classifier-free guidance [22]. We use SegNeXt [19] as the semantic segmentation model to identify transient occlusions in the input images, and then use SAM [24] to segment these occlusions and generate the inpainting masks. Assuming \\( O \\) is the minimum integer such that \\( \\frac{K - 1}{O} < 25 \\), we set the number of images processed at each iteration to \\( N = \\lfloor \\frac{K - 1}{O} \\rfloor + 1 \\). After all images are made consistent, we use ZipNeRF [4] with GLO [35] to reconstruct the 3D scene. All inference is conducted on a single NVIDIA A100 GPU."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "4.2. Evaluation"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We aim to evaluate the ability of UniVerse to alleviate the problem mentioned in the Background of Sec. 3, i.e. the problem of inconsistent images. We evaluate our method on both synthetic datasets and real-world datasets and compare it with the latest methods."
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+ "content": "Dataset: For synthetic datasets, we utilize the NeRF llff dataset [43]. Since all images in this dataset are captured under static, consistent conditions, we randomly adjust their brightness, sharpness, hue, and saturation. We also randomly add Gaussian noise, motion blur, Gaussian blur, and occlusions to simulate inconsistencies. To stress test all methods, we limit the number of images for a single scene to 20-50. For real-world datasets, we use cell phone cameras to collect 7 real-world scenes for evaluation. During capture, in addition to the automatic adjustments by camera programs, we manually change local exposure and ISO settings, and apply random post-processing filters to each view. We show samples of our captured images in Fig. 5."
+ },
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+ "angle": 0,
+ "content": "Metrics and Compared Methods: For quantitative comparison, we use PSNR, SSIM [56], and LPIPS [71] as"
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+ [
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+ "type": "image",
+ "bbox": [
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+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 3. Visual results of novel view synthesis on synthetic datasets, with the corresponding depth map displayed in the bottom left corner."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "content": "Figure 4. Visual results of novel view synthesis on real datasets, with the corresponding depth map displayed in the bottom left corner."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. Samples of our captured images."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "metrics to assess the performance of our method. Meanwhile, we calculate a per-channel affine transformation to align the output color tints with the ground truth tints (Affine-aligned sRGB) [55]. We also present rendered images generated from the same pose as the input view for visual inspection. To demonstrate the superiority of our method, we compare it against the following meth-"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. The quantitative results in novel view synthesis on synthetic datasets. The best and second-best results are highlighted."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": " | sRGB | Affine-aligned sRGB |
| PSNR ↑ | SSIM ↑ | LPIPS ↓ | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| ZipNeRF | 11.52 | 0.2327 | 0.6930 | 14.53 | 0.3548 | 0.6297 |
| ZipNeRF w/GLO | 14.53 | 0.4667 | 0.4394 | 18.58 | 0.5297 | 0.4123 |
| Bilarf | 16.06 | 0.4814 | 0.4489 | 17.68 | 0.5062 | 0.4317 |
| WildGaussians | 13.75 | 0.3972 | 0.6430 | 15.45 | 0.4476 | 0.6244 |
| Ours | 18.09 | 0.5789 | 0.3015 | 20.12 | 0.5926 | 0.2979 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "ods: ZipNeRF [4], ZipNeRF W/GLO [35], Bilarf [55], and WildGaussians [26]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Results: We present the average quantitative results in Tab. 1 and Tab. 2, and the qualitative visual results in Fig. 3 and Fig. 4. Both tables show that UniVerse achieves the best metric values under both settings. Moreover, the figures demonstrate that our method provides the most visually"
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+ "bbox": [
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+ "angle": 0,
+ "content": "27036"
+ }
+ ],
+ [
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. The quantitative results in novel view synthesis on real-world datasets. The best and second-best results are highlighted."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": " | sRGB | Affine-aligned sRGB |
| PSNR ↑ | SSIM ↑ | LPIPS ↓ | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| ZipNeRF | 13.31 | 0.5222 | 0.4310 | 16.38 | 0.5490 | 0.4328 |
| ZipNeRF w/GLO | 16.14 | 0.5668 | 0.3095 | 20.67 | 0.5907 | 0.3125 |
| Bilarf | 15.46 | 0.5459 | 0.3323 | 18.84 | 0.6055 | 0.3169 |
| WildGaussians | 15.05 | 0.4246 | 0.5046 | 17.39 | 0.5747 | 0.4493 |
| Ours | 19.65 | 0.6511 | 0.2532 | 22.91 | 0.6998 | 0.2132 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "pleasing results with fewer artifacts and floaters. In contrast, other compared methods often produce novel views with noticeable artifacts and a significant number of floaters due to unstable optimization and the lack of dense observations, thereby highlighting the superiority of our approach."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.3. Abalation Study"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The Effect of the Design of Turning Images into Videos: As discussed, transforming multi-view images into videos is crucial for unleashing the consistent 3D prior of VDMs. To validate this, we tested the following settings for image restoration and reconstruction: (a) Directly stacking unordered images as the initial video. (b) Sorting images using ThreadPose and stacking them as the initial video. (c) Inserting zero frames (implicit views) into unordered images to form the initial video. (d) Inserting zero frames into ordered images, as described in Sec. 3.1. The results in Tab. 3 show that only our design fully exploits the 3D prior of VDMs, demonstrating its rationality."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Results on novel view synthesis with different image to video settings."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Setting | ThreadPose | zero frames | PSNR | SSIM |
| (a) (directly stack) | X | X | 15.32 | 0.4598 |
| (b) (w/ ThreadPose) | ✓ | X | 17.29 | 0.5876 |
| (c) (w/ zero frames) | X | ✓ | 18.25 | 0.6067 |
| (d) (ours) | ✓ | ✓ | 20.71 | 0.7708 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The Effect of our VDM Design: We introduce four new designs for VDMs in this work: the Multi-input Query Transformer (MiQT), style mask, inpainting mask, and consistent loss. We validate each design as follows:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "(1) Multi-input Query Transformer (MiQT): To assess MiQT's impact, we retrained a model using a single-input QT and compared its robust reconstruction performance with ours. The results in Tab. 4 show MiQT's superiority over QT. This highlights the importance of global semantic information in leveraging VDMs' prior, thereby justifying our design."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "(2) Inpainting Mask: We retrained a VDM without inpainting masks, forcing it to decide which pixels to inpaint. Using a subset of the NeRF-on-the-go dataset [46] contain"
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Results on novel view synthesis with different Query Transformer (QT) settings."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Setting | PSNR | SSIM | LPIPS | Setting | PSNR | SSIM | LPIPS |
| QT | 16.80 | 0.4157 | 0.5015 | MiQT | 17.42 | 0.4511 | 0.4549 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "ing only occlusions as inconsistencies, we found that the VDM failed to inpaint all masked pixels (Fig. 8). Thus, inpainting masks are essential for UniVerse."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "(3) Style Mask: Figure 9 compares results with and without the style mask. Without it, output image tone is uncontrollable despite consistent input tones. Style masks are thus crucial for controlling image appearance and reconstructed 3D scene style."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "(4) Consistent Loss: As elaborated in Sec. 3.2, employing the Consistent Loss is pivotal for directing the VDM to prioritize image consistency. The comparative training outcomes presented in Tab. 5 underscore the superior performance of the Consistent Loss over the regular MSE. This superiority indicates that the Consistent Loss effectively enables the VDM to more adeptly eliminate inconsistencies, thereby substantiating the efficacy of our design approach."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ 0.25,
+ 0.906,
+ 0.45
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 5. Results on novel view synthesis with different training loss function settings."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Setting | PSNR | SSIM | LPIPS | Setting | PSNR | SSIM | LPIPS |
| MSE | 16.19 | 0.3788 | 0.5340 | Consistent | 17.42 | 0.4511 | 0.4549 |
"
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+ {
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+ "angle": 0,
+ "content": "4.4. Further Applications of UniVerse"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Controlling the Style of Reconstructed 3D Scene: The style of the restored images, and consequently the reconstructed 3D scenes, is determined by the style image. By changing the style image, we can alter the style of the entire reconstructed 3D scene, as shown in Fig. 6."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Robust Reconstruction on Sparse Images: UniVerse focuses on making images consistent rather than generating new views. Thus, even after restoring very sparse input images to a consistent state, reconstruction may still fail due to insufficient views. This issue can be easily resolved by using a generative novel view synthesis model like ViewCrafter [67]. As shown in Fig. 7, given 2 inconsistent input images, ViewCrafter [67] synthesizes distorted novel views with strange occlusions. After the images are restored via UniVerse, the novel views synthesized by ViewCrafter become consistent. In other words, as a restoration model, UniVerse can serve as a pre-processor for other models, enabling robust reconstruction."
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+ "content": "Style Image"
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+ "content": "Synthesized Novel Views"
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+ "content": "Figure 6. Controlling the style of reconstructed 3D scene by switching style image."
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+ "content": "Sparse inconsistent images"
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+ "content": "Restore images"
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+ "content": "Synthesized novel views"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 7. Novel views synthesized via ViewCrafter [67]. First line: ViewCrafter synthesizes inconsistent and distorted views from inconsistent images. Second line: After the images are restored by UniVerse, the generated views become consistent."
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+ "content": "Input Image"
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+ "content": "w/o Inpainting Mask"
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+ "angle": 0,
+ "content": "w/ Inpainting Mask"
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+ "angle": 0,
+ "content": "Figure 8. Visualization of results w/o and w/ inpainting masks."
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+ "content": "Input Image"
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+ {
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+ "content": "w/o Style Mask"
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+ "content": "Figure 9. Visualization of results w/o and w/ style masks."
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+ "content": "5. Conclusion & Limitation"
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+ "angle": 0,
+ "content": "This paper proposes UniVerse, a unified robust reconstruction framework that converts inconsistent multi-view im"
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+ "bbox": [
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+ "angle": 0,
+ "content": "ages into initial videos and leverages Video Diffusion Models to restore them into consistent images. By decoupling robust reconstruction into two subtasks (i.e. restoration and reconstruction), UniVerse overcomes the limitations of existing approaches that require very dense observations to reconstruct inconsistent images, achieving state-of-the-art performance on both synthetic and real-world datasets. Moreover, we explore UniVerse's ability to control the style of the reconstructed 3D scene by switching the reference image and its potential for reconstructing very sparse inconsistent observations by applying novel view generation models after restoration. We believe our work offers new insights of decoupling robust reconstruction and restoring images using models with 3D priors to the community."
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+ "content": "Limitations: UniVerse requires synthesizing videos with inconsistencies as training data to fine-tune the VDM for adaptation to a restoration model. While some inconsistencies, like lighting, may be hard to synthesize, [53] have shown tremendous promise for inconsistency synthesis via generative models."
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+ "content": "6. Acknowledgment"
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+ "content": "This work was partially supported by the National Key R&D Program of China (No. 2024YFB2809102), NSFC (No. 62402427, NO. U24B20154), Zhejiang Provincial Natural Science Foundation of China (No. LR25F020003), DeepGlint, Zhejiang University Education Foundation Qizhen Scholar Foundation, and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University."
+ },
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+# UniVerse: Unleashing the Scene Prior of Video Diffusion Models for Robust Radiance Field Reconstruction
+
+Jin $\mathsf{Cao}^{1\dagger}$ Hongrui $\mathsf{Wu}^{2\dagger}$ Ziyong Feng $^3$ Hujun $\mathsf{Bao}^1$ Xiaowei Zhou $^1$ Sida Peng $^{1*}$
+
+$^{1}$ State Key Lab of CAD&CG, Zhejiang University $^{2}$ Tongji University $^{3}$ DeepGlint
+
+
+Figure 1. Given a set of inconsistent multi-view images with inconsistencies such as photometric variation or transient occlusions, as shown in (a), existing robust reconstruction methods often fail to produce a high-quality 3D scene with minimal artifacts and floaters when the views are not dense enough, as illustrated in (b). In contrast, our method first utilizes a Video Diffusion Model to restore all images into a consistent state in (c), and then reconstructs the 3D scene from these restored images, resulting in the high-quality 3D scene in (d). (c) Restored Images
+
+# Abstract
+
+This paper tackles the challenge of robust reconstruction, i.e., the task of reconstructing a 3D scene from a set of inconsistent multi-view images. Some recent works have attempted to simultaneously remove image inconsistencies and perform reconstruction by integrating image degradation modeling into neural 3D scene representations. However, these methods rely heavily on dense observations for robustly optimizing model parameters. To address this issue, we propose to decouple robust reconstruction into two subtasks: restoration and reconstruction, which naturally simplifies the optimization process. To this end, we introduce UniVerse, a unified framework for robust reconstruction based on a video diffusion model. Specifically, UniVerse first converts inconsistent images into initial videos,
+
+then uses a specially designed video diffusion model to restore them into consistent images, and finally reconstructs the 3D scenes from these restored images. Compared with case-by-case per-view degradation modeling, the diffusion model learns a general scene prior from large-scale data, making it applicable to diverse image inconsistencies. Extensive experiments on both synthetic and real-world datasets demonstrate the strong generalization capability and superior performance of our method in robust reconstruction. Moreover, UniVerse can control the style of the reconstructed 3D scene. The code will be released for the reproducibility.
+
+# 1. Introduction
+
+Novel view synthesis have long been a high-profile and complicated task in computer graphics, which plays a significant role in many applications like virtual reality (VR) and autonomous driving. Traditional approaches [48, 50]
+
+reconstruct 3D scenes based on the point cloud representation and multi-view stereo techniques. However, such methods generally suffer from low rendering quality, thus limiting their applications.
+
+In recent years, differentiable rendering-based methods, such as Neural Radiance Fields (NeRF) [2, 3, 38, 40] and 3D Gaussian Splatting (3DGS) [7, 23, 28, 63], have made significant progress in rendering photorealistic novel views. However, these methods assume that all input images are static and captured under consistent conditions. In reality, images are frequently affected by illumination variations caused by changes in camera exposure or environmental lighting, content alterations due to dynamic objects, and motion blur resulting from camera shake. These inconsistencies violate the assumptions of the differentiable-rendering based methods, leading to significant performance degradation [35, 64].
+
+To overcome this problem, previous methods propose learnable embeddings [10, 29, 35, 52] to additionally model the viewpoint-specific content for each image and jointly optimize it with the underlying 3D scene representation to minimize the rendering loss. When scene observations are sufficient, these methods can successfully recover the intrinsic scene structure from the inconsistent images. However, their performance tends to degrades significantly as the number of observations decreases. A plausible reason is that they introduce additional learnable parameters into the optimization process, making it more unstable, needing dense observations for optimization.
+
+In this paper, we propose UniVerse, a video generative model for robust 3D reconstruction from inconsistent multiview images. Our key idea is to exploit the strong consistent prior of video diffusion models [33, 67] to transform all inconsistent images to a consistent state before performing 3D reconstruction. Specifically, given a set of unstructured multi-view images, we first sort them to obtain a camera trajectory and insert blank images along this trajectory to transform images into a video. To better utilize observations, a multiple-input query transformer is proposed to aggregate information from all input images and generate a global semantic embedding, which is injected into the video diffusion model to help the video restoration. In contrast to previous methods that manually model the degradation in each image, the video diffusion model learns a general consistent scene prior from large-scale data, making it more robust in handling diverse inconsistencies.
+
+We apply UniVerse to both synthetic and real-world challenging inconsistent image collections and demonstrate its ability to produce high-fidelity renderings with fewer artifacts and floaters, surpassing previous state-of-the-art methods in terms of PSNR, SSIM, and LPIPS. By selecting a style image, UniVerse can change the style of the generated videos to match that of the style image, thereby alter
+
+ing the style of the final reconstructed 3D scene. Even when the input images are very sparse and inconsistent (e.g., only 2 images with occlusions), UniVerse can still restore them into convincing consistent images, which can be applied to other downstream tasks such as generating new views [67] and performing further reconstruction. Overall, these results demonstrate the effectiveness of UniVerse and highlight the potential of decoupling robust reconstruction.
+
+# 2. Related Works
+
+# 2.1. Video Diffusion Models for 3D Reconstruction
+
+The success of diffusion models has also spurred research in diffusion-based video generation [5, 5, 8, 27, 58], which are often fine-tuned from T2I models using extensive video datasets [1, 9, 62] and can generate consistent videos from text [5, 8, 27] or image inputs [5, 58]. Recent advancements [6, 8, 18, 54, 69, 72] further enhance text-to-video generation visual quality through extra temporal layers and curated datasets. The rapid developments of VDMs provoke significant interest in more controllable video generation, enabling controls like RGB images [5, 58, 59], depth [12, 60], trajectory [41, 65], and semantic maps [42]. Recently, some works further explore camera motion control for VDMs to generate controllable 3D-aware videos [5, 20, 39, 57]. Recently, CamCo [61] and CameraCtrl [21] introduced Plücker coordinates [49] in video diffusion models for camera motion control. ViewCrafter [67] and ReconX [33] further use explicit point clouds to achieve more precise 3D-aware camera control. These works achieve great success in generating consistent 3D-aware videos which can be directly used to reconstruct a 3D scene. Observing the strong consistent 3D prior of VDMs and noting that multi-view images are similar to frames extracted from a video captured by a camera trajectory, we take inconsistent multi-view images as conditions and generate a consistent video, and then extract them from the generated video with all images being consistent and static.
+
+# 2.2. Robust 3D Reconstruction
+
+Reconstructing a 3D scene from a set of 2D images is a long-standing problem in computer vision. Modern approaches, such as NeRF-based methods [15, 17, 40, 45, 66] and 3DGS-based methods [14, 23, 34, 68], have achieved great success and demonstrated expressive reconstruction quality. However, these methods all assume that the input images are captured in a static scene. Their performance declines significantly when reconstructing from unconstrained inconsistent photo collections. To address this challenging in-the-wild task, several attempts [10, 26, 29, 35, 36, 47, 64] have been made to handle appearance variation and transient occlusions. Other works [30, 31] focus on scenes with time-varying appearances, while methods [11, 25, 70] use
+
+
+Input Images
+
+
+(a) Initial Video Construction
+Initial Video
+
+
+(b) Condition Preparation
+
+
+
+
+Inpainting Masks
+Noise
+
+
+
+
+Latents
+Figure 2. The flowchart of UniVerse. Given a set of inconsistent images, we first convert them into an initial video. We then use SAM [24] to identify transient occlusions and generate inpainting masks. These masks are used to set the occluded pixels in the initial video to zero. Next, we encode the video into latents using a VAE Encoder. After setting one image as the style image and assigning it style mask, we concatenate the style masks, inpainting masks, latents, and randomly sampled Gaussian noise along the channel dimension and feed them into the U-Net. For each masked input image, we obtain semantic embeddings using the CLIP image encoder and aggregate them via the Multi-input Query Transformer to form a global semantic embedding. This embedding guides the U-Net in the video generation process. Finally, the U-Net output is decoded by the VAE Decoder to produce the restored video, from which we extract the consistent images and reconstruct a high-quality 3D scene. If too many images for the VDM to restore at once, we iteratively restore them in batches as described.
+
+
+(c) Video Restoration
+
+
+Query Embeddings
+
+
+3D scene
+
+physical rendering models for diverse lighting conditions. Nevertheless, these methods typically couple the process of restoration and reconstruction and directly perform reconstruction on the inconsistent multi-view images, which requires a large amount of training images to identify and remove all inconsistencies. What's more, they typically use handcraft prior to manually model inconsistency in each image [55]. In contrast, our method emphasizes the effectiveness of restoration before reconstruction, decoupling the task and making it much easier. Meanwhile, the VDM we use learns a general consistent scene prior from large-scale data, thus can be more robust facing various inconsistencies. Recently, SimVS [53] utilized a multi-view diffusion model [16] to turn all images into a consistent state given an image as a reference. However, it retains all inconsistencies of the reference image, such as a moving passenger, thus can fail to reconstruct the static scene, while our method removes all inconsistencies in the images and aims to reconstruct the static scene.
+
+# 3. Method
+
+Background. 3D reconstruction aims to recover the 3D structure of a scene from multiple 2D images taken from different viewpoints. While traditional methods like structure-from-motion [48, 50] have been widely used, newer techniques such as NeRF [43] and 3DGS [23] leverage differentiable rendering. Given input images $\{I_i\}_{i=1}^K$ and their corresponding poses $\{P_i\}_{i=1}^K$ , differentiable rendering aims to find a parameterized function $f_\theta$ that takes a camera pose as input and outputs the corresponding image.
+
+The goal is to optimize the parameters $\theta$ or the 3D representation to minimize the following loss function:
+
+$$
+\theta = \arg \min _ {\theta} \sum_ {i = 1} ^ {K} D i f \left(f _ {\theta} \left(P _ {i}\right), I _ {i}\right). \tag {1}
+$$
+
+Here, $Dif(\cdot)$ is a differentiable function, such as MSE or L1 loss, used to measure the difference between two images. Once $\theta$ is obtained, we can render novel views from the 3D scene for any new camera pose $P$ using $f_{\theta}(P)$ , thereby achieving 3D reconstruction. However, these approaches assume that the images $\{I_i\}_{i=1}^K$ are consistent and static. If the assumption isn't hold, the learning of $f_{\theta}$ fails. To address this, UniVerse uses a VDM to restore all input images to be static and consistent. This ensures that the assumption for Eq. (1) is valid, helping $f_{\theta}$ to easily learn the 3D scene.
+
+Overview. Given $K$ inconsistent multi-view images $\{I_i\}_{i=1}^K, I_i \in \mathbb{R}^{3 \times H \times W}$ , our goal is to restore them into $K$ consistent images. We treat the multi-view images as video frames from the same video. We first sort the images into ordered $K$ images based on their camera poses, as described in Sec. 3.1. Then we use a VDM to restore all these $K$ images into a consistent state. Assuming the VDM can generate $f$ frames at a time, we iteratively restore all images, processing $N \leq f$ images per iteration. We select one of the first $N$ images as the style image $I_{sty}$ , and turn the first $N$ images into a initial video as described in Sec. 3.1. For all frames in the initial video, we assign them inpainting masks to indicate where to be inpainted and style masks
+
+to indicate which frame should be taken as the style reference via Segment Anything Model (SAM) [24]. Using the initial video, inpainting masks, and style masks as conditions, we use the VDM to generate a restored video with the same style as the style image, extracting the corresponding $N$ consistent frames. We then remove the corresponding $N$ images from the input unrestored $K$ images since they are already restored, and add the last restored image to the unrestored images as the first image, and set it as style image for the next iteration. We update $K$ to $\max(K - (N - 1), 1)$ and repeat the process until $K \leq 1$ , which means all images are restored. Finally, with all restored $K$ images, we use 3D reconstruction methods like NeRFs [43] to reconstruct them and return a 3D representation. We show this process in Fig.2 and Alg. 1 in Supp.
+
+# 3.1. Turning Multi-view Images into Videos
+
+As discussed, UniVerse first converts the $K$ input multiview images into initial videos. These images are essentially captured by cameras at various poses around a single scene. Assuming all $K$ poses $\{P_i\}_{i=1}^K$ lie on a single camera trajectory, continuously sampling new poses (and thus new views) from this trajectory yields a video if the poses are sufficiently dense. This approach hinges on solving two key problems: (I) determining the trajectory and (II) sampling new poses from it. The detailed algorithm is provided in Sec. 7, Alg. 2 and Fig. 10 the Supp.
+
+Sorting Multi-view Images for Sparse Trajectory. We use ThreadPose to sort the $K$ input poses $\{P_i\}_{i=1}^K$ into an ordered list. We initialize a double linked list with a randomly chosen pose and iteratively add the remaining poses based on their distances to the current head and tail of the list. The distance metric combines rotation and translation differences, weighted to ensure consistent scaling. Finally, we traverse the whole list to construct an ordered set of poses $\{P_i'\}_{i=1}^K$ , which defines an implicit camera trajectory.
+
+Sample Implicit Dense Views from Trajectory At each iteration, given $N$ ordered poses $\{P_i^{\prime}\}_{i = 1}^{N}$ and the corresponding $N$ inconsistent images $\{I_i^{\prime}\}_{i = 1}^{N}$ , our goal is to create an initial video of $f$ frames that includes all $N$ input images. We achieve this by sampling $f - N$ new poses from the trajectory to generate new views. First, we compute the distances $\{d_i\}_{i = 1}^{N - 1}$ between neighboring poses:
+
+$$
+d _ {i} = D _ {P} \left(P _ {i} ^ {\prime}, P _ {i + 1} ^ {\prime}\right), \quad i = 1, 2, \dots , N - 1. \tag {2}
+$$
+
+Here, $D_P(\cdot)$ is a function to compute the distance between two poses, which is defined in $\mathbf{Supp}$ . Next, we assign the number of new poses $n_i$ to be inserted between each pair of neighboring poses $P_{i}^{\prime}$ and $P_{i + 1}^{\prime}$ , proportional to the distance $d_{i}$ . After assigning the number of poses, we aim to
+
+sample new poses and new views. However, since the input images are inconsistent, it can be difficult to use methods like conditional VDM generation [21, 61], or building 3D structures like point clouds [67], to explicitly render a new view given an explicit camera pose. Considering VDM's strong 3D prior and frame interpolation ability, we simply insert $n_i$ zero frames into each $I_i'$ , $I_{i+1}'$ neighboring image pair and expect the VDM to inpaint these zero frames into new views. In this way, we turn $N$ ordered images $\{I_i'\}_{i=1}^N$ into an $f$ -frame initial video with the first image $I_1'$ and the last image $I_N'$ as the first and last frames.
+
+# 3.2. Conditional VDM for Initial Video Restoration
+
+Preliminary: Video Diffusion Models. In diffusion-based video generation, Latent Diffusion Models (LDMs) [37] are often employed to reduce computational costs. In LDMs, video data $x \in \mathbb{R}^{f \times 3 \times H \times W}$ is encoded into the latent space using a pre-trained VAE encoder frame-by-frame, expressed as $z = \mathcal{E}(x)$ , $z \in \mathbb{R}^{f \times C \times h \times w}$ . The forward and reverse processes are then performed in the latent space. The final generated videos are obtained through the VAE decoder $\hat{x} = \mathcal{D}(z)$ . In this work, we build our VDM based on an open-sourced Image-to-Video (I2V) diffusion model DynamiCrafter [58].
+
+Initial Video Restoration. As shown in Fig. 2, at a certain iteration, given the input images and the corresponding initial video, inpainting masks, and style masks, we first use the VAE encoder to encode the initial video into latents and downsample both masks to match the shape of the latents. We then concatenate the latents, inpainting masks, style masks, and randomly sampled Gaussian noise along the channel dimension to form the image inputs.
+
+To better leverage the I2V VDM's ability to control video generation via text-aligned semantic embeddings [58], we extend the Query Transformer in [58] to a Multiple-input Query Transformer. Considering we have $N$ input images per iteration, we pass them through the CLIP image encoder [44] to obtain $N$ embeddings, which are then injected into the Multiple-input Query Transformer via cross-attention as the value and key. This yields a global semantic embedding to aid in generating 3D-aware videos.
+
+With the image inputs and the embedding as conditional inputs, we use the VDM to generate restored latents and decode them using the VAE Decoder to produce the consistent restored video. Finally, we extract the corresponding $N$ frames from the restored $f$ -frame video as the restored images. We discard the other $f - N$ new views, as they can be unreliable without 3D-consistency constraints.
+
+Training VDMs for Consistency. As discussed, Universe aims to make input images consistent. The purpose of sampling dense views, as described in Sec. 3.1, is to trans
+
+form discrete images into a video to leverage the VDM's prior, rather than generating new views. Directly training the VDM using MSE Loss is inappropriate because the simple MSE loss equally weights making the input $N$ frames consistent and generating $f - N$ new views. Given $2 \leq N < f$ , we need to adjust the loss weights for each of the $f$ frames to ensure the VDM focuses on making existing images consistent. To this end, we propose a consistency loss $\mathcal{L}_{con}$ for VDM training. Specifically, assuming the initial video is $\mathbf{v}^{ini} \in \mathbb{R}^{f \times 3 \times H \times W}$ , given the VDM's estimated noise $\epsilon_{\theta}$ and the ground truth noise $\epsilon \in \mathbb{R}^{f \times C \times h \times w}$ during training, we first compute the MSE loss frame-by-frame to obtain the loss vector $lv \in \mathbb{R}^{f}$ :
+
+$$
+l v [ i ] = \| \epsilon_ {\theta} [ i ] - \epsilon [ i ] \| _ {2} ^ {2}, \quad \text {f o r} i = 1, 2, \dots , f, \tag {3}
+$$
+
+where $[i]$ denotes the $i$ -th frame. We then adjust $lv$ as follows:
+
+$$
+l v [ i ] = l v [ i ] \times \left\{ \begin{array}{l l} \omega_ {c} & \text {i f} \mathbf {v} ^ {i n i} [ i ] \text {i s a n i n p u t i m a g e}, \\ \omega_ {n} & \text {o t h e r w i s e (i . e . ,} \mathbf {v} ^ {r o} [ i ] \text {i s a z e r o f r a m e)}. \end{array} \right. \tag {4}
+$$
+
+The weights $\omega_{c}$ and $\omega_{n}$ are computed as:
+
+$$
+\omega_ {c} = \max \left(\frac {N}{f}, \lambda\right) / \frac {N}{f}, \tag {5}
+$$
+
+$$
+\omega_ {n} = \min \left(\frac {f - N}{N}, 1 - \lambda\right) / \frac {f - N}{f}. \tag {6}
+$$
+
+This ensures that the ratio of the loss weights for making images consistent to generating new views is at least $\lambda : (1 - \lambda)$ . In practice, we set $\lambda$ to a large value like 0.98. Additionally, since our VDM takes initial video, inpainting/style masks as input, we need a special training data construction approach, which we discuss in Sec. 4.1.
+
+# 4. Experiment
+
+# 4.1. Implementation Details
+
+VDM Training Details: We employ a progressive training strategy to fine-tune the VDM. Specifically, we fine-tune the $576 \times 1024$ interpolation VDM from ViewCrafter [67]. In the first stage, we train the VDM at a resolution of $320 \times 512$ , with the frame length $f$ set to 25. The entire video denoising U-Net is fine-tuned for 14,520 iterations using a learning rate of $5 \times 10^{-5}$ and a batch size of 8. In the second stage, we continue to fine-tune the video denoising U-Net at a resolution of $576 \times 1024$ for high-resolution adaptation, with 12,000 iterations on a learning rate of $1 \times 10^{-5}$ and a mini-batch size of 8. All training is conducted on 8 NVIDIA A100 GPUs.
+
+Training Data Construction: Our VDM was trained on the DL3DV dataset [32]. Specifically, we first extract 25
+
+frames from the video of DL3DV at a random FPS to simulate the varying levels of density and sparsity in real-world multi-view images. Then we randomly set $n, 0 \leq n \leq 23$ of the 25 frames to zeros. Next, for each frame in the 25 frames, we randomly adjust their brightness, sharpness, hue, saturation, and simultaneously add Gaussian noise, motion blur, Gaussian blur, and occlusions to simulate inconsistencies. We use the VOC2007 dataset [13] to generate the occlusions and inpainting masks. In the masks, "1" indicates that this pixel needs to be inpainted, while "0" indicates the opposite. For zero frames, the inpainting masks are filled with "1". In this way, we generate a initial video and corresponding inpainting masks. Finally, we randomly choose a non-zero frame from the initial video as the style image and generate the style masks. Specifically, for the style frame, the mask is all "1", while for other frames, the mask is "0". We then adjust all frames in the original video to match the style of the style image to obtain the target video. In this way, we generate a training pair. In total, we generate 116,158 video pairs as training data.
+
+Inferencing Details: During inference, we adopt the DDIM sampler [51] with classifier-free guidance [22]. We use SegNeXt [19] as the semantic segmentation model to identify transient occlusions in the input images, and then use SAM [24] to segment these occlusions and generate the inpainting masks. Assuming $O$ is the minimum integer such that $\frac{K - 1}{O} < 25$ , we set the number of images processed at each iteration to $N = \lfloor \frac{K - 1}{O} \rfloor + 1$ . After all images are made consistent, we use ZipNeRF [4] with GLO [35] to reconstruct the 3D scene. All inference is conducted on a single NVIDIA A100 GPU.
+
+# 4.2. Evaluation
+
+We aim to evaluate the ability of UniVerse to alleviate the problem mentioned in the Background of Sec. 3, i.e. the problem of inconsistent images. We evaluate our method on both synthetic datasets and real-world datasets and compare it with the latest methods.
+
+Dataset: For synthetic datasets, we utilize the NeRF llff dataset [43]. Since all images in this dataset are captured under static, consistent conditions, we randomly adjust their brightness, sharpness, hue, and saturation. We also randomly add Gaussian noise, motion blur, Gaussian blur, and occlusions to simulate inconsistencies. To stress test all methods, we limit the number of images for a single scene to 20-50. For real-world datasets, we use cell phone cameras to collect 7 real-world scenes for evaluation. During capture, in addition to the automatic adjustments by camera programs, we manually change local exposure and ISO settings, and apply random post-processing filters to each view. We show samples of our captured images in Fig. 5.
+
+Metrics and Compared Methods: For quantitative comparison, we use PSNR, SSIM [56], and LPIPS [71] as
+
+
+Figure 3. Visual results of novel view synthesis on synthetic datasets, with the corresponding depth map displayed in the bottom left corner.
+
+
+Figure 4. Visual results of novel view synthesis on real datasets, with the corresponding depth map displayed in the bottom left corner.
+
+
+Figure 5. Samples of our captured images.
+
+metrics to assess the performance of our method. Meanwhile, we calculate a per-channel affine transformation to align the output color tints with the ground truth tints (Affine-aligned sRGB) [55]. We also present rendered images generated from the same pose as the input view for visual inspection. To demonstrate the superiority of our method, we compare it against the following meth-
+
+Table 1. The quantitative results in novel view synthesis on synthetic datasets. The best and second-best results are highlighted.
+
+ | sRGB | Affine-aligned sRGB |
| PSNR ↑ | SSIM ↑ | LPIPS ↓ | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| ZipNeRF | 11.52 | 0.2327 | 0.6930 | 14.53 | 0.3548 | 0.6297 |
| ZipNeRF w/GLO | 14.53 | 0.4667 | 0.4394 | 18.58 | 0.5297 | 0.4123 |
| Bilarf | 16.06 | 0.4814 | 0.4489 | 17.68 | 0.5062 | 0.4317 |
| WildGaussians | 13.75 | 0.3972 | 0.6430 | 15.45 | 0.4476 | 0.6244 |
| Ours | 18.09 | 0.5789 | 0.3015 | 20.12 | 0.5926 | 0.2979 |
+
+ods: ZipNeRF [4], ZipNeRF W/GLO [35], Bilarf [55], and WildGaussians [26].
+
+Results: We present the average quantitative results in Tab. 1 and Tab. 2, and the qualitative visual results in Fig. 3 and Fig. 4. Both tables show that UniVerse achieves the best metric values under both settings. Moreover, the figures demonstrate that our method provides the most visually
+
+Table 2. The quantitative results in novel view synthesis on real-world datasets. The best and second-best results are highlighted.
+
+ | sRGB | Affine-aligned sRGB |
| PSNR ↑ | SSIM ↑ | LPIPS ↓ | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| ZipNeRF | 13.31 | 0.5222 | 0.4310 | 16.38 | 0.5490 | 0.4328 |
| ZipNeRF w/GLO | 16.14 | 0.5668 | 0.3095 | 20.67 | 0.5907 | 0.3125 |
| Bilarf | 15.46 | 0.5459 | 0.3323 | 18.84 | 0.6055 | 0.3169 |
| WildGaussians | 15.05 | 0.4246 | 0.5046 | 17.39 | 0.5747 | 0.4493 |
| Ours | 19.65 | 0.6511 | 0.2532 | 22.91 | 0.6998 | 0.2132 |
+
+pleasing results with fewer artifacts and floaters. In contrast, other compared methods often produce novel views with noticeable artifacts and a significant number of floaters due to unstable optimization and the lack of dense observations, thereby highlighting the superiority of our approach.
+
+# 4.3. Abalation Study
+
+The Effect of the Design of Turning Images into Videos: As discussed, transforming multi-view images into videos is crucial for unleashing the consistent 3D prior of VDMs. To validate this, we tested the following settings for image restoration and reconstruction: (a) Directly stacking unordered images as the initial video. (b) Sorting images using ThreadPose and stacking them as the initial video. (c) Inserting zero frames (implicit views) into unordered images to form the initial video. (d) Inserting zero frames into ordered images, as described in Sec. 3.1. The results in Tab. 3 show that only our design fully exploits the 3D prior of VDMs, demonstrating its rationality.
+
+Table 3. Results on novel view synthesis with different image to video settings.
+
+| Setting | ThreadPose | zero frames | PSNR | SSIM |
| (a) (directly stack) | X | X | 15.32 | 0.4598 |
| (b) (w/ ThreadPose) | ✓ | X | 17.29 | 0.5876 |
| (c) (w/ zero frames) | X | ✓ | 18.25 | 0.6067 |
| (d) (ours) | ✓ | ✓ | 20.71 | 0.7708 |
+
+The Effect of our VDM Design: We introduce four new designs for VDMs in this work: the Multi-input Query Transformer (MiQT), style mask, inpainting mask, and consistent loss. We validate each design as follows:
+
+(1) Multi-input Query Transformer (MiQT): To assess MiQT's impact, we retrained a model using a single-input QT and compared its robust reconstruction performance with ours. The results in Tab. 4 show MiQT's superiority over QT. This highlights the importance of global semantic information in leveraging VDMs' prior, thereby justifying our design.
+(2) Inpainting Mask: We retrained a VDM without inpainting masks, forcing it to decide which pixels to inpaint. Using a subset of the NeRF-on-the-go dataset [46] contain
+
+Table 4. Results on novel view synthesis with different Query Transformer (QT) settings.
+
+| Setting | PSNR | SSIM | LPIPS | Setting | PSNR | SSIM | LPIPS |
| QT | 16.80 | 0.4157 | 0.5015 | MiQT | 17.42 | 0.4511 | 0.4549 |
+
+ing only occlusions as inconsistencies, we found that the VDM failed to inpaint all masked pixels (Fig. 8). Thus, inpainting masks are essential for UniVerse.
+
+(3) Style Mask: Figure 9 compares results with and without the style mask. Without it, output image tone is uncontrollable despite consistent input tones. Style masks are thus crucial for controlling image appearance and reconstructed 3D scene style.
+(4) Consistent Loss: As elaborated in Sec. 3.2, employing the Consistent Loss is pivotal for directing the VDM to prioritize image consistency. The comparative training outcomes presented in Tab. 5 underscore the superior performance of the Consistent Loss over the regular MSE. This superiority indicates that the Consistent Loss effectively enables the VDM to more adeptly eliminate inconsistencies, thereby substantiating the efficacy of our design approach.
+
+Table 5. Results on novel view synthesis with different training loss function settings.
+
+| Setting | PSNR | SSIM | LPIPS | Setting | PSNR | SSIM | LPIPS |
| MSE | 16.19 | 0.3788 | 0.5340 | Consistent | 17.42 | 0.4511 | 0.4549 |
+
+# 4.4. Further Applications of UniVerse
+
+Controlling the Style of Reconstructed 3D Scene: The style of the restored images, and consequently the reconstructed 3D scenes, is determined by the style image. By changing the style image, we can alter the style of the entire reconstructed 3D scene, as shown in Fig. 6.
+
+Robust Reconstruction on Sparse Images: UniVerse focuses on making images consistent rather than generating new views. Thus, even after restoring very sparse input images to a consistent state, reconstruction may still fail due to insufficient views. This issue can be easily resolved by using a generative novel view synthesis model like ViewCrafter [67]. As shown in Fig. 7, given 2 inconsistent input images, ViewCrafter [67] synthesizes distorted novel views with strange occlusions. After the images are restored via UniVerse, the novel views synthesized by ViewCrafter become consistent. In other words, as a restoration model, UniVerse can serve as a pre-processor for other models, enabling robust reconstruction.
+
+
+Style Image
+
+
+Figure 6. Controlling the style of reconstructed 3D scene by switching style image.
+
+
+Synthesized Novel Views
+
+
+
+
+
+
+
+
+
+
+Sparse inconsistent images
+Restore images
+
+
+Synthesized novel views
+
+
+Figure 7. Novel views synthesized via ViewCrafter [67]. First line: ViewCrafter synthesizes inconsistent and distorted views from inconsistent images. Second line: After the images are restored by UniVerse, the generated views become consistent.
+Input Image
+
+
+w/o Inpainting Mask
+
+
+w/ Inpainting Mask
+
+
+Figure 8. Visualization of results w/o and w/ inpainting masks.
+Input Image
+Figure 9. Visualization of results w/o and w/ style masks.
+
+
+w/o Style Mask
+
+
+w/StyleMask
+
+# 5. Conclusion & Limitation
+
+This paper proposes UniVerse, a unified robust reconstruction framework that converts inconsistent multi-view im
+
+ages into initial videos and leverages Video Diffusion Models to restore them into consistent images. By decoupling robust reconstruction into two subtasks (i.e. restoration and reconstruction), UniVerse overcomes the limitations of existing approaches that require very dense observations to reconstruct inconsistent images, achieving state-of-the-art performance on both synthetic and real-world datasets. Moreover, we explore UniVerse's ability to control the style of the reconstructed 3D scene by switching the reference image and its potential for reconstructing very sparse inconsistent observations by applying novel view generation models after restoration. We believe our work offers new insights of decoupling robust reconstruction and restoring images using models with 3D priors to the community.
+
+Limitations: UniVerse requires synthesizing videos with inconsistencies as training data to fine-tune the VDM for adaptation to a restoration model. While some inconsistencies, like lighting, may be hard to synthesize, [53] have shown tremendous promise for inconsistency synthesis via generative models.
+
+# 6. Acknowledgment
+
+This work was partially supported by the National Key R&D Program of China (No. 2024YFB2809102), NSFC (No. 62402427, NO. U24B20154), Zhejiang Provincial Natural Science Foundation of China (No. LR25F020003), DeepGlint, Zhejiang University Education Foundation Qizhen Scholar Foundation, and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University.
+
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+ "content": " images, we use 3D reconstruction methods like NeRFs [43] to reconstruct them and return a 3D representation. We show this process in Fig.2 and Alg. 1 in Supp."
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+ "content": " input multiview images into initial videos. These images are essentially captured by cameras at various poses around a single scene. Assuming all "
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+ "type": "text",
+ "content": " lie on a single camera trajectory, continuously sampling new poses (and thus new views) from this trajectory yields a video if the poses are sufficiently dense. This approach hinges on solving two key problems: (I) determining the trajectory and (II) sampling new poses from it. The detailed algorithm is provided in Sec. 7, Alg. 2 and Fig. 10 the Supp."
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+ "content": " into an ordered list. We initialize a double linked list with a randomly chosen pose and iteratively add the remaining poses based on their distances to the current head and tail of the list. The distance metric combines rotation and translation differences, weighted to ensure consistent scaling. Finally, we traverse the whole list to construct an ordered set of poses "
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| PSNR ↑ | SSIM ↑ | LPIPS ↓ | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| ZipNeRF | 11.52 | 0.2327 | 0.6930 | 14.53 | 0.3548 | 0.6297 |
| ZipNeRF w/GLO | 14.53 | 0.4667 | 0.4394 | 18.58 | 0.5297 | 0.4123 |
| Bilarf | 16.06 | 0.4814 | 0.4489 | 17.68 | 0.5062 | 0.4317 |
| WildGaussians | 13.75 | 0.3972 | 0.6430 | 15.45 | 0.4476 | 0.6244 |
| Ours | 18.09 | 0.5789 | 0.3015 | 20.12 | 0.5926 | 0.2979 |
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| ZipNeRF w/GLO | 16.14 | 0.5668 | 0.3095 | 20.67 | 0.5907 | 0.3125 |
| Bilarf | 15.46 | 0.5459 | 0.3323 | 18.84 | 0.6055 | 0.3169 |
| WildGaussians | 15.05 | 0.4246 | 0.5046 | 17.39 | 0.5747 | 0.4493 |
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| (c) (w/ zero frames) | X | ✓ | 18.25 | 0.6067 |
| (d) (ours) | ✓ | ✓ | 20.71 | 0.7708 |
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+ "text": "Unified Adversarial Augmentation for Improving Palmprint Recognition",
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+ "text": "Jianlong Jin $^{1*}$ , Chenglong Zhao $^{2*}$ , Ruixin Zhang $^{2}$ , Sheng Shang $^{1}$ , Yang Zhao $^{1}$ ,",
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+ "text": "1 Hefei University of Technology, 2 Tencent YouTu Lab, 3 Tencent WeChat Pay Lab33",
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+ "Figure 1. Illustrations of challenging cases presented in palmprint datasets and the proposed method. (a) Failed genuine sample pairs selected from the tested public palmprint datasets. We identify the primary issues as geometric distortions (indicated by blue boxes) and textural degradations (indicated by orange boxes). Images with geometric distortions often exhibit clear palmar creases but are challenging to match with those that have normal patterns. Images with textural degradations are difficult to recognize due to the loss of identity characteristics or the presence of additional noise. (b) Qualitative comparison of our method with other current data augmentation methods."
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+ "table_body": " | Training | Identity Consistency | Distribution Consistency | Augmentation |
| Random Augmentation | random preprocessing | X | X | spatial transformation & color shifting |
| Automatic Augmentation | search-based training | X | X | spatial transformation & color shifting |
| Adversarial Examples | adversarial training | X | X | pixel-based perturbations |
| Proposed UAA | adversarial training | ✓ | ✓ | both geometric and textural augmentations |
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+ "text": "Current palmprint recognition models achieve strong performance on constrained datasets, yet exhibit significant limitations in handling challenging palmprint samples with geometric distortions and textural degradations. Data augmentation is widely adopted to improve model generalization. However, existing augmentation methods struggle to generate palmprint-specific variations while preserving identity consistency, leading to suboptimal performance. To address these problems, we propose a Unified Adversarial Augmentation framework (UAA). It first utilizes an adversarial training paradigm for palmprint recognition, optimizing for challenging augmented samples by incorporating the feedback from the recognition network. We enhance palmprint images with both geometric and textual variations. Specifically, it adopts a spatial transformation module and a new identity-preserving module, which synthesizes palmprints with diverse textural variations while maintaining consistent identity. For more effective adversarial augmentation, a dynamic sampling strategy is proposed. Extensive experiments demonstrate the superior",
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+ "text": "1. Introduction",
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+ "text": "Palmprint recognition has garnered widespread attention from academia and industry due to its advantages in convenience, privacy, and security [10]. Compared to fingerprint recognition [55], contactless palmprint recognition offers increased convenience. In contrast to facial recognition [52], palmprint recognition provides better privacy and security, as collecting palmprint data without consent is more difficult. These benefits have led to the rapid development of palmprint-based e-payment [14].",
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+ "text": "Recently, some deep learning-based recognition methods [7, 56] have been proposed and achieved notable success on constrained public palmprint datasets [51, 61, 63]. However, when faced with more complex and challenging datasets [2, 48, 66], they suffer from poor recognition performance. This discrepancy motivates us to investigate the challenging cases in these datasets",
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+ "text": "We have summarized two primary factors that undermine recognition accuracy: geometric distortions and textural degradations, as illustrated in Figure 1. Geometric dis",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "* Equal contribution. † Corresponding authors.",
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+ "text": "This work was done during an internship at Tencent YouTu Lab. Code is available at https://github.com/Umuer/UAA.",
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+ "text": "tortions refer to the deviations in the geometrical structure of palmprints from normal ones. These deviations primarily encompass positional shifts, size variations, and angular alterations. Since palmar creases, a critical identity feature, rely on spatial distribution, even minor geometric distortions can degrade matching accuracy. Textural degradations refer to the deterioration of image quality in palmprint samples, primarily caused by factors such as overexposure, blurriness, shadows, and skin wrinkles. These factors introduce additional distortions and noise into the images, obscuring critical details required for reliable recognition.",
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+ "text": "In order to make the recognition model more robust to these hard samples, a conventional approach employs random data augmentation, including geometric transformations and color enhancement [6]. However, although it is convenient for introducing variability in the training data, it suffers from two limitations: 1) insufficient diversity. Augmentation strategies that rely on common image manipulations, such as blurring or color shifting, fail to simulate the rich and diverse variations present in real-world scenarios. 2) identity disruption. These manipulations require careful manual tuning to avoid disrupting the consistency of palmprint identity features. Consequently, these augmentations provide only a limited improvement in recognizing difficult samples, but may also degrade the recognition accuracy on high-quality samples [29]. Collecting large-scale palmprint datasets with diverse variations is another approach, yet this is costly and raises privacy concerns.",
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+ "text": "To address these problems, we propose a unified adversarial augmentation framework, termed UAA, to generate challenging samples that simultaneously exhibit geometric changes and textural variations. To augment samples with diverse variations, we adopt a differentiable spatial transformation module and an identity-preserving generation module. The spatial transformation module introduces geometric variations to the input samples. Meanwhile, the generation module employs a GAN-based neural network, enhancing palmprints with rich textural attributes while maintaining consistent identity. In contrast, existing automatic augmentation methods, such as AutoAugment [64] and RandAugment [6], utilize a series of common image manipulations. However, these methods provide limited augmentation diversity, which constrains their effectiveness.",
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+ "text": "Augmentation with randomly sampled parameters may struggle to generate images that are challenging to the recognition model. Therefore, we adopt an adversarial training paradigm, which enhances samples by incorporating feedback signals from the recognition network. Our architecture adopts a decoupled design: the spatial transformer and generation module serve as parametric augmentation operators, guided by a learnable control vector that regulates their behavior. During the augmentation process, the control vector is optimized to generate more challeng-",
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+ "text": "ing samples. Some adversarial example methods, like AdvProp [54], apply augmentation by perturbing the entire image, which can distort the original image distribution, thereby limiting the recognition model's generalization in open-set scenarios. Unlike those methods, our method takes input images as identity conditions and pairs them with the optimized control vectors to generate augmented samples with distributional consistency and more diversity.",
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+ "To achieve reliable palmprint recognition on challenging datasets, we propose the unified adversarial augmentation framework, which augments samples with both geometric changes and textural variations. An adversarial training paradigm is first adopted in palmprint recognition, optimizing the augmentation for more challenging samples.",
+ "We introduce a novel identity-preserving palmprint generation network to synthesize palmprint images with consistent identity and diverse textures. Additionally, a momentum-based dynamic sampling strategy is proposed to improve the augmentation process.",
+ "$\\diamond$ Experimental results demonstrate that our proposed method significantly improves the accuracy of palmprint recognition on both challenging and constrained datasets, verifying its effectiveness and superiority."
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+ "text": "Traditional palmprint recognition methods, which encompass local and global feature extraction techniques, have been extensively explored. Local-based methods [9, 15, 23, 32, 39, 51, 69] manually design effective local features from palmprints to enhance recognition. Global-based methods [11, 20, 38, 47, 53] extract low-dimensional features from the entire image to differentiate between various palmprints. However, these methods suffer from poor generalization due to their reliance on hand-crafted features.",
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+ "text": "In palmprint generation [27, 40], RPG-Palm [50] introduces a GAN-based generative model to produce realistic pseudopalprint images. Subsequently, PCE-Palm [26] proposes a two-stage generative model, further enhancing the quality of the generated results. However, they do not consider the generation of challenging samples. Moreover, their primary objective is to generate synthetic data for pre-training recognition models, which is orthogonal to our work of augmenting samples to enhance robustness. Additionally, these methods adopt Bezier creases [67] as identity conditions, synthesizing fake palmprint images with corresponding creases. Unlike prior works, our generation module leverages spatial hierarchical features extracted from real palmprints as identity conditions, which is more suitable for style transfer while preserving identity consistency.",
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+ "type": "text",
+ "text": "2.3. Data Augmentation",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "Automated data augmentation [1, 4-6, 17, 33, 36, 42, 64] has emerged as a promising approach to enhancing the generalization of deep learning models. These methods systematically learn effective augmentation strategies by optimizing the selection, combination, and parameters of various augmentation operations to maximize the model's performance. For instance, AutoAugment [5] employs a reinforcement learning framework to search for optimal augmentation policies, while RandAugment [6] simplifies the search space by reducing it to a combination of magnitude and operation count. However, these methods often rely on a series of common image operations that fail to capture the complex and diverse variations present in real-world palmprint data. They are primarily designed for general classification problems, such as those on ImageNet, and do not adequately address the specific challenges of biometric data, particularly the need for identity consistency.",
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+ "text": "Mixup-based methods [18, 21, 59, 62], which create augmented samples by interpolating between pairs of images and their labels, have gained popularity in recent years. However, palmprints from different individuals have distinct identity features, and mixing two different palmprints would result in a new identity that does not correspond to either of the original individuals. Therefore, applying mixup-based methods to palmprint recognition is not suitable.",
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+ "text": "In facial recognition, techniques such as augmenting datasets with printed glasses [49], hats [31], or adversarial makeup [58] have demonstrated increased robustness. CFSM [37] has utilized GANs for synthesizing adversarial samples, and ARoFace [46] employs spatial transformations to enhance recognition under low-quality conditions. However, these facial-specific methods are less effective when applied to palmprint recognition. Our work first proposes an adversarial augmentation method for improving palmprint recognition.",
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+ "type": "text",
+ "text": "3. Methods",
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+ {
+ "type": "text",
+ "text": "3.1. Overall Framework",
+ "text_level": 1,
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+ "text": "Random data augmentation is widely adopted to improve the generalization of palmprint recognition models. However, these image manipulations make it hard to simulate diverse variations present in palmprint images. To address this limitation, our method introduces a unified adversarial augmentation framework to improve the model's ability to recognize challenging palmprint samples. The overall framework of our proposed method is depicted in Figure 2.",
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+ "type": "text",
+ "text": "The training process encompasses both an adversarial augmentation stage and a recognition stage. During the adversarial augmentation stage, the input image $x$ , paired with control vector $\\mathbf{z}$ , is fed into a unified augmentation module $A$ . This module generates palmprints that maintain consistent identity but exhibit geometric changes and different textural styles. These generated palmprints are then input into the recognition model to compute the classification loss $L$ . The objective of this stage is to produce palmprint samples that are more challenging for the recognition network. Therefore, we maximize the classification loss and update the control vector $\\mathbf{z}$ by backpropagation, while keeping the parameters of the recognition network unchanged.",
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+ "text": "During the recognition stage, the refined vector $\\mathbf{z}^*$ from the adversarial stage is utilized, along with the input images, to pass through the augmentation module $A$ and obtain the augmented samples. The recognition network then processes these augmented images alongside the non-augmented ones, updating its parameters by minimizing the classification loss $L$ . The optimization is formulated as",
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+ "type": "equation",
+ "text": "\n$$\n\\underset {\\theta} {\\operatorname {a r g m i n}} \\left[ L \\left(F _ {\\theta} (x), y\\right) + \\underset {\\mathbf {z}} {\\operatorname {a r g m a x}} L \\left(F _ {\\theta} \\left(A (x, \\mathbf {z})\\right), y\\right) \\right], \\tag {1}\n$$\n",
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+ "type": "text",
+ "text": "where $F_{\\theta}$ denotes the recognition network, and $(x,y)$ represents image-label pairs from the training dataset.",
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+ "type": "text",
+ "text": "3.2. Unified Adversarial Augmentation",
+ "text_level": 1,
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+ "type": "text",
+ "text": "The proposed adversarial augmentation framework comprises augmentation modules, an adversarial augmentation process, and a dynamic sampling strategy. The augmentation modules utilize a differentiable spatial transformer and a pre-trained generative neural network. These modules take palmprint images as identity conditions and learnable control vectors to govern the output, ensuring that the generated images exhibit the desired geometric and textural variations, while maintaining consistency identity. The adversarial augmentation process is described below.",
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+ "type": "text",
+ "text": "During the adversarial augmentation stage, the control vectors are updated to generate challenging samples. This update process is guided by the feedback from the recognition model, ensuring that the augmentations are aligned",
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+ "type": "page_number",
+ "text": "14143",
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+ "type": "image",
+ "img_path": "images/512a100799d0ad7fc69c60e6c6f7efc89c023dfa6cc161127255803793650df6.jpg",
+ "image_caption": [
+ "(a) Overall Framework"
+ ],
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+ },
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+ "img_path": "images/45f7e290a812ebe5df58e5e7eee3661b376f2a90be17215a4a56d5775a0f0fb0.jpg",
+ "image_caption": [
+ "(b) Unified Augmentation Module"
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+ "img_path": "images/93babd8621f6e5e1e24ddff02583d7b688f5d69c367ee9aadbad7bce22ac756a.jpg",
+ "image_caption": [
+ "(c) Adversarial Training Process",
+ "Figure 2. Overall framework of our proposed unified adversarial augmentation method. (a) During the end-to-end training, palmprint images are first extracted from the dataset and then go through the unified adversarial augmentation, where challenging samples are generated to train the recognition network. (b) Detailed view of the unified augmentation modules. The modules comprise a differentiable spatial transformation for geometric enhancement and a pre-trained palmprint generation network for textural enhancement. The augmentation outputs are entirely controlled by the control vector, which combines the geometric parameters $\\mathbf{t}$ and style code $\\mathbf{s}$ , i.e., $\\mathbf{z} \\coloneqq [\\mathbf{t},\\mathbf{s}]$ . (c) Detailed flow of the adversarial training, which consists of an aversarial augmentation stage (Up) and a recognition stage (Down). During the adversarial augmentation stage, We augment input training samples, and optimize the control vector $\\mathbf{z}$ by maximizing the classification loss through backpropagation. During the recognition stage, the augmentation module uses the updated $\\mathbf{z}^*$ to generate challenging samples, and the recognition network then updates its parameters by minimizing the classification loss. ( $F_{\\theta}^{*}$ indicates frozen weights)"
+ ],
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+ {
+ "type": "text",
+ "text": "with the model's current performance and are continuously refined to generate increasingly challenging samples.",
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+ },
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+ "type": "text",
+ "text": "Specifically, the augmentation module takes palmprint images $x$ and control vectors $\\mathbf{z}$ . Before training the recognition network, an optimization process is applied to update $\\mathbf{z}$ , as delineated below,",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {z} ^ {*} = \\underset {\\mathbf {z}} {\\operatorname {a r g m a x}} L \\left(F _ {\\theta} (A (x, \\mathbf {z})), y\\right), \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "where $y$ denotes input labels, $A$ represents augmentation module, $F_{\\theta}$ denotes recognition network, and $L$ is the classification loss. To efficiently optimize $\\mathbf{z}$ with recognition network feedback, we adopt Projected Gradient Descent (PGD) [41], a gradient-based adversarial attack method [13] known for its effectiveness in generating challenging samples within bounded perturbations. The process is",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathbf {z} ^ {k + 1} \\leftarrow \\Pi_ {\\mathbf {z} + S} \\left(\\mathbf {z} ^ {k} + \\alpha \\operatorname {s g n} \\left(\\nabla_ {\\mathbf {z}} L \\left(F _ {\\theta} \\left(A \\left(x, \\mathbf {z} ^ {k}\\right), y\\right)\\right)\\right)\\right), \\tag {3}\n$$\n",
+ "text_format": "latex",
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+ },
+ {
+ "type": "text",
+ "text": "where $\\alpha$ is the step size, $\\operatorname{sgn}(\\cdot)$ is the sign function, $\\nabla_{\\mathbf{z}}L$ denotes the gradient of the loss $L$ , and $k$ represents optimization iterations. The $\\Pi_{\\mathbf{z} + S}$ is a projection operator, which controls updated content in a set of allowed perturbation $S$ .",
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+ "type": "text",
+ "text": "After that, the recognition network is trained, taking challenging samples augmented with refined $\\mathbf{z}^*$ and normal samples, and updating by backpropagation. The process is",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\theta^ {*} = \\underset {\\theta} {\\operatorname {a r g m i n}} \\left[ L \\left(F _ {\\theta} (x, y)\\right) + L \\left(F _ {\\theta} \\left(A \\left(x, \\mathbf {z} ^ {*}\\right)\\right), y\\right) \\right], \\tag {4}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "where $\\theta$ is the weights of recognition network $F_{\\theta}$",
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+ "page_idx": 3
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+ {
+ "type": "text",
+ "text": "Momentum-Based Dynamic Sampling Existing adversarial augmentation methods [37, 46] initialize the control parameters by randomly sampling from a pre-defined Gaussian distribution, i.e., $\\mathbf{z} \\sim \\mathcal{N}(\\boldsymbol{\\mu}, \\boldsymbol{\\Sigma})$ , where $\\boldsymbol{\\mu}$ , $\\boldsymbol{\\Sigma}$ are mean vector and covariance matrix respectively. However, this approach inefficiently explores the augmentation space and generates suboptimal samples. To address this, we propose a momentum-based dynamic sampling strategy that adaptively adjusts the initialization range, focusing on regions proven challenging in previous iterations. Specifically, for the $t$ -th training iteration, the control vector $\\mathbf{z}$ is sampled as,",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathbf {z} _ {t} ^ {0} \\sim \\mathcal {N} \\left(\\beta \\cdot \\mathbf {z} _ {t - 1} ^ {*} + (1 - \\beta) \\cdot \\mu , \\Sigma\\right), \\tag {5}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where $\\beta \\in (0,1)$ is a momentum coefficient, and $\\mathbf{z}^{*}_{t - 1}$ represents the optimized control vector from the previous training iteration. This strategy dynamically shifts the sampling distribution toward regions that previously yielded challenging samples, enabling efficient exploration of the augmentation parameter space.",
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+ {
+ "type": "text",
+ "text": "3.3. Differentiable Spatial Transformer",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 3
+ },
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+ "type": "text",
+ "text": "The differentiable spatial transformation was first introduced in [22]. We briefly outline its implementation below. The spatial transformation involves translation, rotation, and scaling, accepting a parameter $\\mathbf{t} = [t_x,t_y,t_\\theta ,t_s]$",
+ "bbox": [
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+ {
+ "type": "page_number",
+ "text": "14144",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "image",
+ "img_path": "images/a103a4cb9e6512355f4445c682b46ff06abd430fac15d26010bcade22f1cd3fa.jpg",
+ "image_caption": [
+ "Figure 3. The framework of our proposed identity-preserving palmprint generation network."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "and computing the affine transformation matrix as follows,",
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\nA _ {t} = \\left[ \\begin{array}{c c c} t _ {s} \\cos t _ {\\theta} & - t _ {s} \\sin t _ {\\theta} & t _ {x} \\\\ t _ {s} \\sin t _ {\\theta} & t _ {s} \\cos t _ {\\theta} & t _ {y} \\\\ 0 & 0 & 1 \\end{array} \\right], \\tag {6}\n$$\n",
+ "text_format": "latex",
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "where $t_s \\in \\mathbb{R}$ denotes the scaling factor, $t_\\theta \\in [-\\pi, \\pi]$ denotes the scaling factor, and $t_x, t_y \\in \\mathbb{R}$ denote horizontal and vertical shifts, respectively. For an input $H \\times W \\times 3$ RGB image, the same affine transformation matrix is applied to all channels. We apply a bilinear sampling kernel to compute the transformed spatial grid. More details are presented in the Appendix.",
+ "bbox": [
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+ },
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+ "type": "text",
+ "text": "To prevent severe degradation of the transformed image during optimization, we impose empirical constraints on the parameter ranges. Specifically, we limit the rotation angle to $|t_{\\theta}| < 0.25$ , the scaling factor to $|t_s - 1| < 0.2$ , and the translation offsets to $|t_x| < 0.2$ and $|t_y| < 0.2$ relative to the image dimensions. These restrictions ensure that the transformation remains within a reasonable deformation space, maintaining the original palmprint identity features.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "3.4. Identity-Preserving Generation Network",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Common random image manipulations, such as blurring and color shifting, not only fail to simulate realistic textural variations but may also compromise the palmprint identity features. To address this, we propose a novel identity-preserving palmprint generation network.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "The training process is depicted in Figure 3. Our generation model utilizes a dual-encoder architecture, where the encoders $E_{s}$ and $E_{id}$ are designed to extract stylistic and spatial identity information from palmprint images, respectively. The extracted features are then fed into a generator network to produce realistic palmprint images. Inspired by the effectiveness of StyleGAN2 [28], we integrate an adaptive instance normalization (AdaIN) module to ensure that the generated palmprint images closely resemble the distribution of real data.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "During the training phase, a palmprint image $x_{1}$ is first input into the style encoder $E_{s}$ , which produces a style code s. The style encoder, which is a commonly used residual network [16], outputs the mean $\\mu_{s}$ and variance $\\sigma_s^2$ of a flattened feature and further constructs the style code through a",
+ "bbox": [
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+ {
+ "type": "table",
+ "img_path": "images/6596d82b17d2181bca0c4d2fe72c9c6f7e97ca841f198ea3ac64af27de8462d7.jpg",
+ "table_caption": [
+ "Table 1. Details of the eight public palmprint datasets."
+ ],
+ "table_footnote": [],
+ "table_body": "| Datasets | #Images | #IDs | Var. | Dev. |
| MPD [66] | 16,000 | 400 | Large | Mobile phone |
| XJTU-UP [48] | 7900 | 200 | Large | Mobile phone |
| BJTU [2] | 2663 | 296 | Large | Mobile phone |
| CASIA [51] | 5502 | 620 | Small | Digital camera |
| PolyU [60] | 7738 | 388 | Small | Scanner |
| TongJi [63] | 12,000 | 600 | Small | Digital camera |
| IITD [34] | 2601 | 460 | Small | Digital camera |
| NTU-CP-v1 [43] | 2390 | 652 | Large | Digital camera |
",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "reparameterization trick [50]. A KL divergence loss $L_{KL}$ enforces the style code distribution to approximate a standard Gaussian. Additionally, a different palmprint image $x_{2}$ is processed by the encoder $E_{id}$ to extract spatial hierarchical identity features $f_{id}$ . The identity encoder is also a residual network [16]. In practice, we use a frozen pre-trained recognition network as the identity encoder to extract identity features.",
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "For the generation network, the style code $\\mathbf{s}$ is first processed with $L2$ normalization, projecting it onto a hypersphere space. It then passes through multiple layers of MLPs and is integrated into the modulated convolution layer [28]. The spatial identity features are injected into the network through a channel concatenation approach, and a dropout operator is applied for regularization.",
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+ "page_idx": 4
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+ {
+ "type": "text",
+ "text": "After the generation of the palmprint image $x'$ , a suite of loss functions is employed to refine the quality and authenticity of the generated output. Firstly, an adversarial loss $L_{GAN}$ is applied to ensure the synthesized palmprints appear realistic and match the real dataset distribution. To ensure stylistic disentanglement, a style loss $L_{1}$ between $x'$ and $x_{1}$ is implemented. Additionally, a pre-trained recognition model is used to calculate a cosine similarity-based loss $L_{ID}$ to maintain identity consistency between $x'$ and $x_{1}$ . Details of these loss functions are presented in the Appendix. The total loss of the training process is expressed as follows:",
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\nL _ {G E N} = \\lambda_ {K L} L _ {K L} + \\lambda_ {G A N} L _ {G A N} + \\lambda_ {1} L _ {1} + \\lambda_ {I D} L _ {I D}, \\tag {7}\n$$\n",
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "where $\\lambda_{KL},\\lambda_{GAN},\\lambda_{1}$ and $\\lambda_{ID}$ are weights. The generated palmprint images are shown in Figure 4.",
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+ "type": "text",
+ "text": "In conclusion, the final control vector of the unified augmentation module is defined as $\\mathbf{z} := [\\mathbf{t}, \\mathbf{s}]$ .",
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+ {
+ "type": "text",
+ "text": "4. Experiments",
+ "text_level": 1,
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "4.1. Datasets",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "In our experiments, we utilize eight publicly available palmprint datasets, with detailed information presented in Table 1. Notably, the MPD [66] dataset shows a rich variety of variations in palm postures, while the XJTU-UP [48] and BJTU [2] datasets exhibit substantial changes in image aspects, such as lighting and quality. We use official palmprint",
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+ {
+ "type": "page_number",
+ "text": "14145",
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+ },
+ {
+ "type": "table",
+ "img_path": "images/246a8299a972d75c5e1dab0cfdcbf7fd560c83dff6890ff8f3ad82a4fe10a95a.jpg",
+ "table_caption": [
+ "Table 2. Comparative performance on challenging datasets under the open-set protocol, with ResNet-50 as the backbone for all methods."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods | Venue | MPD | XJTU-UP | BJTU |
| TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 | TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 | TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 |
| Baseline [7] | - | 0.4677 | 0.4000 | 0.7153 | 0.8126 | 0.6119 | 0.5424 | 0.8846 | 0.9561 | 0.5004 | 0.4727 | 0.7557 | 0.8285 |
| RandAugment [6] | CVPRW-20 | 0.5065 | 0.4493 | 0.7582 | 0.8447 | 0.7319 | 0.6825 | 0.9355 | 0.9820 | 0.5685 | 0.5446 | 0.8614 | 0.9282 |
| TrivialAugment [45] | ICCV-21 | 0.5414 | 0.4660 | 0.7990 | 0.8864 | 0.7972 | 0.7402 | 0.9637 | 0.9901 | 0.6348 | 0.5927 | 0.8824 | 0.9402 |
| AdaAug [3] | ICLR-22 | 0.5980 | 0.5128 | 0.8465 | 0.9182 | 0.8036 | 0.7653 | 0.9645 | 0.9885 | 0.6257 | 0.5872 | 0.8893 | 0.9591 |
| MADAug [19] | ICCV-23 | 0.6042 | 0.5129 | 0.8610 | 0.9276 | 0.8402 | 0.7900 | 0.9723 | 0.9943 | 0.6644 | 0.5507 | 0.9172 | 0.9701 |
| AdvProp [54] | CVPR-20 | 0.4992 | 0.3958 | 0.7545 | 0.8523 | 0.6300 | 0.5565 | 0.9070 | 0.9674 | 0.5217 | 0.5103 | 0.7906 | 0.8734 |
| Fast AdvProp [44] | ICLR-22 | 0.5310 | 0.4521 | 0.7778 | 0.8606 | 0.7068 | 0.6497 | 0.9251 | 0.9775 | 0.5558 | 0.5276 | 0.8016 | 0.8843 |
| CFSM [37] | ECCV-22 | 0.5597 | 0.4887 | 0.7835 | 0.8636 | 0.7892 | 0.7475 | 0.9501 | 0.9843 | 0.6166 | 0.6027 | 0.8604 | 0.9272 |
| ARoFace [46] | ECCV-24 | 0.6367 | 0.5609 | 0.8763 | 0.9396 | 0.7640 | 0.6820 | 0.9642 | 0.9953 | 0.6510 | 0.6268 | 0.8863 | 0.9452 |
| UAA-p | - | 0.7437 | 0.6546 | 0.9308 | 0.9714 | 0.9228 | 0.8903 | 0.9898 | 0.9977 | 0.7953 | 0.7806 | 0.9671 | 0.9870 |
| UAA-s | - | 0.8075 | 0.7289 | 0.9526 | 0.9821 | 0.9332 | 0.8917 | 0.9911 | 0.9984 | 0.8192 | 0.7892 | 0.9701 | 0.9910 |
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+ "image_caption": [
+ "Figure 4. An illustration of palmprint images synthesized by our proposed identity-preserving palmprint generation network. Each row corresponds to a unique palmprint identity, showing that the identity is consistently maintained across different styles. Each column, generated with the same style code, illustrates the network's ability to apply consistent stylistic variations while keeping the identity of each palmprint intact."
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+ "text": "ROIs where available. For others, we employ a detect-then-crop protocol [65] to extract ROIs from hand images.",
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+ "text": "Previous palmprint recognition works [10, 56, 57] often adopt a closed-set protocol, where the training and testing sets share the same identities, and images are divided based on different sessions. In contrast, we adopt an open-set protocol, dividing identities between the training and testing sets in 1:1 ratio without any identity overlap, which is more challenging and better aligns with real-world demands.",
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+ "text": "Prior research [50, 67] shows that training on each individual palmprint dataset with limited samples could easily lead to model overfitting. Thus, we aggregate the training subsets from each dataset to form a combined training set. We train the recognition model using this mixed dataset and evaluate its performance on various testing sets. The IITD",
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+ "text": "[34] and NTU-CP-V1 [43] are used only for training purposes due to their limited number of images.",
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+ "text": "4.2. Evaluation Metrics",
+ "text_level": 1,
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+ "text": "We evaluate the performance of palmprint recognition methods using a combination of verification and identification metrics. For verification, we calculate the matching scores for all pairs of genuine and imposter samples. Then, we maintain the False Acceptance Rate (FAR) at a fixed value, determine the threshold, and further compute the True Acceptance Rate (TAR), denoted as TAR@FAR. For identification, we employ a $1:N$ matching strategy. Specifically, we select the first image of each identity in the test set as the gallery, with the remaining images serving as probes. We calculate both rank1 and rank5 accuracies to evaluate the model's performance comprehensively.",
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+ "text": "4.3. Implementation Details",
+ "text_level": 1,
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+ "text": "Training of the Generation Networks We set the loss weights $\\lambda_{KL} = 0.01$ , $\\lambda_{GAN} = 1.0$ , $\\lambda_{1} = 1.0$ and $\\lambda_{ID} = 5.0$ , respectively. We employ the Adam optimizer [30] with parameters (0.5, 0.99). The initial learning rate is set to $1 \\times 10^{-3}$ , and a linear weight decay is applied. The generative model is trained for 60 epochs on a NVIDIA V100.",
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+ "text": "Training of the Recognition Networks We adopt Arc-Face [7] as baselines, with modified ResNet-50 [16] serving as the backbone. The recognition model is trained on images of resolution $112 \\times 112$ , with a learning rate of 0.1, and a cosine weight decay is applied. We train the networks for 30 epochs with an overall batch size of 256, distributed across 4 V100 GPUs. All comparative methods are trained using the same training dataset and hyperparameters.",
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+ "text": "Configurations of Proposed Method This method takes the following parameters, i.e., steps $K$ and the step size $\\alpha$ of the PGD optimization, the momentum coefficient $\\beta$ , and the augmentation rate $\\gamma$ , which indicates augmentation for $\\gamma$ proportion of a batch of samples. We set $K = 1$ , $\\beta = 0.5$ , and $\\gamma = 0.5$ for geometric augmentation, and $K = 2$ , $\\beta = 0.25$ , and $\\gamma = 0.5$ for textural augmentation. The $\\alpha$ is",
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+ "type": "page_number",
+ "text": "14146",
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+ {
+ "type": "table",
+ "img_path": "images/5393322c08e46ed25c617ce91a974176d679ce1e86cb601f5fdb70b1f804839a.jpg",
+ "table_caption": [
+ "Table 3. Comparative verification performance on constrained datasets. The results are presented in TAR@FAR."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods | TongJi | PolyU | CASIA |
| 1e-5 | 1e-6 | 1e-5 | 1e-6 | 1e-5 | 1e-6 |
| Baseline [7] | 0.9527 | 0.9288 | 0.9641 | 0.9449 | 0.8753 | 0.8515 |
| RandAugment [6] | 0.9743 | 0.9622 | 0.9603 | 0.9441 | 0.9359 | 0.9133 |
| TrivialAugment [45] | 0.9760 | 0.9629 | 0.9693 | 0.9424 | 0.9476 | 0.9279 |
| AdaAug [3] | 0.9764 | 0.9655 | 0.9758 | 0.9660 | 0.9579 | 0.9476 |
| MADAug [19] | 0.9775 | 0.9651 | 0.9785 | 0.9643 | 0.9524 | 0.9268 |
| AdvProp [54] | 0.9578 | 0.9384 | 0.9670 | 0.9535 | 0.8779 | 0.8540 |
| Fast AdvProp [44] | 0.9592 | 0.9408 | 0.9682 | 0.9529 | 0.8796 | 0.8567 |
| CFSM [37] | 0.9549 | 0.9297 | 0.9714 | 0.9601 | 0.9081 | 0.8937 |
| ARoFace[46] | 0.9730 | 0.9423 | 0.9552 | 0.9329 | 0.9552 | 0.9383 |
| UAA-p | 0.9867 | 0.9740 | 0.9858 | 0.9768 | 0.9818 | 0.9747 |
| UAA-s | 0.9864 | 0.9778 | 0.9731 | 0.9585 | 0.9841 | 0.9766 |
",
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+ {
+ "type": "text",
+ "text": "sampled from $\\mathcal{N}(0.1, 0.001)$ .",
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+ },
+ {
+ "type": "text",
+ "text": "Comparison Methods We choose four automatic augmentation methods, i.e., RandAugment [6], TrivialAugment [45], AdaAug [3], and MADAug [19], two adversarial examples-based methods, i.e., AdvProp [54] and Fast AdvProp [44], and two facial augmentation methods, i.e., CFSM [37] and ARoFace [46] for comparison. These automatic augmentation methods adopt the augmentation space consisting of geometric transformations (i.e., ShearX/Y, TranslateX/Y, Rotate) and color adjusting (i.e., AutoContrast, Invert, Equalize, Solarize, Posterize, Color, Contrast, Brightness, Sharpness, Cutout). Note that these methods are originally designed for general image recognition or facial verification tasks, rather than specifically for palmprint recognition scenarios. We apply them to palmprint recognition models training and try to maintain their parameter configurations proposed in their respective original works, while keeping consistent with the baseline training protocol, like learning rate, batch size, etc.",
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+ {
+ "type": "text",
+ "text": "4.4. Experimental Results",
+ "text_level": 1,
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+ "text": "Performance on Challenging Datasets We choose MPD [66], XJTU-UP [48], and BJTU [2] as challenging datasets and evaluate the performance of different methods on them. Our method is tested in two configurations: 'UAA-p', where the spatial transformation and identity-preserving generation modules are applied in parallel, and 'UAA-s', where these modules are applied sequentially, with geometric augmentation followed by textural augmentation. Table 2 indicates that our method not only shows a substantial improvement over the baseline, but also outperforms other augmentation methods. We provide results with more baselines and more metrics in the Appendix.",
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+ "text": "Performance on Constrained Datasets Compared to those challenging datasets, TongJi [63], PolyU [60], and CASIA [51] are more constrained and exhibit fewer variations. We also assess the performance of different methods on them. As evidenced in Table 3, our method achieves notable performance improvements on these simple datasets as well. These results demonstrate that our method im",
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+ "img_path": "images/3793dacc6fa8bf331435342e0ddf6b75b1ae3f82f98180292c41b2a4da2a36cd.jpg",
+ "table_caption": [
+ "Table 4. Ablation of different components in our proposed method. 'T', 'G', and 'M' denote the spatial transformation module, the palmprint generative network, and the momentum-based sampling, respectively."
+ ],
+ "table_footnote": [],
+ "table_body": "| T | G | M | MPD | XJTU-UP | BJTU |
| 1e-5 | 1e-6 | 1e-5 | 1e-6 | 1e-5 | 1e-6 |
| ✘ | ✘ | ✘ | 0.4677 | 0.4000 | 0.6119 | 0.5424 | 0.5004 | 0.4727 |
| ✓ | ✘ | ✘ | 0.6266 | 0.5318 | 0.7662 | 0.6894 | 0.6657 | 0.6159 |
| ✘ | ✓ | ✘ | 0.5514 | 0.4821 | 0.8118 | 0.7682 | 0.6182 | 0.5590 |
| ✓ | ✓ | ✘ | 0.7557 | 0.6828 | 0.9205 | 0.8837 | 0.7860 | 0.7052 |
| ✓ | ✓ | ✓ | 0.8075 | 0.7289 | 0.9332 | 0.8917 | 0.8192 | 0.7892 |
",
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+ },
+ {
+ "type": "text",
+ "text": "proves robustness on challenging datasets while maintaining high accuracy on constrained datasets.",
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+ {
+ "type": "text",
+ "text": "4.5. Ablation Study",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "Ablation of Different Components The primary constituents of our proposed augmentation framework are the spatial transformation module for geometric augmentation, the identity-preserving palmprint generation network for textural augmentation, and momentum-based dynamic sampling. We denote these three components as 'T', 'G', and 'M', respectively. Experimental results are presented in Table 4. Both geometric and textural augmentation contribute significantly to the recognition of challenging samples. Additionally, the momentum-based dynamic sampling further improves recognition models by introducing an adaptive optimization range.",
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+ {
+ "type": "text",
+ "text": "Visualization of Augmented Samples The proposed method enhances palmprint samples with both geometric changes and textural variations. It utilizes the feedback from the recognition network to optimize the augmentations. We provide visual results of the original and augmented samples, as shown in Figure 5. The visualizations demonstrate that the augmented samples exhibit a range of geometric changes and textural variations. These challenging samples significantly improve the discriminative and generalization ability of recognition models. Table 4 shows the effects of geometric and textural augmentations.",
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+ "type": "text",
+ "text": "Effect of Momentum-Based Dynamic Sampling The proposed sampling method introduces a dynamic sampling space that adaptively adjusts during the training process. It leverages the momentum term to iteratively refine the sampling space, allowing for a more efficient exploration of the parameter space and the generation of increasingly challenging samples. We record the initial control vector $\\mathbf{z}^0$ from each iteration during the training process and plot the statistical results in Figure 6. The figure shows how the sampling space evolves towards challenging regions, correlating with the performance gains in Table 4.",
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+ "type": "text",
+ "text": "4.6. Discussion",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "Identity Consistency To enhance the recognition model, our method generates challenging samples while ensuring",
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+ {
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+ "text": "14147",
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+ {
+ "type": "image",
+ "img_path": "images/30d29c87d85ac320108c8679ef5dedd90112819f0dd81922c02fb1eca4da104b.jpg",
+ "image_caption": [
+ "Figure 5. Visualization of original and adversarial augmented palmprint samples. Compared to original palmprints, augmented images display both geometric changes and textural variations."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ ],
+ "page_idx": 7
+ },
+ {
+ "type": "image",
+ "img_path": "images/d2adf9f098b7ce8c0c571134a60654d6cdeb03a133fc4ccc9716f170d95e7db0.jpg",
+ "image_caption": [
+ "Figure 6. Evolution of the dynamic sampling space over training iterations. The boxplot shows the distribution of the initial control vectors $[t_s, t_\\theta, t_x, t_y]$ for every 100 iterations. We add a vector sampled from a fixed distribution for comparison."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "identity consistency. We address potential concerns about excessive degradation or identity distortion through two key measures. The first is limiting the spatial transformer's scope to prevent extreme deformations. The second is employing a low-dimensional (16-D) L2-normalized style code and spatial hierarchical identity features in the generation module, which stabilize generation and preserve discriminative identity information. A quantitative evaluation of identity consistency is provided in the Appendix.",
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "Relationships with Palmprint Generation Methods Recently, some palmprint generation methods, e.g., BezierPalm [67], have been proposed, which mainly focus on synthesizing fake palmprint datasets to pre-train a recognition model, further improving recognition performance. However, our proposed method, which augments palmprint images during the training process of the recognition network, is complementary to them. We include experiments in the Appendix to demonstrate that, by combining these methods, the proposed UAA achieves better performance.",
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "Limitations Our method enhances palmprint samples with both geometric and textural variations. Since palmprints are typically planar, we adopt a global transformer",
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "to simulate geometric changes. However, this may fail to model local non-planar deformations (e.g., palm bending). We think that further augmenting palmprints with 3D hand models is an interesting direction.",
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "5. Conclusion",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "In this paper, we have summarized geometric distortions and textural degradations as the primary challenges in recognizing difficult palmprint samples. To tackle these problems, we adopt an adversarial training paradigm and a unified augmentation module. It is the first systematic approach to generate palmprint samples with both geometric changes and textural variations to enhance palmprint recognition. Furthermore, a momentum-based dynamic sampling strategy is proposed to improve the augmentation for challenging samples. We conduct extensive experiments on both normal and challenging datasets to validate the effectiveness and superiority of our approach.",
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+ },
+ {
+ "type": "text",
+ "text": "Acknowledgments This work is partly supported by the grants of the National Natural Science Foundation of China under Nos. 62476077, 62076086, and 62272142.",
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+ "text": "14148",
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+ {
+ "type": "text",
+ "text": "References",
+ "text_level": 1,
+ "bbox": [
+ 91,
+ 89,
+ 187,
+ 104
+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "list",
+ "sub_type": "ref_text",
+ "list_items": [
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| Random Augmentation | random preprocessing | X | X | spatial transformation & color shifting |
| Automatic Augmentation | search-based training | X | X | spatial transformation & color shifting |
| Adversarial Examples | adversarial training | X | X | pixel-based perturbations |
| Proposed UAA | adversarial training | ✓ | ✓ | both geometric and textural augmentations |
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+ "content": "Palmprint recognition has garnered widespread attention from academia and industry due to its advantages in convenience, privacy, and security [10]. Compared to fingerprint recognition [55], contactless palmprint recognition offers increased convenience. In contrast to facial recognition [52], palmprint recognition provides better privacy and security, as collecting palmprint data without consent is more difficult. These benefits have led to the rapid development of palmprint-based e-payment [14]."
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+ "content": "* Equal contribution. † Corresponding authors."
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+ "content": "tortions refer to the deviations in the geometrical structure of palmprints from normal ones. These deviations primarily encompass positional shifts, size variations, and angular alterations. Since palmar creases, a critical identity feature, rely on spatial distribution, even minor geometric distortions can degrade matching accuracy. Textural degradations refer to the deterioration of image quality in palmprint samples, primarily caused by factors such as overexposure, blurriness, shadows, and skin wrinkles. These factors introduce additional distortions and noise into the images, obscuring critical details required for reliable recognition."
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+ "content": "In order to make the recognition model more robust to these hard samples, a conventional approach employs random data augmentation, including geometric transformations and color enhancement [6]. However, although it is convenient for introducing variability in the training data, it suffers from two limitations: 1) insufficient diversity. Augmentation strategies that rely on common image manipulations, such as blurring or color shifting, fail to simulate the rich and diverse variations present in real-world scenarios. 2) identity disruption. These manipulations require careful manual tuning to avoid disrupting the consistency of palmprint identity features. Consequently, these augmentations provide only a limited improvement in recognizing difficult samples, but may also degrade the recognition accuracy on high-quality samples [29]. Collecting large-scale palmprint datasets with diverse variations is another approach, yet this is costly and raises privacy concerns."
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+ "content": "Augmentation with randomly sampled parameters may struggle to generate images that are challenging to the recognition model. Therefore, we adopt an adversarial training paradigm, which enhances samples by incorporating feedback signals from the recognition network. Our architecture adopts a decoupled design: the spatial transformer and generation module serve as parametric augmentation operators, guided by a learnable control vector that regulates their behavior. During the augmentation process, the control vector is optimized to generate more challeng-"
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+ "content": "To achieve reliable palmprint recognition on challenging datasets, we propose the unified adversarial augmentation framework, which augments samples with both geometric changes and textural variations. An adversarial training paradigm is first adopted in palmprint recognition, optimizing the augmentation for more challenging samples."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.508,
+ 0.444,
+ 0.905,
+ 0.519
+ ],
+ "angle": 0,
+ "content": "We introduce a novel identity-preserving palmprint generation network to synthesize palmprint images with consistent identity and diverse textures. Additionally, a momentum-based dynamic sampling strategy is proposed to improve the augmentation process."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.508,
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+ "angle": 0,
+ "content": "\\(\\diamond\\) Experimental results demonstrate that our proposed method significantly improves the accuracy of palmprint recognition on both challenging and constrained datasets, verifying its effectiveness and superiority."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2. Related Work"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
+ 0.621,
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+ ],
+ "angle": 0,
+ "content": "2.1. Palmprint Recognition Methods"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.643,
+ 0.905,
+ 0.779
+ ],
+ "angle": 0,
+ "content": "Traditional palmprint recognition methods, which encompass local and global feature extraction techniques, have been extensively explored. Local-based methods [9, 15, 23, 32, 39, 51, 69] manually design effective local features from palmprints to enhance recognition. Global-based methods [11, 20, 38, 47, 53] extract low-dimensional features from the entire image to differentiate between various palmprints. However, these methods suffer from poor generalization due to their reliance on hand-crafted features."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.78,
+ 0.905,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Deep learning-based approaches [8, 12, 24, 25, 35, 56, 68] have demonstrated superior recognition performance compared to traditional methods, owing to their ability to automatically extract complex features from data. These methods primarily focus on specifically designed networks, coupled with margin-based loss functions [7, 29]. However, despite their success, these methods have not yet fully addressed the challenge of recognizing difficult samples."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.945,
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+ ],
+ "angle": 0,
+ "content": "14142"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.091,
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+ ],
+ "angle": 0,
+ "content": "2.2. Palmprint Generation Methods"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.113,
+ 0.484,
+ 0.342
+ ],
+ "angle": 0,
+ "content": "In palmprint generation [27, 40], RPG-Palm [50] introduces a GAN-based generative model to produce realistic pseudopalprint images. Subsequently, PCE-Palm [26] proposes a two-stage generative model, further enhancing the quality of the generated results. However, they do not consider the generation of challenging samples. Moreover, their primary objective is to generate synthetic data for pre-training recognition models, which is orthogonal to our work of augmenting samples to enhance robustness. Additionally, these methods adopt Bezier creases [67] as identity conditions, synthesizing fake palmprint images with corresponding creases. Unlike prior works, our generation module leverages spatial hierarchical features extracted from real palmprints as identity conditions, which is more suitable for style transfer while preserving identity consistency."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.35,
+ 0.279,
+ 0.367
+ ],
+ "angle": 0,
+ "content": "2.3. Data Augmentation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.372,
+ 0.483,
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+ ],
+ "angle": 0,
+ "content": "Automated data augmentation [1, 4-6, 17, 33, 36, 42, 64] has emerged as a promising approach to enhancing the generalization of deep learning models. These methods systematically learn effective augmentation strategies by optimizing the selection, combination, and parameters of various augmentation operations to maximize the model's performance. For instance, AutoAugment [5] employs a reinforcement learning framework to search for optimal augmentation policies, while RandAugment [6] simplifies the search space by reducing it to a combination of magnitude and operation count. However, these methods often rely on a series of common image operations that fail to capture the complex and diverse variations present in real-world palmprint data. They are primarily designed for general classification problems, such as those on ImageNet, and do not adequately address the specific challenges of biometric data, particularly the need for identity consistency."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.63,
+ 0.483,
+ 0.75
+ ],
+ "angle": 0,
+ "content": "Mixup-based methods [18, 21, 59, 62], which create augmented samples by interpolating between pairs of images and their labels, have gained popularity in recent years. However, palmprints from different individuals have distinct identity features, and mixing two different palmprints would result in a new identity that does not correspond to either of the original individuals. Therefore, applying mixup-based methods to palmprint recognition is not suitable."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.751,
+ 0.483,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "In facial recognition, techniques such as augmenting datasets with printed glasses [49], hats [31], or adversarial makeup [58] have demonstrated increased robustness. CFSM [37] has utilized GANs for synthesizing adversarial samples, and ARoFace [46] employs spatial transformations to enhance recognition under low-quality conditions. However, these facial-specific methods are less effective when applied to palmprint recognition. Our work first proposes an adversarial augmentation method for improving palmprint recognition."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.613,
+ 0.106
+ ],
+ "angle": 0,
+ "content": "3. Methods"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.116,
+ 0.704,
+ 0.132
+ ],
+ "angle": 0,
+ "content": "3.1. Overall Framework"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.139,
+ 0.905,
+ 0.26
+ ],
+ "angle": 0,
+ "content": "Random data augmentation is widely adopted to improve the generalization of palmprint recognition models. However, these image manipulations make it hard to simulate diverse variations present in palmprint images. To address this limitation, our method introduces a unified adversarial augmentation framework to improve the model's ability to recognize challenging palmprint samples. The overall framework of our proposed method is depicted in Figure 2."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.262,
+ 0.907,
+ 0.457
+ ],
+ "angle": 0,
+ "content": "The training process encompasses both an adversarial augmentation stage and a recognition stage. During the adversarial augmentation stage, the input image \\( x \\), paired with control vector \\( \\mathbf{z} \\), is fed into a unified augmentation module \\( A \\). This module generates palmprints that maintain consistent identity but exhibit geometric changes and different textural styles. These generated palmprints are then input into the recognition model to compute the classification loss \\( L \\). The objective of this stage is to produce palmprint samples that are more challenging for the recognition network. Therefore, we maximize the classification loss and update the control vector \\( \\mathbf{z} \\) by backpropagation, while keeping the parameters of the recognition network unchanged."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.459,
+ 0.906,
+ 0.565
+ ],
+ "angle": 0,
+ "content": "During the recognition stage, the refined vector \\(\\mathbf{z}^*\\) from the adversarial stage is utilized, along with the input images, to pass through the augmentation module \\(A\\) and obtain the augmented samples. The recognition network then processes these augmented images alongside the non-augmented ones, updating its parameters by minimizing the classification loss \\(L\\). The optimization is formulated as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.528,
+ 0.577,
+ 0.907,
+ 0.612
+ ],
+ "angle": 0,
+ "content": "\\[\n\\underset {\\theta} {\\operatorname {a r g m i n}} \\left[ L \\left(F _ {\\theta} (x), y\\right) + \\underset {\\mathbf {z}} {\\operatorname {a r g m a x}} L \\left(F _ {\\theta} \\left(A (x, \\mathbf {z})\\right), y\\right) \\right], \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.623,
+ 0.905,
+ 0.654
+ ],
+ "angle": 0,
+ "content": "where \\(F_{\\theta}\\) denotes the recognition network, and \\((x,y)\\) represents image-label pairs from the training dataset."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.665,
+ 0.816,
+ 0.682
+ ],
+ "angle": 0,
+ "content": "3.2. Unified Adversarial Augmentation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.689,
+ 0.906,
+ 0.84
+ ],
+ "angle": 0,
+ "content": "The proposed adversarial augmentation framework comprises augmentation modules, an adversarial augmentation process, and a dynamic sampling strategy. The augmentation modules utilize a differentiable spatial transformer and a pre-trained generative neural network. These modules take palmprint images as identity conditions and learnable control vectors to govern the output, ensuring that the generated images exhibit the desired geometric and textural variations, while maintaining consistency identity. The adversarial augmentation process is described below."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.84,
+ 0.906,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "During the adversarial augmentation stage, the control vectors are updated to generate challenging samples. This update process is guided by the feedback from the recognition model, ensuring that the augmentations are aligned"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "14143"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.117,
+ 0.088,
+ 0.885,
+ 0.175
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.446,
+ 0.176,
+ 0.553,
+ 0.186
+ ],
+ "angle": 0,
+ "content": "(a) Overall Framework"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.117,
+ 0.187,
+ 0.486,
+ 0.339
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.223,
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+ 0.382,
+ 0.352
+ ],
+ "angle": 0,
+ "content": "(b) Unified Augmentation Module"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.488,
+ 0.187,
+ 0.882,
+ 0.339
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.609,
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+ ],
+ "angle": 0,
+ "content": "(c) Adversarial Training Process"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
+ 0.358,
+ 0.907,
+ 0.485
+ ],
+ "angle": 0,
+ "content": "Figure 2. Overall framework of our proposed unified adversarial augmentation method. (a) During the end-to-end training, palmprint images are first extracted from the dataset and then go through the unified adversarial augmentation, where challenging samples are generated to train the recognition network. (b) Detailed view of the unified augmentation modules. The modules comprise a differentiable spatial transformation for geometric enhancement and a pre-trained palmprint generation network for textural enhancement. The augmentation outputs are entirely controlled by the control vector, which combines the geometric parameters \\(\\mathbf{t}\\) and style code \\(\\mathbf{s}\\), i.e., \\(\\mathbf{z} \\coloneqq [\\mathbf{t},\\mathbf{s}]\\). (c) Detailed flow of the adversarial training, which consists of an aversarial augmentation stage (Up) and a recognition stage (Down). During the adversarial augmentation stage, We augment input training samples, and optimize the control vector \\(\\mathbf{z}\\) by maximizing the classification loss through backpropagation. During the recognition stage, the augmentation module uses the updated \\(\\mathbf{z}^*\\) to generate challenging samples, and the recognition network then updates its parameters by minimizing the classification loss. (\\(F_{\\theta}^{*}\\) indicates frozen weights)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.5,
+ 0.482,
+ 0.529
+ ],
+ "angle": 0,
+ "content": "with the model's current performance and are continuously refined to generate increasingly challenging samples."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.53,
+ 0.484,
+ 0.589
+ ],
+ "angle": 0,
+ "content": "Specifically, the augmentation module takes palmprint images \\( x \\) and control vectors \\( \\mathbf{z} \\). Before training the recognition network, an optimization process is applied to update \\( \\mathbf{z} \\), as delineated below,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.18,
+ 0.598,
+ 0.482,
+ 0.622
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {z} ^ {*} = \\underset {\\mathbf {z}} {\\operatorname {a r g m a x}} L \\left(F _ {\\theta} (A (x, \\mathbf {z})), y\\right), \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.629,
+ 0.484,
+ 0.734
+ ],
+ "angle": 0,
+ "content": "where \\(y\\) denotes input labels, \\(A\\) represents augmentation module, \\(F_{\\theta}\\) denotes recognition network, and \\(L\\) is the classification loss. To efficiently optimize \\(\\mathbf{z}\\) with recognition network feedback, we adopt Projected Gradient Descent (PGD) [41], a gradient-based adversarial attack method [13] known for its effectiveness in generating challenging samples within bounded perturbations. The process is"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.11,
+ 0.741,
+ 0.482,
+ 0.759
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {z} ^ {k + 1} \\leftarrow \\Pi_ {\\mathbf {z} + S} \\left(\\mathbf {z} ^ {k} + \\alpha \\operatorname {s g n} \\left(\\nabla_ {\\mathbf {z}} L \\left(F _ {\\theta} \\left(A \\left(x, \\mathbf {z} ^ {k}\\right), y\\right)\\right)\\right)\\right), \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.766,
+ 0.483,
+ 0.826
+ ],
+ "angle": 0,
+ "content": "where \\(\\alpha\\) is the step size, \\(\\operatorname{sgn}(\\cdot)\\) is the sign function, \\(\\nabla_{\\mathbf{z}}L\\) denotes the gradient of the loss \\(L\\), and \\(k\\) represents optimization iterations. The \\(\\Pi_{\\mathbf{z} + S}\\) is a projection operator, which controls updated content in a set of allowed perturbation \\(S\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.827,
+ 0.484,
+ 0.872
+ ],
+ "angle": 0,
+ "content": "After that, the recognition network is trained, taking challenging samples augmented with refined \\(\\mathbf{z}^*\\) and normal samples, and updating by backpropagation. The process is"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.115,
+ 0.88,
+ 0.483,
+ 0.904
+ ],
+ "angle": 0,
+ "content": "\\[\n\\theta^ {*} = \\underset {\\theta} {\\operatorname {a r g m i n}} \\left[ L \\left(F _ {\\theta} (x, y)\\right) + L \\left(F _ {\\theta} \\left(A \\left(x, \\mathbf {z} ^ {*}\\right)\\right), y\\right) \\right], \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.5,
+ 0.843,
+ 0.514
+ ],
+ "angle": 0,
+ "content": "where \\(\\theta\\) is the weights of recognition network \\(F_{\\theta}\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.515,
+ 0.907,
+ 0.68
+ ],
+ "angle": 0,
+ "content": "Momentum-Based Dynamic Sampling Existing adversarial augmentation methods [37, 46] initialize the control parameters by randomly sampling from a pre-defined Gaussian distribution, i.e., \\(\\mathbf{z} \\sim \\mathcal{N}(\\boldsymbol{\\mu}, \\boldsymbol{\\Sigma})\\), where \\(\\boldsymbol{\\mu}\\), \\(\\boldsymbol{\\Sigma}\\) are mean vector and covariance matrix respectively. However, this approach inefficiently explores the augmentation space and generates suboptimal samples. To address this, we propose a momentum-based dynamic sampling strategy that adaptively adjusts the initialization range, focusing on regions proven challenging in previous iterations. Specifically, for the \\(t\\)-th training iteration, the control vector \\(\\mathbf{z}\\) is sampled as,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.59,
+ 0.695,
+ 0.907,
+ 0.713
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {z} _ {t} ^ {0} \\sim \\mathcal {N} \\left(\\beta \\cdot \\mathbf {z} _ {t - 1} ^ {*} + (1 - \\beta) \\cdot \\mu , \\Sigma\\right), \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.718,
+ 0.906,
+ 0.809
+ ],
+ "angle": 0,
+ "content": "where \\(\\beta \\in (0,1)\\) is a momentum coefficient, and \\(\\mathbf{z}^{*}_{t - 1}\\) represents the optimized control vector from the previous training iteration. This strategy dynamically shifts the sampling distribution toward regions that previously yielded challenging samples, enabling efficient exploration of the augmentation parameter space."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.818,
+ 0.818,
+ 0.835
+ ],
+ "angle": 0,
+ "content": "3.3. Differentiable Spatial Transformer"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.84,
+ 0.906,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "The differentiable spatial transformation was first introduced in [22]. We briefly outline its implementation below. The spatial transformation involves translation, rotation, and scaling, accepting a parameter \\(\\mathbf{t} = [t_x,t_y,t_\\theta ,t_s]\\)"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.945,
+ 0.519,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "14144"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.1,
+ 0.088,
+ 0.473,
+ 0.226
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.227,
+ 0.483,
+ 0.256
+ ],
+ "angle": 0,
+ "content": "Figure 3. The framework of our proposed identity-preserving palmprint generation network."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.268,
+ 0.48,
+ 0.283
+ ],
+ "angle": 0,
+ "content": "and computing the affine transformation matrix as follows,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.174,
+ 0.288,
+ 0.483,
+ 0.338
+ ],
+ "angle": 0,
+ "content": "\\[\nA _ {t} = \\left[ \\begin{array}{c c c} t _ {s} \\cos t _ {\\theta} & - t _ {s} \\sin t _ {\\theta} & t _ {x} \\\\ t _ {s} \\sin t _ {\\theta} & t _ {s} \\cos t _ {\\theta} & t _ {y} \\\\ 0 & 0 & 1 \\end{array} \\right], \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.343,
+ 0.484,
+ 0.448
+ ],
+ "angle": 0,
+ "content": "where \\( t_s \\in \\mathbb{R} \\) denotes the scaling factor, \\( t_\\theta \\in [-\\pi, \\pi] \\) denotes the scaling factor, and \\( t_x, t_y \\in \\mathbb{R} \\) denote horizontal and vertical shifts, respectively. For an input \\( H \\times W \\times 3 \\) RGB image, the same affine transformation matrix is applied to all channels. We apply a bilinear sampling kernel to compute the transformed spatial grid. More details are presented in the Appendix."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.45,
+ 0.484,
+ 0.571
+ ],
+ "angle": 0,
+ "content": "To prevent severe degradation of the transformed image during optimization, we impose empirical constraints on the parameter ranges. Specifically, we limit the rotation angle to \\( |t_{\\theta}| < 0.25 \\), the scaling factor to \\( |t_s - 1| < 0.2 \\), and the translation offsets to \\( |t_x| < 0.2 \\) and \\( |t_y| < 0.2 \\) relative to the image dimensions. These restrictions ensure that the transformation remains within a reasonable deformation space, maintaining the original palmprint identity features."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.577,
+ 0.439,
+ 0.594
+ ],
+ "angle": 0,
+ "content": "3.4. Identity-Preserving Generation Network"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.599,
+ 0.483,
+ 0.674
+ ],
+ "angle": 0,
+ "content": "Common random image manipulations, such as blurring and color shifting, not only fail to simulate realistic textural variations but may also compromise the palmprint identity features. To address this, we propose a novel identity-preserving palmprint generation network."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.675,
+ 0.483,
+ 0.824
+ ],
+ "angle": 0,
+ "content": "The training process is depicted in Figure 3. Our generation model utilizes a dual-encoder architecture, where the encoders \\( E_{s} \\) and \\( E_{id} \\) are designed to extract stylistic and spatial identity information from palmprint images, respectively. The extracted features are then fed into a generator network to produce realistic palmprint images. Inspired by the effectiveness of StyleGAN2 [28], we integrate an adaptive instance normalization (AdaIN) module to ensure that the generated palmprint images closely resemble the distribution of real data."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.826,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "During the training phase, a palmprint image \\( x_{1} \\) is first input into the style encoder \\( E_{s} \\), which produces a style code s. The style encoder, which is a commonly used residual network [16], outputs the mean \\( \\mu_{s} \\) and variance \\( \\sigma_s^2 \\) of a flattened feature and further constructs the style code through a"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.547,
+ 0.09,
+ 0.871,
+ 0.104
+ ],
+ "angle": 0,
+ "content": "Table 1. Details of the eight public palmprint datasets."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.518,
+ 0.105,
+ 0.905,
+ 0.241
+ ],
+ "angle": 0,
+ "content": "| Datasets | #Images | #IDs | Var. | Dev. |
| MPD [66] | 16,000 | 400 | Large | Mobile phone |
| XJTU-UP [48] | 7900 | 200 | Large | Mobile phone |
| BJTU [2] | 2663 | 296 | Large | Mobile phone |
| CASIA [51] | 5502 | 620 | Small | Digital camera |
| PolyU [60] | 7738 | 388 | Small | Scanner |
| TongJi [63] | 12,000 | 600 | Small | Digital camera |
| IITD [34] | 2601 | 460 | Small | Digital camera |
| NTU-CP-v1 [43] | 2390 | 652 | Large | Digital camera |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.253,
+ 0.905,
+ 0.373
+ ],
+ "angle": 0,
+ "content": "reparameterization trick [50]. A KL divergence loss \\( L_{KL} \\) enforces the style code distribution to approximate a standard Gaussian. Additionally, a different palmprint image \\( x_{2} \\) is processed by the encoder \\( E_{id} \\) to extract spatial hierarchical identity features \\( f_{id} \\). The identity encoder is also a residual network [16]. In practice, we use a frozen pre-trained recognition network as the identity encoder to extract identity features."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.373,
+ 0.906,
+ 0.479
+ ],
+ "angle": 0,
+ "content": "For the generation network, the style code \\(\\mathbf{s}\\) is first processed with \\(L2\\) normalization, projecting it onto a hypersphere space. It then passes through multiple layers of MLPs and is integrated into the modulated convolution layer [28]. The spatial identity features are injected into the network through a channel concatenation approach, and a dropout operator is applied for regularization."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "After the generation of the palmprint image \\( x' \\), a suite of loss functions is employed to refine the quality and authenticity of the generated output. Firstly, an adversarial loss \\( L_{GAN} \\) is applied to ensure the synthesized palmprints appear realistic and match the real dataset distribution. To ensure stylistic disentanglement, a style loss \\( L_{1} \\) between \\( x' \\) and \\( x_{1} \\) is implemented. Additionally, a pre-trained recognition model is used to calculate a cosine similarity-based loss \\( L_{ID} \\) to maintain identity consistency between \\( x' \\) and \\( x_{1} \\). Details of these loss functions are presented in the Appendix. The total loss of the training process is expressed as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\nL _ {G E N} = \\lambda_ {K L} L _ {K L} + \\lambda_ {G A N} L _ {G A N} + \\lambda_ {1} L _ {1} + \\lambda_ {I D} L _ {I D}, \\tag {7}\n\\]"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(\\lambda_{KL},\\lambda_{GAN},\\lambda_{1}\\) and \\(\\lambda_{ID}\\) are weights. The generated palmprint images are shown in Figure 4."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In conclusion, the final control vector of the unified augmentation module is defined as \\(\\mathbf{z} := [\\mathbf{t}, \\mathbf{s}]\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "4.1. Datasets"
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "In our experiments, we utilize eight publicly available palmprint datasets, with detailed information presented in Table 1. Notably, the MPD [66] dataset shows a rich variety of variations in palm postures, while the XJTU-UP [48] and BJTU [2] datasets exhibit substantial changes in image aspects, such as lighting and quality. We use official palmprint"
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+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Comparative performance on challenging datasets under the open-set protocol, with ResNet-50 as the backbone for all methods."
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+ {
+ "type": "table",
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+ "content": "| Methods | Venue | MPD | XJTU-UP | BJTU |
| TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 | TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 | TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 |
| Baseline [7] | - | 0.4677 | 0.4000 | 0.7153 | 0.8126 | 0.6119 | 0.5424 | 0.8846 | 0.9561 | 0.5004 | 0.4727 | 0.7557 | 0.8285 |
| RandAugment [6] | CVPRW-20 | 0.5065 | 0.4493 | 0.7582 | 0.8447 | 0.7319 | 0.6825 | 0.9355 | 0.9820 | 0.5685 | 0.5446 | 0.8614 | 0.9282 |
| TrivialAugment [45] | ICCV-21 | 0.5414 | 0.4660 | 0.7990 | 0.8864 | 0.7972 | 0.7402 | 0.9637 | 0.9901 | 0.6348 | 0.5927 | 0.8824 | 0.9402 |
| AdaAug [3] | ICLR-22 | 0.5980 | 0.5128 | 0.8465 | 0.9182 | 0.8036 | 0.7653 | 0.9645 | 0.9885 | 0.6257 | 0.5872 | 0.8893 | 0.9591 |
| MADAug [19] | ICCV-23 | 0.6042 | 0.5129 | 0.8610 | 0.9276 | 0.8402 | 0.7900 | 0.9723 | 0.9943 | 0.6644 | 0.5507 | 0.9172 | 0.9701 |
| AdvProp [54] | CVPR-20 | 0.4992 | 0.3958 | 0.7545 | 0.8523 | 0.6300 | 0.5565 | 0.9070 | 0.9674 | 0.5217 | 0.5103 | 0.7906 | 0.8734 |
| Fast AdvProp [44] | ICLR-22 | 0.5310 | 0.4521 | 0.7778 | 0.8606 | 0.7068 | 0.6497 | 0.9251 | 0.9775 | 0.5558 | 0.5276 | 0.8016 | 0.8843 |
| CFSM [37] | ECCV-22 | 0.5597 | 0.4887 | 0.7835 | 0.8636 | 0.7892 | 0.7475 | 0.9501 | 0.9843 | 0.6166 | 0.6027 | 0.8604 | 0.9272 |
| ARoFace [46] | ECCV-24 | 0.6367 | 0.5609 | 0.8763 | 0.9396 | 0.7640 | 0.6820 | 0.9642 | 0.9953 | 0.6510 | 0.6268 | 0.8863 | 0.9452 |
| UAA-p | - | 0.7437 | 0.6546 | 0.9308 | 0.9714 | 0.9228 | 0.8903 | 0.9898 | 0.9977 | 0.7953 | 0.7806 | 0.9671 | 0.9870 |
| UAA-s | - | 0.8075 | 0.7289 | 0.9526 | 0.9821 | 0.9332 | 0.8917 | 0.9911 | 0.9984 | 0.8192 | 0.7892 | 0.9701 | 0.9910 |
"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. An illustration of palmprint images synthesized by our proposed identity-preserving palmprint generation network. Each row corresponds to a unique palmprint identity, showing that the identity is consistently maintained across different styles. Each column, generated with the same style code, illustrates the network's ability to apply consistent stylistic variations while keeping the identity of each palmprint intact."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "ROIs where available. For others, we employ a detect-then-crop protocol [65] to extract ROIs from hand images."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Previous palmprint recognition works [10, 56, 57] often adopt a closed-set protocol, where the training and testing sets share the same identities, and images are divided based on different sessions. In contrast, we adopt an open-set protocol, dividing identities between the training and testing sets in 1:1 ratio without any identity overlap, which is more challenging and better aligns with real-world demands."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Prior research [50, 67] shows that training on each individual palmprint dataset with limited samples could easily lead to model overfitting. Thus, we aggregate the training subsets from each dataset to form a combined training set. We train the recognition model using this mixed dataset and evaluate its performance on various testing sets. The IITD"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "[34] and NTU-CP-V1 [43] are used only for training purposes due to their limited number of images."
+ },
+ {
+ "type": "title",
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+ "content": "4.2. Evaluation Metrics"
+ },
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+ "angle": 0,
+ "content": "We evaluate the performance of palmprint recognition methods using a combination of verification and identification metrics. For verification, we calculate the matching scores for all pairs of genuine and imposter samples. Then, we maintain the False Acceptance Rate (FAR) at a fixed value, determine the threshold, and further compute the True Acceptance Rate (TAR), denoted as TAR@FAR. For identification, we employ a \\(1:N\\) matching strategy. Specifically, we select the first image of each identity in the test set as the gallery, with the remaining images serving as probes. We calculate both rank1 and rank5 accuracies to evaluate the model's performance comprehensively."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.3. Implementation Details"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Training of the Generation Networks We set the loss weights \\(\\lambda_{KL} = 0.01\\), \\(\\lambda_{GAN} = 1.0\\), \\(\\lambda_{1} = 1.0\\) and \\(\\lambda_{ID} = 5.0\\), respectively. We employ the Adam optimizer [30] with parameters (0.5, 0.99). The initial learning rate is set to \\(1 \\times 10^{-3}\\), and a linear weight decay is applied. The generative model is trained for 60 epochs on a NVIDIA V100."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Training of the Recognition Networks We adopt Arc-Face [7] as baselines, with modified ResNet-50 [16] serving as the backbone. The recognition model is trained on images of resolution \\( 112 \\times 112 \\), with a learning rate of 0.1, and a cosine weight decay is applied. We train the networks for 30 epochs with an overall batch size of 256, distributed across 4 V100 GPUs. All comparative methods are trained using the same training dataset and hyperparameters."
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Configurations of Proposed Method This method takes the following parameters, i.e., steps \\( K \\) and the step size \\( \\alpha \\) of the PGD optimization, the momentum coefficient \\( \\beta \\), and the augmentation rate \\( \\gamma \\), which indicates augmentation for \\( \\gamma \\) proportion of a batch of samples. We set \\( K = 1 \\), \\( \\beta = 0.5 \\), and \\( \\gamma = 0.5 \\) for geometric augmentation, and \\( K = 2 \\), \\( \\beta = 0.25 \\), and \\( \\gamma = 0.5 \\) for textural augmentation. The \\( \\alpha \\) is"
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+ }
+ ],
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Comparative verification performance on constrained datasets. The results are presented in TAR@FAR."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Methods | TongJi | PolyU | CASIA |
| 1e-5 | 1e-6 | 1e-5 | 1e-6 | 1e-5 | 1e-6 |
| Baseline [7] | 0.9527 | 0.9288 | 0.9641 | 0.9449 | 0.8753 | 0.8515 |
| RandAugment [6] | 0.9743 | 0.9622 | 0.9603 | 0.9441 | 0.9359 | 0.9133 |
| TrivialAugment [45] | 0.9760 | 0.9629 | 0.9693 | 0.9424 | 0.9476 | 0.9279 |
| AdaAug [3] | 0.9764 | 0.9655 | 0.9758 | 0.9660 | 0.9579 | 0.9476 |
| MADAug [19] | 0.9775 | 0.9651 | 0.9785 | 0.9643 | 0.9524 | 0.9268 |
| AdvProp [54] | 0.9578 | 0.9384 | 0.9670 | 0.9535 | 0.8779 | 0.8540 |
| Fast AdvProp [44] | 0.9592 | 0.9408 | 0.9682 | 0.9529 | 0.8796 | 0.8567 |
| CFSM [37] | 0.9549 | 0.9297 | 0.9714 | 0.9601 | 0.9081 | 0.8937 |
| ARoFace[46] | 0.9730 | 0.9423 | 0.9552 | 0.9329 | 0.9552 | 0.9383 |
| UAA-p | 0.9867 | 0.9740 | 0.9858 | 0.9768 | 0.9818 | 0.9747 |
| UAA-s | 0.9864 | 0.9778 | 0.9731 | 0.9585 | 0.9841 | 0.9766 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "sampled from \\(\\mathcal{N}(0.1, 0.001)\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Comparison Methods We choose four automatic augmentation methods, i.e., RandAugment [6], TrivialAugment [45], AdaAug [3], and MADAug [19], two adversarial examples-based methods, i.e., AdvProp [54] and Fast AdvProp [44], and two facial augmentation methods, i.e., CFSM [37] and ARoFace [46] for comparison. These automatic augmentation methods adopt the augmentation space consisting of geometric transformations (i.e., ShearX/Y, TranslateX/Y, Rotate) and color adjusting (i.e., AutoContrast, Invert, Equalize, Solarize, Posterize, Color, Contrast, Brightness, Sharpness, Cutout). Note that these methods are originally designed for general image recognition or facial verification tasks, rather than specifically for palmprint recognition scenarios. We apply them to palmprint recognition models training and try to maintain their parameter configurations proposed in their respective original works, while keeping consistent with the baseline training protocol, like learning rate, batch size, etc."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Experimental Results"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Performance on Challenging Datasets We choose MPD [66], XJTU-UP [48], and BJTU [2] as challenging datasets and evaluate the performance of different methods on them. Our method is tested in two configurations: 'UAA-p', where the spatial transformation and identity-preserving generation modules are applied in parallel, and 'UAA-s', where these modules are applied sequentially, with geometric augmentation followed by textural augmentation. Table 2 indicates that our method not only shows a substantial improvement over the baseline, but also outperforms other augmentation methods. We provide results with more baselines and more metrics in the Appendix."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Performance on Constrained Datasets Compared to those challenging datasets, TongJi [63], PolyU [60], and CASIA [51] are more constrained and exhibit fewer variations. We also assess the performance of different methods on them. As evidenced in Table 3, our method achieves notable performance improvements on these simple datasets as well. These results demonstrate that our method im"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.517,
+ 0.09,
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+ 0.145
+ ],
+ "angle": 0,
+ "content": "Table 4. Ablation of different components in our proposed method. 'T', 'G', and 'M' denote the spatial transformation module, the palmprint generative network, and the momentum-based sampling, respectively."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| T | G | M | MPD | XJTU-UP | BJTU |
| 1e-5 | 1e-6 | 1e-5 | 1e-6 | 1e-5 | 1e-6 |
| ✘ | ✘ | ✘ | 0.4677 | 0.4000 | 0.6119 | 0.5424 | 0.5004 | 0.4727 |
| ✓ | ✘ | ✘ | 0.6266 | 0.5318 | 0.7662 | 0.6894 | 0.6657 | 0.6159 |
| ✘ | ✓ | ✘ | 0.5514 | 0.4821 | 0.8118 | 0.7682 | 0.6182 | 0.5590 |
| ✓ | ✓ | ✘ | 0.7557 | 0.6828 | 0.9205 | 0.8837 | 0.7860 | 0.7052 |
| ✓ | ✓ | ✓ | 0.8075 | 0.7289 | 0.9332 | 0.8917 | 0.8192 | 0.7892 |
"
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+ {
+ "type": "text",
+ "bbox": [
+ 0.517,
+ 0.257,
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+ ],
+ "angle": 0,
+ "content": "proves robustness on challenging datasets while maintaining high accuracy on constrained datasets."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.517,
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+ "angle": 0,
+ "content": "4.5. Ablation Study"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Ablation of Different Components The primary constituents of our proposed augmentation framework are the spatial transformation module for geometric augmentation, the identity-preserving palmprint generation network for textural augmentation, and momentum-based dynamic sampling. We denote these three components as 'T', 'G', and 'M', respectively. Experimental results are presented in Table 4. Both geometric and textural augmentation contribute significantly to the recognition of challenging samples. Additionally, the momentum-based dynamic sampling further improves recognition models by introducing an adaptive optimization range."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.517,
+ 0.504,
+ 0.905,
+ 0.669
+ ],
+ "angle": 0,
+ "content": "Visualization of Augmented Samples The proposed method enhances palmprint samples with both geometric changes and textural variations. It utilizes the feedback from the recognition network to optimize the augmentations. We provide visual results of the original and augmented samples, as shown in Figure 5. The visualizations demonstrate that the augmented samples exhibit a range of geometric changes and textural variations. These challenging samples significantly improve the discriminative and generalization ability of recognition models. Table 4 shows the effects of geometric and textural augmentations."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Effect of Momentum-Based Dynamic Sampling The proposed sampling method introduces a dynamic sampling space that adaptively adjusts during the training process. It leverages the momentum term to iteratively refine the sampling space, allowing for a more efficient exploration of the parameter space and the generation of increasingly challenging samples. We record the initial control vector \\(\\mathbf{z}^0\\) from each iteration during the training process and plot the statistical results in Figure 6. The figure shows how the sampling space evolves towards challenging regions, correlating with the performance gains in Table 4."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.863
+ ],
+ "angle": 0,
+ "content": "4.6. Discussion"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.871,
+ 0.905,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Identity Consistency To enhance the recognition model, our method generates challenging samples while ensuring"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "14147"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.114,
+ 0.089,
+ 0.885,
+ 0.296
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.297,
+ 0.908,
+ 0.327
+ ],
+ "angle": 0,
+ "content": "Figure 5. Visualization of original and adversarial augmented palmprint samples. Compared to original palmprints, augmented images display both geometric changes and textural variations."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.118,
+ 0.334,
+ 0.879,
+ 0.512
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.517,
+ 0.908,
+ 0.547
+ ],
+ "angle": 0,
+ "content": "Figure 6. Evolution of the dynamic sampling space over training iterations. The boxplot shows the distribution of the initial control vectors \\([t_s, t_\\theta, t_x, t_y]\\) for every 100 iterations. We add a vector sampled from a fixed distribution for comparison."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.561,
+ 0.483,
+ 0.697
+ ],
+ "angle": 0,
+ "content": "identity consistency. We address potential concerns about excessive degradation or identity distortion through two key measures. The first is limiting the spatial transformer's scope to prevent extreme deformations. The second is employing a low-dimensional (16-D) L2-normalized style code and spatial hierarchical identity features in the generation module, which stabilize generation and preserve discriminative identity information. A quantitative evaluation of identity consistency is provided in the Appendix."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.701,
+ 0.483,
+ 0.853
+ ],
+ "angle": 0,
+ "content": "Relationships with Palmprint Generation Methods Recently, some palmprint generation methods, e.g., BezierPalm [67], have been proposed, which mainly focus on synthesizing fake palmprint datasets to pre-train a recognition model, further improving recognition performance. However, our proposed method, which augments palmprint images during the training process of the recognition network, is complementary to them. We include experiments in the Appendix to demonstrate that, by combining these methods, the proposed UAA achieves better performance."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.856,
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+ 0.903
+ ],
+ "angle": 0,
+ "content": "Limitations Our method enhances palmprint samples with both geometric and textural variations. Since palmprints are typically planar, we adopt a global transformer"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.561,
+ 0.907,
+ 0.622
+ ],
+ "angle": 0,
+ "content": "to simulate geometric changes. However, this may fail to model local non-planar deformations (e.g., palm bending). We think that further augmenting palmprints with 3D hand models is an interesting direction."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.643,
+ 0.634,
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+ ],
+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.511,
+ 0.672,
+ 0.907,
+ 0.853
+ ],
+ "angle": 0,
+ "content": "In this paper, we have summarized geometric distortions and textural degradations as the primary challenges in recognizing difficult palmprint samples. To tackle these problems, we adopt an adversarial training paradigm and a unified augmentation module. It is the first systematic approach to generate palmprint samples with both geometric changes and textural variations to enhance palmprint recognition. Furthermore, a momentum-based dynamic sampling strategy is proposed to improve the augmentation for challenging samples. We conduct extensive experiments on both normal and challenging datasets to validate the effectiveness and superiority of our approach."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.856,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Acknowledgments This work is partly supported by the grants of the National Natural Science Foundation of China under Nos. 62476077, 62076086, and 62272142."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "14148"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "References"
+ },
+ {
+ "type": "ref_text",
+ "bbox": [
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+# Unified Adversarial Augmentation for Improving Palmprint Recognition
+
+Jianlong Jin $^{1*}$ , Chenglong Zhao $^{2*}$ , Ruixin Zhang $^{2}$ , Sheng Shang $^{1}$ , Yang Zhao $^{1}$ ,
+
+Jun Wang $^{3}$ , Jingyun Zhang $^{3}$ , Shouhong Ding $^{2}$ , Wei Jia $^{1\dagger}$ , Yunsheng Wu $^{2\dagger}$
+
+1 Hefei University of Technology, 2 Tencent YouTu Lab, 3 Tencent WeChat Pay Lab33
+
+jianlong@mail.hfut.edu.cn, lornezhao@tencent.com
+
+
+Normal
+
+
+Normal
+Overexposed
+
+
+Normal
+(a)
+
+
+Shadowed
+Figure 1. Illustrations of challenging cases presented in palmprint datasets and the proposed method. (a) Failed genuine sample pairs selected from the tested public palmprint datasets. We identify the primary issues as geometric distortions (indicated by blue boxes) and textural degradations (indicated by orange boxes). Images with geometric distortions often exhibit clear palmar creases but are challenging to match with those that have normal patterns. Images with textural degradations are difficult to recognize due to the loss of identity characteristics or the presence of additional noise. (b) Qualitative comparison of our method with other current data augmentation methods.
+
+ | Training | Identity Consistency | Distribution Consistency | Augmentation |
| Random Augmentation | random preprocessing | X | X | spatial transformation & color shifting |
| Automatic Augmentation | search-based training | X | X | spatial transformation & color shifting |
| Adversarial Examples | adversarial training | X | X | pixel-based perturbations |
| Proposed UAA | adversarial training | ✓ | ✓ | both geometric and textural augmentations |
+
+(b)
+
+# Abstract
+
+Current palmprint recognition models achieve strong performance on constrained datasets, yet exhibit significant limitations in handling challenging palmprint samples with geometric distortions and textural degradations. Data augmentation is widely adopted to improve model generalization. However, existing augmentation methods struggle to generate palmprint-specific variations while preserving identity consistency, leading to suboptimal performance. To address these problems, we propose a Unified Adversarial Augmentation framework (UAA). It first utilizes an adversarial training paradigm for palmprint recognition, optimizing for challenging augmented samples by incorporating the feedback from the recognition network. We enhance palmprint images with both geometric and textual variations. Specifically, it adopts a spatial transformation module and a new identity-preserving module, which synthesizes palmprints with diverse textural variations while maintaining consistent identity. For more effective adversarial augmentation, a dynamic sampling strategy is proposed. Extensive experiments demonstrate the superior
+
+performance of our method on both challenging and constrained palmprint datasets.
+
+# 1. Introduction
+
+Palmprint recognition has garnered widespread attention from academia and industry due to its advantages in convenience, privacy, and security [10]. Compared to fingerprint recognition [55], contactless palmprint recognition offers increased convenience. In contrast to facial recognition [52], palmprint recognition provides better privacy and security, as collecting palmprint data without consent is more difficult. These benefits have led to the rapid development of palmprint-based e-payment [14].
+
+Recently, some deep learning-based recognition methods [7, 56] have been proposed and achieved notable success on constrained public palmprint datasets [51, 61, 63]. However, when faced with more complex and challenging datasets [2, 48, 66], they suffer from poor recognition performance. This discrepancy motivates us to investigate the challenging cases in these datasets
+
+We have summarized two primary factors that undermine recognition accuracy: geometric distortions and textural degradations, as illustrated in Figure 1. Geometric dis
+
+tortions refer to the deviations in the geometrical structure of palmprints from normal ones. These deviations primarily encompass positional shifts, size variations, and angular alterations. Since palmar creases, a critical identity feature, rely on spatial distribution, even minor geometric distortions can degrade matching accuracy. Textural degradations refer to the deterioration of image quality in palmprint samples, primarily caused by factors such as overexposure, blurriness, shadows, and skin wrinkles. These factors introduce additional distortions and noise into the images, obscuring critical details required for reliable recognition.
+
+In order to make the recognition model more robust to these hard samples, a conventional approach employs random data augmentation, including geometric transformations and color enhancement [6]. However, although it is convenient for introducing variability in the training data, it suffers from two limitations: 1) insufficient diversity. Augmentation strategies that rely on common image manipulations, such as blurring or color shifting, fail to simulate the rich and diverse variations present in real-world scenarios. 2) identity disruption. These manipulations require careful manual tuning to avoid disrupting the consistency of palmprint identity features. Consequently, these augmentations provide only a limited improvement in recognizing difficult samples, but may also degrade the recognition accuracy on high-quality samples [29]. Collecting large-scale palmprint datasets with diverse variations is another approach, yet this is costly and raises privacy concerns.
+
+To address these problems, we propose a unified adversarial augmentation framework, termed UAA, to generate challenging samples that simultaneously exhibit geometric changes and textural variations. To augment samples with diverse variations, we adopt a differentiable spatial transformation module and an identity-preserving generation module. The spatial transformation module introduces geometric variations to the input samples. Meanwhile, the generation module employs a GAN-based neural network, enhancing palmprints with rich textural attributes while maintaining consistent identity. In contrast, existing automatic augmentation methods, such as AutoAugment [64] and RandAugment [6], utilize a series of common image manipulations. However, these methods provide limited augmentation diversity, which constrains their effectiveness.
+
+Augmentation with randomly sampled parameters may struggle to generate images that are challenging to the recognition model. Therefore, we adopt an adversarial training paradigm, which enhances samples by incorporating feedback signals from the recognition network. Our architecture adopts a decoupled design: the spatial transformer and generation module serve as parametric augmentation operators, guided by a learnable control vector that regulates their behavior. During the augmentation process, the control vector is optimized to generate more challeng-
+
+ing samples. Some adversarial example methods, like AdvProp [54], apply augmentation by perturbing the entire image, which can distort the original image distribution, thereby limiting the recognition model's generalization in open-set scenarios. Unlike those methods, our method takes input images as identity conditions and pairs them with the optimized control vectors to generate augmented samples with distributional consistency and more diversity.
+
+Furthermore, we propose a momentum-based dynamic sampling strategy to improve control vector optimization. Existing methods [37, 46] initialize adversarial parameters from static Gaussian distributions, which is less efficient and suffers from suboptimal augmentation. By leveraging the momentum of previous updates, our method dynamically adjusts the sampling space, leading to more efficient exploration of the parameter space and the generation of challenging samples. Our key contributions are as follows
+
+To achieve reliable palmprint recognition on challenging datasets, we propose the unified adversarial augmentation framework, which augments samples with both geometric changes and textural variations. An adversarial training paradigm is first adopted in palmprint recognition, optimizing the augmentation for more challenging samples.
+We introduce a novel identity-preserving palmprint generation network to synthesize palmprint images with consistent identity and diverse textures. Additionally, a momentum-based dynamic sampling strategy is proposed to improve the augmentation process.
+$\diamond$ Experimental results demonstrate that our proposed method significantly improves the accuracy of palmprint recognition on both challenging and constrained datasets, verifying its effectiveness and superiority.
+
+# 2. Related Work
+
+# 2.1. Palmprint Recognition Methods
+
+Traditional palmprint recognition methods, which encompass local and global feature extraction techniques, have been extensively explored. Local-based methods [9, 15, 23, 32, 39, 51, 69] manually design effective local features from palmprints to enhance recognition. Global-based methods [11, 20, 38, 47, 53] extract low-dimensional features from the entire image to differentiate between various palmprints. However, these methods suffer from poor generalization due to their reliance on hand-crafted features.
+
+Deep learning-based approaches [8, 12, 24, 25, 35, 56, 68] have demonstrated superior recognition performance compared to traditional methods, owing to their ability to automatically extract complex features from data. These methods primarily focus on specifically designed networks, coupled with margin-based loss functions [7, 29]. However, despite their success, these methods have not yet fully addressed the challenge of recognizing difficult samples.
+
+# 2.2. Palmprint Generation Methods
+
+In palmprint generation [27, 40], RPG-Palm [50] introduces a GAN-based generative model to produce realistic pseudopalprint images. Subsequently, PCE-Palm [26] proposes a two-stage generative model, further enhancing the quality of the generated results. However, they do not consider the generation of challenging samples. Moreover, their primary objective is to generate synthetic data for pre-training recognition models, which is orthogonal to our work of augmenting samples to enhance robustness. Additionally, these methods adopt Bezier creases [67] as identity conditions, synthesizing fake palmprint images with corresponding creases. Unlike prior works, our generation module leverages spatial hierarchical features extracted from real palmprints as identity conditions, which is more suitable for style transfer while preserving identity consistency.
+
+# 2.3. Data Augmentation
+
+Automated data augmentation [1, 4-6, 17, 33, 36, 42, 64] has emerged as a promising approach to enhancing the generalization of deep learning models. These methods systematically learn effective augmentation strategies by optimizing the selection, combination, and parameters of various augmentation operations to maximize the model's performance. For instance, AutoAugment [5] employs a reinforcement learning framework to search for optimal augmentation policies, while RandAugment [6] simplifies the search space by reducing it to a combination of magnitude and operation count. However, these methods often rely on a series of common image operations that fail to capture the complex and diverse variations present in real-world palmprint data. They are primarily designed for general classification problems, such as those on ImageNet, and do not adequately address the specific challenges of biometric data, particularly the need for identity consistency.
+
+Mixup-based methods [18, 21, 59, 62], which create augmented samples by interpolating between pairs of images and their labels, have gained popularity in recent years. However, palmprints from different individuals have distinct identity features, and mixing two different palmprints would result in a new identity that does not correspond to either of the original individuals. Therefore, applying mixup-based methods to palmprint recognition is not suitable.
+
+In facial recognition, techniques such as augmenting datasets with printed glasses [49], hats [31], or adversarial makeup [58] have demonstrated increased robustness. CFSM [37] has utilized GANs for synthesizing adversarial samples, and ARoFace [46] employs spatial transformations to enhance recognition under low-quality conditions. However, these facial-specific methods are less effective when applied to palmprint recognition. Our work first proposes an adversarial augmentation method for improving palmprint recognition.
+
+# 3. Methods
+
+# 3.1. Overall Framework
+
+Random data augmentation is widely adopted to improve the generalization of palmprint recognition models. However, these image manipulations make it hard to simulate diverse variations present in palmprint images. To address this limitation, our method introduces a unified adversarial augmentation framework to improve the model's ability to recognize challenging palmprint samples. The overall framework of our proposed method is depicted in Figure 2.
+
+The training process encompasses both an adversarial augmentation stage and a recognition stage. During the adversarial augmentation stage, the input image $x$ , paired with control vector $\mathbf{z}$ , is fed into a unified augmentation module $A$ . This module generates palmprints that maintain consistent identity but exhibit geometric changes and different textural styles. These generated palmprints are then input into the recognition model to compute the classification loss $L$ . The objective of this stage is to produce palmprint samples that are more challenging for the recognition network. Therefore, we maximize the classification loss and update the control vector $\mathbf{z}$ by backpropagation, while keeping the parameters of the recognition network unchanged.
+
+During the recognition stage, the refined vector $\mathbf{z}^*$ from the adversarial stage is utilized, along with the input images, to pass through the augmentation module $A$ and obtain the augmented samples. The recognition network then processes these augmented images alongside the non-augmented ones, updating its parameters by minimizing the classification loss $L$ . The optimization is formulated as
+
+$$
+\underset {\theta} {\operatorname {a r g m i n}} \left[ L \left(F _ {\theta} (x), y\right) + \underset {\mathbf {z}} {\operatorname {a r g m a x}} L \left(F _ {\theta} \left(A (x, \mathbf {z})\right), y\right) \right], \tag {1}
+$$
+
+where $F_{\theta}$ denotes the recognition network, and $(x,y)$ represents image-label pairs from the training dataset.
+
+# 3.2. Unified Adversarial Augmentation
+
+The proposed adversarial augmentation framework comprises augmentation modules, an adversarial augmentation process, and a dynamic sampling strategy. The augmentation modules utilize a differentiable spatial transformer and a pre-trained generative neural network. These modules take palmprint images as identity conditions and learnable control vectors to govern the output, ensuring that the generated images exhibit the desired geometric and textural variations, while maintaining consistency identity. The adversarial augmentation process is described below.
+
+During the adversarial augmentation stage, the control vectors are updated to generate challenging samples. This update process is guided by the feedback from the recognition model, ensuring that the augmentations are aligned
+
+
+(a) Overall Framework
+
+
+(b) Unified Augmentation Module
+
+
+(c) Adversarial Training Process
+Figure 2. Overall framework of our proposed unified adversarial augmentation method. (a) During the end-to-end training, palmprint images are first extracted from the dataset and then go through the unified adversarial augmentation, where challenging samples are generated to train the recognition network. (b) Detailed view of the unified augmentation modules. The modules comprise a differentiable spatial transformation for geometric enhancement and a pre-trained palmprint generation network for textural enhancement. The augmentation outputs are entirely controlled by the control vector, which combines the geometric parameters $\mathbf{t}$ and style code $\mathbf{s}$ , i.e., $\mathbf{z} \coloneqq [\mathbf{t},\mathbf{s}]$ . (c) Detailed flow of the adversarial training, which consists of an aversarial augmentation stage (Up) and a recognition stage (Down). During the adversarial augmentation stage, We augment input training samples, and optimize the control vector $\mathbf{z}$ by maximizing the classification loss through backpropagation. During the recognition stage, the augmentation module uses the updated $\mathbf{z}^*$ to generate challenging samples, and the recognition network then updates its parameters by minimizing the classification loss. ( $F_{\theta}^{*}$ indicates frozen weights)
+
+with the model's current performance and are continuously refined to generate increasingly challenging samples.
+
+Specifically, the augmentation module takes palmprint images $x$ and control vectors $\mathbf{z}$ . Before training the recognition network, an optimization process is applied to update $\mathbf{z}$ , as delineated below,
+
+$$
+\mathbf {z} ^ {*} = \underset {\mathbf {z}} {\operatorname {a r g m a x}} L \left(F _ {\theta} (A (x, \mathbf {z})), y\right), \tag {2}
+$$
+
+where $y$ denotes input labels, $A$ represents augmentation module, $F_{\theta}$ denotes recognition network, and $L$ is the classification loss. To efficiently optimize $\mathbf{z}$ with recognition network feedback, we adopt Projected Gradient Descent (PGD) [41], a gradient-based adversarial attack method [13] known for its effectiveness in generating challenging samples within bounded perturbations. The process is
+
+$$
+\mathbf {z} ^ {k + 1} \leftarrow \Pi_ {\mathbf {z} + S} \left(\mathbf {z} ^ {k} + \alpha \operatorname {s g n} \left(\nabla_ {\mathbf {z}} L \left(F _ {\theta} \left(A \left(x, \mathbf {z} ^ {k}\right), y\right)\right)\right)\right), \tag {3}
+$$
+
+where $\alpha$ is the step size, $\operatorname{sgn}(\cdot)$ is the sign function, $\nabla_{\mathbf{z}}L$ denotes the gradient of the loss $L$ , and $k$ represents optimization iterations. The $\Pi_{\mathbf{z} + S}$ is a projection operator, which controls updated content in a set of allowed perturbation $S$ .
+
+After that, the recognition network is trained, taking challenging samples augmented with refined $\mathbf{z}^*$ and normal samples, and updating by backpropagation. The process is
+
+$$
+\theta^ {*} = \underset {\theta} {\operatorname {a r g m i n}} \left[ L \left(F _ {\theta} (x, y)\right) + L \left(F _ {\theta} \left(A \left(x, \mathbf {z} ^ {*}\right)\right), y\right) \right], \tag {4}
+$$
+
+where $\theta$ is the weights of recognition network $F_{\theta}$
+
+Momentum-Based Dynamic Sampling Existing adversarial augmentation methods [37, 46] initialize the control parameters by randomly sampling from a pre-defined Gaussian distribution, i.e., $\mathbf{z} \sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma})$ , where $\boldsymbol{\mu}$ , $\boldsymbol{\Sigma}$ are mean vector and covariance matrix respectively. However, this approach inefficiently explores the augmentation space and generates suboptimal samples. To address this, we propose a momentum-based dynamic sampling strategy that adaptively adjusts the initialization range, focusing on regions proven challenging in previous iterations. Specifically, for the $t$ -th training iteration, the control vector $\mathbf{z}$ is sampled as,
+
+$$
+\mathbf {z} _ {t} ^ {0} \sim \mathcal {N} \left(\beta \cdot \mathbf {z} _ {t - 1} ^ {*} + (1 - \beta) \cdot \mu , \Sigma\right), \tag {5}
+$$
+
+where $\beta \in (0,1)$ is a momentum coefficient, and $\mathbf{z}^{*}_{t - 1}$ represents the optimized control vector from the previous training iteration. This strategy dynamically shifts the sampling distribution toward regions that previously yielded challenging samples, enabling efficient exploration of the augmentation parameter space.
+
+# 3.3. Differentiable Spatial Transformer
+
+The differentiable spatial transformation was first introduced in [22]. We briefly outline its implementation below. The spatial transformation involves translation, rotation, and scaling, accepting a parameter $\mathbf{t} = [t_x,t_y,t_\theta ,t_s]$
+
+
+Figure 3. The framework of our proposed identity-preserving palmprint generation network.
+
+and computing the affine transformation matrix as follows,
+
+$$
+A _ {t} = \left[ \begin{array}{c c c} t _ {s} \cos t _ {\theta} & - t _ {s} \sin t _ {\theta} & t _ {x} \\ t _ {s} \sin t _ {\theta} & t _ {s} \cos t _ {\theta} & t _ {y} \\ 0 & 0 & 1 \end{array} \right], \tag {6}
+$$
+
+where $t_s \in \mathbb{R}$ denotes the scaling factor, $t_\theta \in [-\pi, \pi]$ denotes the scaling factor, and $t_x, t_y \in \mathbb{R}$ denote horizontal and vertical shifts, respectively. For an input $H \times W \times 3$ RGB image, the same affine transformation matrix is applied to all channels. We apply a bilinear sampling kernel to compute the transformed spatial grid. More details are presented in the Appendix.
+
+To prevent severe degradation of the transformed image during optimization, we impose empirical constraints on the parameter ranges. Specifically, we limit the rotation angle to $|t_{\theta}| < 0.25$ , the scaling factor to $|t_s - 1| < 0.2$ , and the translation offsets to $|t_x| < 0.2$ and $|t_y| < 0.2$ relative to the image dimensions. These restrictions ensure that the transformation remains within a reasonable deformation space, maintaining the original palmprint identity features.
+
+# 3.4. Identity-Preserving Generation Network
+
+Common random image manipulations, such as blurring and color shifting, not only fail to simulate realistic textural variations but may also compromise the palmprint identity features. To address this, we propose a novel identity-preserving palmprint generation network.
+
+The training process is depicted in Figure 3. Our generation model utilizes a dual-encoder architecture, where the encoders $E_{s}$ and $E_{id}$ are designed to extract stylistic and spatial identity information from palmprint images, respectively. The extracted features are then fed into a generator network to produce realistic palmprint images. Inspired by the effectiveness of StyleGAN2 [28], we integrate an adaptive instance normalization (AdaIN) module to ensure that the generated palmprint images closely resemble the distribution of real data.
+
+During the training phase, a palmprint image $x_{1}$ is first input into the style encoder $E_{s}$ , which produces a style code s. The style encoder, which is a commonly used residual network [16], outputs the mean $\mu_{s}$ and variance $\sigma_s^2$ of a flattened feature and further constructs the style code through a
+
+Table 1. Details of the eight public palmprint datasets.
+
+| Datasets | #Images | #IDs | Var. | Dev. |
| MPD [66] | 16,000 | 400 | Large | Mobile phone |
| XJTU-UP [48] | 7900 | 200 | Large | Mobile phone |
| BJTU [2] | 2663 | 296 | Large | Mobile phone |
| CASIA [51] | 5502 | 620 | Small | Digital camera |
| PolyU [60] | 7738 | 388 | Small | Scanner |
| TongJi [63] | 12,000 | 600 | Small | Digital camera |
| IITD [34] | 2601 | 460 | Small | Digital camera |
| NTU-CP-v1 [43] | 2390 | 652 | Large | Digital camera |
+
+reparameterization trick [50]. A KL divergence loss $L_{KL}$ enforces the style code distribution to approximate a standard Gaussian. Additionally, a different palmprint image $x_{2}$ is processed by the encoder $E_{id}$ to extract spatial hierarchical identity features $f_{id}$ . The identity encoder is also a residual network [16]. In practice, we use a frozen pre-trained recognition network as the identity encoder to extract identity features.
+
+For the generation network, the style code $\mathbf{s}$ is first processed with $L2$ normalization, projecting it onto a hypersphere space. It then passes through multiple layers of MLPs and is integrated into the modulated convolution layer [28]. The spatial identity features are injected into the network through a channel concatenation approach, and a dropout operator is applied for regularization.
+
+After the generation of the palmprint image $x'$ , a suite of loss functions is employed to refine the quality and authenticity of the generated output. Firstly, an adversarial loss $L_{GAN}$ is applied to ensure the synthesized palmprints appear realistic and match the real dataset distribution. To ensure stylistic disentanglement, a style loss $L_{1}$ between $x'$ and $x_{1}$ is implemented. Additionally, a pre-trained recognition model is used to calculate a cosine similarity-based loss $L_{ID}$ to maintain identity consistency between $x'$ and $x_{1}$ . Details of these loss functions are presented in the Appendix. The total loss of the training process is expressed as follows:
+
+$$
+L _ {G E N} = \lambda_ {K L} L _ {K L} + \lambda_ {G A N} L _ {G A N} + \lambda_ {1} L _ {1} + \lambda_ {I D} L _ {I D}, \tag {7}
+$$
+
+where $\lambda_{KL},\lambda_{GAN},\lambda_{1}$ and $\lambda_{ID}$ are weights. The generated palmprint images are shown in Figure 4.
+
+In conclusion, the final control vector of the unified augmentation module is defined as $\mathbf{z} := [\mathbf{t}, \mathbf{s}]$ .
+
+# 4. Experiments
+
+# 4.1. Datasets
+
+In our experiments, we utilize eight publicly available palmprint datasets, with detailed information presented in Table 1. Notably, the MPD [66] dataset shows a rich variety of variations in palm postures, while the XJTU-UP [48] and BJTU [2] datasets exhibit substantial changes in image aspects, such as lighting and quality. We use official palmprint
+
+Table 2. Comparative performance on challenging datasets under the open-set protocol, with ResNet-50 as the backbone for all methods.
+
+| Methods | Venue | MPD | XJTU-UP | BJTU |
| TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 | TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 | TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 |
| Baseline [7] | - | 0.4677 | 0.4000 | 0.7153 | 0.8126 | 0.6119 | 0.5424 | 0.8846 | 0.9561 | 0.5004 | 0.4727 | 0.7557 | 0.8285 |
| RandAugment [6] | CVPRW-20 | 0.5065 | 0.4493 | 0.7582 | 0.8447 | 0.7319 | 0.6825 | 0.9355 | 0.9820 | 0.5685 | 0.5446 | 0.8614 | 0.9282 |
| TrivialAugment [45] | ICCV-21 | 0.5414 | 0.4660 | 0.7990 | 0.8864 | 0.7972 | 0.7402 | 0.9637 | 0.9901 | 0.6348 | 0.5927 | 0.8824 | 0.9402 |
| AdaAug [3] | ICLR-22 | 0.5980 | 0.5128 | 0.8465 | 0.9182 | 0.8036 | 0.7653 | 0.9645 | 0.9885 | 0.6257 | 0.5872 | 0.8893 | 0.9591 |
| MADAug [19] | ICCV-23 | 0.6042 | 0.5129 | 0.8610 | 0.9276 | 0.8402 | 0.7900 | 0.9723 | 0.9943 | 0.6644 | 0.5507 | 0.9172 | 0.9701 |
| AdvProp [54] | CVPR-20 | 0.4992 | 0.3958 | 0.7545 | 0.8523 | 0.6300 | 0.5565 | 0.9070 | 0.9674 | 0.5217 | 0.5103 | 0.7906 | 0.8734 |
| Fast AdvProp [44] | ICLR-22 | 0.5310 | 0.4521 | 0.7778 | 0.8606 | 0.7068 | 0.6497 | 0.9251 | 0.9775 | 0.5558 | 0.5276 | 0.8016 | 0.8843 |
| CFSM [37] | ECCV-22 | 0.5597 | 0.4887 | 0.7835 | 0.8636 | 0.7892 | 0.7475 | 0.9501 | 0.9843 | 0.6166 | 0.6027 | 0.8604 | 0.9272 |
| ARoFace [46] | ECCV-24 | 0.6367 | 0.5609 | 0.8763 | 0.9396 | 0.7640 | 0.6820 | 0.9642 | 0.9953 | 0.6510 | 0.6268 | 0.8863 | 0.9452 |
| UAA-p | - | 0.7437 | 0.6546 | 0.9308 | 0.9714 | 0.9228 | 0.8903 | 0.9898 | 0.9977 | 0.7953 | 0.7806 | 0.9671 | 0.9870 |
| UAA-s | - | 0.8075 | 0.7289 | 0.9526 | 0.9821 | 0.9332 | 0.8917 | 0.9911 | 0.9984 | 0.8192 | 0.7892 | 0.9701 | 0.9910 |
+
+
+Figure 4. An illustration of palmprint images synthesized by our proposed identity-preserving palmprint generation network. Each row corresponds to a unique palmprint identity, showing that the identity is consistently maintained across different styles. Each column, generated with the same style code, illustrates the network's ability to apply consistent stylistic variations while keeping the identity of each palmprint intact.
+
+ROIs where available. For others, we employ a detect-then-crop protocol [65] to extract ROIs from hand images.
+
+Previous palmprint recognition works [10, 56, 57] often adopt a closed-set protocol, where the training and testing sets share the same identities, and images are divided based on different sessions. In contrast, we adopt an open-set protocol, dividing identities between the training and testing sets in 1:1 ratio without any identity overlap, which is more challenging and better aligns with real-world demands.
+
+Prior research [50, 67] shows that training on each individual palmprint dataset with limited samples could easily lead to model overfitting. Thus, we aggregate the training subsets from each dataset to form a combined training set. We train the recognition model using this mixed dataset and evaluate its performance on various testing sets. The IITD
+
+[34] and NTU-CP-V1 [43] are used only for training purposes due to their limited number of images.
+
+# 4.2. Evaluation Metrics
+
+We evaluate the performance of palmprint recognition methods using a combination of verification and identification metrics. For verification, we calculate the matching scores for all pairs of genuine and imposter samples. Then, we maintain the False Acceptance Rate (FAR) at a fixed value, determine the threshold, and further compute the True Acceptance Rate (TAR), denoted as TAR@FAR. For identification, we employ a $1:N$ matching strategy. Specifically, we select the first image of each identity in the test set as the gallery, with the remaining images serving as probes. We calculate both rank1 and rank5 accuracies to evaluate the model's performance comprehensively.
+
+# 4.3. Implementation Details
+
+Training of the Generation Networks We set the loss weights $\lambda_{KL} = 0.01$ , $\lambda_{GAN} = 1.0$ , $\lambda_{1} = 1.0$ and $\lambda_{ID} = 5.0$ , respectively. We employ the Adam optimizer [30] with parameters (0.5, 0.99). The initial learning rate is set to $1 \times 10^{-3}$ , and a linear weight decay is applied. The generative model is trained for 60 epochs on a NVIDIA V100.
+
+Training of the Recognition Networks We adopt Arc-Face [7] as baselines, with modified ResNet-50 [16] serving as the backbone. The recognition model is trained on images of resolution $112 \times 112$ , with a learning rate of 0.1, and a cosine weight decay is applied. We train the networks for 30 epochs with an overall batch size of 256, distributed across 4 V100 GPUs. All comparative methods are trained using the same training dataset and hyperparameters.
+
+Configurations of Proposed Method This method takes the following parameters, i.e., steps $K$ and the step size $\alpha$ of the PGD optimization, the momentum coefficient $\beta$ , and the augmentation rate $\gamma$ , which indicates augmentation for $\gamma$ proportion of a batch of samples. We set $K = 1$ , $\beta = 0.5$ , and $\gamma = 0.5$ for geometric augmentation, and $K = 2$ , $\beta = 0.25$ , and $\gamma = 0.5$ for textural augmentation. The $\alpha$ is
+
+Table 3. Comparative verification performance on constrained datasets. The results are presented in TAR@FAR.
+
+| Methods | TongJi | PolyU | CASIA |
| 1e-5 | 1e-6 | 1e-5 | 1e-6 | 1e-5 | 1e-6 |
| Baseline [7] | 0.9527 | 0.9288 | 0.9641 | 0.9449 | 0.8753 | 0.8515 |
| RandAugment [6] | 0.9743 | 0.9622 | 0.9603 | 0.9441 | 0.9359 | 0.9133 |
| TrivialAugment [45] | 0.9760 | 0.9629 | 0.9693 | 0.9424 | 0.9476 | 0.9279 |
| AdaAug [3] | 0.9764 | 0.9655 | 0.9758 | 0.9660 | 0.9579 | 0.9476 |
| MADAug [19] | 0.9775 | 0.9651 | 0.9785 | 0.9643 | 0.9524 | 0.9268 |
| AdvProp [54] | 0.9578 | 0.9384 | 0.9670 | 0.9535 | 0.8779 | 0.8540 |
| Fast AdvProp [44] | 0.9592 | 0.9408 | 0.9682 | 0.9529 | 0.8796 | 0.8567 |
| CFSM [37] | 0.9549 | 0.9297 | 0.9714 | 0.9601 | 0.9081 | 0.8937 |
| ARoFace[46] | 0.9730 | 0.9423 | 0.9552 | 0.9329 | 0.9552 | 0.9383 |
| UAA-p | 0.9867 | 0.9740 | 0.9858 | 0.9768 | 0.9818 | 0.9747 |
| UAA-s | 0.9864 | 0.9778 | 0.9731 | 0.9585 | 0.9841 | 0.9766 |
+
+sampled from $\mathcal{N}(0.1, 0.001)$ .
+
+Comparison Methods We choose four automatic augmentation methods, i.e., RandAugment [6], TrivialAugment [45], AdaAug [3], and MADAug [19], two adversarial examples-based methods, i.e., AdvProp [54] and Fast AdvProp [44], and two facial augmentation methods, i.e., CFSM [37] and ARoFace [46] for comparison. These automatic augmentation methods adopt the augmentation space consisting of geometric transformations (i.e., ShearX/Y, TranslateX/Y, Rotate) and color adjusting (i.e., AutoContrast, Invert, Equalize, Solarize, Posterize, Color, Contrast, Brightness, Sharpness, Cutout). Note that these methods are originally designed for general image recognition or facial verification tasks, rather than specifically for palmprint recognition scenarios. We apply them to palmprint recognition models training and try to maintain their parameter configurations proposed in their respective original works, while keeping consistent with the baseline training protocol, like learning rate, batch size, etc.
+
+# 4.4. Experimental Results
+
+Performance on Challenging Datasets We choose MPD [66], XJTU-UP [48], and BJTU [2] as challenging datasets and evaluate the performance of different methods on them. Our method is tested in two configurations: 'UAA-p', where the spatial transformation and identity-preserving generation modules are applied in parallel, and 'UAA-s', where these modules are applied sequentially, with geometric augmentation followed by textural augmentation. Table 2 indicates that our method not only shows a substantial improvement over the baseline, but also outperforms other augmentation methods. We provide results with more baselines and more metrics in the Appendix.
+
+Performance on Constrained Datasets Compared to those challenging datasets, TongJi [63], PolyU [60], and CASIA [51] are more constrained and exhibit fewer variations. We also assess the performance of different methods on them. As evidenced in Table 3, our method achieves notable performance improvements on these simple datasets as well. These results demonstrate that our method im
+
+Table 4. Ablation of different components in our proposed method. 'T', 'G', and 'M' denote the spatial transformation module, the palmprint generative network, and the momentum-based sampling, respectively.
+
+| T | G | M | MPD | XJTU-UP | BJTU |
| 1e-5 | 1e-6 | 1e-5 | 1e-6 | 1e-5 | 1e-6 |
| ✘ | ✘ | ✘ | 0.4677 | 0.4000 | 0.6119 | 0.5424 | 0.5004 | 0.4727 |
| ✓ | ✘ | ✘ | 0.6266 | 0.5318 | 0.7662 | 0.6894 | 0.6657 | 0.6159 |
| ✘ | ✓ | ✘ | 0.5514 | 0.4821 | 0.8118 | 0.7682 | 0.6182 | 0.5590 |
| ✓ | ✓ | ✘ | 0.7557 | 0.6828 | 0.9205 | 0.8837 | 0.7860 | 0.7052 |
| ✓ | ✓ | ✓ | 0.8075 | 0.7289 | 0.9332 | 0.8917 | 0.8192 | 0.7892 |
+
+proves robustness on challenging datasets while maintaining high accuracy on constrained datasets.
+
+# 4.5. Ablation Study
+
+Ablation of Different Components The primary constituents of our proposed augmentation framework are the spatial transformation module for geometric augmentation, the identity-preserving palmprint generation network for textural augmentation, and momentum-based dynamic sampling. We denote these three components as 'T', 'G', and 'M', respectively. Experimental results are presented in Table 4. Both geometric and textural augmentation contribute significantly to the recognition of challenging samples. Additionally, the momentum-based dynamic sampling further improves recognition models by introducing an adaptive optimization range.
+
+Visualization of Augmented Samples The proposed method enhances palmprint samples with both geometric changes and textural variations. It utilizes the feedback from the recognition network to optimize the augmentations. We provide visual results of the original and augmented samples, as shown in Figure 5. The visualizations demonstrate that the augmented samples exhibit a range of geometric changes and textural variations. These challenging samples significantly improve the discriminative and generalization ability of recognition models. Table 4 shows the effects of geometric and textural augmentations.
+
+Effect of Momentum-Based Dynamic Sampling The proposed sampling method introduces a dynamic sampling space that adaptively adjusts during the training process. It leverages the momentum term to iteratively refine the sampling space, allowing for a more efficient exploration of the parameter space and the generation of increasingly challenging samples. We record the initial control vector $\mathbf{z}^0$ from each iteration during the training process and plot the statistical results in Figure 6. The figure shows how the sampling space evolves towards challenging regions, correlating with the performance gains in Table 4.
+
+# 4.6. Discussion
+
+Identity Consistency To enhance the recognition model, our method generates challenging samples while ensuring
+
+
+Figure 5. Visualization of original and adversarial augmented palmprint samples. Compared to original palmprints, augmented images display both geometric changes and textural variations.
+
+
+Figure 6. Evolution of the dynamic sampling space over training iterations. The boxplot shows the distribution of the initial control vectors $[t_s, t_\theta, t_x, t_y]$ for every 100 iterations. We add a vector sampled from a fixed distribution for comparison.
+
+identity consistency. We address potential concerns about excessive degradation or identity distortion through two key measures. The first is limiting the spatial transformer's scope to prevent extreme deformations. The second is employing a low-dimensional (16-D) L2-normalized style code and spatial hierarchical identity features in the generation module, which stabilize generation and preserve discriminative identity information. A quantitative evaluation of identity consistency is provided in the Appendix.
+
+Relationships with Palmprint Generation Methods Recently, some palmprint generation methods, e.g., BezierPalm [67], have been proposed, which mainly focus on synthesizing fake palmprint datasets to pre-train a recognition model, further improving recognition performance. However, our proposed method, which augments palmprint images during the training process of the recognition network, is complementary to them. We include experiments in the Appendix to demonstrate that, by combining these methods, the proposed UAA achieves better performance.
+
+Limitations Our method enhances palmprint samples with both geometric and textural variations. Since palmprints are typically planar, we adopt a global transformer
+
+to simulate geometric changes. However, this may fail to model local non-planar deformations (e.g., palm bending). We think that further augmenting palmprints with 3D hand models is an interesting direction.
+
+# 5. Conclusion
+
+In this paper, we have summarized geometric distortions and textural degradations as the primary challenges in recognizing difficult palmprint samples. To tackle these problems, we adopt an adversarial training paradigm and a unified augmentation module. It is the first systematic approach to generate palmprint samples with both geometric changes and textural variations to enhance palmprint recognition. Furthermore, a momentum-based dynamic sampling strategy is proposed to improve the augmentation for challenging samples. We conduct extensive experiments on both normal and challenging datasets to validate the effectiveness and superiority of our approach.
+
+Acknowledgments This work is partly supported by the grants of the National Natural Science Foundation of China under Nos. 62476077, 62076086, and 62272142.
+
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+[68] Shuping Zhao, Lunke Fei, Bob Zhang, Jie Wen, and Jinrong Cui. Towards mobile palmprint recognition via multi-view hierarchical graph learning. IEEE Transactions on Information Forensics and Security, 2024. 2
+[69] Qian Zheng, Ajay Kumar, and Gang Pan. Suspecting less and doing better: New insights on palmprint identification for faster and more accurate matching. IEEE TIFS, 11(3): 633-641, 2015. 2
\ No newline at end of file
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| Adversarial Examples | adversarial training | X | X | pixel-based perturbations |
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+ "content": " are designed to extract stylistic and spatial identity information from palmprint images, respectively. The extracted features are then fed into a generator network to produce realistic palmprint images. Inspired by the effectiveness of StyleGAN2 [28], we integrate an adaptive instance normalization (AdaIN) module to ensure that the generated palmprint images closely resemble the distribution of real data."
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| MPD [66] | 16,000 | 400 | Large | Mobile phone |
| XJTU-UP [48] | 7900 | 200 | Large | Mobile phone |
| BJTU [2] | 2663 | 296 | Large | Mobile phone |
| CASIA [51] | 5502 | 620 | Small | Digital camera |
| PolyU [60] | 7738 | 388 | Small | Scanner |
| TongJi [63] | 12,000 | 600 | Small | Digital camera |
| IITD [34] | 2601 | 460 | Small | Digital camera |
| NTU-CP-v1 [43] | 2390 | 652 | Large | Digital camera |
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| TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 | TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 | TAR @ FAR 1e-5 | 1e-6 | Identification rank1 | rank5 |
| Baseline [7] | - | 0.4677 | 0.4000 | 0.7153 | 0.8126 | 0.6119 | 0.5424 | 0.8846 | 0.9561 | 0.5004 | 0.4727 | 0.7557 | 0.8285 |
| RandAugment [6] | CVPRW-20 | 0.5065 | 0.4493 | 0.7582 | 0.8447 | 0.7319 | 0.6825 | 0.9355 | 0.9820 | 0.5685 | 0.5446 | 0.8614 | 0.9282 |
| TrivialAugment [45] | ICCV-21 | 0.5414 | 0.4660 | 0.7990 | 0.8864 | 0.7972 | 0.7402 | 0.9637 | 0.9901 | 0.6348 | 0.5927 | 0.8824 | 0.9402 |
| AdaAug [3] | ICLR-22 | 0.5980 | 0.5128 | 0.8465 | 0.9182 | 0.8036 | 0.7653 | 0.9645 | 0.9885 | 0.6257 | 0.5872 | 0.8893 | 0.9591 |
| MADAug [19] | ICCV-23 | 0.6042 | 0.5129 | 0.8610 | 0.9276 | 0.8402 | 0.7900 | 0.9723 | 0.9943 | 0.6644 | 0.5507 | 0.9172 | 0.9701 |
| AdvProp [54] | CVPR-20 | 0.4992 | 0.3958 | 0.7545 | 0.8523 | 0.6300 | 0.5565 | 0.9070 | 0.9674 | 0.5217 | 0.5103 | 0.7906 | 0.8734 |
| Fast AdvProp [44] | ICLR-22 | 0.5310 | 0.4521 | 0.7778 | 0.8606 | 0.7068 | 0.6497 | 0.9251 | 0.9775 | 0.5558 | 0.5276 | 0.8016 | 0.8843 |
| CFSM [37] | ECCV-22 | 0.5597 | 0.4887 | 0.7835 | 0.8636 | 0.7892 | 0.7475 | 0.9501 | 0.9843 | 0.6166 | 0.6027 | 0.8604 | 0.9272 |
| ARoFace [46] | ECCV-24 | 0.6367 | 0.5609 | 0.8763 | 0.9396 | 0.7640 | 0.6820 | 0.9642 | 0.9953 | 0.6510 | 0.6268 | 0.8863 | 0.9452 |
| UAA-p | - | 0.7437 | 0.6546 | 0.9308 | 0.9714 | 0.9228 | 0.8903 | 0.9898 | 0.9977 | 0.7953 | 0.7806 | 0.9671 | 0.9870 |
| UAA-s | - | 0.8075 | 0.7289 | 0.9526 | 0.9821 | 0.9332 | 0.8917 | 0.9911 | 0.9984 | 0.8192 | 0.7892 | 0.9701 | 0.9910 |
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+ "content": "Figure 4. An illustration of palmprint images synthesized by our proposed identity-preserving palmprint generation network. Each row corresponds to a unique palmprint identity, showing that the identity is consistently maintained across different styles. Each column, generated with the same style code, illustrates the network's ability to apply consistent stylistic variations while keeping the identity of each palmprint intact."
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+ "content": "ROIs where available. For others, we employ a detect-then-crop protocol [65] to extract ROIs from hand images."
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+ "content": "Prior research [50, 67] shows that training on each individual palmprint dataset with limited samples could easily lead to model overfitting. Thus, we aggregate the training subsets from each dataset to form a combined training set. We train the recognition model using this mixed dataset and evaluate its performance on various testing sets. The IITD"
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+ "content": " matching strategy. Specifically, we select the first image of each identity in the test set as the gallery, with the remaining images serving as probes. We calculate both rank1 and rank5 accuracies to evaluate the model's performance comprehensively."
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| 1e-5 | 1e-6 | 1e-5 | 1e-6 | 1e-5 | 1e-6 |
| Baseline [7] | 0.9527 | 0.9288 | 0.9641 | 0.9449 | 0.8753 | 0.8515 |
| RandAugment [6] | 0.9743 | 0.9622 | 0.9603 | 0.9441 | 0.9359 | 0.9133 |
| TrivialAugment [45] | 0.9760 | 0.9629 | 0.9693 | 0.9424 | 0.9476 | 0.9279 |
| AdaAug [3] | 0.9764 | 0.9655 | 0.9758 | 0.9660 | 0.9579 | 0.9476 |
| MADAug [19] | 0.9775 | 0.9651 | 0.9785 | 0.9643 | 0.9524 | 0.9268 |
| AdvProp [54] | 0.9578 | 0.9384 | 0.9670 | 0.9535 | 0.8779 | 0.8540 |
| Fast AdvProp [44] | 0.9592 | 0.9408 | 0.9682 | 0.9529 | 0.8796 | 0.8567 |
| CFSM [37] | 0.9549 | 0.9297 | 0.9714 | 0.9601 | 0.9081 | 0.8937 |
| ARoFace[46] | 0.9730 | 0.9423 | 0.9552 | 0.9329 | 0.9552 | 0.9383 |
| UAA-p | 0.9867 | 0.9740 | 0.9858 | 0.9768 | 0.9818 | 0.9747 |
| UAA-s | 0.9864 | 0.9778 | 0.9731 | 0.9585 | 0.9841 | 0.9766 |
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| 1e-5 | 1e-6 | 1e-5 | 1e-6 | 1e-5 | 1e-6 |
| ✘ | ✘ | ✘ | 0.4677 | 0.4000 | 0.6119 | 0.5424 | 0.5004 | 0.4727 |
| ✓ | ✘ | ✘ | 0.6266 | 0.5318 | 0.7662 | 0.6894 | 0.6657 | 0.6159 |
| ✘ | ✓ | ✘ | 0.5514 | 0.4821 | 0.8118 | 0.7682 | 0.6182 | 0.5590 |
| ✓ | ✓ | ✘ | 0.7557 | 0.6828 | 0.9205 | 0.8837 | 0.7860 | 0.7052 |
| ✓ | ✓ | ✓ | 0.8075 | 0.7289 | 0.9332 | 0.8917 | 0.8192 | 0.7892 |
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+ "content": "Relationships with Palmprint Generation Methods Recently, some palmprint generation methods, e.g., BezierPalm [67], have been proposed, which mainly focus on synthesizing fake palmprint datasets to pre-train a recognition model, further improving recognition performance. However, our proposed method, which augments palmprint images during the training process of the recognition network, is complementary to them. We include experiments in the Appendix to demonstrate that, by combining these methods, the proposed UAA achieves better performance."
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+ "content": "Acknowledgments This work is partly supported by the grants of the National Natural Science Foundation of China under Nos. 62476077, 62076086, and 62272142."
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diff --git a/2025/Unified Category-Level Object Detection and Pose Estimation from RGB Images using 3D Prototypes/5a18f1d0-5854-4d52-9b3d-42b8f051f9c6_content_list.json b/2025/Unified Category-Level Object Detection and Pose Estimation from RGB Images using 3D Prototypes/5a18f1d0-5854-4d52-9b3d-42b8f051f9c6_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..d7c1bcef6df9bc1620a9b7ba6fcb6eca59f38a91
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+++ b/2025/Unified Category-Level Object Detection and Pose Estimation from RGB Images using 3D Prototypes/5a18f1d0-5854-4d52-9b3d-42b8f051f9c6_content_list.json
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+ {
+ "type": "text",
+ "text": "Unified Category-Level Object Detection and Pose Estimation from RGB Images using 3D Prototypes",
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+ "text": "Tom Fischer\\*1,2 Xiaojie Zhang\\*1,2 Eddy Ilg\\* 1 Saarland University \\*2 University of Technology Nuremberg",
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+ "type": "text",
+ "text": "Abstract",
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+ {
+ "type": "text",
+ "text": "Recognizing objects in images is a fundamental problem in computer vision. Although detecting objects in 2D images is common, many applications require determining their pose in 3D space. Traditional category-level methods rely on RGB-D inputs, which may not always be available, or employ two-stage approaches that use separate models and representations for detection and pose estimation. For the first time, we introduce a unified model that integrates detection and pose estimation into a single framework for RGB images by leveraging neural mesh models with learned features and multi-model RANSAC. Our approach achieves state-of-the-art results for RGB category-level pose estimation on REAL275, improving on the current state-of-the-art by $22.9\\%$ averaged across all scale-agnostic metrics. Finally, we demonstrate that our unified method exhibits greater robustness compared to single-stage baselines. Our code and models are available at github.com/Fischer-Tom/unified-detection-and-pose-estimation.",
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+ "type": "text",
+ "text": "1. Introduction",
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+ {
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+ "text": "Finding out whether an object is present in an image, where it is located, and how it is oriented in space, are fundamental problems of scene understanding. They are commonly referred to as object detection and pose estimation, and are critically relevant for applications in robotics [27, 53, 54], autonomous driving [28, 43] and augmented reality [39]. In object pose estimation, one distinguishes between methods that work only on known instances [19, 29, 32, 44, 60], and methods that are able to generalize within object categories [12, 15, 33, 35, 51, 52, 58, 59].",
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+ "type": "text",
+ "text": "Category-level pose estimation has made significant progress in recent years [12, 15, 33, 35, 51, 52, 58, 59]. However, most current work still relies on accurate depth information to recover precise poses [12, 58], restricting the",
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+ "image_caption": [
+ "Figure 1. The top shows existing pipelines that are made up of separate stages for object detection and and single-object pose estimation. In the bottom, we show our pipeline that uses a single representation and model for detection and pose estimation."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "use to devices and working conditions where depth can be captured. Pose estimation from RGB images alone [15, 30, 36, 52, 59] is less explored and a much harder task.",
+ "bbox": [
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+ "page_idx": 0
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+ "type": "text",
+ "text": "Methods can be further classified according to the used detection approach. Although there are some RGB-D methods that utilize a shared representation with individual detection and pose heads [24, 51], most methods completely decouple the problem and use separate models and representations. All current RGB methods fall into this category of two-stage methods and use separate models per task, where as shown in Figure 1, objects are first detected, cropped, and then passed into a single-object pose estimator. This naturally places strong emphasis on the accuracy of the detection model, as failures cannot be recovered later, and comes with the downside of having to maintain two separate models.",
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+ "type": "text",
+ "text": "For the first time, we show that a single unified model can be established for both tasks in the case of RGB images, and that this approach leads to improved accuracy and robustness. Our model leverages neural mesh models [2, 38] as a 3D representation of object categories, where a 2D feature extractor for images and the neural features on the",
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+ "type": "header",
+ "text": "CVF",
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+ "page_idx": 0
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+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "*Equal contribution. Corresponding email: {tom.fischer, xiaojie.zhang}@utn.de.",
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+ "type": "text",
+ "text": "meshes are learned jointly during training. During inference, the image features are matched with features of the 3D meshes and multi-model RANSAC PnP [5] is used to detect different object instances and estimate their poses.",
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+ "type": "text",
+ "text": "Our approach achieves a new state of the art and outperforms the current RGB-only state-of-the-art [59] in pose estimation by $22.9\\%$ when averaged across all scale-agnostic metrics. The results show that a common error source in two-stage pipelines is the detector and that our single-stage model is significantly more robust than its two-stage counterparts. In summary, our contributions are:",
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+ "- We propose the first single-stage framework for category-level multi-object pose estimation from single RGB images.",
+ "- For the first time, we leverage neural mesh models jointly for object detection and pose estimation by combining them with multi-model RANSAC PnP and subsequent pose refinement.",
+ "- We achieve state-of-the-art performance on pose estimation benchmark REAL275 w.r.t. to accuracy and robustness, verifying the effectiveness of our object representation and single-stage multi-object inference pipeline."
+ ],
+ "bbox": [
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+ "text": "2. Related Work",
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+ {
+ "type": "text",
+ "text": "Both object detection [8, 41] and object pose estimation [37] are long-standing tasks in computer vision. Although the first has converged to broadly accepted models, a variety of approaches are still being explored for the latter. Early pose estimation methods [6, 14, 42] operate by matching hand-crafted features to instance-level 3D models. Today, deep learning has replaced feature descriptors, but many works are still restricted to estimate poses of object instances that were present during training [19, 29, 32, 44, 60].",
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+ "text": "Category-level pose estimation [12, 35, 51, 58, 59] was introduced by [51] to allow generalization to unseen instances within a set of established categories without requiring additional training or accurate CAD models during inference. The strong variation in geometry and scale within categories makes this a highly challenging problem. Shape-prior-free methods [12, 33, 35, 51] try to learn a generalizable representation without any guidance from CAD models during training.",
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+ "type": "text",
+ "text": "Shape-prior-based methods, on the other hand, use CAD models and/or simple derived properties such as sizes or bounding boxes to integrate geometric priors. The pose is then either regressed directly from a trained network, or solved for using predicted correspondences in the form of a Normalized Object Coordinate Space (NOCS) [51] with the (often deformed) shape prior using a non-differentiable alignment algorithm such as PnP [21, 31] or the Umyama algorithm [49]. Our method falls into the above category,",
+ "bbox": [
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+ "page_idx": 1
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+ "type": "text",
+ "text": "but estimates the correspondences from feature matching with 3D neural meshes.",
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+ "text": "Neural Mesh Models [2] are shape-prior-based methods and were initially proposed for robust category-level single-object rotation estimation. Follow-up work extended it to 6D pose estimation [38], however, they still relied on single-object training datasets and both methods [2, 38] are constrained to per-category networks that have to be calibrated against each other or require a (multi-label) classification model to identify present object categories. Later works removed the need for separate feature representations to allow robust classification, but they cannot estimate translations or handle multiple objects [16, 26]. Our work removes all these restrictions and can both detect objects and estimate their poses with a single, shared representation.",
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+ "type": "text",
+ "text": "2.1. Two-Stage Methods",
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+ "text": "The vast majority of object pose estimation methods first locates the objects using off-the-shelf detection models [18, 41] to detect Regions of Interest (RoI) as 2D segmentation masks or bounding boxes. The objects are then cropped from the image and processed by a second model to predict the final poses, splitting the approaches into two stages.",
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+ "text": "RGB-D Approaches have access to the incomplete point clouds of the observed instances derived from the depth map. These can be used for regression in combination with [34] or without [12, 35, 50] shape priors, or to align them with a shape prior [9, 48] using the Umayama algorithm [49]. In contrast to the above, our method does not require depth as input.",
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+ "text": "RGB-Only Approaches face a more challenging problem due to the inherent ambiguity in this setting, which is why these methods are less prominent. In particular, the lack of depth information introduces a fundamental ambiguity between distance and scale, making it impossible to recover these properties from observations. To this end, Zhang et al. [59] introduced a set of scale-agnostic metrics that we also utilize in our work. OLD-Net [15] and DMSR [52] leverage a shape prior-based alignment technique and LaPose [59] uses a shape prior-based regression approach. MSOS [30], on the other hand, does not utilize any shape prior and directly estimates NOCS shape and the metric-scale shape of the object for downstream alignment. Although these two-stage approaches are successful in practice, they learn separate representations for both stages and are prone to errors of the first stage. In contrast to the above, we present a single-stage method with higher accuracy and robustness.",
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+ "text": "2.2. Single-Stage Methods",
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+ "text": "Single-stage methods couple detection and pose estimation into an end-to-end architecture. Existing work on end-to-end pose estimation focuses mainly on the instance-level",
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+ "text": "9791",
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+ "img_path": "images/bf29930ab648717aceef8f3163000f743ce91e9006b00662706558720115af73.jpg",
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+ "Figure 2. We present a unified framework for solving detection and pose estimation with 3D object prototypes. Feature Extraction (Sec. 3.3): Given an RGB image, a frozen DINOv2 model with trainable adapters is combined with a Geometric Feature Decoder to produce two feature maps $\\overline{\\mathbf{F}}_{2D}$ , $\\mathbf{F}_{2D}$ and foreground segmentations $\\bar{\\mathbf{H}}$ , $\\mathbf{H}$ . 3D Prototype Learning (Sec. 3.4): During training, the Adapters and the Geometric Feature Decoder are jointly trained with a set of Neural Mesh Models [2] using a contrastive loss. Detection & 6D Pose Estimation (Sec. 3.6 a): After training, 6D object poses are obtained with a multi-model fitting algorithm from dense 2D/3D correspondences between category-level features $\\overline{\\mathbf{F}}_{2D}$ and all vertex features. 9D Pose Refinement (Sec. 3.6 b): For each identified instance, a deformation parameter is optimized for by aligning correspondences from instance-level features $\\mathbf{F}_{2D}$ with its 6D pose."
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+ "text": "setting [7, 11, 22, 23, 46, 47, 55, 57]. However, there are category-level methods that utilize a shared representation and task-specific heads. NOCS [51] uses a shared feature extraction backbone that provides ROIs paired with individual heads for NOCS-map and instance segmentation. The category-level approaches [24, 25] require RGB-D as input and are shape-prior-based regression methods that perform joint center-point detection, reconstruction, and pose estimation. CenterPose [36] comes close to an RGB-only single-stage method, but requires the class labels of the objects present in an image and therefore is not a stand-alone method. In contrast, our work proposes the first RGB-only single-stage approach to unify the complete detection and pose estimation in a shared representation.",
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+ "type": "text",
+ "text": "3. Method",
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+ "text": "We present a single-stage framework for RGB-only object detection and category-level 9D pose estimation. Our method aligns image features with a set of 3D object prototypes to infer object properties from 2D/3D correspondences obtained from feature matching. An overview is shown in Fig. 2.",
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+ "type": "text",
+ "text": "3.1. Task Definition",
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+ "type": "text",
+ "text": "Given an input image $\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}$ and camera intrinsics $\\mathbf{K} \\in \\mathbb{R}^{3 \\times 3}$ , our goal is to estimate the set of object properties:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {O} (\\mathbf {I}, \\mathbf {K}) = \\{(c _ {i}, \\mathbf {s} _ {i}, \\mathbf {R} _ {i}, \\mathbf {t} _ {i}) \\} _ {i = 1} ^ {N}, \\qquad (1)\n$$\n",
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+ "type": "text",
+ "text": "where each object $i$ is described by category $c_{i}$ , 3D size $\\mathbf{s}_i\\in \\mathbb{R}^3$ , rotation $\\mathbf{R}_i\\in SO(3)$ , and translation $\\mathbf{t}_i\\in \\mathbb{R}^3$ . We define its scalar instance scale as $\\sigma_{i} = \\| \\mathbf{s}_{i}\\|_{2}$ . Throughout the remaining parts of this section, we refer to sets in script font (i.e. $\\mathcal{O}$ ); vectors, tuples, and tensors in bold font (i.e. $\\mathbf{R}$ ); and scalars in standard math font (i.e. $c$ ).",
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+ "type": "text",
+ "text": "3.2. Representation",
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+ "text": "We represent 3D object prototypes with Neural Mesh Models [2, 16, 26, 38], which have shown high generalization and robustness for single-object pose estimation. Each category $c$ has a prototypical mesh $\\mathbf{M}^c = (\\mathbf{V}^c, \\mathbf{A}^c, \\mathbf{F}_{3D}^c)$ , where $\\mathbf{V}^c \\in \\mathbb{R}^{V \\times 3}$ are vertex coordinates in object space, $\\mathbf{A}^c \\in \\mathbb{Z}^{A \\times 3}$ are triangle indices, and $\\mathbf{F}_{3D}^c \\in \\mathbb{R}^{V \\times D}$ are learned vertex features. The geometry of each mesh is obtained by regularly sampling the surface of the bounding box obtained from the average size $\\overline{\\mathbf{s}}^c$ of the training set, which we normalize to have $\\| \\overline{\\mathbf{s}}^c \\|_2 = 1$ . We also keep a scaling factor $\\bar{\\sigma}^c$ that transforms the mesh into one that has the mean scale of the category. If camera poses are available, scenes can be composed from the object prototypes and rendered into an image.",
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+ "type": "text",
+ "text": "3.3. Feature Extraction",
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+ "text": "Accurate object localization from 2D/3D correspondences requires that the object geometry aligns well with the visual observations. In category-level pose estimation, one does not have access to instance-level geometries. To address this, we train a 2D feature extractor $\\Phi$ that learns to map the",
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+ "type": "page_number",
+ "text": "9792",
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+ "type": "text",
+ "text": "input image $\\mathbf{I}$ to a rendering of a scene composed of cuboid prototypes parameterized by $\\mathcal{O}(\\mathbf{I},\\mathbf{K})$",
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+ "type": "text",
+ "text": "Modeling. As solving for 9D poses from correspondences alone is challenging and tends to fail in practice, we first perform an initial 6D pose estimation, where we rely on a feature map $\\overline{\\mathbf{F}}_{2D}$ that is aligned with the prototypes that follow category-level sizes $\\overline{\\mathbf{s}}^c$ . Next, we perform a size refinement with a feature map $\\mathbf{F}_{2D}$ , which is aligned with deformed prototypes that match the instance-level sizes $\\mathbf{s}_i$ . Since both feature maps are conditioned on the same neural textures, $\\overline{\\mathbf{F}}_{2D}$ can be imagined as a warped variant of $\\mathbf{F}_{2D}$ .",
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+ "type": "text",
+ "text": "Backbone. The feature extractor $\\Phi$ is trained jointly with the vertex features. This introduces ambiguities that make a good initialization crucial to guide each $\\mathbf{F}_{3D}^{c}$ towards a meaningful representation. Therefore, we build $\\Phi$ on top of the self-supervised pre-trained DINOv2 ViT [40] and embed task-specific information using Parameter-Efficient Fine-Tuning (PEFT) [56]. Following [10], we use a low-rank adaptation (Adapter) in the MLP in each transformer block:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nx _ {l} ^ {\\prime} = \\operatorname {M L P} (\\operatorname {L N} (x _ {l})) + x _ {l} + \\lambda (\\operatorname {G e L U} (\\operatorname {L N} (x _ {l}) \\cdot D)) \\cdot U, \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "where $x_{l}$ is the output of the previous multi-head attention, $\\lambda$ is a scaling factor [10] and $D, U$ are the down- and up-projection matrices.",
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+ "type": "text",
+ "text": "Geometric Feature Decoder. To obtain the features corresponding to the object prototype geometry, we first apply a shared transformer encoder to the backbone features, and subsequently two transformer decoders to obtain $\\overline{\\mathbf{F}}_{2D},\\mathbf{F}_{2D}$ . Finally, both feature maps are upsampled to a certain output resolution using a combination of bilinear upsampling and shared convolution layers.",
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+ "type": "text",
+ "text": "3.4. Training",
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+ "type": "text",
+ "text": "We consider a training sample with $N$ objects and outline the loss calculation for an object $i$ with prototypical mesh $\\mathbf{M}_i = (\\mathbf{V},\\mathbf{A},\\mathbf{F}_{3D})$ , intrinsic matrix $\\mathbf{K}$ , and pose $\\hat{\\mathbf{R}}_i,\\hat{\\mathbf{t}}_i$ .",
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+ "text": "Setup. We first obtain pixel-level training annotations from rasterize $(\\mathbf{M}_i, \\mathbf{K}, \\hat{\\mathbf{R}}_i, \\hat{\\mathbf{t}}_i)$ to obtain projected image location $p_k$ and binary visibility $o_k$ for each vertex $v_k \\in \\mathbf{V}$ . Given a 2D feature map $\\mathbf{F}$ , we define the annotation set as $\\mathcal{Y}(\\mathbf{M}_i, \\mathbf{F}) = \\{ (\\theta_k, f_k, o_k) \\mid \\forall v_k \\in \\mathbf{V} \\}$ , where $f_k$ is the pixel feature at projection $p_k$ in $\\mathbf{F}$ , and $\\theta_k$ is the corresponding vertex feature from $\\mathbf{F}_{3D}$ .",
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+ "type": "text",
+ "text": "Optimizing $\\Phi$ . Following [2], we model the probability distribution of any feature $f$ being generated from vertex $v_{k}$ by defining $P(f|\\theta_k)$ using a von Mises-Fisher (vMF) distribution to express the likelihood:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nP (f | \\theta_ {k}, \\kappa) = C (\\kappa) e ^ {\\kappa \\left(f ^ {\\top} \\cdot \\theta_ {k}\\right)}, \\tag {3}\n$$\n",
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+ "type": "text",
+ "text": "with mean $\\theta_{\\kappa}$ , concentration parameter $\\kappa$ , and normalization constant $C(\\kappa)$ .",
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+ "type": "text",
+ "text": "Accurate object poses are obtained when $f_{k}$ can be matched to $\\theta_{k}$ , leading to precise 2D/3D correspondences. We optimize for this task using contrastive learning by maximizing Eq. (3) with the feature $f_{k}$ , and minimize the likelihood of all other vertices:",
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+ "type": "equation",
+ "text": "\n$$\n\\max \\quad P \\left(f _ {k} \\mid \\theta_ {k}, \\kappa\\right), \\tag {4}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\min \\sum_ {\\theta_ {m} \\in \\bar {\\theta} _ {k}} P \\left(f _ {k} \\mid \\theta_ {m}, \\kappa\\right), \\tag {5}\n$$\n",
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+ "type": "text",
+ "text": "where the negatives $\\overline{\\theta}_k$ are the features of all noncorresponding vertices including those from different classes. Equations 4 and 5 can be combined into a single loss by taking the negative log-likelihood:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} (\\mathcal {Y} (\\mathbf {M} _ {i}, \\mathbf {F})) = - \\sum_ {k} o _ {k} \\cdot \\log \\left(\\frac {e ^ {\\kappa \\left(f _ {k} \\cdot \\theta_ {k}\\right)}}{\\sum_ {\\theta_ {m} \\in \\bar {\\theta} _ {k}} e ^ {\\kappa \\left(f _ {k} ^ {\\top} \\cdot \\theta_ {m}\\right)}}\\right), \\tag {6}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where considering $\\kappa$ as a global hyperparameters allows canceling out the normalization constants $C(\\kappa)$ . We compute the full training loss as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {t r a i n}} = \\sum_ {i} \\frac {\\mathcal {L} \\left(\\mathcal {Y} \\left(\\mathbf {M} ^ {c _ {i}} , \\overline {{\\mathbf {F}}} _ {2 D}\\right)\\right) + \\mathcal {L} \\left(\\mathcal {Y} \\left(\\phi \\left(\\mathbf {M} ^ {c _ {i}}\\right) , \\mathbf {F} _ {2 D}\\right)\\right)}{2 N}, \\tag {7}\n$$\n",
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+ "type": "text",
+ "text": "where $\\phi (\\mathbf{M}) = (\\phi (\\mathbf{V}),\\mathbf{A},\\mathbf{F}_{3D})$ is the deformation operation we discussed in Sec. 3.3. For mean and deformed meshes we scale the vertices with ground-truth scale $\\sigma_{i}$ before rasterizing.",
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+ "type": "text",
+ "text": "Optimizing Vertex Features. Previous work [2, 3, 16, 38] advocates for an exponential moving average strategy when updating vertex features. We found that this approach is sensitive to initialization and hyperparameters that lead to highly varying performance between training runs. For a more stable and consistent training, we optimize them through backpropagation with $\\Phi$ using the same loss in Eq. (7).",
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+ "type": "text",
+ "text": "3.5. Foreground Detection",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Although the contrastive loss in Eq. (7) helps localize objects implicitly, background regions still produce false-positive matches. Inspired by the emergent behavior of foreground segmentation in ViT attention maps [1], we extract foreground masks $\\overline{\\mathbf{H}}$ , $\\mathbf{H}$ using cross-attention between foreground tokens and decoder features.",
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+ "type": "text",
+ "text": "We initialize two foreground tokens $\\overline{b}, b$ with the CLS—token of the backbone ViT. After each decoder layer or upsampling step, the per-pixel affinity to the foreground token is measured via cross attention:",
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+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {b} ^ {i + 1}, \\boldsymbol {W} ^ {i + 1} = \\operatorname {C r o s s A t t n} \\left(\\boldsymbol {b} ^ {i}, F ^ {i}\\right), \\tag {8}\n$$\n",
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+ "type": "text",
+ "text": "where $F^i$ are the current image features, $\\pmb{b}^{i + 1}$ is the updated foreground token, and $\\pmb{W}^{i + 1}$ are the attention weights. At",
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+ "type": "page_number",
+ "text": "9793",
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+ "type": "text",
+ "text": "the final level, we use min-max normalization to obtain the segmentation $\\mathbf{H} = \\min \\max (\\mathbf{W}^N)$ . The mean-shape segmentation $\\overline{\\mathbf{H}}$ is predicted in the same way.",
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+ "type": "text",
+ "text": "We supervise the final segmentations with masks obtained from rendering the prototypes using ground-truth poses. Since it is a popular choice for segmentation [13, 18] and we have found practical success with it, we adopted the dice loss [45] to optimize the attention weights:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {m a s k}} = \\frac {\\mathcal {L} _ {\\text {d i c e}} (\\mathbf {H} , \\mathbf {H} _ {G T}) + \\mathcal {L} _ {\\text {d i c e}} (\\overline {{\\mathbf {H}}} , \\overline {{\\mathbf {H}}} _ {G T})}{2}. \\tag {9}\n$$\n",
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+ "type": "text",
+ "text": "3.6. Inference",
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+ "type": "text",
+ "text": "During inference time, we determine the objects contained in an image $\\mathbf{I}$ using the trained feature extractor $\\Phi$ and the prototypes through correspondences from feature matching. First, $\\Phi$ is queried for the feature maps $\\overline{\\mathbf{F}}_{2D},\\mathbf{F}_{2D}$ and the foreground heatmaps $\\overline{\\mathbf{H}},\\mathbf{H}$ , which are thresholded using a confidence parameter $t_1$ to obtain binary foreground segmentations. Then, two dense correspondence mappings $\\bar{\\mathcal{N}}_{3D}^{2D},\\mathcal{N}_{3D}^{2D}$ are established between the prototypes and the feature maps. Considering $\\overline{\\mathbf{F}}_{2D}$ , the set of correspondences is established as:",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\bar {\\mathcal {N}} _ {3 D} ^ {2 D} = \\left\\{\\left(\\boldsymbol {p} _ {i}, v _ {k}, \\rho (v _ {k})\\right) \\mid \\boldsymbol {p} _ {i} \\in \\overline {{\\mathbf {F}}} _ {2 D}, \\right. \\\\ v _ {k} = \\underset {\\theta_ {k} \\in \\bigcup_ {c} \\mathbf {F} _ {3 D} ^ {c}} {\\arg \\max } f _ {i} ^ {\\top} \\theta_ {k} \\}, \\tag {10} \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "where the membership function $\\rho(v_k) = c$ returns the category label $c$ of the mesh to which the matched vertex $v_k$ belongs. We remove noisy correspondences which fall outside of $\\overline{\\mathbf{H}}$ or have a similarity score below a second confidence threshold $t_2$ .",
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+ "text": "a) Detection and 6D Pose Estimation. We use the correspondence set $\\bar{\\mathcal{N}}_{3D}^{2D}$ to simultaneously detect objects and estimate their initial 6D pose. If it is known a-priori that there is only a single instance per category in the scene, one could group correspondences by category label and solve this problem via sequential application of PnP [31] paired with RANSAC [17]. However, this assumption is rarely valid in practice. To handle scenes with multiple instances from the same category, we use Progressive-X (ProgX) [5], a multi-model fitting algorithm that enables PnP to detect multiple object poses. ProgX extends GraphCut RANSAC [4] to the multi-model setting via a sequential hypothesis generation algorithm that can separate correspondences into individual instances. For each class $c$ , we run ProgX on the subset $\\bar{\\mathcal{N}}^c \\subset \\bar{\\mathcal{N}}_{3D}^{2D}$ to obtain a set of 6D poses:",
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+ "text": "\n$$\n\\mathcal {P} _ {6 D} = \\bigcup_ {c} \\left\\{\\left(\\overline {{\\mathbf {R}}}, \\bar {\\mathbf {t}}, c\\right) \\mid \\forall \\left(\\overline {{\\mathbf {R}}}, \\bar {\\mathbf {t}}\\right) \\in \\mathrm {M M - P n P} \\left(\\overline {{\\mathcal {N}}} ^ {c}\\right) \\right\\}, \\tag {11}\n$$\n",
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+ "text": "b) 9D Pose Refinement. For each detected object $i$ , we refine the initial pose $(\\overline{\\mathbf{R}}_i, \\overline{\\mathbf{t}}_i, c) \\in \\mathcal{P}_{6D}$ to account",
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+ "text": "for instance-specific size and improve their accuracy using $\\mathcal{N}_{3D}^{2D}$ . We select a subset $\\mathcal{N}_i\\subset \\mathcal{N}_{3D}^{2D}$ , where 1) the 2D point lies within $\\mathbf{H}$ , 2) its similarity score is above the threshold $t_2$ , and 3) its 2D coordinate was considered an inlier according to the 6D pose and category-level geometry.",
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+ "text": "We deform the category-level mesh by scaling vertices along the principal axes with a deformation multiplier $\\mathbf{d} \\in \\mathbb{R}^3$ . Refinement is done by minimizing the reprojection error:",
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+ "text": "\n$$\n\\boldsymbol {E} (\\mathbf {K}, \\mathbf {R}, \\mathbf {t}, \\mathbf {d}, \\mathcal {N} _ {i}) = \\sum_ {v _ {k}, \\boldsymbol {p} _ {k} \\in \\mathcal {N} _ {i}} \\| (\\mathbf {K R} (\\mathbf {d} \\odot v _ {k}) + \\mathbf {t}) - \\boldsymbol {p} _ {k} \\| _ {2} ^ {2}. \\tag {12}\n$$\n",
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+ "text": "The optimization proceeds in two steps, where the deformation is obtained using the 6D rotation and translation, which are subsequently refined using the deformation:",
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+ "text": "\n$$\n\\mathbf {d} _ {i} = \\min _ {\\mathbf {d}} \\boldsymbol {E} (\\mathbf {K}, \\overline {{\\mathbf {R}}} _ {i}, \\bar {\\mathbf {t}} _ {i}, \\mathbf {d}, \\mathcal {N} _ {i}) \\tag {13}\n$$\n",
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+ "text": "\n$$\n\\mathbf {R} _ {i}, \\mathbf {t} _ {i} = \\min _ {\\mathbf {R}, \\mathbf {t}} \\boldsymbol {E} (\\mathbf {K}, \\mathbf {R}, \\mathbf {t}, \\mathbf {d} _ {i}, \\mathcal {N} _ {i}). \\tag {14}\n$$\n",
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+ "text": "The final pose of object $i$ is then given as $(\\mathbf{R}_i, \\mathbf{t}_i, \\mathbf{s}_i, c_i)$ , where $\\mathbf{s}_i$ is obtained as the size of the bounding box of $\\mathbf{V}^{c_i}$ multiplied with $\\mathbf{d}_i$ .",
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+ "type": "text",
+ "text": "4. Experiments",
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+ "text": "In the following, we explain our experimental setup and then discuss the results of our single-stage pose estimation approach on real, synthetic, and corrupted data. For further results and more detailed comparisons, we refer the reader to our supplemental material.",
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+ "text": "4.1. Experiment Setup",
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+ "text": "Datasets. We evaluate our method on the popular category-level 9D pose estimation benchmarks CAMERA25 [51] and REAL275 [51]. REAL275 is a real-world dataset that consists of 4.3K training images of 7 scenes and 2.75K testing images of 6 scenes. CAMERA25 supplements the real data with 275K synthetic training images and 25K evaluation images of rendered objects with real-world backgrounds. Both datasets contain objects from six categories: bottle, bowl, camera, can, laptop, and mug.",
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+ "text": "Evaluation Metrics. Following previous work [59], we use scale-agnostic evaluation metrics to remove the scale-depth ambiguity. To evaluate 3D detection and object size estimation, we report the mean average of the Normalized 3D Intersection over Union (NIoU) metric at thresholds $25\\%$ , $50\\%$ , and $75\\%$ . For pose estimation, we individually report the rotation error and scale-normalized translation error at the different thresholds $0.2d$ , $0.5d$ , $5^{\\circ}$ , $10^{\\circ}$ , and on joint thresholds $5^{\\circ}0.2d$ , $5^{\\circ}0.5d$ , $10^{\\circ}0.2d$ , $10^{\\circ}0.5d$ . In addition, we also report results on absolute metrics for comparable thresholds. Our work focuses on joint detection and pose estimation; therefore, we do not remove objects with",
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+ "text": "9794",
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+ "table_body": "| Method | N IoU25 | N IoU50 | N IoU75 | 5°0.2d | 5°0.5d | 10°0.2d | 10°0.5d | 0.2d | 0.5d | 5° | 10° |
| MSOS [30] | 36.9 | 9.7 | 0.7 | - | - | 3.3 | 15.3 | 10.6 | 50.8 | - | 17.0 |
| OLD-Net [15] | 35.4 | 11.4 | 0.4 | 0.9 | 3.0 | 5.0 | 16.0 | 12.4 | 46.2 | 4.2 | 20.9 |
| DMSR [52] | 57.2 | 38.4 | 9.5 | 15.1 | 23.7 | 25.6 | 45.2 | 35.0 | 67.3 | 27.4 | 52.0 |
| LaPose [59] | 70.7 | 47.9 | 15.8 | 15.7 | 21.3 | 37.4 | 57.4 | 46.9 | 78.8 | 23.4 | 60.7 |
| Ours | 75.2 | 53.7 | 19.2 | 25.1 | 31.8 | 43.7 | 66.1 | 53.5 | 83.7 | 32.1 | 68.8 |
",
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+ "type": "table",
+ "img_path": "images/690a531f23cdd54399d357f5a2aa9a18703835ac272c9f1751c1eef270d6973f.jpg",
+ "table_caption": [
+ "Table 1. Comparison with state-of-the-art methods on REAL275 using scale-agnostic evaluation metrics. As visible, we set a new state of the art by outperforming the baseline methods in all metrics."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | NIOU25 | NIOU50 | NIOU75 | 5°0.2d | 5°0.5d | 10°0.2d | 10°0.5d | 0.2d | 0.5d | 5° | 10° |
| MSOS [30] | 35.1 | 9.9 | 0.8 | - | - | 5.9 | 31.6 | 8.9 | 47.2 | - | 48.6 |
| OLD-Net [15] | 48.7 | 19.5 | 1.7 | 4.7 | 15.9 | 12.9 | 39.6 | 19.1 | 60.0 | 20.5 | 50.5 |
| DMSR [52] | 73.6 | 45.1 | 11.1 | 26.1 | 43.6 | 38.2 | 67.5 | 42.5 | 79.6 | 47.3 | 74.2 |
| LaPose[59] | 74.1 | 45.2 | 12.5 | 29.4 | 53.9 | 39.2 | 74.4 | 41.2 | 80.2 | 58.5 | 82.7 |
| Ours | 73.9 | 47.6 | 18.1 | 37.2 | 57.6 | 45.2 | 75.5 | 47.6 | 83.4 | 60.5 | 80.8 |
",
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+ "img_path": "images/62b61e9eb44d01b21d48d74df1ef2cb1d229bd2bc921cf40c85322cd8b43f659.jpg",
+ "table_caption": [
+ "Table 2. Comparison with state-of-the-art methods on CAMERA25 using scale-agnostic evaluation metrics. We assume that the lower $10^{\\circ}$ performance is due to small objects in CAMERA25, yielding less correspondences. Our method achieves the highest accuracy on 9 out of the 11 metrics."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | IoU50 | IoU75 | 5°5cm | 5°10cm | 10°5cm | 10°10cm |
| MSOS [30] | 13.6 | 1.0 | - | - | - | 11.8 |
| OLD-Net [15] | 8.1 | 0.3 | 0.5 | 2.0 | 2.8 | 10.4 |
| DMSR [52] | 15.9 | 3.3 | 6.1 | 13.4 | 10.5 | 25.0 |
| LaPose [59] | 17.5 | 2.6 | 6.3 | 13.6 | 12.5 | 30.5 |
| Ours | 17.5 | 2.6 | 7.2 | 17.7 | 10.4 | 29.4 |
",
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+ "text": "Table 3. Results on REAL275 using absolute metrics. Predicting object scales from RGB images alone is challenging and not having 2D bounding boxes during inference exacerbates this problem, leading to worse performance of our trained scale prediction network, and consequently less precise metric scale translations. Nevertheless, our method is competitive in performance, either matching or outperforming the baselines in 3 out of the 6 considered metrics.",
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+ "text": "low detection thresholds as in previous work [51], but evaluate performance on all detected objects as proposed by [59].",
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+ "type": "text",
+ "text": "Implementation Details. To train our model on the REAL275 dataset, we use a mixture of $25\\%$ real-world images and $75\\%$ synthetic images from the CAMERA25 training set, similar to [51]. For the results on CAMERA25, we follow prior work [15, 30, 52, 59] and train a separate model without the REAL275 images.",
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+ "type": "text",
+ "text": "For each baseline, we use the detection results from [48] for a fair comparison and reproduce the numbers with the public checkpoints of their methods where possible. Notably, MSOS [30] does not have code publicly available at the time of writing, which is why we use the numbers provided by [59]. For more implementation details about our method, we refer the reader to our supplementary material.",
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+ "text": "4.2. Comparison with State-of-the-Art Methods",
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+ "type": "text",
+ "text": "Results with Scale-Agnostic Metrics. In Tab. 1, we compare our method with state-of-the-art RGB-only category-level pose estimation methods on the REAL275 benchmark under scale-agnostic evaluation metrics. As visible, our method consistently outperforms all baselines under scale-agnostic metrics.",
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+ "type": "text",
+ "text": "As can be seen in Tab. 2, our method also shows strong performance on synthetic data. While it falls behind on coarse rotation accuracy, it still outperforms baselines in 9 out of 11 metrics. A likely reason is that CAMERA25 contains many smaller objects (high depth or small scale), and performance could likely be increased by using higher-resolution features at the cost of slower inference speed.",
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+ "type": "text",
+ "text": "Results with Absolute Metrics. To measure pose estimation quality under metric scale, we follow [59] and decouple scale prediction from pose estimation. Since we do not use a dedicated detection model, we cannot use their pre-trained model. Instead, we train the same scale network using their code to predict a per-instance scale parameter, given the 2D projection of our object prototype with the estimated pose.",
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+ "type": "text",
+ "text": "We show the performance of our method in combination with the scale prediction network Tab. 3. Our results are competitive due to the strong performance in the normalized space. However, we could not reproduce the same level of performance from[59] for the scale estimation network. We believe that this is due to the network that was trained on 2D bounding boxes being more robust during inference than our version, which was trained on the prototype projections.",
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+ "type": "text",
+ "text": "Qualitative Results. Finally, Fig. 3 shows estimated",
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+ "table_body": "| Source | Method | ΔNIOU25 | ΔNIOU50 | ΔNIOU75 | Δ5°0.2d | Δ5°0.5d | Δ10°0.2d | Δ10°0.5d | Δ0.2d | Δ0.5d | Δ5° | Δ10° |
| ROI | OLD-Net[15] | -14.4% | -24.6% | -50.0% | -44.4% | -36.7% | -28.0% | -23.8% | -16.1% | -10.8% | -23.8% | -18.2% |
| DMSR[52] | -3.3% | -7.3% | -13.7% | -17.9% | -18.1% | -8.2% | -10.4% | -4.6% | -2.7% | -17.5% | -11.5% |
| LaPose[59] | -9.3% | -16.9% | -18.4% | -28.7% | -23.9% | -25.4% | -16.6% | -18.3% | -6.2% | -21.4% | -14.3% |
| Image | OLD-Net[15] | -28.0% | -38.6% | -50.0% | -55.6% | -43.3% | -46.0% | -41.3% | -34.7% | -26.4% | -23.8% | -24.9% |
| DMSR[52] | -13.8% | -14.3% | -22.1% | -24.5% | -27.8% | -16.4% | -22.1% | -13.1% | -15.2% | -26.6% | -22.5% |
| LaPose[59] | -22.9% | -24.6% | -22.8% | -29.3% | -28.6% | -29.4% | -27.7% | -25.6% | -21.2% | -26.1% | -25.9% |
| Ours | -11.0% | -14.0% | -21.7% | -17.2% | -13.5% | -16.0% | -12.9% | -12.7% | -9.5% | -13.5% | -12.6% |
",
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+ "table_caption": [
+ "Table 4. Robustness experiments on the REAL275 [51] benchmark. We report loss in accuracy compared to the model evaluated on uncorrupted data averaged over 8 types of corruptions. The top shows results for corruption-free detection with only corrupted crops during pose estimation and the bottom shows corruptions during both stages. Corruptions during pose estimation alone already reduce the performance significantly. However, the on the image level the two-stage approaches suffer even more, indicating that failures in the detection are severe. Our single-stage approach is much less affected by noise and shows the greatest robustness."
+ ],
+ "table_footnote": [],
+ "table_body": "| Detection Source | NIOU25 | NIOU50 | NIOU75 | 5°0.2d | 5°0.5d | 10°0.2d | 10°0.5d | 0.2d | 0.5d | 5° | 10° |
| GT Object Mask | 72.1 | 50.3 | 17.8 | 23.0 | 29.6 | 40.4 | 61.4 | 50.4 | 81.0 | 29.9 | 63.7 |
| GT Proto. Mask | 79.5 | 55.3 | 19.5 | 25.6 | 32.2 | 44.1 | 66.7 | 53.4 | 84.2 | 32.5 | 69.2 |
| Mask-RCNN [18] | 70.4 | 48.8 | 17.7 | 22.4 | 28.7 | 38.9 | 58.4 | 48.9 | 79.1 | 28.9 | 60.4 |
| None (ours) | 75.2 | 53.7 | 19.2 | 25.1 | 31.8 | 43.7 | 66.1 | 53.5 | 83.7 | 32.1 | 68.8 |
",
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+ "type": "text",
+ "text": "Table 5. To isolate the pose estimation accuracy of our method, we frame the problem as single-object pose estimation by providing different ROIs. As visible, our method comes close to the upper bound (GT Proto. Mask), showing our model can detect objects well and simultaneously reason about their poses with high accuracy. Our method also works well on the tight \"GT Object Masks\" but the performance drops significantly when using the fine-tuned Mask-RCNN, indicating that our approach outperforms it.",
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+ "text": "poses on REAL275 of our method and the baselines. As can be seen, two-stage approaches suffer from the error propagation of detection failures, whereas our method identifies objects much more confidently. Additionally, our method significantly improves the rotation accuracy which is most notable in the laptop category. For more detailed per-category results, we refer the reader to our supplemental material.",
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+ "text": "4.3. Robustness to Image Degradations",
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+ "text": "Setting. To verify the robustness of two-stage vs. single-stage pose estimation, we conduct experiments on the REAL275 dataset with added corruptions from the imagecorruptions [20] library. We choose 8 corruptions of different types and report the average performance in the main part of the paper. For the choice of corruptions and per-corruption performance, we refer the reader to the supplemental material. For consistency, each method is evaluated using the same set of images and has been trained with the same data augmentations.",
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+ "text": "We design two sets of experiments to study the robustness of the two-stage baselines. To measure the robustness of the pose estimator in isolation, we run the detector on clean images and apply the corruption only on its provided RoI. To evaluate the robustness of the whole framework, we apply corruptions on an image level. As it is the most commonly used model, we use the pre-trained Mask-RCNN [18] from [48] to get detection results for all base",
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+ "text": "lines. Note that we omit MSOS [30] from the robustness experiments, since to the best of our knowledge their code is not (or no longer) public.",
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+ "text": "Results. We report the decrease in performance under image corruptions for the full task at the bottom of Tab. 4. Our performance drops by only $14\\%$ when considering the mean and median on all metrics. In comparison, baselines suffer much more, losing anywhere from $19\\% - 37\\%$ mean or $22\\% - 38\\%$ median performance.",
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+ "text": "4.4. Pose Estimation Quality",
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+ "text": "By framing detection and pose estimation as a single-stage problem, it is hard to quantify the success of either component individually. To measure the quality of our pose estimation in isolation, we try to decouple our framework into two stages. We do so by obtaining masks from three different sources. First, we use ground-truth object segmentation masks. Second, we use projected object prototype masks using ground-truth 9D poses. Third, we use bounding boxes provided by the same fine-tuned Mask-RCNN [18] as our baselines. The masks are then used to identify per-object correspondences for single-object pose estimation. To be consistent with our main method, we also use Progressive-X [5] as the solver, but we limit the maximum of predicted models to one per RoI.",
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+ "type": "text",
+ "text": "Tab. 5 shows the results of providing RoIs to our method. It is important to note that using instance-level detections from either Mask-RCNN or the ground-truth segmentation",
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+ "Figure 3. Qualitative comparison on REAL275[51]. We compare our model (second to last column) with all baselines and with ground truth (last column). Some failures due to poor detection results of the baselines are highlighted (row 2, 3, and 5). In rows 1 and 4 our method outperforms baselines in terms of rotation accuracy."
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+ "text": "mask is not ideal for our method as it is optimized to work with the projected prototype masks. However, we find that our method also works well with the tightly fitting ground-truth segmentation masks (first row) but the performance drops steeply when using the predicted Mask-RCNN masks. The upper bound is shown in the second row, which provides ground-truth detections and 2D correspondences to our method. As can be seen, our method (fourth row) only falls noticeably behind in the $NIOU_{25}$ and performs close to the upper bound on all other metrics. This shows that our joint approach outperforms Mask-RCNN in detection performance.",
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+ "text": "5. Conclusion",
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+ "text": "In this work, we introduced the first unified RGB-only category-level detection and pose estimation framework that operates with a single representation. Using neural",
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+ "text": "mesh models as 3D object prototypes leads to robust feature representations that can be used for 2D/3D correspondence estimation and downstream multi-model pose estimation to jointly solve the detection and pose estimation tasks. We achieve state-of-the-art results for pose estimation on the popular REAL275 benchmark, and our evaluation has shown that our single-stage model is significantly more robust to image degradations than its two-stage counterparts.",
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+ "text": "We gratefully acknowledge the stimulating research environment of the GRK 2853/1 \"Neuroexplicit Models of Language, Vision, and Action\", funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project number 471607914. The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Com",
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+ "text": "puting Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the BayernKI project b266be. BayernKI funding is provided by Bavarian state authorities.",
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+ "[50] Boyan Wan, Yifei Shi, and Kai Xu. Socs: Semantically-aware object coordinate space for category-level 6d object pose estimation under large shape variations. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14065-14074, 2023. 2",
+ "[51] He Wang, Srinath Sridhar, Jingwei Huang, Julien Valentin, Shuran Song, and Leonidas J Guibas. Normalized object coordinate space for category-level 6d object pose and size estimation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2642-2651, 2019. 1, 2, 3, 5, 6, 7, 8",
+ "[52] Jiaxin Wei, Xibin Song, Weizhe Liu, Laurent Kneip, Hongdong Li, and Pan Ji. Rgb-based category-level object pose estimation via decoupled metric scale recovery. In 2024 IEEE International Conference on Robotics and Automation (ICRA), pages 2036-2042. IEEE, 2024. 1, 2, 6, 7",
+ "[53] Bowen Wen, Wenzhao Lian, Kostas Bekris, and Stefan Schaal. Catgrasp: Learning category-level task-relevant grasping in clutter from simulation. In 2022 International Conference on Robotics and Automation (ICRA), pages 6401-6408. IEEE, 2022. 1",
+ "[54] Bowen Wen, Wenzhao Lian, Kostas Bekris, and Stefan Schaal. You only demonstrate once: Category-level manipulation from single visual demonstration. arXiv preprint arXiv:2201.12716, 2022. 1",
+ "[55] Yu Xiang, Tanner Schmidt, Venkatraman Narayanan, and Dieter Fox. PoseCNN: A convolutional neural network for 6d object pose estimation in cluttered scenes. arXiv preprint arXiv:1711.00199, 2017. 3",
+ "[56] Yi Xin, Siqi Luo, Haodi Zhou, Junlong Du, Xiaohong Liu, Yue Fan, Qing Li, and Yuntao Du. Parameter-efficient fine-tuning for pre-trained vision models: A survey. arXiv preprint arXiv:2402.02242, 2024. 4",
+ "[57] Sergey Zakharov, Ivan Shugurov, and Slobodan Ilic. Dpod: 6d pose object detector and refiner. In Proceedings of the IEEE/CVF international conference on computer vision, pages 1941-1950, 2019. 3",
+ "[58] Jiyao Zhang, Mingdong Wu, and Hao Dong. Genpose: generative category-level object pose estimation via diffusion models. In Proceedings of the 37th International Conference on Neural Information Processing Systems, pages 54627-54644, 2023. 1, 2",
+ "[59] Ruida Zhang, Ziqin Huang, Gu Wang, Chenyangguang Zhang, Yan Di, Xingxing Zuo, Jiwen Tang, and Xiangyang Ji. Lapose: Laplacian mixture shape modeling for rgb-based category-level object pose estimation. In European Conference on Computer Vision, pages 467-484. Springer, 2024. 1, 2, 5, 6, 7",
+ "[60] Jun Zhou, Kai Chen, Linlin Xu, Qi Dou, and Jing Qin. Deep fusion transformer network with weighted vector-wise keypoints voting for robust 6d object pose estimation. In"
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diff --git a/2025/Unified Category-Level Object Detection and Pose Estimation from RGB Images using 3D Prototypes/5a18f1d0-5854-4d52-9b3d-42b8f051f9c6_model.json b/2025/Unified Category-Level Object Detection and Pose Estimation from RGB Images using 3D Prototypes/5a18f1d0-5854-4d52-9b3d-42b8f051f9c6_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..3e17568356547c518935f440d8c90edd85884745
--- /dev/null
+++ b/2025/Unified Category-Level Object Detection and Pose Estimation from RGB Images using 3D Prototypes/5a18f1d0-5854-4d52-9b3d-42b8f051f9c6_model.json
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+[
+ [
+ {
+ "type": "header",
+ "bbox": [
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+ "angle": 0,
+ "content": "CVF"
+ },
+ {
+ "type": "header",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.197,
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+ "angle": 0,
+ "content": "Unified Category-Level Object Detection and Pose Estimation from RGB Images using 3D Prototypes"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Tom Fischer\\*1,2 Xiaojie Zhang\\*1,2 Eddy Ilg\\* 1 Saarland University \\*2 University of Technology Nuremberg"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.274,
+ 0.327,
+ 0.29
+ ],
+ "angle": 0,
+ "content": "Abstract"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.486,
+ 0.593
+ ],
+ "angle": 0,
+ "content": "Recognizing objects in images is a fundamental problem in computer vision. Although detecting objects in 2D images is common, many applications require determining their pose in 3D space. Traditional category-level methods rely on RGB-D inputs, which may not always be available, or employ two-stage approaches that use separate models and representations for detection and pose estimation. For the first time, we introduce a unified model that integrates detection and pose estimation into a single framework for RGB images by leveraging neural mesh models with learned features and multi-model RANSAC. Our approach achieves state-of-the-art results for RGB category-level pose estimation on REAL275, improving on the current state-of-the-art by \\(22.9\\%\\) averaged across all scale-agnostic metrics. Finally, we demonstrate that our unified method exhibits greater robustness compared to single-stage baselines. Our code and models are available at github.com/Fischer-Tom/unified-detection-and-pose-estimation."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.625,
+ 0.222,
+ 0.64
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Finding out whether an object is present in an image, where it is located, and how it is oriented in space, are fundamental problems of scene understanding. They are commonly referred to as object detection and pose estimation, and are critically relevant for applications in robotics [27, 53, 54], autonomous driving [28, 43] and augmented reality [39]. In object pose estimation, one distinguishes between methods that work only on known instances [19, 29, 32, 44, 60], and methods that are able to generalize within object categories [12, 15, 33, 35, 51, 52, 58, 59]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Category-level pose estimation has made significant progress in recent years [12, 15, 33, 35, 51, 52, 58, 59]. However, most current work still relies on accurate depth information to recover precise poses [12, 58], restricting the"
+ },
+ {
+ "type": "image",
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+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 1. The top shows existing pipelines that are made up of separate stages for object detection and and single-object pose estimation. In the bottom, we show our pipeline that uses a single representation and model for detection and pose estimation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "use to devices and working conditions where depth can be captured. Pose estimation from RGB images alone [15, 30, 36, 52, 59] is less explored and a much harder task."
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+ "content": "Methods can be further classified according to the used detection approach. Although there are some RGB-D methods that utilize a shared representation with individual detection and pose heads [24, 51], most methods completely decouple the problem and use separate models and representations. All current RGB methods fall into this category of two-stage methods and use separate models per task, where as shown in Figure 1, objects are first detected, cropped, and then passed into a single-object pose estimator. This naturally places strong emphasis on the accuracy of the detection model, as failures cannot be recovered later, and comes with the downside of having to maintain two separate models."
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+ "type": "text",
+ "bbox": [
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+ "content": "For the first time, we show that a single unified model can be established for both tasks in the case of RGB images, and that this approach leads to improved accuracy and robustness. Our model leverages neural mesh models [2, 38] as a 3D representation of object categories, where a 2D feature extractor for images and the neural features on the"
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+ "type": "page_footnote",
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+ "content": "*Equal contribution. Corresponding email: {tom.fischer, xiaojie.zhang}@utn.de."
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+ "content": "meshes are learned jointly during training. During inference, the image features are matched with features of the 3D meshes and multi-model RANSAC PnP [5] is used to detect different object instances and estimate their poses."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Our approach achieves a new state of the art and outperforms the current RGB-only state-of-the-art [59] in pose estimation by \\(22.9\\%\\) when averaged across all scale-agnostic metrics. The results show that a common error source in two-stage pipelines is the detector and that our single-stage model is significantly more robust than its two-stage counterparts. In summary, our contributions are:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We propose the first single-stage framework for category-level multi-object pose estimation from single RGB images."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- For the first time, we leverage neural mesh models jointly for object detection and pose estimation by combining them with multi-model RANSAC PnP and subsequent pose refinement."
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "- We achieve state-of-the-art performance on pose estimation benchmark REAL275 w.r.t. to accuracy and robustness, verifying the effectiveness of our object representation and single-stage multi-object inference pipeline."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "content": "2. Related Work"
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+ "angle": 0,
+ "content": "Both object detection [8, 41] and object pose estimation [37] are long-standing tasks in computer vision. Although the first has converged to broadly accepted models, a variety of approaches are still being explored for the latter. Early pose estimation methods [6, 14, 42] operate by matching hand-crafted features to instance-level 3D models. Today, deep learning has replaced feature descriptors, but many works are still restricted to estimate poses of object instances that were present during training [19, 29, 32, 44, 60]."
+ },
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+ "type": "text",
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+ "content": "Category-level pose estimation [12, 35, 51, 58, 59] was introduced by [51] to allow generalization to unseen instances within a set of established categories without requiring additional training or accurate CAD models during inference. The strong variation in geometry and scale within categories makes this a highly challenging problem. Shape-prior-free methods [12, 33, 35, 51] try to learn a generalizable representation without any guidance from CAD models during training."
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+ "content": "Shape-prior-based methods, on the other hand, use CAD models and/or simple derived properties such as sizes or bounding boxes to integrate geometric priors. The pose is then either regressed directly from a trained network, or solved for using predicted correspondences in the form of a Normalized Object Coordinate Space (NOCS) [51] with the (often deformed) shape prior using a non-differentiable alignment algorithm such as PnP [21, 31] or the Umyama algorithm [49]. Our method falls into the above category,"
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+ "content": "but estimates the correspondences from feature matching with 3D neural meshes."
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+ "content": "Neural Mesh Models [2] are shape-prior-based methods and were initially proposed for robust category-level single-object rotation estimation. Follow-up work extended it to 6D pose estimation [38], however, they still relied on single-object training datasets and both methods [2, 38] are constrained to per-category networks that have to be calibrated against each other or require a (multi-label) classification model to identify present object categories. Later works removed the need for separate feature representations to allow robust classification, but they cannot estimate translations or handle multiple objects [16, 26]. Our work removes all these restrictions and can both detect objects and estimate their poses with a single, shared representation."
+ },
+ {
+ "type": "title",
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+ "content": "2.1. Two-Stage Methods"
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+ "angle": 0,
+ "content": "The vast majority of object pose estimation methods first locates the objects using off-the-shelf detection models [18, 41] to detect Regions of Interest (RoI) as 2D segmentation masks or bounding boxes. The objects are then cropped from the image and processed by a second model to predict the final poses, splitting the approaches into two stages."
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+ "angle": 0,
+ "content": "RGB-D Approaches have access to the incomplete point clouds of the observed instances derived from the depth map. These can be used for regression in combination with [34] or without [12, 35, 50] shape priors, or to align them with a shape prior [9, 48] using the Umayama algorithm [49]. In contrast to the above, our method does not require depth as input."
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+ "type": "text",
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+ "angle": 0,
+ "content": "RGB-Only Approaches face a more challenging problem due to the inherent ambiguity in this setting, which is why these methods are less prominent. In particular, the lack of depth information introduces a fundamental ambiguity between distance and scale, making it impossible to recover these properties from observations. To this end, Zhang et al. [59] introduced a set of scale-agnostic metrics that we also utilize in our work. OLD-Net [15] and DMSR [52] leverage a shape prior-based alignment technique and LaPose [59] uses a shape prior-based regression approach. MSOS [30], on the other hand, does not utilize any shape prior and directly estimates NOCS shape and the metric-scale shape of the object for downstream alignment. Although these two-stage approaches are successful in practice, they learn separate representations for both stages and are prone to errors of the first stage. In contrast to the above, we present a single-stage method with higher accuracy and robustness."
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+ "content": "2.2. Single-Stage Methods"
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+ "angle": 0,
+ "content": "Single-stage methods couple detection and pose estimation into an end-to-end architecture. Existing work on end-to-end pose estimation focuses mainly on the instance-level"
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+ "content": null
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+ "content": "Figure 2. We present a unified framework for solving detection and pose estimation with 3D object prototypes. Feature Extraction (Sec. 3.3): Given an RGB image, a frozen DINOv2 model with trainable adapters is combined with a Geometric Feature Decoder to produce two feature maps \\(\\overline{\\mathbf{F}}_{2D}\\), \\(\\mathbf{F}_{2D}\\) and foreground segmentations \\(\\bar{\\mathbf{H}}\\), \\(\\mathbf{H}\\). 3D Prototype Learning (Sec. 3.4): During training, the Adapters and the Geometric Feature Decoder are jointly trained with a set of Neural Mesh Models [2] using a contrastive loss. Detection & 6D Pose Estimation (Sec. 3.6 a): After training, 6D object poses are obtained with a multi-model fitting algorithm from dense 2D/3D correspondences between category-level features \\(\\overline{\\mathbf{F}}_{2D}\\) and all vertex features. 9D Pose Refinement (Sec. 3.6 b): For each identified instance, a deformation parameter is optimized for by aligning correspondences from instance-level features \\(\\mathbf{F}_{2D}\\) with its 6D pose."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "setting [7, 11, 22, 23, 46, 47, 55, 57]. However, there are category-level methods that utilize a shared representation and task-specific heads. NOCS [51] uses a shared feature extraction backbone that provides ROIs paired with individual heads for NOCS-map and instance segmentation. The category-level approaches [24, 25] require RGB-D as input and are shape-prior-based regression methods that perform joint center-point detection, reconstruction, and pose estimation. CenterPose [36] comes close to an RGB-only single-stage method, but requires the class labels of the objects present in an image and therefore is not a stand-alone method. In contrast, our work proposes the first RGB-only single-stage approach to unify the complete detection and pose estimation in a shared representation."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "3. Method"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We present a single-stage framework for RGB-only object detection and category-level 9D pose estimation. Our method aligns image features with a set of 3D object prototypes to infer object properties from 2D/3D correspondences obtained from feature matching. An overview is shown in Fig. 2."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "content": "3.1. Task Definition"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Given an input image \\(\\mathbf{I} \\in \\mathbb{R}^{H \\times W \\times 3}\\) and camera intrinsics \\(\\mathbf{K} \\in \\mathbb{R}^{3 \\times 3}\\), our goal is to estimate the set of object properties:"
+ },
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+ "type": "equation",
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+ "content": "\\[\n\\mathcal {O} (\\mathbf {I}, \\mathbf {K}) = \\{(c _ {i}, \\mathbf {s} _ {i}, \\mathbf {R} _ {i}, \\mathbf {t} _ {i}) \\} _ {i = 1} ^ {N}, \\qquad (1)\n\\]"
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+ "bbox": [
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+ "angle": 0,
+ "content": "where each object \\(i\\) is described by category \\(c_{i}\\), 3D size \\(\\mathbf{s}_i\\in \\mathbb{R}^3\\), rotation \\(\\mathbf{R}_i\\in SO(3)\\), and translation \\(\\mathbf{t}_i\\in \\mathbb{R}^3\\). We define its scalar instance scale as \\(\\sigma_{i} = \\| \\mathbf{s}_{i}\\|_{2}\\). Throughout the remaining parts of this section, we refer to sets in script font (i.e. \\(\\mathcal{O}\\)); vectors, tuples, and tensors in bold font (i.e. \\(\\mathbf{R}\\)); and scalars in standard math font (i.e. \\(c\\))."
+ },
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+ "type": "title",
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+ "content": "3.2. Representation"
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+ "type": "text",
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+ "angle": 0,
+ "content": "We represent 3D object prototypes with Neural Mesh Models [2, 16, 26, 38], which have shown high generalization and robustness for single-object pose estimation. Each category \\(c\\) has a prototypical mesh \\(\\mathbf{M}^c = (\\mathbf{V}^c, \\mathbf{A}^c, \\mathbf{F}_{3D}^c)\\), where \\(\\mathbf{V}^c \\in \\mathbb{R}^{V \\times 3}\\) are vertex coordinates in object space, \\(\\mathbf{A}^c \\in \\mathbb{Z}^{A \\times 3}\\) are triangle indices, and \\(\\mathbf{F}_{3D}^c \\in \\mathbb{R}^{V \\times D}\\) are learned vertex features. The geometry of each mesh is obtained by regularly sampling the surface of the bounding box obtained from the average size \\(\\overline{\\mathbf{s}}^c\\) of the training set, which we normalize to have \\(\\| \\overline{\\mathbf{s}}^c \\|_2 = 1\\). We also keep a scaling factor \\(\\bar{\\sigma}^c\\) that transforms the mesh into one that has the mean scale of the category. If camera poses are available, scenes can be composed from the object prototypes and rendered into an image."
+ },
+ {
+ "type": "title",
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+ "content": "3.3. Feature Extraction"
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+ "angle": 0,
+ "content": "Accurate object localization from 2D/3D correspondences requires that the object geometry aligns well with the visual observations. In category-level pose estimation, one does not have access to instance-level geometries. To address this, we train a 2D feature extractor \\(\\Phi\\) that learns to map the"
+ },
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+ "type": "page_number",
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "input image \\(\\mathbf{I}\\) to a rendering of a scene composed of cuboid prototypes parameterized by \\(\\mathcal{O}(\\mathbf{I},\\mathbf{K})\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.122,
+ 0.484,
+ 0.258
+ ],
+ "angle": 0,
+ "content": "Modeling. As solving for 9D poses from correspondences alone is challenging and tends to fail in practice, we first perform an initial 6D pose estimation, where we rely on a feature map \\(\\overline{\\mathbf{F}}_{2D}\\) that is aligned with the prototypes that follow category-level sizes \\(\\overline{\\mathbf{s}}^c\\). Next, we perform a size refinement with a feature map \\(\\mathbf{F}_{2D}\\), which is aligned with deformed prototypes that match the instance-level sizes \\(\\mathbf{s}_i\\). Since both feature maps are conditioned on the same neural textures, \\(\\overline{\\mathbf{F}}_{2D}\\) can be imagined as a warped variant of \\(\\mathbf{F}_{2D}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.258,
+ 0.484,
+ 0.394
+ ],
+ "angle": 0,
+ "content": "Backbone. The feature extractor \\(\\Phi\\) is trained jointly with the vertex features. This introduces ambiguities that make a good initialization crucial to guide each \\(\\mathbf{F}_{3D}^{c}\\) towards a meaningful representation. Therefore, we build \\(\\Phi\\) on top of the self-supervised pre-trained DINOv2 ViT [40] and embed task-specific information using Parameter-Efficient Fine-Tuning (PEFT) [56]. Following [10], we use a low-rank adaptation (Adapter) in the MLP in each transformer block:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.1,
+ 0.405,
+ 0.483,
+ 0.423
+ ],
+ "angle": 0,
+ "content": "\\[\nx _ {l} ^ {\\prime} = \\operatorname {M L P} (\\operatorname {L N} (x _ {l})) + x _ {l} + \\lambda (\\operatorname {G e L U} (\\operatorname {L N} (x _ {l}) \\cdot D)) \\cdot U, \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.434,
+ 0.484,
+ 0.478
+ ],
+ "angle": 0,
+ "content": "where \\( x_{l} \\) is the output of the previous multi-head attention, \\( \\lambda \\) is a scaling factor [10] and \\( D, U \\) are the down- and up-projection matrices."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.48,
+ 0.484,
+ 0.587
+ ],
+ "angle": 0,
+ "content": "Geometric Feature Decoder. To obtain the features corresponding to the object prototype geometry, we first apply a shared transformer encoder to the backbone features, and subsequently two transformer decoders to obtain \\(\\overline{\\mathbf{F}}_{2D},\\mathbf{F}_{2D}\\). Finally, both feature maps are upsampled to a certain output resolution using a combination of bilinear upsampling and shared convolution layers."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.595,
+ 0.196,
+ 0.611
+ ],
+ "angle": 0,
+ "content": "3.4. Training"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.617,
+ 0.483,
+ 0.662
+ ],
+ "angle": 0,
+ "content": "We consider a training sample with \\(N\\) objects and outline the loss calculation for an object \\(i\\) with prototypical mesh \\(\\mathbf{M}_i = (\\mathbf{V},\\mathbf{A},\\mathbf{F}_{3D})\\), intrinsic matrix \\(\\mathbf{K}\\), and pose \\(\\hat{\\mathbf{R}}_i,\\hat{\\mathbf{t}}_i\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.663,
+ 0.484,
+ 0.767
+ ],
+ "angle": 0,
+ "content": "Setup. We first obtain pixel-level training annotations from rasterize \\((\\mathbf{M}_i, \\mathbf{K}, \\hat{\\mathbf{R}}_i, \\hat{\\mathbf{t}}_i)\\) to obtain projected image location \\(p_k\\) and binary visibility \\(o_k\\) for each vertex \\(v_k \\in \\mathbf{V}\\). Given a 2D feature map \\(\\mathbf{F}\\), we define the annotation set as \\(\\mathcal{Y}(\\mathbf{M}_i, \\mathbf{F}) = \\{ (\\theta_k, f_k, o_k) \\mid \\forall v_k \\in \\mathbf{V} \\}\\), where \\(f_k\\) is the pixel feature at projection \\(p_k\\) in \\(\\mathbf{F}\\), and \\(\\theta_k\\) is the corresponding vertex feature from \\(\\mathbf{F}_{3D}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.768,
+ 0.483,
+ 0.829
+ ],
+ "angle": 0,
+ "content": "Optimizing \\(\\Phi\\). Following [2], we model the probability distribution of any feature \\(f\\) being generated from vertex \\(v_{k}\\) by defining \\(P(f|\\theta_k)\\) using a von Mises-Fisher (vMF) distribution to express the likelihood:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.188,
+ 0.839,
+ 0.483,
+ 0.86
+ ],
+ "angle": 0,
+ "content": "\\[\nP (f | \\theta_ {k}, \\kappa) = C (\\kappa) e ^ {\\kappa \\left(f ^ {\\top} \\cdot \\theta_ {k}\\right)}, \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.871,
+ 0.483,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "with mean \\(\\theta_{\\kappa}\\), concentration parameter \\(\\kappa\\), and normalization constant \\(C(\\kappa)\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.092,
+ 0.906,
+ 0.166
+ ],
+ "angle": 0,
+ "content": "Accurate object poses are obtained when \\( f_{k} \\) can be matched to \\( \\theta_{k} \\), leading to precise 2D/3D correspondences. We optimize for this task using contrastive learning by maximizing Eq. (3) with the feature \\( f_{k} \\), and minimize the likelihood of all other vertices:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.628,
+ 0.177,
+ 0.907,
+ 0.194
+ ],
+ "angle": 0,
+ "content": "\\[\n\\max \\quad P \\left(f _ {k} \\mid \\theta_ {k}, \\kappa\\right), \\tag {4}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.629,
+ 0.197,
+ 0.907,
+ 0.233
+ ],
+ "angle": 0,
+ "content": "\\[\n\\min \\sum_ {\\theta_ {m} \\in \\bar {\\theta} _ {k}} P \\left(f _ {k} \\mid \\theta_ {m}, \\kappa\\right), \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.243,
+ 0.906,
+ 0.304
+ ],
+ "angle": 0,
+ "content": "where the negatives \\(\\overline{\\theta}_k\\) are the features of all noncorresponding vertices including those from different classes. Equations 4 and 5 can be combined into a single loss by taking the negative log-likelihood:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.522,
+ 0.312,
+ 0.906,
+ 0.366
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} (\\mathcal {Y} (\\mathbf {M} _ {i}, \\mathbf {F})) = - \\sum_ {k} o _ {k} \\cdot \\log \\left(\\frac {e ^ {\\kappa \\left(f _ {k} \\cdot \\theta_ {k}\\right)}}{\\sum_ {\\theta_ {m} \\in \\bar {\\theta} _ {k}} e ^ {\\kappa \\left(f _ {k} ^ {\\top} \\cdot \\theta_ {m}\\right)}}\\right), \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.367,
+ 0.906,
+ 0.412
+ ],
+ "angle": 0,
+ "content": "where considering \\(\\kappa\\) as a global hyperparameters allows canceling out the normalization constants \\(C(\\kappa)\\). We compute the full training loss as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.52,
+ 0.421,
+ 0.905,
+ 0.472
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {t r a i n}} = \\sum_ {i} \\frac {\\mathcal {L} \\left(\\mathcal {Y} \\left(\\mathbf {M} ^ {c _ {i}} , \\overline {{\\mathbf {F}}} _ {2 D}\\right)\\right) + \\mathcal {L} \\left(\\mathcal {Y} \\left(\\phi \\left(\\mathbf {M} ^ {c _ {i}}\\right) , \\mathbf {F} _ {2 D}\\right)\\right)}{2 N}, \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.472,
+ 0.906,
+ 0.532
+ ],
+ "angle": 0,
+ "content": "where \\(\\phi (\\mathbf{M}) = (\\phi (\\mathbf{V}),\\mathbf{A},\\mathbf{F}_{3D})\\) is the deformation operation we discussed in Sec. 3.3. For mean and deformed meshes we scale the vertices with ground-truth scale \\(\\sigma_{i}\\) before rasterizing."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.532,
+ 0.906,
+ 0.655
+ ],
+ "angle": 0,
+ "content": "Optimizing Vertex Features. Previous work [2, 3, 16, 38] advocates for an exponential moving average strategy when updating vertex features. We found that this approach is sensitive to initialization and hyperparameters that lead to highly varying performance between training runs. For a more stable and consistent training, we optimize them through backpropagation with \\(\\Phi\\) using the same loss in Eq. (7)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
+ 0.661,
+ 0.719,
+ 0.677
+ ],
+ "angle": 0,
+ "content": "3.5. Foreground Detection"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.684,
+ 0.906,
+ 0.773
+ ],
+ "angle": 0,
+ "content": "Although the contrastive loss in Eq. (7) helps localize objects implicitly, background regions still produce false-positive matches. Inspired by the emergent behavior of foreground segmentation in ViT attention maps [1], we extract foreground masks \\(\\overline{\\mathbf{H}}\\), \\(\\mathbf{H}\\) using cross-attention between foreground tokens and decoder features."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.774,
+ 0.906,
+ 0.834
+ ],
+ "angle": 0,
+ "content": "We initialize two foreground tokens \\(\\overline{b}, b\\) with the CLS—token of the backbone ViT. After each decoder layer or upsampling step, the per-pixel affinity to the foreground token is measured via cross attention:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.595,
+ 0.843,
+ 0.905,
+ 0.862
+ ],
+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {b} ^ {i + 1}, \\boldsymbol {W} ^ {i + 1} = \\operatorname {C r o s s A t t n} \\left(\\boldsymbol {b} ^ {i}, F ^ {i}\\right), \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.87,
+ 0.906,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "where \\(F^i\\) are the current image features, \\(\\pmb{b}^{i + 1}\\) is the updated foreground token, and \\(\\pmb{W}^{i + 1}\\) are the attention weights. At"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.482,
+ 0.945,
+ 0.516,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "9793"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.483,
+ 0.137
+ ],
+ "angle": 0,
+ "content": "the final level, we use min-max normalization to obtain the segmentation \\(\\mathbf{H} = \\min \\max (\\mathbf{W}^N)\\). The mean-shape segmentation \\(\\overline{\\mathbf{H}}\\) is predicted in the same way."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.137,
+ 0.484,
+ 0.213
+ ],
+ "angle": 0,
+ "content": "We supervise the final segmentations with masks obtained from rendering the prototypes using ground-truth poses. Since it is a popular choice for segmentation [13, 18] and we have found practical success with it, we adopted the dice loss [45] to optimize the attention weights:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.132,
+ 0.223,
+ 0.483,
+ 0.255
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {m a s k}} = \\frac {\\mathcal {L} _ {\\text {d i c e}} (\\mathbf {H} , \\mathbf {H} _ {G T}) + \\mathcal {L} _ {\\text {d i c e}} (\\overline {{\\mathbf {H}}} , \\overline {{\\mathbf {H}}} _ {G T})}{2}. \\tag {9}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.265,
+ 0.202,
+ 0.279
+ ],
+ "angle": 0,
+ "content": "3.6. Inference"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.287,
+ 0.484,
+ 0.437
+ ],
+ "angle": 0,
+ "content": "During inference time, we determine the objects contained in an image \\(\\mathbf{I}\\) using the trained feature extractor \\(\\Phi\\) and the prototypes through correspondences from feature matching. First, \\(\\Phi\\) is queried for the feature maps \\(\\overline{\\mathbf{F}}_{2D},\\mathbf{F}_{2D}\\) and the foreground heatmaps \\(\\overline{\\mathbf{H}},\\mathbf{H}\\), which are thresholded using a confidence parameter \\(t_1\\) to obtain binary foreground segmentations. Then, two dense correspondence mappings \\(\\bar{\\mathcal{N}}_{3D}^{2D},\\mathcal{N}_{3D}^{2D}\\) are established between the prototypes and the feature maps. Considering \\(\\overline{\\mathbf{F}}_{2D}\\), the set of correspondences is established as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.157,
+ 0.448,
+ 0.482,
+ 0.499
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\bar {\\mathcal {N}} _ {3 D} ^ {2 D} = \\left\\{\\left(\\boldsymbol {p} _ {i}, v _ {k}, \\rho (v _ {k})\\right) \\mid \\boldsymbol {p} _ {i} \\in \\overline {{\\mathbf {F}}} _ {2 D}, \\right. \\\\ v _ {k} = \\underset {\\theta_ {k} \\in \\bigcup_ {c} \\mathbf {F} _ {3 D} ^ {c}} {\\arg \\max } f _ {i} ^ {\\top} \\theta_ {k} \\}, \\tag {10} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.505,
+ 0.484,
+ 0.579
+ ],
+ "angle": 0,
+ "content": "where the membership function \\(\\rho(v_k) = c\\) returns the category label \\(c\\) of the mesh to which the matched vertex \\(v_k\\) belongs. We remove noisy correspondences which fall outside of \\(\\overline{\\mathbf{H}}\\) or have a similarity score below a second confidence threshold \\(t_2\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.581,
+ 0.484,
+ 0.821
+ ],
+ "angle": 0,
+ "content": "a) Detection and 6D Pose Estimation. We use the correspondence set \\(\\bar{\\mathcal{N}}_{3D}^{2D}\\) to simultaneously detect objects and estimate their initial 6D pose. If it is known a-priori that there is only a single instance per category in the scene, one could group correspondences by category label and solve this problem via sequential application of PnP [31] paired with RANSAC [17]. However, this assumption is rarely valid in practice. To handle scenes with multiple instances from the same category, we use Progressive-X (ProgX) [5], a multi-model fitting algorithm that enables PnP to detect multiple object poses. ProgX extends GraphCut RANSAC [4] to the multi-model setting via a sequential hypothesis generation algorithm that can separate correspondences into individual instances. For each class \\(c\\), we run ProgX on the subset \\(\\bar{\\mathcal{N}}^c \\subset \\bar{\\mathcal{N}}_{3D}^{2D}\\) to obtain a set of 6D poses:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.117,
+ 0.832,
+ 0.483,
+ 0.861
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {P} _ {6 D} = \\bigcup_ {c} \\left\\{\\left(\\overline {{\\mathbf {R}}}, \\bar {\\mathbf {t}}, c\\right) \\mid \\forall \\left(\\overline {{\\mathbf {R}}}, \\bar {\\mathbf {t}}\\right) \\in \\mathrm {M M - P n P} \\left(\\overline {{\\mathcal {N}}} ^ {c}\\right) \\right\\}, \\tag {11}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.871,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "b) 9D Pose Refinement. For each detected object \\(i\\), we refine the initial pose \\((\\overline{\\mathbf{R}}_i, \\overline{\\mathbf{t}}_i, c) \\in \\mathcal{P}_{6D}\\) to account"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.168
+ ],
+ "angle": 0,
+ "content": "for instance-specific size and improve their accuracy using \\(\\mathcal{N}_{3D}^{2D}\\). We select a subset \\(\\mathcal{N}_i\\subset \\mathcal{N}_{3D}^{2D}\\), where 1) the 2D point lies within \\(\\mathbf{H}\\), 2) its similarity score is above the threshold \\(t_2\\), and 3) its 2D coordinate was considered an inlier according to the 6D pose and category-level geometry."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.168,
+ 0.905,
+ 0.226
+ ],
+ "angle": 0,
+ "content": "We deform the category-level mesh by scaling vertices along the principal axes with a deformation multiplier \\(\\mathbf{d} \\in \\mathbb{R}^3\\). Refinement is done by minimizing the reprojection error:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.524,
+ 0.236,
+ 0.905,
+ 0.279
+ ],
+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {E} (\\mathbf {K}, \\mathbf {R}, \\mathbf {t}, \\mathbf {d}, \\mathcal {N} _ {i}) = \\sum_ {v _ {k}, \\boldsymbol {p} _ {k} \\in \\mathcal {N} _ {i}} \\| (\\mathbf {K R} (\\mathbf {d} \\odot v _ {k}) + \\mathbf {t}) - \\boldsymbol {p} _ {k} \\| _ {2} ^ {2}. \\tag {12}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.28,
+ 0.905,
+ 0.325
+ ],
+ "angle": 0,
+ "content": "The optimization proceeds in two steps, where the deformation is obtained using the 6D rotation and translation, which are subsequently refined using the deformation:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.618,
+ 0.335,
+ 0.905,
+ 0.358
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {d} _ {i} = \\min _ {\\mathbf {d}} \\boldsymbol {E} (\\mathbf {K}, \\overline {{\\mathbf {R}}} _ {i}, \\bar {\\mathbf {t}} _ {i}, \\mathbf {d}, \\mathcal {N} _ {i}) \\tag {13}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.596,
+ 0.361,
+ 0.905,
+ 0.383
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {R} _ {i}, \\mathbf {t} _ {i} = \\min _ {\\mathbf {R}, \\mathbf {t}} \\boldsymbol {E} (\\mathbf {K}, \\mathbf {R}, \\mathbf {t}, \\mathbf {d} _ {i}, \\mathcal {N} _ {i}). \\tag {14}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.394,
+ 0.905,
+ 0.439
+ ],
+ "angle": 0,
+ "content": "The final pose of object \\(i\\) is then given as \\((\\mathbf{R}_i, \\mathbf{t}_i, \\mathbf{s}_i, c_i)\\), where \\(\\mathbf{s}_i\\) is obtained as the size of the bounding box of \\(\\mathbf{V}^{c_i}\\) multiplied with \\(\\mathbf{d}_i\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.452,
+ 0.646,
+ 0.469
+ ],
+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.478,
+ 0.906,
+ 0.553
+ ],
+ "angle": 0,
+ "content": "In the following, we explain our experimental setup and then discuss the results of our single-stage pose estimation approach on real, synthetic, and corrupted data. For further results and more detailed comparisons, we refer the reader to our supplemental material."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.562,
+ 0.691,
+ 0.579
+ ],
+ "angle": 0,
+ "content": "4.1. Experiment Setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.584,
+ 0.906,
+ 0.719
+ ],
+ "angle": 0,
+ "content": "Datasets. We evaluate our method on the popular category-level 9D pose estimation benchmarks CAMERA25 [51] and REAL275 [51]. REAL275 is a real-world dataset that consists of 4.3K training images of 7 scenes and 2.75K testing images of 6 scenes. CAMERA25 supplements the real data with 275K synthetic training images and 25K evaluation images of rendered objects with real-world backgrounds. Both datasets contain objects from six categories: bottle, bowl, camera, can, laptop, and mug."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.72,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Evaluation Metrics. Following previous work [59], we use scale-agnostic evaluation metrics to remove the scale-depth ambiguity. To evaluate 3D detection and object size estimation, we report the mean average of the Normalized 3D Intersection over Union (NIoU) metric at thresholds \\(25\\%\\), \\(50\\%\\), and \\(75\\%\\). For pose estimation, we individually report the rotation error and scale-normalized translation error at the different thresholds \\(0.2d\\), \\(0.5d\\), \\(5^{\\circ}\\), \\(10^{\\circ}\\), and on joint thresholds \\(5^{\\circ}0.2d\\), \\(5^{\\circ}0.5d\\), \\(10^{\\circ}0.2d\\), \\(10^{\\circ}0.5d\\). In addition, we also report results on absolute metrics for comparable thresholds. Our work focuses on joint detection and pose estimation; therefore, we do not remove objects with"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.482,
+ 0.945,
+ 0.516,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "9794"
+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
+ 0.1,
+ 0.089,
+ 0.9,
+ 0.19
+ ],
+ "angle": 0,
+ "content": "| Method | N IoU25 | N IoU50 | N IoU75 | 5°0.2d | 5°0.5d | 10°0.2d | 10°0.5d | 0.2d | 0.5d | 5° | 10° |
| MSOS [30] | 36.9 | 9.7 | 0.7 | - | - | 3.3 | 15.3 | 10.6 | 50.8 | - | 17.0 |
| OLD-Net [15] | 35.4 | 11.4 | 0.4 | 0.9 | 3.0 | 5.0 | 16.0 | 12.4 | 46.2 | 4.2 | 20.9 |
| DMSR [52] | 57.2 | 38.4 | 9.5 | 15.1 | 23.7 | 25.6 | 45.2 | 35.0 | 67.3 | 27.4 | 52.0 |
| LaPose [59] | 70.7 | 47.9 | 15.8 | 15.7 | 21.3 | 37.4 | 57.4 | 46.9 | 78.8 | 23.4 | 60.7 |
| Ours | 75.2 | 53.7 | 19.2 | 25.1 | 31.8 | 43.7 | 66.1 | 53.5 | 83.7 | 32.1 | 68.8 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
+ 0.201,
+ 0.907,
+ 0.23
+ ],
+ "angle": 0,
+ "content": "Table 1. Comparison with state-of-the-art methods on REAL275 using scale-agnostic evaluation metrics. As visible, we set a new state of the art by outperforming the baseline methods in all metrics."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.102,
+ 0.244,
+ 0.898,
+ 0.345
+ ],
+ "angle": 0,
+ "content": "| Method | NIOU25 | NIOU50 | NIOU75 | 5°0.2d | 5°0.5d | 10°0.2d | 10°0.5d | 0.2d | 0.5d | 5° | 10° |
| MSOS [30] | 35.1 | 9.9 | 0.8 | - | - | 5.9 | 31.6 | 8.9 | 47.2 | - | 48.6 |
| OLD-Net [15] | 48.7 | 19.5 | 1.7 | 4.7 | 15.9 | 12.9 | 39.6 | 19.1 | 60.0 | 20.5 | 50.5 |
| DMSR [52] | 73.6 | 45.1 | 11.1 | 26.1 | 43.6 | 38.2 | 67.5 | 42.5 | 79.6 | 47.3 | 74.2 |
| LaPose[59] | 74.1 | 45.2 | 12.5 | 29.4 | 53.9 | 39.2 | 74.4 | 41.2 | 80.2 | 58.5 | 82.7 |
| Ours | 73.9 | 47.6 | 18.1 | 37.2 | 57.6 | 45.2 | 75.5 | 47.6 | 83.4 | 60.5 | 80.8 |
"
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+ "content": "Table 2. Comparison with state-of-the-art methods on CAMERA25 using scale-agnostic evaluation metrics. We assume that the lower \\(10^{\\circ}\\) performance is due to small objects in CAMERA25, yielding less correspondences. Our method achieves the highest accuracy on 9 out of the 11 metrics."
+ },
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+ "content": "| Method | IoU50 | IoU75 | 5°5cm | 5°10cm | 10°5cm | 10°10cm |
| MSOS [30] | 13.6 | 1.0 | - | - | - | 11.8 |
| OLD-Net [15] | 8.1 | 0.3 | 0.5 | 2.0 | 2.8 | 10.4 |
| DMSR [52] | 15.9 | 3.3 | 6.1 | 13.4 | 10.5 | 25.0 |
| LaPose [59] | 17.5 | 2.6 | 6.3 | 13.6 | 12.5 | 30.5 |
| Ours | 17.5 | 2.6 | 7.2 | 17.7 | 10.4 | 29.4 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "content": "Table 3. Results on REAL275 using absolute metrics. Predicting object scales from RGB images alone is challenging and not having 2D bounding boxes during inference exacerbates this problem, leading to worse performance of our trained scale prediction network, and consequently less precise metric scale translations. Nevertheless, our method is competitive in performance, either matching or outperforming the baselines in 3 out of the 6 considered metrics."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "low detection thresholds as in previous work [51], but evaluate performance on all detected objects as proposed by [59]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Implementation Details. To train our model on the REAL275 dataset, we use a mixture of \\(25\\%\\) real-world images and \\(75\\%\\) synthetic images from the CAMERA25 training set, similar to [51]. For the results on CAMERA25, we follow prior work [15, 30, 52, 59] and train a separate model without the REAL275 images."
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+ "content": "For each baseline, we use the detection results from [48] for a fair comparison and reproduce the numbers with the public checkpoints of their methods where possible. Notably, MSOS [30] does not have code publicly available at the time of writing, which is why we use the numbers provided by [59]. For more implementation details about our method, we refer the reader to our supplementary material."
+ },
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+ "content": "4.2. Comparison with State-of-the-Art Methods"
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+ "content": "Results with Scale-Agnostic Metrics. In Tab. 1, we compare our method with state-of-the-art RGB-only category-level pose estimation methods on the REAL275 benchmark under scale-agnostic evaluation metrics. As visible, our method consistently outperforms all baselines under scale-agnostic metrics."
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+ "content": "As can be seen in Tab. 2, our method also shows strong performance on synthetic data. While it falls behind on coarse rotation accuracy, it still outperforms baselines in 9 out of 11 metrics. A likely reason is that CAMERA25 contains many smaller objects (high depth or small scale), and performance could likely be increased by using higher-resolution features at the cost of slower inference speed."
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+ "content": "Results with Absolute Metrics. To measure pose estimation quality under metric scale, we follow [59] and decouple scale prediction from pose estimation. Since we do not use a dedicated detection model, we cannot use their pre-trained model. Instead, we train the same scale network using their code to predict a per-instance scale parameter, given the 2D projection of our object prototype with the estimated pose."
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+ "content": "We show the performance of our method in combination with the scale prediction network Tab. 3. Our results are competitive due to the strong performance in the normalized space. However, we could not reproduce the same level of performance from[59] for the scale estimation network. We believe that this is due to the network that was trained on 2D bounding boxes being more robust during inference than our version, which was trained on the prototype projections."
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+ "angle": 0,
+ "content": "Qualitative Results. Finally, Fig. 3 shows estimated"
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+ "content": "| Source | Method | ΔNIOU25 | ΔNIOU50 | ΔNIOU75 | Δ5°0.2d | Δ5°0.5d | Δ10°0.2d | Δ10°0.5d | Δ0.2d | Δ0.5d | Δ5° | Δ10° |
| ROI | OLD-Net[15] | -14.4% | -24.6% | -50.0% | -44.4% | -36.7% | -28.0% | -23.8% | -16.1% | -10.8% | -23.8% | -18.2% |
| DMSR[52] | -3.3% | -7.3% | -13.7% | -17.9% | -18.1% | -8.2% | -10.4% | -4.6% | -2.7% | -17.5% | -11.5% |
| LaPose[59] | -9.3% | -16.9% | -18.4% | -28.7% | -23.9% | -25.4% | -16.6% | -18.3% | -6.2% | -21.4% | -14.3% |
| Image | OLD-Net[15] | -28.0% | -38.6% | -50.0% | -55.6% | -43.3% | -46.0% | -41.3% | -34.7% | -26.4% | -23.8% | -24.9% |
| DMSR[52] | -13.8% | -14.3% | -22.1% | -24.5% | -27.8% | -16.4% | -22.1% | -13.1% | -15.2% | -26.6% | -22.5% |
| LaPose[59] | -22.9% | -24.6% | -22.8% | -29.3% | -28.6% | -29.4% | -27.7% | -25.6% | -21.2% | -26.1% | -25.9% |
| Ours | -11.0% | -14.0% | -21.7% | -17.2% | -13.5% | -16.0% | -12.9% | -12.7% | -9.5% | -13.5% | -12.6% |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Robustness experiments on the REAL275 [51] benchmark. We report loss in accuracy compared to the model evaluated on uncorrupted data averaged over 8 types of corruptions. The top shows results for corruption-free detection with only corrupted crops during pose estimation and the bottom shows corruptions during both stages. Corruptions during pose estimation alone already reduce the performance significantly. However, the on the image level the two-stage approaches suffer even more, indicating that failures in the detection are severe. Our single-stage approach is much less affected by noise and shows the greatest robustness."
+ },
+ {
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+ "content": "| Detection Source | NIOU25 | NIOU50 | NIOU75 | 5°0.2d | 5°0.5d | 10°0.2d | 10°0.5d | 0.2d | 0.5d | 5° | 10° |
| GT Object Mask | 72.1 | 50.3 | 17.8 | 23.0 | 29.6 | 40.4 | 61.4 | 50.4 | 81.0 | 29.9 | 63.7 |
| GT Proto. Mask | 79.5 | 55.3 | 19.5 | 25.6 | 32.2 | 44.1 | 66.7 | 53.4 | 84.2 | 32.5 | 69.2 |
| Mask-RCNN [18] | 70.4 | 48.8 | 17.7 | 22.4 | 28.7 | 38.9 | 58.4 | 48.9 | 79.1 | 28.9 | 60.4 |
| None (ours) | 75.2 | 53.7 | 19.2 | 25.1 | 31.8 | 43.7 | 66.1 | 53.5 | 83.7 | 32.1 | 68.8 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "content": "Table 5. To isolate the pose estimation accuracy of our method, we frame the problem as single-object pose estimation by providing different ROIs. As visible, our method comes close to the upper bound (GT Proto. Mask), showing our model can detect objects well and simultaneously reason about their poses with high accuracy. Our method also works well on the tight \"GT Object Masks\" but the performance drops significantly when using the fine-tuned Mask-RCNN, indicating that our approach outperforms it."
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "poses on REAL275 of our method and the baselines. As can be seen, two-stage approaches suffer from the error propagation of detection failures, whereas our method identifies objects much more confidently. Additionally, our method significantly improves the rotation accuracy which is most notable in the laptop category. For more detailed per-category results, we refer the reader to our supplemental material."
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+ "content": "4.3. Robustness to Image Degradations"
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+ "content": "Setting. To verify the robustness of two-stage vs. single-stage pose estimation, we conduct experiments on the REAL275 dataset with added corruptions from the imagecorruptions [20] library. We choose 8 corruptions of different types and report the average performance in the main part of the paper. For the choice of corruptions and per-corruption performance, we refer the reader to the supplemental material. For consistency, each method is evaluated using the same set of images and has been trained with the same data augmentations."
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+ "content": "We design two sets of experiments to study the robustness of the two-stage baselines. To measure the robustness of the pose estimator in isolation, we run the detector on clean images and apply the corruption only on its provided RoI. To evaluate the robustness of the whole framework, we apply corruptions on an image level. As it is the most commonly used model, we use the pre-trained Mask-RCNN [18] from [48] to get detection results for all base"
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+ "angle": 0,
+ "content": "lines. Note that we omit MSOS [30] from the robustness experiments, since to the best of our knowledge their code is not (or no longer) public."
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+ "content": "Results. We report the decrease in performance under image corruptions for the full task at the bottom of Tab. 4. Our performance drops by only \\(14\\%\\) when considering the mean and median on all metrics. In comparison, baselines suffer much more, losing anywhere from \\(19\\% - 37\\%\\) mean or \\(22\\% - 38\\%\\) median performance."
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+ "content": "4.4. Pose Estimation Quality"
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+ "content": "By framing detection and pose estimation as a single-stage problem, it is hard to quantify the success of either component individually. To measure the quality of our pose estimation in isolation, we try to decouple our framework into two stages. We do so by obtaining masks from three different sources. First, we use ground-truth object segmentation masks. Second, we use projected object prototype masks using ground-truth 9D poses. Third, we use bounding boxes provided by the same fine-tuned Mask-RCNN [18] as our baselines. The masks are then used to identify per-object correspondences for single-object pose estimation. To be consistent with our main method, we also use Progressive-X [5] as the solver, but we limit the maximum of predicted models to one per RoI."
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+ "content": "Tab. 5 shows the results of providing RoIs to our method. It is important to note that using instance-level detections from either Mask-RCNN or the ground-truth segmentation"
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+ "content": "Ground Truth"
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+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 3. Qualitative comparison on REAL275[51]. We compare our model (second to last column) with all baselines and with ground truth (last column). Some failures due to poor detection results of the baselines are highlighted (row 2, 3, and 5). In rows 1 and 4 our method outperforms baselines in terms of rotation accuracy."
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+ "type": "text",
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+ "angle": 0,
+ "content": "mask is not ideal for our method as it is optimized to work with the projected prototype masks. However, we find that our method also works well with the tightly fitting ground-truth segmentation masks (first row) but the performance drops steeply when using the predicted Mask-RCNN masks. The upper bound is shown in the second row, which provides ground-truth detections and 2D correspondences to our method. As can be seen, our method (fourth row) only falls noticeably behind in the \\( NIOU_{25} \\) and performs close to the upper bound on all other metrics. This shows that our joint approach outperforms Mask-RCNN in detection performance."
+ },
+ {
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+ "content": "5. Conclusion"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this work, we introduced the first unified RGB-only category-level detection and pose estimation framework that operates with a single representation. Using neural"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "mesh models as 3D object prototypes leads to robust feature representations that can be used for 2D/3D correspondence estimation and downstream multi-model pose estimation to jointly solve the detection and pose estimation tasks. We achieve state-of-the-art results for pose estimation on the popular REAL275 benchmark, and our evaluation has shown that our single-stage model is significantly more robust to image degradations than its two-stage counterparts."
+ },
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+ "content": "Acknowledgements"
+ },
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+ "type": "text",
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+ "content": "We gratefully acknowledge the stimulating research environment of the GRK 2853/1 \"Neuroexplicit Models of Language, Vision, and Action\", funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project number 471607914. The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Com"
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+ },
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+ "content": null
+ },
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+ ],
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+# Unified Category-Level Object Detection and Pose Estimation from RGB Images using 3D Prototypes
+
+Tom Fischer\*1,2 Xiaojie Zhang\*1,2 Eddy Ilg\* 1 Saarland University \*2 University of Technology Nuremberg
+
+# Abstract
+
+Recognizing objects in images is a fundamental problem in computer vision. Although detecting objects in 2D images is common, many applications require determining their pose in 3D space. Traditional category-level methods rely on RGB-D inputs, which may not always be available, or employ two-stage approaches that use separate models and representations for detection and pose estimation. For the first time, we introduce a unified model that integrates detection and pose estimation into a single framework for RGB images by leveraging neural mesh models with learned features and multi-model RANSAC. Our approach achieves state-of-the-art results for RGB category-level pose estimation on REAL275, improving on the current state-of-the-art by $22.9\%$ averaged across all scale-agnostic metrics. Finally, we demonstrate that our unified method exhibits greater robustness compared to single-stage baselines. Our code and models are available at github.com/Fischer-Tom/unified-detection-and-pose-estimation.
+
+# 1. Introduction
+
+Finding out whether an object is present in an image, where it is located, and how it is oriented in space, are fundamental problems of scene understanding. They are commonly referred to as object detection and pose estimation, and are critically relevant for applications in robotics [27, 53, 54], autonomous driving [28, 43] and augmented reality [39]. In object pose estimation, one distinguishes between methods that work only on known instances [19, 29, 32, 44, 60], and methods that are able to generalize within object categories [12, 15, 33, 35, 51, 52, 58, 59].
+
+Category-level pose estimation has made significant progress in recent years [12, 15, 33, 35, 51, 52, 58, 59]. However, most current work still relies on accurate depth information to recover precise poses [12, 58], restricting the
+
+
+Figure 1. The top shows existing pipelines that are made up of separate stages for object detection and and single-object pose estimation. In the bottom, we show our pipeline that uses a single representation and model for detection and pose estimation.
+
+use to devices and working conditions where depth can be captured. Pose estimation from RGB images alone [15, 30, 36, 52, 59] is less explored and a much harder task.
+
+Methods can be further classified according to the used detection approach. Although there are some RGB-D methods that utilize a shared representation with individual detection and pose heads [24, 51], most methods completely decouple the problem and use separate models and representations. All current RGB methods fall into this category of two-stage methods and use separate models per task, where as shown in Figure 1, objects are first detected, cropped, and then passed into a single-object pose estimator. This naturally places strong emphasis on the accuracy of the detection model, as failures cannot be recovered later, and comes with the downside of having to maintain two separate models.
+
+For the first time, we show that a single unified model can be established for both tasks in the case of RGB images, and that this approach leads to improved accuracy and robustness. Our model leverages neural mesh models [2, 38] as a 3D representation of object categories, where a 2D feature extractor for images and the neural features on the
+
+meshes are learned jointly during training. During inference, the image features are matched with features of the 3D meshes and multi-model RANSAC PnP [5] is used to detect different object instances and estimate their poses.
+
+Our approach achieves a new state of the art and outperforms the current RGB-only state-of-the-art [59] in pose estimation by $22.9\%$ when averaged across all scale-agnostic metrics. The results show that a common error source in two-stage pipelines is the detector and that our single-stage model is significantly more robust than its two-stage counterparts. In summary, our contributions are:
+
+- We propose the first single-stage framework for category-level multi-object pose estimation from single RGB images.
+- For the first time, we leverage neural mesh models jointly for object detection and pose estimation by combining them with multi-model RANSAC PnP and subsequent pose refinement.
+- We achieve state-of-the-art performance on pose estimation benchmark REAL275 w.r.t. to accuracy and robustness, verifying the effectiveness of our object representation and single-stage multi-object inference pipeline.
+
+# 2. Related Work
+
+Both object detection [8, 41] and object pose estimation [37] are long-standing tasks in computer vision. Although the first has converged to broadly accepted models, a variety of approaches are still being explored for the latter. Early pose estimation methods [6, 14, 42] operate by matching hand-crafted features to instance-level 3D models. Today, deep learning has replaced feature descriptors, but many works are still restricted to estimate poses of object instances that were present during training [19, 29, 32, 44, 60].
+
+Category-level pose estimation [12, 35, 51, 58, 59] was introduced by [51] to allow generalization to unseen instances within a set of established categories without requiring additional training or accurate CAD models during inference. The strong variation in geometry and scale within categories makes this a highly challenging problem. Shape-prior-free methods [12, 33, 35, 51] try to learn a generalizable representation without any guidance from CAD models during training.
+
+Shape-prior-based methods, on the other hand, use CAD models and/or simple derived properties such as sizes or bounding boxes to integrate geometric priors. The pose is then either regressed directly from a trained network, or solved for using predicted correspondences in the form of a Normalized Object Coordinate Space (NOCS) [51] with the (often deformed) shape prior using a non-differentiable alignment algorithm such as PnP [21, 31] or the Umyama algorithm [49]. Our method falls into the above category,
+
+but estimates the correspondences from feature matching with 3D neural meshes.
+
+Neural Mesh Models [2] are shape-prior-based methods and were initially proposed for robust category-level single-object rotation estimation. Follow-up work extended it to 6D pose estimation [38], however, they still relied on single-object training datasets and both methods [2, 38] are constrained to per-category networks that have to be calibrated against each other or require a (multi-label) classification model to identify present object categories. Later works removed the need for separate feature representations to allow robust classification, but they cannot estimate translations or handle multiple objects [16, 26]. Our work removes all these restrictions and can both detect objects and estimate their poses with a single, shared representation.
+
+# 2.1. Two-Stage Methods
+
+The vast majority of object pose estimation methods first locates the objects using off-the-shelf detection models [18, 41] to detect Regions of Interest (RoI) as 2D segmentation masks or bounding boxes. The objects are then cropped from the image and processed by a second model to predict the final poses, splitting the approaches into two stages.
+
+RGB-D Approaches have access to the incomplete point clouds of the observed instances derived from the depth map. These can be used for regression in combination with [34] or without [12, 35, 50] shape priors, or to align them with a shape prior [9, 48] using the Umayama algorithm [49]. In contrast to the above, our method does not require depth as input.
+
+RGB-Only Approaches face a more challenging problem due to the inherent ambiguity in this setting, which is why these methods are less prominent. In particular, the lack of depth information introduces a fundamental ambiguity between distance and scale, making it impossible to recover these properties from observations. To this end, Zhang et al. [59] introduced a set of scale-agnostic metrics that we also utilize in our work. OLD-Net [15] and DMSR [52] leverage a shape prior-based alignment technique and LaPose [59] uses a shape prior-based regression approach. MSOS [30], on the other hand, does not utilize any shape prior and directly estimates NOCS shape and the metric-scale shape of the object for downstream alignment. Although these two-stage approaches are successful in practice, they learn separate representations for both stages and are prone to errors of the first stage. In contrast to the above, we present a single-stage method with higher accuracy and robustness.
+
+# 2.2. Single-Stage Methods
+
+Single-stage methods couple detection and pose estimation into an end-to-end architecture. Existing work on end-to-end pose estimation focuses mainly on the instance-level
+
+
+Figure 2. We present a unified framework for solving detection and pose estimation with 3D object prototypes. Feature Extraction (Sec. 3.3): Given an RGB image, a frozen DINOv2 model with trainable adapters is combined with a Geometric Feature Decoder to produce two feature maps $\overline{\mathbf{F}}_{2D}$ , $\mathbf{F}_{2D}$ and foreground segmentations $\bar{\mathbf{H}}$ , $\mathbf{H}$ . 3D Prototype Learning (Sec. 3.4): During training, the Adapters and the Geometric Feature Decoder are jointly trained with a set of Neural Mesh Models [2] using a contrastive loss. Detection & 6D Pose Estimation (Sec. 3.6 a): After training, 6D object poses are obtained with a multi-model fitting algorithm from dense 2D/3D correspondences between category-level features $\overline{\mathbf{F}}_{2D}$ and all vertex features. 9D Pose Refinement (Sec. 3.6 b): For each identified instance, a deformation parameter is optimized for by aligning correspondences from instance-level features $\mathbf{F}_{2D}$ with its 6D pose.
+
+setting [7, 11, 22, 23, 46, 47, 55, 57]. However, there are category-level methods that utilize a shared representation and task-specific heads. NOCS [51] uses a shared feature extraction backbone that provides ROIs paired with individual heads for NOCS-map and instance segmentation. The category-level approaches [24, 25] require RGB-D as input and are shape-prior-based regression methods that perform joint center-point detection, reconstruction, and pose estimation. CenterPose [36] comes close to an RGB-only single-stage method, but requires the class labels of the objects present in an image and therefore is not a stand-alone method. In contrast, our work proposes the first RGB-only single-stage approach to unify the complete detection and pose estimation in a shared representation.
+
+# 3. Method
+
+We present a single-stage framework for RGB-only object detection and category-level 9D pose estimation. Our method aligns image features with a set of 3D object prototypes to infer object properties from 2D/3D correspondences obtained from feature matching. An overview is shown in Fig. 2.
+
+# 3.1. Task Definition
+
+Given an input image $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$ and camera intrinsics $\mathbf{K} \in \mathbb{R}^{3 \times 3}$ , our goal is to estimate the set of object properties:
+
+$$
+\mathcal {O} (\mathbf {I}, \mathbf {K}) = \{(c _ {i}, \mathbf {s} _ {i}, \mathbf {R} _ {i}, \mathbf {t} _ {i}) \} _ {i = 1} ^ {N}, \qquad (1)
+$$
+
+where each object $i$ is described by category $c_{i}$ , 3D size $\mathbf{s}_i\in \mathbb{R}^3$ , rotation $\mathbf{R}_i\in SO(3)$ , and translation $\mathbf{t}_i\in \mathbb{R}^3$ . We define its scalar instance scale as $\sigma_{i} = \| \mathbf{s}_{i}\|_{2}$ . Throughout the remaining parts of this section, we refer to sets in script font (i.e. $\mathcal{O}$ ); vectors, tuples, and tensors in bold font (i.e. $\mathbf{R}$ ); and scalars in standard math font (i.e. $c$ ).
+
+# 3.2. Representation
+
+We represent 3D object prototypes with Neural Mesh Models [2, 16, 26, 38], which have shown high generalization and robustness for single-object pose estimation. Each category $c$ has a prototypical mesh $\mathbf{M}^c = (\mathbf{V}^c, \mathbf{A}^c, \mathbf{F}_{3D}^c)$ , where $\mathbf{V}^c \in \mathbb{R}^{V \times 3}$ are vertex coordinates in object space, $\mathbf{A}^c \in \mathbb{Z}^{A \times 3}$ are triangle indices, and $\mathbf{F}_{3D}^c \in \mathbb{R}^{V \times D}$ are learned vertex features. The geometry of each mesh is obtained by regularly sampling the surface of the bounding box obtained from the average size $\overline{\mathbf{s}}^c$ of the training set, which we normalize to have $\| \overline{\mathbf{s}}^c \|_2 = 1$ . We also keep a scaling factor $\bar{\sigma}^c$ that transforms the mesh into one that has the mean scale of the category. If camera poses are available, scenes can be composed from the object prototypes and rendered into an image.
+
+# 3.3. Feature Extraction
+
+Accurate object localization from 2D/3D correspondences requires that the object geometry aligns well with the visual observations. In category-level pose estimation, one does not have access to instance-level geometries. To address this, we train a 2D feature extractor $\Phi$ that learns to map the
+
+input image $\mathbf{I}$ to a rendering of a scene composed of cuboid prototypes parameterized by $\mathcal{O}(\mathbf{I},\mathbf{K})$
+
+Modeling. As solving for 9D poses from correspondences alone is challenging and tends to fail in practice, we first perform an initial 6D pose estimation, where we rely on a feature map $\overline{\mathbf{F}}_{2D}$ that is aligned with the prototypes that follow category-level sizes $\overline{\mathbf{s}}^c$ . Next, we perform a size refinement with a feature map $\mathbf{F}_{2D}$ , which is aligned with deformed prototypes that match the instance-level sizes $\mathbf{s}_i$ . Since both feature maps are conditioned on the same neural textures, $\overline{\mathbf{F}}_{2D}$ can be imagined as a warped variant of $\mathbf{F}_{2D}$ .
+
+Backbone. The feature extractor $\Phi$ is trained jointly with the vertex features. This introduces ambiguities that make a good initialization crucial to guide each $\mathbf{F}_{3D}^{c}$ towards a meaningful representation. Therefore, we build $\Phi$ on top of the self-supervised pre-trained DINOv2 ViT [40] and embed task-specific information using Parameter-Efficient Fine-Tuning (PEFT) [56]. Following [10], we use a low-rank adaptation (Adapter) in the MLP in each transformer block:
+
+$$
+x _ {l} ^ {\prime} = \operatorname {M L P} (\operatorname {L N} (x _ {l})) + x _ {l} + \lambda (\operatorname {G e L U} (\operatorname {L N} (x _ {l}) \cdot D)) \cdot U, \tag {2}
+$$
+
+where $x_{l}$ is the output of the previous multi-head attention, $\lambda$ is a scaling factor [10] and $D, U$ are the down- and up-projection matrices.
+
+Geometric Feature Decoder. To obtain the features corresponding to the object prototype geometry, we first apply a shared transformer encoder to the backbone features, and subsequently two transformer decoders to obtain $\overline{\mathbf{F}}_{2D},\mathbf{F}_{2D}$ . Finally, both feature maps are upsampled to a certain output resolution using a combination of bilinear upsampling and shared convolution layers.
+
+# 3.4. Training
+
+We consider a training sample with $N$ objects and outline the loss calculation for an object $i$ with prototypical mesh $\mathbf{M}_i = (\mathbf{V},\mathbf{A},\mathbf{F}_{3D})$ , intrinsic matrix $\mathbf{K}$ , and pose $\hat{\mathbf{R}}_i,\hat{\mathbf{t}}_i$ .
+
+Setup. We first obtain pixel-level training annotations from rasterize $(\mathbf{M}_i, \mathbf{K}, \hat{\mathbf{R}}_i, \hat{\mathbf{t}}_i)$ to obtain projected image location $p_k$ and binary visibility $o_k$ for each vertex $v_k \in \mathbf{V}$ . Given a 2D feature map $\mathbf{F}$ , we define the annotation set as $\mathcal{Y}(\mathbf{M}_i, \mathbf{F}) = \{ (\theta_k, f_k, o_k) \mid \forall v_k \in \mathbf{V} \}$ , where $f_k$ is the pixel feature at projection $p_k$ in $\mathbf{F}$ , and $\theta_k$ is the corresponding vertex feature from $\mathbf{F}_{3D}$ .
+
+Optimizing $\Phi$ . Following [2], we model the probability distribution of any feature $f$ being generated from vertex $v_{k}$ by defining $P(f|\theta_k)$ using a von Mises-Fisher (vMF) distribution to express the likelihood:
+
+$$
+P (f | \theta_ {k}, \kappa) = C (\kappa) e ^ {\kappa \left(f ^ {\top} \cdot \theta_ {k}\right)}, \tag {3}
+$$
+
+with mean $\theta_{\kappa}$ , concentration parameter $\kappa$ , and normalization constant $C(\kappa)$ .
+
+Accurate object poses are obtained when $f_{k}$ can be matched to $\theta_{k}$ , leading to precise 2D/3D correspondences. We optimize for this task using contrastive learning by maximizing Eq. (3) with the feature $f_{k}$ , and minimize the likelihood of all other vertices:
+
+$$
+\max \quad P \left(f _ {k} \mid \theta_ {k}, \kappa\right), \tag {4}
+$$
+
+$$
+\min \sum_ {\theta_ {m} \in \bar {\theta} _ {k}} P \left(f _ {k} \mid \theta_ {m}, \kappa\right), \tag {5}
+$$
+
+where the negatives $\overline{\theta}_k$ are the features of all noncorresponding vertices including those from different classes. Equations 4 and 5 can be combined into a single loss by taking the negative log-likelihood:
+
+$$
+\mathcal {L} (\mathcal {Y} (\mathbf {M} _ {i}, \mathbf {F})) = - \sum_ {k} o _ {k} \cdot \log \left(\frac {e ^ {\kappa \left(f _ {k} \cdot \theta_ {k}\right)}}{\sum_ {\theta_ {m} \in \bar {\theta} _ {k}} e ^ {\kappa \left(f _ {k} ^ {\top} \cdot \theta_ {m}\right)}}\right), \tag {6}
+$$
+
+where considering $\kappa$ as a global hyperparameters allows canceling out the normalization constants $C(\kappa)$ . We compute the full training loss as:
+
+$$
+\mathcal {L} _ {\text {t r a i n}} = \sum_ {i} \frac {\mathcal {L} \left(\mathcal {Y} \left(\mathbf {M} ^ {c _ {i}} , \overline {{\mathbf {F}}} _ {2 D}\right)\right) + \mathcal {L} \left(\mathcal {Y} \left(\phi \left(\mathbf {M} ^ {c _ {i}}\right) , \mathbf {F} _ {2 D}\right)\right)}{2 N}, \tag {7}
+$$
+
+where $\phi (\mathbf{M}) = (\phi (\mathbf{V}),\mathbf{A},\mathbf{F}_{3D})$ is the deformation operation we discussed in Sec. 3.3. For mean and deformed meshes we scale the vertices with ground-truth scale $\sigma_{i}$ before rasterizing.
+
+Optimizing Vertex Features. Previous work [2, 3, 16, 38] advocates for an exponential moving average strategy when updating vertex features. We found that this approach is sensitive to initialization and hyperparameters that lead to highly varying performance between training runs. For a more stable and consistent training, we optimize them through backpropagation with $\Phi$ using the same loss in Eq. (7).
+
+# 3.5. Foreground Detection
+
+Although the contrastive loss in Eq. (7) helps localize objects implicitly, background regions still produce false-positive matches. Inspired by the emergent behavior of foreground segmentation in ViT attention maps [1], we extract foreground masks $\overline{\mathbf{H}}$ , $\mathbf{H}$ using cross-attention between foreground tokens and decoder features.
+
+We initialize two foreground tokens $\overline{b}, b$ with the CLS—token of the backbone ViT. After each decoder layer or upsampling step, the per-pixel affinity to the foreground token is measured via cross attention:
+
+$$
+\boldsymbol {b} ^ {i + 1}, \boldsymbol {W} ^ {i + 1} = \operatorname {C r o s s A t t n} \left(\boldsymbol {b} ^ {i}, F ^ {i}\right), \tag {8}
+$$
+
+where $F^i$ are the current image features, $\pmb{b}^{i + 1}$ is the updated foreground token, and $\pmb{W}^{i + 1}$ are the attention weights. At
+
+the final level, we use min-max normalization to obtain the segmentation $\mathbf{H} = \min \max (\mathbf{W}^N)$ . The mean-shape segmentation $\overline{\mathbf{H}}$ is predicted in the same way.
+
+We supervise the final segmentations with masks obtained from rendering the prototypes using ground-truth poses. Since it is a popular choice for segmentation [13, 18] and we have found practical success with it, we adopted the dice loss [45] to optimize the attention weights:
+
+$$
+\mathcal {L} _ {\text {m a s k}} = \frac {\mathcal {L} _ {\text {d i c e}} (\mathbf {H} , \mathbf {H} _ {G T}) + \mathcal {L} _ {\text {d i c e}} (\overline {{\mathbf {H}}} , \overline {{\mathbf {H}}} _ {G T})}{2}. \tag {9}
+$$
+
+# 3.6. Inference
+
+During inference time, we determine the objects contained in an image $\mathbf{I}$ using the trained feature extractor $\Phi$ and the prototypes through correspondences from feature matching. First, $\Phi$ is queried for the feature maps $\overline{\mathbf{F}}_{2D},\mathbf{F}_{2D}$ and the foreground heatmaps $\overline{\mathbf{H}},\mathbf{H}$ , which are thresholded using a confidence parameter $t_1$ to obtain binary foreground segmentations. Then, two dense correspondence mappings $\bar{\mathcal{N}}_{3D}^{2D},\mathcal{N}_{3D}^{2D}$ are established between the prototypes and the feature maps. Considering $\overline{\mathbf{F}}_{2D}$ , the set of correspondences is established as:
+
+$$
+\begin{array}{l} \bar {\mathcal {N}} _ {3 D} ^ {2 D} = \left\{\left(\boldsymbol {p} _ {i}, v _ {k}, \rho (v _ {k})\right) \mid \boldsymbol {p} _ {i} \in \overline {{\mathbf {F}}} _ {2 D}, \right. \\ v _ {k} = \underset {\theta_ {k} \in \bigcup_ {c} \mathbf {F} _ {3 D} ^ {c}} {\arg \max } f _ {i} ^ {\top} \theta_ {k} \}, \tag {10} \\ \end{array}
+$$
+
+where the membership function $\rho(v_k) = c$ returns the category label $c$ of the mesh to which the matched vertex $v_k$ belongs. We remove noisy correspondences which fall outside of $\overline{\mathbf{H}}$ or have a similarity score below a second confidence threshold $t_2$ .
+
+a) Detection and 6D Pose Estimation. We use the correspondence set $\bar{\mathcal{N}}_{3D}^{2D}$ to simultaneously detect objects and estimate their initial 6D pose. If it is known a-priori that there is only a single instance per category in the scene, one could group correspondences by category label and solve this problem via sequential application of PnP [31] paired with RANSAC [17]. However, this assumption is rarely valid in practice. To handle scenes with multiple instances from the same category, we use Progressive-X (ProgX) [5], a multi-model fitting algorithm that enables PnP to detect multiple object poses. ProgX extends GraphCut RANSAC [4] to the multi-model setting via a sequential hypothesis generation algorithm that can separate correspondences into individual instances. For each class $c$ , we run ProgX on the subset $\bar{\mathcal{N}}^c \subset \bar{\mathcal{N}}_{3D}^{2D}$ to obtain a set of 6D poses:
+
+$$
+\mathcal {P} _ {6 D} = \bigcup_ {c} \left\{\left(\overline {{\mathbf {R}}}, \bar {\mathbf {t}}, c\right) \mid \forall \left(\overline {{\mathbf {R}}}, \bar {\mathbf {t}}\right) \in \mathrm {M M - P n P} \left(\overline {{\mathcal {N}}} ^ {c}\right) \right\}, \tag {11}
+$$
+
+b) 9D Pose Refinement. For each detected object $i$ , we refine the initial pose $(\overline{\mathbf{R}}_i, \overline{\mathbf{t}}_i, c) \in \mathcal{P}_{6D}$ to account
+
+for instance-specific size and improve their accuracy using $\mathcal{N}_{3D}^{2D}$ . We select a subset $\mathcal{N}_i\subset \mathcal{N}_{3D}^{2D}$ , where 1) the 2D point lies within $\mathbf{H}$ , 2) its similarity score is above the threshold $t_2$ , and 3) its 2D coordinate was considered an inlier according to the 6D pose and category-level geometry.
+
+We deform the category-level mesh by scaling vertices along the principal axes with a deformation multiplier $\mathbf{d} \in \mathbb{R}^3$ . Refinement is done by minimizing the reprojection error:
+
+$$
+\boldsymbol {E} (\mathbf {K}, \mathbf {R}, \mathbf {t}, \mathbf {d}, \mathcal {N} _ {i}) = \sum_ {v _ {k}, \boldsymbol {p} _ {k} \in \mathcal {N} _ {i}} \| (\mathbf {K R} (\mathbf {d} \odot v _ {k}) + \mathbf {t}) - \boldsymbol {p} _ {k} \| _ {2} ^ {2}. \tag {12}
+$$
+
+The optimization proceeds in two steps, where the deformation is obtained using the 6D rotation and translation, which are subsequently refined using the deformation:
+
+$$
+\mathbf {d} _ {i} = \min _ {\mathbf {d}} \boldsymbol {E} (\mathbf {K}, \overline {{\mathbf {R}}} _ {i}, \bar {\mathbf {t}} _ {i}, \mathbf {d}, \mathcal {N} _ {i}) \tag {13}
+$$
+
+$$
+\mathbf {R} _ {i}, \mathbf {t} _ {i} = \min _ {\mathbf {R}, \mathbf {t}} \boldsymbol {E} (\mathbf {K}, \mathbf {R}, \mathbf {t}, \mathbf {d} _ {i}, \mathcal {N} _ {i}). \tag {14}
+$$
+
+The final pose of object $i$ is then given as $(\mathbf{R}_i, \mathbf{t}_i, \mathbf{s}_i, c_i)$ , where $\mathbf{s}_i$ is obtained as the size of the bounding box of $\mathbf{V}^{c_i}$ multiplied with $\mathbf{d}_i$ .
+
+# 4. Experiments
+
+In the following, we explain our experimental setup and then discuss the results of our single-stage pose estimation approach on real, synthetic, and corrupted data. For further results and more detailed comparisons, we refer the reader to our supplemental material.
+
+# 4.1. Experiment Setup
+
+Datasets. We evaluate our method on the popular category-level 9D pose estimation benchmarks CAMERA25 [51] and REAL275 [51]. REAL275 is a real-world dataset that consists of 4.3K training images of 7 scenes and 2.75K testing images of 6 scenes. CAMERA25 supplements the real data with 275K synthetic training images and 25K evaluation images of rendered objects with real-world backgrounds. Both datasets contain objects from six categories: bottle, bowl, camera, can, laptop, and mug.
+
+Evaluation Metrics. Following previous work [59], we use scale-agnostic evaluation metrics to remove the scale-depth ambiguity. To evaluate 3D detection and object size estimation, we report the mean average of the Normalized 3D Intersection over Union (NIoU) metric at thresholds $25\%$ , $50\%$ , and $75\%$ . For pose estimation, we individually report the rotation error and scale-normalized translation error at the different thresholds $0.2d$ , $0.5d$ , $5^{\circ}$ , $10^{\circ}$ , and on joint thresholds $5^{\circ}0.2d$ , $5^{\circ}0.5d$ , $10^{\circ}0.2d$ , $10^{\circ}0.5d$ . In addition, we also report results on absolute metrics for comparable thresholds. Our work focuses on joint detection and pose estimation; therefore, we do not remove objects with
+
+| Method | N IoU25 | N IoU50 | N IoU75 | 5°0.2d | 5°0.5d | 10°0.2d | 10°0.5d | 0.2d | 0.5d | 5° | 10° |
| MSOS [30] | 36.9 | 9.7 | 0.7 | - | - | 3.3 | 15.3 | 10.6 | 50.8 | - | 17.0 |
| OLD-Net [15] | 35.4 | 11.4 | 0.4 | 0.9 | 3.0 | 5.0 | 16.0 | 12.4 | 46.2 | 4.2 | 20.9 |
| DMSR [52] | 57.2 | 38.4 | 9.5 | 15.1 | 23.7 | 25.6 | 45.2 | 35.0 | 67.3 | 27.4 | 52.0 |
| LaPose [59] | 70.7 | 47.9 | 15.8 | 15.7 | 21.3 | 37.4 | 57.4 | 46.9 | 78.8 | 23.4 | 60.7 |
| Ours | 75.2 | 53.7 | 19.2 | 25.1 | 31.8 | 43.7 | 66.1 | 53.5 | 83.7 | 32.1 | 68.8 |
+
+Table 1. Comparison with state-of-the-art methods on REAL275 using scale-agnostic evaluation metrics. As visible, we set a new state of the art by outperforming the baseline methods in all metrics.
+
+| Method | NIOU25 | NIOU50 | NIOU75 | 5°0.2d | 5°0.5d | 10°0.2d | 10°0.5d | 0.2d | 0.5d | 5° | 10° |
| MSOS [30] | 35.1 | 9.9 | 0.8 | - | - | 5.9 | 31.6 | 8.9 | 47.2 | - | 48.6 |
| OLD-Net [15] | 48.7 | 19.5 | 1.7 | 4.7 | 15.9 | 12.9 | 39.6 | 19.1 | 60.0 | 20.5 | 50.5 |
| DMSR [52] | 73.6 | 45.1 | 11.1 | 26.1 | 43.6 | 38.2 | 67.5 | 42.5 | 79.6 | 47.3 | 74.2 |
| LaPose[59] | 74.1 | 45.2 | 12.5 | 29.4 | 53.9 | 39.2 | 74.4 | 41.2 | 80.2 | 58.5 | 82.7 |
| Ours | 73.9 | 47.6 | 18.1 | 37.2 | 57.6 | 45.2 | 75.5 | 47.6 | 83.4 | 60.5 | 80.8 |
+
+Table 2. Comparison with state-of-the-art methods on CAMERA25 using scale-agnostic evaluation metrics. We assume that the lower $10^{\circ}$ performance is due to small objects in CAMERA25, yielding less correspondences. Our method achieves the highest accuracy on 9 out of the 11 metrics.
+
+| Method | IoU50 | IoU75 | 5°5cm | 5°10cm | 10°5cm | 10°10cm |
| MSOS [30] | 13.6 | 1.0 | - | - | - | 11.8 |
| OLD-Net [15] | 8.1 | 0.3 | 0.5 | 2.0 | 2.8 | 10.4 |
| DMSR [52] | 15.9 | 3.3 | 6.1 | 13.4 | 10.5 | 25.0 |
| LaPose [59] | 17.5 | 2.6 | 6.3 | 13.6 | 12.5 | 30.5 |
| Ours | 17.5 | 2.6 | 7.2 | 17.7 | 10.4 | 29.4 |
+
+Table 3. Results on REAL275 using absolute metrics. Predicting object scales from RGB images alone is challenging and not having 2D bounding boxes during inference exacerbates this problem, leading to worse performance of our trained scale prediction network, and consequently less precise metric scale translations. Nevertheless, our method is competitive in performance, either matching or outperforming the baselines in 3 out of the 6 considered metrics.
+
+low detection thresholds as in previous work [51], but evaluate performance on all detected objects as proposed by [59].
+
+Implementation Details. To train our model on the REAL275 dataset, we use a mixture of $25\%$ real-world images and $75\%$ synthetic images from the CAMERA25 training set, similar to [51]. For the results on CAMERA25, we follow prior work [15, 30, 52, 59] and train a separate model without the REAL275 images.
+
+For each baseline, we use the detection results from [48] for a fair comparison and reproduce the numbers with the public checkpoints of their methods where possible. Notably, MSOS [30] does not have code publicly available at the time of writing, which is why we use the numbers provided by [59]. For more implementation details about our method, we refer the reader to our supplementary material.
+
+# 4.2. Comparison with State-of-the-Art Methods
+
+Results with Scale-Agnostic Metrics. In Tab. 1, we compare our method with state-of-the-art RGB-only category-level pose estimation methods on the REAL275 benchmark under scale-agnostic evaluation metrics. As visible, our method consistently outperforms all baselines under scale-agnostic metrics.
+
+As can be seen in Tab. 2, our method also shows strong performance on synthetic data. While it falls behind on coarse rotation accuracy, it still outperforms baselines in 9 out of 11 metrics. A likely reason is that CAMERA25 contains many smaller objects (high depth or small scale), and performance could likely be increased by using higher-resolution features at the cost of slower inference speed.
+
+Results with Absolute Metrics. To measure pose estimation quality under metric scale, we follow [59] and decouple scale prediction from pose estimation. Since we do not use a dedicated detection model, we cannot use their pre-trained model. Instead, we train the same scale network using their code to predict a per-instance scale parameter, given the 2D projection of our object prototype with the estimated pose.
+
+We show the performance of our method in combination with the scale prediction network Tab. 3. Our results are competitive due to the strong performance in the normalized space. However, we could not reproduce the same level of performance from[59] for the scale estimation network. We believe that this is due to the network that was trained on 2D bounding boxes being more robust during inference than our version, which was trained on the prototype projections.
+
+Qualitative Results. Finally, Fig. 3 shows estimated
+
+| Source | Method | ΔNIOU25 | ΔNIOU50 | ΔNIOU75 | Δ5°0.2d | Δ5°0.5d | Δ10°0.2d | Δ10°0.5d | Δ0.2d | Δ0.5d | Δ5° | Δ10° |
| ROI | OLD-Net[15] | -14.4% | -24.6% | -50.0% | -44.4% | -36.7% | -28.0% | -23.8% | -16.1% | -10.8% | -23.8% | -18.2% |
| DMSR[52] | -3.3% | -7.3% | -13.7% | -17.9% | -18.1% | -8.2% | -10.4% | -4.6% | -2.7% | -17.5% | -11.5% |
| LaPose[59] | -9.3% | -16.9% | -18.4% | -28.7% | -23.9% | -25.4% | -16.6% | -18.3% | -6.2% | -21.4% | -14.3% |
| Image | OLD-Net[15] | -28.0% | -38.6% | -50.0% | -55.6% | -43.3% | -46.0% | -41.3% | -34.7% | -26.4% | -23.8% | -24.9% |
| DMSR[52] | -13.8% | -14.3% | -22.1% | -24.5% | -27.8% | -16.4% | -22.1% | -13.1% | -15.2% | -26.6% | -22.5% |
| LaPose[59] | -22.9% | -24.6% | -22.8% | -29.3% | -28.6% | -29.4% | -27.7% | -25.6% | -21.2% | -26.1% | -25.9% |
| Ours | -11.0% | -14.0% | -21.7% | -17.2% | -13.5% | -16.0% | -12.9% | -12.7% | -9.5% | -13.5% | -12.6% |
+
+Table 4. Robustness experiments on the REAL275 [51] benchmark. We report loss in accuracy compared to the model evaluated on uncorrupted data averaged over 8 types of corruptions. The top shows results for corruption-free detection with only corrupted crops during pose estimation and the bottom shows corruptions during both stages. Corruptions during pose estimation alone already reduce the performance significantly. However, the on the image level the two-stage approaches suffer even more, indicating that failures in the detection are severe. Our single-stage approach is much less affected by noise and shows the greatest robustness.
+
+| Detection Source | NIOU25 | NIOU50 | NIOU75 | 5°0.2d | 5°0.5d | 10°0.2d | 10°0.5d | 0.2d | 0.5d | 5° | 10° |
| GT Object Mask | 72.1 | 50.3 | 17.8 | 23.0 | 29.6 | 40.4 | 61.4 | 50.4 | 81.0 | 29.9 | 63.7 |
| GT Proto. Mask | 79.5 | 55.3 | 19.5 | 25.6 | 32.2 | 44.1 | 66.7 | 53.4 | 84.2 | 32.5 | 69.2 |
| Mask-RCNN [18] | 70.4 | 48.8 | 17.7 | 22.4 | 28.7 | 38.9 | 58.4 | 48.9 | 79.1 | 28.9 | 60.4 |
| None (ours) | 75.2 | 53.7 | 19.2 | 25.1 | 31.8 | 43.7 | 66.1 | 53.5 | 83.7 | 32.1 | 68.8 |
+
+Table 5. To isolate the pose estimation accuracy of our method, we frame the problem as single-object pose estimation by providing different ROIs. As visible, our method comes close to the upper bound (GT Proto. Mask), showing our model can detect objects well and simultaneously reason about their poses with high accuracy. Our method also works well on the tight "GT Object Masks" but the performance drops significantly when using the fine-tuned Mask-RCNN, indicating that our approach outperforms it.
+
+poses on REAL275 of our method and the baselines. As can be seen, two-stage approaches suffer from the error propagation of detection failures, whereas our method identifies objects much more confidently. Additionally, our method significantly improves the rotation accuracy which is most notable in the laptop category. For more detailed per-category results, we refer the reader to our supplemental material.
+
+# 4.3. Robustness to Image Degradations
+
+Setting. To verify the robustness of two-stage vs. single-stage pose estimation, we conduct experiments on the REAL275 dataset with added corruptions from the imagecorruptions [20] library. We choose 8 corruptions of different types and report the average performance in the main part of the paper. For the choice of corruptions and per-corruption performance, we refer the reader to the supplemental material. For consistency, each method is evaluated using the same set of images and has been trained with the same data augmentations.
+
+We design two sets of experiments to study the robustness of the two-stage baselines. To measure the robustness of the pose estimator in isolation, we run the detector on clean images and apply the corruption only on its provided RoI. To evaluate the robustness of the whole framework, we apply corruptions on an image level. As it is the most commonly used model, we use the pre-trained Mask-RCNN [18] from [48] to get detection results for all base
+
+lines. Note that we omit MSOS [30] from the robustness experiments, since to the best of our knowledge their code is not (or no longer) public.
+
+Results. We report the decrease in performance under image corruptions for the full task at the bottom of Tab. 4. Our performance drops by only $14\%$ when considering the mean and median on all metrics. In comparison, baselines suffer much more, losing anywhere from $19\% - 37\%$ mean or $22\% - 38\%$ median performance.
+
+# 4.4. Pose Estimation Quality
+
+By framing detection and pose estimation as a single-stage problem, it is hard to quantify the success of either component individually. To measure the quality of our pose estimation in isolation, we try to decouple our framework into two stages. We do so by obtaining masks from three different sources. First, we use ground-truth object segmentation masks. Second, we use projected object prototype masks using ground-truth 9D poses. Third, we use bounding boxes provided by the same fine-tuned Mask-RCNN [18] as our baselines. The masks are then used to identify per-object correspondences for single-object pose estimation. To be consistent with our main method, we also use Progressive-X [5] as the solver, but we limit the maximum of predicted models to one per RoI.
+
+Tab. 5 shows the results of providing RoIs to our method. It is important to note that using instance-level detections from either Mask-RCNN or the ground-truth segmentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+OLD-Net
+
+
+DMSR
+
+
+LaPose
+
+
+Ours
+Figure 3. Qualitative comparison on REAL275[51]. We compare our model (second to last column) with all baselines and with ground truth (last column). Some failures due to poor detection results of the baselines are highlighted (row 2, 3, and 5). In rows 1 and 4 our method outperforms baselines in terms of rotation accuracy.
+
+
+Ground Truth
+
+mask is not ideal for our method as it is optimized to work with the projected prototype masks. However, we find that our method also works well with the tightly fitting ground-truth segmentation masks (first row) but the performance drops steeply when using the predicted Mask-RCNN masks. The upper bound is shown in the second row, which provides ground-truth detections and 2D correspondences to our method. As can be seen, our method (fourth row) only falls noticeably behind in the $NIOU_{25}$ and performs close to the upper bound on all other metrics. This shows that our joint approach outperforms Mask-RCNN in detection performance.
+
+# 5. Conclusion
+
+In this work, we introduced the first unified RGB-only category-level detection and pose estimation framework that operates with a single representation. Using neural
+
+mesh models as 3D object prototypes leads to robust feature representations that can be used for 2D/3D correspondence estimation and downstream multi-model pose estimation to jointly solve the detection and pose estimation tasks. We achieve state-of-the-art results for pose estimation on the popular REAL275 benchmark, and our evaluation has shown that our single-stage model is significantly more robust to image degradations than its two-stage counterparts.
+
+# Acknowledgements
+
+We gratefully acknowledge the stimulating research environment of the GRK 2853/1 "Neuroexplicit Models of Language, Vision, and Action", funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under project number 471607914. The authors gratefully acknowledge the scientific support and HPC resources provided by the Erlangen National High Performance Com
+
+puting Center (NHR@FAU) of the Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU) under the BayernKI project b266be. BayernKI funding is provided by Bavarian state authorities.
+
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\ No newline at end of file
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+ "content": "Recognizing objects in images is a fundamental problem in computer vision. Although detecting objects in 2D images is common, many applications require determining their pose in 3D space. Traditional category-level methods rely on RGB-D inputs, which may not always be available, or employ two-stage approaches that use separate models and representations for detection and pose estimation. For the first time, we introduce a unified model that integrates detection and pose estimation into a single framework for RGB images by leveraging neural mesh models with learned features and multi-model RANSAC. Our approach achieves state-of-the-art results for RGB category-level pose estimation on REAL275, improving on the current state-of-the-art by "
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+ "content": " using a von Mises-Fisher (vMF) distribution to express the likelihood:"
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+ "content": " using the same loss in Eq. (7)."
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+ "content": "Although the contrastive loss in Eq. (7) helps localize objects implicitly, background regions still produce false-positive matches. Inspired by the emergent behavior of foreground segmentation in ViT attention maps [1], we extract foreground masks "
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+ "content": " with the CLS—token of the backbone ViT. After each decoder layer or upsampling step, the per-pixel affinity to the foreground token is measured via cross attention:"
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+ "content": "\\boldsymbol {b} ^ {i + 1}, \\boldsymbol {W} ^ {i + 1} = \\operatorname {C r o s s A t t n} \\left(\\boldsymbol {b} ^ {i}, F ^ {i}\\right), \\tag {8}",
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+ "content": "We supervise the final segmentations with masks obtained from rendering the prototypes using ground-truth poses. Since it is a popular choice for segmentation [13, 18] and we have found practical success with it, we adopted the dice loss [45] to optimize the attention weights:"
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+ "content": "\\mathcal {L} _ {\\text {m a s k}} = \\frac {\\mathcal {L} _ {\\text {d i c e}} (\\mathbf {H} , \\mathbf {H} _ {G T}) + \\mathcal {L} _ {\\text {d i c e}} (\\overline {{\\mathbf {H}}} , \\overline {{\\mathbf {H}}} _ {G T})}{2}. \\tag {9}",
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+ "content": " and the prototypes through correspondences from feature matching. First, "
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+ "content": "\\bar{\\mathcal{N}}_{3D}^{2D},\\mathcal{N}_{3D}^{2D}"
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+ "content": "Datasets. We evaluate our method on the popular category-level 9D pose estimation benchmarks CAMERA25 [51] and REAL275 [51]. REAL275 is a real-world dataset that consists of 4.3K training images of 7 scenes and 2.75K testing images of 6 scenes. CAMERA25 supplements the real data with 275K synthetic training images and 25K evaluation images of rendered objects with real-world backgrounds. Both datasets contain objects from six categories: bottle, bowl, camera, can, laptop, and mug."
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+ "content": "Evaluation Metrics. Following previous work [59], we use scale-agnostic evaluation metrics to remove the scale-depth ambiguity. To evaluate 3D detection and object size estimation, we report the mean average of the Normalized 3D Intersection over Union (NIoU) metric at thresholds "
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| DMSR [52] | 15.9 | 3.3 | 6.1 | 13.4 | 10.5 | 25.0 |
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| DMSR[52] | -3.3% | -7.3% | -13.7% | -17.9% | -18.1% | -8.2% | -10.4% | -4.6% | -2.7% | -17.5% | -11.5% |
| LaPose[59] | -9.3% | -16.9% | -18.4% | -28.7% | -23.9% | -25.4% | -16.6% | -18.3% | -6.2% | -21.4% | -14.3% |
| Image | OLD-Net[15] | -28.0% | -38.6% | -50.0% | -55.6% | -43.3% | -46.0% | -41.3% | -34.7% | -26.4% | -23.8% | -24.9% |
| DMSR[52] | -13.8% | -14.3% | -22.1% | -24.5% | -27.8% | -16.4% | -22.1% | -13.1% | -15.2% | -26.6% | -22.5% |
| LaPose[59] | -22.9% | -24.6% | -22.8% | -29.3% | -28.6% | -29.4% | -27.7% | -25.6% | -21.2% | -26.1% | -25.9% |
| Ours | -11.0% | -14.0% | -21.7% | -17.2% | -13.5% | -16.0% | -12.9% | -12.7% | -9.5% | -13.5% | -12.6% |
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| GT Proto. Mask | 79.5 | 55.3 | 19.5 | 25.6 | 32.2 | 44.1 | 66.7 | 53.4 | 84.2 | 32.5 | 69.2 |
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diff --git a/2025/Unified Multi-Agent Trajectory Modeling with Masked Trajectory Diffusion/08038fe6-7601-45f0-b544-974df2316e72_content_list.json b/2025/Unified Multi-Agent Trajectory Modeling with Masked Trajectory Diffusion/08038fe6-7601-45f0-b544-974df2316e72_content_list.json
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+ "text": "Unified Multi-Agent Trajectory Modeling with Masked Trajectory Diffusion",
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+ "text": "Songru Yang, Zhenwei Shi, Zhengxia Zou* \nDepartment of Aerospace Intelligent Science and Technology, School of Astronautics, Beihang University, Beijing, China \n{songruang2001, shizhenwei, zhengxiazou}@buaa.edu.cn",
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+ "text": "Understanding movements in multi-agent scenarios is a fundamental problem in intelligent systems. Previous research assumes complete and synchronized observations. However, real-world partial observation caused by occlusions leads to inevitable model failure, which demands a unified framework for coexisting trajectory prediction, imputation, and recovery. Unlike previous attempts that handled observed and unobserved behaviors in a coupled manner, we explore a decoupled denoising diffusion modeling paradigm with a unidirectional information valve to separate the interference from uncertain behaviors. Building on this, we proposed a Unified Masked Trajectory Diffusion model (UniMTD) for arbitrary levels of missing observations. We designed a unidirectional attention as a valve unit to control the direction of information flow between the observed and masked areas, gradually refining the missing observations toward a real-world distribution. We construct it into a unidirectional MoE structure to handle varying proportions of missing observations. A Cached Diffusion model is further designed to improve generation quality while reducing computation and time overhead. Our method has achieved a great leap across human motions and vehicle traffic. UniMTD efficiently achieves $74\\%$ improvement in $\\min ADE_{20}$ and reaches SOTA with advantages of $91\\%$ , $66\\%$ , $69\\%$ , and $58\\%$ across 4 fidelity metrics on out-of-boundary, velocity, and trajectory length.",
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+ "text": "1. Introduction",
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+ "text": "Understanding multi-agent behavior is a critical foundation in various domains, including autonomous driving [35], action analysis [15, 26, 74], video surveillance [79, 83], and scene generation [69]. Trajectory modeling, which analyzes and generates the position sequence of multiple agents within the same scene, is particularly straightforward and effective for understanding agents' behavior.",
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+ "text": "Existing methods have made significant strides in trajectory prediction [4, 59, 72, 76, 86, 87], imputation [46, 84, 85], and recovery [20, 22] across multiple fields, such as human sports and traffic trajectory. However, existing approaches cannot handle multiple tasks simultaneously, leaving a gap between methods and real-world scenarios where all three tasks coexist, as shown in Fig.1 (a). Recently, increasing attempts have been made to break the task boundaries. [36, 40, 53, 73] employed multi-task frameworks to combine trajectory imputation and prediction. [24, 57, 62, 88] distilled complete trajectory knowledge into partially observed models. Lately, [71] first exploited mask formats as conditional input to unify all three tasks in a BERT-SSM structure.",
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+ "text": "Even though significant efforts have been devoted, existing approaches handled observed and unobserved behaviors in a coupled manner and encountered challenges in generating realistic multi-agent trajectories. Their suboptimal performance is inevitable for 2 reasons. First, they failed to realize that coupling the accurate representations and the uncertain ones with significant noise is deviating its latent space from the real-world behavior distribution. Second, more than an attached condition, the observation masks are precise boundaries between accuracy and uncertainty that need to be explicitly incorporated into the decoupling.",
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+ "text": "In this work, we reexamine unified trajectory modeling from coupled to decoupled manner. We introduce UniMTD, a unified framework for trajectory modeling in a decoupled denoising diffusion modeling paradigm, as a 'panacea' for arbitrary levels of missing observations in real practice. To achieve decoupling according to observation masks, a unidirectional attention as the valve unit is proposed. By controlling one-way information flow between observed and masked tokens, it can separate the uncertain noise, maintain the accuracy of the latent space, and consistently project the masked representations into the preserved space. For decoding, we consider the pre-completed encoder output as the deterministic component of the trajectory pattern and directly reuse it as intermediate parts in the diffusion model to efficiently improve trajectory generation quality. Main",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "Figure 1. (a) Above is a diagram of a traffic accident caused by the blue vehicle's observation failure of the pedestrian due to the obstruction. From the perspective of multi-agent trajectory modeling, the blue car is fully observed. The white car/van and brown car require prediction and imputation. The pedestrian with severe observation missing needs trajectory recovery. Below are real-world cases. In the first row, the pedestrian crashed due to being blocked. In the second row, the vehicle suddenly entered the view, resulting in an accident. (b) UniMTD (Ours) at the outermost side represents the minimum errors (averaged normalized error across three human datasets) on all 5 metrics. (c) Diagram of main differences and advantages of our method compared with previous methods during the encoding and decoding processes."
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+ "text": "differences and improvements are shown in Fig.1 (c)",
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+ "text": "Specifically, in the encoder, we propose an unidirectional attention (UA) as the valve unit. The UA is composed of a unidirectional masking (UM) and a progressive removal (PR) process. The UM allows one-way attention from observed to unobserved tokens, forcing the model to focus on the accurate information and confining the unobserved behaviors to learn from them. The PR removes the UM on the well-learned unobserved behaviors to further project it into the accurate distribution. The UA is built in a Unidirectional MoE (UMoE) with a local-global experts (LGE) division and a complex adaptive router (CAR) for multi-level observation missing. In the decoder, we design a cached diffusion model (CDiff) reusing the pre-calculated deterministic coordinates and features to conduct a truncated diffusion process, which enables us to improve the quality of trajectory modeling at an extremely low cost in terms of model size $(< 5\\%)$ and time $(< 5\\%)$ compared to the original DDPM.",
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+ "text": "We construct our datasets in both multi-agent vehicle traffic and human behavior scenarios. In both qualitative and quantitative results, UniMTD significantly surpasses existing methods in similar tasks across all 5 evaluation metrics with undamaged efficiency as shown in Fig.1 (b). It achieves $74\\%$ advantage in accuracy and $91\\%$ , $66\\%$ , $69\\%$ , and $58\\%$ advantages across 4 fidelity metrics on out-of-boundary, velocity, and trajectory length. In summary, the main contributions of our work are as follows:",
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+ "- We introduce UniMTD, a novel unified trajectory modeling framework, transforming various trajectory-related tasks into an observed-unobserved decoupled masked diffusion paradigm.",
+ "- We design a unidirectional attention as a valve unit to decouple accurate and uncertain latent space and further construct a unidirectional MoE apt for arbitrary levels of"
+ ],
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+ "type": "text",
+ "text": "missing observations. A cached diffusion model is also designed to generate high-quality trajectories with low time and computation burden.",
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+ "type": "text",
+ "text": "- We conduct extensive experiments on our framework across multiple human movement and traffic datasets to validate our consistent and outstanding performance with further analysis of our design.",
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+ "type": "text",
+ "text": "2. Related Works",
+ "text_level": 1,
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+ "type": "text",
+ "text": "2.1. Prediction, Imputation and Recovery",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "Trajectory prediction predicts future behaviors based on historical observations. In the early studies, kinematics [38, 42] and filter-based [37, 82] methods were widely used. Started by Social-LSTM[1], neural networks such as RNN, LSTM, and GRU [8, 9, 11, 51, 67, 81] are designed to handle sequential data and agent interaction in trajectory prediction. With the popularity of generative methods, more recent studies have adopted generative frameworks such as GAN [3, 21, 28, 39], VAE [13, 29, 41, 70], and Diffusion models [27, 45, 47, 65] as future trajectory generators, enabling models to generate more realistic behaviors. The generative decoders fundamentally rely on a rich representation extracted from the encoder, which has led to the rise of MAE-based pre-training methods such as Traj-mae [14, 66, 68, 75], which are applied to a wide range of downstream tasks through fine-tuning.",
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+ "type": "text",
+ "text": "Imputation typically serves as a preprocessing method for slight data missing. Traditional statistical methods include interpolation [49], regression [6], and EM algorithms [55]. Statistical methods are efficient but struggle with complex sequences. Deep learning frameworks use RNNs [7, 77], autoregressive models [5, 16], or generative techniques such as GAN, VAE, and Diffusion Model",
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+ "type": "page_number",
+ "text": "27564",
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+ "type": "text",
+ "text": "[19, 48, 52, 78] to generate reconstructed sequences. Existing research on trajectory imputation in multi-agent scenarios is scarce: NAOMI [46] introduces a non-autoregressive imputation method, while Graph Imputer [50] utilized bidirectional features to impute soccer player trajectories.",
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "Trajectory recovery is similar to imputation but differs in the observation ratio. When less than $20\\%$ observations are left caused by severe data loss or insufficient sampling, trajectory recovery as a conditional generation task needs to reconstruct the entire trajectory's motion pattern based on sparse information. Current research involves recovering trajectory data from GPS points [18, 64], but research on multi-agent scenarios is still blank.",
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+ },
+ {
+ "type": "text",
+ "text": "Although promising results have been achieved, the above methods have trouble generalizing across tasks. To mitigate cascade errors, the latest research has focused on trajectory prediction with slightly noised data, [24, 36, 40, 53, 57, 62, 73, 88], but these efforts are meeting challenges in generalizing to related tasks and obtaining accurate and realistic prediction results.",
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+ {
+ "type": "text",
+ "text": "2.2. Mask Modeling",
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+ "type": "text",
+ "text": "Mask modeling, since its inception in [23], has been extensively applied to pre-training tasks in trajectory prediction [14, 66, 68, 75] but is still incapable of handling multi-agent scenes with observation missing. [10] first extended mask modeling to generative tasks, iteratively predicting masked tokens, which is naturally adaptable to generation, inpainting, editing, etc. Various tasks can be considered as masking strategies within a unified framework.",
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+ "type": "text",
+ "text": "Compared to the successful vision and language mask modeling [10, 23, 30, 34], trajectory modeling has higher mask proportion ( $>50\\%$ ), which limits the learning of the real distribution [62]. Besides, the random mask makes it impossible to use the MAE strategy [89] to batch-separate the noise. Moreover, unlike [10], lacking a powerful domain-pretrained tokenizer and decoder like VQGAN [25] or CLIP [54] prevents trajectory modeling in the latent space, and efficiency burdens are making a large number of iterative inferences not preferred.",
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+ {
+ "type": "text",
+ "text": "2.3. Diffusion Models",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "Diffusion models [31] capable of generating high-quality samples through an iterative denoising process, which have recently achieved remarkable results in the fields of image and video generation [32, 63], time series forecast [43, 56], and remote sensing [12, 32, 44], etc. For trajectory modeling, MID [27] is the first diffusion-based method modeling the ambiguous walkable regions to desired trajectories. For the main concerns on computational and time cost, LeapFrog [47] distilled major denoising steps into an initializer to reduce the time costs in pre-trained MID. IDM [45] revealed that introducing goal information reduces de",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "noising steps.",
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "Above methods require a full-parameter diffusion model with time and computational redundancies, and CDiff greatly reduces both of them.",
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+ "type": "text",
+ "text": "3. UniMTD",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "3.1. Overall Framework",
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+ {
+ "type": "text",
+ "text": "The overall framework of UniMTD is depicted in Fig.2 (a). Take incomplete trajectories with arbitrary masks as input, the unidirectional encoder composed of UMoE and the diffusion generator with CDiff collaborate to generate completed versions of the input.",
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+ "type": "text",
+ "text": "3.2. Unidirectional Encoder",
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+ "text": "The unidirectional encoder is composed of UMoE blocks, which include UA, LGE, and CAR.",
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+ "type": "text",
+ "text": "3.2.1. Twin Structure",
+ "text_level": 1,
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+ "type": "text",
+ "text": "The entire encoder is designed in a twin structure $\\mathrm{E}_M$ and $\\mathrm{E}_U$ with shared weights, inspired by [17] to project masked and unmasked behaviors into the same latent space and provide an accurate reference $\\mathbf{f}_{\\mathrm{ref}}$ for the progressive removal. During the training phase, $\\mathrm{E}_M$ and $\\mathrm{E}_U$ encode masked and complete trajectories to $\\mathbf{f}_{\\mathrm{M}}$ and $\\mathbf{f}_{\\mathrm{U}}$ respectively. We aligned them in the latent space by MSE loss on masked positions. In the testing phase, only $\\mathrm{E}_M$ is used to obtain $\\mathbf{f}_{\\mathrm{M}} = \\mathbf{f}_{\\mathrm{st}}$ .",
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+ "type": "text",
+ "text": "3.2.2. Unidirectional Attention",
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+ "type": "text",
+ "text": "The unidirectional attention (UA) is proposed to preserve accurate latent space according to the clean observations. It shoulders 2 tasks: separate the noise from significant observation missing; project the masked tokens into the accurate latent space and extract complete spatiotemporal trajectory features. Thus, unidirectional masking and progressive removal are designed to meet the demands, respectively.",
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+ "type": "text",
+ "text": "Unidirectional masking (UM) is designed to control the information transformation to operate only from the observed data to themselves and the missing data, making the encoding process unidirectional for masked trajectory modeling. By explicitly isolating the observed and the missing data, we can ensure that even with only highly sparse clean observations, they are free from noise interference.",
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+ "type": "text",
+ "text": "Specifically, similar to the causal mask [61], UM sets the attention weights corresponding to the positions of missing data to 0, meaning that all tokens can only perform attention calculations with tokens that have not been masked. For temporal masking, assuming $i$ th trajectory $\\mathbf{x}_i \\in \\mathbb{R}^{T \\times 2}$ of length $T$ and the corresponding mask $\\mathbf{m}_i \\in \\mathbb{R}^T$ , the temporal $\\mathbf{UM}_i \\in \\mathbb{R}^{T \\times T}$ can be obtained as follows:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\mathbf {U M} _ {i} = \\left[ \\mathbf {U M} _ {i} ^ {0}, \\mathbf {U M} _ {i} ^ {1}, \\dots , \\mathbf {U M} _ {i} ^ {T} \\right] ^ {\\top}, \\\\ \\mathbf {U M} _ {i} ^ {j} = \\left\\{ \\begin{array}{l l} 0, & \\text {w h e r e} \\mathbf {m} _ {i} = 1 \\\\ - \\operatorname {I n f}, & \\text {w h e r e} \\mathbf {m} _ {i} = 0 \\end{array} , j \\in [ 0, T ] \\right. \\tag {1} \\\\ \\end{array}\n$$\n",
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+ "type": "page_number",
+ "text": "27565",
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+ {
+ "type": "image",
+ "img_path": "images/f1149cf340d9e1bffcd7d26e79dfb074ed0cf63f0387158e12d12157a179897e.jpg",
+ "image_caption": [
+ "(a)",
+ "Masked Trajectory",
+ "(b)"
+ ],
+ "image_footnote": [],
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+ "page_idx": 3
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+ {
+ "type": "image",
+ "img_path": "images/2d3dcf35f93975050995d29ac6d21bca355cea6ee0e5fb88f66829aad79c43ea.jpg",
+ "image_caption": [
+ "(c)"
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+ "type": "image",
+ "img_path": "images/4b42ed839047e69ebaf3997e8f36bd7996a872d9e2c7d68b93401df75deccd0e.jpg",
+ "image_caption": [
+ "Figure 2. (a) The overall framework of UniMTD, including unidirectional encoder with UMoE, and diffusion generator with CDiff. (b) The detailed calculation of UA, including PR (left) and UM (right). (c) The detailed design of UMoE (left) and CDiff (right)."
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+ "type": "text",
+ "text": "For social masking, $N$ multi-agent trajectories at timestep $t$ is $\\mathbf{x}^t\\in \\mathbb{R}^{N\\times 2}$ and the corresponding mask $\\mathbf{m}^t\\in \\mathbb{R}^N$ , the social $\\mathbf{UM}_t\\in \\mathbb{R}^{N\\times N}$ can be obtained as same as temporal masking.",
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+ "type": "text",
+ "text": "Through the above masking strategy, UM allows the information exchange among the clean tokens to form an accurate latent space, and the noisy tokens are confined to gathering information from it.",
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+ "type": "text",
+ "text": "Progressive Removal (PR) is implemented as a refinement process progressively removing the UM mask to project the masked representations into the preserved latent space. Although the continuous existence of UM ensures an accurate latent space, the isolated tokens are not conducive to the extraction of consistent and complete trajectory features. Therefore, when the masked tokens conform to the",
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+ "type": "text",
+ "text": "accurate latent distribution, the mask on them should be removed. The process is depicted in Fig.2 (b-left).",
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+ "type": "text",
+ "text": "Applied layer by layer, PR employs a 3-layer LSTM Score(\\cdot) to estimate the confidence $\\mathbf{p}_l$ of the $l$ layer's masked features conforming to the reference accurate latent features. For each layer, $k$ masked tokens with the most confidence are unmasked ( $m_k^l$ from $0 \\to 1$ ) and used as a condition for predicting other masked tokens in the next layer. The $l$ th layer mask can be formulated as:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {f} _ {\\mathbf {s t}} ^ {l} = \\operatorname {L a y e r} ^ {l - 1} \\left(\\mathbf {f} _ {\\mathbf {s t}} ^ {(l - 1)}, \\mathbf {m} ^ {l - 1}\\right),\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {p} _ {l} = \\operatorname {s o f t m a x} \\left(\\frac {1}{\\operatorname {S c o r e} \\left(\\mathbf {f} _ {\\mathbf {s t}} ^ {l} , \\mathbf {f} _ {\\mathbf {r e f}} ^ {l}\\right)}\\right), \\tag {2}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\nm _ {(n, t)} ^ {l} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} p _ {(n, t)} ^ {l} \\in \\operatorname {T o p k} \\left(\\mathbf {p} _ {\\mathbf {i}}\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right.\n$$\n",
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+ "type": "page_number",
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+ "type": "text",
+ "text": "where $\\mathbf{f_{st}}^l$ is spatiotemporal features of $l$ th layer, and $\\mathbf{p}_l$ is the confidence. The Score $(\\cdot)$ network can be trained as follows:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} = \\frac {1}{L} \\sum_ {l = 1} ^ {L} \\operatorname {M S E} \\left(\\operatorname {L S T M} \\left(\\mathbf {f} _ {\\mathbf {s t}} ^ {l}, l\\right), \\left\\| \\mathbf {f} _ {\\mathbf {s t}} ^ {l} - \\mathbf {f} _ {\\mathbf {r e f}} ^ {l} \\right\\| _ {2}\\right) \\tag {3}\n$$\n",
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+ "type": "text",
+ "text": "The overall calculation of unidirectional attention is depicted in Fig.2 (b-right), and can be formulated as follows:",
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+ "page_idx": 4
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\operatorname {U A} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top} \\cdot \\operatorname {P R} (\\mathbf {U M})}{\\sqrt {d _ {k}}}\\right) \\mathbf {V} \\tag {4}\n$$\n",
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+ "type": "text",
+ "text": "3.2.3. Unidirectional MoE",
+ "text_level": 1,
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "The unidirectional MoE (UMoE) includes local/global experts (LE/GE) and a complex adaptive router (CAR). Detailed structures are shown in Fig.2 (c-left).",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "As for trajectory, each coordinate lacks specific meaning, and the behavior is mainly described in a global view. Routing different experts for each time step leads to inconsistent features and weak expert specificity. To address this, we divide LE/GE and use a UA layer as a shared expert $\\mathrm{LE}(\\cdot)$ activates for all local movement tokens to extract common knowledge $\\mathbf{z}_{\\mathbf{c}}$ and maintains the motion stability. Meanwhile, the unmasked tokens of each agent are pooled into global features and routed to a group of sparsely activated experts $\\mathrm{GES}(\\cdot)$ for specific behavior knowledge $\\mathbf{z}_{\\mathbf{s}}$ , emphasizing the expert specialization among the unique behaviors across multiple agents. We also design a complexity adaptive router to allocate a dynamic number of experts $\\mathbf{k}_{\\mathbf{e}}$ according to mask ratios to handle the multi-level complexity inherent in arbitrary mask formats. The calculation in UMoE can be formulated as follows:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathbf {z} _ {\\mathbf {c}} = \\operatorname {L E} \\left(\\mathbf {f} _ {s t}, \\operatorname {P R} (\\mathbf {U M})\\right) \\in \\mathbb {R} ^ {B \\times N \\times T \\times D},\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {k} _ {\\mathrm {e}} = \\operatorname {N o r m a l i z e} (1 - \\operatorname {P R} (\\mathbf {U M})) \\cdot N _ {e},\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {w} _ {e} = \\operatorname {T o p k} \\left(\\mathbf {f} _ {\\text {m e t a}}, \\mathbf {f} _ {s t}, \\mathbf {k} _ {\\mathbf {e}}\\right) \\in \\mathbb {R} ^ {B \\times N \\times k _ {e}},\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {z} _ {\\mathbf {s}} = \\sum_ {i = 0} ^ {k _ {e}} \\mathbf {w} _ {e} ^ {i} \\cdot \\operatorname {G E} _ {i} (\\operatorname {p o o l} (\\mathbf {f} _ {s t})) \\in \\mathbb {R} ^ {B \\times N \\times D}, \\tag {5}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {z} _ {\\mathbf {s}} \\xrightarrow {\\text {r e p e a t}} \\mathbf {z} _ {\\mathbf {s}} \\in \\mathbb {R} ^ {B \\times N \\times T \\times D},\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {z} = \\mathbf {z _ {c}} \\cdot \\mathbf {z _ {s}}\n$$\n",
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+ "type": "text",
+ "text": "3.3. Diffusion Generator",
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+ "text": "The Diffusion Generator comprises a cached diffusion model and a tiny CNN decoder.",
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+ "text": "3.3.1. Cached Diffusion Model",
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+ "text": "The MAE decoding lacks diversity, and the iterative paradigm incurs high computational and time costs. Combine the strengths of the two and make up for their weaknesses, as shown in Fig.2 (c-right), we propose a cache mechanism to replace the deeper features and a large number of preceding inverse diffusion steps using the deterministic feature $\\mathbf{z} \\in \\mathbb{R}^{(B \\cdot l) \\times T \\times d}$ and coordinate $\\hat{\\mathbf{X}}_{\\gamma + 1} \\in$",
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+ "text": "$\\mathbb{R}^{(B \\cdot l) \\times T \\times 2}$ of the encoder. In this way, we have reduced the noise estimator $f_{\\epsilon}$ with 6 attention layers and 200 steps to only a single layer and 5 steps. The denoising process can be revised as follows:",
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+ "text": "\n$$\n\\mathbf {z} _ {\\gamma} = \\operatorname {A t t e n t i o n L a y e r} \\left(\\tilde {\\mathbf {X}} _ {\\gamma + 1}\\right) + \\mathbf {z},\n$$\n",
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+ "text": "\n$$\n\\epsilon_ {\\boldsymbol {\\theta}} ^ {\\gamma} = f _ {\\epsilon} (\\hat {\\mathbf {X}} _ {0} \\cdot \\mathbf {M} + \\hat {\\mathbf {X}} _ {\\gamma + 1} \\cdot (1 - \\mathbf {M}), \\mathbf {z} _ {\\gamma}),\n$$\n",
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+ "text": "\n$$\n\\hat {\\mathbf {X}} _ {\\gamma} = \\frac {1}{\\sqrt {\\alpha_ {\\gamma}}} \\left(\\hat {\\mathbf {X}} _ {\\gamma + 1} - \\frac {1 - \\alpha_ {\\gamma}}{\\sqrt {1 - \\bar {\\alpha} _ {\\gamma}}} \\epsilon_ {\\theta} ^ {\\gamma}\\right) + \\sqrt {1 - \\alpha_ {\\gamma}} \\cdot \\epsilon \\tag {6}\n$$\n",
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+ "text": "where $\\alpha_{\\gamma}$ and $\\bar{\\alpha}_{\\gamma} = \\prod_{i=1}^{\\gamma} \\alpha_{i}$ are parameters at denoising step $\\gamma$ . $\\epsilon \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})$ are gaussian noises.",
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+ "type": "text",
+ "text": "4. Experiments",
+ "text_level": 1,
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+ "text": "4.1. Benchmarks and Setup",
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+ "text": "Datasets: We applied diverse trajectory datasets to verify the applicability of UniMTD on various fields, including three human motion datasets and one vehicle motion dataset with three subsets of different difficulty: Basketball $\\mathbf{U}^{*}$ [80], Soccer- $\\mathbf{U}^{*}$ [58], Football- $\\mathbf{U}^{*}$ , and Vehicle- $\\mathbf{U}$ (Easy/Ordinary/Hard) $^{*}$ [60] constructed following [73]. The mask strategy is consistent with [71] for comparison.",
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+ "text": "Evaluation Protocol: We generate a total of $k = 20$ candidate trajectories based on the masked trajectory input and use the $\\min\\mathrm{ADE}_{20}$ as the accuracy evaluation metric. Furthermore, four additional metrics to reflect the generation quality of agent movements'velocity, range, and behavior differences are employed to comprehensively assess the generation quality. (1) $\\min\\mathrm{ADE}_{20}$ : Minimum average displacement error between the generated trajectories and the ground truth across the 20 generated trajectories, (2) Out-of-Boundary (OOB): The percentage of generated locations that fall outside the predefined court boundaries, (3) Step: The average change in step size across the generated trajectories, (4) Path-L: The average length of the trajectories for each agent, (5) Path-D: The maximum difference in trajectory lengths among all agents. The calculations are consistent with [71].",
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+ "type": "text",
+ "text": "4.2. Quantitative Results",
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+ "text": "Quantitative results are recorded in Tab.1 on the Basketball-U, Soccer-U, and the Football-U and Tab.2 on the Vehicle-U. Across all datasets, compared with mathematical interpolation methods, general deep learning frameworks, and specialized methods for relevant tasks, our UniMTD",
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+ "type": "page_footnote",
+ "text": "*https://github.com/linouk23/NBA-Player-Movements",
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+ "text": "\\*https://github.com/AtomScott/SportsLabKit",
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+ "text": "\\*https://github.com/nfl-football-ops/Big-Data-Bowl",
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+ "text": "\\*https://github.com/shijieS/OmniMOTDataset",
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+ "text": "27567",
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+ "type": "table",
+ "img_path": "images/a03de47e060a65b0c244567c2c91d418930ee981a6c2500d8c17839123d27a96.jpg",
+ "table_caption": [
+ "Table 1. Quantitative results on datasets Basketball- $\\mathbf{U}$ (in feet),Soccer- $\\mathbf{U}$ (in pixels),and Football- $\\mathbf{U}$ (in yards)"
+ ],
+ "table_footnote": [],
+ "table_body": "| Dataset | Basketball-U (In Feet) | Soccer-U (In Pixels) | Football-U (In Yards) |
| Method | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D |
| Mean | 14.58 | 0 | 0.99 | 52.39 | 737.58 | 417.68 | 0 | 4.32 | 213.05 | 8022.51 | 14.18 | 0 | 0.52 | 25.06 | 606.07 |
| Medium | 14.56 | 0 | 0.98 | 51.80 | 743.36 | 418.06 | 0 | 4.39 | 214.55 | 8041.98 | 14.23 | 0 | 0.52 | 24.96 | 600.22 |
| Linear Fit | 13.54 | 4.47e-03 | 0.56 | 42.86 | 453.38 | 398.34 | 0 | 0.70 | 112.34 | 2047.19 | 12.66 | 1.49e-04 | 0.17 | 15.83 | 207.57 |
| LSTM[33] | 7.10 | 9.02e-04 | 0.76 | 58.48 | 449.58 | 186.93 | 4.74e-05 | 7.50 | 652.98 | 4542.78 | 7.20 | 2.24e-04 | 0.43 | 34.06 | 228.13 |
| Transformer[61] | 6.71 | 2.38e-03 | 0.79 | 59.34 | 517.54 | 170.94 | 6.59e-05 | 6.66 | 566.14 | 4269.08 | 6.84 | 5.68e-04 | 0.42 | 33.01 | 202.10 |
| MAT[80] | 6.68 | 1.36e-03 | 0.88 | 58.83 | 483.46 | 170.46 | 7.56e-05 | 6.45 | 562.44 | 3953.34 | 6.36 | 4.57e-04 | 0.40 | 31.32 | 186.11 |
| Naomi[46] | 6.52 | 2.02e-03 | 0.81 | 69.10 | 450.66 | 145.20 | 8.78e-05 | 7.47 | 649.62 | 4414.99 | 6.77 | 7.66e-04 | 0.67 | 42.74 | 259.11 |
| INAM[52] | 6.53 | 3.16e-03 | 0.70 | 58.54 | 439.87 | 134.86 | 4.04e-05 | 6.37 | 547.02 | 4102.37 | 5.80 | 8.30e-04 | 0.39 | 32.10 | 177.04 |
| SSSD[2] | 6.18 | 1.82e-03 | 0.47 | 46.87 | 393.12 | 118.71 | 4.51e-05 | 5.11 | 425.98 | 3252.66 | 5.08 | 6.81e-04 | 0.39 | 23.10 | 122.42 |
| GC-VRNN[73] | 5.81 | 9.28e-04 | 0.37 | 28.08 | 235.99 | 105.87 | 1.29e-05 | 4.92 | 506.32 | 3463.26 | 4.95 | 7.12e-04 | 0.29 | 32.48 | 149.87 |
| UniTraj[71] | 4.77 | 6.12e-04 | 0.27 | 34.25 | 240.83 | 94.59 | 1.29e-05 | 4.52 | 349.73 | 2805.79 | 3.55 | 1.12e-04 | 0.23 | 19.26 | 114.58 |
| Ground Truth | 0 | 0 | 0.17 | 37.61 | 269.49 | 0 | 0 | 0.52 | 112.92 | 951.00 | 0 | 0 | 0.03 | 12.56 | 76.68 |
| UniMTD (Ours) | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 13.65 | 0 | 0.95 | 124.39 | 1688.11 | 0.91 | 2.84e-05 | 0.09 | 13.45 | 107.38 |
",
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+ "img_path": "images/8ac786f447bce0cd5baf3251e5cca8101ad9a61fe15ebd79dc3d4e83ac491ca4.jpg",
+ "table_caption": [
+ "Table 2. Quantitative results on datasets Vehicle-U with Easy, Ordinary, and Hard scenarios (in pixels)"
+ ],
+ "table_footnote": [],
+ "table_body": "| Dataset | Vehicle-U Easy (In Pixels) | Vehicle-U Ordinary (In Pixels) | Vehicle-U Hard (In Pixels) |
| Method | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D |
| Transformer [61] | 107.93 | 5.61e-03 | 7.12 | 457.18 | 5913.21 | 92.47 | 4.77e-03 | 6.79 | 376.59 | 5723.45 | 108.76 | 1.07e-02 | 7.04 | 472.83 | 5835.42 |
| SSSD [2] | 30.99 | 1.82e-03 | 0.47 | 228.30 | 1611.98 | 28.90 | 9.51e-04 | 0.41 | 119.57 | 1829.07 | 30.65 | 5.92e-03 | 0.50 | 131.65 | 2160.53 |
| UniTraj [71] | 77.65 | 3.94e-03 | 2.42 | 165.28 | 4036.13 | 66.05 | 2.11e-03 | 4.01 | 257.17 | 5350.69 | 79.39 | 7.48e-03 | 4.70 | 255.12 | 5204.53 |
| Ground Truth | 0 | 0 | 0.06 | 43.30 | 1574.39 | 0 | 0 | 0.04 | 28.51 | 2030.48 | 0 | 0 | 0.05 | 28.92 | 1940.34 |
| UniMTD(Ours) | 13.12 | 9.04e-04 | 0.75 | 79.15 | 1726.57 | 10.62 | 3.28e-04 | 0.65 | 62.37 | 2079.77 | 15.40 | 2.97e-03 | 0.86 | 75.19 | 2100.29 |
",
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+ {
+ "type": "text",
+ "text": "achieves the SOTA performance, leading by a large margin across all 5 metrics.",
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+ "text": "Specifically, for datasets *Basketball-U*, *Soccer-U*, and *Football-U* depicting complex human behavior, UniMTD outperforms the current best-performing UniTraj by averaged 74% and surpasses the Diffusion model-based SSSD by averaged 80% on the $\\min\\mathrm{ADE}_{20}$ metric, indicating a great leap in accuracy of behavior modeling. For OOB, Step, Path-L, and Path-D, UniMTD has achieved 91%, 66%, 69%, and 58% averaged advantages across data-driven methods, indicating that our generated trajectories align more closely with real motion patterns. For datasets Vehicle-U, UniMTD achieves SOTA performance, with averaged 56%, 33%, 44%, 15% advantages on $\\min\\mathrm{ADE}_{20}$ , OOB, Path-L, Path-D across all three subsets, and the step metric is the second-best. Different from human sports in limited scenes, the vehicle dataset exhibits a significant amount of behaviors entering and leaving the scene, involving more large-scale, high-dynamic scenarios. This may lead to an increase in OOB and give advantages to the SSSD method based on a 200-step diffusion model with strong abilities to express detailed and local behaviors, such as step-by-step velocity. Our SOTA performance on the majority of metrics across all datasets demonstrates the model's versatility in different scenarios.",
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+ "text": "Regarding the inference time, for a scenario containing 11 agents, UniTraj requires 0.16s, UniMTD requires 0.18s, while SSSD, which also uses the diffusion model, requires more than 10s. This is because our CDiff reduces the number of denoising steps from 200 to 5 and simplifies the cal",
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+ "text": "culation, thus improving the inference efficiency.",
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+ {
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+ "text": "4.3. Qualitative Results",
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+ "text": "In Fig.3, we qualitatively compared the results between the prediction model, UniTraj, SSSD, UniMTD, and the UniMTD without CDiff or UA on the Basketball-U dataset. The results in the seventh column illustrate that our UniMTD generates behaviors with superior accuracy and fidelity, especially in the recovery of arc (purple) and circle (green, blue) trajectories. In the second column, models trained solely on prediction naturally cannot adapt to imputation and recovery but are unexpectedly not satisfactory on prediction. This result indicates that the unified modeling may benefit its subtasks. In the third column, UniTraj can generate behaviors with misconnection and even failure in recovery. In the fourth column, SSSD obtains inaccurate but detailed behavior sequences in prediction and imputation and also fails in the recovery task. In the fifth column, the woCDiff model generates averaged results with significant connection errors and overly smooth behaviors. In the sixth column, the woUA model discloses fluctuations and distortions due to the unseparated uncertain mask noise.",
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+ "text": "The qualitative evaluation results confirm the significant superiority of our method in quantitative results and also demonstrate our correct insights into UA and CDiff designs.",
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+ "text": "4.4. Model Analysis",
+ "text_level": 1,
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+ "text": "4.4.1. Ablation Study",
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+ "text": "Tab.3 demonstrates the results of our ablation studies conducted on the Basketball-U dataset. The upper part records",
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+ "img_path": "images/ab465485f695bee271a3697c4158b115843c72ac86debb9291197b52e2bde198.jpg",
+ "image_caption": [
+ "Figure 3. The qualitative comparison of different methods under specific unified mask format across prediction, imputation, recovery, and a mixed scenario of these three. The ground truth is on the left, and our method is shown on the right side. Players 1-5 are in different colors, and the observed area is black."
+ ],
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+ "img_path": "images/84e40b59c4b1415b019e5bc011ca2364143df715f33af4d4403ff63e8b3074ff.jpg",
+ "image_caption": [
+ "Figure 4. The statistical analysis of the distribution of player and masking ratios across experts 1-3. The typical movement patterns of each expert are given on the right."
+ ],
+ "image_footnote": [],
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+ "text": "the performance variations when key parameters and model capacity are modified, while the lower part documents the performance variations when CDiff, PR, CAR (replaced by Top2 router), UMoEs (replaced by UA layers), and UM (UA to full attention) are successively removed.",
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+ "text": "For the upper part, when the number of experts increases $(N_{e} = 16)$ or decreases $(N_{e} = 4)$ , only the OOB and Path-L metrics improve, while all other metrics deteriorate. When the model capacity is directly increased, the minADE and step improve, while other metrics deteriorate. From the overall trend, as the model becomes more complex, both accuracy and fidelity metrics show the potential for contin",
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+ "text": "ued improvement, but this improvement may come at the cost of deterioration in other metrics.",
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+ "text": "For the lower part, w/o CDiff indicates that CDiff improved the accuracy with only a cost of $< 5\\%$ size inflation. w/o UMoE indicates that replacing UMoE with UA layers leads to severe degradations on both accuracy and fidelity. w/o CAR indicates that CAR can better handle the multi-level complexity inherent in arbitrary observation loss than commonly used top-k routing. w/o PR and w/o UM demonstrate a performance nosedive when observed and unobserved behaviors are coupled, indicating that UA contributes to both accuracy and fidelity with almost no ad",
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+ "img_path": "images/d3ecef9fe4ae8ae19cfaa546b2bdb1751def25253ea4b9fd5db596cea2b34990.jpg",
+ "table_caption": [
+ "Table 3. Ablation experiment on Basketball-U"
+ ],
+ "table_footnote": [],
+ "table_body": "| Variants | minADE↓ | OOB↓ | Step | Path-L | Path-D | Size (M) |
| UniMTD | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 37.19 |
| Ne=4 | 2.13 | 5.40e-06 | 0.25 | 36.28 | 335.40 | 27.71 |
| Ne=16 | 1.90 | 1.32e-06 | 0.24 | 35.88 | 202.67 | 41.93 |
| 6UMoEs | 1.85 | 1.18e-05 | 0.21 | 35.45 | 215.08 | 53.18 |
| w/o CDiff | 1.95 | 1.32e-06 | 0.26 | 37.13 | 245.75 | 35.86 |
| w/o PR | 2.12 | 1.32e-07 | 0.27 | 38.44 | 203.72 | 35.54 |
| w/o CAR | 2.22 | 6.32e-06 | 0.26 | 37.18 | 319.15 | 35.54 |
| w/o UMoE | 2.92 | 9.21e-07 | 0.37 | 39.70 | 331.99 | 17.33 |
| w/o UM | 4.44 | 5.69e-5 | 0.44 | 51.19 | 398.76 | 17.33 |
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+ "img_path": "images/4ced9b37d8c53b7ff718eb76ce86731445422e634c866aaf3c3a9f4562616c0b.jpg",
+ "table_caption": [
+ "Table 4. Ablation experiment of CDiff efficiency on Basketball-U"
+ ],
+ "table_footnote": [],
+ "table_body": "| Variants | minADE↓ | OOB↓ | Step | Path-L | Path-D | Time (s) |
| Step=2 | 1.99 | 3.68e-06 | 0.25 | 37.31 | 216.41 | 0.17 |
| Step=5 | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 0.18 |
| Step=15 | 2.14 | 6.28e-05 | 0.28 | 37.41 | 203.65 | 0.51 |
| Step=50 | 2.73 | 2.25e-03 | 0.33 | 42.46 | 319.55 | 1.85 |
| Step=100 | 15.19 | 6.83e-02 | 3.22 | 207.11 | 5165.04 | 3.13 |
| Naive DDPM | 2.69 | 3.11e-5 | 0.28 | 39.19 | 304.65 | >10s |
",
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+ "type": "text",
+ "text": "ditional learnable parameters.",
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+ },
+ {
+ "type": "text",
+ "text": "In the following sections, we further conduct validation on CDiff, UMoE, and UA according to the original design insights.",
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+ "type": "text",
+ "text": "4.4.2. CDiff Efficiency Analysis",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Tab.4 records the impact of truncated denoising steps on trajectory modeling quality and efficiency.",
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+ "text": "In the top 5 rows, when step $>15$ , as steps increased, the inference time surged while the performance decreased. Suppose the input is too noisy compared to $\\hat{\\mathbf{X}}_0$ . The single Attention Layer cannot bridge the noisy input and accurate deeper features, leading to contamination and performance damage. In the last row, we compared the standard diffusion model in [27], demonstrating improved efficiency and performance. This is because the $\\hat{\\mathbf{X}}_0$ ensures the accuracy of CDiff modeling, while DDPM directly samples from the noise, which is prone to generating high-frequency tremors in highly-dynamic scenes.",
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+ "text": "4.4.3. UMoE Specialization Analysis",
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+ "text": "To validate the specialization in UMoE, we statistically analyzed the distribution of player and masking ratios corresponding to each expert (experts 1-3 as examples) on the left of Fig.4 and visualized the specialized movement patterns of each expert on the right.",
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+ "image_caption": [
+ "Figure 5. The comparison of the feature errors on masked and unmasked tokens. Different methods are in different colors."
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+ "text": "Masked trajectory modeling can be regarded as removing masked noise to restore the complete trajectory. We compared the denoising capabilities on the features of the encoder, that is, the feature robustness to mask noise. Specifically, we input the complete and masked trajectories successively and compare the features' $L1$ distances. The results of masked and unmasked tokens are in Fig. 5.",
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+ "text": "Compared with UniTraj and the woUA version, our method achieves the least error. The gap between the errors of unmasked tokens is greatly magnified in the distance of masked tokens prediction, indicating the importance of maintaining accurate, clean tokens for the overall quality of features and the effectiveness of the proposed UA.",
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+ "text": "5. Conclusion",
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+ "text": "In this work, we propose UniMTD, a novel unified multiagent trajectory modeling framework with an observed-unobserved decoupled masked diffusion paradigm. Essentially, we decouple observed-unobserved behavior to separate the interference from the uncertain latent space. To achieve this, we design a unidirectional attention as valve units to control the information flow between the accurate and the uncertain latent spaces. We further construct a unidirectional MoE and a cached diffusion model to handle the inherent multi-complexity and the efficiency requirements in trajectory modeling under arbitrary mask levels. Through extensive experiments and comprehensive evaluations, UniMTD consistently outperforms existing SOTA methods across trajectory prediction, completion, and recovery tasks with an averaged $>50\\%$ advantage on accuracy and fidelity. Establishing itself as a SOTA solution with significant potential for further exploration in the embodied foundation model.",
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+ "text": "6. Acknowledgements",
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+ "text": "The work was supported by the National Natural Science Foundation of China under Grant 62471014, 62125102, and U24B20177, the Beijing Natural Science Foundation under Grant JL23005, and the Fundamental Research Funds for the Central Universities.",
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+ ],
+ "bbox": [
+ 91,
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+ 480,
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+ ],
+ "page_idx": 11
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+ "Transportation research part C: emerging technologies, 142: 103787, 2022. 1",
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+ ],
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diff --git a/2025/Unified Multi-Agent Trajectory Modeling with Masked Trajectory Diffusion/08038fe6-7601-45f0-b544-974df2316e72_model.json b/2025/Unified Multi-Agent Trajectory Modeling with Masked Trajectory Diffusion/08038fe6-7601-45f0-b544-974df2316e72_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..0e56523553683d49cdbf98bd68a7e1eb1533e486
--- /dev/null
+++ b/2025/Unified Multi-Agent Trajectory Modeling with Masked Trajectory Diffusion/08038fe6-7601-45f0-b544-974df2316e72_model.json
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+[
+ [
+ {
+ "type": "header",
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+ "angle": 0,
+ "content": "CVF"
+ },
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+ "type": "header",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.116,
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+ "angle": 0,
+ "content": "Unified Multi-Agent Trajectory Modeling with Masked Trajectory Diffusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Songru Yang, Zhenwei Shi, Zhengxia Zou* \nDepartment of Aerospace Intelligent Science and Technology, School of Astronautics, Beihang University, Beijing, China \n{songruang2001, shizhenwei, zhengxiazou}@buaa.edu.cn"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.248,
+ 0.287,
+ 0.327,
+ 0.303
+ ],
+ "angle": 0,
+ "content": "Abstract"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.319,
+ 0.482,
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+ "angle": 0,
+ "content": "Understanding movements in multi-agent scenarios is a fundamental problem in intelligent systems. Previous research assumes complete and synchronized observations. However, real-world partial observation caused by occlusions leads to inevitable model failure, which demands a unified framework for coexisting trajectory prediction, imputation, and recovery. Unlike previous attempts that handled observed and unobserved behaviors in a coupled manner, we explore a decoupled denoising diffusion modeling paradigm with a unidirectional information valve to separate the interference from uncertain behaviors. Building on this, we proposed a Unified Masked Trajectory Diffusion model (UniMTD) for arbitrary levels of missing observations. We designed a unidirectional attention as a valve unit to control the direction of information flow between the observed and masked areas, gradually refining the missing observations toward a real-world distribution. We construct it into a unidirectional MoE structure to handle varying proportions of missing observations. A Cached Diffusion model is further designed to improve generation quality while reducing computation and time overhead. Our method has achieved a great leap across human motions and vehicle traffic. UniMTD efficiently achieves \\(74\\%\\) improvement in \\(\\min ADE_{20}\\) and reaches SOTA with advantages of \\(91\\%\\), \\(66\\%\\), \\(69\\%\\), and \\(58\\%\\) across 4 fidelity metrics on out-of-boundary, velocity, and trajectory length."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.092,
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Understanding multi-agent behavior is a critical foundation in various domains, including autonomous driving [35], action analysis [15, 26, 74], video surveillance [79, 83], and scene generation [69]. Trajectory modeling, which analyzes and generates the position sequence of multiple agents within the same scene, is particularly straightforward and effective for understanding agents' behavior."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Existing methods have made significant strides in trajectory prediction [4, 59, 72, 76, 86, 87], imputation [46, 84, 85], and recovery [20, 22] across multiple fields, such as human sports and traffic trajectory. However, existing approaches cannot handle multiple tasks simultaneously, leaving a gap between methods and real-world scenarios where all three tasks coexist, as shown in Fig.1 (a). Recently, increasing attempts have been made to break the task boundaries. [36, 40, 53, 73] employed multi-task frameworks to combine trajectory imputation and prediction. [24, 57, 62, 88] distilled complete trajectory knowledge into partially observed models. Lately, [71] first exploited mask formats as conditional input to unify all three tasks in a BERT-SSM structure."
+ },
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+ "type": "text",
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+ "content": "Even though significant efforts have been devoted, existing approaches handled observed and unobserved behaviors in a coupled manner and encountered challenges in generating realistic multi-agent trajectories. Their suboptimal performance is inevitable for 2 reasons. First, they failed to realize that coupling the accurate representations and the uncertain ones with significant noise is deviating its latent space from the real-world behavior distribution. Second, more than an attached condition, the observation masks are precise boundaries between accuracy and uncertainty that need to be explicitly incorporated into the decoupling."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this work, we reexamine unified trajectory modeling from coupled to decoupled manner. We introduce UniMTD, a unified framework for trajectory modeling in a decoupled denoising diffusion modeling paradigm, as a 'panacea' for arbitrary levels of missing observations in real practice. To achieve decoupling according to observation masks, a unidirectional attention as the valve unit is proposed. By controlling one-way information flow between observed and masked tokens, it can separate the uncertain noise, maintain the accuracy of the latent space, and consistently project the masked representations into the preserved space. For decoding, we consider the pre-completed encoder output as the deterministic component of the trajectory pattern and directly reuse it as intermediate parts in the diffusion model to efficiently improve trajectory generation quality. Main"
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+ "type": "page_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "* Corresponding author"
+ },
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+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "27563"
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+ "angle": 0,
+ "content": null
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+ "type": "image",
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+ "type": "image_caption",
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+ "content": "Figure 1. (a) Above is a diagram of a traffic accident caused by the blue vehicle's observation failure of the pedestrian due to the obstruction. From the perspective of multi-agent trajectory modeling, the blue car is fully observed. The white car/van and brown car require prediction and imputation. The pedestrian with severe observation missing needs trajectory recovery. Below are real-world cases. In the first row, the pedestrian crashed due to being blocked. In the second row, the vehicle suddenly entered the view, resulting in an accident. (b) UniMTD (Ours) at the outermost side represents the minimum errors (averaged normalized error across three human datasets) on all 5 metrics. (c) Diagram of main differences and advantages of our method compared with previous methods during the encoding and decoding processes."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "differences and improvements are shown in Fig.1 (c)"
+ },
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+ "type": "text",
+ "bbox": [
+ 0.089,
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+ "angle": 0,
+ "content": "Specifically, in the encoder, we propose an unidirectional attention (UA) as the valve unit. The UA is composed of a unidirectional masking (UM) and a progressive removal (PR) process. The UM allows one-way attention from observed to unobserved tokens, forcing the model to focus on the accurate information and confining the unobserved behaviors to learn from them. The PR removes the UM on the well-learned unobserved behaviors to further project it into the accurate distribution. The UA is built in a Unidirectional MoE (UMoE) with a local-global experts (LGE) division and a complex adaptive router (CAR) for multi-level observation missing. In the decoder, we design a cached diffusion model (CDiff) reusing the pre-calculated deterministic coordinates and features to conduct a truncated diffusion process, which enables us to improve the quality of trajectory modeling at an extremely low cost in terms of model size \\((< 5\\%)\\) and time \\((< 5\\%)\\) compared to the original DDPM."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We construct our datasets in both multi-agent vehicle traffic and human behavior scenarios. In both qualitative and quantitative results, UniMTD significantly surpasses existing methods in similar tasks across all 5 evaluation metrics with undamaged efficiency as shown in Fig.1 (b). It achieves \\(74\\%\\) advantage in accuracy and \\(91\\%\\), \\(66\\%\\), \\(69\\%\\), and \\(58\\%\\) advantages across 4 fidelity metrics on out-of-boundary, velocity, and trajectory length. In summary, the main contributions of our work are as follows:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "- We introduce UniMTD, a novel unified trajectory modeling framework, transforming various trajectory-related tasks into an observed-unobserved decoupled masked diffusion paradigm."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "- We design a unidirectional attention as a valve unit to decouple accurate and uncertain latent space and further construct a unidirectional MoE apt for arbitrary levels of"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.091,
+ 0.796,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "missing observations. A cached diffusion model is also designed to generate high-quality trajectories with low time and computation burden."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We conduct extensive experiments on our framework across multiple human movement and traffic datasets to validate our consistent and outstanding performance with further analysis of our design."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2. Related Works"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "2.1. Prediction, Imputation and Recovery"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.511,
+ 0.554,
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+ ],
+ "angle": 0,
+ "content": "Trajectory prediction predicts future behaviors based on historical observations. In the early studies, kinematics [38, 42] and filter-based [37, 82] methods were widely used. Started by Social-LSTM[1], neural networks such as RNN, LSTM, and GRU [8, 9, 11, 51, 67, 81] are designed to handle sequential data and agent interaction in trajectory prediction. With the popularity of generative methods, more recent studies have adopted generative frameworks such as GAN [3, 21, 28, 39], VAE [13, 29, 41, 70], and Diffusion models [27, 45, 47, 65] as future trajectory generators, enabling models to generate more realistic behaviors. The generative decoders fundamentally rely on a rich representation extracted from the encoder, which has led to the rise of MAE-based pre-training methods such as Traj-mae [14, 66, 68, 75], which are applied to a wide range of downstream tasks through fine-tuning."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Imputation typically serves as a preprocessing method for slight data missing. Traditional statistical methods include interpolation [49], regression [6], and EM algorithms [55]. Statistical methods are efficient but struggle with complex sequences. Deep learning frameworks use RNNs [7, 77], autoregressive models [5, 16], or generative techniques such as GAN, VAE, and Diffusion Model"
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+ "type": "page_number",
+ "bbox": [
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+ "bbox": [
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+ "angle": 0,
+ "content": "[19, 48, 52, 78] to generate reconstructed sequences. Existing research on trajectory imputation in multi-agent scenarios is scarce: NAOMI [46] introduces a non-autoregressive imputation method, while Graph Imputer [50] utilized bidirectional features to impute soccer player trajectories."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Trajectory recovery is similar to imputation but differs in the observation ratio. When less than \\(20\\%\\) observations are left caused by severe data loss or insufficient sampling, trajectory recovery as a conditional generation task needs to reconstruct the entire trajectory's motion pattern based on sparse information. Current research involves recovering trajectory data from GPS points [18, 64], but research on multi-agent scenarios is still blank."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Although promising results have been achieved, the above methods have trouble generalizing across tasks. To mitigate cascade errors, the latest research has focused on trajectory prediction with slightly noised data, [24, 36, 40, 53, 57, 62, 73, 88], but these efforts are meeting challenges in generalizing to related tasks and obtaining accurate and realistic prediction results."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.2. Mask Modeling"
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+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Mask modeling, since its inception in [23], has been extensively applied to pre-training tasks in trajectory prediction [14, 66, 68, 75] but is still incapable of handling multi-agent scenes with observation missing. [10] first extended mask modeling to generative tasks, iteratively predicting masked tokens, which is naturally adaptable to generation, inpainting, editing, etc. Various tasks can be considered as masking strategies within a unified framework."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Compared to the successful vision and language mask modeling [10, 23, 30, 34], trajectory modeling has higher mask proportion (\\(>50\\%\\)), which limits the learning of the real distribution [62]. Besides, the random mask makes it impossible to use the MAE strategy [89] to batch-separate the noise. Moreover, unlike [10], lacking a powerful domain-pretrained tokenizer and decoder like VQGAN [25] or CLIP [54] prevents trajectory modeling in the latent space, and efficiency burdens are making a large number of iterative inferences not preferred."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
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+ "angle": 0,
+ "content": "2.3. Diffusion Models"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Diffusion models [31] capable of generating high-quality samples through an iterative denoising process, which have recently achieved remarkable results in the fields of image and video generation [32, 63], time series forecast [43, 56], and remote sensing [12, 32, 44], etc. For trajectory modeling, MID [27] is the first diffusion-based method modeling the ambiguous walkable regions to desired trajectories. For the main concerns on computational and time cost, LeapFrog [47] distilled major denoising steps into an initializer to reduce the time costs in pre-trained MID. IDM [45] revealed that introducing goal information reduces de"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.514,
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+ 0.608,
+ 0.107
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+ "angle": 0,
+ "content": "noising steps."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "Above methods require a full-parameter diffusion model with time and computational redundancies, and CDiff greatly reduces both of them."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3. UniMTD"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
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+ "angle": 0,
+ "content": "3.1. Overall Framework"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.212,
+ 0.906,
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+ ],
+ "angle": 0,
+ "content": "The overall framework of UniMTD is depicted in Fig.2 (a). Take incomplete trajectories with arbitrary masks as input, the unidirectional encoder composed of UMoE and the diffusion generator with CDiff collaborate to generate completed versions of the input."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
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+ 0.731,
+ 0.311
+ ],
+ "angle": 0,
+ "content": "3.2. Unidirectional Encoder"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.318,
+ 0.906,
+ 0.349
+ ],
+ "angle": 0,
+ "content": "The unidirectional encoder is composed of UMoE blocks, which include UA, LGE, and CAR."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
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+ "angle": 0,
+ "content": "3.2.1. Twin Structure"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "The entire encoder is designed in a twin structure \\(\\mathrm{E}_M\\) and \\(\\mathrm{E}_U\\) with shared weights, inspired by [17] to project masked and unmasked behaviors into the same latent space and provide an accurate reference \\(\\mathbf{f}_{\\mathrm{ref}}\\) for the progressive removal. During the training phase, \\(\\mathrm{E}_M\\) and \\(\\mathrm{E}_U\\) encode masked and complete trajectories to \\(\\mathbf{f}_{\\mathrm{M}}\\) and \\(\\mathbf{f}_{\\mathrm{U}}\\) respectively. We aligned them in the latent space by MSE loss on masked positions. In the testing phase, only \\(\\mathrm{E}_M\\) is used to obtain \\(\\mathbf{f}_{\\mathrm{M}} = \\mathbf{f}_{\\mathrm{st}}\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
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+ "angle": 0,
+ "content": "3.2.2. Unidirectional Attention"
+ },
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+ "type": "text",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "The unidirectional attention (UA) is proposed to preserve accurate latent space according to the clean observations. It shoulders 2 tasks: separate the noise from significant observation missing; project the masked tokens into the accurate latent space and extract complete spatiotemporal trajectory features. Thus, unidirectional masking and progressive removal are designed to meet the demands, respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.628,
+ 0.906,
+ 0.733
+ ],
+ "angle": 0,
+ "content": "Unidirectional masking (UM) is designed to control the information transformation to operate only from the observed data to themselves and the missing data, making the encoding process unidirectional for masked trajectory modeling. By explicitly isolating the observed and the missing data, we can ensure that even with only highly sparse clean observations, they are free from noise interference."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "Specifically, similar to the causal mask [61], UM sets the attention weights corresponding to the positions of missing data to 0, meaning that all tokens can only perform attention calculations with tokens that have not been masked. For temporal masking, assuming \\(i\\)th trajectory \\(\\mathbf{x}_i \\in \\mathbb{R}^{T \\times 2}\\) of length \\(T\\) and the corresponding mask \\(\\mathbf{m}_i \\in \\mathbb{R}^T\\), the temporal \\(\\mathbf{UM}_i \\in \\mathbb{R}^{T \\times T}\\) can be obtained as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathbf {U M} _ {i} = \\left[ \\mathbf {U M} _ {i} ^ {0}, \\mathbf {U M} _ {i} ^ {1}, \\dots , \\mathbf {U M} _ {i} ^ {T} \\right] ^ {\\top}, \\\\ \\mathbf {U M} _ {i} ^ {j} = \\left\\{ \\begin{array}{l l} 0, & \\text {w h e r e} \\mathbf {m} _ {i} = 1 \\\\ - \\operatorname {I n f}, & \\text {w h e r e} \\mathbf {m} _ {i} = 0 \\end{array} , j \\in [ 0, T ] \\right. \\tag {1} \\\\ \\end{array}\n\\]"
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+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "27565"
+ }
+ ],
+ [
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.099,
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+ "angle": 0,
+ "content": "(a)"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.138,
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+ ],
+ "angle": 0,
+ "content": "Masked Trajectory"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.119,
+ 0.117,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "(b)"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.12,
+ 0.299,
+ 0.893,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.099,
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+ ],
+ "angle": 0,
+ "content": "(c)"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.12,
+ 0.437,
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+ 0.613
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.623,
+ 0.907,
+ 0.653
+ ],
+ "angle": 0,
+ "content": "Figure 2. (a) The overall framework of UniMTD, including unidirectional encoder with UMoE, and diffusion generator with CDiff. (b) The detailed calculation of UA, including PR (left) and UM (right). (c) The detailed design of UMoE (left) and CDiff (right)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.666,
+ 0.483,
+ 0.727
+ ],
+ "angle": 0,
+ "content": "For social masking, \\(N\\) multi-agent trajectories at timestep \\(t\\) is \\(\\mathbf{x}^t\\in \\mathbb{R}^{N\\times 2}\\) and the corresponding mask \\(\\mathbf{m}^t\\in \\mathbb{R}^N\\), the social \\(\\mathbf{UM}_t\\in \\mathbb{R}^{N\\times N}\\) can be obtained as same as temporal masking."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.73,
+ 0.484,
+ 0.791
+ ],
+ "angle": 0,
+ "content": "Through the above masking strategy, UM allows the information exchange among the clean tokens to form an accurate latent space, and the noisy tokens are confined to gathering information from it."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.796,
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+ ],
+ "angle": 0,
+ "content": "Progressive Removal (PR) is implemented as a refinement process progressively removing the UM mask to project the masked representations into the preserved latent space. Although the continuous existence of UM ensures an accurate latent space, the isolated tokens are not conducive to the extraction of consistent and complete trajectory features. Therefore, when the masked tokens conform to the"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.666,
+ 0.905,
+ 0.696
+ ],
+ "angle": 0,
+ "content": "accurate latent distribution, the mask on them should be removed. The process is depicted in Fig.2 (b-left)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.697,
+ 0.907,
+ 0.802
+ ],
+ "angle": 0,
+ "content": "Applied layer by layer, PR employs a 3-layer LSTM Score(\\cdot) to estimate the confidence \\(\\mathbf{p}_l\\) of the \\(l\\) layer's masked features conforming to the reference accurate latent features. For each layer, \\(k\\) masked tokens with the most confidence are unmasked (\\(m_k^l\\) from \\(0 \\to 1\\)) and used as a condition for predicting other masked tokens in the next layer. The \\(l\\)th layer mask can be formulated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.584,
+ 0.806,
+ 0.808,
+ 0.826
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {f} _ {\\mathbf {s t}} ^ {l} = \\operatorname {L a y e r} ^ {l - 1} \\left(\\mathbf {f} _ {\\mathbf {s t}} ^ {(l - 1)}, \\mathbf {m} ^ {l - 1}\\right),\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.585,
+ 0.829,
+ 0.905,
+ 0.864
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {p} _ {l} = \\operatorname {s o f t m a x} \\left(\\frac {1}{\\operatorname {S c o r e} \\left(\\mathbf {f} _ {\\mathbf {s t}} ^ {l} , \\mathbf {f} _ {\\mathbf {r e f}} ^ {l}\\right)}\\right), \\tag {2}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.585,
+ 0.865,
+ 0.832,
+ 0.905
+ ],
+ "angle": 0,
+ "content": "\\[\nm _ {(n, t)} ^ {l} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} p _ {(n, t)} ^ {l} \\in \\operatorname {T o p k} \\left(\\mathbf {p} _ {\\mathbf {i}}\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right.\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
+ 0.945,
+ 0.52,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "27566"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.09,
+ 0.482,
+ 0.135
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbf{f_{st}}^l\\) is spatiotemporal features of \\(l\\)th layer, and \\(\\mathbf{p}_l\\) is the confidence. The Score \\((\\cdot)\\) network can be trained as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.108,
+ 0.139,
+ 0.483,
+ 0.179
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} = \\frac {1}{L} \\sum_ {l = 1} ^ {L} \\operatorname {M S E} \\left(\\operatorname {L S T M} \\left(\\mathbf {f} _ {\\mathbf {s t}} ^ {l}, l\\right), \\left\\| \\mathbf {f} _ {\\mathbf {s t}} ^ {l} - \\mathbf {f} _ {\\mathbf {r e f}} ^ {l} \\right\\| _ {2}\\right) \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.182,
+ 0.483,
+ 0.213
+ ],
+ "angle": 0,
+ "content": "The overall calculation of unidirectional attention is depicted in Fig.2 (b-right), and can be formulated as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.117,
+ 0.226,
+ 0.483,
+ 0.261
+ ],
+ "angle": 0,
+ "content": "\\[\n\\operatorname {U A} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {\\top} \\cdot \\operatorname {P R} (\\mathbf {U M})}{\\sqrt {d _ {k}}}\\right) \\mathbf {V} \\tag {4}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.263,
+ 0.276,
+ 0.277
+ ],
+ "angle": 0,
+ "content": "3.2.3. Unidirectional MoE"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.282,
+ 0.483,
+ 0.327
+ ],
+ "angle": 0,
+ "content": "The unidirectional MoE (UMoE) includes local/global experts (LE/GE) and a complex adaptive router (CAR). Detailed structures are shown in Fig.2 (c-left)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.328,
+ 0.484,
+ 0.568
+ ],
+ "angle": 0,
+ "content": "As for trajectory, each coordinate lacks specific meaning, and the behavior is mainly described in a global view. Routing different experts for each time step leads to inconsistent features and weak expert specificity. To address this, we divide LE/GE and use a UA layer as a shared expert \\(\\mathrm{LE}(\\cdot)\\) activates for all local movement tokens to extract common knowledge \\(\\mathbf{z}_{\\mathbf{c}}\\) and maintains the motion stability. Meanwhile, the unmasked tokens of each agent are pooled into global features and routed to a group of sparsely activated experts \\(\\mathrm{GES}(\\cdot)\\) for specific behavior knowledge \\(\\mathbf{z}_{\\mathbf{s}}\\), emphasizing the expert specialization among the unique behaviors across multiple agents. We also design a complexity adaptive router to allocate a dynamic number of experts \\(\\mathbf{k}_{\\mathbf{e}}\\) according to mask ratios to handle the multi-level complexity inherent in arbitrary mask formats. The calculation in UMoE can be formulated as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.14,
+ 0.569,
+ 0.417,
+ 0.587
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {z} _ {\\mathbf {c}} = \\operatorname {L E} \\left(\\mathbf {f} _ {s t}, \\operatorname {P R} (\\mathbf {U M})\\right) \\in \\mathbb {R} ^ {B \\times N \\times T \\times D},\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.143,
+ 0.589,
+ 0.397,
+ 0.607
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {k} _ {\\mathrm {e}} = \\operatorname {N o r m a l i z e} (1 - \\operatorname {P R} (\\mathbf {U M})) \\cdot N _ {e},\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.143,
+ 0.609,
+ 0.413,
+ 0.627
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {w} _ {e} = \\operatorname {T o p k} \\left(\\mathbf {f} _ {\\text {m e t a}}, \\mathbf {f} _ {s t}, \\mathbf {k} _ {\\mathbf {e}}\\right) \\in \\mathbb {R} ^ {B \\times N \\times k _ {e}},\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.14,
+ 0.632,
+ 0.483,
+ 0.672
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {z} _ {\\mathbf {s}} = \\sum_ {i = 0} ^ {k _ {e}} \\mathbf {w} _ {e} ^ {i} \\cdot \\operatorname {G E} _ {i} (\\operatorname {p o o l} (\\mathbf {f} _ {s t})) \\in \\mathbb {R} ^ {B \\times N \\times D}, \\tag {5}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.143,
+ 0.676,
+ 0.334,
+ 0.695
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {z} _ {\\mathbf {s}} \\xrightarrow {\\text {r e p e a t}} \\mathbf {z} _ {\\mathbf {s}} \\in \\mathbb {R} ^ {B \\times N \\times T \\times D},\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.143,
+ 0.7,
+ 0.22,
+ 0.713
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {z} = \\mathbf {z _ {c}} \\cdot \\mathbf {z _ {s}}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.718,
+ 0.283,
+ 0.732
+ ],
+ "angle": 0,
+ "content": "3.3. Diffusion Generator"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.74,
+ 0.483,
+ 0.769
+ ],
+ "angle": 0,
+ "content": "The Diffusion Generator comprises a cached diffusion model and a tiny CNN decoder."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.776,
+ 0.307,
+ 0.79
+ ],
+ "angle": 0,
+ "content": "3.3.1. Cached Diffusion Model"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.795,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "The MAE decoding lacks diversity, and the iterative paradigm incurs high computational and time costs. Combine the strengths of the two and make up for their weaknesses, as shown in Fig.2 (c-right), we propose a cache mechanism to replace the deeper features and a large number of preceding inverse diffusion steps using the deterministic feature \\(\\mathbf{z} \\in \\mathbb{R}^{(B \\cdot l) \\times T \\times d}\\) and coordinate \\(\\hat{\\mathbf{X}}_{\\gamma + 1} \\in\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.09,
+ 0.906,
+ 0.151
+ ],
+ "angle": 0,
+ "content": "\\(\\mathbb{R}^{(B \\cdot l) \\times T \\times 2}\\) of the encoder. In this way, we have reduced the noise estimator \\(f_{\\epsilon}\\) with 6 attention layers and 200 steps to only a single layer and 5 steps. The denoising process can be revised as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.523,
+ 0.155,
+ 0.632,
+ 0.173
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\mathbf {X}} _ {0} = \\operatorname {C N N} (\\mathbf {z}),\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.525,
+ 0.177,
+ 0.895,
+ 0.197
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\mathbf {X}} _ {\\gamma + 1} = \\sqrt {\\bar {\\alpha} _ {\\gamma}} \\hat {\\mathbf {X}} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {\\gamma}} (\\hat {\\mathbf {X}} _ {0} \\cdot \\mathbf {M} + \\boldsymbol {\\epsilon} \\cdot (1 - \\mathbf {M})),\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.525,
+ 0.2,
+ 0.753,
+ 0.217
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {z} _ {\\gamma} = \\operatorname {A t t e n t i o n L a y e r} \\left(\\tilde {\\mathbf {X}} _ {\\gamma + 1}\\right) + \\mathbf {z},\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.525,
+ 0.22,
+ 0.803,
+ 0.24
+ ],
+ "angle": 0,
+ "content": "\\[\n\\epsilon_ {\\boldsymbol {\\theta}} ^ {\\gamma} = f _ {\\epsilon} (\\hat {\\mathbf {X}} _ {0} \\cdot \\mathbf {M} + \\hat {\\mathbf {X}} _ {\\gamma + 1} \\cdot (1 - \\mathbf {M}), \\mathbf {z} _ {\\gamma}),\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.525,
+ 0.241,
+ 0.905,
+ 0.287
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\mathbf {X}} _ {\\gamma} = \\frac {1}{\\sqrt {\\alpha_ {\\gamma}}} \\left(\\hat {\\mathbf {X}} _ {\\gamma + 1} - \\frac {1 - \\alpha_ {\\gamma}}{\\sqrt {1 - \\bar {\\alpha} _ {\\gamma}}} \\epsilon_ {\\theta} ^ {\\gamma}\\right) + \\sqrt {1 - \\alpha_ {\\gamma}} \\cdot \\epsilon \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.288,
+ 0.905,
+ 0.318
+ ],
+ "angle": 0,
+ "content": "where \\(\\alpha_{\\gamma}\\) and \\(\\bar{\\alpha}_{\\gamma} = \\prod_{i=1}^{\\gamma} \\alpha_{i}\\) are parameters at denoising step \\(\\gamma\\). \\(\\epsilon \\sim \\mathcal{N}(\\mathbf{0}, \\mathbf{I})\\) are gaussian noises."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.334,
+ 0.646,
+ 0.35
+ ],
+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.359,
+ 0.729,
+ 0.375
+ ],
+ "angle": 0,
+ "content": "4.1. Benchmarks and Setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.381,
+ 0.906,
+ 0.487
+ ],
+ "angle": 0,
+ "content": "Datasets: We applied diverse trajectory datasets to verify the applicability of UniMTD on various fields, including three human motion datasets and one vehicle motion dataset with three subsets of different difficulty: Basketball\\(\\mathbf{U}^{*}\\) [80], Soccer-\\(\\mathbf{U}^{*}\\) [58], Football-\\(\\mathbf{U}^{*}\\), and Vehicle-\\(\\mathbf{U}\\) (Easy/Ordinary/Hard)\\(^{*}\\) [60] constructed following [73]. The mask strategy is consistent with [71] for comparison."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.488,
+ 0.907,
+ 0.729
+ ],
+ "angle": 0,
+ "content": "Evaluation Protocol: We generate a total of \\( k = 20 \\) candidate trajectories based on the masked trajectory input and use the \\( \\min\\mathrm{ADE}_{20} \\) as the accuracy evaluation metric. Furthermore, four additional metrics to reflect the generation quality of agent movements'velocity, range, and behavior differences are employed to comprehensively assess the generation quality. (1) \\( \\min\\mathrm{ADE}_{20} \\): Minimum average displacement error between the generated trajectories and the ground truth across the 20 generated trajectories, (2) Out-of-Boundary (OOB): The percentage of generated locations that fall outside the predefined court boundaries, (3) Step: The average change in step size across the generated trajectories, (4) Path-L: The average length of the trajectories for each agent, (5) Path-D: The maximum difference in trajectory lengths among all agents. The calculations are consistent with [71]."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.741,
+ 0.707,
+ 0.756
+ ],
+ "angle": 0,
+ "content": "4.2. Quantitative Results"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.763,
+ 0.906,
+ 0.839
+ ],
+ "angle": 0,
+ "content": "Quantitative results are recorded in Tab.1 on the Basketball-U, Soccer-U, and the Football-U and Tab.2 on the Vehicle-U. Across all datasets, compared with mathematical interpolation methods, general deep learning frameworks, and specialized methods for relevant tasks, our UniMTD"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.531,
+ 0.85,
+ 0.821,
+ 0.863
+ ],
+ "angle": 0,
+ "content": "*https://github.com/linouk23/NBA-Player-Movements"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.533,
+ 0.863,
+ 0.771,
+ 0.876
+ ],
+ "angle": 0,
+ "content": "\\*https://github.com/AtomScott/SportsLabKit"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.534,
+ 0.876,
+ 0.806,
+ 0.888
+ ],
+ "angle": 0,
+ "content": "\\*https://github.com/nfl-football-ops/Big-Data-Bowl"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.535,
+ 0.888,
+ 0.779,
+ 0.9
+ ],
+ "angle": 0,
+ "content": "\\*https://github.com/shijieS/OmniMOTDataset"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.531,
+ 0.85,
+ 0.821,
+ 0.9
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
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+ ],
+ "angle": 0,
+ "content": "27567"
+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.17,
+ 0.09,
+ 0.827,
+ 0.104
+ ],
+ "angle": 0,
+ "content": "Table 1. Quantitative results on datasets Basketball- \\( \\mathbf{U} \\) (in feet),Soccer- \\( \\mathbf{U} \\) (in pixels),and Football- \\( \\mathbf{U} \\) (in yards)"
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.094,
+ 0.115,
+ 0.905,
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+ ],
+ "angle": 0,
+ "content": "| Dataset | Basketball-U (In Feet) | Soccer-U (In Pixels) | Football-U (In Yards) |
| Method | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D |
| Mean | 14.58 | 0 | 0.99 | 52.39 | 737.58 | 417.68 | 0 | 4.32 | 213.05 | 8022.51 | 14.18 | 0 | 0.52 | 25.06 | 606.07 |
| Medium | 14.56 | 0 | 0.98 | 51.80 | 743.36 | 418.06 | 0 | 4.39 | 214.55 | 8041.98 | 14.23 | 0 | 0.52 | 24.96 | 600.22 |
| Linear Fit | 13.54 | 4.47e-03 | 0.56 | 42.86 | 453.38 | 398.34 | 0 | 0.70 | 112.34 | 2047.19 | 12.66 | 1.49e-04 | 0.17 | 15.83 | 207.57 |
| LSTM[33] | 7.10 | 9.02e-04 | 0.76 | 58.48 | 449.58 | 186.93 | 4.74e-05 | 7.50 | 652.98 | 4542.78 | 7.20 | 2.24e-04 | 0.43 | 34.06 | 228.13 |
| Transformer[61] | 6.71 | 2.38e-03 | 0.79 | 59.34 | 517.54 | 170.94 | 6.59e-05 | 6.66 | 566.14 | 4269.08 | 6.84 | 5.68e-04 | 0.42 | 33.01 | 202.10 |
| MAT[80] | 6.68 | 1.36e-03 | 0.88 | 58.83 | 483.46 | 170.46 | 7.56e-05 | 6.45 | 562.44 | 3953.34 | 6.36 | 4.57e-04 | 0.40 | 31.32 | 186.11 |
| Naomi[46] | 6.52 | 2.02e-03 | 0.81 | 69.10 | 450.66 | 145.20 | 8.78e-05 | 7.47 | 649.62 | 4414.99 | 6.77 | 7.66e-04 | 0.67 | 42.74 | 259.11 |
| INAM[52] | 6.53 | 3.16e-03 | 0.70 | 58.54 | 439.87 | 134.86 | 4.04e-05 | 6.37 | 547.02 | 4102.37 | 5.80 | 8.30e-04 | 0.39 | 32.10 | 177.04 |
| SSSD[2] | 6.18 | 1.82e-03 | 0.47 | 46.87 | 393.12 | 118.71 | 4.51e-05 | 5.11 | 425.98 | 3252.66 | 5.08 | 6.81e-04 | 0.39 | 23.10 | 122.42 |
| GC-VRNN[73] | 5.81 | 9.28e-04 | 0.37 | 28.08 | 235.99 | 105.87 | 1.29e-05 | 4.92 | 506.32 | 3463.26 | 4.95 | 7.12e-04 | 0.29 | 32.48 | 149.87 |
| UniTraj[71] | 4.77 | 6.12e-04 | 0.27 | 34.25 | 240.83 | 94.59 | 1.29e-05 | 4.52 | 349.73 | 2805.79 | 3.55 | 1.12e-04 | 0.23 | 19.26 | 114.58 |
| Ground Truth | 0 | 0 | 0.17 | 37.61 | 269.49 | 0 | 0 | 0.52 | 112.92 | 951.00 | 0 | 0 | 0.03 | 12.56 | 76.68 |
| UniMTD (Ours) | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 13.65 | 0 | 0.95 | 124.39 | 1688.11 | 0.91 | 2.84e-05 | 0.09 | 13.45 | 107.38 |
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+ "content": "Table 2. Quantitative results on datasets Vehicle-U with Easy, Ordinary, and Hard scenarios (in pixels)"
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+ "type": "table",
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+ "angle": 0,
+ "content": "| Dataset | Vehicle-U Easy (In Pixels) | Vehicle-U Ordinary (In Pixels) | Vehicle-U Hard (In Pixels) |
| Method | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D |
| Transformer [61] | 107.93 | 5.61e-03 | 7.12 | 457.18 | 5913.21 | 92.47 | 4.77e-03 | 6.79 | 376.59 | 5723.45 | 108.76 | 1.07e-02 | 7.04 | 472.83 | 5835.42 |
| SSSD [2] | 30.99 | 1.82e-03 | 0.47 | 228.30 | 1611.98 | 28.90 | 9.51e-04 | 0.41 | 119.57 | 1829.07 | 30.65 | 5.92e-03 | 0.50 | 131.65 | 2160.53 |
| UniTraj [71] | 77.65 | 3.94e-03 | 2.42 | 165.28 | 4036.13 | 66.05 | 2.11e-03 | 4.01 | 257.17 | 5350.69 | 79.39 | 7.48e-03 | 4.70 | 255.12 | 5204.53 |
| Ground Truth | 0 | 0 | 0.06 | 43.30 | 1574.39 | 0 | 0 | 0.04 | 28.51 | 2030.48 | 0 | 0 | 0.05 | 28.92 | 1940.34 |
| UniMTD(Ours) | 13.12 | 9.04e-04 | 0.75 | 79.15 | 1726.57 | 10.62 | 3.28e-04 | 0.65 | 62.37 | 2079.77 | 15.40 | 2.97e-03 | 0.86 | 75.19 | 2100.29 |
"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "achieves the SOTA performance, leading by a large margin across all 5 metrics."
+ },
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+ "bbox": [
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+ "content": "Specifically, for datasets *Basketball-U*, *Soccer-U*, and *Football-U* depicting complex human behavior, UniMTD outperforms the current best-performing UniTraj by averaged 74% and surpasses the Diffusion model-based SSSD by averaged 80% on the \\(\\min\\mathrm{ADE}_{20}\\) metric, indicating a great leap in accuracy of behavior modeling. For OOB, Step, Path-L, and Path-D, UniMTD has achieved 91%, 66%, 69%, and 58% averaged advantages across data-driven methods, indicating that our generated trajectories align more closely with real motion patterns. For datasets Vehicle-U, UniMTD achieves SOTA performance, with averaged 56%, 33%, 44%, 15% advantages on \\(\\min\\mathrm{ADE}_{20}\\), OOB, Path-L, Path-D across all three subsets, and the step metric is the second-best. Different from human sports in limited scenes, the vehicle dataset exhibits a significant amount of behaviors entering and leaving the scene, involving more large-scale, high-dynamic scenarios. This may lead to an increase in OOB and give advantages to the SSSD method based on a 200-step diffusion model with strong abilities to express detailed and local behaviors, such as step-by-step velocity. Our SOTA performance on the majority of metrics across all datasets demonstrates the model's versatility in different scenarios."
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+ "content": "Regarding the inference time, for a scenario containing 11 agents, UniTraj requires 0.16s, UniMTD requires 0.18s, while SSSD, which also uses the diffusion model, requires more than 10s. This is because our CDiff reduces the number of denoising steps from 200 to 5 and simplifies the cal"
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+ "angle": 0,
+ "content": "culation, thus improving the inference efficiency."
+ },
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+ "angle": 0,
+ "content": "4.3. Qualitative Results"
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+ "content": "In Fig.3, we qualitatively compared the results between the prediction model, UniTraj, SSSD, UniMTD, and the UniMTD without CDiff or UA on the Basketball-U dataset. The results in the seventh column illustrate that our UniMTD generates behaviors with superior accuracy and fidelity, especially in the recovery of arc (purple) and circle (green, blue) trajectories. In the second column, models trained solely on prediction naturally cannot adapt to imputation and recovery but are unexpectedly not satisfactory on prediction. This result indicates that the unified modeling may benefit its subtasks. In the third column, UniTraj can generate behaviors with misconnection and even failure in recovery. In the fourth column, SSSD obtains inaccurate but detailed behavior sequences in prediction and imputation and also fails in the recovery task. In the fifth column, the woCDiff model generates averaged results with significant connection errors and overly smooth behaviors. In the sixth column, the woUA model discloses fluctuations and distortions due to the unseparated uncertain mask noise."
+ },
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+ "angle": 0,
+ "content": "The qualitative evaluation results confirm the significant superiority of our method in quantitative results and also demonstrate our correct insights into UA and CDiff designs."
+ },
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+ "content": "4.4. Model Analysis"
+ },
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+ "content": "4.4.1. Ablation Study"
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+ "angle": 0,
+ "content": "Tab.3 demonstrates the results of our ablation studies conducted on the Basketball-U dataset. The upper part records"
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+ "content": "Figure 3. The qualitative comparison of different methods under specific unified mask format across prediction, imputation, recovery, and a mixed scenario of these three. The ground truth is on the left, and our method is shown on the right side. Players 1-5 are in different colors, and the observed area is black."
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+ "content": "Figure 4. The statistical analysis of the distribution of player and masking ratios across experts 1-3. The typical movement patterns of each expert are given on the right."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "the performance variations when key parameters and model capacity are modified, while the lower part documents the performance variations when CDiff, PR, CAR (replaced by Top2 router), UMoEs (replaced by UA layers), and UM (UA to full attention) are successively removed."
+ },
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+ "content": "For the upper part, when the number of experts increases \\((N_{e} = 16)\\) or decreases \\((N_{e} = 4)\\), only the OOB and Path-L metrics improve, while all other metrics deteriorate. When the model capacity is directly increased, the minADE and step improve, while other metrics deteriorate. From the overall trend, as the model becomes more complex, both accuracy and fidelity metrics show the potential for contin"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "ued improvement, but this improvement may come at the cost of deterioration in other metrics."
+ },
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+ "bbox": [
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+ "content": "For the lower part, w/o CDiff indicates that CDiff improved the accuracy with only a cost of \\(< 5\\%\\) size inflation. w/o UMoE indicates that replacing UMoE with UA layers leads to severe degradations on both accuracy and fidelity. w/o CAR indicates that CAR can better handle the multi-level complexity inherent in arbitrary observation loss than commonly used top-k routing. w/o PR and w/o UM demonstrate a performance nosedive when observed and unobserved behaviors are coupled, indicating that UA contributes to both accuracy and fidelity with almost no ad"
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+ "content": "Table 3. Ablation experiment on Basketball-U"
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+ "bbox": [
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+ "content": "| Variants | minADE↓ | OOB↓ | Step | Path-L | Path-D | Size (M) |
| UniMTD | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 37.19 |
| Ne=4 | 2.13 | 5.40e-06 | 0.25 | 36.28 | 335.40 | 27.71 |
| Ne=16 | 1.90 | 1.32e-06 | 0.24 | 35.88 | 202.67 | 41.93 |
| 6UMoEs | 1.85 | 1.18e-05 | 0.21 | 35.45 | 215.08 | 53.18 |
| w/o CDiff | 1.95 | 1.32e-06 | 0.26 | 37.13 | 245.75 | 35.86 |
| w/o PR | 2.12 | 1.32e-07 | 0.27 | 38.44 | 203.72 | 35.54 |
| w/o CAR | 2.22 | 6.32e-06 | 0.26 | 37.18 | 319.15 | 35.54 |
| w/o UMoE | 2.92 | 9.21e-07 | 0.37 | 39.70 | 331.99 | 17.33 |
| w/o UM | 4.44 | 5.69e-5 | 0.44 | 51.19 | 398.76 | 17.33 |
"
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+ "content": "Table 4. Ablation experiment of CDiff efficiency on Basketball-U"
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+ "bbox": [
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+ "content": "| Variants | minADE↓ | OOB↓ | Step | Path-L | Path-D | Time (s) |
| Step=2 | 1.99 | 3.68e-06 | 0.25 | 37.31 | 216.41 | 0.17 |
| Step=5 | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 0.18 |
| Step=15 | 2.14 | 6.28e-05 | 0.28 | 37.41 | 203.65 | 0.51 |
| Step=50 | 2.73 | 2.25e-03 | 0.33 | 42.46 | 319.55 | 1.85 |
| Step=100 | 15.19 | 6.83e-02 | 3.22 | 207.11 | 5165.04 | 3.13 |
| Naive DDPM | 2.69 | 3.11e-5 | 0.28 | 39.19 | 304.65 | >10s |
"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "ditional learnable parameters."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In the following sections, we further conduct validation on CDiff, UMoE, and UA according to the original design insights."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4.2. CDiff Efficiency Analysis"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Tab.4 records the impact of truncated denoising steps on trajectory modeling quality and efficiency."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In the top 5 rows, when step \\(>15\\), as steps increased, the inference time surged while the performance decreased. Suppose the input is too noisy compared to \\(\\hat{\\mathbf{X}}_0\\). The single Attention Layer cannot bridge the noisy input and accurate deeper features, leading to contamination and performance damage. In the last row, we compared the standard diffusion model in [27], demonstrating improved efficiency and performance. This is because the \\(\\hat{\\mathbf{X}}_0\\) ensures the accuracy of CDiff modeling, while DDPM directly samples from the noise, which is prone to generating high-frequency tremors in highly-dynamic scenes."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4.3. UMoE Specialization Analysis"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To validate the specialization in UMoE, we statistically analyzed the distribution of player and masking ratios corresponding to each expert (experts 1-3 as examples) on the left of Fig.4 and visualized the specialized movement patterns of each expert on the right."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Compared across experts, the specialization in mask distribution is concentrated in several patterns. For instance, expert 2 specializes in visibility at around 0.1, 0.5, and 0.7. Experts are different in their preference for players, such as expert 1 prefers players 1, 8, 9. We also find specialized behavior patterns in the samples assigned to each expert, such as expert 3 processes most trajectories with arc movement after a sharp turn."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. The comparison of the feature errors on masked and unmasked tokens. Different methods are in different colors."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4.4. UA Feature Robustness Analysis"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ 0.5
+ ],
+ "angle": 0,
+ "content": "Masked trajectory modeling can be regarded as removing masked noise to restore the complete trajectory. We compared the denoising capabilities on the features of the encoder, that is, the feature robustness to mask noise. Specifically, we input the complete and masked trajectories successively and compare the features' \\( L1 \\) distances. The results of masked and unmasked tokens are in Fig. 5."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Compared with UniTraj and the woUA version, our method achieves the least error. The gap between the errors of unmasked tokens is greatly magnified in the distance of masked tokens prediction, indicating the importance of maintaining accurate, clean tokens for the overall quality of features and the effectiveness of the proposed UA."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.629,
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+ ],
+ "angle": 0,
+ "content": "In this work, we propose UniMTD, a novel unified multiagent trajectory modeling framework with an observed-unobserved decoupled masked diffusion paradigm. Essentially, we decouple observed-unobserved behavior to separate the interference from the uncertain latent space. To achieve this, we design a unidirectional attention as valve units to control the information flow between the accurate and the uncertain latent spaces. We further construct a unidirectional MoE and a cached diffusion model to handle the inherent multi-complexity and the efficiency requirements in trajectory modeling under arbitrary mask levels. Through extensive experiments and comprehensive evaluations, UniMTD consistently outperforms existing SOTA methods across trajectory prediction, completion, and recovery tasks with an averaged \\(>50\\%\\) advantage on accuracy and fidelity. Establishing itself as a SOTA solution with significant potential for further exploration in the embodied foundation model."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ }
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+ [
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "6. Acknowledgements"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "The work was supported by the National Natural Science Foundation of China under Grant 62471014, 62125102, and U24B20177, the Beijing Natural Science Foundation under Grant JL23005, and the Fundamental Research Funds for the Central Universities."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "References"
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+ {
+ "type": "ref_text",
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+ ],
+ "angle": 0,
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+# Unified Multi-Agent Trajectory Modeling with Masked Trajectory Diffusion
+
+Songru Yang, Zhenwei Shi, Zhengxia Zou*
+Department of Aerospace Intelligent Science and Technology, School of Astronautics, Beihang University, Beijing, China
+{songruang2001, shizhenwei, zhengxiazou}@buaa.edu.cn
+
+# Abstract
+
+Understanding movements in multi-agent scenarios is a fundamental problem in intelligent systems. Previous research assumes complete and synchronized observations. However, real-world partial observation caused by occlusions leads to inevitable model failure, which demands a unified framework for coexisting trajectory prediction, imputation, and recovery. Unlike previous attempts that handled observed and unobserved behaviors in a coupled manner, we explore a decoupled denoising diffusion modeling paradigm with a unidirectional information valve to separate the interference from uncertain behaviors. Building on this, we proposed a Unified Masked Trajectory Diffusion model (UniMTD) for arbitrary levels of missing observations. We designed a unidirectional attention as a valve unit to control the direction of information flow between the observed and masked areas, gradually refining the missing observations toward a real-world distribution. We construct it into a unidirectional MoE structure to handle varying proportions of missing observations. A Cached Diffusion model is further designed to improve generation quality while reducing computation and time overhead. Our method has achieved a great leap across human motions and vehicle traffic. UniMTD efficiently achieves $74\%$ improvement in $\min ADE_{20}$ and reaches SOTA with advantages of $91\%$ , $66\%$ , $69\%$ , and $58\%$ across 4 fidelity metrics on out-of-boundary, velocity, and trajectory length.
+
+# 1. Introduction
+
+Understanding multi-agent behavior is a critical foundation in various domains, including autonomous driving [35], action analysis [15, 26, 74], video surveillance [79, 83], and scene generation [69]. Trajectory modeling, which analyzes and generates the position sequence of multiple agents within the same scene, is particularly straightforward and effective for understanding agents' behavior.
+
+Existing methods have made significant strides in trajectory prediction [4, 59, 72, 76, 86, 87], imputation [46, 84, 85], and recovery [20, 22] across multiple fields, such as human sports and traffic trajectory. However, existing approaches cannot handle multiple tasks simultaneously, leaving a gap between methods and real-world scenarios where all three tasks coexist, as shown in Fig.1 (a). Recently, increasing attempts have been made to break the task boundaries. [36, 40, 53, 73] employed multi-task frameworks to combine trajectory imputation and prediction. [24, 57, 62, 88] distilled complete trajectory knowledge into partially observed models. Lately, [71] first exploited mask formats as conditional input to unify all three tasks in a BERT-SSM structure.
+
+Even though significant efforts have been devoted, existing approaches handled observed and unobserved behaviors in a coupled manner and encountered challenges in generating realistic multi-agent trajectories. Their suboptimal performance is inevitable for 2 reasons. First, they failed to realize that coupling the accurate representations and the uncertain ones with significant noise is deviating its latent space from the real-world behavior distribution. Second, more than an attached condition, the observation masks are precise boundaries between accuracy and uncertainty that need to be explicitly incorporated into the decoupling.
+
+In this work, we reexamine unified trajectory modeling from coupled to decoupled manner. We introduce UniMTD, a unified framework for trajectory modeling in a decoupled denoising diffusion modeling paradigm, as a 'panacea' for arbitrary levels of missing observations in real practice. To achieve decoupling according to observation masks, a unidirectional attention as the valve unit is proposed. By controlling one-way information flow between observed and masked tokens, it can separate the uncertain noise, maintain the accuracy of the latent space, and consistently project the masked representations into the preserved space. For decoding, we consider the pre-completed encoder output as the deterministic component of the trajectory pattern and directly reuse it as intermediate parts in the diffusion model to efficiently improve trajectory generation quality. Main
+
+
+Figure 1. (a) Above is a diagram of a traffic accident caused by the blue vehicle's observation failure of the pedestrian due to the obstruction. From the perspective of multi-agent trajectory modeling, the blue car is fully observed. The white car/van and brown car require prediction and imputation. The pedestrian with severe observation missing needs trajectory recovery. Below are real-world cases. In the first row, the pedestrian crashed due to being blocked. In the second row, the vehicle suddenly entered the view, resulting in an accident. (b) UniMTD (Ours) at the outermost side represents the minimum errors (averaged normalized error across three human datasets) on all 5 metrics. (c) Diagram of main differences and advantages of our method compared with previous methods during the encoding and decoding processes.
+
+
+
+
+
+differences and improvements are shown in Fig.1 (c)
+
+Specifically, in the encoder, we propose an unidirectional attention (UA) as the valve unit. The UA is composed of a unidirectional masking (UM) and a progressive removal (PR) process. The UM allows one-way attention from observed to unobserved tokens, forcing the model to focus on the accurate information and confining the unobserved behaviors to learn from them. The PR removes the UM on the well-learned unobserved behaviors to further project it into the accurate distribution. The UA is built in a Unidirectional MoE (UMoE) with a local-global experts (LGE) division and a complex adaptive router (CAR) for multi-level observation missing. In the decoder, we design a cached diffusion model (CDiff) reusing the pre-calculated deterministic coordinates and features to conduct a truncated diffusion process, which enables us to improve the quality of trajectory modeling at an extremely low cost in terms of model size $(< 5\%)$ and time $(< 5\%)$ compared to the original DDPM.
+
+We construct our datasets in both multi-agent vehicle traffic and human behavior scenarios. In both qualitative and quantitative results, UniMTD significantly surpasses existing methods in similar tasks across all 5 evaluation metrics with undamaged efficiency as shown in Fig.1 (b). It achieves $74\%$ advantage in accuracy and $91\%$ , $66\%$ , $69\%$ , and $58\%$ advantages across 4 fidelity metrics on out-of-boundary, velocity, and trajectory length. In summary, the main contributions of our work are as follows:
+
+- We introduce UniMTD, a novel unified trajectory modeling framework, transforming various trajectory-related tasks into an observed-unobserved decoupled masked diffusion paradigm.
+- We design a unidirectional attention as a valve unit to decouple accurate and uncertain latent space and further construct a unidirectional MoE apt for arbitrary levels of
+
+missing observations. A cached diffusion model is also designed to generate high-quality trajectories with low time and computation burden.
+
+- We conduct extensive experiments on our framework across multiple human movement and traffic datasets to validate our consistent and outstanding performance with further analysis of our design.
+
+# 2. Related Works
+
+# 2.1. Prediction, Imputation and Recovery
+
+Trajectory prediction predicts future behaviors based on historical observations. In the early studies, kinematics [38, 42] and filter-based [37, 82] methods were widely used. Started by Social-LSTM[1], neural networks such as RNN, LSTM, and GRU [8, 9, 11, 51, 67, 81] are designed to handle sequential data and agent interaction in trajectory prediction. With the popularity of generative methods, more recent studies have adopted generative frameworks such as GAN [3, 21, 28, 39], VAE [13, 29, 41, 70], and Diffusion models [27, 45, 47, 65] as future trajectory generators, enabling models to generate more realistic behaviors. The generative decoders fundamentally rely on a rich representation extracted from the encoder, which has led to the rise of MAE-based pre-training methods such as Traj-mae [14, 66, 68, 75], which are applied to a wide range of downstream tasks through fine-tuning.
+
+Imputation typically serves as a preprocessing method for slight data missing. Traditional statistical methods include interpolation [49], regression [6], and EM algorithms [55]. Statistical methods are efficient but struggle with complex sequences. Deep learning frameworks use RNNs [7, 77], autoregressive models [5, 16], or generative techniques such as GAN, VAE, and Diffusion Model
+
+[19, 48, 52, 78] to generate reconstructed sequences. Existing research on trajectory imputation in multi-agent scenarios is scarce: NAOMI [46] introduces a non-autoregressive imputation method, while Graph Imputer [50] utilized bidirectional features to impute soccer player trajectories.
+
+Trajectory recovery is similar to imputation but differs in the observation ratio. When less than $20\%$ observations are left caused by severe data loss or insufficient sampling, trajectory recovery as a conditional generation task needs to reconstruct the entire trajectory's motion pattern based on sparse information. Current research involves recovering trajectory data from GPS points [18, 64], but research on multi-agent scenarios is still blank.
+
+Although promising results have been achieved, the above methods have trouble generalizing across tasks. To mitigate cascade errors, the latest research has focused on trajectory prediction with slightly noised data, [24, 36, 40, 53, 57, 62, 73, 88], but these efforts are meeting challenges in generalizing to related tasks and obtaining accurate and realistic prediction results.
+
+# 2.2. Mask Modeling
+
+Mask modeling, since its inception in [23], has been extensively applied to pre-training tasks in trajectory prediction [14, 66, 68, 75] but is still incapable of handling multi-agent scenes with observation missing. [10] first extended mask modeling to generative tasks, iteratively predicting masked tokens, which is naturally adaptable to generation, inpainting, editing, etc. Various tasks can be considered as masking strategies within a unified framework.
+
+Compared to the successful vision and language mask modeling [10, 23, 30, 34], trajectory modeling has higher mask proportion ( $>50\%$ ), which limits the learning of the real distribution [62]. Besides, the random mask makes it impossible to use the MAE strategy [89] to batch-separate the noise. Moreover, unlike [10], lacking a powerful domain-pretrained tokenizer and decoder like VQGAN [25] or CLIP [54] prevents trajectory modeling in the latent space, and efficiency burdens are making a large number of iterative inferences not preferred.
+
+# 2.3. Diffusion Models
+
+Diffusion models [31] capable of generating high-quality samples through an iterative denoising process, which have recently achieved remarkable results in the fields of image and video generation [32, 63], time series forecast [43, 56], and remote sensing [12, 32, 44], etc. For trajectory modeling, MID [27] is the first diffusion-based method modeling the ambiguous walkable regions to desired trajectories. For the main concerns on computational and time cost, LeapFrog [47] distilled major denoising steps into an initializer to reduce the time costs in pre-trained MID. IDM [45] revealed that introducing goal information reduces de
+
+noising steps.
+
+Above methods require a full-parameter diffusion model with time and computational redundancies, and CDiff greatly reduces both of them.
+
+# 3. UniMTD
+
+# 3.1. Overall Framework
+
+The overall framework of UniMTD is depicted in Fig.2 (a). Take incomplete trajectories with arbitrary masks as input, the unidirectional encoder composed of UMoE and the diffusion generator with CDiff collaborate to generate completed versions of the input.
+
+# 3.2. Unidirectional Encoder
+
+The unidirectional encoder is composed of UMoE blocks, which include UA, LGE, and CAR.
+
+# 3.2.1. Twin Structure
+
+The entire encoder is designed in a twin structure $\mathrm{E}_M$ and $\mathrm{E}_U$ with shared weights, inspired by [17] to project masked and unmasked behaviors into the same latent space and provide an accurate reference $\mathbf{f}_{\mathrm{ref}}$ for the progressive removal. During the training phase, $\mathrm{E}_M$ and $\mathrm{E}_U$ encode masked and complete trajectories to $\mathbf{f}_{\mathrm{M}}$ and $\mathbf{f}_{\mathrm{U}}$ respectively. We aligned them in the latent space by MSE loss on masked positions. In the testing phase, only $\mathrm{E}_M$ is used to obtain $\mathbf{f}_{\mathrm{M}} = \mathbf{f}_{\mathrm{st}}$ .
+
+# 3.2.2. Unidirectional Attention
+
+The unidirectional attention (UA) is proposed to preserve accurate latent space according to the clean observations. It shoulders 2 tasks: separate the noise from significant observation missing; project the masked tokens into the accurate latent space and extract complete spatiotemporal trajectory features. Thus, unidirectional masking and progressive removal are designed to meet the demands, respectively.
+
+Unidirectional masking (UM) is designed to control the information transformation to operate only from the observed data to themselves and the missing data, making the encoding process unidirectional for masked trajectory modeling. By explicitly isolating the observed and the missing data, we can ensure that even with only highly sparse clean observations, they are free from noise interference.
+
+Specifically, similar to the causal mask [61], UM sets the attention weights corresponding to the positions of missing data to 0, meaning that all tokens can only perform attention calculations with tokens that have not been masked. For temporal masking, assuming $i$ th trajectory $\mathbf{x}_i \in \mathbb{R}^{T \times 2}$ of length $T$ and the corresponding mask $\mathbf{m}_i \in \mathbb{R}^T$ , the temporal $\mathbf{UM}_i \in \mathbb{R}^{T \times T}$ can be obtained as follows:
+
+$$
+\begin{array}{l} \mathbf {U M} _ {i} = \left[ \mathbf {U M} _ {i} ^ {0}, \mathbf {U M} _ {i} ^ {1}, \dots , \mathbf {U M} _ {i} ^ {T} \right] ^ {\top}, \\ \mathbf {U M} _ {i} ^ {j} = \left\{ \begin{array}{l l} 0, & \text {w h e r e} \mathbf {m} _ {i} = 1 \\ - \operatorname {I n f}, & \text {w h e r e} \mathbf {m} _ {i} = 0 \end{array} , j \in [ 0, T ] \right. \tag {1} \\ \end{array}
+$$
+
+
+(a)
+Masked Trajectory
+(b)
+
+
+(c)
+
+
+Figure 2. (a) The overall framework of UniMTD, including unidirectional encoder with UMoE, and diffusion generator with CDiff. (b) The detailed calculation of UA, including PR (left) and UM (right). (c) The detailed design of UMoE (left) and CDiff (right).
+
+For social masking, $N$ multi-agent trajectories at timestep $t$ is $\mathbf{x}^t\in \mathbb{R}^{N\times 2}$ and the corresponding mask $\mathbf{m}^t\in \mathbb{R}^N$ , the social $\mathbf{UM}_t\in \mathbb{R}^{N\times N}$ can be obtained as same as temporal masking.
+
+Through the above masking strategy, UM allows the information exchange among the clean tokens to form an accurate latent space, and the noisy tokens are confined to gathering information from it.
+
+Progressive Removal (PR) is implemented as a refinement process progressively removing the UM mask to project the masked representations into the preserved latent space. Although the continuous existence of UM ensures an accurate latent space, the isolated tokens are not conducive to the extraction of consistent and complete trajectory features. Therefore, when the masked tokens conform to the
+
+accurate latent distribution, the mask on them should be removed. The process is depicted in Fig.2 (b-left).
+
+Applied layer by layer, PR employs a 3-layer LSTM Score(\cdot) to estimate the confidence $\mathbf{p}_l$ of the $l$ layer's masked features conforming to the reference accurate latent features. For each layer, $k$ masked tokens with the most confidence are unmasked ( $m_k^l$ from $0 \to 1$ ) and used as a condition for predicting other masked tokens in the next layer. The $l$ th layer mask can be formulated as:
+
+$$
+\mathbf {f} _ {\mathbf {s t}} ^ {l} = \operatorname {L a y e r} ^ {l - 1} \left(\mathbf {f} _ {\mathbf {s t}} ^ {(l - 1)}, \mathbf {m} ^ {l - 1}\right),
+$$
+
+$$
+\mathbf {p} _ {l} = \operatorname {s o f t m a x} \left(\frac {1}{\operatorname {S c o r e} \left(\mathbf {f} _ {\mathbf {s t}} ^ {l} , \mathbf {f} _ {\mathbf {r e f}} ^ {l}\right)}\right), \tag {2}
+$$
+
+$$
+m _ {(n, t)} ^ {l} = \left\{ \begin{array}{l l} 1, & \text {i f} p _ {(n, t)} ^ {l} \in \operatorname {T o p k} \left(\mathbf {p} _ {\mathbf {i}}\right) \\ 0, & \text {o t h e r w i s e} \end{array} \right.
+$$
+
+where $\mathbf{f_{st}}^l$ is spatiotemporal features of $l$ th layer, and $\mathbf{p}_l$ is the confidence. The Score $(\cdot)$ network can be trained as follows:
+
+$$
+\mathcal {L} = \frac {1}{L} \sum_ {l = 1} ^ {L} \operatorname {M S E} \left(\operatorname {L S T M} \left(\mathbf {f} _ {\mathbf {s t}} ^ {l}, l\right), \left\| \mathbf {f} _ {\mathbf {s t}} ^ {l} - \mathbf {f} _ {\mathbf {r e f}} ^ {l} \right\| _ {2}\right) \tag {3}
+$$
+
+The overall calculation of unidirectional attention is depicted in Fig.2 (b-right), and can be formulated as follows:
+
+$$
+\operatorname {U A} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q K} ^ {\top} \cdot \operatorname {P R} (\mathbf {U M})}{\sqrt {d _ {k}}}\right) \mathbf {V} \tag {4}
+$$
+
+# 3.2.3. Unidirectional MoE
+
+The unidirectional MoE (UMoE) includes local/global experts (LE/GE) and a complex adaptive router (CAR). Detailed structures are shown in Fig.2 (c-left).
+
+As for trajectory, each coordinate lacks specific meaning, and the behavior is mainly described in a global view. Routing different experts for each time step leads to inconsistent features and weak expert specificity. To address this, we divide LE/GE and use a UA layer as a shared expert $\mathrm{LE}(\cdot)$ activates for all local movement tokens to extract common knowledge $\mathbf{z}_{\mathbf{c}}$ and maintains the motion stability. Meanwhile, the unmasked tokens of each agent are pooled into global features and routed to a group of sparsely activated experts $\mathrm{GES}(\cdot)$ for specific behavior knowledge $\mathbf{z}_{\mathbf{s}}$ , emphasizing the expert specialization among the unique behaviors across multiple agents. We also design a complexity adaptive router to allocate a dynamic number of experts $\mathbf{k}_{\mathbf{e}}$ according to mask ratios to handle the multi-level complexity inherent in arbitrary mask formats. The calculation in UMoE can be formulated as follows:
+
+$$
+\mathbf {z} _ {\mathbf {c}} = \operatorname {L E} \left(\mathbf {f} _ {s t}, \operatorname {P R} (\mathbf {U M})\right) \in \mathbb {R} ^ {B \times N \times T \times D},
+$$
+
+$$
+\mathbf {k} _ {\mathrm {e}} = \operatorname {N o r m a l i z e} (1 - \operatorname {P R} (\mathbf {U M})) \cdot N _ {e},
+$$
+
+$$
+\mathbf {w} _ {e} = \operatorname {T o p k} \left(\mathbf {f} _ {\text {m e t a}}, \mathbf {f} _ {s t}, \mathbf {k} _ {\mathbf {e}}\right) \in \mathbb {R} ^ {B \times N \times k _ {e}},
+$$
+
+$$
+\mathbf {z} _ {\mathbf {s}} = \sum_ {i = 0} ^ {k _ {e}} \mathbf {w} _ {e} ^ {i} \cdot \operatorname {G E} _ {i} (\operatorname {p o o l} (\mathbf {f} _ {s t})) \in \mathbb {R} ^ {B \times N \times D}, \tag {5}
+$$
+
+$$
+\mathbf {z} _ {\mathbf {s}} \xrightarrow {\text {r e p e a t}} \mathbf {z} _ {\mathbf {s}} \in \mathbb {R} ^ {B \times N \times T \times D},
+$$
+
+$$
+\mathbf {z} = \mathbf {z _ {c}} \cdot \mathbf {z _ {s}}
+$$
+
+# 3.3. Diffusion Generator
+
+The Diffusion Generator comprises a cached diffusion model and a tiny CNN decoder.
+
+# 3.3.1. Cached Diffusion Model
+
+The MAE decoding lacks diversity, and the iterative paradigm incurs high computational and time costs. Combine the strengths of the two and make up for their weaknesses, as shown in Fig.2 (c-right), we propose a cache mechanism to replace the deeper features and a large number of preceding inverse diffusion steps using the deterministic feature $\mathbf{z} \in \mathbb{R}^{(B \cdot l) \times T \times d}$ and coordinate $\hat{\mathbf{X}}_{\gamma + 1} \in$
+
+$\mathbb{R}^{(B \cdot l) \times T \times 2}$ of the encoder. In this way, we have reduced the noise estimator $f_{\epsilon}$ with 6 attention layers and 200 steps to only a single layer and 5 steps. The denoising process can be revised as follows:
+
+$$
+\hat {\mathbf {X}} _ {0} = \operatorname {C N N} (\mathbf {z}),
+$$
+
+$$
+\hat {\mathbf {X}} _ {\gamma + 1} = \sqrt {\bar {\alpha} _ {\gamma}} \hat {\mathbf {X}} _ {0} + \sqrt {1 - \bar {\alpha} _ {\gamma}} (\hat {\mathbf {X}} _ {0} \cdot \mathbf {M} + \boldsymbol {\epsilon} \cdot (1 - \mathbf {M})),
+$$
+
+$$
+\mathbf {z} _ {\gamma} = \operatorname {A t t e n t i o n L a y e r} \left(\tilde {\mathbf {X}} _ {\gamma + 1}\right) + \mathbf {z},
+$$
+
+$$
+\epsilon_ {\boldsymbol {\theta}} ^ {\gamma} = f _ {\epsilon} (\hat {\mathbf {X}} _ {0} \cdot \mathbf {M} + \hat {\mathbf {X}} _ {\gamma + 1} \cdot (1 - \mathbf {M}), \mathbf {z} _ {\gamma}),
+$$
+
+$$
+\hat {\mathbf {X}} _ {\gamma} = \frac {1}{\sqrt {\alpha_ {\gamma}}} \left(\hat {\mathbf {X}} _ {\gamma + 1} - \frac {1 - \alpha_ {\gamma}}{\sqrt {1 - \bar {\alpha} _ {\gamma}}} \epsilon_ {\theta} ^ {\gamma}\right) + \sqrt {1 - \alpha_ {\gamma}} \cdot \epsilon \tag {6}
+$$
+
+where $\alpha_{\gamma}$ and $\bar{\alpha}_{\gamma} = \prod_{i=1}^{\gamma} \alpha_{i}$ are parameters at denoising step $\gamma$ . $\epsilon \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ are gaussian noises.
+
+# 4. Experiments
+
+# 4.1. Benchmarks and Setup
+
+Datasets: We applied diverse trajectory datasets to verify the applicability of UniMTD on various fields, including three human motion datasets and one vehicle motion dataset with three subsets of different difficulty: Basketball $\mathbf{U}^{*}$ [80], Soccer- $\mathbf{U}^{*}$ [58], Football- $\mathbf{U}^{*}$ , and Vehicle- $\mathbf{U}$ (Easy/Ordinary/Hard) $^{*}$ [60] constructed following [73]. The mask strategy is consistent with [71] for comparison.
+
+Evaluation Protocol: We generate a total of $k = 20$ candidate trajectories based on the masked trajectory input and use the $\min\mathrm{ADE}_{20}$ as the accuracy evaluation metric. Furthermore, four additional metrics to reflect the generation quality of agent movements'velocity, range, and behavior differences are employed to comprehensively assess the generation quality. (1) $\min\mathrm{ADE}_{20}$ : Minimum average displacement error between the generated trajectories and the ground truth across the 20 generated trajectories, (2) Out-of-Boundary (OOB): The percentage of generated locations that fall outside the predefined court boundaries, (3) Step: The average change in step size across the generated trajectories, (4) Path-L: The average length of the trajectories for each agent, (5) Path-D: The maximum difference in trajectory lengths among all agents. The calculations are consistent with [71].
+
+# 4.2. Quantitative Results
+
+Quantitative results are recorded in Tab.1 on the Basketball-U, Soccer-U, and the Football-U and Tab.2 on the Vehicle-U. Across all datasets, compared with mathematical interpolation methods, general deep learning frameworks, and specialized methods for relevant tasks, our UniMTD
+
+Table 1. Quantitative results on datasets Basketball- $\mathbf{U}$ (in feet),Soccer- $\mathbf{U}$ (in pixels),and Football- $\mathbf{U}$ (in yards)
+
+| Dataset | Basketball-U (In Feet) | Soccer-U (In Pixels) | Football-U (In Yards) |
| Method | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D |
| Mean | 14.58 | 0 | 0.99 | 52.39 | 737.58 | 417.68 | 0 | 4.32 | 213.05 | 8022.51 | 14.18 | 0 | 0.52 | 25.06 | 606.07 |
| Medium | 14.56 | 0 | 0.98 | 51.80 | 743.36 | 418.06 | 0 | 4.39 | 214.55 | 8041.98 | 14.23 | 0 | 0.52 | 24.96 | 600.22 |
| Linear Fit | 13.54 | 4.47e-03 | 0.56 | 42.86 | 453.38 | 398.34 | 0 | 0.70 | 112.34 | 2047.19 | 12.66 | 1.49e-04 | 0.17 | 15.83 | 207.57 |
| LSTM[33] | 7.10 | 9.02e-04 | 0.76 | 58.48 | 449.58 | 186.93 | 4.74e-05 | 7.50 | 652.98 | 4542.78 | 7.20 | 2.24e-04 | 0.43 | 34.06 | 228.13 |
| Transformer[61] | 6.71 | 2.38e-03 | 0.79 | 59.34 | 517.54 | 170.94 | 6.59e-05 | 6.66 | 566.14 | 4269.08 | 6.84 | 5.68e-04 | 0.42 | 33.01 | 202.10 |
| MAT[80] | 6.68 | 1.36e-03 | 0.88 | 58.83 | 483.46 | 170.46 | 7.56e-05 | 6.45 | 562.44 | 3953.34 | 6.36 | 4.57e-04 | 0.40 | 31.32 | 186.11 |
| Naomi[46] | 6.52 | 2.02e-03 | 0.81 | 69.10 | 450.66 | 145.20 | 8.78e-05 | 7.47 | 649.62 | 4414.99 | 6.77 | 7.66e-04 | 0.67 | 42.74 | 259.11 |
| INAM[52] | 6.53 | 3.16e-03 | 0.70 | 58.54 | 439.87 | 134.86 | 4.04e-05 | 6.37 | 547.02 | 4102.37 | 5.80 | 8.30e-04 | 0.39 | 32.10 | 177.04 |
| SSSD[2] | 6.18 | 1.82e-03 | 0.47 | 46.87 | 393.12 | 118.71 | 4.51e-05 | 5.11 | 425.98 | 3252.66 | 5.08 | 6.81e-04 | 0.39 | 23.10 | 122.42 |
| GC-VRNN[73] | 5.81 | 9.28e-04 | 0.37 | 28.08 | 235.99 | 105.87 | 1.29e-05 | 4.92 | 506.32 | 3463.26 | 4.95 | 7.12e-04 | 0.29 | 32.48 | 149.87 |
| UniTraj[71] | 4.77 | 6.12e-04 | 0.27 | 34.25 | 240.83 | 94.59 | 1.29e-05 | 4.52 | 349.73 | 2805.79 | 3.55 | 1.12e-04 | 0.23 | 19.26 | 114.58 |
| Ground Truth | 0 | 0 | 0.17 | 37.61 | 269.49 | 0 | 0 | 0.52 | 112.92 | 951.00 | 0 | 0 | 0.03 | 12.56 | 76.68 |
| UniMTD (Ours) | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 13.65 | 0 | 0.95 | 124.39 | 1688.11 | 0.91 | 2.84e-05 | 0.09 | 13.45 | 107.38 |
+
+Table 2. Quantitative results on datasets Vehicle-U with Easy, Ordinary, and Hard scenarios (in pixels)
+
+| Dataset | Vehicle-U Easy (In Pixels) | Vehicle-U Ordinary (In Pixels) | Vehicle-U Hard (In Pixels) |
| Method | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D |
| Transformer [61] | 107.93 | 5.61e-03 | 7.12 | 457.18 | 5913.21 | 92.47 | 4.77e-03 | 6.79 | 376.59 | 5723.45 | 108.76 | 1.07e-02 | 7.04 | 472.83 | 5835.42 |
| SSSD [2] | 30.99 | 1.82e-03 | 0.47 | 228.30 | 1611.98 | 28.90 | 9.51e-04 | 0.41 | 119.57 | 1829.07 | 30.65 | 5.92e-03 | 0.50 | 131.65 | 2160.53 |
| UniTraj [71] | 77.65 | 3.94e-03 | 2.42 | 165.28 | 4036.13 | 66.05 | 2.11e-03 | 4.01 | 257.17 | 5350.69 | 79.39 | 7.48e-03 | 4.70 | 255.12 | 5204.53 |
| Ground Truth | 0 | 0 | 0.06 | 43.30 | 1574.39 | 0 | 0 | 0.04 | 28.51 | 2030.48 | 0 | 0 | 0.05 | 28.92 | 1940.34 |
| UniMTD(Ours) | 13.12 | 9.04e-04 | 0.75 | 79.15 | 1726.57 | 10.62 | 3.28e-04 | 0.65 | 62.37 | 2079.77 | 15.40 | 2.97e-03 | 0.86 | 75.19 | 2100.29 |
+
+achieves the SOTA performance, leading by a large margin across all 5 metrics.
+
+Specifically, for datasets *Basketball-U*, *Soccer-U*, and *Football-U* depicting complex human behavior, UniMTD outperforms the current best-performing UniTraj by averaged 74% and surpasses the Diffusion model-based SSSD by averaged 80% on the $\min\mathrm{ADE}_{20}$ metric, indicating a great leap in accuracy of behavior modeling. For OOB, Step, Path-L, and Path-D, UniMTD has achieved 91%, 66%, 69%, and 58% averaged advantages across data-driven methods, indicating that our generated trajectories align more closely with real motion patterns. For datasets Vehicle-U, UniMTD achieves SOTA performance, with averaged 56%, 33%, 44%, 15% advantages on $\min\mathrm{ADE}_{20}$ , OOB, Path-L, Path-D across all three subsets, and the step metric is the second-best. Different from human sports in limited scenes, the vehicle dataset exhibits a significant amount of behaviors entering and leaving the scene, involving more large-scale, high-dynamic scenarios. This may lead to an increase in OOB and give advantages to the SSSD method based on a 200-step diffusion model with strong abilities to express detailed and local behaviors, such as step-by-step velocity. Our SOTA performance on the majority of metrics across all datasets demonstrates the model's versatility in different scenarios.
+
+Regarding the inference time, for a scenario containing 11 agents, UniTraj requires 0.16s, UniMTD requires 0.18s, while SSSD, which also uses the diffusion model, requires more than 10s. This is because our CDiff reduces the number of denoising steps from 200 to 5 and simplifies the cal
+
+culation, thus improving the inference efficiency.
+
+# 4.3. Qualitative Results
+
+In Fig.3, we qualitatively compared the results between the prediction model, UniTraj, SSSD, UniMTD, and the UniMTD without CDiff or UA on the Basketball-U dataset. The results in the seventh column illustrate that our UniMTD generates behaviors with superior accuracy and fidelity, especially in the recovery of arc (purple) and circle (green, blue) trajectories. In the second column, models trained solely on prediction naturally cannot adapt to imputation and recovery but are unexpectedly not satisfactory on prediction. This result indicates that the unified modeling may benefit its subtasks. In the third column, UniTraj can generate behaviors with misconnection and even failure in recovery. In the fourth column, SSSD obtains inaccurate but detailed behavior sequences in prediction and imputation and also fails in the recovery task. In the fifth column, the woCDiff model generates averaged results with significant connection errors and overly smooth behaviors. In the sixth column, the woUA model discloses fluctuations and distortions due to the unseparated uncertain mask noise.
+
+The qualitative evaluation results confirm the significant superiority of our method in quantitative results and also demonstrate our correct insights into UA and CDiff designs.
+
+# 4.4. Model Analysis
+
+# 4.4.1. Ablation Study
+
+Tab.3 demonstrates the results of our ablation studies conducted on the Basketball-U dataset. The upper part records
+
+
+Figure 3. The qualitative comparison of different methods under specific unified mask format across prediction, imputation, recovery, and a mixed scenario of these three. The ground truth is on the left, and our method is shown on the right side. Players 1-5 are in different colors, and the observed area is black.
+
+
+Figure 4. The statistical analysis of the distribution of player and masking ratios across experts 1-3. The typical movement patterns of each expert are given on the right.
+
+the performance variations when key parameters and model capacity are modified, while the lower part documents the performance variations when CDiff, PR, CAR (replaced by Top2 router), UMoEs (replaced by UA layers), and UM (UA to full attention) are successively removed.
+
+For the upper part, when the number of experts increases $(N_{e} = 16)$ or decreases $(N_{e} = 4)$ , only the OOB and Path-L metrics improve, while all other metrics deteriorate. When the model capacity is directly increased, the minADE and step improve, while other metrics deteriorate. From the overall trend, as the model becomes more complex, both accuracy and fidelity metrics show the potential for contin
+
+ued improvement, but this improvement may come at the cost of deterioration in other metrics.
+
+For the lower part, w/o CDiff indicates that CDiff improved the accuracy with only a cost of $< 5\%$ size inflation. w/o UMoE indicates that replacing UMoE with UA layers leads to severe degradations on both accuracy and fidelity. w/o CAR indicates that CAR can better handle the multi-level complexity inherent in arbitrary observation loss than commonly used top-k routing. w/o PR and w/o UM demonstrate a performance nosedive when observed and unobserved behaviors are coupled, indicating that UA contributes to both accuracy and fidelity with almost no ad
+
+Table 3. Ablation experiment on Basketball-U
+
+| Variants | minADE↓ | OOB↓ | Step | Path-L | Path-D | Size (M) |
| UniMTD | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 37.19 |
| Ne=4 | 2.13 | 5.40e-06 | 0.25 | 36.28 | 335.40 | 27.71 |
| Ne=16 | 1.90 | 1.32e-06 | 0.24 | 35.88 | 202.67 | 41.93 |
| 6UMoEs | 1.85 | 1.18e-05 | 0.21 | 35.45 | 215.08 | 53.18 |
| w/o CDiff | 1.95 | 1.32e-06 | 0.26 | 37.13 | 245.75 | 35.86 |
| w/o PR | 2.12 | 1.32e-07 | 0.27 | 38.44 | 203.72 | 35.54 |
| w/o CAR | 2.22 | 6.32e-06 | 0.26 | 37.18 | 319.15 | 35.54 |
| w/o UMoE | 2.92 | 9.21e-07 | 0.37 | 39.70 | 331.99 | 17.33 |
| w/o UM | 4.44 | 5.69e-5 | 0.44 | 51.19 | 398.76 | 17.33 |
+
+Table 4. Ablation experiment of CDiff efficiency on Basketball-U
+
+| Variants | minADE↓ | OOB↓ | Step | Path-L | Path-D | Time (s) |
| Step=2 | 1.99 | 3.68e-06 | 0.25 | 37.31 | 216.41 | 0.17 |
| Step=5 | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 0.18 |
| Step=15 | 2.14 | 6.28e-05 | 0.28 | 37.41 | 203.65 | 0.51 |
| Step=50 | 2.73 | 2.25e-03 | 0.33 | 42.46 | 319.55 | 1.85 |
| Step=100 | 15.19 | 6.83e-02 | 3.22 | 207.11 | 5165.04 | 3.13 |
| Naive DDPM | 2.69 | 3.11e-5 | 0.28 | 39.19 | 304.65 | >10s |
+
+ditional learnable parameters.
+
+In the following sections, we further conduct validation on CDiff, UMoE, and UA according to the original design insights.
+
+# 4.4.2. CDiff Efficiency Analysis
+
+Tab.4 records the impact of truncated denoising steps on trajectory modeling quality and efficiency.
+
+In the top 5 rows, when step $>15$ , as steps increased, the inference time surged while the performance decreased. Suppose the input is too noisy compared to $\hat{\mathbf{X}}_0$ . The single Attention Layer cannot bridge the noisy input and accurate deeper features, leading to contamination and performance damage. In the last row, we compared the standard diffusion model in [27], demonstrating improved efficiency and performance. This is because the $\hat{\mathbf{X}}_0$ ensures the accuracy of CDiff modeling, while DDPM directly samples from the noise, which is prone to generating high-frequency tremors in highly-dynamic scenes.
+
+# 4.4.3. UMoE Specialization Analysis
+
+To validate the specialization in UMoE, we statistically analyzed the distribution of player and masking ratios corresponding to each expert (experts 1-3 as examples) on the left of Fig.4 and visualized the specialized movement patterns of each expert on the right.
+
+Compared across experts, the specialization in mask distribution is concentrated in several patterns. For instance, expert 2 specializes in visibility at around 0.1, 0.5, and 0.7. Experts are different in their preference for players, such as expert 1 prefers players 1, 8, 9. We also find specialized behavior patterns in the samples assigned to each expert, such as expert 3 processes most trajectories with arc movement after a sharp turn.
+
+
+Figure 5. The comparison of the feature errors on masked and unmasked tokens. Different methods are in different colors.
+
+# 4.4.4. UA Feature Robustness Analysis
+
+Masked trajectory modeling can be regarded as removing masked noise to restore the complete trajectory. We compared the denoising capabilities on the features of the encoder, that is, the feature robustness to mask noise. Specifically, we input the complete and masked trajectories successively and compare the features' $L1$ distances. The results of masked and unmasked tokens are in Fig. 5.
+
+Compared with UniTraj and the woUA version, our method achieves the least error. The gap between the errors of unmasked tokens is greatly magnified in the distance of masked tokens prediction, indicating the importance of maintaining accurate, clean tokens for the overall quality of features and the effectiveness of the proposed UA.
+
+# 5. Conclusion
+
+In this work, we propose UniMTD, a novel unified multiagent trajectory modeling framework with an observed-unobserved decoupled masked diffusion paradigm. Essentially, we decouple observed-unobserved behavior to separate the interference from the uncertain latent space. To achieve this, we design a unidirectional attention as valve units to control the information flow between the accurate and the uncertain latent spaces. We further construct a unidirectional MoE and a cached diffusion model to handle the inherent multi-complexity and the efficiency requirements in trajectory modeling under arbitrary mask levels. Through extensive experiments and comprehensive evaluations, UniMTD consistently outperforms existing SOTA methods across trajectory prediction, completion, and recovery tasks with an averaged $>50\%$ advantage on accuracy and fidelity. Establishing itself as a SOTA solution with significant potential for further exploration in the embodied foundation model.
+
+# 6. Acknowledgements
+
+The work was supported by the National Natural Science Foundation of China under Grant 62471014, 62125102, and U24B20177, the Beijing Natural Science Foundation under Grant JL23005, and the Fundamental Research Funds for the Central Universities.
+
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+ "content": " as the accuracy evaluation metric. Furthermore, four additional metrics to reflect the generation quality of agent movements'velocity, range, and behavior differences are employed to comprehensively assess the generation quality. (1) "
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+ "content": ": Minimum average displacement error between the generated trajectories and the ground truth across the 20 generated trajectories, (2) Out-of-Boundary (OOB): The percentage of generated locations that fall outside the predefined court boundaries, (3) Step: The average change in step size across the generated trajectories, (4) Path-L: The average length of the trajectories for each agent, (5) Path-D: The maximum difference in trajectory lengths among all agents. The calculations are consistent with [71]."
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+ "content": "Quantitative results are recorded in Tab.1 on the Basketball-U, Soccer-U, and the Football-U and Tab.2 on the Vehicle-U. Across all datasets, compared with mathematical interpolation methods, general deep learning frameworks, and specialized methods for relevant tasks, our UniMTD"
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| Method | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D |
| Mean | 14.58 | 0 | 0.99 | 52.39 | 737.58 | 417.68 | 0 | 4.32 | 213.05 | 8022.51 | 14.18 | 0 | 0.52 | 25.06 | 606.07 |
| Medium | 14.56 | 0 | 0.98 | 51.80 | 743.36 | 418.06 | 0 | 4.39 | 214.55 | 8041.98 | 14.23 | 0 | 0.52 | 24.96 | 600.22 |
| Linear Fit | 13.54 | 4.47e-03 | 0.56 | 42.86 | 453.38 | 398.34 | 0 | 0.70 | 112.34 | 2047.19 | 12.66 | 1.49e-04 | 0.17 | 15.83 | 207.57 |
| LSTM[33] | 7.10 | 9.02e-04 | 0.76 | 58.48 | 449.58 | 186.93 | 4.74e-05 | 7.50 | 652.98 | 4542.78 | 7.20 | 2.24e-04 | 0.43 | 34.06 | 228.13 |
| Transformer[61] | 6.71 | 2.38e-03 | 0.79 | 59.34 | 517.54 | 170.94 | 6.59e-05 | 6.66 | 566.14 | 4269.08 | 6.84 | 5.68e-04 | 0.42 | 33.01 | 202.10 |
| MAT[80] | 6.68 | 1.36e-03 | 0.88 | 58.83 | 483.46 | 170.46 | 7.56e-05 | 6.45 | 562.44 | 3953.34 | 6.36 | 4.57e-04 | 0.40 | 31.32 | 186.11 |
| Naomi[46] | 6.52 | 2.02e-03 | 0.81 | 69.10 | 450.66 | 145.20 | 8.78e-05 | 7.47 | 649.62 | 4414.99 | 6.77 | 7.66e-04 | 0.67 | 42.74 | 259.11 |
| INAM[52] | 6.53 | 3.16e-03 | 0.70 | 58.54 | 439.87 | 134.86 | 4.04e-05 | 6.37 | 547.02 | 4102.37 | 5.80 | 8.30e-04 | 0.39 | 32.10 | 177.04 |
| SSSD[2] | 6.18 | 1.82e-03 | 0.47 | 46.87 | 393.12 | 118.71 | 4.51e-05 | 5.11 | 425.98 | 3252.66 | 5.08 | 6.81e-04 | 0.39 | 23.10 | 122.42 |
| GC-VRNN[73] | 5.81 | 9.28e-04 | 0.37 | 28.08 | 235.99 | 105.87 | 1.29e-05 | 4.92 | 506.32 | 3463.26 | 4.95 | 7.12e-04 | 0.29 | 32.48 | 149.87 |
| UniTraj[71] | 4.77 | 6.12e-04 | 0.27 | 34.25 | 240.83 | 94.59 | 1.29e-05 | 4.52 | 349.73 | 2805.79 | 3.55 | 1.12e-04 | 0.23 | 19.26 | 114.58 |
| Ground Truth | 0 | 0 | 0.17 | 37.61 | 269.49 | 0 | 0 | 0.52 | 112.92 | 951.00 | 0 | 0 | 0.03 | 12.56 | 76.68 |
| UniMTD (Ours) | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 13.65 | 0 | 0.95 | 124.39 | 1688.11 | 0.91 | 2.84e-05 | 0.09 | 13.45 | 107.38 |
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| Method | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D | minADE↓ | OOB↓ | Step | Path-L | Path-D |
| Transformer [61] | 107.93 | 5.61e-03 | 7.12 | 457.18 | 5913.21 | 92.47 | 4.77e-03 | 6.79 | 376.59 | 5723.45 | 108.76 | 1.07e-02 | 7.04 | 472.83 | 5835.42 |
| SSSD [2] | 30.99 | 1.82e-03 | 0.47 | 228.30 | 1611.98 | 28.90 | 9.51e-04 | 0.41 | 119.57 | 1829.07 | 30.65 | 5.92e-03 | 0.50 | 131.65 | 2160.53 |
| UniTraj [71] | 77.65 | 3.94e-03 | 2.42 | 165.28 | 4036.13 | 66.05 | 2.11e-03 | 4.01 | 257.17 | 5350.69 | 79.39 | 7.48e-03 | 4.70 | 255.12 | 5204.53 |
| Ground Truth | 0 | 0 | 0.06 | 43.30 | 1574.39 | 0 | 0 | 0.04 | 28.51 | 2030.48 | 0 | 0 | 0.05 | 28.92 | 1940.34 |
| UniMTD(Ours) | 13.12 | 9.04e-04 | 0.75 | 79.15 | 1726.57 | 10.62 | 3.28e-04 | 0.65 | 62.37 | 2079.77 | 15.40 | 2.97e-03 | 0.86 | 75.19 | 2100.29 |
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| UniMTD | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 37.19 |
| Ne=4 | 2.13 | 5.40e-06 | 0.25 | 36.28 | 335.40 | 27.71 |
| Ne=16 | 1.90 | 1.32e-06 | 0.24 | 35.88 | 202.67 | 41.93 |
| 6UMoEs | 1.85 | 1.18e-05 | 0.21 | 35.45 | 215.08 | 53.18 |
| w/o CDiff | 1.95 | 1.32e-06 | 0.26 | 37.13 | 245.75 | 35.86 |
| w/o PR | 2.12 | 1.32e-07 | 0.27 | 38.44 | 203.72 | 35.54 |
| w/o CAR | 2.22 | 6.32e-06 | 0.26 | 37.18 | 319.15 | 35.54 |
| w/o UMoE | 2.92 | 9.21e-07 | 0.37 | 39.70 | 331.99 | 17.33 |
| w/o UM | 4.44 | 5.69e-5 | 0.44 | 51.19 | 398.76 | 17.33 |
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| Step=2 | 1.99 | 3.68e-06 | 0.25 | 37.31 | 216.41 | 0.17 |
| Step=5 | 1.88 | 9.61e-06 | 0.23 | 35.07 | 270.50 | 0.18 |
| Step=15 | 2.14 | 6.28e-05 | 0.28 | 37.41 | 203.65 | 0.51 |
| Step=50 | 2.73 | 2.25e-03 | 0.33 | 42.46 | 319.55 | 1.85 |
| Step=100 | 15.19 | 6.83e-02 | 3.22 | 207.11 | 5165.04 | 3.13 |
| Naive DDPM | 2.69 | 3.11e-5 | 0.28 | 39.19 | 304.65 | >10s |
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diff --git a/2025/Unified Multimodal Understanding via Byte-Pair Visual Encoding/2a101af7-25d6-43b6-aca5-d28a774d787a_content_list.json b/2025/Unified Multimodal Understanding via Byte-Pair Visual Encoding/2a101af7-25d6-43b6-aca5-d28a774d787a_content_list.json
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+ {
+ "type": "text",
+ "text": "Unified Multimodal Understanding via Byte-Pair Visual Encoding",
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+ "bbox": [
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+ "type": "text",
+ "text": "Wanpeng Zhang $^{1,4}$ Yicheng Feng $^{1,4}$ Hao Luo $^{1,4}$ Yijiang Li $^{2}$ Zihao Yue $^{3}$ Sipeng Zheng $^{4}$ Zongqing Lu $^{1,4\\dagger}$",
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+ "text": "$^{1}$ School of Computer Science, Peking University $^{2}$ University of California, San Diego $^{3}$ School of Information, Renmin University of China $^{4}$ BeingBeyond",
+ "bbox": [
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+ "type": "text",
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+ {
+ "type": "text",
+ "text": "Multimodal large language models (MLLMs) have made significant progress in vision-language understanding, yet effectively aligning different modalities remains a fundamental challenge. We present a framework that unifies multimodal understanding by applying byte-pair encoding to visual tokens. Unlike conventional approaches that rely on modality-specific encoders, our method directly incorporates structural information into visual tokens, mirroring successful tokenization strategies in text-only language models. We introduce the priority-guided encoding that considers both frequency and spatial consistency, coupled with a multi-stage training procedure based on curriculum-driven data composition. These enhancements enable the transformer model to better capture cross-modal relationships and reason with visual information. Comprehensive experiments demonstrate improved performance across diverse vision-language tasks. By bridging the gap between visual and textual representations, our approach contributes to the advancement of more capable multimodal foundation models. For further details, visit our website: https://beingbeyond.github.io/Being-VL-0.5.",
+ "bbox": [
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+ "type": "text",
+ "text": "1. Introduction",
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+ "page_idx": 0
+ },
+ {
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+ "text": "Multimodal Large Language Models (MLLMs) have made significant progress in integrating information from various modalities[33, 61, 65]. Nevertheless, effectively representing visual information and aligning it seamlessly with texts still remains a core challenge [4, 51, 66]. Conventional approaches primarily generate visual embeddings using modality-specific encoders [12, 23, 69] (such as CLIP [42]), yet recent research suggests that directly discretizing visual information can facilitate a more unified token representation [36, 37, 54, 73]. In a recent study, researchers introduced a visual encoding scheme to vision",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "modality [72], analogous to the byte-pair encoding (BPE) tokenization [25, 41, 49] in LLMs. Previous work [72] theoretically demonstrated that structurally integrating discrete tokens enhances information preservation, thereby enabling the Transformer models [56] to more effectively learn from two-dimensional visual data. Although the preliminary results are promising, translating this theoretical framework into practical multimodal models poses significant challenges: (1) devising sophisticated token encoding strategies beyond simple frequency counting; (2) identifying data composition strategies that maximize visual-language alignment; and (3) designing effective training procedures to fully leverage these BPE-encoded visual tokens. In this paper, we address these challenges by exploring practical implementations and optimization strategies for BPE-based visual tokenization. Our comprehensive analysis highlights key factors that significantly influence performance across modalities and proposes corresponding optimization.",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Specifically, we introduce a priority-guided encoding scheme that accounts for both co-occurrence frequency and spatial consistency of visual patterns. This novel approach generates semantically enriched visual tokens, thereby preserving the inherent structural information in images more effectively. Moreover, we propose data composition strategies that leverage a curriculum-based approach tailored for optimizing multimodal learning, explicitly designed to complement the visual BPE tokenization process. Unlike conventional visual encoders [42, 67], which extract visual features through a single forward pass [60, 68], visual BPE tokenization generates hierarchical representations where encoded tokens progressively capture increasingly intricate visual patterns. Given this hierarchical property, an aligned learning curriculum is necessary; tokens must first acquire foundational semantic meanings through elementary visual-text associations before advancing toward more sophisticated visual reasoning tasks. Consequently, a multi-stage training procedure is further derived with stage-specific parameter freezing strategies: (1) embedding alignment with frozen language model parameters, (2) selective fine-tuning",
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+ "text": "CVF",
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+ "page_idx": 0
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+ {
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "type": "page_footnote",
+ "text": "$^{\\dagger}$ Correspondence to Zongqing Lu $<$ zongqing.lu@pku.edu.cn>.",
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+ "type": "text",
+ "text": "of early transformer layers, and (3) full model fine-tuning. This incremental training approach facilitates more effective cross-modal knowledge transfer while maintaining the linguistic capabilities inherent to the foundation model.",
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+ "type": "text",
+ "text": "We conduct experiments to demonstrate that our proposed optimization achieve substantial performance improvements compared to baselines. In addition to quantitative improvements, we provide detailed analyses of token patterns, computational efficiency, and qualitative improvements in visual comprehension capabilities. Our contributions are summarized as follows:",
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+ "- A discrete tokenization approach that preserves structural information in images through priority-guided encoding, providing unified visual representation for MLLMs.",
+ "- A progressive training strategy that combines stage-specific parameter freezing, allowing our trained model Being-VL-0.5 to build better visual understanding.",
+ "- Empirical evidence across multiple benchmarks and extensive analysis that validates the effectiveness of our unified encoding methods and elucidates the reason why it advances visual-language understanding."
+ ],
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+ "text": "2. Related Work",
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+ "type": "text",
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+ "type": "text",
+ "text": "The core challenge of MLLMs lies in effectively representing and integrating information from different modalities. The research community has primarily developed two representative approaches: methods based on continuous representations and methods based on discrete tokens.",
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+ "text": "Continuous token representation methods have emerged as the mainstream paradigm, with representative works such as LLaVA [32, 33], Emu [52, 58], DeepSeek-VL [35, 59], and Qwen-VL [1, 2, 57]. These models use pre-trained visual encoders (e.g., CLIP [42]) to map images into continuous representations, which are then aligned with language models through projection layers [15, 70]. Although this approach has achieved significant results, it faces two fundamental challenges: first, the modality gap between encoders and language models [5, 22], wherein the high-dimensional continuous features provided by visual encoders differ from the discrete token representations expected by language models; second, the information bottleneck problem, wherein images compressed through visual encoders may lose substantial detailed information, particularly affecting low-frequency visual patterns [43]. Recent analysis [3, 21, 62] indicates that this architectural design makes models prone to visual hallucinations, generating descriptions even when relevant visual information is absent.",
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+ "text": "Discrete token representation methods have gained increasing attention in recent years [36, 37, 54, 73]. These methods typically use vector quantization models (such as VQ-GAN [11] or VQVAE [45, 55]) to discretize images",
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+ "type": "text",
+ "text": "into a series of tokens, thereby enabling visual information to be processed in a form similar to text. The advantage of this approach lies in its ability to process multimodal inputs in a unified manner, thus reducing inter-modal differences. However, existing discrete token methods also have significant limitations: most works simply quantize images into fixed-size tokens without considering the semantic structure of visual content; information loss during quantization may lead to the loss of fine-grained visual details; and the unbalanced representation of key visual concepts in the token space can result in limited recognition capability for certain visual patterns.",
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+ "text": "These methods differ significantly from tokenization strategies used in natural language processing. In the NLP domain, algorithms such as BPE form semantically meaningful tokens by combining frequently co-occurring character sequences [14], a strategy that has proven beneficial for Transformer learning [39, 40]. Research by [44] demonstrates that for Markov sequence data, even smaller Transformer models can significantly reduce prediction loss when using appropriate tokenization strategies.",
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+ "type": "text",
+ "text": "2.2. BPE Tokenization for Visual Data",
+ "text_level": 1,
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+ "text": "Extending BPE tokenization to the visual domain is an emerging research direction [6, 46]. The core idea is to form a more semantical visual vocabulary by combining frequently co-occurring patterns based on quantized images. Being-VL-0 [72] first proposed a theoretical framework for applying BPE to quantized visual data, demonstrating that for two-dimensional data conforming to specific generative processes, using visual BPE can significantly reduce model prediction loss. Their analysis indicates that compared to unigram models based on independent and identically distributed assumptions, BPE tokenization can more effectively capture structured patterns in visual data.",
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+ "text": "However, significant challenges remain in the transition from theory to practice. The implementation of Being-VL-0 [72] uses primarily frequency-based encoding without considering spatial relationships that are crucial in visual data. The relationship between vocabulary size and performance, as well as strategies that balance frequency with spatial consistency, remain underexplored. Besides, designing effective training procedures that leverage the unique properties of BPE visual tokens is also important. Research on parameter freezing strategies [17, 53] suggests that different settings at various training stages can impact the performance, but these findings have not been systematically applied to visual BPE training. Our work addresses these gaps by exploring enhancement strategies for visual BPE tokenization across vocabulary construction, data composition, and training procedures. Through these contributions, we aim to advance the practical application of BPE visual tokenization in multimodal foundation models.",
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+ "type": "page_number",
+ "text": "12977",
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+ "type": "image",
+ "img_path": "images/db652e2583dd4c0c78b303a116c009974ff67a24e692e72deef771f7ed4cc21d.jpg",
+ "image_caption": [
+ "Figure 1. Overview of our framework. The upper part shows the BPE vocabulary construction process: starting from a training dataset, we identify candidate token pairs and apply our priority scoring mechanism (combining frequency and spatial consistency) to iteratively extend the vocabulary with new encoded tokens. The lower part illustrates the MLLM pipeline: an input image is first quantized using a VQ-GAN codebook, then encoded using the trained vocabulary. The resulting visual tokens (e.g., token 381 representing the whole \"cat\" and 249 representing the whole \"box\") are seamlessly integrated with text tokens to form a unified sequence for multimodal understanding."
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+ {
+ "type": "text",
+ "text": "3. Method",
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+ "text": "In this section, we first introduce key concepts and notation for our visual tokenization framework. Then we present the detailed training pipeline for our Being-VL-0.5 model.",
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+ "type": "text",
+ "text": "3.1. Visual Tokenization Pipeline",
+ "text_level": 1,
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+ "text": "The core of our approach involves transforming visual information into token sequences that can be processed by language models. This transformation occurs through a pipeline with the following key steps:",
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+ "type": "text",
+ "text": "Vector Quantization (VQ). Given an image $I$ divided into patches, we first apply a VQ model with a codebook $V = \\{v_{1}, v_{2}, \\dots, v_{K}\\}$ containing $K$ entries. This process maps each image patch to its closest codebook entry, producing a grid of discrete indices $Q(I) = \\{q_{i,j}\\}_{i,j=1}^{h,w}$ , where $h$ and $w$ represent the height and width of the patch grid.",
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+ "text": "BPE Visual Tokenization. The BPE visual tokenization process, denoted as $T(Q(I))$ , identifies frequently co-occurring patterns in the quantized representation and encodes them into new tokens, creating an extended vocabulary $D = V \\cup V_{ext}$ , where $V_{ext}$ represents the set of encoded tokens. Formally, the tokenization function $T: Q(I) \\to (t_1, t_2, \\dots, t_n)$ maps the quantized image to a sequence of tokens $t_i \\in D$ , where $n \\leq h \\times w$ due to the encoding of multiple indices into single tokens.",
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+ "type": "text",
+ "text": "This approach parallels BPE tokenization in text processing but adapts it for two-dimensional visual data, incor",
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+ "type": "text",
+ "text": "porating spatial relationships that are unique to the visual modality.",
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+ "type": "text",
+ "text": "3.2. Token-Based MLLM",
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+ "type": "text",
+ "text": "Unified Token Sequence. We formalize our token-based multimodal language model as a conditional probability distribution over token sequences. Given a text input $X = (x_{1}, x_{2}, \\ldots, x_{m})$ and an image input $I$ , the model processes the combined sequence and generates output tokens autoregressively. The combined input consists of special tokens marking the beginning and end of the tokenized image representation:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nS = \\left(x _ {1}, \\dots , x _ {m}, [ \\mathrm {B O I} ], t _ {1}, \\dots , t _ {n}, [ \\mathrm {E O I} ], \\dots\\right), \\tag {1}\n$$\n",
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+ "type": "text",
+ "text": "where [BOI] and [EOI] are special tokens indicating the image boundary in the sequence.",
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+ "type": "text",
+ "text": "Autoregressive Modeling. The model defines a probability distribution over the next token given all previous tokens:",
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+ {
+ "type": "equation",
+ "text": "\n$$\np \\left(s _ {i} \\mid s _ {< i}\\right) = \\operatorname {S o f t m a x} \\left(f _ {\\theta} \\left(E \\left(s _ {1}\\right), E \\left(s _ {2}\\right), \\dots , E \\left(s _ {i - 1}\\right)\\right)\\right), \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "where $f_{\\theta}$ represents the transformer-based language model with parameters $\\theta$ , and $E(s_{i})$ represents the embedding of token $s_{i}$ . For model generation, tokens are sampled sequentially:",
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+ "type": "equation",
+ "text": "\n$$\n\\hat {s} _ {i} \\sim p \\left(s _ {i} \\mid \\hat {s} _ {1}, \\hat {s} _ {2}, \\dots , \\hat {s} _ {i - 1}, x _ {1}, x _ {2}, \\dots , x _ {m}, t _ {1}, t _ {2}, \\dots , t _ {n}\\right). \\tag {3}\n$$\n",
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+ "type": "page_number",
+ "text": "12978",
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+ "type": "text",
+ "text": "Training Objective. The model is trained to minimize the negative log-likelihood of the target sequence $Y = (y_{1}, y_{2}, \\dots, y_{l})$ conditioned on the input:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} (\\theta) = - \\mathbb {E} _ {(X, I, Y) \\sim \\mathcal {D}} \\left[ \\sum_ {i = 1} ^ {| Y |} \\log p _ {\\theta} \\left(y _ {i} \\mid y _ {< i}, X, T (Q (I))\\right) \\right], \\tag {4}\n$$\n",
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+ "type": "text",
+ "text": "where $\\mathcal{D}$ represents the training dataset containing input-output triplets.",
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+ {
+ "type": "text",
+ "text": "3.3. Framework Overview",
+ "text_level": 1,
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+ "type": "text",
+ "text": "As formalized in the preliminaries above, our token-based multimodal model processes visual information through a pipeline that includes vector quantization $Q(\\cdot)$ and visual tokenization $T(\\cdot)$ before integration with text tokens in a language model. Our optimizations target each component of this pipeline while considering their interdependencies.",
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+ "type": "text",
+ "text": "Specifically, our framework enhances this pipeline through: (1) Enhanced Vocabulary Construction; (2) Optimized Data Composition Strategies; (3) Efficient Multi-Stage Training. These components work together to improve the model's ability to process visual information, align visual and textual representations, and generate accurate responses to multimodal inputs.",
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+ "type": "text",
+ "text": "Figure 1 illustrates the overall framework, which operates in two phases. In the vocabulary construction phase (upper part), we train a BPE vocabulary using our priority-guided encoding scheme that considers both co-occurrence frequency and spatial consistency. This approach creates an extended vocabulary that effectively captures meaningful visual patterns beyond what frequency-only methods can achieve. In the application phase (lower part), input images are first quantized through a VQ-GAN model, then encoded using the trained vocabulary. The resulting visual tokens are integrated with text tokens to form a unified sequence for the language model.",
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+ "type": "text",
+ "text": "3.4. Vocabulary Construction",
+ "text_level": 1,
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+ "type": "text",
+ "text": "The effectiveness of token-based representations hinges on creating a vocabulary that efficiently captures meaningful patterns in the data. Our enhanced vocabulary construction method extends beyond simple frequency-based encoding to incorporate structural information specific to visual data, while relying exclusively on image statistics without reference to textual information.",
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+ "type": "text",
+ "text": "In standard BPE tokenization, token pairs are encoded based solely on their co-occurrence frequency. While effective for text, this can be suboptimal for visual data where spatial relationships play crucial roles. We introduce a priority function $P(a,b)$ that guides the encoding process with a more comprehensive evaluation of candidate token pairs:",
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+ "type": "equation",
+ "text": "\n$$\nP (a, b) = F (a, b) + \\alpha \\cdot S (a, b). \\tag {5}\n$$\n",
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+ "sub_type": "algorithm",
+ "code_caption": [
+ "Algorithm 1 Priority-Guided Encoding"
+ ],
+ "code_body": "Input: Quantized training data $\\mathcal{C}$ , initial vocabulary $V$ , target vocabulary size $N_{\\mathrm{vocab}}$ $D \\gets V$ \nwhile $N_{\\mathrm{vocab}} <$ target size do \n Compute $F(a, b)$ and $S(a, b)$ for all adjacent token pairs in $\\mathcal{C}$ \n Calculate priority $P(a, b) = F(a, b) + \\alpha \\cdot S(a, b)$ and select top- $k$ pairs by priority: $\\{(a_1, b_1), \\ldots, (a_k, b_k)\\}$ . \n $(a^*, b^*) \\gets \\arg \\max_{i \\in \\{1, \\ldots, k\\}} P(a_i, b_i)$ \n Create new token $c = (a^*, b^*)$ $D \\gets D \\cup \\{c\\}$ \n Update $\\mathcal{C}$ by replacing all adjacent occurrences of $(a^*, b^*)$ with $c$ (horizontally or vertically). \nend while \nreturn $D$",
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+ "type": "text",
+ "text": "This function combines two key factors:",
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+ "type": "list",
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+ "list_items": [
+ "- Co-occurrence frequency $F(a, b)$ : The raw frequency with which tokens $a$ and $b$ appear adjacent to each other, normalized across the training corpus of quantized images.",
+ "- Spatial consistency $S(a, b)$ : A measure of how consistently the token pair maintains spatial relationships across different images, calculated as:"
+ ],
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+ {
+ "type": "equation",
+ "text": "\n$$\nS (a, b) = \\frac {1}{N _ {a , b}} \\sum_ {i = 1} ^ {N _ {a, b}} d \\left(u _ {i} (a, b), \\bar {u} (a, b)\\right). \\tag {6}\n$$\n",
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+ "type": "text",
+ "text": "Here, $u_{i}(a,b)$ represents the relative positioning of tokens $a$ and $b$ in instance $i$ , $\\bar{u}(a,b)$ is the average relative positioning across all instances, $N_{a,b}$ is the number of co-occurrences, and the spatial distance function is defined as:",
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+ "type": "equation",
+ "text": "\n$$\nd \\left(u _ {1}, u _ {2}\\right) = \\exp \\left(- \\frac {\\left\\| u _ {1} - u _ {2} \\right\\| ^ {2}}{2 \\sigma^ {2}}\\right), \\tag {7}\n$$\n",
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+ "type": "text",
+ "text": "where $\\| u_1 - u_2 \\|$ is the Euclidean distance between the two relative position vectors, and $\\sigma$ is a scaling parameter that controls how quickly similarity decreases with distance. This formulation ensures that token pairs with consistent spatial relationships across images receive higher scores.",
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+ "type": "text",
+ "text": "The weighting parameter $\\alpha$ controls the relative importance of each factor and is determined through cross-validation on a development set. This dual-factor approach ensures that encoded tokens represent not only frequent patterns but also spatially consistent visual structures. It's important to emphasize that this entire process relies exclusively on image data, with no dependency on textual information or captions. The algorithm identifies patterns based solely on the statistical and structural properties of the visual content. Algorithm 1 outlines our priority-guided encoding process with diversity filtering. For complete details, please refer to Algorithm 2 in the Appendix.",
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+ "type": "page_number",
+ "text": "12979",
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+ {
+ "type": "text",
+ "text": "3.5. Model Expanding",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "Once we have constructed our enhanced visual vocabulary $D$ , we need to expand the pre-trained language model to accommodate these new tokens. This expansion process serves as the bridge between our tokenization approach and the subsequent model training. Given a pre-trained language model $M$ with a text vocabulary $V_{\\mathrm{text}}$ and corresponding embedding weights $E_{\\mathrm{text}} \\in \\mathbb{R}^{|V_{\\mathrm{text}}| \\times d}$ (where $d$ is the embedding dimension), we expand the embedding layer to incorporate the visual vocabulary $D$ :",
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+ {
+ "type": "equation",
+ "text": "\n$$\nE _ {\\text {e x p a n d e d}} = \\left[ E _ {\\text {t e x t}}, E _ {\\text {v i s u a l}} \\right] \\in \\mathbb {R} ^ {\\left(\\left| V _ {\\text {t e x t}} \\right| + | D |\\right) \\times d}, \\tag {8}\n$$\n",
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+ "type": "text",
+ "text": "where $E_{\\mathrm{visual}} \\in \\mathbb{R}^{|D| \\times d}$ represents the newly added embeddings for visual tokens. This expansion increases the model's vocabulary size from $|V_{\\mathrm{text}}|$ to $|V_{\\mathrm{text}}| + |D|$ .",
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+ "type": "text",
+ "text": "For the initialization of the newly added visual token embeddings, we adopt He initialization [20], i.e., $E_{\\mathrm{visual}}[i,j] \\sim \\mathcal{N}(0,\\sqrt{2 / d_l})$ , where $d_{l}$ is the embedding dimension. This initialization helps maintain proper signal magnitude throughout the network, preventing vanishing or exploding gradients during the early stages of training.",
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+ "type": "text",
+ "text": "The process is illustrated in the top part of Figure 2. We first extend a VQ token embedding corresponding to the VQ-GAN codebook, and then extend a BPE token embedding corresponding to the BPE vocabulary. The extended weights from these two components constitute the initialization of the visual part. By default, we standardize both dimensions of them to 8K, corresponding to an 8K VQ codebook and an 8K BPE vocabulary, respectively.",
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+ {
+ "type": "text",
+ "text": "3.6. Multi-Stage Training",
+ "text_level": 1,
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+ "type": "text",
+ "text": "With the expanded model supporting both text and visual tokens, we now introduce our multi-stage training pipeline. Our approach combines strategic data composition with stage-specific parameter freezing to maximize the effectiveness of visual tokenization. Figure 2 illustrates the overall process.",
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+ {
+ "type": "text",
+ "text": "3.6.1. Curriculum-Based Data Composition",
+ "text_level": 1,
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+ "type": "text",
+ "text": "We develop a curriculum-based data composition strategy, which is designed to complement the BPE visual tokenization. Unlike traditional visual encoders that extract features in a single forward pass, BPE visual tokenization creates a hierarchical representation where encoded tokens incrementally capture more complex visual patterns. This hierarchical nature of BPE tokens requires a matching learning curriculum: tokens must first establish basic semantic meanings through simple visual-text associations before they can be effectively utilized for complex reasoning.",
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+ "type": "text",
+ "text": "Specifically, we categorize our training data into four types based on complexity: Foundation Data (basic image-capture pairs), Perception Data (detailed visual attributes), Reasoning Data (complex visual QA), and Instruction Data",
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+ {
+ "type": "image",
+ "img_path": "images/06618111a5c7a4c5da0057f3cf1ced993c1bbc89e175fc43ec547de450aafc87.jpg",
+ "image_caption": [
+ "Figure 2. Illustration of our multi-stage training strategy. The bottom part shows multimodal data being processed into unified tokens. The middle curves represent the data distribution across training stages, showing a gradual shift from basic concepts (Stage 1) to more balanced (Stage 2) and finally complex reasoning-focused data (Stage 3). The top part illustrates how we expand a text-only LLM to incorporate visual capabilities through weight initialization and alignment, resulting in a unified multimodal model. This curriculum approach mirrors the hierarchical nature of BPE visual tokens, which progressively capture more complex visual patterns throughout the learning process."
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+ "type": "text",
+ "text": "(multi-turn interactions). Details of all types of datasets can be found in the Appendix A.4.",
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+ "text": "We employ a curriculum that progressively shifts emphasis across training stages, formalized as a composition ratio $R_{i}(s) = w_{i}(s) / \\sum_{j}w_{j}(s)$ , where $R_{i}(s)$ represents the proportion of data type $i$ at stage $s$ with corresponding weight $w_{i}(s)$ . Each stage employs distinct composition ratios, transitioning from foundation-heavy in early stages to instruction-focused in later stages. This curriculum ensures that visual tokens first establish basic meanings before tackling complex reasoning tasks.",
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+ "text": "This stage-specific curriculum ensures that the model first develops strong foundational visual understanding before focusing on more complex tasks, aligning with the parameter freezing strategy of each stage.",
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+ "text": "3.6.2. Progressive Parameter Unfreezing",
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+ "text": "Complementing our data curriculum, we implement stage-specific parameter freezing to control which components of the model are updated at each stage. The parameter update can be expressed as:",
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+ "text": "\n$$\n\\theta_ {s + 1} = \\theta_ {s} - \\eta \\cdot M _ {s} \\odot \\nabla_ {\\theta} \\mathcal {L}, \\tag {9}\n$$\n",
+ "text_format": "latex",
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+ "text": "where $\\theta_{s}$ represents the model parameters at stage $s$ , $\\eta$ is the learning rate, $\\nabla_{\\theta}\\mathcal{L}$ is the loss gradient, $\\odot$ denotes elementwise multiplication, and $M_{s}$ is a binary mask that determines which parameters are updated during stage $s$ .",
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+ "text": "12980",
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+ "type": "table",
+ "img_path": "images/fa89eeeb116324f56b074261220538681c5ee91ddca9d2aa9d261af1f5d81f4b.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Model | Params | Tokenizer | Benchmark |
| VQAv2 | MMBench | MME-P | SciQA-IMG | POPE | VizWiz |
| Continuous Embedding-Based Models |
| InstructBLIP | 7B | Continuous | 75.2 | 38.3 | 1212.8 | 60.5 | 81.5 | 34.5 |
| LLaVA-1.5 | 7B | Continuous | 78.5 | 64.3 | 1510.7 | 66.8 | 85.9 | 50.0 |
| mPLUG-Owl2 | 8B | Continuous | 79.4 | 64.5 | 1450.2 | - | 86.1 | 54.5 |
| HyperLLaVA | 7B | Continuous | 79.1 | 65.9 | 1481.2 | 70.4 | 86.3 | 51.9 |
| ShareGPT4V | 7B | Continuous | 80.6 | 68.8 | 1567.4 | 68.4 | - | 57.2 |
| VILA-1.5 | 8B | Continuous | 80.9 | 72.3 | - | - | 84.4 | 58.7 |
| LLaVA-Next | 7B | Continuous | 81.8 | 67.4 | 1519.0 | 70.1 | 86.5 | 57.6 |
| Discrete Token-Based Models |
| Chameleon | 7B | Discrete | 56.2 | 37.3 | 1297.5 | - | 78.2 | 46.4 |
| Being-VL-0 | 8B | Discrete | 60.6 | 44.0 | 1316.2 | 64.3 | 81.3 | 48.2 |
| Unified-IO-2 | 7B | Discrete | 79.4 | 71.5 | - | 86.2 | 87.7 | - |
| Being-VL-0.5 w/o BPE | 8B | Discrete | 54.3 | 38.2 | 1301.2 | 57.8 | 76.1 | 45.0 |
| Being-VL-0.5 | 8B | Discrete | 80.2 | 71.8 | 1525.8 | 70.3 | 84.3 | 57.4 |
| Being-VL-0.5+ | 8B | Discrete | 80.6 | 72.1 | 1536.3 | 69.0 | 86.0 | 57.8 |
",
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+ "type": "text",
+ "text": "Table 1. Performance comparison of different visual-language models across standard benchmarks. Models are grouped by tokenizer type (Continuous / Discrete). The best performance in each group is bolded, while second-best result in each group is underlined.",
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+ "text": "Our training pipeline consists of three stages with different masks and objectives:",
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+ "text": "Stage 1: Embedding Alignment focuses exclusively on training the newly extended visual token embeddings while freezing the rest of the model. The mask is defined as $M_1[i] = 1$ if parameter $i$ belongs to new embeddings, 0 otherwise. This alignment establishes basic visual-linguistic associations without disrupting pre-trained language capabilities.",
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+ "text": "Stage 2: Selective Fine-tuning unfreezes early transformer layers while keeping later layers frozen, with $M_2[i] = 1$ if parameter $i$ is in layers 1 to $k$ (25% of total layers in our default implementation), 0 otherwise. This enhances cross-modal interactions in the feature integration layers using a broader range of data types.",
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+ "text": "Stage 3: Full Fine-tuning unfreezes all parameters $(M_3[i] = 1, \\forall i)$ and emphasizes complex reasoning and instruction-following data. This stage refines the model's advanced capabilities while building upon the foundation established in earlier stages.",
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+ "text": "4. Experiments",
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+ "text": "In this section, we empirically evaluate our designed framework and training pipelines. Based on the methods described in Section 3, we train our model Being-VL-0.5 with an 8K extended vocabulary and a variant Being-VL-0.5 $^{+}$ with a 16K extended vocabulary. We first describe our experimental setup, then present comprehensive results demonstrating the effectiveness of our approach compared to baselines. We further conduct analyses of each component to validate our design choices. Considering the limited space, please refer to the Appendix A for hyperparameter choices and further analyses of our experiments.",
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+ "text": "4.1. Experiments Setup",
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+ "text": "Evaluation Benchmarks: We conduct evaluation on widely-used benchmarks [27, 28] that assess different aspects of visual understanding: VQAv2 [16] and VizWiz [19] for general visual question answering, MMBench [34] for comprehensive multimodal understanding, MME-P [13] for perception capabilities, SciQA-IMG [38] for scientific reasoning, and POPE [29] for hallucination evaluation.",
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+ "text": "Baselines: We primarily focus on open-source models with comparable parameters and similar training data scales to ensure that performance differences reflect architectural choices rather than scale advantages. We compare our Being-VL-0.5 against two kinds of baselines: continuous embedding-based models and discrete token-based models. Continuous embedding-based models include InstructBLIP [9], LLaVA-1.5/LLaVA-Next [31, 32], mPLUG-Owl2 [63, 64], HyperLLaVA [71], ShareGPT4V [8], and VILA-1.5 [30]. Discrete token-based models include Chameleon [54], Being-VL-0 [72], and Unified-IO-2 [37]. We also compare 'Being-VL-0.5 w/o BPE', which is a variant that completely removes the BPE part and retains only the base VQ token embedding. This is used to investigate the effectiveness of our framework's core BPE design.",
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+ "text": "4.2. General Visual Understanding",
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+ "text": "Table 1 presents our models' performance compared to baselines. Our framework effectively narrows the performance gap between discrete token-based models and continuous embedding-based models. Both Being-VL-0.5 and Being-VL-0.5+ achieve competitive performance across all benchmarks, with Being-VL-0.5+ reaching 80.6 on VQAv2 and 72.1 on MMBench, comparable to the best continuous embedding-based models like VILA-1.5 (80.9 and",
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+ "text": "12981",
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+ "img_path": "images/2cff28a442eebb210829a62dff94fded0e222679a92461557e00526ab700dde8.jpg",
+ "image_caption": [
+ "Figure 3. Visualization of embedding weight distributions across three model variants. The heatmaps represent sampled weights from the embedding matrices (4096 dimensions), wherein color intensity indicates weight magnitude (blue for negative, red for positive). The depth of the color indicates the activation magnitude of the corresponding token embedding during model inference. Top: LLM+VQ (Being-VL-0.5 w/o BPE) with text tokens (32K) + VQ tokens (8K). Middle: LLM+VQ+BPE-8K (Being-VL-0.5) with text tokens (32K) + VQ tokens (8K) + BPE tokens (8K). Bottom: LLM+VQ+BPE-16K (Being-VL-0.5+) with text tokens (32K) + VQ tokens (8K) + BPE tokens (16K)."
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+ "text": "72.3 respectively). Being-VL-0.5 $^{+}$ demonstrates strong perception capabilities with 1536.3 on MME-P, outperforming many continuous embedding models.",
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+ "text": "Among discrete token-based approaches, Being-VL-0 represents the work most closely aligned with our method, as both implement BPE-based visual tokenization. Our method outperforms Being-VL-0 across all benchmarks, with notable gains on MMBench (71.8 vs. 44.0) and MMEP (1525.8 vs. 1316.2). These improvements are attributable to our enhanced vocabulary construction and optimized training strategies. Unified-IO-2 achieves stronger performance on SciQA-IMG (86.2 vs. our 70.3), but it is worth noting that our models evaluate this benchmark in a zero-shot manner without task-specific fine-tuning.",
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+ "text": "Additionally, our method achieves an optimal balance between capturing low-level visual details and modeling high-level semantic concepts, with reduced hallucination on POPE (84.3 for Being-VL-0.5, 86.0 for Being-VL-0.5 $^{+}$ ) compared to earlier discrete token approaches. When evaluating the overall performance across all benchmarks, our method demonstrates competitive results while maintaining the advantages of unified token representation.",
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+ "text": "Furthermore, the significant performance drop of 'Being-VL-0.5 w/o BPE' on all benchmarks also highlights the necessity of the BPE vocabulary as a core part of our framework. We also conducted a qualitative case study, which provides additional evidence of Being-VL-0.5's comprehensive visual understanding. For detailed results, please refer to Section B.",
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+ "img_path": "images/e81fda853cfabca271d273adc7c702dcb49ff387e6b48d246ef3b8146fbc3300.jpg",
+ "image_caption": [
+ "Figure 4. Scaling potential and training efficiency comparison for different vocabulary sizes (4K, 8K, 16K). Performance curves (solid lines) show relative performance gains as training data increases, while efficiency curves (dashed lines) illustrate the performance-to-cost ratio. All metrics are normalized relative to the 4K vocabulary model at standard training data amount $(1.0\\times)$ ."
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+ "text": "4.3. BPE Token Activation Mechanism",
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+ "type": "text",
+ "text": "Figure 3 visualizes embedding weight distributions across our model variants, revealing key insights into how BPE tokenization helps unifying multimodal knowledge. In the base LLM+VQ model (top), which is a variant removing BPE vocabulary, we observe a contrast between text (0-32K) and visual tokens (32K-40K). Text tokens exhibit predominantly low-magnitude weights (lighter colors), while visual tokens exhibit significantly higher magnitudes (deeper colors). This imbalance suggests that the model struggles to establish a unified representation space across modalities. With BPE tokenization (middle and bottom panels), this pattern changes substantially. These two models show more balanced weight distributions, suggesting BPE helps bridge the representation gap between modalities, creating a more unified semantic space for visual-textual interaction. This visualization elucidates why models with improved BPE patterns yield superior performance, thereby outperforming Being-VL-0.",
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+ "text": "However, some BPE tokens exhibit minimal activation (near-zero weights), appearing as white vertical stripes. This pattern is more evident in the 16K variant, where more embeddings remain unused. Intuitively, we hypothesize that this is because the current training does not fully utilize these 16K tokens, which may explain why Being-VL-0.5 $^{+}$ underperforms Being-VL-0.5 on certain tasks. Concurrently, this observation inspires us to examine the trade-offs between representational capacity and learning efficiency.",
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+ "text": "12982",
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+ "table_footnote": [],
+ "table_body": "| Configuration | Curriculum | Progressive | Avg. Score |
| Perception | Reasoning |
| Standard | ✓ | ✓ | 80.3 | 71.1 |
| Progressive only | - | ✓ | 74.9 | 65.1 |
| Curriculum only | ✓ | - | 76.8 | 67.5 |
| Single stage | - | - | 71.2 | 62.3 |
",
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+ "text": "4.4. Scaling Potential and Training Efficiency",
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+ "text": "To further investigate the trade-offs between vocabulary size, performance scaling, and training efficiency, we conducted extended experiments using the same checkpoint. Figure 4 presents our findings comparing three vocabulary sizes (4K/8K/16K) across varying data scales. For performance evaluation, we computed the normalized mean scores across four benchmarks (MME, POPE, VQAv2, and MMBench) and normalized them relative to the 4K vocabulary model at standard training data $(1.0\\times)$ , providing an intuitive comparison of relative performance gains.",
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+ "text": "The horizontal axis serves dual purposes: for performance curves, it represents the relative amount of training data; for efficiency curves, it represents the total cost factor, incorporating computational resources $\\times$ training time. Specifically, total cost increases with both vocabulary size and data amount. Our results reveal an important tradeoff: while the 16K vocabulary shows superior scaling potential, eventually outperforming both 4K and 8K models as training data increases beyond $1.5\\times$ , its efficiency (performance-to-cost ratio) remains consistently lower than smaller vocabulary models. In contrast, the 8K vocabulary achieves a better balance, showing strong performance scaling while maintaining reasonable efficiency.",
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+ "text": "4.5. Analysis of Multi-Stage Training",
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+ "text": "We conduct ablation studies to investigate the impact of the multi-stage training. Table 2 shows that our standard approach achieves clear improvements over the single-stage training (12.8% and 14.1% higher on perception and reasoning tasks respectively), demonstrating the effectiveness of the overall strategy. The results reveal that both curriculum-based data composition and progressive parameter unfreezing contribute to the performance, with curriculum data composition showing a stronger impact.",
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+ "text": "Table 3 shows that the shifting of data types matters significantly. Our curriculum design outperforms both reverse ordering and random mixing. This aligns with our design principle that visual BPE tokens should first establish basic semantic meanings before tackling complex reasoning tasks. Similarly, Table 4 highlights the value of our three-stage progressive approach for parameter unfreezing. The simplified two-stage method shows modest perfor",
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+ "img_path": "images/9995fc9a095735847d16f4daa0296ed2ed6414ffe69eaeb774a385aa9d9792a1.jpg",
+ "table_caption": [
+ "Table 2. Ablation study on different components in training. Configurations marked with “-” use a fixed data mixture ratio throughout training or employ a standard full fine-tuning approach."
+ ],
+ "table_footnote": [],
+ "table_body": "| Curriculum Strategy | Avg. Score |
| Perception | Reasoning |
| Progressive (FD → PD → RD → ID) | 80.3 | 71.1 |
| Reverse (ID → RD → PD → FD) | 73.4 | 64.0 |
| Random | 77.3 | 68.4 |
",
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+ "img_path": "images/e1ea72492fc5264bb4617aca3b00714cd4f216d200a1808e289f2b507e1dd78d.jpg",
+ "table_caption": [
+ "Table 3. Analysis of different curriculum strategies. FD, PD, RD, and ID refer to Foundation Data, Perception Data, Reasoning Data, and Instruction Data as described in Section 3.6.1."
+ ],
+ "table_footnote": [],
+ "table_body": "| Unfreezing Strategy | Avg. Score |
| Perception | Reasoning |
| 3-stage (align → selective → full) | 80.3 | 71.1 |
| 2-stage (align → full) | 78.2 | 69.3 |
| Reverse order | 72.1 | 63.0 |
",
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+ "text": "Table 4. Analysis of different parameter unfreezing strategies.",
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+ "text": "mance differences (2.7% lower on perception tasks), while reverse unfreezing leads to more notable performance drops (11.4% lower on perception tasks), suggesting that the order of parameter updates affects how well the model integrates visual and textual information.",
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+ "type": "text",
+ "text": "5. Conclusions, Limitations, and Future Work",
+ "text_level": 1,
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+ "text": "This paper presents a unified visual tokenization framework that enhances multimodal understanding through three key innovations: priority-guided vocabulary construction that considers both frequency and spatial patterns, curriculum-based data composition that aligns with token complexity progression, and a specialized multi-stage training procedure. Our comprehensive experiments across diverse benchmarks demonstrate that this approach effectively bridges the gap between visual and textual modalities, achieving competitive performance compared to continuous embedding-based methods while maintaining the advantages of a unified token representation.",
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+ "type": "text",
+ "text": "Our current study focused on models with 8B parameters due to computational constraints. While these models already show promising results, our scaling analysis indicates potential for further improvements with more training data. The observed relationship between vocabulary size and performance suggests that further scaling could achieve even stronger multimodal understanding capabilities.",
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+ "type": "text",
+ "text": "A natural extension of our unified token-based approach is multimodal generation. Unlike models using separate encoders for different modalities, our framework enables the model to generate visual tokens in the same way it generates text tokens, establishing a truly unified representation paradigm. Although the current work concentrates on understanding tasks, extending our approach to incorporate generation capabilities constitutes a promising direction for future research.",
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+ "text": "12983",
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+ {
+ "type": "text",
+ "text": "Acknowledgments",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "This work was supported by NSFC under Grant 62450001. The authors would like to thank the anonymous reviewers for their valuable comments and advice.",
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+ "text": "References",
+ "text_level": 1,
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+ "list_items": [
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+ "bbox": [
+ 0.092,
+ 0.306,
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+ 0.348
+ ],
+ "angle": 0,
+ "content": "- A progressive training strategy that combines stage-specific parameter freezing, allowing our trained model Being-VL-0.5 to build better visual understanding."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.092,
+ 0.351,
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+ "angle": 0,
+ "content": "- Empirical evidence across multiple benchmarks and extensive analysis that validates the effectiveness of our unified encoding methods and elucidates the reason why it advances visual-language understanding."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "angle": 0,
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2. Related Work"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.453,
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+ ],
+ "angle": 0,
+ "content": "2.1. Representation Methods in MLLMs"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "The core challenge of MLLMs lies in effectively representing and integrating information from different modalities. The research community has primarily developed two representative approaches: methods based on continuous representations and methods based on discrete tokens."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Continuous token representation methods have emerged as the mainstream paradigm, with representative works such as LLaVA [32, 33], Emu [52, 58], DeepSeek-VL [35, 59], and Qwen-VL [1, 2, 57]. These models use pre-trained visual encoders (e.g., CLIP [42]) to map images into continuous representations, which are then aligned with language models through projection layers [15, 70]. Although this approach has achieved significant results, it faces two fundamental challenges: first, the modality gap between encoders and language models [5, 22], wherein the high-dimensional continuous features provided by visual encoders differ from the discrete token representations expected by language models; second, the information bottleneck problem, wherein images compressed through visual encoders may lose substantial detailed information, particularly affecting low-frequency visual patterns [43]. Recent analysis [3, 21, 62] indicates that this architectural design makes models prone to visual hallucinations, generating descriptions even when relevant visual information is absent."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Discrete token representation methods have gained increasing attention in recent years [36, 37, 54, 73]. These methods typically use vector quantization models (such as VQ-GAN [11] or VQVAE [45, 55]) to discretize images"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.272
+ ],
+ "angle": 0,
+ "content": "into a series of tokens, thereby enabling visual information to be processed in a form similar to text. The advantage of this approach lies in its ability to process multimodal inputs in a unified manner, thus reducing inter-modal differences. However, existing discrete token methods also have significant limitations: most works simply quantize images into fixed-size tokens without considering the semantic structure of visual content; information loss during quantization may lead to the loss of fine-grained visual details; and the unbalanced representation of key visual concepts in the token space can result in limited recognition capability for certain visual patterns."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.274,
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+ "angle": 0,
+ "content": "These methods differ significantly from tokenization strategies used in natural language processing. In the NLP domain, algorithms such as BPE form semantically meaningful tokens by combining frequently co-occurring character sequences [14], a strategy that has proven beneficial for Transformer learning [39, 40]. Research by [44] demonstrates that for Markov sequence data, even smaller Transformer models can significantly reduce prediction loss when using appropriate tokenization strategies."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.2. BPE Tokenization for Visual Data"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.447,
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+ ],
+ "angle": 0,
+ "content": "Extending BPE tokenization to the visual domain is an emerging research direction [6, 46]. The core idea is to form a more semantical visual vocabulary by combining frequently co-occurring patterns based on quantized images. Being-VL-0 [72] first proposed a theoretical framework for applying BPE to quantized visual data, demonstrating that for two-dimensional data conforming to specific generative processes, using visual BPE can significantly reduce model prediction loss. Their analysis indicates that compared to unigram models based on independent and identically distributed assumptions, BPE tokenization can more effectively capture structured patterns in visual data."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "However, significant challenges remain in the transition from theory to practice. The implementation of Being-VL-0 [72] uses primarily frequency-based encoding without considering spatial relationships that are crucial in visual data. The relationship between vocabulary size and performance, as well as strategies that balance frequency with spatial consistency, remain underexplored. Besides, designing effective training procedures that leverage the unique properties of BPE visual tokens is also important. Research on parameter freezing strategies [17, 53] suggests that different settings at various training stages can impact the performance, but these findings have not been systematically applied to visual BPE training. Our work addresses these gaps by exploring enhancement strategies for visual BPE tokenization across vocabulary construction, data composition, and training procedures. Through these contributions, we aim to advance the practical application of BPE visual tokenization in multimodal foundation models."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "12977"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.129,
+ 0.09,
+ 0.873,
+ 0.361
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
+ 0.375,
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+ ],
+ "angle": 0,
+ "content": "Figure 1. Overview of our framework. The upper part shows the BPE vocabulary construction process: starting from a training dataset, we identify candidate token pairs and apply our priority scoring mechanism (combining frequency and spatial consistency) to iteratively extend the vocabulary with new encoded tokens. The lower part illustrates the MLLM pipeline: an input image is first quantized using a VQ-GAN codebook, then encoded using the trained vocabulary. The resulting visual tokens (e.g., token 381 representing the whole \"cat\" and 249 representing the whole \"box\") are seamlessly integrated with text tokens to form a unified sequence for multimodal understanding."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.485
+ ],
+ "angle": 0,
+ "content": "3. Method"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.497,
+ 0.484,
+ 0.543
+ ],
+ "angle": 0,
+ "content": "In this section, we first introduce key concepts and notation for our visual tokenization framework. Then we present the detailed training pipeline for our Being-VL-0.5 model."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.1. Visual Tokenization Pipeline"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "The core of our approach involves transforming visual information into token sequences that can be processed by language models. This transformation occurs through a pipeline with the following key steps:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Vector Quantization (VQ). Given an image \\(I\\) divided into patches, we first apply a VQ model with a codebook \\(V = \\{v_{1}, v_{2}, \\dots, v_{K}\\}\\) containing \\(K\\) entries. This process maps each image patch to its closest codebook entry, producing a grid of discrete indices \\(Q(I) = \\{q_{i,j}\\}_{i,j=1}^{h,w}\\), where \\(h\\) and \\(w\\) represent the height and width of the patch grid."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "BPE Visual Tokenization. The BPE visual tokenization process, denoted as \\( T(Q(I)) \\), identifies frequently co-occurring patterns in the quantized representation and encodes them into new tokens, creating an extended vocabulary \\( D = V \\cup V_{ext} \\), where \\( V_{ext} \\) represents the set of encoded tokens. Formally, the tokenization function \\( T: Q(I) \\to (t_1, t_2, \\dots, t_n) \\) maps the quantized image to a sequence of tokens \\( t_i \\in D \\), where \\( n \\leq h \\times w \\) due to the encoding of multiple indices into single tokens."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.871,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "This approach parallels BPE tokenization in text processing but adapts it for two-dimensional visual data, incor"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.472,
+ 0.907,
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+ ],
+ "angle": 0,
+ "content": "porating spatial relationships that are unique to the visual modality."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.2. Token-Based MLLM"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Unified Token Sequence. We formalize our token-based multimodal language model as a conditional probability distribution over token sequences. Given a text input \\( X = (x_{1}, x_{2}, \\ldots, x_{m}) \\) and an image input \\( I \\), the model processes the combined sequence and generates output tokens autoregressively. The combined input consists of special tokens marking the beginning and end of the tokenized image representation:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.54,
+ 0.666,
+ 0.907,
+ 0.684
+ ],
+ "angle": 0,
+ "content": "\\[\nS = \\left(x _ {1}, \\dots , x _ {m}, [ \\mathrm {B O I} ], t _ {1}, \\dots , t _ {n}, [ \\mathrm {E O I} ], \\dots\\right), \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.694,
+ 0.906,
+ 0.724
+ ],
+ "angle": 0,
+ "content": "where [BOI] and [EOI] are special tokens indicating the image boundary in the sequence."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "Autoregressive Modeling. The model defines a probability distribution over the next token given all previous tokens:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.527,
+ 0.767,
+ 0.905,
+ 0.797
+ ],
+ "angle": 0,
+ "content": "\\[\np \\left(s _ {i} \\mid s _ {< i}\\right) = \\operatorname {S o f t m a x} \\left(f _ {\\theta} \\left(E \\left(s _ {1}\\right), E \\left(s _ {2}\\right), \\dots , E \\left(s _ {i - 1}\\right)\\right)\\right), \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.798,
+ 0.907,
+ 0.858
+ ],
+ "angle": 0,
+ "content": "where \\( f_{\\theta} \\) represents the transformer-based language model with parameters \\( \\theta \\), and \\( E(s_{i}) \\) represents the embedding of token \\( s_{i} \\). For model generation, tokens are sampled sequentially:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.53,
+ 0.871,
+ 0.905,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {s} _ {i} \\sim p \\left(s _ {i} \\mid \\hat {s} _ {1}, \\hat {s} _ {2}, \\dots , \\hat {s} _ {i - 1}, x _ {1}, x _ {2}, \\dots , x _ {m}, t _ {1}, t _ {2}, \\dots , t _ {n}\\right). \\tag {3}\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "12978"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Training Objective. The model is trained to minimize the negative log-likelihood of the target sequence \\( Y = (y_{1}, y_{2}, \\dots, y_{l}) \\) conditioned on the input:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.093,
+ 0.147,
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+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} (\\theta) = - \\mathbb {E} _ {(X, I, Y) \\sim \\mathcal {D}} \\left[ \\sum_ {i = 1} ^ {| Y |} \\log p _ {\\theta} \\left(y _ {i} \\mid y _ {< i}, X, T (Q (I))\\right) \\right], \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.208,
+ 0.483,
+ 0.239
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathcal{D}\\) represents the training dataset containing input-output triplets."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3.3. Framework Overview"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "As formalized in the preliminaries above, our token-based multimodal model processes visual information through a pipeline that includes vector quantization \\( Q(\\cdot) \\) and visual tokenization \\( T(\\cdot) \\) before integration with text tokens in a language model. Our optimizations target each component of this pipeline while considering their interdependencies."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Specifically, our framework enhances this pipeline through: (1) Enhanced Vocabulary Construction; (2) Optimized Data Composition Strategies; (3) Efficient Multi-Stage Training. These components work together to improve the model's ability to process visual information, align visual and textual representations, and generate accurate responses to multimodal inputs."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.467,
+ 0.483,
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+ ],
+ "angle": 0,
+ "content": "Figure 1 illustrates the overall framework, which operates in two phases. In the vocabulary construction phase (upper part), we train a BPE vocabulary using our priority-guided encoding scheme that considers both co-occurrence frequency and spatial consistency. This approach creates an extended vocabulary that effectively captures meaningful visual patterns beyond what frequency-only methods can achieve. In the application phase (lower part), input images are first quantized through a VQ-GAN model, then encoded using the trained vocabulary. The resulting visual tokens are integrated with text tokens to form a unified sequence for the language model."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.4. Vocabulary Construction"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.678,
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+ ],
+ "angle": 0,
+ "content": "The effectiveness of token-based representations hinges on creating a vocabulary that efficiently captures meaningful patterns in the data. Our enhanced vocabulary construction method extends beyond simple frequency-based encoding to incorporate structural information specific to visual data, while relying exclusively on image statistics without reference to textual information."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "In standard BPE tokenization, token pairs are encoded based solely on their co-occurrence frequency. While effective for text, this can be suboptimal for visual data where spatial relationships play crucial roles. We introduce a priority function \\( P(a,b) \\) that guides the encoding process with a more comprehensive evaluation of candidate token pairs:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.179,
+ 0.885,
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+ 0.902
+ ],
+ "angle": 0,
+ "content": "\\[\nP (a, b) = F (a, b) + \\alpha \\cdot S (a, b). \\tag {5}\n\\]"
+ },
+ {
+ "type": "code_caption",
+ "bbox": [
+ 0.516,
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+ "angle": 0,
+ "content": "Algorithm 1 Priority-Guided Encoding"
+ },
+ {
+ "type": "algorithm",
+ "bbox": [
+ 0.517,
+ 0.109,
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+ 0.337
+ ],
+ "angle": 0,
+ "content": "Input: Quantized training data \\(\\mathcal{C}\\), initial vocabulary \\(V\\), target vocabulary size \\(N_{\\mathrm{vocab}}\\) \n\\(D \\gets V\\) \nwhile \\(N_{\\mathrm{vocab}} <\\) target size do \n Compute \\(F(a, b)\\) and \\(S(a, b)\\) for all adjacent token pairs in \\(\\mathcal{C}\\) \n Calculate priority \\(P(a, b) = F(a, b) + \\alpha \\cdot S(a, b)\\) and select top-\\(k\\) pairs by priority: \\(\\{(a_1, b_1), \\ldots, (a_k, b_k)\\}\\). \n \\((a^*, b^*) \\gets \\arg \\max_{i \\in \\{1, \\ldots, k\\}} P(a_i, b_i)\\) \n Create new token \\(c = (a^*, b^*)\\) \n \\(D \\gets D \\cup \\{c\\}\\) \n Update \\(\\mathcal{C}\\) by replacing all adjacent occurrences of \\((a^*, b^*)\\) with \\(c\\) (horizontally or vertically). \nend while \nreturn \\(D\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.532,
+ 0.362,
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+ ],
+ "angle": 0,
+ "content": "This function combines two key factors:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.437
+ ],
+ "angle": 0,
+ "content": "- Co-occurrence frequency \\( F(a, b) \\): The raw frequency with which tokens \\( a \\) and \\( b \\) appear adjacent to each other, normalized across the training corpus of quantized images."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.514,
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+ 0.484
+ ],
+ "angle": 0,
+ "content": "- Spatial consistency \\( S(a, b) \\): A measure of how consistently the token pair maintains spatial relationships across different images, calculated as:"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.514,
+ 0.378,
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+ 0.484
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\nS (a, b) = \\frac {1}{N _ {a , b}} \\sum_ {i = 1} ^ {N _ {a, b}} d \\left(u _ {i} (a, b), \\bar {u} (a, b)\\right). \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.539,
+ 0.907,
+ 0.6
+ ],
+ "angle": 0,
+ "content": "Here, \\( u_{i}(a,b) \\) represents the relative positioning of tokens \\( a \\) and \\( b \\) in instance \\( i \\), \\( \\bar{u}(a,b) \\) is the average relative positioning across all instances, \\( N_{a,b} \\) is the number of co-occurrences, and the spatial distance function is defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.588,
+ 0.605,
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+ 0.639
+ ],
+ "angle": 0,
+ "content": "\\[\nd \\left(u _ {1}, u _ {2}\\right) = \\exp \\left(- \\frac {\\left\\| u _ {1} - u _ {2} \\right\\| ^ {2}}{2 \\sigma^ {2}}\\right), \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.644,
+ 0.907,
+ 0.72
+ ],
+ "angle": 0,
+ "content": "where \\( \\| u_1 - u_2 \\| \\) is the Euclidean distance between the two relative position vectors, and \\( \\sigma \\) is a scaling parameter that controls how quickly similarity decreases with distance. This formulation ensures that token pairs with consistent spatial relationships across images receive higher scores."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ 0.902
+ ],
+ "angle": 0,
+ "content": "The weighting parameter \\(\\alpha\\) controls the relative importance of each factor and is determined through cross-validation on a development set. This dual-factor approach ensures that encoded tokens represent not only frequent patterns but also spatially consistent visual structures. It's important to emphasize that this entire process relies exclusively on image data, with no dependency on textual information or captions. The algorithm identifies patterns based solely on the statistical and structural properties of the visual content. Algorithm 1 outlines our priority-guided encoding process with diversity filtering. For complete details, please refer to Algorithm 2 in the Appendix."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
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+ ],
+ "angle": 0,
+ "content": "12979"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.5. Model Expanding"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.113,
+ 0.484,
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+ ],
+ "angle": 0,
+ "content": "Once we have constructed our enhanced visual vocabulary \\(D\\), we need to expand the pre-trained language model to accommodate these new tokens. This expansion process serves as the bridge between our tokenization approach and the subsequent model training. Given a pre-trained language model \\(M\\) with a text vocabulary \\(V_{\\mathrm{text}}\\) and corresponding embedding weights \\(E_{\\mathrm{text}} \\in \\mathbb{R}^{|V_{\\mathrm{text}}| \\times d}\\) (where \\(d\\) is the embedding dimension), we expand the embedding layer to incorporate the visual vocabulary \\(D\\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.139,
+ 0.256,
+ 0.483,
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+ "angle": 0,
+ "content": "\\[\nE _ {\\text {e x p a n d e d}} = \\left[ E _ {\\text {t e x t}}, E _ {\\text {v i s u a l}} \\right] \\in \\mathbb {R} ^ {\\left(\\left| V _ {\\text {t e x t}} \\right| + | D |\\right) \\times d}, \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\( E_{\\mathrm{visual}} \\in \\mathbb{R}^{|D| \\times d} \\) represents the newly added embeddings for visual tokens. This expansion increases the model's vocabulary size from \\( |V_{\\mathrm{text}}| \\) to \\( |V_{\\mathrm{text}}| + |D| \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "For the initialization of the newly added visual token embeddings, we adopt He initialization [20], i.e., \\( E_{\\mathrm{visual}}[i,j] \\sim \\mathcal{N}(0,\\sqrt{2 / d_l}) \\), where \\( d_{l} \\) is the embedding dimension. This initialization helps maintain proper signal magnitude throughout the network, preventing vanishing or exploding gradients during the early stages of training."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The process is illustrated in the top part of Figure 2. We first extend a VQ token embedding corresponding to the VQ-GAN codebook, and then extend a BPE token embedding corresponding to the BPE vocabulary. The extended weights from these two components constitute the initialization of the visual part. By default, we standardize both dimensions of them to 8K, corresponding to an 8K VQ codebook and an 8K BPE vocabulary, respectively."
+ },
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+ "type": "title",
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+ "content": "3.6. Multi-Stage Training"
+ },
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+ "content": "With the expanded model supporting both text and visual tokens, we now introduce our multi-stage training pipeline. Our approach combines strategic data composition with stage-specific parameter freezing to maximize the effectiveness of visual tokenization. Figure 2 illustrates the overall process."
+ },
+ {
+ "type": "title",
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+ "content": "3.6.1. Curriculum-Based Data Composition"
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+ "type": "text",
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+ "content": "We develop a curriculum-based data composition strategy, which is designed to complement the BPE visual tokenization. Unlike traditional visual encoders that extract features in a single forward pass, BPE visual tokenization creates a hierarchical representation where encoded tokens incrementally capture more complex visual patterns. This hierarchical nature of BPE tokens requires a matching learning curriculum: tokens must first establish basic semantic meanings through simple visual-text associations before they can be effectively utilized for complex reasoning."
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+ "type": "text",
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+ "content": "Specifically, we categorize our training data into four types based on complexity: Foundation Data (basic image-capture pairs), Perception Data (detailed visual attributes), Reasoning Data (complex visual QA), and Instruction Data"
+ },
+ {
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+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 2. Illustration of our multi-stage training strategy. The bottom part shows multimodal data being processed into unified tokens. The middle curves represent the data distribution across training stages, showing a gradual shift from basic concepts (Stage 1) to more balanced (Stage 2) and finally complex reasoning-focused data (Stage 3). The top part illustrates how we expand a text-only LLM to incorporate visual capabilities through weight initialization and alignment, resulting in a unified multimodal model. This curriculum approach mirrors the hierarchical nature of BPE visual tokens, which progressively capture more complex visual patterns throughout the learning process."
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+ "angle": 0,
+ "content": "(multi-turn interactions). Details of all types of datasets can be found in the Appendix A.4."
+ },
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+ "type": "text",
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+ "content": "We employ a curriculum that progressively shifts emphasis across training stages, formalized as a composition ratio \\( R_{i}(s) = w_{i}(s) / \\sum_{j}w_{j}(s) \\), where \\( R_{i}(s) \\) represents the proportion of data type \\( i \\) at stage \\( s \\) with corresponding weight \\( w_{i}(s) \\). Each stage employs distinct composition ratios, transitioning from foundation-heavy in early stages to instruction-focused in later stages. This curriculum ensures that visual tokens first establish basic meanings before tackling complex reasoning tasks."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "This stage-specific curriculum ensures that the model first develops strong foundational visual understanding before focusing on more complex tasks, aligning with the parameter freezing strategy of each stage."
+ },
+ {
+ "type": "title",
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+ "content": "3.6.2. Progressive Parameter Unfreezing"
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+ "content": "Complementing our data curriculum, we implement stage-specific parameter freezing to control which components of the model are updated at each stage. The parameter update can be expressed as:"
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+ "type": "equation",
+ "bbox": [
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+ "content": "\\[\n\\theta_ {s + 1} = \\theta_ {s} - \\eta \\cdot M _ {s} \\odot \\nabla_ {\\theta} \\mathcal {L}, \\tag {9}\n\\]"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(\\theta_{s}\\) represents the model parameters at stage \\(s\\), \\(\\eta\\) is the learning rate, \\(\\nabla_{\\theta}\\mathcal{L}\\) is the loss gradient, \\(\\odot\\) denotes elementwise multiplication, and \\(M_{s}\\) is a binary mask that determines which parameters are updated during stage \\(s\\)."
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+ [
+ {
+ "type": "table",
+ "bbox": [
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+ "content": "| Model | Params | Tokenizer | Benchmark |
| VQAv2 | MMBench | MME-P | SciQA-IMG | POPE | VizWiz |
| Continuous Embedding-Based Models |
| InstructBLIP | 7B | Continuous | 75.2 | 38.3 | 1212.8 | 60.5 | 81.5 | 34.5 |
| LLaVA-1.5 | 7B | Continuous | 78.5 | 64.3 | 1510.7 | 66.8 | 85.9 | 50.0 |
| mPLUG-Owl2 | 8B | Continuous | 79.4 | 64.5 | 1450.2 | - | 86.1 | 54.5 |
| HyperLLaVA | 7B | Continuous | 79.1 | 65.9 | 1481.2 | 70.4 | 86.3 | 51.9 |
| ShareGPT4V | 7B | Continuous | 80.6 | 68.8 | 1567.4 | 68.4 | - | 57.2 |
| VILA-1.5 | 8B | Continuous | 80.9 | 72.3 | - | - | 84.4 | 58.7 |
| LLaVA-Next | 7B | Continuous | 81.8 | 67.4 | 1519.0 | 70.1 | 86.5 | 57.6 |
| Discrete Token-Based Models |
| Chameleon | 7B | Discrete | 56.2 | 37.3 | 1297.5 | - | 78.2 | 46.4 |
| Being-VL-0 | 8B | Discrete | 60.6 | 44.0 | 1316.2 | 64.3 | 81.3 | 48.2 |
| Unified-IO-2 | 7B | Discrete | 79.4 | 71.5 | - | 86.2 | 87.7 | - |
| Being-VL-0.5 w/o BPE | 8B | Discrete | 54.3 | 38.2 | 1301.2 | 57.8 | 76.1 | 45.0 |
| Being-VL-0.5 | 8B | Discrete | 80.2 | 71.8 | 1525.8 | 70.3 | 84.3 | 57.4 |
| Being-VL-0.5+ | 8B | Discrete | 80.6 | 72.1 | 1536.3 | 69.0 | 86.0 | 57.8 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. Performance comparison of different visual-language models across standard benchmarks. Models are grouped by tokenizer type (Continuous / Discrete). The best performance in each group is bolded, while second-best result in each group is underlined."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Our training pipeline consists of three stages with different masks and objectives:"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Stage 1: Embedding Alignment focuses exclusively on training the newly extended visual token embeddings while freezing the rest of the model. The mask is defined as \\( M_1[i] = 1 \\) if parameter \\( i \\) belongs to new embeddings, 0 otherwise. This alignment establishes basic visual-linguistic associations without disrupting pre-trained language capabilities."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Stage 2: Selective Fine-tuning unfreezes early transformer layers while keeping later layers frozen, with \\( M_2[i] = 1 \\) if parameter \\( i \\) is in layers 1 to \\( k \\) (25% of total layers in our default implementation), 0 otherwise. This enhances cross-modal interactions in the feature integration layers using a broader range of data types."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Stage 3: Full Fine-tuning unfreezes all parameters \\((M_3[i] = 1, \\forall i)\\) and emphasizes complex reasoning and instruction-following data. This stage refines the model's advanced capabilities while building upon the foundation established in earlier stages."
+ },
+ {
+ "type": "title",
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+ "content": "4. Experiments"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this section, we empirically evaluate our designed framework and training pipelines. Based on the methods described in Section 3, we train our model Being-VL-0.5 with an 8K extended vocabulary and a variant Being-VL-0.5\\(^{+}\\) with a 16K extended vocabulary. We first describe our experimental setup, then present comprehensive results demonstrating the effectiveness of our approach compared to baselines. We further conduct analyses of each component to validate our design choices. Considering the limited space, please refer to the Appendix A for hyperparameter choices and further analyses of our experiments."
+ },
+ {
+ "type": "title",
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+ "content": "4.1. Experiments Setup"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Evaluation Benchmarks: We conduct evaluation on widely-used benchmarks [27, 28] that assess different aspects of visual understanding: VQAv2 [16] and VizWiz [19] for general visual question answering, MMBench [34] for comprehensive multimodal understanding, MME-P [13] for perception capabilities, SciQA-IMG [38] for scientific reasoning, and POPE [29] for hallucination evaluation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Baselines: We primarily focus on open-source models with comparable parameters and similar training data scales to ensure that performance differences reflect architectural choices rather than scale advantages. We compare our Being-VL-0.5 against two kinds of baselines: continuous embedding-based models and discrete token-based models. Continuous embedding-based models include InstructBLIP [9], LLaVA-1.5/LLaVA-Next [31, 32], mPLUG-Owl2 [63, 64], HyperLLaVA [71], ShareGPT4V [8], and VILA-1.5 [30]. Discrete token-based models include Chameleon [54], Being-VL-0 [72], and Unified-IO-2 [37]. We also compare 'Being-VL-0.5 w/o BPE', which is a variant that completely removes the BPE part and retains only the base VQ token embedding. This is used to investigate the effectiveness of our framework's core BPE design."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. General Visual Understanding"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1 presents our models' performance compared to baselines. Our framework effectively narrows the performance gap between discrete token-based models and continuous embedding-based models. Both Being-VL-0.5 and Being-VL-0.5+ achieve competitive performance across all benchmarks, with Being-VL-0.5+ reaching 80.6 on VQAv2 and 72.1 on MMBench, comparable to the best continuous embedding-based models like VILA-1.5 (80.9 and"
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+ }
+ ],
+ [
+ {
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+ "bbox": [
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+ "angle": 0,
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+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 3. Visualization of embedding weight distributions across three model variants. The heatmaps represent sampled weights from the embedding matrices (4096 dimensions), wherein color intensity indicates weight magnitude (blue for negative, red for positive). The depth of the color indicates the activation magnitude of the corresponding token embedding during model inference. Top: LLM+VQ (Being-VL-0.5 w/o BPE) with text tokens (32K) + VQ tokens (8K). Middle: LLM+VQ+BPE-8K (Being-VL-0.5) with text tokens (32K) + VQ tokens (8K) + BPE tokens (8K). Bottom: LLM+VQ+BPE-16K (Being-VL-0.5+) with text tokens (32K) + VQ tokens (8K) + BPE tokens (16K)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "72.3 respectively). Being-VL-0.5\\(^{+}\\) demonstrates strong perception capabilities with 1536.3 on MME-P, outperforming many continuous embedding models."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Among discrete token-based approaches, Being-VL-0 represents the work most closely aligned with our method, as both implement BPE-based visual tokenization. Our method outperforms Being-VL-0 across all benchmarks, with notable gains on MMBench (71.8 vs. 44.0) and MMEP (1525.8 vs. 1316.2). These improvements are attributable to our enhanced vocabulary construction and optimized training strategies. Unified-IO-2 achieves stronger performance on SciQA-IMG (86.2 vs. our 70.3), but it is worth noting that our models evaluate this benchmark in a zero-shot manner without task-specific fine-tuning."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Additionally, our method achieves an optimal balance between capturing low-level visual details and modeling high-level semantic concepts, with reduced hallucination on POPE (84.3 for Being-VL-0.5, 86.0 for Being-VL-0.5\\(^{+}\\)) compared to earlier discrete token approaches. When evaluating the overall performance across all benchmarks, our method demonstrates competitive results while maintaining the advantages of unified token representation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Furthermore, the significant performance drop of 'Being-VL-0.5 w/o BPE' on all benchmarks also highlights the necessity of the BPE vocabulary as a core part of our framework. We also conducted a qualitative case study, which provides additional evidence of Being-VL-0.5's comprehensive visual understanding. For detailed results, please refer to Section B."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. Scaling potential and training efficiency comparison for different vocabulary sizes (4K, 8K, 16K). Performance curves (solid lines) show relative performance gains as training data increases, while efficiency curves (dashed lines) illustrate the performance-to-cost ratio. All metrics are normalized relative to the 4K vocabulary model at standard training data amount \\((1.0\\times)\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.3. BPE Token Activation Mechanism"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 3 visualizes embedding weight distributions across our model variants, revealing key insights into how BPE tokenization helps unifying multimodal knowledge. In the base LLM+VQ model (top), which is a variant removing BPE vocabulary, we observe a contrast between text (0-32K) and visual tokens (32K-40K). Text tokens exhibit predominantly low-magnitude weights (lighter colors), while visual tokens exhibit significantly higher magnitudes (deeper colors). This imbalance suggests that the model struggles to establish a unified representation space across modalities. With BPE tokenization (middle and bottom panels), this pattern changes substantially. These two models show more balanced weight distributions, suggesting BPE helps bridge the representation gap between modalities, creating a more unified semantic space for visual-textual interaction. This visualization elucidates why models with improved BPE patterns yield superior performance, thereby outperforming Being-VL-0."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "However, some BPE tokens exhibit minimal activation (near-zero weights), appearing as white vertical stripes. This pattern is more evident in the 16K variant, where more embeddings remain unused. Intuitively, we hypothesize that this is because the current training does not fully utilize these 16K tokens, which may explain why Being-VL-0.5\\(^{+}\\) underperforms Being-VL-0.5 on certain tasks. Concurrently, this observation inspires us to examine the trade-offs between representational capacity and learning efficiency."
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+ {
+ "type": "page_number",
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+ "content": "12982"
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+ [
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Configuration | Curriculum | Progressive | Avg. Score |
| Perception | Reasoning |
| Standard | ✓ | ✓ | 80.3 | 71.1 |
| Progressive only | - | ✓ | 74.9 | 65.1 |
| Curriculum only | ✓ | - | 76.8 | 67.5 |
| Single stage | - | - | 71.2 | 62.3 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Ablation study on different components in training. Configurations marked with “-” use a fixed data mixture ratio throughout training or employ a standard full fine-tuning approach."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Scaling Potential and Training Efficiency"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To further investigate the trade-offs between vocabulary size, performance scaling, and training efficiency, we conducted extended experiments using the same checkpoint. Figure 4 presents our findings comparing three vocabulary sizes (4K/8K/16K) across varying data scales. For performance evaluation, we computed the normalized mean scores across four benchmarks (MME, POPE, VQAv2, and MMBench) and normalized them relative to the 4K vocabulary model at standard training data \\((1.0\\times)\\), providing an intuitive comparison of relative performance gains."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The horizontal axis serves dual purposes: for performance curves, it represents the relative amount of training data; for efficiency curves, it represents the total cost factor, incorporating computational resources \\(\\times\\) training time. Specifically, total cost increases with both vocabulary size and data amount. Our results reveal an important tradeoff: while the 16K vocabulary shows superior scaling potential, eventually outperforming both 4K and 8K models as training data increases beyond \\(1.5\\times\\), its efficiency (performance-to-cost ratio) remains consistently lower than smaller vocabulary models. In contrast, the 8K vocabulary achieves a better balance, showing strong performance scaling while maintaining reasonable efficiency."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.5. Analysis of Multi-Stage Training"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We conduct ablation studies to investigate the impact of the multi-stage training. Table 2 shows that our standard approach achieves clear improvements over the single-stage training (12.8% and 14.1% higher on perception and reasoning tasks respectively), demonstrating the effectiveness of the overall strategy. The results reveal that both curriculum-based data composition and progressive parameter unfreezing contribute to the performance, with curriculum data composition showing a stronger impact."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3 shows that the shifting of data types matters significantly. Our curriculum design outperforms both reverse ordering and random mixing. This aligns with our design principle that visual BPE tokens should first establish basic semantic meanings before tackling complex reasoning tasks. Similarly, Table 4 highlights the value of our three-stage progressive approach for parameter unfreezing. The simplified two-stage method shows modest perfor"
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Curriculum Strategy | Avg. Score |
| Perception | Reasoning |
| Progressive (FD → PD → RD → ID) | 80.3 | 71.1 |
| Reverse (ID → RD → PD → FD) | 73.4 | 64.0 |
| Random | 77.3 | 68.4 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Analysis of different curriculum strategies. FD, PD, RD, and ID refer to Foundation Data, Perception Data, Reasoning Data, and Instruction Data as described in Section 3.6.1."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Unfreezing Strategy | Avg. Score |
| Perception | Reasoning |
| 3-stage (align → selective → full) | 80.3 | 71.1 |
| 2-stage (align → full) | 78.2 | 69.3 |
| Reverse order | 72.1 | 63.0 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Analysis of different parameter unfreezing strategies."
+ },
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+ "type": "text",
+ "bbox": [
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+ 0.348,
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+ "angle": 0,
+ "content": "mance differences (2.7% lower on perception tasks), while reverse unfreezing leads to more notable performance drops (11.4% lower on perception tasks), suggesting that the order of parameter updates affects how well the model integrates visual and textual information."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Conclusions, Limitations, and Future Work"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "This paper presents a unified visual tokenization framework that enhances multimodal understanding through three key innovations: priority-guided vocabulary construction that considers both frequency and spatial patterns, curriculum-based data composition that aligns with token complexity progression, and a specialized multi-stage training procedure. Our comprehensive experiments across diverse benchmarks demonstrate that this approach effectively bridges the gap between visual and textual modalities, achieving competitive performance compared to continuous embedding-based methods while maintaining the advantages of a unified token representation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "A natural extension of our unified token-based approach is multimodal generation. Unlike models using separate encoders for different modalities, our framework enables the model to generate visual tokens in the same way it generates text tokens, establishing a truly unified representation paradigm. Although the current work concentrates on understanding tasks, extending our approach to incorporate generation capabilities constitutes a promising direction for future research."
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+ "content": "This work was supported by NSFC under Grant 62450001. The authors would like to thank the anonymous reviewers for their valuable comments and advice."
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+# Unified Multimodal Understanding via Byte-Pair Visual Encoding
+
+Wanpeng Zhang $^{1,4}$ Yicheng Feng $^{1,4}$ Hao Luo $^{1,4}$ Yijiang Li $^{2}$ Zihao Yue $^{3}$ Sipeng Zheng $^{4}$ Zongqing Lu $^{1,4\dagger}$
+
+$^{1}$ School of Computer Science, Peking University $^{2}$ University of California, San Diego $^{3}$ School of Information, Renmin University of China $^{4}$ BeingBeyond
+
+# Abstract
+
+Multimodal large language models (MLLMs) have made significant progress in vision-language understanding, yet effectively aligning different modalities remains a fundamental challenge. We present a framework that unifies multimodal understanding by applying byte-pair encoding to visual tokens. Unlike conventional approaches that rely on modality-specific encoders, our method directly incorporates structural information into visual tokens, mirroring successful tokenization strategies in text-only language models. We introduce the priority-guided encoding that considers both frequency and spatial consistency, coupled with a multi-stage training procedure based on curriculum-driven data composition. These enhancements enable the transformer model to better capture cross-modal relationships and reason with visual information. Comprehensive experiments demonstrate improved performance across diverse vision-language tasks. By bridging the gap between visual and textual representations, our approach contributes to the advancement of more capable multimodal foundation models. For further details, visit our website: https://beingbeyond.github.io/Being-VL-0.5.
+
+# 1. Introduction
+
+Multimodal Large Language Models (MLLMs) have made significant progress in integrating information from various modalities[33, 61, 65]. Nevertheless, effectively representing visual information and aligning it seamlessly with texts still remains a core challenge [4, 51, 66]. Conventional approaches primarily generate visual embeddings using modality-specific encoders [12, 23, 69] (such as CLIP [42]), yet recent research suggests that directly discretizing visual information can facilitate a more unified token representation [36, 37, 54, 73]. In a recent study, researchers introduced a visual encoding scheme to vision
+
+modality [72], analogous to the byte-pair encoding (BPE) tokenization [25, 41, 49] in LLMs. Previous work [72] theoretically demonstrated that structurally integrating discrete tokens enhances information preservation, thereby enabling the Transformer models [56] to more effectively learn from two-dimensional visual data. Although the preliminary results are promising, translating this theoretical framework into practical multimodal models poses significant challenges: (1) devising sophisticated token encoding strategies beyond simple frequency counting; (2) identifying data composition strategies that maximize visual-language alignment; and (3) designing effective training procedures to fully leverage these BPE-encoded visual tokens. In this paper, we address these challenges by exploring practical implementations and optimization strategies for BPE-based visual tokenization. Our comprehensive analysis highlights key factors that significantly influence performance across modalities and proposes corresponding optimization.
+
+Specifically, we introduce a priority-guided encoding scheme that accounts for both co-occurrence frequency and spatial consistency of visual patterns. This novel approach generates semantically enriched visual tokens, thereby preserving the inherent structural information in images more effectively. Moreover, we propose data composition strategies that leverage a curriculum-based approach tailored for optimizing multimodal learning, explicitly designed to complement the visual BPE tokenization process. Unlike conventional visual encoders [42, 67], which extract visual features through a single forward pass [60, 68], visual BPE tokenization generates hierarchical representations where encoded tokens progressively capture increasingly intricate visual patterns. Given this hierarchical property, an aligned learning curriculum is necessary; tokens must first acquire foundational semantic meanings through elementary visual-text associations before advancing toward more sophisticated visual reasoning tasks. Consequently, a multi-stage training procedure is further derived with stage-specific parameter freezing strategies: (1) embedding alignment with frozen language model parameters, (2) selective fine-tuning
+
+of early transformer layers, and (3) full model fine-tuning. This incremental training approach facilitates more effective cross-modal knowledge transfer while maintaining the linguistic capabilities inherent to the foundation model.
+
+We conduct experiments to demonstrate that our proposed optimization achieve substantial performance improvements compared to baselines. In addition to quantitative improvements, we provide detailed analyses of token patterns, computational efficiency, and qualitative improvements in visual comprehension capabilities. Our contributions are summarized as follows:
+
+- A discrete tokenization approach that preserves structural information in images through priority-guided encoding, providing unified visual representation for MLLMs.
+- A progressive training strategy that combines stage-specific parameter freezing, allowing our trained model Being-VL-0.5 to build better visual understanding.
+- Empirical evidence across multiple benchmarks and extensive analysis that validates the effectiveness of our unified encoding methods and elucidates the reason why it advances visual-language understanding.
+
+# 2. Related Work
+
+# 2.1. Representation Methods in MLLMs
+
+The core challenge of MLLMs lies in effectively representing and integrating information from different modalities. The research community has primarily developed two representative approaches: methods based on continuous representations and methods based on discrete tokens.
+
+Continuous token representation methods have emerged as the mainstream paradigm, with representative works such as LLaVA [32, 33], Emu [52, 58], DeepSeek-VL [35, 59], and Qwen-VL [1, 2, 57]. These models use pre-trained visual encoders (e.g., CLIP [42]) to map images into continuous representations, which are then aligned with language models through projection layers [15, 70]. Although this approach has achieved significant results, it faces two fundamental challenges: first, the modality gap between encoders and language models [5, 22], wherein the high-dimensional continuous features provided by visual encoders differ from the discrete token representations expected by language models; second, the information bottleneck problem, wherein images compressed through visual encoders may lose substantial detailed information, particularly affecting low-frequency visual patterns [43]. Recent analysis [3, 21, 62] indicates that this architectural design makes models prone to visual hallucinations, generating descriptions even when relevant visual information is absent.
+
+Discrete token representation methods have gained increasing attention in recent years [36, 37, 54, 73]. These methods typically use vector quantization models (such as VQ-GAN [11] or VQVAE [45, 55]) to discretize images
+
+into a series of tokens, thereby enabling visual information to be processed in a form similar to text. The advantage of this approach lies in its ability to process multimodal inputs in a unified manner, thus reducing inter-modal differences. However, existing discrete token methods also have significant limitations: most works simply quantize images into fixed-size tokens without considering the semantic structure of visual content; information loss during quantization may lead to the loss of fine-grained visual details; and the unbalanced representation of key visual concepts in the token space can result in limited recognition capability for certain visual patterns.
+
+These methods differ significantly from tokenization strategies used in natural language processing. In the NLP domain, algorithms such as BPE form semantically meaningful tokens by combining frequently co-occurring character sequences [14], a strategy that has proven beneficial for Transformer learning [39, 40]. Research by [44] demonstrates that for Markov sequence data, even smaller Transformer models can significantly reduce prediction loss when using appropriate tokenization strategies.
+
+# 2.2. BPE Tokenization for Visual Data
+
+Extending BPE tokenization to the visual domain is an emerging research direction [6, 46]. The core idea is to form a more semantical visual vocabulary by combining frequently co-occurring patterns based on quantized images. Being-VL-0 [72] first proposed a theoretical framework for applying BPE to quantized visual data, demonstrating that for two-dimensional data conforming to specific generative processes, using visual BPE can significantly reduce model prediction loss. Their analysis indicates that compared to unigram models based on independent and identically distributed assumptions, BPE tokenization can more effectively capture structured patterns in visual data.
+
+However, significant challenges remain in the transition from theory to practice. The implementation of Being-VL-0 [72] uses primarily frequency-based encoding without considering spatial relationships that are crucial in visual data. The relationship between vocabulary size and performance, as well as strategies that balance frequency with spatial consistency, remain underexplored. Besides, designing effective training procedures that leverage the unique properties of BPE visual tokens is also important. Research on parameter freezing strategies [17, 53] suggests that different settings at various training stages can impact the performance, but these findings have not been systematically applied to visual BPE training. Our work addresses these gaps by exploring enhancement strategies for visual BPE tokenization across vocabulary construction, data composition, and training procedures. Through these contributions, we aim to advance the practical application of BPE visual tokenization in multimodal foundation models.
+
+
+Figure 1. Overview of our framework. The upper part shows the BPE vocabulary construction process: starting from a training dataset, we identify candidate token pairs and apply our priority scoring mechanism (combining frequency and spatial consistency) to iteratively extend the vocabulary with new encoded tokens. The lower part illustrates the MLLM pipeline: an input image is first quantized using a VQ-GAN codebook, then encoded using the trained vocabulary. The resulting visual tokens (e.g., token 381 representing the whole "cat" and 249 representing the whole "box") are seamlessly integrated with text tokens to form a unified sequence for multimodal understanding.
+
+# 3. Method
+
+In this section, we first introduce key concepts and notation for our visual tokenization framework. Then we present the detailed training pipeline for our Being-VL-0.5 model.
+
+# 3.1. Visual Tokenization Pipeline
+
+The core of our approach involves transforming visual information into token sequences that can be processed by language models. This transformation occurs through a pipeline with the following key steps:
+
+Vector Quantization (VQ). Given an image $I$ divided into patches, we first apply a VQ model with a codebook $V = \{v_{1}, v_{2}, \dots, v_{K}\}$ containing $K$ entries. This process maps each image patch to its closest codebook entry, producing a grid of discrete indices $Q(I) = \{q_{i,j}\}_{i,j=1}^{h,w}$ , where $h$ and $w$ represent the height and width of the patch grid.
+
+BPE Visual Tokenization. The BPE visual tokenization process, denoted as $T(Q(I))$ , identifies frequently co-occurring patterns in the quantized representation and encodes them into new tokens, creating an extended vocabulary $D = V \cup V_{ext}$ , where $V_{ext}$ represents the set of encoded tokens. Formally, the tokenization function $T: Q(I) \to (t_1, t_2, \dots, t_n)$ maps the quantized image to a sequence of tokens $t_i \in D$ , where $n \leq h \times w$ due to the encoding of multiple indices into single tokens.
+
+This approach parallels BPE tokenization in text processing but adapts it for two-dimensional visual data, incor
+
+porating spatial relationships that are unique to the visual modality.
+
+# 3.2. Token-Based MLLM
+
+Unified Token Sequence. We formalize our token-based multimodal language model as a conditional probability distribution over token sequences. Given a text input $X = (x_{1}, x_{2}, \ldots, x_{m})$ and an image input $I$ , the model processes the combined sequence and generates output tokens autoregressively. The combined input consists of special tokens marking the beginning and end of the tokenized image representation:
+
+$$
+S = \left(x _ {1}, \dots , x _ {m}, [ \mathrm {B O I} ], t _ {1}, \dots , t _ {n}, [ \mathrm {E O I} ], \dots\right), \tag {1}
+$$
+
+where [BOI] and [EOI] are special tokens indicating the image boundary in the sequence.
+
+Autoregressive Modeling. The model defines a probability distribution over the next token given all previous tokens:
+
+$$
+p \left(s _ {i} \mid s _ {< i}\right) = \operatorname {S o f t m a x} \left(f _ {\theta} \left(E \left(s _ {1}\right), E \left(s _ {2}\right), \dots , E \left(s _ {i - 1}\right)\right)\right), \tag {2}
+$$
+
+where $f_{\theta}$ represents the transformer-based language model with parameters $\theta$ , and $E(s_{i})$ represents the embedding of token $s_{i}$ . For model generation, tokens are sampled sequentially:
+
+$$
+\hat {s} _ {i} \sim p \left(s _ {i} \mid \hat {s} _ {1}, \hat {s} _ {2}, \dots , \hat {s} _ {i - 1}, x _ {1}, x _ {2}, \dots , x _ {m}, t _ {1}, t _ {2}, \dots , t _ {n}\right). \tag {3}
+$$
+
+Training Objective. The model is trained to minimize the negative log-likelihood of the target sequence $Y = (y_{1}, y_{2}, \dots, y_{l})$ conditioned on the input:
+
+$$
+\mathcal {L} (\theta) = - \mathbb {E} _ {(X, I, Y) \sim \mathcal {D}} \left[ \sum_ {i = 1} ^ {| Y |} \log p _ {\theta} \left(y _ {i} \mid y _ {< i}, X, T (Q (I))\right) \right], \tag {4}
+$$
+
+where $\mathcal{D}$ represents the training dataset containing input-output triplets.
+
+# 3.3. Framework Overview
+
+As formalized in the preliminaries above, our token-based multimodal model processes visual information through a pipeline that includes vector quantization $Q(\cdot)$ and visual tokenization $T(\cdot)$ before integration with text tokens in a language model. Our optimizations target each component of this pipeline while considering their interdependencies.
+
+Specifically, our framework enhances this pipeline through: (1) Enhanced Vocabulary Construction; (2) Optimized Data Composition Strategies; (3) Efficient Multi-Stage Training. These components work together to improve the model's ability to process visual information, align visual and textual representations, and generate accurate responses to multimodal inputs.
+
+Figure 1 illustrates the overall framework, which operates in two phases. In the vocabulary construction phase (upper part), we train a BPE vocabulary using our priority-guided encoding scheme that considers both co-occurrence frequency and spatial consistency. This approach creates an extended vocabulary that effectively captures meaningful visual patterns beyond what frequency-only methods can achieve. In the application phase (lower part), input images are first quantized through a VQ-GAN model, then encoded using the trained vocabulary. The resulting visual tokens are integrated with text tokens to form a unified sequence for the language model.
+
+# 3.4. Vocabulary Construction
+
+The effectiveness of token-based representations hinges on creating a vocabulary that efficiently captures meaningful patterns in the data. Our enhanced vocabulary construction method extends beyond simple frequency-based encoding to incorporate structural information specific to visual data, while relying exclusively on image statistics without reference to textual information.
+
+In standard BPE tokenization, token pairs are encoded based solely on their co-occurrence frequency. While effective for text, this can be suboptimal for visual data where spatial relationships play crucial roles. We introduce a priority function $P(a,b)$ that guides the encoding process with a more comprehensive evaluation of candidate token pairs:
+
+$$
+P (a, b) = F (a, b) + \alpha \cdot S (a, b). \tag {5}
+$$
+
+Algorithm 1 Priority-Guided Encoding
+Input: Quantized training data $\mathcal{C}$ , initial vocabulary $V$ , target vocabulary size $N_{\mathrm{vocab}}$ $D \gets V$
+while $N_{\mathrm{vocab}} <$ target size do
+ Compute $F(a, b)$ and $S(a, b)$ for all adjacent token pairs in $\mathcal{C}$
+ Calculate priority $P(a, b) = F(a, b) + \alpha \cdot S(a, b)$ and select top- $k$ pairs by priority: $\{(a_1, b_1), \ldots, (a_k, b_k)\}$ .
+ $(a^*, b^*) \gets \arg \max_{i \in \{1, \ldots, k\}} P(a_i, b_i)$
+ Create new token $c = (a^*, b^*)$ $D \gets D \cup \{c\}$
+ Update $\mathcal{C}$ by replacing all adjacent occurrences of $(a^*, b^*)$ with $c$ (horizontally or vertically).
+end while
+return $D$
+
+This function combines two key factors:
+
+- Co-occurrence frequency $F(a, b)$ : The raw frequency with which tokens $a$ and $b$ appear adjacent to each other, normalized across the training corpus of quantized images.
+- Spatial consistency $S(a, b)$ : A measure of how consistently the token pair maintains spatial relationships across different images, calculated as:
+
+$$
+S (a, b) = \frac {1}{N _ {a , b}} \sum_ {i = 1} ^ {N _ {a, b}} d \left(u _ {i} (a, b), \bar {u} (a, b)\right). \tag {6}
+$$
+
+Here, $u_{i}(a,b)$ represents the relative positioning of tokens $a$ and $b$ in instance $i$ , $\bar{u}(a,b)$ is the average relative positioning across all instances, $N_{a,b}$ is the number of co-occurrences, and the spatial distance function is defined as:
+
+$$
+d \left(u _ {1}, u _ {2}\right) = \exp \left(- \frac {\left\| u _ {1} - u _ {2} \right\| ^ {2}}{2 \sigma^ {2}}\right), \tag {7}
+$$
+
+where $\| u_1 - u_2 \|$ is the Euclidean distance between the two relative position vectors, and $\sigma$ is a scaling parameter that controls how quickly similarity decreases with distance. This formulation ensures that token pairs with consistent spatial relationships across images receive higher scores.
+
+The weighting parameter $\alpha$ controls the relative importance of each factor and is determined through cross-validation on a development set. This dual-factor approach ensures that encoded tokens represent not only frequent patterns but also spatially consistent visual structures. It's important to emphasize that this entire process relies exclusively on image data, with no dependency on textual information or captions. The algorithm identifies patterns based solely on the statistical and structural properties of the visual content. Algorithm 1 outlines our priority-guided encoding process with diversity filtering. For complete details, please refer to Algorithm 2 in the Appendix.
+
+# 3.5. Model Expanding
+
+Once we have constructed our enhanced visual vocabulary $D$ , we need to expand the pre-trained language model to accommodate these new tokens. This expansion process serves as the bridge between our tokenization approach and the subsequent model training. Given a pre-trained language model $M$ with a text vocabulary $V_{\mathrm{text}}$ and corresponding embedding weights $E_{\mathrm{text}} \in \mathbb{R}^{|V_{\mathrm{text}}| \times d}$ (where $d$ is the embedding dimension), we expand the embedding layer to incorporate the visual vocabulary $D$ :
+
+$$
+E _ {\text {e x p a n d e d}} = \left[ E _ {\text {t e x t}}, E _ {\text {v i s u a l}} \right] \in \mathbb {R} ^ {\left(\left| V _ {\text {t e x t}} \right| + | D |\right) \times d}, \tag {8}
+$$
+
+where $E_{\mathrm{visual}} \in \mathbb{R}^{|D| \times d}$ represents the newly added embeddings for visual tokens. This expansion increases the model's vocabulary size from $|V_{\mathrm{text}}|$ to $|V_{\mathrm{text}}| + |D|$ .
+
+For the initialization of the newly added visual token embeddings, we adopt He initialization [20], i.e., $E_{\mathrm{visual}}[i,j] \sim \mathcal{N}(0,\sqrt{2 / d_l})$ , where $d_{l}$ is the embedding dimension. This initialization helps maintain proper signal magnitude throughout the network, preventing vanishing or exploding gradients during the early stages of training.
+
+The process is illustrated in the top part of Figure 2. We first extend a VQ token embedding corresponding to the VQ-GAN codebook, and then extend a BPE token embedding corresponding to the BPE vocabulary. The extended weights from these two components constitute the initialization of the visual part. By default, we standardize both dimensions of them to 8K, corresponding to an 8K VQ codebook and an 8K BPE vocabulary, respectively.
+
+# 3.6. Multi-Stage Training
+
+With the expanded model supporting both text and visual tokens, we now introduce our multi-stage training pipeline. Our approach combines strategic data composition with stage-specific parameter freezing to maximize the effectiveness of visual tokenization. Figure 2 illustrates the overall process.
+
+# 3.6.1. Curriculum-Based Data Composition
+
+We develop a curriculum-based data composition strategy, which is designed to complement the BPE visual tokenization. Unlike traditional visual encoders that extract features in a single forward pass, BPE visual tokenization creates a hierarchical representation where encoded tokens incrementally capture more complex visual patterns. This hierarchical nature of BPE tokens requires a matching learning curriculum: tokens must first establish basic semantic meanings through simple visual-text associations before they can be effectively utilized for complex reasoning.
+
+Specifically, we categorize our training data into four types based on complexity: Foundation Data (basic image-capture pairs), Perception Data (detailed visual attributes), Reasoning Data (complex visual QA), and Instruction Data
+
+
+Figure 2. Illustration of our multi-stage training strategy. The bottom part shows multimodal data being processed into unified tokens. The middle curves represent the data distribution across training stages, showing a gradual shift from basic concepts (Stage 1) to more balanced (Stage 2) and finally complex reasoning-focused data (Stage 3). The top part illustrates how we expand a text-only LLM to incorporate visual capabilities through weight initialization and alignment, resulting in a unified multimodal model. This curriculum approach mirrors the hierarchical nature of BPE visual tokens, which progressively capture more complex visual patterns throughout the learning process.
+
+(multi-turn interactions). Details of all types of datasets can be found in the Appendix A.4.
+
+We employ a curriculum that progressively shifts emphasis across training stages, formalized as a composition ratio $R_{i}(s) = w_{i}(s) / \sum_{j}w_{j}(s)$ , where $R_{i}(s)$ represents the proportion of data type $i$ at stage $s$ with corresponding weight $w_{i}(s)$ . Each stage employs distinct composition ratios, transitioning from foundation-heavy in early stages to instruction-focused in later stages. This curriculum ensures that visual tokens first establish basic meanings before tackling complex reasoning tasks.
+
+This stage-specific curriculum ensures that the model first develops strong foundational visual understanding before focusing on more complex tasks, aligning with the parameter freezing strategy of each stage.
+
+# 3.6.2. Progressive Parameter Unfreezing
+
+Complementing our data curriculum, we implement stage-specific parameter freezing to control which components of the model are updated at each stage. The parameter update can be expressed as:
+
+$$
+\theta_ {s + 1} = \theta_ {s} - \eta \cdot M _ {s} \odot \nabla_ {\theta} \mathcal {L}, \tag {9}
+$$
+
+where $\theta_{s}$ represents the model parameters at stage $s$ , $\eta$ is the learning rate, $\nabla_{\theta}\mathcal{L}$ is the loss gradient, $\odot$ denotes elementwise multiplication, and $M_{s}$ is a binary mask that determines which parameters are updated during stage $s$ .
+
+| Model | Params | Tokenizer | Benchmark |
| VQAv2 | MMBench | MME-P | SciQA-IMG | POPE | VizWiz |
| Continuous Embedding-Based Models |
| InstructBLIP | 7B | Continuous | 75.2 | 38.3 | 1212.8 | 60.5 | 81.5 | 34.5 |
| LLaVA-1.5 | 7B | Continuous | 78.5 | 64.3 | 1510.7 | 66.8 | 85.9 | 50.0 |
| mPLUG-Owl2 | 8B | Continuous | 79.4 | 64.5 | 1450.2 | - | 86.1 | 54.5 |
| HyperLLaVA | 7B | Continuous | 79.1 | 65.9 | 1481.2 | 70.4 | 86.3 | 51.9 |
| ShareGPT4V | 7B | Continuous | 80.6 | 68.8 | 1567.4 | 68.4 | - | 57.2 |
| VILA-1.5 | 8B | Continuous | 80.9 | 72.3 | - | - | 84.4 | 58.7 |
| LLaVA-Next | 7B | Continuous | 81.8 | 67.4 | 1519.0 | 70.1 | 86.5 | 57.6 |
| Discrete Token-Based Models |
| Chameleon | 7B | Discrete | 56.2 | 37.3 | 1297.5 | - | 78.2 | 46.4 |
| Being-VL-0 | 8B | Discrete | 60.6 | 44.0 | 1316.2 | 64.3 | 81.3 | 48.2 |
| Unified-IO-2 | 7B | Discrete | 79.4 | 71.5 | - | 86.2 | 87.7 | - |
| Being-VL-0.5 w/o BPE | 8B | Discrete | 54.3 | 38.2 | 1301.2 | 57.8 | 76.1 | 45.0 |
| Being-VL-0.5 | 8B | Discrete | 80.2 | 71.8 | 1525.8 | 70.3 | 84.3 | 57.4 |
| Being-VL-0.5+ | 8B | Discrete | 80.6 | 72.1 | 1536.3 | 69.0 | 86.0 | 57.8 |
+
+Table 1. Performance comparison of different visual-language models across standard benchmarks. Models are grouped by tokenizer type (Continuous / Discrete). The best performance in each group is bolded, while second-best result in each group is underlined.
+
+Our training pipeline consists of three stages with different masks and objectives:
+
+Stage 1: Embedding Alignment focuses exclusively on training the newly extended visual token embeddings while freezing the rest of the model. The mask is defined as $M_1[i] = 1$ if parameter $i$ belongs to new embeddings, 0 otherwise. This alignment establishes basic visual-linguistic associations without disrupting pre-trained language capabilities.
+
+Stage 2: Selective Fine-tuning unfreezes early transformer layers while keeping later layers frozen, with $M_2[i] = 1$ if parameter $i$ is in layers 1 to $k$ (25% of total layers in our default implementation), 0 otherwise. This enhances cross-modal interactions in the feature integration layers using a broader range of data types.
+
+Stage 3: Full Fine-tuning unfreezes all parameters $(M_3[i] = 1, \forall i)$ and emphasizes complex reasoning and instruction-following data. This stage refines the model's advanced capabilities while building upon the foundation established in earlier stages.
+
+# 4. Experiments
+
+In this section, we empirically evaluate our designed framework and training pipelines. Based on the methods described in Section 3, we train our model Being-VL-0.5 with an 8K extended vocabulary and a variant Being-VL-0.5 $^{+}$ with a 16K extended vocabulary. We first describe our experimental setup, then present comprehensive results demonstrating the effectiveness of our approach compared to baselines. We further conduct analyses of each component to validate our design choices. Considering the limited space, please refer to the Appendix A for hyperparameter choices and further analyses of our experiments.
+
+# 4.1. Experiments Setup
+
+Evaluation Benchmarks: We conduct evaluation on widely-used benchmarks [27, 28] that assess different aspects of visual understanding: VQAv2 [16] and VizWiz [19] for general visual question answering, MMBench [34] for comprehensive multimodal understanding, MME-P [13] for perception capabilities, SciQA-IMG [38] for scientific reasoning, and POPE [29] for hallucination evaluation.
+
+Baselines: We primarily focus on open-source models with comparable parameters and similar training data scales to ensure that performance differences reflect architectural choices rather than scale advantages. We compare our Being-VL-0.5 against two kinds of baselines: continuous embedding-based models and discrete token-based models. Continuous embedding-based models include InstructBLIP [9], LLaVA-1.5/LLaVA-Next [31, 32], mPLUG-Owl2 [63, 64], HyperLLaVA [71], ShareGPT4V [8], and VILA-1.5 [30]. Discrete token-based models include Chameleon [54], Being-VL-0 [72], and Unified-IO-2 [37]. We also compare 'Being-VL-0.5 w/o BPE', which is a variant that completely removes the BPE part and retains only the base VQ token embedding. This is used to investigate the effectiveness of our framework's core BPE design.
+
+# 4.2. General Visual Understanding
+
+Table 1 presents our models' performance compared to baselines. Our framework effectively narrows the performance gap between discrete token-based models and continuous embedding-based models. Both Being-VL-0.5 and Being-VL-0.5+ achieve competitive performance across all benchmarks, with Being-VL-0.5+ reaching 80.6 on VQAv2 and 72.1 on MMBench, comparable to the best continuous embedding-based models like VILA-1.5 (80.9 and
+
+
+Figure 3. Visualization of embedding weight distributions across three model variants. The heatmaps represent sampled weights from the embedding matrices (4096 dimensions), wherein color intensity indicates weight magnitude (blue for negative, red for positive). The depth of the color indicates the activation magnitude of the corresponding token embedding during model inference. Top: LLM+VQ (Being-VL-0.5 w/o BPE) with text tokens (32K) + VQ tokens (8K). Middle: LLM+VQ+BPE-8K (Being-VL-0.5) with text tokens (32K) + VQ tokens (8K) + BPE tokens (8K). Bottom: LLM+VQ+BPE-16K (Being-VL-0.5+) with text tokens (32K) + VQ tokens (8K) + BPE tokens (16K).
+
+72.3 respectively). Being-VL-0.5 $^{+}$ demonstrates strong perception capabilities with 1536.3 on MME-P, outperforming many continuous embedding models.
+
+Among discrete token-based approaches, Being-VL-0 represents the work most closely aligned with our method, as both implement BPE-based visual tokenization. Our method outperforms Being-VL-0 across all benchmarks, with notable gains on MMBench (71.8 vs. 44.0) and MMEP (1525.8 vs. 1316.2). These improvements are attributable to our enhanced vocabulary construction and optimized training strategies. Unified-IO-2 achieves stronger performance on SciQA-IMG (86.2 vs. our 70.3), but it is worth noting that our models evaluate this benchmark in a zero-shot manner without task-specific fine-tuning.
+
+Additionally, our method achieves an optimal balance between capturing low-level visual details and modeling high-level semantic concepts, with reduced hallucination on POPE (84.3 for Being-VL-0.5, 86.0 for Being-VL-0.5 $^{+}$ ) compared to earlier discrete token approaches. When evaluating the overall performance across all benchmarks, our method demonstrates competitive results while maintaining the advantages of unified token representation.
+
+Furthermore, the significant performance drop of 'Being-VL-0.5 w/o BPE' on all benchmarks also highlights the necessity of the BPE vocabulary as a core part of our framework. We also conducted a qualitative case study, which provides additional evidence of Being-VL-0.5's comprehensive visual understanding. For detailed results, please refer to Section B.
+
+
+Figure 4. Scaling potential and training efficiency comparison for different vocabulary sizes (4K, 8K, 16K). Performance curves (solid lines) show relative performance gains as training data increases, while efficiency curves (dashed lines) illustrate the performance-to-cost ratio. All metrics are normalized relative to the 4K vocabulary model at standard training data amount $(1.0\times)$ .
+
+# 4.3. BPE Token Activation Mechanism
+
+Figure 3 visualizes embedding weight distributions across our model variants, revealing key insights into how BPE tokenization helps unifying multimodal knowledge. In the base LLM+VQ model (top), which is a variant removing BPE vocabulary, we observe a contrast between text (0-32K) and visual tokens (32K-40K). Text tokens exhibit predominantly low-magnitude weights (lighter colors), while visual tokens exhibit significantly higher magnitudes (deeper colors). This imbalance suggests that the model struggles to establish a unified representation space across modalities. With BPE tokenization (middle and bottom panels), this pattern changes substantially. These two models show more balanced weight distributions, suggesting BPE helps bridge the representation gap between modalities, creating a more unified semantic space for visual-textual interaction. This visualization elucidates why models with improved BPE patterns yield superior performance, thereby outperforming Being-VL-0.
+
+However, some BPE tokens exhibit minimal activation (near-zero weights), appearing as white vertical stripes. This pattern is more evident in the 16K variant, where more embeddings remain unused. Intuitively, we hypothesize that this is because the current training does not fully utilize these 16K tokens, which may explain why Being-VL-0.5 $^{+}$ underperforms Being-VL-0.5 on certain tasks. Concurrently, this observation inspires us to examine the trade-offs between representational capacity and learning efficiency.
+
+| Configuration | Curriculum | Progressive | Avg. Score |
| Perception | Reasoning |
| Standard | ✓ | ✓ | 80.3 | 71.1 |
| Progressive only | - | ✓ | 74.9 | 65.1 |
| Curriculum only | ✓ | - | 76.8 | 67.5 |
| Single stage | - | - | 71.2 | 62.3 |
+
+# 4.4. Scaling Potential and Training Efficiency
+
+To further investigate the trade-offs between vocabulary size, performance scaling, and training efficiency, we conducted extended experiments using the same checkpoint. Figure 4 presents our findings comparing three vocabulary sizes (4K/8K/16K) across varying data scales. For performance evaluation, we computed the normalized mean scores across four benchmarks (MME, POPE, VQAv2, and MMBench) and normalized them relative to the 4K vocabulary model at standard training data $(1.0\times)$ , providing an intuitive comparison of relative performance gains.
+
+The horizontal axis serves dual purposes: for performance curves, it represents the relative amount of training data; for efficiency curves, it represents the total cost factor, incorporating computational resources $\times$ training time. Specifically, total cost increases with both vocabulary size and data amount. Our results reveal an important tradeoff: while the 16K vocabulary shows superior scaling potential, eventually outperforming both 4K and 8K models as training data increases beyond $1.5\times$ , its efficiency (performance-to-cost ratio) remains consistently lower than smaller vocabulary models. In contrast, the 8K vocabulary achieves a better balance, showing strong performance scaling while maintaining reasonable efficiency.
+
+# 4.5. Analysis of Multi-Stage Training
+
+We conduct ablation studies to investigate the impact of the multi-stage training. Table 2 shows that our standard approach achieves clear improvements over the single-stage training (12.8% and 14.1% higher on perception and reasoning tasks respectively), demonstrating the effectiveness of the overall strategy. The results reveal that both curriculum-based data composition and progressive parameter unfreezing contribute to the performance, with curriculum data composition showing a stronger impact.
+
+Table 3 shows that the shifting of data types matters significantly. Our curriculum design outperforms both reverse ordering and random mixing. This aligns with our design principle that visual BPE tokens should first establish basic semantic meanings before tackling complex reasoning tasks. Similarly, Table 4 highlights the value of our three-stage progressive approach for parameter unfreezing. The simplified two-stage method shows modest perfor
+
+Table 2. Ablation study on different components in training. Configurations marked with “-” use a fixed data mixture ratio throughout training or employ a standard full fine-tuning approach.
+
+| Curriculum Strategy | Avg. Score |
| Perception | Reasoning |
| Progressive (FD → PD → RD → ID) | 80.3 | 71.1 |
| Reverse (ID → RD → PD → FD) | 73.4 | 64.0 |
| Random | 77.3 | 68.4 |
+
+Table 3. Analysis of different curriculum strategies. FD, PD, RD, and ID refer to Foundation Data, Perception Data, Reasoning Data, and Instruction Data as described in Section 3.6.1.
+
+| Unfreezing Strategy | Avg. Score |
| Perception | Reasoning |
| 3-stage (align → selective → full) | 80.3 | 71.1 |
| 2-stage (align → full) | 78.2 | 69.3 |
| Reverse order | 72.1 | 63.0 |
+
+Table 4. Analysis of different parameter unfreezing strategies.
+
+mance differences (2.7% lower on perception tasks), while reverse unfreezing leads to more notable performance drops (11.4% lower on perception tasks), suggesting that the order of parameter updates affects how well the model integrates visual and textual information.
+
+# 5. Conclusions, Limitations, and Future Work
+
+This paper presents a unified visual tokenization framework that enhances multimodal understanding through three key innovations: priority-guided vocabulary construction that considers both frequency and spatial patterns, curriculum-based data composition that aligns with token complexity progression, and a specialized multi-stage training procedure. Our comprehensive experiments across diverse benchmarks demonstrate that this approach effectively bridges the gap between visual and textual modalities, achieving competitive performance compared to continuous embedding-based methods while maintaining the advantages of a unified token representation.
+
+Our current study focused on models with 8B parameters due to computational constraints. While these models already show promising results, our scaling analysis indicates potential for further improvements with more training data. The observed relationship between vocabulary size and performance suggests that further scaling could achieve even stronger multimodal understanding capabilities.
+
+A natural extension of our unified token-based approach is multimodal generation. Unlike models using separate encoders for different modalities, our framework enables the model to generate visual tokens in the same way it generates text tokens, establishing a truly unified representation paradigm. Although the current work concentrates on understanding tasks, extending our approach to incorporate generation capabilities constitutes a promising direction for future research.
+
+# Acknowledgments
+
+This work was supported by NSFC under Grant 62450001. The authors would like to thank the anonymous reviewers for their valuable comments and advice.
+
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+ "content": "As formalized in the preliminaries above, our token-based multimodal model processes visual information through a pipeline that includes vector quantization "
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+ "type": "text",
+ "content": " before integration with text tokens in a language model. Our optimizations target each component of this pipeline while considering their interdependencies."
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+ "content": "Specifically, our framework enhances this pipeline through: (1) Enhanced Vocabulary Construction; (2) Optimized Data Composition Strategies; (3) Efficient Multi-Stage Training. These components work together to improve the model's ability to process visual information, align visual and textual representations, and generate accurate responses to multimodal inputs."
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+ "content": "Figure 1 illustrates the overall framework, which operates in two phases. In the vocabulary construction phase (upper part), we train a BPE vocabulary using our priority-guided encoding scheme that considers both co-occurrence frequency and spatial consistency. This approach creates an extended vocabulary that effectively captures meaningful visual patterns beyond what frequency-only methods can achieve. In the application phase (lower part), input images are first quantized through a VQ-GAN model, then encoded using the trained vocabulary. The resulting visual tokens are integrated with text tokens to form a unified sequence for the language model."
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+ "content": "The effectiveness of token-based representations hinges on creating a vocabulary that efficiently captures meaningful patterns in the data. Our enhanced vocabulary construction method extends beyond simple frequency-based encoding to incorporate structural information specific to visual data, while relying exclusively on image statistics without reference to textual information."
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+ "type": "text",
+ "content": "In standard BPE tokenization, token pairs are encoded based solely on their co-occurrence frequency. While effective for text, this can be suboptimal for visual data where spatial relationships play crucial roles. We introduce a priority function "
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+ "type": "text",
+ "content": " that guides the encoding process with a more comprehensive evaluation of candidate token pairs:"
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+ "type": "interline_equation",
+ "content": "P (a, b) = F (a, b) + \\alpha \\cdot S (a, b). \\tag {5}",
+ "image_path": "c795b8739a5ea810260936cb8a1d16dc3e4c09eaaa4159b1fe8fb762228ee81b.jpg"
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+ "content": "Algorithm 1 Priority-Guided Encoding"
+ }
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+ "content": "Input: Quantized training data "
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+ "content": "\\mathcal{C}"
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+ "type": "text",
+ "content": ", initial vocabulary "
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+ "content": "V"
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+ "content": ", target vocabulary size "
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+ "type": "inline_equation",
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+ "type": "inline_equation",
+ "content": "D \\gets V"
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+ "type": "text",
+ "content": " \nwhile "
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+ "type": "inline_equation",
+ "content": "N_{\\mathrm{vocab}} <"
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+ "type": "text",
+ "content": " target size do \n Compute "
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+ "type": "inline_equation",
+ "content": "F(a, b)"
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+ "content": " for all adjacent token pairs in "
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+ "type": "text",
+ "content": " \n Calculate priority "
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+ "type": "inline_equation",
+ "content": "P(a, b) = F(a, b) + \\alpha \\cdot S(a, b)"
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+ "type": "text",
+ "content": " and select top-"
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+ "type": "inline_equation",
+ "content": "\\{(a_1, b_1), \\ldots, (a_k, b_k)\\}"
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+ "type": "inline_equation",
+ "content": "(a^*, b^*) \\gets \\arg \\max_{i \\in \\{1, \\ldots, k\\}} P(a_i, b_i)"
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+ "type": "text",
+ "content": " \n Create new token "
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+ "type": "inline_equation",
+ "content": "c = (a^*, b^*)"
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+ "type": "text",
+ "content": " \n Update "
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+ "type": "text",
+ "content": " by replacing all adjacent occurrences of "
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+ "type": "text",
+ "content": " (horizontally or vertically). \nend while \nreturn "
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+ "html": "| Model | Params | Tokenizer | Benchmark |
| VQAv2 | MMBench | MME-P | SciQA-IMG | POPE | VizWiz |
| Continuous Embedding-Based Models |
| InstructBLIP | 7B | Continuous | 75.2 | 38.3 | 1212.8 | 60.5 | 81.5 | 34.5 |
| LLaVA-1.5 | 7B | Continuous | 78.5 | 64.3 | 1510.7 | 66.8 | 85.9 | 50.0 |
| mPLUG-Owl2 | 8B | Continuous | 79.4 | 64.5 | 1450.2 | - | 86.1 | 54.5 |
| HyperLLaVA | 7B | Continuous | 79.1 | 65.9 | 1481.2 | 70.4 | 86.3 | 51.9 |
| ShareGPT4V | 7B | Continuous | 80.6 | 68.8 | 1567.4 | 68.4 | - | 57.2 |
| VILA-1.5 | 8B | Continuous | 80.9 | 72.3 | - | - | 84.4 | 58.7 |
| LLaVA-Next | 7B | Continuous | 81.8 | 67.4 | 1519.0 | 70.1 | 86.5 | 57.6 |
| Discrete Token-Based Models |
| Chameleon | 7B | Discrete | 56.2 | 37.3 | 1297.5 | - | 78.2 | 46.4 |
| Being-VL-0 | 8B | Discrete | 60.6 | 44.0 | 1316.2 | 64.3 | 81.3 | 48.2 |
| Unified-IO-2 | 7B | Discrete | 79.4 | 71.5 | - | 86.2 | 87.7 | - |
| Being-VL-0.5 w/o BPE | 8B | Discrete | 54.3 | 38.2 | 1301.2 | 57.8 | 76.1 | 45.0 |
| Being-VL-0.5 | 8B | Discrete | 80.2 | 71.8 | 1525.8 | 70.3 | 84.3 | 57.4 |
| Being-VL-0.5+ | 8B | Discrete | 80.6 | 72.1 | 1536.3 | 69.0 | 86.0 | 57.8 |
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+ "content": "Evaluation Benchmarks: We conduct evaluation on widely-used benchmarks [27, 28] that assess different aspects of visual understanding: VQAv2 [16] and VizWiz [19] for general visual question answering, MMBench [34] for comprehensive multimodal understanding, MME-P [13] for perception capabilities, SciQA-IMG [38] for scientific reasoning, and POPE [29] for hallucination evaluation."
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| Curriculum only | ✓ | - | 76.8 | 67.5 |
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| Reverse (ID → RD → PD → FD) | 73.4 | 64.0 |
| Random | 77.3 | 68.4 |
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| 3-stage (align → selective → full) | 80.3 | 71.1 |
| 2-stage (align → full) | 78.2 | 69.3 |
| Reverse order | 72.1 | 63.0 |
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+ "Figure 1. COSINE is a unified open-world segmentation model that consolidates open-vocabulary and in-context segmentation. COSINE can simultaneously support text prompts (green boxes) and image prompts (blue boxes) as inputs to perform various segmentation tasks, including semantic segmentation, instance segmentation, panoptic segmentation, referring segmentation, and video object segmentation. In addition, COSINE can collaboratively use different types of prompts to perform various segmentation tasks."
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+ "Video Object Segmentation"
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+ "type": "text",
+ "text": "Abstract",
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+ "text": "In this work, we present COSINE, a unified open-world segmentation model that Consolidates Open-vocabulary Segmentation and IN-context sEgmentation with multimodal prompts (e.g., text and image). COSINE exploits foundation models to extract representations for an input image and corresponding multi-modal prompts, and a SegDecoder to align these representations, model their interaction, and obtain masks specified by input prompts across different granularities. In this way, COSINE overcomes architectural discrepancies, divergent learning objectives, and distinct representation learning strategies of",
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+ "type": "text",
+ "text": "previous pipelines for open-vocabulary segmentation and incontext segmentation. Comprehensive experiments demonstrate that COSINE has significant performance improvements in both open-vocabulary and in-context segmentation tasks. Our exploratory analyses highlight that the synergistic collaboration between using visual and textual prompts leads to significantly improved generalization over single-modality approaches. Our code is released at https://github.com/aim-uofa/COSINE.",
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+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
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+ "text": "Image segmentation [17, 24, 61] aims to provide accurate conceptual localization, enabling precise understanding and",
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+ "type": "header",
+ "text": "CVF",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "type": "page_footnote",
+ "text": "*Equal contribution. †HC is the corresponding author.",
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+ "type": "page_number",
+ "text": "21557",
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+ "text": "content analysis of images at the pixel level. Recently, image segmentation has gradually evolved from closed-world scenarios [3, 8, 13, 29, 41, 59] to open-world settings [18, 20, 26, 44, 48, 55, 62]. Unlike traditional closed-world segmentation models, which are limited to recognizing a fixed set of categories encountered during training, open-world segmentation models can localize arbitrary relevant objects in the wild based on user-provided prompts. Such models can enhance adaptability and robustness in unpredictable dynamic environments, such as autonomous driving and interactive robotics.",
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+ "text": "The current landscape of open-world segmentation research primarily revolves around two distinct paradigms: (1) Open-vocabulary segmentation [11, 23, 48, 49, 55, 56], which replaces learnable classifiers with textual embeddings derived from category descriptors, thereby extending conventional closed-set segmentation frameworks to recognize novel categories through natural language alignment; and (2) In-context segmentation [20, 26, 27, 32, 44, 57], which leverages contextual cues from example images to facilitate adaptive object segmentation in query images. Despite significant progress in both directions, current methods predominantly address these tasks in isolation, failing to holistically tackle the complexities of open-world segmentation. Relying solely on text may lead to insufficient fine-grained semantic abstraction, whereas image-based exemplars often lack explicit category boundaries and semantic alignment. This raises a critical question: Can we unify open-vocabulary segmentation and in-context segmentation within a single framework, leveraging the complementary strengths of textual and visual modalities to enhance open-world segmentation capabilities?",
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+ "text": "We compare these two paradigms and identify the following problems in unifying them: 1) Architectural Discrepancies: Existing methods exhibit substantial structural differences. For instance, SegGPT [44] employs a ViT-like [10] encoder-only architecture for in-context segmentation, whereas ODISE [48] adopts a Mask2Former-like [3] encoder-decoder structure for open-vocabulary segmentation. 2) Divergent Learning Objectives: Open-vocabulary segmentation primarily focuses on image-text semantic alignment, aiming to learn the association between images and class descriptions for recognizing novel categories in an open-world setting. In contrast, in-context segmentation emphasizes reference-query relationship modeling, leveraging contextual cues from example images to achieve adaptive target segmentation. 3) Distinct Representation Learning Strategies: Open-vocabulary segmentation typically relies on multimodal models (e.g., CLIP [38], Stable Diffusion [39]) to leverage text embeddings for category matching, whereas in-context segmentation predominantly utilizes vision foundation models (e.g., MAE [14], DINoV2 [36]), performing target localization on visual features. These fundamental dif",
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+ "text": "ferences pose challenges in designing a unified framework that effectively integrates both paradigms while preserving their advantages.",
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+ "text": "To address these challenges, we present COSINE, a unified open-world segmentation model that Consolidates Open-vocabulary Segmentation and IN-context sEgmentation. Specifically, we first deploy a frozen Model Pool consisting of multiple foundation models to extract representations for the target image and different modality prompts (e.g., text and image), and convert them into token sequences. This standardization of the input format facilitates structural unification across both tasks, thereby enabling a single decoder-only segmentation model, named SegDecoder, to jointly process them. The SegDecoder contains an ImagePrompt Aligner module and a Multi-Modality Decoder. The Image-Prompt Aligner module aligns the image with various prompts, reducing the modality gap and learning a unified multi-modal representation space. The Multi-Modality Decoder is used to model the interaction between object queries, the image, and different modality prompts, enabling the effective generation of masks at different granularities (e.g., semantic, instance). COSINE optimizes the lightweight SegDecoder only, effectively unleashing the potential of the foundation models for open-world segmentation. As illustrated in Fig. 1, COSINE can concurrently address open-vocabulary and in-context segmentation tasks at multiple granularities, including semantic, instance, and panoptic segmentation. Comprehensive experiments demonstrate that COSINE effectively unifies both settings within a single model, achieving state-of-the-art performance. In particular, our exploratory analyses highlight the synergistic collaboration between the visual and textual branches, leading to significantly improved generalization over single-modality approaches. We believe our findings offer valuable insights to the research community.",
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+ "text": "Our main contributions are as follows: (1) To our knowledge, our method is the first to unify in-context segmentation and open-vocabulary segmentation. We present a simple but effective framework, COSINE, which unleashes the potential of frozen foundation models across various segmentation tasks. (2) Our comprehensive experiments demonstrate that COSINE achieves significant performance improvements in both open-vocabulary and in-context segmentation tasks. (3) We further observe that the synergistic collaboration between different modality branches enhances generalization in open-world segmentation, providing valuable insights for the research community.",
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+ "text": "2. Related Work",
+ "text_level": 1,
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+ "text": "Open-World Segmentation. Image segmentation [17, 24, 61], which aims to localize and organize meaningful concepts at the pixel level, has evolved from closed-world scenarios [3, 8, 13, 29, 41, 59] to open-world set",
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+ "text": "tings [18, 20, 26, 44, 48, 55, 62]. Open-world segmentation can be broadly categorized into two paradigms: Open-vocabulary segmentation [11, 23, 48, 49, 55, 56] focuses on recognizing and segmenting objects from an open set of categories. ODISE [48] leverages text-to-image diffusion models to learn rich semantic representations, enabling the generation of open-vocabulary panoptic masks. FCCLIP [55] develops a segmentation model built on a shared frozen convolutional CLIP backbone, utilizing two-way open-vocabulary classification to improve performance on novel classes. OpenSeeD [56] unifies open-vocabulary segmentation and detection by jointly learning from segmentation and detection datasets, addressing task and data discrepancies through decoupled decoding and conditioned mask decoding. In-context segmentation [20, 26, 27, 32, 44, 57] enables segmentation guided by example images. SegGPT [44] introduces a random coloring scheme within in-context learning to enhance model generalization. PerSAM [57] employs one-shot data to generate positive-negative location priors and infuses high-level semantics from SAM [18] to guide personalized segmentation. Matcher [26] proposes a training-free framework that utilizes vision foundation models for few-shot segmentation tasks. DINOv [20] integrates visual in-context prompting to unify referring and generic segmentation tasks, introducing a specialized encoder-decoder architecture. SINE [27] resolves ambiguity in in-context segmentation by unifying tasks across various granularities. Unlike these methods, COSINE unifies open-vocabulary and in-context segmentation, fostering synergistic collaboration between these two branches, and significantly enhancing the model's open-world generalization performance.",
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+ "text": "Vision Foundation Models. Leveraging contrastive and generative training, vision foundation models, when combined with large-scale single-/multi-modal datasets, exhibit remarkable generalization capabilities. Pre-trained by masked image modeling [1, 10, 28, 47], MAE [14] demonstrating strong transfer performance across downstream tasks. DINOv2 [36], through image and patch-level discriminative self-supervised learning, learns versatile visual features applicable to a wide range of downstream tasks. CLIP[38] learns multi-modal representations by image-text contrastive learning and demonstrates outstanding zero-shot image classification performance. The Segment Anything Model (SAM)[18] achieves impressive zero-shot, class-agnostic segmentation performance by training on a large-scale segmentation dataset. This work aims to train an open-world segmentation model with strong generalization capabilities, leveraging the potential of existing foundation models, even under constraints in data and computational resources.",
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+ "type": "text",
+ "text": "3. Method",
+ "text_level": 1,
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+ "type": "text",
+ "text": "We present COSINE, a unified open-world segmentation model that Consolidates Open-vocabulary Segmentation and",
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+ "type": "text",
+ "text": "IN-context sEgmentation. COSINE supports diverse modalities of input, such as images and text, by framing them as promptable segmentation tasks, offering powerful open-world perception capabilities. Our goal is not to achieve state-of-the-art performance across all open-vocabulary or in-context segmentation tasks, but to validate that diverse modal information can synergistically collaborate and extend knowledge across tasks, thereby enhancing the model's modeling capabilities and generalization performance.",
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+ "type": "text",
+ "text": "3.1. Overview",
+ "text_level": 1,
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+ "type": "text",
+ "text": "As shown in Fig. 2(a), COSINE follows a simple design philosophy, consisting of a Model Pool for extracting features from a target image and different modality prompts (e.g., text and example image), and a decoder-only segmentation model, named SegDecoder, which takes image and prompt features as inputs and outputs results for various segmentation tasks. Unlike previous segmentation methods [18, 20, 56] that train all parameters of models, COSINE fixes the foundation models in the Model Pool and only trains the relatively lightweight SegDecoder. Our approach enables lower training overhead while unleashing the potential of the foundation models for open-world perception.",
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+ "text": "Model Pool. Model Pool includes different vision models (DINOv2 and CLIP vision encoder) and language models (CLIP text encoder). The inputs of Model Pool include a target image, its image prompts and text prompts. For the target image, we use all vision models to encode it into the image features $\\mathcal{F} = \\{\\mathbf{F}_i\\}_i^P$ . Then, we use DINOv2 to encode the images of visual prompts into image features and use the in-context masks to pool the features into prompt tokens $\\mathcal{V} = \\{\\mathbf{v}_i\\}_i^M$ . The language model is used to extract the text prompt features $\\mathcal{T} = \\{\\mathbf{t}_i\\}_i^N$ . The image and prompt representations extracted by different foundation models contain rich multi-modal information, and the modalities complement each other, facilitating efficient transfer to downstream perception tasks.",
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+ "text": "3.2. SegDecoder",
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+ "text": "The architecture of SegDecoder is shown in Fig. 2 (b), which include a set of adapters, an Image-Prompt Alignmenter, a Pixel decoder and a Multi-Modality Decoder.",
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+ "text": "We deploy different adapters, including Feature Blender, V-Adapter and T-Adapter, for different features with the following objectives: (1) blending different image features, (2) aligning the feature dimensions of the image and various modality prompts, and (3) mapping the representations from different modalities to a shared space. Feature Blender consists of two convolutional layers that take the concatenated image features as input and outputs the blended image feature $\\mathbf{F} \\in \\mathbb{R}^{C \\times H \\times W}$ . Similarly, V-Adapter (T-Adapter) maps image (text) prompts into $\\mathbf{V} \\in \\mathbb{R}^{M \\times C}(\\mathbf{T} \\in \\mathbb{R}^{N \\times C})$ .",
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+ "Figure 2. The architecture of COSINE. (a) COSINE consists a Model Pool (e.g., DINOv2 and CLIP) used to extract image and prompt features and a SegDecoder used for unified open-world segmentation tasks. (b) SegDecoder consists a set of adapters, an Image-Prompt Alignmenter, a Pixel decoder and a Multi-Modality Decoder for modality alignment between the image and prompts, effectively enhancing open-world perception modeling. (c) and (d) show the details of Image-Prompt Alignmenter and Multi-Modality Decoder."
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+ "text": "edge from multiple models, while each prompt only encode knowledge from a single modality, leading to a disparity between them. To mitigate the disparity, we employ an Image-Prompt Aligner to align and harmonize these heterogeneous representations. As shown in Fig. 2(c), the ImagePrompt Aligner is implemented by a set of self-attention, cross-attention, and feed-forward networks (FFN). Through the shared network structure, the Aligner aligns the image and different modality prompts, enhancing their representations in the multi-modal space, enabling high-quality segmentation results using prompts from any modality. Specifically, the blended image feature $\\mathbf{F}$ and the prompt features $\\mathbf{V}$ and $\\mathbf{T}$ are aligned in the multi-modal representation space through the Image-Prompt Aligner module:",
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+ "type": "equation",
+ "text": "\n$$\n\\left\\langle \\mathbf {F} ^ {\\prime}, \\mathbf {V} ^ {\\prime}, \\mathbf {T} ^ {\\prime} \\right\\rangle = \\text {A l i g n m e n t} (\\mathbf {F}, \\mathbf {V}, \\mathbf {T}; \\theta), \\tag {1}\n$$\n",
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+ "text": "where $\\mathbf{F}^{\\prime}\\in \\mathbb{R}^{C\\times H\\times W}$ is the enhanced image feature, and $\\mathbf{V}^{\\prime}\\in \\mathbb{R}^{M\\times C}$ and $\\mathbf{T}^{\\prime}\\in \\mathbb{R}^{N\\times C}$ are the enhanced prompt features. $\\theta$ is the parameters of the Image-Prompt Aligner.",
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+ "text": "Pixel Decoder. The aim of the Pixel Decoder is to output high-resolution mask features. For single-scale image feature, the Pixel Decoder is implemented as a small network consisting of two transpose convolution layers. It takes the blended image feature $\\mathbf{F}$ as input, performs $4\\times$ upsampling,",
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+ "type": "text",
+ "text": "and generates the mask feature $\\mathbf{F}_{mask} \\in \\mathbb{R}^{C \\times H' \\times W'}$ .",
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+ "text": "Multi-Modality Decoder. As show in Fig. 2(d), we introduce a Multi-Modality Decoder to refine the different modality prompts and object queries $\\mathbf{Q} \\in \\mathbb{R}^{K \\times C}$ . Following [27], the Multi-Modality Decoder adopts a dual-path design, utilizing both self-attention and cross-attention [3] to facilitate interaction between object queries, different modality prompts, and the image features, while simultaneously refining the object queries and prompts. The process of the Multi-Modality Decoder can be summarized as follows:",
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+ "type": "equation",
+ "text": "\n$$\n\\langle \\mathbf {Q} _ {r}, \\mathbf {V} _ {r}, \\mathbf {T} _ {r} \\rangle = D e c o d e r (\\mathbf {Q}, \\mathbf {V} ^ {\\prime}, \\mathbf {T} ^ {\\prime}, \\mathbf {F} ^ {\\prime}, \\mathbf {F} _ {m a s k}; \\phi), \\tag {2}\n$$\n",
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+ "text": "where $\\mathbf{Q}_r, \\mathbf{V}_r$ and $\\mathbf{T}_r$ are refined object queries, visual and text prompts. $\\phi$ is the parameters of the Multi-Modality Decoder. By using $\\mathbf{V}_r$ and $\\mathbf{T}_r$ as classifiers, COSINE can obtain the classification scores $\\mathbf{S}_v$ and $\\mathbf{S}_t$ for in-context segmentation and open-vocabulary segmentation. This can be illustrated in the following equation:",
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+ "text": "\n$$\n\\mathbf {S} _ {v} = \\mathbf {Q} _ {r} \\mathbf {V} _ {r} ^ {\\top}, \\mathbf {S} _ {v} \\in \\mathbb {R} ^ {K \\times M},\n$$\n",
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+ "text": "The mask results $\\mathbf{M}$ can be obtained via the following operation:",
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+ "text": "\n$$\n\\mathbf {M} = M L P \\left(\\mathbf {Q} _ {r}\\right) \\mathbf {F} _ {m a s k}, \\mathbf {M} \\in \\mathbb {R} ^ {K \\times H ^ {'} \\times W ^ {'}}. (4)\n$$\n",
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+ "text": "Note that $\\mathbf{S}_v$ and $\\mathbf{S}_t$ are not computed independently. In practice, the vision and text prompts are concatenated and jointly processed to produce a unified score matrix. The separate notation of $\\mathbf{S}_v$ and $\\mathbf{S}_t$ is adopted purely for clarity of presentation.",
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+ "text": "Multi-Scale Feature Injection. Similar to previous approaches [22, 55], we can obtain multi-scale image features from these foundation models to enhance the performance of SegDecoder. We employ a multi-scale deformable attention Transformer [64] as the Pixel Decoder and use these multiscale image features as inputs to both the Image-Prompt Aligner and the Multi-Modality Decoder.",
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+ "text": "3.3. Training and Inference",
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+ "text": "Image and Text Prompts Co-training. During the training phase, we experientially maintain a 1:1 sample ratio between image and text prompts for each batch, ensuring that the model effectively balances in-context and open-vocabulary segmentation tasks within an open-world framework. For in-context segmentation, we employ two distinct sampling strategies for image prompts: (1) sampling diverse images of the same class to serve as both the target image and the image prompt, thereby enhancing the model's capability to discern target semantics, and (2) randomly cropping a single image to generate multiple views of the same object, which strengthens the model's ability to recognize objects across varying perspectives. For open-vocabulary segmentation, we sample a set of class names that encompass the target image classes as prompts. The architecture of the SegDecoder is designed to process both in-context and open-vocabulary segmentation tasks uniformly, facilitating the use of a shared loss function for optimization. In line with prior DETR-based approaches [2, 3, 27, 64], we use bipartite matching to match predictions with ground-truth. Subsequently, we optimize the model using cross-entropy loss for classification, along with binary mask loss and Dice loss [33] for mask prediction.",
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+ "text": "Multi-Modal Prompts Collaborative Inference. The SegDecoder architecture empowers COSINE to seamlessly process inputs from single-modality prompts, enabling it to tackle both open-vocabulary segmentation and in-context segmentation tasks. Furthermore, COSINE supports collaborative inference by leveraging prompts from multiple modalities. By integrating image and text prompts, COSINE generates mask predictions based on blended instructions. Notably, in addition to utilizing single-modality prompts, we introduce a straightforward averaging fusion mechanism to blend image prompts $\\mathbf{V}$ and text prompts $\\mathbf{T}$ . This fusion strategy allows complementary information from different modalities to enhance COSINE's generalization capabilities in open-world scenarios.",
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+ "text": "4. Experiments",
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+ "text": "4.1. Experiments Setting",
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+ "text": "Training Data. We train our model with publicly available academic segmentation datasets, encompassing semantic, instance, and panoptic segmentation tasks. Specifically, we leverage datasets including: COCO [24] is a widely used dataset that supports multiple tasks, including object detection, instance segmentation, and panoptic segmentation. It comprises 80 \"things\" categories and 53 \"stuff\" categories, with a total of 118K training images and 5K validation images. Objects365 [40] is a large-scale, high-quality dataset designed for object detection. It includes 365 object categories, 638K images, and approximately 10 million bounding boxes. Following the approach in [27], we utilize Objects365-SAM, an enhanced version of the Objects365 dataset where instance segmentation annotations are extended with SAM [18]. In addition, we incorporate referring segmentation datasets to endow COSINE with the capability of understanding referring expressions. Specifically, following LISA [19], we utilize refCLEF, refCOCO, refCOCO+ [16], and refCOCOg [31], which are widely adopted benchmarks for referring expression comprehension and segmentation. More implementation details are provided in the Appendix B.",
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+ "text": "4.2. Main Results",
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+ "text": "We simultaneously evaluate COSINE's ability to process prompts in both the visual and textual modalities. For the visual modality, we select few-shot (semantic/instance) segmentation and video object segmentation tasks, while for the textual modality, we choose open-vocabulary (semantic/panoptic) segmentation and referring segmentation tasks. We compare COSINE against task-specific expert models as well as several general-purpose segmentation models. The results, presented in Table 1, demonstrate that COSINE exhibits a significant advantage in most tasks.",
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+ "text": "Few-Shot Semantic Segmentation. Following the evaluation protocol of [26], we evaluate COSINE on the LVIS [12] dataset for few-shot semantic segmentation. Compared with the specialized few-shot model DiffewS [63] and the in-context model, SINE [27], COSINE achieves better performance in both one-shot and few-shot settings. COSINE decouples low-level mask features from high-level image and prompt features. Using a query-based decoder, it achieves strong contextual understanding and accurate masks. COSINE outperforms SegGPT [44], demonstrating its effective contextual reasoning. As shown in the first column of Table 1, COSINE even outperforms the SAM-based model, Matcher [26], despite being trained on only a small amount of segmentation data.",
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+ "text": "Few-Shot Instance Segmentation. We evaluate the few-shot instance segmentation performance of COSINE on the",
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+ "table_body": "| Methods | Venue | few-shot sem. LVIS-92i | few-shot ins. LVIS | open-voc. pano. ADE20K | Cityscapes | open-voc. sem. A-847 | PC-459 |
| one-shot | few-shot | AP | APr | PQ | AP | mIoU | PQ | mIoU | mIoU | mIoU |
| few-shot model |
| HSNet [34] | ICCV'21 | 17.4 | 22.9 | - | - | - | - | - | - | - | - | - |
| VAT [15] | ECCV'22 | 18.5 | 22.7 | - | - | - | - | - | - | - | - | - |
| DiffewS [63] | NeurIPS'24 | 31.4 | 35.4 | - | - | - | - | - | - | - | - | - |
| in-context model |
| SegGPT [44] | ICCV'23 | 18.6 | 25.4 | - | - | - | - | - | - | - | - | - |
| PerSAM-F [57] | ICLR'24 | 18.4 | - | - | - | - | - | - | - | - | - | - |
| Matcher [26] | ICLR'24 | 33.0 | 40.0 | - | - | - | - | - | - | - | - | - |
| SINE [27] | NeurIPS'24 | 31.2 | 35.5 | 8.6 | 7.1 | - | - | - | - | - | - | - |
| open-vocabulary model |
| ODISE [48] | CVPR'23 | - | - | - | - | 23.4 | 13.9 | 28.7 | 23.9 | - | 11.1 | 14.5 |
| FC-CLIP [55] | NeurIPS'23 | - | - | - | - | 26.8 | 16.8 | 34.1 | 44.0 | 56.2 | 14.8 | 18.2 |
| HIPIE [42] | NeurIPS'23 | - | - | - | - | 22.9 | 19.0 | 29.0 | - | - | 9.7 | 14.4 |
| SED [46] | CVPR'24 | - | - | - | - | - | - | - | - | - | 13.9 | 22.6 |
| universal model |
| X-Decoder [65] | CVPR'23 | - | - | - | - | 21.8 | 13.1 | 29.6 | 38.1 | 52.0 | 9.2 | 16.1 |
| UNINEXT* [51] | CVPR'23 | - | - | - | - | 8.9 | 14.9 | 6.4 | - | - | 1.8 | 5.8 |
| OpenSeeD [56] | ICCV'23 | - | - | - | - | 19.7 | 15.0 | 23.4 | 41.4 | 47.8 | - | - |
| DINOv [20] | CVPR'24 | - | - | 15.4 | 14.5 | 23.2 | 15.1 | 25.3 | - | - | - | - |
| OMG-Seg [21] | CVPR'24 | - | - | - | - | 27.9 | - | - | - | - | - | - |
| PSALM [58] | ECCV'24 | - | - | - | - | - | 13.9 | 24.4 | - | - | - | 14.0 |
| COSINE† this work | 34.2 | 39.1 | 17.4 | 23.3 | 28.1 | 16.7 | 35.2 | 37.1 | 53.4 | 15.2 | 19.6 |
| COSINE | | 35.2 | 40.7 | 20.3 | 25.8 | 31.0 | 21.1 | 35.7 | 42.0 | 56.1 | 15.6 | 19.2 |
",
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+ "text": "Table 1. Results of different open world segmentation tasks including few-shot semantic segmentation, open-vocabulary panoptic segmentation and semantic segmentation. * We report the performance evaluated in [42]. † indicates the single-scale variant of COSINE.",
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+ "text": "long-tailed dataset LVIS [12], which contains over 1,000 categories. For each category, we randomly select 10 samples (or all available samples if fewer than 10 are present). We report the AP for all categories and the APr for rare categories. As shown in Table 1, COSINE achieves an AP of 20.3, significantly outperforming the universal model DINOv. Furthermore, COSINE achieves an APr of 25.8, demonstrating stronger generalization to rare categories compared to previous methods. These results highlight COSINE's superior adaptability to open-world scenarios.",
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+ "text": "Open-Vocabulary Panoptic Segmentation. Following ODISE [48] and FC-CLIP [55], we evaluate COSINE on the ADE20K [61] and Cityscapes [7] datasets for open-vocabulary panoptic segmentation. We compare COSINE with specialized open-vocabulary models, including ODISE, FC-CLIP, and HIPIE [42], as well as general-purpose models such as X-Decoder [65] and OpenSeeD [56]. As shown in Table 1, COSINE achieves outstanding performance on ADE20K, reaching a PQ of 31.0 and an AP of 21.1. Additionally, on Cityscapes, COSINE attains performance comparable to state-of-the-art methods, further demonstrating its effectiveness in open-vocabulary panoptic segmentation.",
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+ "text": "Open-Vocabulary Semantic Segmentation. For open-vocabulary semantic segmentation, COSINE outperforms all universal models and the majority of open-vocabulary models, including the LLM-based model PSALM [58]. As shown in Table 1, COSINE achieves a mIoU of 15.6 on the A-847 dataset [60] and 19.2 on the PC-459 dataset [35], demonstrating its ability to recognize and segment novel categories effectively. Notably, while COSINE slightly lags behind specialized open-vocabulary semantic segmentation models such as SED [46], its key advantage lies in its versatility, enabling flexible support for a wide range of segmentation tasks.",
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+ "text": "Video Object Segmentation. We evaluate COSINE on video object segmentation using DAVIS 2017 [37] and YouTube-VOS 2019 [50] datasets. As shown in Table 3, we compare COSINE with both video-trained models (gray rows) and models that do not use explicit video data. Videotrained models, such as Cutie [6] and XMem [4], achieve strong performance by leveraging temporal information and explicitly training on video datasets. COSINE, despite not using video data, achieves competitive performance without requiring video supervision, making it a more generaliz-",
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+ "table_body": "| Method | Venue | refCOCO | refCOCO+ | refCOCOg |
| val | testA | testB | val | testA | testB | val(U) | test(U) |
| MAttNet [54] | CVPR'18 | 56.5 | 62.4 | 51.7 | 46.7 | 52.4 | 40.1 | 47.6 | 48.6 |
| MCN [30] | CVPR'20 | 62.4 | 64.2 | 59.7 | 50.6 | 55.0 | 44.7 | 49.2 | 49.4 |
| VLT [9] | ICCV'21 | 67.5 | 70.5 | 65.2 | 56.3 | 61.0 | 50.1 | 55.0 | 57.7 |
| LAVT [53] | CVPR'22 | 72.7 | 75.8 | 68.8 | 62.1 | 68.4 | 55.1 | 61.2 | 62.1 |
| CRIS [45] | CVPR'22 | 70.5 | 73.2 | 66.1 | 62.3 | 68.1 | 53.7 | 59.9 | 60.4 |
| ReLA [25] | CVPR'23 | 73.8 | 76.5 | 70.2 | 66.0 | 71.0 | 57.7 | 65.0 | 66.0 |
| X-Decoder [65] | CVPR'23 | - | - | - | - | - | - | 64.6 | - |
| SEEM [66] | NeurIPS'23 | - | - | - | - | - | - | 65.7 | - |
| LISA [19] | CVPR'24 | 74.9 | 79.1 | 72.3 | 65.1 | 70.8 | 58.1 | 67.9 | 70.6 |
| COSINE | this work | 77.2 | 80.7 | 71.1 | 66.4 | 73.2 | 56.4 | 67.4 | 68.5 |
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+ "Table 2. Results of referring segmentation on refCOCO, refCOCO+ and RefCOCOg. We report the metric of cIoU."
+ ],
+ "table_footnote": [
+ "Table 3. Results of video object segmentation on DAVIS 2017, and YouTube-VOS 2019. Gray indicates the model is trained on target datasets with video data."
+ ],
+ "table_body": "| Methods | Venue | DAVIS 2017 | YT-VOS 2019 |
| J&F | G |
| with video data |
| AOT [52] | NeurIPS'21 | 85.4 | 85.3 |
| XMem [4] | ECCV'22 | 87.7 | 85.5 |
| DEVA [5] | ICCV'23 | 86.8 | 85.5 |
| Cutie [6] | CVPR'24 | 88.8 | 86.1 |
| without video data |
| Painter [43] | CVPR'23 | 34.6 | 20.6 |
| SegGPT [44] | ICCV'23 | 75.6 | 73.1 |
| SEEM [66] | NeurIPS'23 | 58.9 | - |
| DINOv [20] | CVPR'24 | 73.3 | 52.0 |
| PerSAM-F [57] | ICLR'24 | 76.1 | 46.6 |
| SINE [27] | NeurIPS'24 | 77.0 | 66.4 |
| COSINE | this work | 76.7 | 66.0 |
| COSINE-FT | | 80.2 | 70.0 |
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+ "text": "able and scalable approach. Compared with general-purpose segmentation models, COSINE achieves state-of-the-art performance among methods that do not use video data. On DAVIS 2017, COSINE obtains a $J \\& F$ score of 76.7, significantly outperforming SEEM [66] and DINOv [20], and achieving comparable performance to PerSAM-F [57] and SINE [27]. We also introduce a fine-tuned variant, COSINE-FT, which improves the overall performance across both datasets by further tuning on the pure image prompt dataset. This demonstrates that COSINE's segmentation capabilities can be significantly enhanced through fine-tuning, making it a versatile and scalable approach adaptable to both static and dynamic scene understanding.",
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+ "text": "Referring Segmentation. We test COSINE on the referring segmentation task following the evaluation protocol of LISA [19], which requires further fine-tuning on the referring segmentation dataset. As shown in Table 2, COSINE not only surpasses all traditional methods and general-purpose",
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+ "table_body": "| Prompt | LVIS-92i | ADE20K |
| vision | text | 1-shot | 5-shot | PQ | AP | mIoU |
| ✓ | | 24.5 | 27.8 | - | - | - |
| ✓ | - | - | 13.2 | 7.6 | 30.2 |
| ✓ | ✓ | 27.7 | 32.1 | 17.7 | 8.1 | 30.4 |
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+ "Table 4. Effect of the interaction between visual and textual branches during Training. All models are trained for 10k steps."
+ ],
+ "table_footnote": [
+ "Table 5. Effect of the interaction between visual and textual branches during inference."
+ ],
+ "table_body": "| Prompt | LVIS-92i | ADE20K |
| vision | text | 1-shot | 5-shot | PQ | AP | mIoU |
| ✓ | | 35.2 | 40.7 | 23.8 | 15.8 | 26.3 |
| ✓ | 37.8 | - | 31.0 | 21.1 | 35.7 |
| ✓ | ✓ | 43.1 | 45.9 | 31.4 | 21.3 | 36.3 |
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+ "text": "segmentation models but also achieves performance comparable to the LLM-based model LISA [19]. This further validates COSINE's capability in handling long text descriptions and complex semantic understanding.",
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+ "text": "4.3. Exploration of Visual-Textual Interaction",
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+ "text": "As mentioned earlier, COSINE consists of a textual branch that processes text prompts and a visual branch that processes visual prompts. Few works have explored the interaction between these two modalities. COSINE is the first to investigate their interplay from two perspectives: during training and inference.",
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+ "text": "Training Phase. We aim to investigate whether jointly training both branches with multimodal data can enhance the performance of each individual branch. Specifically, we train the model for 10k steps using data from a single modality and multi-modality data, respectively. As shown in Table 4, we demonstrate that introducing the textual branch during training significantly improves the performance of the visual branch, and conversely, the visual branch also enhances the textual branch's performance. This finding highlights the mutual benefits of multimodal training in segmentation.",
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+ "text": "21563",
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+ "table_footnote": [],
+ "table_body": "| #ID | Model | LVIS-92i | ADE20K |
| 1-shot | 5-shot | PQ | AP | mIoU |
| 0 | COSINE (Full Model) | 27.7 | 32.1 | 17.7 | 8.1 | 30.4 |
| 1 | only DINOv2 Encoder | 27.7 | 32.0 | 9.7 | 4.2 | 18.6 |
| 2 | only CLIP Encoder | 24.4 | 28.0 | 11.4 | 3.3 | 27.0 |
| 3 | w/o Feature Blending | 24.4 | 29.0 | 9.4 | 2.6 | 26.3 |
| 4 | w/o Image-Prompt Aligner | 26.3 | 31.3 | 12.0 | 6.4 | 30.1 |
| 5 | w/o Prompt Refining | 27.0 | 31.2 | 16.5 | 6.6 | 30.9 |
",
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+ "text": "Table 6. Ablation study. All models are trained for ${10}\\mathrm{k}$ steps.",
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+ "text": "Inference Phase. We further investigate whether providing both visual and textual prompts during inference can improve model performance. We validate this hypothesis on few-shot semantic segmentation and open-vocabulary panoptic segmentation tasks, as shown in Table 5. Our results reveal that for tasks originally supported by the visual branch, such as LVIS-92 $^i$ , incorporating an additional text prompt during inference leads to significant performance gains. Similarly, for tasks primarily supported by the textual branch, such as ADE20K, introducing a visual prompt during inference also enhances performance. These findings confirm that CO-SINE can flexibly process prompts from multiple modalities, resulting in more robust segmentation. This insight also provides valuable inspiration for future research on universal segmentation models.",
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+ "text": "4.4. Ablation Study",
+ "text_level": 1,
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+ "text": "As shown in Table 6, we validate the impact of each design within our model, including the Model Pool(#1, #2), the Feature Blender(#3), the Image-Prompt Aligner(#4), and the Multi-Modality Decoder(#5). Specifically, a comparison with model #1 and #2 reveals that different pre-trained models are informationally complementary, enhancing both in-context and open-vocabulary segmentation performance. The comparison with model #3 demonstrates that merely concatenating different foundation models is insufficient. An explicit blending of representations is necessary to learn a unified multi-modal representation. Furthermore, comparisons with models #4 and #5 indicate that the introduced Aligner and Decoder are both simple and effective.",
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+ "text": "4.5. Visualization Analysis",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "Qualitative Results. As shown in Fig. 3, we visualize the segmentation results under both open-vocabulary and in-context settings, as well as the results obtained by combining both types of prompts. Additionally, we provide visualizations of referring segmentation and VOS results. These results demonstrate that COSINE achieves highly accurate predictions across various modalities and granularities, highlighting its strong potential for open-world generalization.",
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+ "text": "Prompt Synergy. As shown in Fig. 4, COSINE can generalize to real-world domains such as industrial inspection, medical imaging. The industrial inspection case shows ef",
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+ "img_path": "images/38dcac228db4f3866de18d3ba25047afeba91555cb61493fb342fcaf391e520e.jpg",
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+ "Figure 3. Qualitative results. COSINE can perform various open-world segmentation tasks with different modal prompts (image and text). For few-shot segmentation, the left image is the example image and the right is the result.",
+ "Figure 4. Visualization of prompt synergy. The top row shows the input prompts, the bottom row presents the corresponding outputs."
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+ "text": "fective collaboration between visual and textual prompts, accurately segmenting targets that would produce incorrect masks under a single modality. These results highlight the potential of multimodal prompt synergy in COSINE for complex segmentation. By integrating visual and textual cues, COSINE captures fine-grained details that are difficult to express with a single modality.",
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+ "text": "In this work, we present COSINE, a unified open-world segmentation model that unifies open-vocabulary Segmentation and in-context segmentation. COSINE supports diverse modalities of input, such as images and text, offering powerful open-world perception capabilities. Our exploratory analysis highlights that the synergistic collaboration between visual and textual branches enhances generalization in open-world segmentation, providing valuable insights for the research community. More discussion and limitations are provided in the Appendix A.",
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+ "text": "This work was supported by the National Key R&D Program of China (No. 2022ZD0160101), the Ningbo Science and Technology Bureau (No. 2024Z291), and the National Natural Science Foundation of China (No. 62206244).",
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+ "type": "image_caption",
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+ "angle": 0,
+ "content": "Video Object Segmentation"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "content": "Figure 1. COSINE is a unified open-world segmentation model that consolidates open-vocabulary and in-context segmentation. COSINE can simultaneously support text prompts (green boxes) and image prompts (blue boxes) as inputs to perform various segmentation tasks, including semantic segmentation, instance segmentation, panoptic segmentation, referring segmentation, and video object segmentation. In addition, COSINE can collaboratively use different types of prompts to perform various segmentation tasks."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "Abstract"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.712,
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+ "angle": 0,
+ "content": "In this work, we present COSINE, a unified open-world segmentation model that Consolidates Open-vocabulary Segmentation and IN-context sEgmentation with multimodal prompts (e.g., text and image). COSINE exploits foundation models to extract representations for an input image and corresponding multi-modal prompts, and a SegDecoder to align these representations, model their interaction, and obtain masks specified by input prompts across different granularities. In this way, COSINE overcomes architectural discrepancies, divergent learning objectives, and distinct representation learning strategies of"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.682,
+ 0.909,
+ 0.818
+ ],
+ "angle": 0,
+ "content": "previous pipelines for open-vocabulary segmentation and incontext segmentation. Comprehensive experiments demonstrate that COSINE has significant performance improvements in both open-vocabulary and in-context segmentation tasks. Our exploratory analyses highlight that the synergistic collaboration between using visual and textual prompts leads to significantly improved generalization over single-modality approaches. Our code is released at https://github.com/aim-uofa/COSINE."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "Image segmentation [17, 24, 61] aims to provide accurate conceptual localization, enabling precise understanding and"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "*Equal contribution. †HC is the corresponding author."
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "21557"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.486,
+ 0.258
+ ],
+ "angle": 0,
+ "content": "content analysis of images at the pixel level. Recently, image segmentation has gradually evolved from closed-world scenarios [3, 8, 13, 29, 41, 59] to open-world settings [18, 20, 26, 44, 48, 55, 62]. Unlike traditional closed-world segmentation models, which are limited to recognizing a fixed set of categories encountered during training, open-world segmentation models can localize arbitrary relevant objects in the wild based on user-provided prompts. Such models can enhance adaptability and robustness in unpredictable dynamic environments, such as autonomous driving and interactive robotics."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.093,
+ 0.262,
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+ "angle": 0,
+ "content": "The current landscape of open-world segmentation research primarily revolves around two distinct paradigms: (1) Open-vocabulary segmentation [11, 23, 48, 49, 55, 56], which replaces learnable classifiers with textual embeddings derived from category descriptors, thereby extending conventional closed-set segmentation frameworks to recognize novel categories through natural language alignment; and (2) In-context segmentation [20, 26, 27, 32, 44, 57], which leverages contextual cues from example images to facilitate adaptive object segmentation in query images. Despite significant progress in both directions, current methods predominantly address these tasks in isolation, failing to holistically tackle the complexities of open-world segmentation. Relying solely on text may lead to insufficient fine-grained semantic abstraction, whereas image-based exemplars often lack explicit category boundaries and semantic alignment. This raises a critical question: Can we unify open-vocabulary segmentation and in-context segmentation within a single framework, leveraging the complementary strengths of textual and visual modalities to enhance open-world segmentation capabilities?"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We compare these two paradigms and identify the following problems in unifying them: 1) Architectural Discrepancies: Existing methods exhibit substantial structural differences. For instance, SegGPT [44] employs a ViT-like [10] encoder-only architecture for in-context segmentation, whereas ODISE [48] adopts a Mask2Former-like [3] encoder-decoder structure for open-vocabulary segmentation. 2) Divergent Learning Objectives: Open-vocabulary segmentation primarily focuses on image-text semantic alignment, aiming to learn the association between images and class descriptions for recognizing novel categories in an open-world setting. In contrast, in-context segmentation emphasizes reference-query relationship modeling, leveraging contextual cues from example images to achieve adaptive target segmentation. 3) Distinct Representation Learning Strategies: Open-vocabulary segmentation typically relies on multimodal models (e.g., CLIP [38], Stable Diffusion [39]) to leverage text embeddings for category matching, whereas in-context segmentation predominantly utilizes vision foundation models (e.g., MAE [14], DINoV2 [36]), performing target localization on visual features. These fundamental dif"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "ferences pose challenges in designing a unified framework that effectively integrates both paradigms while preserving their advantages."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.138,
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+ "angle": 0,
+ "content": "To address these challenges, we present COSINE, a unified open-world segmentation model that Consolidates Open-vocabulary Segmentation and IN-context sEgmentation. Specifically, we first deploy a frozen Model Pool consisting of multiple foundation models to extract representations for the target image and different modality prompts (e.g., text and image), and convert them into token sequences. This standardization of the input format facilitates structural unification across both tasks, thereby enabling a single decoder-only segmentation model, named SegDecoder, to jointly process them. The SegDecoder contains an ImagePrompt Aligner module and a Multi-Modality Decoder. The Image-Prompt Aligner module aligns the image with various prompts, reducing the modality gap and learning a unified multi-modal representation space. The Multi-Modality Decoder is used to model the interaction between object queries, the image, and different modality prompts, enabling the effective generation of masks at different granularities (e.g., semantic, instance). COSINE optimizes the lightweight SegDecoder only, effectively unleashing the potential of the foundation models for open-world segmentation. As illustrated in Fig. 1, COSINE can concurrently address open-vocabulary and in-context segmentation tasks at multiple granularities, including semantic, instance, and panoptic segmentation. Comprehensive experiments demonstrate that COSINE effectively unifies both settings within a single model, achieving state-of-the-art performance. In particular, our exploratory analyses highlight the synergistic collaboration between the visual and textual branches, leading to significantly improved generalization over single-modality approaches. We believe our findings offer valuable insights to the research community."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Our main contributions are as follows: (1) To our knowledge, our method is the first to unify in-context segmentation and open-vocabulary segmentation. We present a simple but effective framework, COSINE, which unleashes the potential of frozen foundation models across various segmentation tasks. (2) Our comprehensive experiments demonstrate that COSINE achieves significant performance improvements in both open-vocabulary and in-context segmentation tasks. (3) We further observe that the synergistic collaboration between different modality branches enhances generalization in open-world segmentation, providing valuable insights for the research community."
+ },
+ {
+ "type": "title",
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+ "content": "2. Related Work"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Open-World Segmentation. Image segmentation [17, 24, 61], which aims to localize and organize meaningful concepts at the pixel level, has evolved from closed-world scenarios [3, 8, 13, 29, 41, 59] to open-world set"
+ },
+ {
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+ }
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+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "tings [18, 20, 26, 44, 48, 55, 62]. Open-world segmentation can be broadly categorized into two paradigms: Open-vocabulary segmentation [11, 23, 48, 49, 55, 56] focuses on recognizing and segmenting objects from an open set of categories. ODISE [48] leverages text-to-image diffusion models to learn rich semantic representations, enabling the generation of open-vocabulary panoptic masks. FCCLIP [55] develops a segmentation model built on a shared frozen convolutional CLIP backbone, utilizing two-way open-vocabulary classification to improve performance on novel classes. OpenSeeD [56] unifies open-vocabulary segmentation and detection by jointly learning from segmentation and detection datasets, addressing task and data discrepancies through decoupled decoding and conditioned mask decoding. In-context segmentation [20, 26, 27, 32, 44, 57] enables segmentation guided by example images. SegGPT [44] introduces a random coloring scheme within in-context learning to enhance model generalization. PerSAM [57] employs one-shot data to generate positive-negative location priors and infuses high-level semantics from SAM [18] to guide personalized segmentation. Matcher [26] proposes a training-free framework that utilizes vision foundation models for few-shot segmentation tasks. DINOv [20] integrates visual in-context prompting to unify referring and generic segmentation tasks, introducing a specialized encoder-decoder architecture. SINE [27] resolves ambiguity in in-context segmentation by unifying tasks across various granularities. Unlike these methods, COSINE unifies open-vocabulary and in-context segmentation, fostering synergistic collaboration between these two branches, and significantly enhancing the model's open-world generalization performance."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.56,
+ 0.486,
+ 0.833
+ ],
+ "angle": 0,
+ "content": "Vision Foundation Models. Leveraging contrastive and generative training, vision foundation models, when combined with large-scale single-/multi-modal datasets, exhibit remarkable generalization capabilities. Pre-trained by masked image modeling [1, 10, 28, 47], MAE [14] demonstrating strong transfer performance across downstream tasks. DINOv2 [36], through image and patch-level discriminative self-supervised learning, learns versatile visual features applicable to a wide range of downstream tasks. CLIP[38] learns multi-modal representations by image-text contrastive learning and demonstrates outstanding zero-shot image classification performance. The Segment Anything Model (SAM)[18] achieves impressive zero-shot, class-agnostic segmentation performance by training on a large-scale segmentation dataset. This work aims to train an open-world segmentation model with strong generalization capabilities, leveraging the potential of existing foundation models, even under constraints in data and computational resources."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3. Method"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "We present COSINE, a unified open-world segmentation model that Consolidates Open-vocabulary Segmentation and"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ 0.909,
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+ ],
+ "angle": 0,
+ "content": "IN-context sEgmentation. COSINE supports diverse modalities of input, such as images and text, by framing them as promptable segmentation tasks, offering powerful open-world perception capabilities. Our goal is not to achieve state-of-the-art performance across all open-vocabulary or in-context segmentation tasks, but to validate that diverse modal information can synergistically collaborate and extend knowledge across tasks, thereby enhancing the model's modeling capabilities and generalization performance."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.1. Overview"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "As shown in Fig. 2(a), COSINE follows a simple design philosophy, consisting of a Model Pool for extracting features from a target image and different modality prompts (e.g., text and example image), and a decoder-only segmentation model, named SegDecoder, which takes image and prompt features as inputs and outputs results for various segmentation tasks. Unlike previous segmentation methods [18, 20, 56] that train all parameters of models, COSINE fixes the foundation models in the Model Pool and only trains the relatively lightweight SegDecoder. Our approach enables lower training overhead while unleashing the potential of the foundation models for open-world perception."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Model Pool. Model Pool includes different vision models (DINOv2 and CLIP vision encoder) and language models (CLIP text encoder). The inputs of Model Pool include a target image, its image prompts and text prompts. For the target image, we use all vision models to encode it into the image features \\(\\mathcal{F} = \\{\\mathbf{F}_i\\}_i^P\\). Then, we use DINOv2 to encode the images of visual prompts into image features and use the in-context masks to pool the features into prompt tokens \\(\\mathcal{V} = \\{\\mathbf{v}_i\\}_i^M\\). The language model is used to extract the text prompt features \\(\\mathcal{T} = \\{\\mathbf{t}_i\\}_i^N\\). The image and prompt representations extracted by different foundation models contain rich multi-modal information, and the modalities complement each other, facilitating efficient transfer to downstream perception tasks."
+ },
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+ "type": "title",
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+ "angle": 0,
+ "content": "3.2. SegDecoder"
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "The architecture of SegDecoder is shown in Fig. 2 (b), which include a set of adapters, an Image-Prompt Alignmenter, a Pixel decoder and a Multi-Modality Decoder."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We deploy different adapters, including Feature Blender, V-Adapter and T-Adapter, for different features with the following objectives: (1) blending different image features, (2) aligning the feature dimensions of the image and various modality prompts, and (3) mapping the representations from different modalities to a shared space. Feature Blender consists of two convolutional layers that take the concatenated image features as input and outputs the blended image feature \\(\\mathbf{F} \\in \\mathbb{R}^{C \\times H \\times W}\\). Similarly, V-Adapter (T-Adapter) maps image (text) prompts into \\(\\mathbf{V} \\in \\mathbb{R}^{M \\times C}(\\mathbf{T} \\in \\mathbb{R}^{N \\times C})\\)."
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "Image-Prompt Aligner. The image features integrate knowl-"
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 2. The architecture of COSINE. (a) COSINE consists a Model Pool (e.g., DINOv2 and CLIP) used to extract image and prompt features and a SegDecoder used for unified open-world segmentation tasks. (b) SegDecoder consists a set of adapters, an Image-Prompt Alignmenter, a Pixel decoder and a Multi-Modality Decoder for modality alignment between the image and prompts, effectively enhancing open-world perception modeling. (c) and (d) show the details of Image-Prompt Alignmenter and Multi-Modality Decoder."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.517,
+ 0.486,
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+ ],
+ "angle": 0,
+ "content": "edge from multiple models, while each prompt only encode knowledge from a single modality, leading to a disparity between them. To mitigate the disparity, we employ an Image-Prompt Aligner to align and harmonize these heterogeneous representations. As shown in Fig. 2(c), the ImagePrompt Aligner is implemented by a set of self-attention, cross-attention, and feed-forward networks (FFN). Through the shared network structure, the Aligner aligns the image and different modality prompts, enhancing their representations in the multi-modal space, enabling high-quality segmentation results using prompts from any modality. Specifically, the blended image feature \\(\\mathbf{F}\\) and the prompt features \\(\\mathbf{V}\\) and \\(\\mathbf{T}\\) are aligned in the multi-modal representation space through the Image-Prompt Aligner module:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.15,
+ 0.739,
+ 0.484,
+ 0.765
+ ],
+ "angle": 0,
+ "content": "\\[\n\\left\\langle \\mathbf {F} ^ {\\prime}, \\mathbf {V} ^ {\\prime}, \\mathbf {T} ^ {\\prime} \\right\\rangle = \\text {A l i g n m e n t} (\\mathbf {F}, \\mathbf {V}, \\mathbf {T}; \\theta), \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbf{F}^{\\prime}\\in \\mathbb{R}^{C\\times H\\times W}\\) is the enhanced image feature, and \\(\\mathbf{V}^{\\prime}\\in \\mathbb{R}^{M\\times C}\\) and \\(\\mathbf{T}^{\\prime}\\in \\mathbb{R}^{N\\times C}\\) are the enhanced prompt features. \\(\\theta\\) is the parameters of the Image-Prompt Aligner."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Pixel Decoder. The aim of the Pixel Decoder is to output high-resolution mask features. For single-scale image feature, the Pixel Decoder is implemented as a small network consisting of two transpose convolution layers. It takes the blended image feature \\(\\mathbf{F}\\) as input, performs \\(4\\times\\) upsampling,"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "and generates the mask feature \\(\\mathbf{F}_{mask} \\in \\mathbb{R}^{C \\times H' \\times W'}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "Multi-Modality Decoder. As show in Fig. 2(d), we introduce a Multi-Modality Decoder to refine the different modality prompts and object queries \\(\\mathbf{Q} \\in \\mathbb{R}^{K \\times C}\\). Following [27], the Multi-Modality Decoder adopts a dual-path design, utilizing both self-attention and cross-attention [3] to facilitate interaction between object queries, different modality prompts, and the image features, while simultaneously refining the object queries and prompts. The process of the Multi-Modality Decoder can be summarized as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.526,
+ 0.676,
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+ 0.702
+ ],
+ "angle": 0,
+ "content": "\\[\n\\langle \\mathbf {Q} _ {r}, \\mathbf {V} _ {r}, \\mathbf {T} _ {r} \\rangle = D e c o d e r (\\mathbf {Q}, \\mathbf {V} ^ {\\prime}, \\mathbf {T} ^ {\\prime}, \\mathbf {F} ^ {\\prime}, \\mathbf {F} _ {m a s k}; \\phi), \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.706,
+ 0.907,
+ 0.797
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbf{Q}_r, \\mathbf{V}_r\\) and \\(\\mathbf{T}_r\\) are refined object queries, visual and text prompts. \\(\\phi\\) is the parameters of the Multi-Modality Decoder. By using \\(\\mathbf{V}_r\\) and \\(\\mathbf{T}_r\\) as classifiers, COSINE can obtain the classification scores \\(\\mathbf{S}_v\\) and \\(\\mathbf{S}_t\\) for in-context segmentation and open-vocabulary segmentation. This can be illustrated in the following equation:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.605,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {S} _ {v} = \\mathbf {Q} _ {r} \\mathbf {V} _ {r} ^ {\\top}, \\mathbf {S} _ {v} \\in \\mathbb {R} ^ {K \\times M},\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.615,
+ 0.818,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {S} _ {t} = \\mathbf {Q} _ {r} \\mathbf {T} _ {r} ^ {\\top}, \\mathbf {S} _ {t} \\in \\mathbb {R} ^ {K \\times N}. \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The mask results \\(\\mathbf{M}\\) can be obtained via the following operation:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.555,
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+ 0.903
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {M} = M L P \\left(\\mathbf {Q} _ {r}\\right) \\mathbf {F} _ {m a s k}, \\mathbf {M} \\in \\mathbb {R} ^ {K \\times H ^ {'} \\times W ^ {'}}. (4)\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "21560"
+ }
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+ [
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Note that \\(\\mathbf{S}_v\\) and \\(\\mathbf{S}_t\\) are not computed independently. In practice, the vision and text prompts are concatenated and jointly processed to produce a unified score matrix. The separate notation of \\(\\mathbf{S}_v\\) and \\(\\mathbf{S}_t\\) is adopted purely for clarity of presentation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Multi-Scale Feature Injection. Similar to previous approaches [22, 55], we can obtain multi-scale image features from these foundation models to enhance the performance of SegDecoder. We employ a multi-scale deformable attention Transformer [64] as the Pixel Decoder and use these multiscale image features as inputs to both the Image-Prompt Aligner and the Multi-Modality Decoder."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "3.3. Training and Inference"
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+ "content": "Image and Text Prompts Co-training. During the training phase, we experientially maintain a 1:1 sample ratio between image and text prompts for each batch, ensuring that the model effectively balances in-context and open-vocabulary segmentation tasks within an open-world framework. For in-context segmentation, we employ two distinct sampling strategies for image prompts: (1) sampling diverse images of the same class to serve as both the target image and the image prompt, thereby enhancing the model's capability to discern target semantics, and (2) randomly cropping a single image to generate multiple views of the same object, which strengthens the model's ability to recognize objects across varying perspectives. For open-vocabulary segmentation, we sample a set of class names that encompass the target image classes as prompts. The architecture of the SegDecoder is designed to process both in-context and open-vocabulary segmentation tasks uniformly, facilitating the use of a shared loss function for optimization. In line with prior DETR-based approaches [2, 3, 27, 64], we use bipartite matching to match predictions with ground-truth. Subsequently, we optimize the model using cross-entropy loss for classification, along with binary mask loss and Dice loss [33] for mask prediction."
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+ "content": "Multi-Modal Prompts Collaborative Inference. The SegDecoder architecture empowers COSINE to seamlessly process inputs from single-modality prompts, enabling it to tackle both open-vocabulary segmentation and in-context segmentation tasks. Furthermore, COSINE supports collaborative inference by leveraging prompts from multiple modalities. By integrating image and text prompts, COSINE generates mask predictions based on blended instructions. Notably, in addition to utilizing single-modality prompts, we introduce a straightforward averaging fusion mechanism to blend image prompts \\(\\mathbf{V}\\) and text prompts \\(\\mathbf{T}\\). This fusion strategy allows complementary information from different modalities to enhance COSINE's generalization capabilities in open-world scenarios."
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+ "content": "4. Experiments"
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+ "content": "4.1. Experiments Setting"
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+ "content": "Training Data. We train our model with publicly available academic segmentation datasets, encompassing semantic, instance, and panoptic segmentation tasks. Specifically, we leverage datasets including: COCO [24] is a widely used dataset that supports multiple tasks, including object detection, instance segmentation, and panoptic segmentation. It comprises 80 \"things\" categories and 53 \"stuff\" categories, with a total of 118K training images and 5K validation images. Objects365 [40] is a large-scale, high-quality dataset designed for object detection. It includes 365 object categories, 638K images, and approximately 10 million bounding boxes. Following the approach in [27], we utilize Objects365-SAM, an enhanced version of the Objects365 dataset where instance segmentation annotations are extended with SAM [18]. In addition, we incorporate referring segmentation datasets to endow COSINE with the capability of understanding referring expressions. Specifically, following LISA [19], we utilize refCLEF, refCOCO, refCOCO+ [16], and refCOCOg [31], which are widely adopted benchmarks for referring expression comprehension and segmentation. More implementation details are provided in the Appendix B."
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+ "content": "4.2. Main Results"
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+ "content": "We simultaneously evaluate COSINE's ability to process prompts in both the visual and textual modalities. For the visual modality, we select few-shot (semantic/instance) segmentation and video object segmentation tasks, while for the textual modality, we choose open-vocabulary (semantic/panoptic) segmentation and referring segmentation tasks. We compare COSINE against task-specific expert models as well as several general-purpose segmentation models. The results, presented in Table 1, demonstrate that COSINE exhibits a significant advantage in most tasks."
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+ "content": "Few-Shot Semantic Segmentation. Following the evaluation protocol of [26], we evaluate COSINE on the LVIS [12] dataset for few-shot semantic segmentation. Compared with the specialized few-shot model DiffewS [63] and the in-context model, SINE [27], COSINE achieves better performance in both one-shot and few-shot settings. COSINE decouples low-level mask features from high-level image and prompt features. Using a query-based decoder, it achieves strong contextual understanding and accurate masks. COSINE outperforms SegGPT [44], demonstrating its effective contextual reasoning. As shown in the first column of Table 1, COSINE even outperforms the SAM-based model, Matcher [26], despite being trained on only a small amount of segmentation data."
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+ "content": "Few-Shot Instance Segmentation. We evaluate the few-shot instance segmentation performance of COSINE on the"
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+ "content": "| Methods | Venue | few-shot sem. LVIS-92i | few-shot ins. LVIS | open-voc. pano. ADE20K | Cityscapes | open-voc. sem. A-847 | PC-459 |
| one-shot | few-shot | AP | APr | PQ | AP | mIoU | PQ | mIoU | mIoU | mIoU |
| few-shot model |
| HSNet [34] | ICCV'21 | 17.4 | 22.9 | - | - | - | - | - | - | - | - | - |
| VAT [15] | ECCV'22 | 18.5 | 22.7 | - | - | - | - | - | - | - | - | - |
| DiffewS [63] | NeurIPS'24 | 31.4 | 35.4 | - | - | - | - | - | - | - | - | - |
| in-context model |
| SegGPT [44] | ICCV'23 | 18.6 | 25.4 | - | - | - | - | - | - | - | - | - |
| PerSAM-F [57] | ICLR'24 | 18.4 | - | - | - | - | - | - | - | - | - | - |
| Matcher [26] | ICLR'24 | 33.0 | 40.0 | - | - | - | - | - | - | - | - | - |
| SINE [27] | NeurIPS'24 | 31.2 | 35.5 | 8.6 | 7.1 | - | - | - | - | - | - | - |
| open-vocabulary model |
| ODISE [48] | CVPR'23 | - | - | - | - | 23.4 | 13.9 | 28.7 | 23.9 | - | 11.1 | 14.5 |
| FC-CLIP [55] | NeurIPS'23 | - | - | - | - | 26.8 | 16.8 | 34.1 | 44.0 | 56.2 | 14.8 | 18.2 |
| HIPIE [42] | NeurIPS'23 | - | - | - | - | 22.9 | 19.0 | 29.0 | - | - | 9.7 | 14.4 |
| SED [46] | CVPR'24 | - | - | - | - | - | - | - | - | - | 13.9 | 22.6 |
| universal model |
| X-Decoder [65] | CVPR'23 | - | - | - | - | 21.8 | 13.1 | 29.6 | 38.1 | 52.0 | 9.2 | 16.1 |
| UNINEXT* [51] | CVPR'23 | - | - | - | - | 8.9 | 14.9 | 6.4 | - | - | 1.8 | 5.8 |
| OpenSeeD [56] | ICCV'23 | - | - | - | - | 19.7 | 15.0 | 23.4 | 41.4 | 47.8 | - | - |
| DINOv [20] | CVPR'24 | - | - | 15.4 | 14.5 | 23.2 | 15.1 | 25.3 | - | - | - | - |
| OMG-Seg [21] | CVPR'24 | - | - | - | - | 27.9 | - | - | - | - | - | - |
| PSALM [58] | ECCV'24 | - | - | - | - | - | 13.9 | 24.4 | - | - | - | 14.0 |
| COSINE† this work | 34.2 | 39.1 | 17.4 | 23.3 | 28.1 | 16.7 | 35.2 | 37.1 | 53.4 | 15.2 | 19.6 |
| COSINE | | 35.2 | 40.7 | 20.3 | 25.8 | 31.0 | 21.1 | 35.7 | 42.0 | 56.1 | 15.6 | 19.2 |
"
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+ "content": "Table 1. Results of different open world segmentation tasks including few-shot semantic segmentation, open-vocabulary panoptic segmentation and semantic segmentation. * We report the performance evaluated in [42]. † indicates the single-scale variant of COSINE."
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+ "content": "long-tailed dataset LVIS [12], which contains over 1,000 categories. For each category, we randomly select 10 samples (or all available samples if fewer than 10 are present). We report the AP for all categories and the APr for rare categories. As shown in Table 1, COSINE achieves an AP of 20.3, significantly outperforming the universal model DINOv. Furthermore, COSINE achieves an APr of 25.8, demonstrating stronger generalization to rare categories compared to previous methods. These results highlight COSINE's superior adaptability to open-world scenarios."
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+ "content": "Open-Vocabulary Panoptic Segmentation. Following ODISE [48] and FC-CLIP [55], we evaluate COSINE on the ADE20K [61] and Cityscapes [7] datasets for open-vocabulary panoptic segmentation. We compare COSINE with specialized open-vocabulary models, including ODISE, FC-CLIP, and HIPIE [42], as well as general-purpose models such as X-Decoder [65] and OpenSeeD [56]. As shown in Table 1, COSINE achieves outstanding performance on ADE20K, reaching a PQ of 31.0 and an AP of 21.1. Additionally, on Cityscapes, COSINE attains performance comparable to state-of-the-art methods, further demonstrating its effectiveness in open-vocabulary panoptic segmentation."
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+ "content": "Open-Vocabulary Semantic Segmentation. For open-vocabulary semantic segmentation, COSINE outperforms all universal models and the majority of open-vocabulary models, including the LLM-based model PSALM [58]. As shown in Table 1, COSINE achieves a mIoU of 15.6 on the A-847 dataset [60] and 19.2 on the PC-459 dataset [35], demonstrating its ability to recognize and segment novel categories effectively. Notably, while COSINE slightly lags behind specialized open-vocabulary semantic segmentation models such as SED [46], its key advantage lies in its versatility, enabling flexible support for a wide range of segmentation tasks."
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+ "content": "Video Object Segmentation. We evaluate COSINE on video object segmentation using DAVIS 2017 [37] and YouTube-VOS 2019 [50] datasets. As shown in Table 3, we compare COSINE with both video-trained models (gray rows) and models that do not use explicit video data. Videotrained models, such as Cutie [6] and XMem [4], achieve strong performance by leveraging temporal information and explicitly training on video datasets. COSINE, despite not using video data, achieves competitive performance without requiring video supervision, making it a more generaliz-"
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+ "content": "| Method | Venue | refCOCO | refCOCO+ | refCOCOg |
| val | testA | testB | val | testA | testB | val(U) | test(U) |
| MAttNet [54] | CVPR'18 | 56.5 | 62.4 | 51.7 | 46.7 | 52.4 | 40.1 | 47.6 | 48.6 |
| MCN [30] | CVPR'20 | 62.4 | 64.2 | 59.7 | 50.6 | 55.0 | 44.7 | 49.2 | 49.4 |
| VLT [9] | ICCV'21 | 67.5 | 70.5 | 65.2 | 56.3 | 61.0 | 50.1 | 55.0 | 57.7 |
| LAVT [53] | CVPR'22 | 72.7 | 75.8 | 68.8 | 62.1 | 68.4 | 55.1 | 61.2 | 62.1 |
| CRIS [45] | CVPR'22 | 70.5 | 73.2 | 66.1 | 62.3 | 68.1 | 53.7 | 59.9 | 60.4 |
| ReLA [25] | CVPR'23 | 73.8 | 76.5 | 70.2 | 66.0 | 71.0 | 57.7 | 65.0 | 66.0 |
| X-Decoder [65] | CVPR'23 | - | - | - | - | - | - | 64.6 | - |
| SEEM [66] | NeurIPS'23 | - | - | - | - | - | - | 65.7 | - |
| LISA [19] | CVPR'24 | 74.9 | 79.1 | 72.3 | 65.1 | 70.8 | 58.1 | 67.9 | 70.6 |
| COSINE | this work | 77.2 | 80.7 | 71.1 | 66.4 | 73.2 | 56.4 | 67.4 | 68.5 |
"
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+ "content": "Table 2. Results of referring segmentation on refCOCO, refCOCO+ and RefCOCOg. We report the metric of cIoU."
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+ "content": "| Methods | Venue | DAVIS 2017 | YT-VOS 2019 |
| J&F | G |
| with video data |
| AOT [52] | NeurIPS'21 | 85.4 | 85.3 |
| XMem [4] | ECCV'22 | 87.7 | 85.5 |
| DEVA [5] | ICCV'23 | 86.8 | 85.5 |
| Cutie [6] | CVPR'24 | 88.8 | 86.1 |
| without video data |
| Painter [43] | CVPR'23 | 34.6 | 20.6 |
| SegGPT [44] | ICCV'23 | 75.6 | 73.1 |
| SEEM [66] | NeurIPS'23 | 58.9 | - |
| DINOv [20] | CVPR'24 | 73.3 | 52.0 |
| PerSAM-F [57] | ICLR'24 | 76.1 | 46.6 |
| SINE [27] | NeurIPS'24 | 77.0 | 66.4 |
| COSINE | this work | 76.7 | 66.0 |
| COSINE-FT | | 80.2 | 70.0 |
"
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+ "bbox": [
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+ "content": "Table 3. Results of video object segmentation on DAVIS 2017, and YouTube-VOS 2019. Gray indicates the model is trained on target datasets with video data."
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "able and scalable approach. Compared with general-purpose segmentation models, COSINE achieves state-of-the-art performance among methods that do not use video data. On DAVIS 2017, COSINE obtains a \\( J \\& F \\) score of 76.7, significantly outperforming SEEM [66] and DINOv [20], and achieving comparable performance to PerSAM-F [57] and SINE [27]. We also introduce a fine-tuned variant, COSINE-FT, which improves the overall performance across both datasets by further tuning on the pure image prompt dataset. This demonstrates that COSINE's segmentation capabilities can be significantly enhanced through fine-tuning, making it a versatile and scalable approach adaptable to both static and dynamic scene understanding."
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+ "content": "Referring Segmentation. We test COSINE on the referring segmentation task following the evaluation protocol of LISA [19], which requires further fine-tuning on the referring segmentation dataset. As shown in Table 2, COSINE not only surpasses all traditional methods and general-purpose"
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+ "angle": 0,
+ "content": "| Prompt | LVIS-92i | ADE20K |
| vision | text | 1-shot | 5-shot | PQ | AP | mIoU |
| ✓ | | 24.5 | 27.8 | - | - | - |
| ✓ | - | - | 13.2 | 7.6 | 30.2 |
| ✓ | ✓ | 27.7 | 32.1 | 17.7 | 8.1 | 30.4 |
"
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+ "content": "Table 4. Effect of the interaction between visual and textual branches during Training. All models are trained for 10k steps."
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+ "content": "| Prompt | LVIS-92i | ADE20K |
| vision | text | 1-shot | 5-shot | PQ | AP | mIoU |
| ✓ | | 35.2 | 40.7 | 23.8 | 15.8 | 26.3 |
| ✓ | 37.8 | - | 31.0 | 21.1 | 35.7 |
| ✓ | ✓ | 43.1 | 45.9 | 31.4 | 21.3 | 36.3 |
"
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+ "content": "Table 5. Effect of the interaction between visual and textual branches during inference."
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+ "angle": 0,
+ "content": "segmentation models but also achieves performance comparable to the LLM-based model LISA [19]. This further validates COSINE's capability in handling long text descriptions and complex semantic understanding."
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+ "content": "4.3. Exploration of Visual-Textual Interaction"
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+ "angle": 0,
+ "content": "As mentioned earlier, COSINE consists of a textual branch that processes text prompts and a visual branch that processes visual prompts. Few works have explored the interaction between these two modalities. COSINE is the first to investigate their interplay from two perspectives: during training and inference."
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+ "content": "Training Phase. We aim to investigate whether jointly training both branches with multimodal data can enhance the performance of each individual branch. Specifically, we train the model for 10k steps using data from a single modality and multi-modality data, respectively. As shown in Table 4, we demonstrate that introducing the textual branch during training significantly improves the performance of the visual branch, and conversely, the visual branch also enhances the textual branch's performance. This finding highlights the mutual benefits of multimodal training in segmentation."
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+ "content": "| #ID | Model | LVIS-92i | ADE20K |
| 1-shot | 5-shot | PQ | AP | mIoU |
| 0 | COSINE (Full Model) | 27.7 | 32.1 | 17.7 | 8.1 | 30.4 |
| 1 | only DINOv2 Encoder | 27.7 | 32.0 | 9.7 | 4.2 | 18.6 |
| 2 | only CLIP Encoder | 24.4 | 28.0 | 11.4 | 3.3 | 27.0 |
| 3 | w/o Feature Blending | 24.4 | 29.0 | 9.4 | 2.6 | 26.3 |
| 4 | w/o Image-Prompt Aligner | 26.3 | 31.3 | 12.0 | 6.4 | 30.1 |
| 5 | w/o Prompt Refining | 27.0 | 31.2 | 16.5 | 6.6 | 30.9 |
"
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+ "content": "Table 6. Ablation study. All models are trained for \\( {10}\\mathrm{k} \\) steps."
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+ "content": "Inference Phase. We further investigate whether providing both visual and textual prompts during inference can improve model performance. We validate this hypothesis on few-shot semantic segmentation and open-vocabulary panoptic segmentation tasks, as shown in Table 5. Our results reveal that for tasks originally supported by the visual branch, such as LVIS-92\\(^i\\), incorporating an additional text prompt during inference leads to significant performance gains. Similarly, for tasks primarily supported by the textual branch, such as ADE20K, introducing a visual prompt during inference also enhances performance. These findings confirm that CO-SINE can flexibly process prompts from multiple modalities, resulting in more robust segmentation. This insight also provides valuable inspiration for future research on universal segmentation models."
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+ "content": "4.4. Ablation Study"
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+ "content": "As shown in Table 6, we validate the impact of each design within our model, including the Model Pool(#1, #2), the Feature Blender(#3), the Image-Prompt Aligner(#4), and the Multi-Modality Decoder(#5). Specifically, a comparison with model #1 and #2 reveals that different pre-trained models are informationally complementary, enhancing both in-context and open-vocabulary segmentation performance. The comparison with model #3 demonstrates that merely concatenating different foundation models is insufficient. An explicit blending of representations is necessary to learn a unified multi-modal representation. Furthermore, comparisons with models #4 and #5 indicate that the introduced Aligner and Decoder are both simple and effective."
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+ "content": "4.5. Visualization Analysis"
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+ "angle": 0,
+ "content": "Qualitative Results. As shown in Fig. 3, we visualize the segmentation results under both open-vocabulary and in-context settings, as well as the results obtained by combining both types of prompts. Additionally, we provide visualizations of referring segmentation and VOS results. These results demonstrate that COSINE achieves highly accurate predictions across various modalities and granularities, highlighting its strong potential for open-world generalization."
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+ "content": "Prompt Synergy. As shown in Fig. 4, COSINE can generalize to real-world domains such as industrial inspection, medical imaging. The industrial inspection case shows ef"
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+ "angle": 0,
+ "content": "Figure 3. Qualitative results. COSINE can perform various open-world segmentation tasks with different modal prompts (image and text). For few-shot segmentation, the left image is the example image and the right is the result."
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+ "angle": 0,
+ "content": "Figure 4. Visualization of prompt synergy. The top row shows the input prompts, the bottom row presents the corresponding outputs."
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+ "bbox": [
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+ "angle": 0,
+ "content": "fective collaboration between visual and textual prompts, accurately segmenting targets that would produce incorrect masks under a single modality. These results highlight the potential of multimodal prompt synergy in COSINE for complex segmentation. By integrating visual and textual cues, COSINE captures fine-grained details that are difficult to express with a single modality."
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+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "In this work, we present COSINE, a unified open-world segmentation model that unifies open-vocabulary Segmentation and in-context segmentation. COSINE supports diverse modalities of input, such as images and text, offering powerful open-world perception capabilities. Our exploratory analysis highlights that the synergistic collaboration between visual and textual branches enhances generalization in open-world segmentation, providing valuable insights for the research community. More discussion and limitations are provided in the Appendix A."
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+ "type": "title",
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+ "content": "Acknowledgments"
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+ "content": "This work was supported by the National Key R&D Program of China (No. 2022ZD0160101), the Ningbo Science and Technology Bureau (No. 2024Z291), and the National Natural Science Foundation of China (No. 62206244)."
+ },
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+ },
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+ ],
+ "angle": 0,
+ "content": "21566"
+ }
+ ],
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
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+ "bbox": [
+ 0.48,
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+ 0.957
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+ "angle": 0,
+ "content": "21567"
+ }
+ ]
+]
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+# Unified Open-World Segmentation with Multi-Modal Prompts
+
+Yang Liu $^{1*}$
+
+Yufei Yin $^{2*}$ Bo Fen
+
+Chenchen Jing $^{3}$ Hao Wang $^{4}$
+
+Muzhi Zhu $^{1}$ Hao Chen $^{1\dagger}$ Shiyu Li $^{4}$ Chunhua Shen $^{1}$
+
+Yuling Xi
+
+1 Zhejiang University
+
+2 Hangzhou Dianzi University
+
+3 Zhejiang University of Technology
+
+4 Apple
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Combined Prompt Segmentation
+
+
+
+
+Figure 1. COSINE is a unified open-world segmentation model that consolidates open-vocabulary and in-context segmentation. COSINE can simultaneously support text prompts (green boxes) and image prompts (blue boxes) as inputs to perform various segmentation tasks, including semantic segmentation, instance segmentation, panoptic segmentation, referring segmentation, and video object segmentation. In addition, COSINE can collaboratively use different types of prompts to perform various segmentation tasks.
+
+
+Video Object Segmentation
+
+
+
+
+
+
+
+# Abstract
+
+In this work, we present COSINE, a unified open-world segmentation model that Consolidates Open-vocabulary Segmentation and IN-context sEgmentation with multimodal prompts (e.g., text and image). COSINE exploits foundation models to extract representations for an input image and corresponding multi-modal prompts, and a SegDecoder to align these representations, model their interaction, and obtain masks specified by input prompts across different granularities. In this way, COSINE overcomes architectural discrepancies, divergent learning objectives, and distinct representation learning strategies of
+
+previous pipelines for open-vocabulary segmentation and incontext segmentation. Comprehensive experiments demonstrate that COSINE has significant performance improvements in both open-vocabulary and in-context segmentation tasks. Our exploratory analyses highlight that the synergistic collaboration between using visual and textual prompts leads to significantly improved generalization over single-modality approaches. Our code is released at https://github.com/aim-uofa/COSINE.
+
+# 1. Introduction
+
+Image segmentation [17, 24, 61] aims to provide accurate conceptual localization, enabling precise understanding and
+
+content analysis of images at the pixel level. Recently, image segmentation has gradually evolved from closed-world scenarios [3, 8, 13, 29, 41, 59] to open-world settings [18, 20, 26, 44, 48, 55, 62]. Unlike traditional closed-world segmentation models, which are limited to recognizing a fixed set of categories encountered during training, open-world segmentation models can localize arbitrary relevant objects in the wild based on user-provided prompts. Such models can enhance adaptability and robustness in unpredictable dynamic environments, such as autonomous driving and interactive robotics.
+
+The current landscape of open-world segmentation research primarily revolves around two distinct paradigms: (1) Open-vocabulary segmentation [11, 23, 48, 49, 55, 56], which replaces learnable classifiers with textual embeddings derived from category descriptors, thereby extending conventional closed-set segmentation frameworks to recognize novel categories through natural language alignment; and (2) In-context segmentation [20, 26, 27, 32, 44, 57], which leverages contextual cues from example images to facilitate adaptive object segmentation in query images. Despite significant progress in both directions, current methods predominantly address these tasks in isolation, failing to holistically tackle the complexities of open-world segmentation. Relying solely on text may lead to insufficient fine-grained semantic abstraction, whereas image-based exemplars often lack explicit category boundaries and semantic alignment. This raises a critical question: Can we unify open-vocabulary segmentation and in-context segmentation within a single framework, leveraging the complementary strengths of textual and visual modalities to enhance open-world segmentation capabilities?
+
+We compare these two paradigms and identify the following problems in unifying them: 1) Architectural Discrepancies: Existing methods exhibit substantial structural differences. For instance, SegGPT [44] employs a ViT-like [10] encoder-only architecture for in-context segmentation, whereas ODISE [48] adopts a Mask2Former-like [3] encoder-decoder structure for open-vocabulary segmentation. 2) Divergent Learning Objectives: Open-vocabulary segmentation primarily focuses on image-text semantic alignment, aiming to learn the association between images and class descriptions for recognizing novel categories in an open-world setting. In contrast, in-context segmentation emphasizes reference-query relationship modeling, leveraging contextual cues from example images to achieve adaptive target segmentation. 3) Distinct Representation Learning Strategies: Open-vocabulary segmentation typically relies on multimodal models (e.g., CLIP [38], Stable Diffusion [39]) to leverage text embeddings for category matching, whereas in-context segmentation predominantly utilizes vision foundation models (e.g., MAE [14], DINoV2 [36]), performing target localization on visual features. These fundamental dif
+
+ferences pose challenges in designing a unified framework that effectively integrates both paradigms while preserving their advantages.
+
+To address these challenges, we present COSINE, a unified open-world segmentation model that Consolidates Open-vocabulary Segmentation and IN-context sEgmentation. Specifically, we first deploy a frozen Model Pool consisting of multiple foundation models to extract representations for the target image and different modality prompts (e.g., text and image), and convert them into token sequences. This standardization of the input format facilitates structural unification across both tasks, thereby enabling a single decoder-only segmentation model, named SegDecoder, to jointly process them. The SegDecoder contains an ImagePrompt Aligner module and a Multi-Modality Decoder. The Image-Prompt Aligner module aligns the image with various prompts, reducing the modality gap and learning a unified multi-modal representation space. The Multi-Modality Decoder is used to model the interaction between object queries, the image, and different modality prompts, enabling the effective generation of masks at different granularities (e.g., semantic, instance). COSINE optimizes the lightweight SegDecoder only, effectively unleashing the potential of the foundation models for open-world segmentation. As illustrated in Fig. 1, COSINE can concurrently address open-vocabulary and in-context segmentation tasks at multiple granularities, including semantic, instance, and panoptic segmentation. Comprehensive experiments demonstrate that COSINE effectively unifies both settings within a single model, achieving state-of-the-art performance. In particular, our exploratory analyses highlight the synergistic collaboration between the visual and textual branches, leading to significantly improved generalization over single-modality approaches. We believe our findings offer valuable insights to the research community.
+
+Our main contributions are as follows: (1) To our knowledge, our method is the first to unify in-context segmentation and open-vocabulary segmentation. We present a simple but effective framework, COSINE, which unleashes the potential of frozen foundation models across various segmentation tasks. (2) Our comprehensive experiments demonstrate that COSINE achieves significant performance improvements in both open-vocabulary and in-context segmentation tasks. (3) We further observe that the synergistic collaboration between different modality branches enhances generalization in open-world segmentation, providing valuable insights for the research community.
+
+# 2. Related Work
+
+Open-World Segmentation. Image segmentation [17, 24, 61], which aims to localize and organize meaningful concepts at the pixel level, has evolved from closed-world scenarios [3, 8, 13, 29, 41, 59] to open-world set
+
+tings [18, 20, 26, 44, 48, 55, 62]. Open-world segmentation can be broadly categorized into two paradigms: Open-vocabulary segmentation [11, 23, 48, 49, 55, 56] focuses on recognizing and segmenting objects from an open set of categories. ODISE [48] leverages text-to-image diffusion models to learn rich semantic representations, enabling the generation of open-vocabulary panoptic masks. FCCLIP [55] develops a segmentation model built on a shared frozen convolutional CLIP backbone, utilizing two-way open-vocabulary classification to improve performance on novel classes. OpenSeeD [56] unifies open-vocabulary segmentation and detection by jointly learning from segmentation and detection datasets, addressing task and data discrepancies through decoupled decoding and conditioned mask decoding. In-context segmentation [20, 26, 27, 32, 44, 57] enables segmentation guided by example images. SegGPT [44] introduces a random coloring scheme within in-context learning to enhance model generalization. PerSAM [57] employs one-shot data to generate positive-negative location priors and infuses high-level semantics from SAM [18] to guide personalized segmentation. Matcher [26] proposes a training-free framework that utilizes vision foundation models for few-shot segmentation tasks. DINOv [20] integrates visual in-context prompting to unify referring and generic segmentation tasks, introducing a specialized encoder-decoder architecture. SINE [27] resolves ambiguity in in-context segmentation by unifying tasks across various granularities. Unlike these methods, COSINE unifies open-vocabulary and in-context segmentation, fostering synergistic collaboration between these two branches, and significantly enhancing the model's open-world generalization performance.
+
+Vision Foundation Models. Leveraging contrastive and generative training, vision foundation models, when combined with large-scale single-/multi-modal datasets, exhibit remarkable generalization capabilities. Pre-trained by masked image modeling [1, 10, 28, 47], MAE [14] demonstrating strong transfer performance across downstream tasks. DINOv2 [36], through image and patch-level discriminative self-supervised learning, learns versatile visual features applicable to a wide range of downstream tasks. CLIP[38] learns multi-modal representations by image-text contrastive learning and demonstrates outstanding zero-shot image classification performance. The Segment Anything Model (SAM)[18] achieves impressive zero-shot, class-agnostic segmentation performance by training on a large-scale segmentation dataset. This work aims to train an open-world segmentation model with strong generalization capabilities, leveraging the potential of existing foundation models, even under constraints in data and computational resources.
+
+# 3. Method
+
+We present COSINE, a unified open-world segmentation model that Consolidates Open-vocabulary Segmentation and
+
+IN-context sEgmentation. COSINE supports diverse modalities of input, such as images and text, by framing them as promptable segmentation tasks, offering powerful open-world perception capabilities. Our goal is not to achieve state-of-the-art performance across all open-vocabulary or in-context segmentation tasks, but to validate that diverse modal information can synergistically collaborate and extend knowledge across tasks, thereby enhancing the model's modeling capabilities and generalization performance.
+
+# 3.1. Overview
+
+As shown in Fig. 2(a), COSINE follows a simple design philosophy, consisting of a Model Pool for extracting features from a target image and different modality prompts (e.g., text and example image), and a decoder-only segmentation model, named SegDecoder, which takes image and prompt features as inputs and outputs results for various segmentation tasks. Unlike previous segmentation methods [18, 20, 56] that train all parameters of models, COSINE fixes the foundation models in the Model Pool and only trains the relatively lightweight SegDecoder. Our approach enables lower training overhead while unleashing the potential of the foundation models for open-world perception.
+
+Model Pool. Model Pool includes different vision models (DINOv2 and CLIP vision encoder) and language models (CLIP text encoder). The inputs of Model Pool include a target image, its image prompts and text prompts. For the target image, we use all vision models to encode it into the image features $\mathcal{F} = \{\mathbf{F}_i\}_i^P$ . Then, we use DINOv2 to encode the images of visual prompts into image features and use the in-context masks to pool the features into prompt tokens $\mathcal{V} = \{\mathbf{v}_i\}_i^M$ . The language model is used to extract the text prompt features $\mathcal{T} = \{\mathbf{t}_i\}_i^N$ . The image and prompt representations extracted by different foundation models contain rich multi-modal information, and the modalities complement each other, facilitating efficient transfer to downstream perception tasks.
+
+# 3.2. SegDecoder
+
+The architecture of SegDecoder is shown in Fig. 2 (b), which include a set of adapters, an Image-Prompt Alignmenter, a Pixel decoder and a Multi-Modality Decoder.
+
+We deploy different adapters, including Feature Blender, V-Adapter and T-Adapter, for different features with the following objectives: (1) blending different image features, (2) aligning the feature dimensions of the image and various modality prompts, and (3) mapping the representations from different modalities to a shared space. Feature Blender consists of two convolutional layers that take the concatenated image features as input and outputs the blended image feature $\mathbf{F} \in \mathbb{R}^{C \times H \times W}$ . Similarly, V-Adapter (T-Adapter) maps image (text) prompts into $\mathbf{V} \in \mathbb{R}^{M \times C}(\mathbf{T} \in \mathbb{R}^{N \times C})$ .
+
+Image-Prompt Aligner. The image features integrate knowl-
+
+
+Figure 2. The architecture of COSINE. (a) COSINE consists a Model Pool (e.g., DINOv2 and CLIP) used to extract image and prompt features and a SegDecoder used for unified open-world segmentation tasks. (b) SegDecoder consists a set of adapters, an Image-Prompt Alignmenter, a Pixel decoder and a Multi-Modality Decoder for modality alignment between the image and prompts, effectively enhancing open-world perception modeling. (c) and (d) show the details of Image-Prompt Alignmenter and Multi-Modality Decoder.
+
+
+
+
+
+edge from multiple models, while each prompt only encode knowledge from a single modality, leading to a disparity between them. To mitigate the disparity, we employ an Image-Prompt Aligner to align and harmonize these heterogeneous representations. As shown in Fig. 2(c), the ImagePrompt Aligner is implemented by a set of self-attention, cross-attention, and feed-forward networks (FFN). Through the shared network structure, the Aligner aligns the image and different modality prompts, enhancing their representations in the multi-modal space, enabling high-quality segmentation results using prompts from any modality. Specifically, the blended image feature $\mathbf{F}$ and the prompt features $\mathbf{V}$ and $\mathbf{T}$ are aligned in the multi-modal representation space through the Image-Prompt Aligner module:
+
+$$
+\left\langle \mathbf {F} ^ {\prime}, \mathbf {V} ^ {\prime}, \mathbf {T} ^ {\prime} \right\rangle = \text {A l i g n m e n t} (\mathbf {F}, \mathbf {V}, \mathbf {T}; \theta), \tag {1}
+$$
+
+where $\mathbf{F}^{\prime}\in \mathbb{R}^{C\times H\times W}$ is the enhanced image feature, and $\mathbf{V}^{\prime}\in \mathbb{R}^{M\times C}$ and $\mathbf{T}^{\prime}\in \mathbb{R}^{N\times C}$ are the enhanced prompt features. $\theta$ is the parameters of the Image-Prompt Aligner.
+
+Pixel Decoder. The aim of the Pixel Decoder is to output high-resolution mask features. For single-scale image feature, the Pixel Decoder is implemented as a small network consisting of two transpose convolution layers. It takes the blended image feature $\mathbf{F}$ as input, performs $4\times$ upsampling,
+
+and generates the mask feature $\mathbf{F}_{mask} \in \mathbb{R}^{C \times H' \times W'}$ .
+
+Multi-Modality Decoder. As show in Fig. 2(d), we introduce a Multi-Modality Decoder to refine the different modality prompts and object queries $\mathbf{Q} \in \mathbb{R}^{K \times C}$ . Following [27], the Multi-Modality Decoder adopts a dual-path design, utilizing both self-attention and cross-attention [3] to facilitate interaction between object queries, different modality prompts, and the image features, while simultaneously refining the object queries and prompts. The process of the Multi-Modality Decoder can be summarized as follows:
+
+$$
+\langle \mathbf {Q} _ {r}, \mathbf {V} _ {r}, \mathbf {T} _ {r} \rangle = D e c o d e r (\mathbf {Q}, \mathbf {V} ^ {\prime}, \mathbf {T} ^ {\prime}, \mathbf {F} ^ {\prime}, \mathbf {F} _ {m a s k}; \phi), \tag {2}
+$$
+
+where $\mathbf{Q}_r, \mathbf{V}_r$ and $\mathbf{T}_r$ are refined object queries, visual and text prompts. $\phi$ is the parameters of the Multi-Modality Decoder. By using $\mathbf{V}_r$ and $\mathbf{T}_r$ as classifiers, COSINE can obtain the classification scores $\mathbf{S}_v$ and $\mathbf{S}_t$ for in-context segmentation and open-vocabulary segmentation. This can be illustrated in the following equation:
+
+$$
+\mathbf {S} _ {v} = \mathbf {Q} _ {r} \mathbf {V} _ {r} ^ {\top}, \mathbf {S} _ {v} \in \mathbb {R} ^ {K \times M},
+$$
+
+$$
+\mathbf {S} _ {t} = \mathbf {Q} _ {r} \mathbf {T} _ {r} ^ {\top}, \mathbf {S} _ {t} \in \mathbb {R} ^ {K \times N}. \tag {3}
+$$
+
+The mask results $\mathbf{M}$ can be obtained via the following operation:
+
+$$
+\mathbf {M} = M L P \left(\mathbf {Q} _ {r}\right) \mathbf {F} _ {m a s k}, \mathbf {M} \in \mathbb {R} ^ {K \times H ^ {'} \times W ^ {'}}. (4)
+$$
+
+Note that $\mathbf{S}_v$ and $\mathbf{S}_t$ are not computed independently. In practice, the vision and text prompts are concatenated and jointly processed to produce a unified score matrix. The separate notation of $\mathbf{S}_v$ and $\mathbf{S}_t$ is adopted purely for clarity of presentation.
+
+Multi-Scale Feature Injection. Similar to previous approaches [22, 55], we can obtain multi-scale image features from these foundation models to enhance the performance of SegDecoder. We employ a multi-scale deformable attention Transformer [64] as the Pixel Decoder and use these multiscale image features as inputs to both the Image-Prompt Aligner and the Multi-Modality Decoder.
+
+# 3.3. Training and Inference
+
+Image and Text Prompts Co-training. During the training phase, we experientially maintain a 1:1 sample ratio between image and text prompts for each batch, ensuring that the model effectively balances in-context and open-vocabulary segmentation tasks within an open-world framework. For in-context segmentation, we employ two distinct sampling strategies for image prompts: (1) sampling diverse images of the same class to serve as both the target image and the image prompt, thereby enhancing the model's capability to discern target semantics, and (2) randomly cropping a single image to generate multiple views of the same object, which strengthens the model's ability to recognize objects across varying perspectives. For open-vocabulary segmentation, we sample a set of class names that encompass the target image classes as prompts. The architecture of the SegDecoder is designed to process both in-context and open-vocabulary segmentation tasks uniformly, facilitating the use of a shared loss function for optimization. In line with prior DETR-based approaches [2, 3, 27, 64], we use bipartite matching to match predictions with ground-truth. Subsequently, we optimize the model using cross-entropy loss for classification, along with binary mask loss and Dice loss [33] for mask prediction.
+
+Multi-Modal Prompts Collaborative Inference. The SegDecoder architecture empowers COSINE to seamlessly process inputs from single-modality prompts, enabling it to tackle both open-vocabulary segmentation and in-context segmentation tasks. Furthermore, COSINE supports collaborative inference by leveraging prompts from multiple modalities. By integrating image and text prompts, COSINE generates mask predictions based on blended instructions. Notably, in addition to utilizing single-modality prompts, we introduce a straightforward averaging fusion mechanism to blend image prompts $\mathbf{V}$ and text prompts $\mathbf{T}$ . This fusion strategy allows complementary information from different modalities to enhance COSINE's generalization capabilities in open-world scenarios.
+
+# 4. Experiments
+
+# 4.1. Experiments Setting
+
+Training Data. We train our model with publicly available academic segmentation datasets, encompassing semantic, instance, and panoptic segmentation tasks. Specifically, we leverage datasets including: COCO [24] is a widely used dataset that supports multiple tasks, including object detection, instance segmentation, and panoptic segmentation. It comprises 80 "things" categories and 53 "stuff" categories, with a total of 118K training images and 5K validation images. Objects365 [40] is a large-scale, high-quality dataset designed for object detection. It includes 365 object categories, 638K images, and approximately 10 million bounding boxes. Following the approach in [27], we utilize Objects365-SAM, an enhanced version of the Objects365 dataset where instance segmentation annotations are extended with SAM [18]. In addition, we incorporate referring segmentation datasets to endow COSINE with the capability of understanding referring expressions. Specifically, following LISA [19], we utilize refCLEF, refCOCO, refCOCO+ [16], and refCOCOg [31], which are widely adopted benchmarks for referring expression comprehension and segmentation. More implementation details are provided in the Appendix B.
+
+# 4.2. Main Results
+
+We simultaneously evaluate COSINE's ability to process prompts in both the visual and textual modalities. For the visual modality, we select few-shot (semantic/instance) segmentation and video object segmentation tasks, while for the textual modality, we choose open-vocabulary (semantic/panoptic) segmentation and referring segmentation tasks. We compare COSINE against task-specific expert models as well as several general-purpose segmentation models. The results, presented in Table 1, demonstrate that COSINE exhibits a significant advantage in most tasks.
+
+Few-Shot Semantic Segmentation. Following the evaluation protocol of [26], we evaluate COSINE on the LVIS [12] dataset for few-shot semantic segmentation. Compared with the specialized few-shot model DiffewS [63] and the in-context model, SINE [27], COSINE achieves better performance in both one-shot and few-shot settings. COSINE decouples low-level mask features from high-level image and prompt features. Using a query-based decoder, it achieves strong contextual understanding and accurate masks. COSINE outperforms SegGPT [44], demonstrating its effective contextual reasoning. As shown in the first column of Table 1, COSINE even outperforms the SAM-based model, Matcher [26], despite being trained on only a small amount of segmentation data.
+
+Few-Shot Instance Segmentation. We evaluate the few-shot instance segmentation performance of COSINE on the
+
+| Methods | Venue | few-shot sem. LVIS-92i | few-shot ins. LVIS | open-voc. pano. ADE20K | Cityscapes | open-voc. sem. A-847 | PC-459 |
| one-shot | few-shot | AP | APr | PQ | AP | mIoU | PQ | mIoU | mIoU | mIoU |
| few-shot model |
| HSNet [34] | ICCV'21 | 17.4 | 22.9 | - | - | - | - | - | - | - | - | - |
| VAT [15] | ECCV'22 | 18.5 | 22.7 | - | - | - | - | - | - | - | - | - |
| DiffewS [63] | NeurIPS'24 | 31.4 | 35.4 | - | - | - | - | - | - | - | - | - |
| in-context model |
| SegGPT [44] | ICCV'23 | 18.6 | 25.4 | - | - | - | - | - | - | - | - | - |
| PerSAM-F [57] | ICLR'24 | 18.4 | - | - | - | - | - | - | - | - | - | - |
| Matcher [26] | ICLR'24 | 33.0 | 40.0 | - | - | - | - | - | - | - | - | - |
| SINE [27] | NeurIPS'24 | 31.2 | 35.5 | 8.6 | 7.1 | - | - | - | - | - | - | - |
| open-vocabulary model |
| ODISE [48] | CVPR'23 | - | - | - | - | 23.4 | 13.9 | 28.7 | 23.9 | - | 11.1 | 14.5 |
| FC-CLIP [55] | NeurIPS'23 | - | - | - | - | 26.8 | 16.8 | 34.1 | 44.0 | 56.2 | 14.8 | 18.2 |
| HIPIE [42] | NeurIPS'23 | - | - | - | - | 22.9 | 19.0 | 29.0 | - | - | 9.7 | 14.4 |
| SED [46] | CVPR'24 | - | - | - | - | - | - | - | - | - | 13.9 | 22.6 |
| universal model |
| X-Decoder [65] | CVPR'23 | - | - | - | - | 21.8 | 13.1 | 29.6 | 38.1 | 52.0 | 9.2 | 16.1 |
| UNINEXT* [51] | CVPR'23 | - | - | - | - | 8.9 | 14.9 | 6.4 | - | - | 1.8 | 5.8 |
| OpenSeeD [56] | ICCV'23 | - | - | - | - | 19.7 | 15.0 | 23.4 | 41.4 | 47.8 | - | - |
| DINOv [20] | CVPR'24 | - | - | 15.4 | 14.5 | 23.2 | 15.1 | 25.3 | - | - | - | - |
| OMG-Seg [21] | CVPR'24 | - | - | - | - | 27.9 | - | - | - | - | - | - |
| PSALM [58] | ECCV'24 | - | - | - | - | - | 13.9 | 24.4 | - | - | - | 14.0 |
| COSINE† this work | 34.2 | 39.1 | 17.4 | 23.3 | 28.1 | 16.7 | 35.2 | 37.1 | 53.4 | 15.2 | 19.6 |
| COSINE | | 35.2 | 40.7 | 20.3 | 25.8 | 31.0 | 21.1 | 35.7 | 42.0 | 56.1 | 15.6 | 19.2 |
+
+Table 1. Results of different open world segmentation tasks including few-shot semantic segmentation, open-vocabulary panoptic segmentation and semantic segmentation. * We report the performance evaluated in [42]. † indicates the single-scale variant of COSINE.
+
+long-tailed dataset LVIS [12], which contains over 1,000 categories. For each category, we randomly select 10 samples (or all available samples if fewer than 10 are present). We report the AP for all categories and the APr for rare categories. As shown in Table 1, COSINE achieves an AP of 20.3, significantly outperforming the universal model DINOv. Furthermore, COSINE achieves an APr of 25.8, demonstrating stronger generalization to rare categories compared to previous methods. These results highlight COSINE's superior adaptability to open-world scenarios.
+
+Open-Vocabulary Panoptic Segmentation. Following ODISE [48] and FC-CLIP [55], we evaluate COSINE on the ADE20K [61] and Cityscapes [7] datasets for open-vocabulary panoptic segmentation. We compare COSINE with specialized open-vocabulary models, including ODISE, FC-CLIP, and HIPIE [42], as well as general-purpose models such as X-Decoder [65] and OpenSeeD [56]. As shown in Table 1, COSINE achieves outstanding performance on ADE20K, reaching a PQ of 31.0 and an AP of 21.1. Additionally, on Cityscapes, COSINE attains performance comparable to state-of-the-art methods, further demonstrating its effectiveness in open-vocabulary panoptic segmentation.
+
+Open-Vocabulary Semantic Segmentation. For open-vocabulary semantic segmentation, COSINE outperforms all universal models and the majority of open-vocabulary models, including the LLM-based model PSALM [58]. As shown in Table 1, COSINE achieves a mIoU of 15.6 on the A-847 dataset [60] and 19.2 on the PC-459 dataset [35], demonstrating its ability to recognize and segment novel categories effectively. Notably, while COSINE slightly lags behind specialized open-vocabulary semantic segmentation models such as SED [46], its key advantage lies in its versatility, enabling flexible support for a wide range of segmentation tasks.
+
+Video Object Segmentation. We evaluate COSINE on video object segmentation using DAVIS 2017 [37] and YouTube-VOS 2019 [50] datasets. As shown in Table 3, we compare COSINE with both video-trained models (gray rows) and models that do not use explicit video data. Videotrained models, such as Cutie [6] and XMem [4], achieve strong performance by leveraging temporal information and explicitly training on video datasets. COSINE, despite not using video data, achieves competitive performance without requiring video supervision, making it a more generaliz-
+
+| Method | Venue | refCOCO | refCOCO+ | refCOCOg |
| val | testA | testB | val | testA | testB | val(U) | test(U) |
| MAttNet [54] | CVPR'18 | 56.5 | 62.4 | 51.7 | 46.7 | 52.4 | 40.1 | 47.6 | 48.6 |
| MCN [30] | CVPR'20 | 62.4 | 64.2 | 59.7 | 50.6 | 55.0 | 44.7 | 49.2 | 49.4 |
| VLT [9] | ICCV'21 | 67.5 | 70.5 | 65.2 | 56.3 | 61.0 | 50.1 | 55.0 | 57.7 |
| LAVT [53] | CVPR'22 | 72.7 | 75.8 | 68.8 | 62.1 | 68.4 | 55.1 | 61.2 | 62.1 |
| CRIS [45] | CVPR'22 | 70.5 | 73.2 | 66.1 | 62.3 | 68.1 | 53.7 | 59.9 | 60.4 |
| ReLA [25] | CVPR'23 | 73.8 | 76.5 | 70.2 | 66.0 | 71.0 | 57.7 | 65.0 | 66.0 |
| X-Decoder [65] | CVPR'23 | - | - | - | - | - | - | 64.6 | - |
| SEEM [66] | NeurIPS'23 | - | - | - | - | - | - | 65.7 | - |
| LISA [19] | CVPR'24 | 74.9 | 79.1 | 72.3 | 65.1 | 70.8 | 58.1 | 67.9 | 70.6 |
| COSINE | this work | 77.2 | 80.7 | 71.1 | 66.4 | 73.2 | 56.4 | 67.4 | 68.5 |
+
+Table 2. Results of referring segmentation on refCOCO, refCOCO+ and RefCOCOg. We report the metric of cIoU.
+
+| Methods | Venue | DAVIS 2017 | YT-VOS 2019 |
| J&F | G |
| with video data |
| AOT [52] | NeurIPS'21 | 85.4 | 85.3 |
| XMem [4] | ECCV'22 | 87.7 | 85.5 |
| DEVA [5] | ICCV'23 | 86.8 | 85.5 |
| Cutie [6] | CVPR'24 | 88.8 | 86.1 |
| without video data |
| Painter [43] | CVPR'23 | 34.6 | 20.6 |
| SegGPT [44] | ICCV'23 | 75.6 | 73.1 |
| SEEM [66] | NeurIPS'23 | 58.9 | - |
| DINOv [20] | CVPR'24 | 73.3 | 52.0 |
| PerSAM-F [57] | ICLR'24 | 76.1 | 46.6 |
| SINE [27] | NeurIPS'24 | 77.0 | 66.4 |
| COSINE | this work | 76.7 | 66.0 |
| COSINE-FT | | 80.2 | 70.0 |
+
+Table 3. Results of video object segmentation on DAVIS 2017, and YouTube-VOS 2019. Gray indicates the model is trained on target datasets with video data.
+
+able and scalable approach. Compared with general-purpose segmentation models, COSINE achieves state-of-the-art performance among methods that do not use video data. On DAVIS 2017, COSINE obtains a $J \& F$ score of 76.7, significantly outperforming SEEM [66] and DINOv [20], and achieving comparable performance to PerSAM-F [57] and SINE [27]. We also introduce a fine-tuned variant, COSINE-FT, which improves the overall performance across both datasets by further tuning on the pure image prompt dataset. This demonstrates that COSINE's segmentation capabilities can be significantly enhanced through fine-tuning, making it a versatile and scalable approach adaptable to both static and dynamic scene understanding.
+
+Referring Segmentation. We test COSINE on the referring segmentation task following the evaluation protocol of LISA [19], which requires further fine-tuning on the referring segmentation dataset. As shown in Table 2, COSINE not only surpasses all traditional methods and general-purpose
+
+| Prompt | LVIS-92i | ADE20K |
| vision | text | 1-shot | 5-shot | PQ | AP | mIoU |
| ✓ | | 24.5 | 27.8 | - | - | - |
| ✓ | - | - | 13.2 | 7.6 | 30.2 |
| ✓ | ✓ | 27.7 | 32.1 | 17.7 | 8.1 | 30.4 |
+
+Table 4. Effect of the interaction between visual and textual branches during Training. All models are trained for 10k steps.
+
+| Prompt | LVIS-92i | ADE20K |
| vision | text | 1-shot | 5-shot | PQ | AP | mIoU |
| ✓ | | 35.2 | 40.7 | 23.8 | 15.8 | 26.3 |
| ✓ | 37.8 | - | 31.0 | 21.1 | 35.7 |
| ✓ | ✓ | 43.1 | 45.9 | 31.4 | 21.3 | 36.3 |
+
+Table 5. Effect of the interaction between visual and textual branches during inference.
+
+segmentation models but also achieves performance comparable to the LLM-based model LISA [19]. This further validates COSINE's capability in handling long text descriptions and complex semantic understanding.
+
+# 4.3. Exploration of Visual-Textual Interaction
+
+As mentioned earlier, COSINE consists of a textual branch that processes text prompts and a visual branch that processes visual prompts. Few works have explored the interaction between these two modalities. COSINE is the first to investigate their interplay from two perspectives: during training and inference.
+
+Training Phase. We aim to investigate whether jointly training both branches with multimodal data can enhance the performance of each individual branch. Specifically, we train the model for 10k steps using data from a single modality and multi-modality data, respectively. As shown in Table 4, we demonstrate that introducing the textual branch during training significantly improves the performance of the visual branch, and conversely, the visual branch also enhances the textual branch's performance. This finding highlights the mutual benefits of multimodal training in segmentation.
+
+| #ID | Model | LVIS-92i | ADE20K |
| 1-shot | 5-shot | PQ | AP | mIoU |
| 0 | COSINE (Full Model) | 27.7 | 32.1 | 17.7 | 8.1 | 30.4 |
| 1 | only DINOv2 Encoder | 27.7 | 32.0 | 9.7 | 4.2 | 18.6 |
| 2 | only CLIP Encoder | 24.4 | 28.0 | 11.4 | 3.3 | 27.0 |
| 3 | w/o Feature Blending | 24.4 | 29.0 | 9.4 | 2.6 | 26.3 |
| 4 | w/o Image-Prompt Aligner | 26.3 | 31.3 | 12.0 | 6.4 | 30.1 |
| 5 | w/o Prompt Refining | 27.0 | 31.2 | 16.5 | 6.6 | 30.9 |
+
+Table 6. Ablation study. All models are trained for ${10}\mathrm{k}$ steps.
+
+Inference Phase. We further investigate whether providing both visual and textual prompts during inference can improve model performance. We validate this hypothesis on few-shot semantic segmentation and open-vocabulary panoptic segmentation tasks, as shown in Table 5. Our results reveal that for tasks originally supported by the visual branch, such as LVIS-92 $^i$ , incorporating an additional text prompt during inference leads to significant performance gains. Similarly, for tasks primarily supported by the textual branch, such as ADE20K, introducing a visual prompt during inference also enhances performance. These findings confirm that CO-SINE can flexibly process prompts from multiple modalities, resulting in more robust segmentation. This insight also provides valuable inspiration for future research on universal segmentation models.
+
+# 4.4. Ablation Study
+
+As shown in Table 6, we validate the impact of each design within our model, including the Model Pool(#1, #2), the Feature Blender(#3), the Image-Prompt Aligner(#4), and the Multi-Modality Decoder(#5). Specifically, a comparison with model #1 and #2 reveals that different pre-trained models are informationally complementary, enhancing both in-context and open-vocabulary segmentation performance. The comparison with model #3 demonstrates that merely concatenating different foundation models is insufficient. An explicit blending of representations is necessary to learn a unified multi-modal representation. Furthermore, comparisons with models #4 and #5 indicate that the introduced Aligner and Decoder are both simple and effective.
+
+# 4.5. Visualization Analysis
+
+Qualitative Results. As shown in Fig. 3, we visualize the segmentation results under both open-vocabulary and in-context settings, as well as the results obtained by combining both types of prompts. Additionally, we provide visualizations of referring segmentation and VOS results. These results demonstrate that COSINE achieves highly accurate predictions across various modalities and granularities, highlighting its strong potential for open-world generalization.
+
+Prompt Synergy. As shown in Fig. 4, COSINE can generalize to real-world domains such as industrial inspection, medical imaging. The industrial inspection case shows ef
+
+
+
+
+Figure 3. Qualitative results. COSINE can perform various open-world segmentation tasks with different modal prompts (image and text). For few-shot segmentation, the left image is the example image and the right is the result.
+Figure 4. Visualization of prompt synergy. The top row shows the input prompts, the bottom row presents the corresponding outputs.
+
+fective collaboration between visual and textual prompts, accurately segmenting targets that would produce incorrect masks under a single modality. These results highlight the potential of multimodal prompt synergy in COSINE for complex segmentation. By integrating visual and textual cues, COSINE captures fine-grained details that are difficult to express with a single modality.
+
+# 5. Conclusion
+
+In this work, we present COSINE, a unified open-world segmentation model that unifies open-vocabulary Segmentation and in-context segmentation. COSINE supports diverse modalities of input, such as images and text, offering powerful open-world perception capabilities. Our exploratory analysis highlights that the synergistic collaboration between visual and textual branches enhances generalization in open-world segmentation, providing valuable insights for the research community. More discussion and limitations are provided in the Appendix A.
+
+# Acknowledgments
+
+This work was supported by the National Key R&D Program of China (No. 2022ZD0160101), the Ningbo Science and Technology Bureau (No. 2024Z291), and the National Natural Science Foundation of China (No. 62206244).
+
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\ No newline at end of file
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| one-shot | few-shot | AP | APr | PQ | AP | mIoU | PQ | mIoU | mIoU | mIoU |
| few-shot model |
| HSNet [34] | ICCV'21 | 17.4 | 22.9 | - | - | - | - | - | - | - | - | - |
| VAT [15] | ECCV'22 | 18.5 | 22.7 | - | - | - | - | - | - | - | - | - |
| DiffewS [63] | NeurIPS'24 | 31.4 | 35.4 | - | - | - | - | - | - | - | - | - |
| in-context model |
| SegGPT [44] | ICCV'23 | 18.6 | 25.4 | - | - | - | - | - | - | - | - | - |
| PerSAM-F [57] | ICLR'24 | 18.4 | - | - | - | - | - | - | - | - | - | - |
| Matcher [26] | ICLR'24 | 33.0 | 40.0 | - | - | - | - | - | - | - | - | - |
| SINE [27] | NeurIPS'24 | 31.2 | 35.5 | 8.6 | 7.1 | - | - | - | - | - | - | - |
| open-vocabulary model |
| ODISE [48] | CVPR'23 | - | - | - | - | 23.4 | 13.9 | 28.7 | 23.9 | - | 11.1 | 14.5 |
| FC-CLIP [55] | NeurIPS'23 | - | - | - | - | 26.8 | 16.8 | 34.1 | 44.0 | 56.2 | 14.8 | 18.2 |
| HIPIE [42] | NeurIPS'23 | - | - | - | - | 22.9 | 19.0 | 29.0 | - | - | 9.7 | 14.4 |
| SED [46] | CVPR'24 | - | - | - | - | - | - | - | - | - | 13.9 | 22.6 |
| universal model |
| X-Decoder [65] | CVPR'23 | - | - | - | - | 21.8 | 13.1 | 29.6 | 38.1 | 52.0 | 9.2 | 16.1 |
| UNINEXT* [51] | CVPR'23 | - | - | - | - | 8.9 | 14.9 | 6.4 | - | - | 1.8 | 5.8 |
| OpenSeeD [56] | ICCV'23 | - | - | - | - | 19.7 | 15.0 | 23.4 | 41.4 | 47.8 | - | - |
| DINOv [20] | CVPR'24 | - | - | 15.4 | 14.5 | 23.2 | 15.1 | 25.3 | - | - | - | - |
| OMG-Seg [21] | CVPR'24 | - | - | - | - | 27.9 | - | - | - | - | - | - |
| PSALM [58] | ECCV'24 | - | - | - | - | - | 13.9 | 24.4 | - | - | - | 14.0 |
| COSINE† this work | 34.2 | 39.1 | 17.4 | 23.3 | 28.1 | 16.7 | 35.2 | 37.1 | 53.4 | 15.2 | 19.6 |
| COSINE | | 35.2 | 40.7 | 20.3 | 25.8 | 31.0 | 21.1 | 35.7 | 42.0 | 56.1 | 15.6 | 19.2 |
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| MAttNet [54] | CVPR'18 | 56.5 | 62.4 | 51.7 | 46.7 | 52.4 | 40.1 | 47.6 | 48.6 |
| MCN [30] | CVPR'20 | 62.4 | 64.2 | 59.7 | 50.6 | 55.0 | 44.7 | 49.2 | 49.4 |
| VLT [9] | ICCV'21 | 67.5 | 70.5 | 65.2 | 56.3 | 61.0 | 50.1 | 55.0 | 57.7 |
| LAVT [53] | CVPR'22 | 72.7 | 75.8 | 68.8 | 62.1 | 68.4 | 55.1 | 61.2 | 62.1 |
| CRIS [45] | CVPR'22 | 70.5 | 73.2 | 66.1 | 62.3 | 68.1 | 53.7 | 59.9 | 60.4 |
| ReLA [25] | CVPR'23 | 73.8 | 76.5 | 70.2 | 66.0 | 71.0 | 57.7 | 65.0 | 66.0 |
| X-Decoder [65] | CVPR'23 | - | - | - | - | - | - | 64.6 | - |
| SEEM [66] | NeurIPS'23 | - | - | - | - | - | - | 65.7 | - |
| LISA [19] | CVPR'24 | 74.9 | 79.1 | 72.3 | 65.1 | 70.8 | 58.1 | 67.9 | 70.6 |
| COSINE | this work | 77.2 | 80.7 | 71.1 | 66.4 | 73.2 | 56.4 | 67.4 | 68.5 |
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| J&F | G |
| with video data |
| AOT [52] | NeurIPS'21 | 85.4 | 85.3 |
| XMem [4] | ECCV'22 | 87.7 | 85.5 |
| DEVA [5] | ICCV'23 | 86.8 | 85.5 |
| Cutie [6] | CVPR'24 | 88.8 | 86.1 |
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| Painter [43] | CVPR'23 | 34.6 | 20.6 |
| SegGPT [44] | ICCV'23 | 75.6 | 73.1 |
| SEEM [66] | NeurIPS'23 | 58.9 | - |
| DINOv [20] | CVPR'24 | 73.3 | 52.0 |
| PerSAM-F [57] | ICLR'24 | 76.1 | 46.6 |
| SINE [27] | NeurIPS'24 | 77.0 | 66.4 |
| COSINE | this work | 76.7 | 66.0 |
| COSINE-FT | | 80.2 | 70.0 |
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| ✓ | - | - | 13.2 | 7.6 | 30.2 |
| ✓ | ✓ | 27.7 | 32.1 | 17.7 | 8.1 | 30.4 |
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| ✓ | 37.8 | - | 31.0 | 21.1 | 35.7 |
| ✓ | ✓ | 43.1 | 45.9 | 31.4 | 21.3 | 36.3 |
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| 0 | COSINE (Full Model) | 27.7 | 32.1 | 17.7 | 8.1 | 30.4 |
| 1 | only DINOv2 Encoder | 27.7 | 32.0 | 9.7 | 4.2 | 18.6 |
| 2 | only CLIP Encoder | 24.4 | 28.0 | 11.4 | 3.3 | 27.0 |
| 3 | w/o Feature Blending | 24.4 | 29.0 | 9.4 | 2.6 | 26.3 |
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| 5 | w/o Prompt Refining | 27.0 | 31.2 | 16.5 | 6.6 | 30.9 |
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diff --git a/2025/Unified Video Generation via Next-Set Prediction in Continuous Domain/d5450109-c459-4393-bfbc-3a6281b76964_content_list.json b/2025/Unified Video Generation via Next-Set Prediction in Continuous Domain/d5450109-c459-4393-bfbc-3a6281b76964_content_list.json
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+ {
+ "type": "text",
+ "text": "Unified Visual Generation via Next-Set Prediction in Continuous Domain",
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+ "bbox": [
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+ "type": "text",
+ "text": "Zhanzhou Feng $^{1\\dagger}$ , Qingpei Guo $^{2}$ , Xinyu Xiao $^{2}$ , Ruihan Xu $^{1\\dagger}$ , Ming Yang $^{2}$ , Shiliang Zhang $^{1}$",
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+ "text": "$^{1}$ State Key Laboratory of Multimedia Information Processing, School of Computer Science, Peking University, Beijing, China.",
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+ "text": "$^{2}$ Ant Group",
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+ },
+ {
+ "type": "text",
+ "text": "fengzz@stu.pku.edu.cn, smilexiao2020@gmail.com, {qingpei.gqp, m.yang}@antgroup.com,",
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+ "text": "{xuruihan, slzhang.jdl}@pku.edu.cn",
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+ "type": "text",
+ "text": "Abstract",
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+ "type": "text",
+ "text": "Existing video generation strategies can be categorized into two categories, i.e., the diffusion and autoregressive (AR) methods. While AR methods achieve high efficiency by predicting the next token based on known visual cues, they generally fall short of diffusion models in terms of video quality. To bridge this gap, this paper introduces a novel continuous-domain next-set prediction strategy. Our approach groups related tokens to be generated into one single set, and simultaneously predicts their probability distributions, thereby better exploiting their spatial and temporal dependencies. Specifically, we propose two token partitioning strategies: Spatial Progressive Partitioning for image tokens and Temporal Next-Frame Partitioning for video tokens. Additionally, we construct a denoising sampler to generate outputs from the token set distribution within a continuous domain. This method unifies image and video generation under a cohesive next-set prediction framework. Experimental results indicate that our method achieves video quality comparable to recent diffusion models, while significantly reducing inference costs. Notably, our method surpasses the recent token prediction approach Emu3, in video quality despite using approximately $90\\%$ fewer parameters. Visualizations further confirm the effectiveness of our method in capturing intricate details and movements, such as water droplets and facial expressions.",
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+ "type": "text",
+ "text": "1. Introduction",
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+ "text": "Over the last few years, video generation has made remarkable progress and shows huge potentials in films, television, advertising, and gaming industries. Recent advancements, such as Sora [5], Wan2.1 [53], Hunyuan [63], and Seaweed [33] have achieved impressive results in generating",
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+ "type": "image",
+ "img_path": "images/1a39220b13b253765fc1f1a033899a8c22726ad1058ed8c9866050639d6ac8a2.jpg",
+ "image_caption": [
+ "Figure 1. Illustration of diffusion model, AR model, and our method for video generation in (a), (b), and (c), respectively. The diffusion model such as SVD [3], jointly models the entire video distribution in a continuous domain. AR model like VideoPoet [25] predicts the next-token within a limited codebook space. Differently, our method presents continuous-domain next-set prediction, which leads to a comparable video quality to diffusion with significantly faster inference speed. FVD [56] is reported on UCF-101 [47] zero-shot setting."
+ ],
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+ {
+ "type": "text",
+ "text": "realistic visual signals and following precise text instructions [76]. Diffusion models and autoregressive models (AR) are two mainstream video generation methods. Diffusion models [22, 42, 77, 78] dominate continuous data generation by progressively adding and removing noise to match target distributions, enabling sampling in a continuous domain. Inspired by the success in language [1], code [1, 29], robotic [13] and comprehensive tasks [36], AR models are introduced to visual generation by quantizing image patches into discrete tokens.",
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+ "text": "CVF",
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+ "page_idx": 0
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+ {
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "† Work done during internship at Ant Group.",
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+ "type": "page_number",
+ "text": "19427",
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+ "type": "text",
+ "text": "Diffusion and AR follow different intuitions to conduct 1) distribution prediction and 2) sampling, which are two key components in video generation. 1) For distribution prediction, diffusion model learns the joint distribution of the entire video, while AR model predicts the marginal probability of next token from visible tokens. This marginal probability in AR models is advantageous for aligning visual and language data in a shared discrete space, facilitating a unified framework for multimodal generation. 2) For the sampling, existing video generation works often couple model architecture with sampling methods, i.e., continuous sampling for diffusion and discrete sampling for AR models. VQ-based AR uses a finite codebook space, which causes quantization errors and sacrifices the continuity of generated content. Therefore, the overall video quality of AR models lags behind that of diffusion models. Fig. 1 illustrates two representative models SVD [3] for diffusion models and VideoPoet [25] for AR methods.",
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+ "text": "This works aims to improve both the inference speed and generated visual quality of decoder-only AR method, as AR shows great potentials for flexible in-context learning and leveraging well-developed infrastructure for LLMs. As shown in Fig.1(c), instead of following the next-token prediction in pervious AR works, we group related tokens to be generated into the one single set, and predicts their probability distributions simultaneously. This next set prediction ensures better visual continuity by leveraging spatial and temporal dependencies among related tokens, and reduces the required inference iterations. We further combine the AR marginal probability modeling with continuous sampling. An Llama-like [55] AR Transformer is constructed to predict continuous distributions for a set of tokens at each step given certain conditions. This continuous sampling enhances the generated visual quality by reducing quantization errors.",
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+ "text": "As for the implementation, we design the Spatial Progressive Partitioning (SPP) for image tokens partition and Temporal Next-Frame Partitioning (TNP) for video token partition to achieve token set generation. Token distributions are predicted jointly within each set, and new sets are predicted sequentially conditioned on previous sets. A small denoising model then samples stochastically from the predicted distribution, achieving diverse visual sampling following [31]. This next-set prediction unifies image and video distribution prediction into a single AR model, enabling fast inference and leveraging spatial knowledge to assist temporal modeling.",
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+ "text": "There are many efforts attempting to improve VQ tokenizers to enhance the discrete space for video generation, such as 3D-VQ tokenizer [72], lookup-free quantization [73] and residual vector quantization [66]. Unlike previous AR video methods predicting discrete categorical distribution, this work predicts continuous proba",
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+ "text": "bility distribution and proposes a novel next set prediction paradigm. Compared to recent works like MAR [31] and NOVA [11], which introduce continuous domain sampling into masked modeling, our approach adopts a decoder-only generation framework, compatible with the architecture of mainstream language models. This design is versatile and supports KV-cache [45] for acceleration. Experimental results show that the proposed method achieves significant improvements across FVD and VBench metrics, improving existing AR works in both generation fidelity and efficiency with smaller model sizes. For instance, it outperforms the EMU3 [60] in video quality with about $10\\%$ of its parameter size. Visual comparisons in the appendix video demonstrate that our method achieves smoother motion and higher dynamic quality than recent works like NOVA [11]. This work also boosts the AR model performance to be comparable to that of diffusion models, with significantly higher efficiency.",
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+ "text": "The contribution of this work can be summarized as a unified visual generation framework via next-set prediction in continuous domain. Our next-set prediction requires fewer inference steps, leading to substantially faster speed, compared to previous AR video generation methods that predict the next token. The introduction of continuous domain prediction allows the model to generate detailed contents and smooth transitions in images and videos. Our method also supports flexible in-context learning and enables unified image and video generation from text-based, image-based, and video-based inputs within a single framework. To the best of our knowledge, this is an original work to integrate the continuous domain sampling and unified next set prediction into decoder-only AR video generation. We will release all implementations to facilitate exploration of AR visual generation.",
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+ "text": "Video Generation in Discrete Domain. Though visual data are analog and continuous in nature, early works [51?] attempt to introduce discrete sampling. Large Language Models (LLM) based image generation methods can be categorized into autoregressive image generation works [9, 54, 71] and masked image modeling works [6, 7]. To leverage the power of LLM, VQ-VAE [57] and dVAE [41] quantize the image patches into discrete tokens to facilitate representing a categorical distribution. These tokens are fed into autoregressive models as if they were lexical words.",
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+ "text": "In the field of video generation, some efforts attempt to improve VQ tokenizers tailored for video data. Some early works such as VideoGPT [68] and CogVideo [23] use an image pretrained 2D VQVAE for video tokenization. MAGVIT [72] expands the 2D convolutions in VQ tokenizer to 3D convolutions with a temporal axis. Building on this, MAGVIT-v2 [73] introduces a lookup-free",
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+ "text": "19428",
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+ "type": "text",
+ "text": "quantization method that allows a much larger codebook thereby reducing quantization errors. VideoPoet [25] adopts MAGVIT-v2 [73] decoder and uses a cascade two-stage framework to generate video. VILA-U [66] utilizes an autoregressive next-token prediction framework and employs residual vector quantization across multiple depths to mitigate quantization errors. EMU3 [60] adopts next-token prediction to generate multiple modalities within a shared discrete space. Chameleon [52] pioneers a unified mixed-modal autoregressive framework that seamlessly integrates text and image understanding with generation. Though the previous AR works perform well in efficiency [15, 16] and in-context learning [6, 14], the overall generation quality is still inferior to that of continuous counterparts [42].",
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+ "text": "Video Generation in Continuous Domain. Recent advancements in image and video generation have been largely led by diffusion models [3-5, 35, 38, 42, 59, 74]. Diffusion model is initially proposed in unconditional pixel generation task [22] and has demonstrated dominant performance in generating high-resolution image content [42]. The proposal of DiTs [38] has been shifting the backbone design from U-Net architecture to transformer-based architectures. Movie Gen [39] introduces a family of large-scale models for video, image and synchronized audio generation, achieving a state-of-the-art result and pushing the boundaries of multimodal generation. Some works [18, 32, 41, 49, 50] cascade AR models with a pretrained diffusion model, using two separate networks for text and visual generation, respectively. Although these pretrained models [42] are composable, they are not trained end-to-end in a unified framework, and the visual quality largely depends on diffusion model pretraining. Recently, MAR [31] and NOVA [11] introduce continuous generation to masked modeling built on encoder-decoder architectures which lack support for KV-Cache [45] and are not directly compatible with LLMs.",
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+ "text": "In contrast to previous works, this paper proposes a next-set prediction framework equipping with continuous-domain sampling ability without relying on pretrained diffusion models. Experimental results show that the proposed method boosts the AR video generation performance to be competitive with diffusion models using lightweight framework and fast inference speed.",
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+ "text": "Given a condition $C \\coloneqq \\{x\\}$ consisting of tokens from prompt texts or images, image and video generation task can be consistently defined as generating a sequence of frames $\\{\\pmb{f}^t\\}_{t=1:T}$ , where $T = 1$ for image generation, and $T > 1$ for video generation. We denote the $t$ -th frame $\\pmb{f}^t \\coloneqq \\{x_n^t\\}_{n=1:N}$ as a sequence of tokens $x_n^t \\in \\mathbb{R}^d$ , where $N$ is the number of tokens in this frame and $d$ is the dimension.",
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+ "text": "In order to generate the sequence of $x_{n}^{t}$ , autoregressive model learns the probability distribution with a unidirectional dependency, where the probability distribution of next token is conditioned on prior generated ones. Using image generation as a simple illustration, the likelihood of typical decoder-only AR generation can be formulated as",
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+ "text": "\n$$\n\\mathrm {p} \\left(\\left\\{x _ {n} \\right\\} _ {n = 1: N} \\mid C\\right) = \\prod_ {n} ^ {N} \\mathrm {p} \\left(x _ {n} \\mid x _ {< n}, C\\right), \\tag {1}\n$$\n",
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+ "text": "where the frame ID $t$ is omitted for brevity. The above discrete next-token prediction is unable to effectively leverage the spatial and temporal dependencies among visual tokens.",
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+ "text": "We thus group related tokens into one set, and perform next set prediction under the AR framework, to pursue better quality and speed. This can be conducted by dividing target token sequence $\\{x_{n}\\}_{n = 1:N}$ into $K$ sets $\\{s^k\\}_{k = 1:K}$ where each set $s^k$ consists of multiple tokens. Image generation via next set prediction can be denoted as,",
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+ "text": "\n$$\n\\mathrm {p} \\left(\\left\\{\\boldsymbol {s} ^ {k} \\right\\} _ {k = 1: K} \\mid C\\right) = \\prod_ {k} ^ {K} \\mathrm {p} \\left(\\boldsymbol {s} ^ {k} \\mid \\boldsymbol {s} ^ {< k}, C\\right). \\tag {2}\n$$\n",
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+ "text": "Video can be generated in this pipeline by first generating the first frame $\\pmb{f}^{1} = \\{x_{n}^{1}\\}_{n = 1:N}$ following Eq. (2), then generating the subsequent frames with $T - 1$ steps, i.e.,",
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+ "text": "\n$$\n\\mathrm {p} \\left(\\left\\{\\boldsymbol {f} ^ {t} \\right\\} _ {t = 1: T} | \\boldsymbol {C}\\right) = \\prod_ {t} ^ {T} \\mathrm {p} \\left(\\boldsymbol {f} ^ {t} \\mid \\boldsymbol {f} ^ {< t}, \\boldsymbol {C}\\right). \\tag {3}\n$$\n",
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+ "text": "The above strategy groups related tokens into one single set. By grouping visually similar tokens, or temporally related tokens, it essentially leverages the spatial-temporal dependency in images and videos to improve efficiency and quality.",
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+ "text": "Proper strategy for partitioning tokens plays a crucial role in determining generation difficulty and quality. For image generation, we generate spatially adjacent image tokens as a set and iteratively increase the number of tokens in each set. For video generation, we take the tokens in the next frame as a set. The above intuitions lead to the SPP and TNP for image and video token partitions in Sec.4.2 and Sec.4.3, respectively. The next-set prediction largely reduces inference steps from the total number of tokens to the number of token sets, for example, reducing from sequence length $32 \\times 16 \\times 16 = 6272$ to $K = 63$ in our default image generation setting.",
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+ "text": "Besides the next-set prediction, we further introduce a continuous domain sampler $\\mathrm{D}(\\cdot)$ to replace the discrete categorical sampling to preserve continuity of generated contents. In contrast to the previous decoder-only AR works [25, 60] that predict a discrete categorical distribution, we train a decoder-only autoregressive networks $\\mathrm{G}_{\\theta}(\\cdot)$",
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+ "text": "19429",
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+ "img_path": "images/d28a5da6b059cc06989659d45ad4c2236564e3e92843910203170f2e0e4103fb.jpg",
+ "image_caption": [
+ "Figure 2. Overview of the video generation of our method. We take the 2nd frame generation as an example. Our method consists of two main components: the autoregressive generation model $\\mathrm{G}_{\\theta}$ and the continuous-domain sampler $\\mathrm{D}$ . $\\mathrm{G}_{\\theta}$ predicts the probability distribution $z$ of the next-set tokens based on the given condition, while $\\mathrm{D}$ performs stochastically sampling within the predicted continuous-domain distribution $z$ ."
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+ {
+ "type": "text",
+ "text": "in the continuous domain without vector quantization (VQ), where $\\theta$ denotes trainable parameters. At the $k$ -th step of image generation, $\\mathrm{G}_{\\theta}$ is fed a set of special [mask] tokens $\\{p\\}$ added with position embeddings as input and predicts the next set of continuous probability distribution tokens $\\{z\\}$ . D then samples $s^k$ from distributions $\\{z\\}$ . This process can be formulated as",
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+ "text": "\n$$\n\\boldsymbol {s} ^ {k} = \\mathrm {D} \\left(\\mathrm {G} _ {\\theta} (\\{p \\} \\mid \\boldsymbol {s} ^ {< k})\\right). \\tag {4}\n$$\n",
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+ "text": "$\\mathrm{G}_{\\theta}$ is a Llama-like [55] decoder-only AR model [48] consisting of multiple Transformer blocks, whose structure hyperparameters are given in Sec. 5.1. Notably, we use a single Transformer model as $\\mathrm{G}_{\\theta}$ for both image and video generation. The training objective aims to optimize the individual conditional probabilities of a known sequence at each step, which can be denoted as",
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+ "text": "\n$$\n\\mathcal {L} = - \\sum_ {k} ^ {K} \\sum_ {x \\in \\boldsymbol {s} ^ {k}} \\mathcal {L} (x, \\theta | \\boldsymbol {s} ^ {< k}, C), \\tag {5}\n$$\n",
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+ "type": "text",
+ "text": "where $x$ denotes a token included in the set $\\pmb{s}^k$ .",
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+ "text": "As shown in Fig. 2, the model $\\mathrm{G}_{\\theta}$ unifies image and video generation into the next set prediction autoregression. Next set prediction accelerates inference, while the continuous domain sampler enhances visual quality by alleviating quantization loss from VQ. Next section proceeds to introduce details of tokenization, token partition, and training.",
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+ "type": "text",
+ "text": "4. Methodology",
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+ "text": "4.1. Tokenization",
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+ "text": "Given text prompts or images as conditions, we first tokenize those inputs into the initial condition $C$ using visual and language tokenizers.",
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+ "text": "Visual data are analog and continuous signal in nature. In contrast to VQ tokenizers used in previous AR works [25, 60], we adopt a variational autoencoder (VAE) [42] without VQ to map each image patch to continuous representations. Continuous features preserve the inherent visual continuity, and can enhance subtle details and motion cues for generation. We adopt a 2D VAE to bypass the need for 3D tokenizers [3] following [3], and feed the output of a 2D image-based VAE directly into the AR model. The 2D VAE is computation efficient, and provides faster speed compared to 3D VAEs. Formally, the tokenized representation $\\{x\\}$ can be computed as",
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+ "text": "\n$$\n\\{x \\} = E (I), \\tag {6}\n$$\n",
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+ "type": "text",
+ "text": "where $E(\\cdot)$ is the VAE encoder, and $I$ denotes an image in the pixel space.",
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+ "text": "The language modality is retained their natural discrete representation. A text prompt is encoded into a 1024-dimensions latent space using the popular CLIP [40] text encoder. Text embedding is not the primary focus of this work, thus we selected CLIP mainly for its lightweight model and efficiency, which reduces GPU memory usage and inference time.",
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+ "text": "4.2. Spatial Progressive Partitioning (SPP)",
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+ "text": "The intuition of SPP is to generate highly similar contents in parallel, thereby to reduce the required inference iterations. Visual content exhibits locality, where adjacent regions are related and share common cues. We thus partition neighboring tokens into one set to leverage such spatial dependency. Additionally, different generation stages present varying levels of difficulty. As few visual clues available at the start, generating too many tokens simultaneously may cause semantic conflicts between visual contents. Setting a small number of tokens in each set is beneficial for lowering generation difficulty and improving quality in the initial AR steps. We thus progressively increase the number of tokens in each set.",
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+ "text": "Since it is not feasible to identify which tokens will be similar before generation, we leverage the spatial locality of images and group spatially adjacent tokens into a set. Following the raster-scan order, we first arrange image tokens into a sequence. Specifically, neighboring image tokens are grouped into one set, and the number of tokens in each set increases following a sine curve. A sine curve steadily increases the set size, also prevents generating too many tokens in later steps. The number of tokens in set $s^k$ is deter",
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+ "type": "text",
+ "text": "mined by",
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+ "text": "\n$$\nm ^ {k} = \\left\\lfloor \\alpha \\cdot \\sin \\left(\\frac {k \\cdot \\pi}{2 K}\\right) \\right\\rfloor , \\tag {7}\n$$\n",
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+ "type": "text",
+ "text": "where $\\lfloor \\cdot \\rfloor$ denotes the floor function, and $\\alpha$ is a constant determined by the number of tokens $N$ and the number of sets $K$ as",
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+ "type": "equation",
+ "text": "\n$$\n\\alpha = \\frac {N}{\\sum_ {k = 1} ^ {K} \\sin \\frac {k \\cdot \\pi}{2 K}}. \\tag {8}\n$$\n",
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+ "text": "Since $K$ is typically smaller than $N$ , e.g., $K = 32$ and $N = 196$ , this formulation ensures sine increasing trend and the sum of tokens across all sets equals to $N$ .",
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+ "text": "The image sequence is surrounded with specific begin-of-image ([BOI]) and end-of-image ([EOI]) tokens. Once the [BOI] token along with subsequent mask tokens are fed into the network, the next-set masked image generation process begins. Similarly, the [EOI] token signifies the end of this process.",
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+ "type": "text",
+ "text": "4.3. Temporal Next-frame Partitioning (TNP)",
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+ "type": "text",
+ "text": "This part explains the partition of token sets for video generation. Human typically perceive the world in a linear temporal sequence, focusing on what happens next. Making token set prediction in chronological order aligns with how humans observe and predict physical world dynamics. Given frames $\\pmb{f}^{| Model | Type | #params | FID ↓ | IS ↑ |
| MaskGIT [6] | Masked | 227M | 7.32 | 156.0 |
| RCG [30] | Masked | 502M | 3.49 | 215.5 |
| U-ViT-H[2] | Diff | 501M | 2.29 | 278.2 |
| DiT-XL[38] | Diff | 675M | 2.27 | 278.2 |
| ViTVQ [70] | AR | 1.7B | 4.17 | 175.1 |
| VAR-d24 [54] | AR | 1.0B | 2.09 | 312.09 |
| MAR-H [31] | AR | 943M | 1.55 | 303.7 |
| Ours | AR | 775M | 2.07 | 311.7 |
",
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+ "text": "5. Experiment",
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+ "text": "5.1. Experiment Setup",
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+ "text": "Dataset. For text-to-image training, we use 1.26M images from ImageNet-1K [12] with resolution of $512 \\times 512$ , with description of class labels as captions. For text-to-video generation, the model is trained on approximately 6M higher-quality samples [26] from Pandas-70M [10] data, finetuned on high-quality in-house text-video pairs.",
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+ "text": "Implementation details. The publicly available VAE tokenizers provided by LDM [42] is used to encode each image patch. The VAE encoder downsamples the image resolution by a factor of 16, generating a latent dimension of 16. Following DiT [38], we patchify latent representation using a patch size of $2 \\times 2$ . The latent representation is then projected through a linear layer to match the dimension of the Transformer. We train a base model (343M) and a larger model (775M), which respectively consist of 24 and 36 Transformer blocks, with a width of 1024 and 1280. Their corresponding denoising samplers D consist of 6 or 12 MLPs blocks with a width of 1024 or 1536. Sampling process 100 and 1000 denoising steps for training and inference, respectively, following [31, 37]. Target video clip is provided at a size of $32 \\times 512 \\times 512$ . By default, the number of image sets $K$ is set to 32.",
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+ "text": "Training is conducted on four nodes, each equipped with 8 NVIDIA H800 GPUs. To accelerate convergence, the model is first trained on text-to-image task using ImageNet-1K data for 800 epochs from scratch. We then transfer the weights for text-to-video training for 25 epochs. Across all experiments, the AdamW optimizer [34] is used with a weight decay of 0.02 and a base learning rate of 1e-4.",
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+ "text": "Evaluation protocol includes widely used metrics such as Fréchet Image Distance (FID) [20] for image generation, and Fréchet Video Distance (FVD) [56], CLIP similarity score (CLIPSIM) [64], Inception Score (IS) [44], along with a comprehensive toolkit VBench [24] for evaluating video generation performance. We employ a zero-shot generation evaluation protocol, where the model has not been trained on the data of target benchmarks. Evaluation benchmark includes text-to-video generation on ImageNet",
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+ "image_caption": [
+ "Text condition: A red apple covered in water droplets on a dark background."
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+ "Text condition: Underwater circular water wave appears in a clear sea."
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+ "img_path": "images/5777e328aaefa962903963f51f61119dd7476540409c281575049ebf50a15091.jpg",
+ "image_caption": [
+ "Text condition: Magnificent scenery of the dam."
+ ],
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+ {
+ "type": "image",
+ "img_path": "images/d379010a45298cb90c876da89d69c132851cb9e2591649a5993069a10a699c2d.jpg",
+ "image_caption": [
+ "Figure 3. Text-to-image generation. For each text condition, we show four examples to show the diversity of output."
+ ],
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+ {
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+ "img_path": "images/773015140dce04950346918c9f15b819e361866fb55c082c7dc3763f27c74a3f.jpg",
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+ "text": "1K [12] and text-to-video generation on MSR-VTT [67] and UCF-101 [47]. The results are reported with classifier-free guidance (CFG) [21]. Note that the higher CLIPSIM and IS (indicated as $\\uparrow$ ) and lower FID and FVD (indicated as $\\downarrow$ ) mean better performance.",
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+ "type": "text",
+ "text": "5.2. Main Results",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Image generation. Table 1 compares our method with Masked image modeling (MIM) [6, 30], diffusion models [2, 38] and autoregressive (AR) models [31, 54]. The results demonstrate that our method shows comparable performance with recent works in both visual quality and model compactness. Our approach also outperforms recent AR models such as VAR [54] in these two aspects.",
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+ "text": "Video generation. We conduct a zero-shot comparison with recent open source and proprietary text-to-video models on widely used MSR-VTT [67] and UCF-101 [47] benchmarks in Table 2. As shown in the table, our method demonstrates highly competitive results compared to other diffusion models on FVD. Our method improves the AR model in both quality and efficiency. For example, compared to VideoPoet [25], we achieve better FVD scores (247 vs. 355 on UCF-101) with a much smaller model size (0.2B vs. 8B) and lower latency (1.1s vs. 2.0s per frame). Additionally, our method shows a significant advantage in IS (41.47 vs. 38.44), verifying that the continuous-domain sampler is capable of generating diverse video. Average frame generation latency is measured on a single NVIDIA A100 GPU with $32 \\times 512 \\times 512$ video size. The results show that our method generates better prediction distribution and enhances inference efficiency.",
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+ "text": "19432",
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+ "type": "table",
+ "img_path": "images/c5b54bd4e2f21b21a70f127a839f563cec594858dd6d6a7e7ddd878621cd6771.jpg",
+ "table_caption": [
+ "Table 2. Video generation metrics on MSR-VTT [67] and UCF-101 [47] benchmarks. Latency is measure on a NVIDIA A100. † indicates that latency was measured using the official code. ↑ and ↓ denote higher or lower is better."
+ ],
+ "table_footnote": [],
+ "table_body": "| Model | Venue | MSR-VTT [67] | UCF-101 [47] | Type | #params | Latency ↓ (s/frame) |
| CLIPSIM ↑ | FVD ↓ | FVD ↓ | IS ↑ |
| Make-A-Video[46] | 2023 ICLR | 0.3049 | - | 367 | 33.00 | Diff | 9.6B | - |
| CogVideo[23] | 2023 ICLR | 0.2631 | 1294 | 702 | 25.27 | DIff | - | - |
| Video LDM[4] | 2023 CVPR | 0.2929 | - | 551 | 33.45 | DIff | - | - |
| SVD [3] | 2023 arxiv | - | - | 242 | - | Diff | 1521M | \\( 1.9^{\\dagger} \\) |
| InternVid[62] | 2024 ICLR | 0.2951 | - | 617 | 21.04 | DIff | - | - |
| Videofactory[59] | 2024 Open. | 0.3005 | - | 410 | - | Diff | 1601M | - |
| Show-1[74] | 2024 IJCV | 0.3072 | 538 | 394 | 35.42 | Diff | - | - |
| NUWA [65] | 2022 ECCV | 0.2439 | - | - | - | AR | - | - |
| TATS [17] | 2022 ECCV | - | - | 420 | 57.63 | AR | - | - |
| VideoPoet [25] | 2024 ICML | 0.3049 | 213 | 355 | 38.44 | AR | 8B | 2.0 |
| Ours | 2025 ICCV | 0.2942 | 197 | 247 | 39.13 | AR | 343M | 1.1 |
| Ours | 2025 ICCV | 0.3092 | 182 | 204 | 41.47 | AR | 775M | 1.6 |
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+ "img_path": "images/3313fa740d6384da44ec0089a98524b05a02f02233f84a387a3934a43cb922a9.jpg",
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+ "Table 3. Comparison with recent text-to-video models on VBench [24]. Due to space limitations, we selected 9 out of the 16 evaluation dimensions. The horizontal line separates Diffusion models and AR models. Higher scores reflect better performance."
+ ],
+ "table_footnote": [],
+ "table_body": "| Models | Temporal Quality | Frame Quality | Condition Consist. | #params. | Average score |
| Motion smooth. | Dynamic degree | Subject consist. | Temporal flickering | Aesthetic quality | Image quality | Multiple objects | Human action | Object class |
| ModelScope [58] | 95.79 | 66.39 | 89.87 | 98.28 | 56.39 | 58.57 | 38.98 | 92.40 | 82.25 | 1.7B | 75.44 |
| LaVie [61] | 96.38 | 49.72 | 91.41 | 98.30 | 54.94 | 59.78 | 33.32 | 96.80 | 91.82 | 3B | 74.72 |
| Show-1 Zhang et al. [74] | 98.24 | 44.44 | 95.53 | 99.12 | 57.35 | 58.66 | 45.47 | 95.60 | 93.07 | 4B | 76.39 |
| OpenSora V1.2 [75] | 98.50 | 42.39 | 96.75 | 99.12 | 56.85 | 60.94 | 51.83 | 91.20 | 82.22 | 1B | 75.53 |
| AnimateDiff-V2 [19] | 97.76 | 40.83 | 95.30 | 98.75 | 67.16 | 70.10 | 36.88 | 92.60 | 90.90 | 1B | 76.70 |
| Gen-2 [43] | 99.58 | 18.89 | 97.61 | 99.56 | 66.96 | 67.42 | 55.47 | 89.20 | 90.92 | - | 76.18 |
| Pika [27] | 99.50 | 47.50 | 96.94 | 99.74 | 62.04 | 61.87 | 43.08 | 86.20 | 88.72 | - | 76.18 |
| VideoCrafter-2.0 [8] | 97.73 | 42.50 | 96.85 | 98.93 | 63.13 | 67.22 | 40.66 | 95.00 | 92.55 | 2B | 77.17 |
| T2V-Turbo (VC2) [28] | 97.34 | 49.17 | 96.28 | 97.48 | 63.04 | 72.47 | 54.65 | 95.20 | 93.96 | 2B | 79.95 |
| CogVideoX-2B [69] | 96.92 | 70.97 | 96.23 | 98.89 | 61.98 | 61.68 | 62.11 | 99.40 | 85.23 | 2B | 81.49 |
| Gen-3 [43] | 99.23 | 60.14 | 97.10 | 98.61 | 63.34 | 66.82 | 53.64 | 96.40 | 87.81 | - | 80.34 |
| Emu3 [60] | 98.93 | 79.27 | 95.32 | 98.57 | 59.64 | 62.63 | 44.64 | 77.71 | 86.17 | 8B | 78.10 |
| NOVA [11] | - | - | - | - | 54.52 | - | 73.46 | 91.20 | 91.36 | 0.6B | 78.48 |
| Ours | 98.67 | 54.21 | 96.73 | 98.92 | 63.93 | 67.76 | 52.19 | 93.86 | 89.57 | 0.8B | 79.54 |
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+ "text": "Following [60], we evaluate the text-to-video generation on VBench [24] across three key dimensions: temporal quality, frame quality, and condition consistency in Table 3. VBench provides a comprehensive toolkit for video generation assessment. Due to space constraints, we report 9 representative metrics and their average scores. For temporal quality, our method achieves scores of 98.67, 96.73, and 98.92 in motion smoothness, object consistency, and temporal flickering, respectively, matching the performance of state-of-the-art diffusion methods. In the dynamics degree metric, which measures the presence of large movements, our model obtains the score of 54.21, indicating sufficiently dynamic contents are generated. Compare to the larger EMU3 [25], our model demonstrates a strong performance-to-efficiency trade-off. It achieves comparable or better results than those of open-source diffusion models, with a smaller model size, i.e., 0.8B.",
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+ "text": "Discussion. The above results indicate our model outperforms discrete AR models, and achieves competitive performance with diffusion models with fewer parameters and",
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+ "text": "faster inference speed. This demonstrates that, with the proposed continuous-domain sampling and next-set generation strategies, AR methods have strong potentials for versatile in-context learning and unified language-visual generation.",
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+ "text": "5.3. Qualitative Results",
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+ "text": "High-quality image generation. Fig. 3 shows results of text-to-image generation. We generate four samples for each text condition. Our method produces diverse contents under the same prompt, such as both whole apple and close-up shots. The results highlight our method's ability to capture fine details, like water droplets on the apple and flowing waves in the $1^{st}$ and $2^{nd}$ cases. Additionally, our method can generate realistic lighting effects, such as the reflection of the sky on the water in the case of scenery of the dam.",
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+ "text": "High-quality video generation. Fig. 4 shows the results for text-to-video and image-to-video generation tasks. Our method effectively models smooth temporal dependencies between frames. In text-to-video examples (a), the first aerial view sequence shows a yard gradually enlarging as",
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+ "image_caption": [
+ "Text condition: Aerial video of the lush greenery forest and the ranger yard.",
+ "Text condition: The Cathedral is illuminated as fireworks explode overhead.",
+ "Image condition"
+ ],
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+ "image_caption": [
+ "Text condition: Man with a beard and black hat sits in room, speaking to the camera."
+ ],
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+ "image_caption": [
+ "(a) Text-to-video generation",
+ "Figure 4. Generation results on text-to-video and image-to-video tasks."
+ ],
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+ "image_caption": [],
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+ {
+ "type": "image",
+ "img_path": "images/6f29393016157f89203c4bd44af6d5382d47055211b7b9195c273490c1d20ca1.jpg",
+ "image_caption": [
+ "(b) Image-to-video generation"
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+ "img_path": "images/ccd4e63372288d233101f2ffed882a3a5a981bf9c5284cebab83f14b63c8a9f6.jpg",
+ "table_caption": [
+ "Table 4. The effect of discrete and continuous-domain tokenizers. The tokenizers are provided by publicly available LDM [42]."
+ ],
+ "table_footnote": [],
+ "table_body": "| Tokenizer | FID ↓ | FVD ↓ | Temporal flickering ↑ | Motion smoothness↑ |
| VQ-VAE [42] | 2.49 | 314 | 97.87 | 97.85 |
| VAE [42] | 2.05 | 247 | 98.92 | 98.67 |
",
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+ "text": "the camera zooms in until it exits the frame. The second example captures a smooth fireworks show from liftoff to explosion. The third showcases a man speaking to the camera with realistic facial expressions, accessories, and natural movements like blinking and head-turning. In imaged-to-video examples (b), key visual elements are consistently preserved, such as the animated panda's facial expressions, the Husky's head-turning motion, and the aerial view of a winter farmland.",
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+ "text": "More generated videos and images, along with visual comparisons to related works, including OpenSora-1.1B [75], CogVideoX-2B [69], ModelScope-1.7B [58], and NOVA [11] are presented in the supplementary materials. These visual results demonstrate that our method generates high-quality contents and smooth motions under the AR framework.",
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+ "text": "5.4. Ablation Study",
+ "text_level": 1,
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+ "text": "Compare to VQ tokenizer. Previous AR video generation methods [25, 60] use a VQ tokenizer for discretizing video signals. Tab. 4 compares the impact of a continuous-domain tokenizer and sampler versus those of discrete VQ on FID (ImageNet), FVD (UCF-101), and VBench metrics (temporal flickering, motion smoothness). The continuous-domain tokenizer improves FID in image generation and shows more substantial gains in video metrics, enhancing FVD, temporal flickering, and motion smoothness by 64, $1.05\\%$ , and $0.82\\%$ , respectively. These demonstrate that continuous-domain sampling benefits both image and video",
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+ "table_caption": [
+ "Table 5. Impact of number $K$ on ImageNet benchmark."
+ ],
+ "table_footnote": [],
+ "table_body": "| K | FID ↓ | IS ↑ | Latency (s) ↓ |
| 8 | 4.46 | 224.7 | 6.45 |
| 16 | 2.73 | 278.2 | 9.92 |
| 32 | 2.05 | 302.4 | 13.11 |
| 64 | 1.86 | 309.2 | 20.08 |
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+ "text": "generation, especially for video tasks.",
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+ "text": "Number of sets. We partition image patches into $K$ sets, and predict each set simultaneously. Tab. 5 compares the effects of different $K$ values on image generation. The inference speed is mainly controlled by $K$ , the number of sets. Smaller values, such as $K = 8$ , reduce inference latency to 6.45 seconds but degrade the output quality. We choose $K = 32$ as a reasonable trade-off between performance and inference speed.",
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+ "text": "6. Conclusion",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "This paper introduces a unified continuous-domain autoregressive model for the image and video generation. Our method consists of two components: 1) an AR model predicting token distributions in the continuous domain. The SPP and TNP are introduced for partitioning image and video tokens, respectively. 2) A lightweight denoising sampler stochastically sampling tokens from the predicted distribution. In contrast to diffusion models jointly modeling all tokens, or prior AR methods with VQ tokenization and next-token prediction, our approach models the marginal distribution with continuous next-set prediction. Experiments show competitive FID, FVD, and IS scores to diffusion models on multiple benchmarks, with fewer than 1B parameters and a per-frame generation time of 1.1 seconds. VBench results and visualizations further validate the model's capability to generate subtle details and movements.",
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+ {
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+ "text": "Acknowledgement This work is supported in part by Grant No. 2023-JCJQ-LA-001-088, in part by Natural Science Foundation of China under Grant No. U20B2052, 61936011, in part by the Okawa Foundation Research Award, in part by Ant Group Research Intern Program, in part by the Ant Group Research Fund, and in part by the Kunpeng&Ascend Center of Excellence, Peking University.",
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+ {
+ "type": "text",
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new file mode 100644
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+ "content": "Existing video generation strategies can be categorized into two categories, i.e., the diffusion and autoregressive (AR) methods. While AR methods achieve high efficiency by predicting the next token based on known visual cues, they generally fall short of diffusion models in terms of video quality. To bridge this gap, this paper introduces a novel continuous-domain next-set prediction strategy. Our approach groups related tokens to be generated into one single set, and simultaneously predicts their probability distributions, thereby better exploiting their spatial and temporal dependencies. Specifically, we propose two token partitioning strategies: Spatial Progressive Partitioning for image tokens and Temporal Next-Frame Partitioning for video tokens. Additionally, we construct a denoising sampler to generate outputs from the token set distribution within a continuous domain. This method unifies image and video generation under a cohesive next-set prediction framework. Experimental results indicate that our method achieves video quality comparable to recent diffusion models, while significantly reducing inference costs. Notably, our method surpasses the recent token prediction approach Emu3, in video quality despite using approximately \\(90\\%\\) fewer parameters. Visualizations further confirm the effectiveness of our method in capturing intricate details and movements, such as water droplets and facial expressions."
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+ "content": "Figure 1. Illustration of diffusion model, AR model, and our method for video generation in (a), (b), and (c), respectively. The diffusion model such as SVD [3], jointly models the entire video distribution in a continuous domain. AR model like VideoPoet [25] predicts the next-token within a limited codebook space. Differently, our method presents continuous-domain next-set prediction, which leads to a comparable video quality to diffusion with significantly faster inference speed. FVD [56] is reported on UCF-101 [47] zero-shot setting."
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+ "content": "realistic visual signals and following precise text instructions [76]. Diffusion models and autoregressive models (AR) are two mainstream video generation methods. Diffusion models [22, 42, 77, 78] dominate continuous data generation by progressively adding and removing noise to match target distributions, enabling sampling in a continuous domain. Inspired by the success in language [1], code [1, 29], robotic [13] and comprehensive tasks [36], AR models are introduced to visual generation by quantizing image patches into discrete tokens."
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+ "content": "Diffusion and AR follow different intuitions to conduct 1) distribution prediction and 2) sampling, which are two key components in video generation. 1) For distribution prediction, diffusion model learns the joint distribution of the entire video, while AR model predicts the marginal probability of next token from visible tokens. This marginal probability in AR models is advantageous for aligning visual and language data in a shared discrete space, facilitating a unified framework for multimodal generation. 2) For the sampling, existing video generation works often couple model architecture with sampling methods, i.e., continuous sampling for diffusion and discrete sampling for AR models. VQ-based AR uses a finite codebook space, which causes quantization errors and sacrifices the continuity of generated content. Therefore, the overall video quality of AR models lags behind that of diffusion models. Fig. 1 illustrates two representative models SVD [3] for diffusion models and VideoPoet [25] for AR methods."
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+ "content": "This works aims to improve both the inference speed and generated visual quality of decoder-only AR method, as AR shows great potentials for flexible in-context learning and leveraging well-developed infrastructure for LLMs. As shown in Fig.1(c), instead of following the next-token prediction in pervious AR works, we group related tokens to be generated into the one single set, and predicts their probability distributions simultaneously. This next set prediction ensures better visual continuity by leveraging spatial and temporal dependencies among related tokens, and reduces the required inference iterations. We further combine the AR marginal probability modeling with continuous sampling. An Llama-like [55] AR Transformer is constructed to predict continuous distributions for a set of tokens at each step given certain conditions. This continuous sampling enhances the generated visual quality by reducing quantization errors."
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+ "content": "As for the implementation, we design the Spatial Progressive Partitioning (SPP) for image tokens partition and Temporal Next-Frame Partitioning (TNP) for video token partition to achieve token set generation. Token distributions are predicted jointly within each set, and new sets are predicted sequentially conditioned on previous sets. A small denoising model then samples stochastically from the predicted distribution, achieving diverse visual sampling following [31]. This next-set prediction unifies image and video distribution prediction into a single AR model, enabling fast inference and leveraging spatial knowledge to assist temporal modeling."
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+ "content": "There are many efforts attempting to improve VQ tokenizers to enhance the discrete space for video generation, such as 3D-VQ tokenizer [72], lookup-free quantization [73] and residual vector quantization [66]. Unlike previous AR video methods predicting discrete categorical distribution, this work predicts continuous proba"
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+ "content": "bility distribution and proposes a novel next set prediction paradigm. Compared to recent works like MAR [31] and NOVA [11], which introduce continuous domain sampling into masked modeling, our approach adopts a decoder-only generation framework, compatible with the architecture of mainstream language models. This design is versatile and supports KV-cache [45] for acceleration. Experimental results show that the proposed method achieves significant improvements across FVD and VBench metrics, improving existing AR works in both generation fidelity and efficiency with smaller model sizes. For instance, it outperforms the EMU3 [60] in video quality with about \\(10\\%\\) of its parameter size. Visual comparisons in the appendix video demonstrate that our method achieves smoother motion and higher dynamic quality than recent works like NOVA [11]. This work also boosts the AR model performance to be comparable to that of diffusion models, with significantly higher efficiency."
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+ "content": "The contribution of this work can be summarized as a unified visual generation framework via next-set prediction in continuous domain. Our next-set prediction requires fewer inference steps, leading to substantially faster speed, compared to previous AR video generation methods that predict the next token. The introduction of continuous domain prediction allows the model to generate detailed contents and smooth transitions in images and videos. Our method also supports flexible in-context learning and enables unified image and video generation from text-based, image-based, and video-based inputs within a single framework. To the best of our knowledge, this is an original work to integrate the continuous domain sampling and unified next set prediction into decoder-only AR video generation. We will release all implementations to facilitate exploration of AR visual generation."
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+ "content": "Video Generation in Discrete Domain. Though visual data are analog and continuous in nature, early works [51?] attempt to introduce discrete sampling. Large Language Models (LLM) based image generation methods can be categorized into autoregressive image generation works [9, 54, 71] and masked image modeling works [6, 7]. To leverage the power of LLM, VQ-VAE [57] and dVAE [41] quantize the image patches into discrete tokens to facilitate representing a categorical distribution. These tokens are fed into autoregressive models as if they were lexical words."
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+ "content": "In the field of video generation, some efforts attempt to improve VQ tokenizers tailored for video data. Some early works such as VideoGPT [68] and CogVideo [23] use an image pretrained 2D VQVAE for video tokenization. MAGVIT [72] expands the 2D convolutions in VQ tokenizer to 3D convolutions with a temporal axis. Building on this, MAGVIT-v2 [73] introduces a lookup-free"
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+ "content": "quantization method that allows a much larger codebook thereby reducing quantization errors. VideoPoet [25] adopts MAGVIT-v2 [73] decoder and uses a cascade two-stage framework to generate video. VILA-U [66] utilizes an autoregressive next-token prediction framework and employs residual vector quantization across multiple depths to mitigate quantization errors. EMU3 [60] adopts next-token prediction to generate multiple modalities within a shared discrete space. Chameleon [52] pioneers a unified mixed-modal autoregressive framework that seamlessly integrates text and image understanding with generation. Though the previous AR works perform well in efficiency [15, 16] and in-context learning [6, 14], the overall generation quality is still inferior to that of continuous counterparts [42]."
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+ "type": "text",
+ "bbox": [
+ 0.093,
+ 0.304,
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+ ],
+ "angle": 0,
+ "content": "Video Generation in Continuous Domain. Recent advancements in image and video generation have been largely led by diffusion models [3-5, 35, 38, 42, 59, 74]. Diffusion model is initially proposed in unconditional pixel generation task [22] and has demonstrated dominant performance in generating high-resolution image content [42]. The proposal of DiTs [38] has been shifting the backbone design from U-Net architecture to transformer-based architectures. Movie Gen [39] introduces a family of large-scale models for video, image and synchronized audio generation, achieving a state-of-the-art result and pushing the boundaries of multimodal generation. Some works [18, 32, 41, 49, 50] cascade AR models with a pretrained diffusion model, using two separate networks for text and visual generation, respectively. Although these pretrained models [42] are composable, they are not trained end-to-end in a unified framework, and the visual quality largely depends on diffusion model pretraining. Recently, MAR [31] and NOVA [11] introduce continuous generation to masked modeling built on encoder-decoder architectures which lack support for KV-Cache [45] and are not directly compatible with LLMs."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.636,
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+ ],
+ "angle": 0,
+ "content": "In contrast to previous works, this paper proposes a next-set prediction framework equipping with continuous-domain sampling ability without relying on pretrained diffusion models. Experimental results show that the proposed method boosts the AR video generation performance to be competitive with diffusion models using lightweight framework and fast inference speed."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3. Formulation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Given a condition \\( C \\coloneqq \\{x\\} \\) consisting of tokens from prompt texts or images, image and video generation task can be consistently defined as generating a sequence of frames \\( \\{\\pmb{f}^t\\}_{t=1:T} \\), where \\( T = 1 \\) for image generation, and \\( T > 1 \\) for video generation. We denote the \\( t \\)-th frame \\( \\pmb{f}^t \\coloneqq \\{x_n^t\\}_{n=1:N} \\) as a sequence of tokens \\( x_n^t \\in \\mathbb{R}^d \\), where \\( N \\) is the number of tokens in this frame and \\( d \\) is the dimension."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
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+ ],
+ "angle": 0,
+ "content": "In order to generate the sequence of \\( x_{n}^{t} \\), autoregressive model learns the probability distribution with a unidirectional dependency, where the probability distribution of next token is conditioned on prior generated ones. Using image generation as a simple illustration, the likelihood of typical decoder-only AR generation can be formulated as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.576,
+ 0.194,
+ 0.905,
+ 0.235
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {p} \\left(\\left\\{x _ {n} \\right\\} _ {n = 1: N} \\mid C\\right) = \\prod_ {n} ^ {N} \\mathrm {p} \\left(x _ {n} \\mid x _ {< n}, C\\right), \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.245,
+ 0.905,
+ 0.291
+ ],
+ "angle": 0,
+ "content": "where the frame ID \\( t \\) is omitted for brevity. The above discrete next-token prediction is unable to effectively leverage the spatial and temporal dependencies among visual tokens."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "We thus group related tokens into one set, and perform next set prediction under the AR framework, to pursue better quality and speed. This can be conducted by dividing target token sequence \\(\\{x_{n}\\}_{n = 1:N}\\) into \\(K\\) sets \\(\\{s^k\\}_{k = 1:K}\\) where each set \\(s^k\\) consists of multiple tokens. Image generation via next set prediction can be denoted as,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.578,
+ 0.393,
+ 0.905,
+ 0.435
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {p} \\left(\\left\\{\\boldsymbol {s} ^ {k} \\right\\} _ {k = 1: K} \\mid C\\right) = \\prod_ {k} ^ {K} \\mathrm {p} \\left(\\boldsymbol {s} ^ {k} \\mid \\boldsymbol {s} ^ {< k}, C\\right). \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.445,
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+ ],
+ "angle": 0,
+ "content": "Video can be generated in this pipeline by first generating the first frame \\( \\pmb{f}^{1} = \\{x_{n}^{1}\\}_{n = 1:N} \\) following Eq. (2), then generating the subsequent frames with \\( T - 1 \\) steps, i.e.,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.58,
+ 0.502,
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+ 0.543
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {p} \\left(\\left\\{\\boldsymbol {f} ^ {t} \\right\\} _ {t = 1: T} | \\boldsymbol {C}\\right) = \\prod_ {t} ^ {T} \\mathrm {p} \\left(\\boldsymbol {f} ^ {t} \\mid \\boldsymbol {f} ^ {< t}, \\boldsymbol {C}\\right). \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.554,
+ 0.905,
+ 0.629
+ ],
+ "angle": 0,
+ "content": "The above strategy groups related tokens into one single set. By grouping visually similar tokens, or temporally related tokens, it essentially leverages the spatial-temporal dependency in images and videos to improve efficiency and quality."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.63,
+ 0.906,
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+ ],
+ "angle": 0,
+ "content": "Proper strategy for partitioning tokens plays a crucial role in determining generation difficulty and quality. For image generation, we generate spatially adjacent image tokens as a set and iteratively increase the number of tokens in each set. For video generation, we take the tokens in the next frame as a set. The above intuitions lead to the SPP and TNP for image and video token partitions in Sec.4.2 and Sec.4.3, respectively. The next-set prediction largely reduces inference steps from the total number of tokens to the number of token sets, for example, reducing from sequence length \\( 32 \\times 16 \\times 16 = 6272 \\) to \\( K = 63 \\) in our default image generation setting."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.811,
+ 0.906,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Besides the next-set prediction, we further introduce a continuous domain sampler \\(\\mathrm{D}(\\cdot)\\) to replace the discrete categorical sampling to preserve continuity of generated contents. In contrast to the previous decoder-only AR works [25, 60] that predict a discrete categorical distribution, we train a decoder-only autoregressive networks \\(\\mathrm{G}_{\\theta}(\\cdot)\\)"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "19429"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.094,
+ 0.088,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.337,
+ 0.485,
+ 0.435
+ ],
+ "angle": 0,
+ "content": "Figure 2. Overview of the video generation of our method. We take the 2nd frame generation as an example. Our method consists of two main components: the autoregressive generation model \\( \\mathrm{G}_{\\theta} \\) and the continuous-domain sampler \\( \\mathrm{D} \\). \\( \\mathrm{G}_{\\theta} \\) predicts the probability distribution \\( z \\) of the next-set tokens based on the given condition, while \\( \\mathrm{D} \\) performs stochastically sampling within the predicted continuous-domain distribution \\( z \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.464,
+ 0.484,
+ 0.569
+ ],
+ "angle": 0,
+ "content": "in the continuous domain without vector quantization (VQ), where \\(\\theta\\) denotes trainable parameters. At the \\(k\\)-th step of image generation, \\(\\mathrm{G}_{\\theta}\\) is fed a set of special [mask] tokens \\(\\{p\\}\\) added with position embeddings as input and predicts the next set of continuous probability distribution tokens \\(\\{z\\}\\). D then samples \\(s^k\\) from distributions \\(\\{z\\}\\). This process can be formulated as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.202,
+ 0.582,
+ 0.483,
+ 0.601
+ ],
+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {s} ^ {k} = \\mathrm {D} \\left(\\mathrm {G} _ {\\theta} (\\{p \\} \\mid \\boldsymbol {s} ^ {< k})\\right). \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.617,
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+ ],
+ "angle": 0,
+ "content": "\\(\\mathrm{G}_{\\theta}\\) is a Llama-like [55] decoder-only AR model [48] consisting of multiple Transformer blocks, whose structure hyperparameters are given in Sec. 5.1. Notably, we use a single Transformer model as \\(\\mathrm{G}_{\\theta}\\) for both image and video generation. The training objective aims to optimize the individual conditional probabilities of a known sequence at each step, which can be denoted as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.177,
+ 0.74,
+ 0.483,
+ 0.782
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} = - \\sum_ {k} ^ {K} \\sum_ {x \\in \\boldsymbol {s} ^ {k}} \\mathcal {L} (x, \\theta | \\boldsymbol {s} ^ {< k}, C), \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.794,
+ 0.403,
+ 0.809
+ ],
+ "angle": 0,
+ "content": "where \\(x\\) denotes a token included in the set \\(\\pmb{s}^k\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.811,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "As shown in Fig. 2, the model \\( \\mathrm{G}_{\\theta} \\) unifies image and video generation into the next set prediction autoregression. Next set prediction accelerates inference, while the continuous domain sampler enhances visual quality by alleviating quantization loss from VQ. Next section proceeds to introduce details of tokenization, token partition, and training."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "4. Methodology"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "4.1. Tokenization"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.137,
+ 0.905,
+ 0.182
+ ],
+ "angle": 0,
+ "content": "Given text prompts or images as conditions, we first tokenize those inputs into the initial condition \\( C \\) using visual and language tokenizers."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.183,
+ 0.907,
+ 0.364
+ ],
+ "angle": 0,
+ "content": "Visual data are analog and continuous signal in nature. In contrast to VQ tokenizers used in previous AR works [25, 60], we adopt a variational autoencoder (VAE) [42] without VQ to map each image patch to continuous representations. Continuous features preserve the inherent visual continuity, and can enhance subtle details and motion cues for generation. We adopt a 2D VAE to bypass the need for 3D tokenizers [3] following [3], and feed the output of a 2D image-based VAE directly into the AR model. The 2D VAE is computation efficient, and provides faster speed compared to 3D VAEs. Formally, the tokenized representation \\(\\{x\\}\\) can be computed as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.665,
+ 0.375,
+ 0.905,
+ 0.391
+ ],
+ "angle": 0,
+ "content": "\\[\n\\{x \\} = E (I), \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.402,
+ 0.905,
+ 0.432
+ ],
+ "angle": 0,
+ "content": "where \\( E(\\cdot) \\) is the VAE encoder, and \\( I \\) denotes an image in the pixel space."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.433,
+ 0.906,
+ 0.537
+ ],
+ "angle": 0,
+ "content": "The language modality is retained their natural discrete representation. A text prompt is encoded into a 1024-dimensions latent space using the popular CLIP [40] text encoder. Text embedding is not the primary focus of this work, thus we selected CLIP mainly for its lightweight model and efficiency, which reduces GPU memory usage and inference time."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Spatial Progressive Partitioning (SPP)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.569,
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+ ],
+ "angle": 0,
+ "content": "The intuition of SPP is to generate highly similar contents in parallel, thereby to reduce the required inference iterations. Visual content exhibits locality, where adjacent regions are related and share common cues. We thus partition neighboring tokens into one set to leverage such spatial dependency. Additionally, different generation stages present varying levels of difficulty. As few visual clues available at the start, generating too many tokens simultaneously may cause semantic conflicts between visual contents. Setting a small number of tokens in each set is beneficial for lowering generation difficulty and improving quality in the initial AR steps. We thus progressively increase the number of tokens in each set."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.765,
+ 0.909,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Since it is not feasible to identify which tokens will be similar before generation, we leverage the spatial locality of images and group spatially adjacent tokens into a set. Following the raster-scan order, we first arrange image tokens into a sequence. Specifically, neighboring image tokens are grouped into one set, and the number of tokens in each set increases following a sine curve. A sine curve steadily increases the set size, also prevents generating too many tokens in later steps. The number of tokens in set \\( s^k \\) is deter"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "19430"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.092,
+ 0.158,
+ 0.106
+ ],
+ "angle": 0,
+ "content": "mined by"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.208,
+ 0.106,
+ 0.483,
+ 0.137
+ ],
+ "angle": 0,
+ "content": "\\[\nm ^ {k} = \\left\\lfloor \\alpha \\cdot \\sin \\left(\\frac {k \\cdot \\pi}{2 K}\\right) \\right\\rfloor , \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.142,
+ 0.483,
+ 0.185
+ ],
+ "angle": 0,
+ "content": "where \\(\\lfloor \\cdot \\rfloor\\) denotes the floor function, and \\(\\alpha\\) is a constant determined by the number of tokens \\(N\\) and the number of sets \\(K\\) as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.218,
+ 0.183,
+ 0.483,
+ 0.22
+ ],
+ "angle": 0,
+ "content": "\\[\n\\alpha = \\frac {N}{\\sum_ {k = 1} ^ {K} \\sin \\frac {k \\cdot \\pi}{2 K}}. \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.225,
+ 0.483,
+ 0.27
+ ],
+ "angle": 0,
+ "content": "Since \\( K \\) is typically smaller than \\( N \\), e.g., \\( K = 32 \\) and \\( N = 196 \\), this formulation ensures sine increasing trend and the sum of tokens across all sets equals to \\( N \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.271,
+ 0.484,
+ 0.362
+ ],
+ "angle": 0,
+ "content": "The image sequence is surrounded with specific begin-of-image ([BOI]) and end-of-image ([EOI]) tokens. Once the [BOI] token along with subsequent mask tokens are fed into the network, the next-set masked image generation process begins. Similarly, the [EOI] token signifies the end of this process."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.09,
+ 0.372,
+ 0.443,
+ 0.387
+ ],
+ "angle": 0,
+ "content": "4.3. Temporal Next-frame Partitioning (TNP)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.394,
+ 0.484,
+ 0.514
+ ],
+ "angle": 0,
+ "content": "This part explains the partition of token sets for video generation. Human typically perceive the world in a linear temporal sequence, focusing on what happens next. Making token set prediction in chronological order aligns with how humans observe and predict physical world dynamics. Given frames \\( \\pmb{f}^{| Model | Type | #params | FID ↓ | IS ↑ |
| MaskGIT [6] | Masked | 227M | 7.32 | 156.0 |
| RCG [30] | Masked | 502M | 3.49 | 215.5 |
| U-ViT-H[2] | Diff | 501M | 2.29 | 278.2 |
| DiT-XL[38] | Diff | 675M | 2.27 | 278.2 |
| ViTVQ [70] | AR | 1.7B | 4.17 | 175.1 |
| VAR-d24 [54] | AR | 1.0B | 2.09 | 312.09 |
| MAR-H [31] | AR | 943M | 1.55 | 303.7 |
| Ours | AR | 775M | 2.07 | 311.7 |
"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
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+ ],
+ "angle": 0,
+ "content": "5. Experiment"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "5.1. Experiment Setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.323,
+ 0.484,
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+ ],
+ "angle": 0,
+ "content": "Dataset. For text-to-image training, we use 1.26M images from ImageNet-1K [12] with resolution of \\(512 \\times 512\\), with description of class labels as captions. For text-to-video generation, the model is trained on approximately 6M higher-quality samples [26] from Pandas-70M [10] data, finetuned on high-quality in-house text-video pairs."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.415,
+ 0.484,
+ 0.656
+ ],
+ "angle": 0,
+ "content": "Implementation details. The publicly available VAE tokenizers provided by LDM [42] is used to encode each image patch. The VAE encoder downsamples the image resolution by a factor of 16, generating a latent dimension of 16. Following DiT [38], we patchify latent representation using a patch size of \\(2 \\times 2\\). The latent representation is then projected through a linear layer to match the dimension of the Transformer. We train a base model (343M) and a larger model (775M), which respectively consist of 24 and 36 Transformer blocks, with a width of 1024 and 1280. Their corresponding denoising samplers D consist of 6 or 12 MLPs blocks with a width of 1024 or 1536. Sampling process 100 and 1000 denoising steps for training and inference, respectively, following [31, 37]. Target video clip is provided at a size of \\(32 \\times 512 \\times 512\\). By default, the number of image sets \\(K\\) is set to 32."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Training is conducted on four nodes, each equipped with 8 NVIDIA H800 GPUs. To accelerate convergence, the model is first trained on text-to-image task using ImageNet-1K data for 800 epochs from scratch. We then transfer the weights for text-to-video training for 25 epochs. Across all experiments, the AdamW optimizer [34] is used with a weight decay of 0.02 and a base learning rate of 1e-4."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Evaluation protocol includes widely used metrics such as Fréchet Image Distance (FID) [20] for image generation, and Fréchet Video Distance (FVD) [56], CLIP similarity score (CLIPSIM) [64], Inception Score (IS) [44], along with a comprehensive toolkit VBench [24] for evaluating video generation performance. We employ a zero-shot generation evaluation protocol, where the model has not been trained on the data of target benchmarks. Evaluation benchmark includes text-to-video generation on ImageNet"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ 0.161
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
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+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Text condition: A red apple covered in water droplets on a dark background."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ 0.179,
+ 0.615,
+ 0.249
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "content": null
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+ {
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+ {
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+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ 0.253,
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+ ],
+ "angle": 0,
+ "content": "Text condition: Underwater circular water wave appears in a clear sea."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ {
+ "type": "image",
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+ "angle": 0,
+ "content": null
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+ {
+ "type": "image",
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ 0.344,
+ 0.831,
+ 0.357
+ ],
+ "angle": 0,
+ "content": "Text condition: Magnificent scenery of the dam."
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.513,
+ 0.369,
+ 0.907,
+ 0.398
+ ],
+ "angle": 0,
+ "content": "Figure 3. Text-to-image generation. For each text condition, we show four examples to show the diversity of output."
+ },
+ {
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+ "content": "1K [12] and text-to-video generation on MSR-VTT [67] and UCF-101 [47]. The results are reported with classifier-free guidance (CFG) [21]. Note that the higher CLIPSIM and IS (indicated as \\(\\uparrow\\)) and lower FID and FVD (indicated as \\(\\downarrow\\)) mean better performance."
+ },
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+ "content": "5.2. Main Results"
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+ "content": "Image generation. Table 1 compares our method with Masked image modeling (MIM) [6, 30], diffusion models [2, 38] and autoregressive (AR) models [31, 54]. The results demonstrate that our method shows comparable performance with recent works in both visual quality and model compactness. Our approach also outperforms recent AR models such as VAR [54] in these two aspects."
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+ "content": "Video generation. We conduct a zero-shot comparison with recent open source and proprietary text-to-video models on widely used MSR-VTT [67] and UCF-101 [47] benchmarks in Table 2. As shown in the table, our method demonstrates highly competitive results compared to other diffusion models on FVD. Our method improves the AR model in both quality and efficiency. For example, compared to VideoPoet [25], we achieve better FVD scores (247 vs. 355 on UCF-101) with a much smaller model size (0.2B vs. 8B) and lower latency (1.1s vs. 2.0s per frame). Additionally, our method shows a significant advantage in IS (41.47 vs. 38.44), verifying that the continuous-domain sampler is capable of generating diverse video. Average frame generation latency is measured on a single NVIDIA A100 GPU with \\(32 \\times 512 \\times 512\\) video size. The results show that our method generates better prediction distribution and enhances inference efficiency."
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+ "content": "Table 2. Video generation metrics on MSR-VTT [67] and UCF-101 [47] benchmarks. Latency is measure on a NVIDIA A100. † indicates that latency was measured using the official code. ↑ and ↓ denote higher or lower is better."
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+ "content": "| Model | Venue | MSR-VTT [67] | UCF-101 [47] | Type | #params | Latency ↓ (s/frame) |
| CLIPSIM ↑ | FVD ↓ | FVD ↓ | IS ↑ |
| Make-A-Video[46] | 2023 ICLR | 0.3049 | - | 367 | 33.00 | Diff | 9.6B | - |
| CogVideo[23] | 2023 ICLR | 0.2631 | 1294 | 702 | 25.27 | DIff | - | - |
| Video LDM[4] | 2023 CVPR | 0.2929 | - | 551 | 33.45 | DIff | - | - |
| SVD [3] | 2023 arxiv | - | - | 242 | - | Diff | 1521M | \\( 1.9^{\\dagger} \\) |
| InternVid[62] | 2024 ICLR | 0.2951 | - | 617 | 21.04 | DIff | - | - |
| Videofactory[59] | 2024 Open. | 0.3005 | - | 410 | - | Diff | 1601M | - |
| Show-1[74] | 2024 IJCV | 0.3072 | 538 | 394 | 35.42 | Diff | - | - |
| NUWA [65] | 2022 ECCV | 0.2439 | - | - | - | AR | - | - |
| TATS [17] | 2022 ECCV | - | - | 420 | 57.63 | AR | - | - |
| VideoPoet [25] | 2024 ICML | 0.3049 | 213 | 355 | 38.44 | AR | 8B | 2.0 |
| Ours | 2025 ICCV | 0.2942 | 197 | 247 | 39.13 | AR | 343M | 1.1 |
| Ours | 2025 ICCV | 0.3092 | 182 | 204 | 41.47 | AR | 775M | 1.6 |
"
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+ "content": "Table 3. Comparison with recent text-to-video models on VBench [24]. Due to space limitations, we selected 9 out of the 16 evaluation dimensions. The horizontal line separates Diffusion models and AR models. Higher scores reflect better performance."
+ },
+ {
+ "type": "table",
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+ "content": "| Models | Temporal Quality | Frame Quality | Condition Consist. | #params. | Average score |
| Motion smooth. | Dynamic degree | Subject consist. | Temporal flickering | Aesthetic quality | Image quality | Multiple objects | Human action | Object class |
| ModelScope [58] | 95.79 | 66.39 | 89.87 | 98.28 | 56.39 | 58.57 | 38.98 | 92.40 | 82.25 | 1.7B | 75.44 |
| LaVie [61] | 96.38 | 49.72 | 91.41 | 98.30 | 54.94 | 59.78 | 33.32 | 96.80 | 91.82 | 3B | 74.72 |
| Show-1 Zhang et al. [74] | 98.24 | 44.44 | 95.53 | 99.12 | 57.35 | 58.66 | 45.47 | 95.60 | 93.07 | 4B | 76.39 |
| OpenSora V1.2 [75] | 98.50 | 42.39 | 96.75 | 99.12 | 56.85 | 60.94 | 51.83 | 91.20 | 82.22 | 1B | 75.53 |
| AnimateDiff-V2 [19] | 97.76 | 40.83 | 95.30 | 98.75 | 67.16 | 70.10 | 36.88 | 92.60 | 90.90 | 1B | 76.70 |
| Gen-2 [43] | 99.58 | 18.89 | 97.61 | 99.56 | 66.96 | 67.42 | 55.47 | 89.20 | 90.92 | - | 76.18 |
| Pika [27] | 99.50 | 47.50 | 96.94 | 99.74 | 62.04 | 61.87 | 43.08 | 86.20 | 88.72 | - | 76.18 |
| VideoCrafter-2.0 [8] | 97.73 | 42.50 | 96.85 | 98.93 | 63.13 | 67.22 | 40.66 | 95.00 | 92.55 | 2B | 77.17 |
| T2V-Turbo (VC2) [28] | 97.34 | 49.17 | 96.28 | 97.48 | 63.04 | 72.47 | 54.65 | 95.20 | 93.96 | 2B | 79.95 |
| CogVideoX-2B [69] | 96.92 | 70.97 | 96.23 | 98.89 | 61.98 | 61.68 | 62.11 | 99.40 | 85.23 | 2B | 81.49 |
| Gen-3 [43] | 99.23 | 60.14 | 97.10 | 98.61 | 63.34 | 66.82 | 53.64 | 96.40 | 87.81 | - | 80.34 |
| Emu3 [60] | 98.93 | 79.27 | 95.32 | 98.57 | 59.64 | 62.63 | 44.64 | 77.71 | 86.17 | 8B | 78.10 |
| NOVA [11] | - | - | - | - | 54.52 | - | 73.46 | 91.20 | 91.36 | 0.6B | 78.48 |
| Ours | 98.67 | 54.21 | 96.73 | 98.92 | 63.93 | 67.76 | 52.19 | 93.86 | 89.57 | 0.8B | 79.54 |
"
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+ "content": "Following [60], we evaluate the text-to-video generation on VBench [24] across three key dimensions: temporal quality, frame quality, and condition consistency in Table 3. VBench provides a comprehensive toolkit for video generation assessment. Due to space constraints, we report 9 representative metrics and their average scores. For temporal quality, our method achieves scores of 98.67, 96.73, and 98.92 in motion smoothness, object consistency, and temporal flickering, respectively, matching the performance of state-of-the-art diffusion methods. In the dynamics degree metric, which measures the presence of large movements, our model obtains the score of 54.21, indicating sufficiently dynamic contents are generated. Compare to the larger EMU3 [25], our model demonstrates a strong performance-to-efficiency trade-off. It achieves comparable or better results than those of open-source diffusion models, with a smaller model size, i.e., 0.8B."
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+ "content": "Discussion. The above results indicate our model outperforms discrete AR models, and achieves competitive performance with diffusion models with fewer parameters and"
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+ "bbox": [
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+ "angle": 0,
+ "content": "faster inference speed. This demonstrates that, with the proposed continuous-domain sampling and next-set generation strategies, AR methods have strong potentials for versatile in-context learning and unified language-visual generation."
+ },
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+ "content": "5.3. Qualitative Results"
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+ "angle": 0,
+ "content": "High-quality image generation. Fig. 3 shows results of text-to-image generation. We generate four samples for each text condition. Our method produces diverse contents under the same prompt, such as both whole apple and close-up shots. The results highlight our method's ability to capture fine details, like water droplets on the apple and flowing waves in the \\(1^{st}\\) and \\(2^{nd}\\) cases. Additionally, our method can generate realistic lighting effects, such as the reflection of the sky on the water in the case of scenery of the dam."
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+ "content": "High-quality video generation. Fig. 4 shows the results for text-to-video and image-to-video generation tasks. Our method effectively models smooth temporal dependencies between frames. In text-to-video examples (a), the first aerial view sequence shows a yard gradually enlarging as"
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+ "bbox": [
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+ "content": "Text condition: Aerial video of the lush greenery forest and the ranger yard."
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+ "type": "image",
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+ "content": "Text condition: The Cathedral is illuminated as fireworks explode overhead."
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+ "content": "Text condition: Man with a beard and black hat sits in room, speaking to the camera."
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+ "content": "(a) Text-to-video generation"
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+ "content": "Image condition"
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+ "content": "(b) Image-to-video generation"
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+ "content": "Figure 4. Generation results on text-to-video and image-to-video tasks."
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+ "content": "Table 4. The effect of discrete and continuous-domain tokenizers. The tokenizers are provided by publicly available LDM [42]."
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+ "bbox": [
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+ "angle": 0,
+ "content": "| Tokenizer | FID ↓ | FVD ↓ | Temporal flickering ↑ | Motion smoothness↑ |
| VQ-VAE [42] | 2.49 | 314 | 97.87 | 97.85 |
| VAE [42] | 2.05 | 247 | 98.92 | 98.67 |
"
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+ "bbox": [
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+ "angle": 0,
+ "content": "the camera zooms in until it exits the frame. The second example captures a smooth fireworks show from liftoff to explosion. The third showcases a man speaking to the camera with realistic facial expressions, accessories, and natural movements like blinking and head-turning. In imaged-to-video examples (b), key visual elements are consistently preserved, such as the animated panda's facial expressions, the Husky's head-turning motion, and the aerial view of a winter farmland."
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+ "angle": 0,
+ "content": "More generated videos and images, along with visual comparisons to related works, including OpenSora-1.1B [75], CogVideoX-2B [69], ModelScope-1.7B [58], and NOVA [11] are presented in the supplementary materials. These visual results demonstrate that our method generates high-quality contents and smooth motions under the AR framework."
+ },
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+ "content": "5.4. Ablation Study"
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+ "angle": 0,
+ "content": "Compare to VQ tokenizer. Previous AR video generation methods [25, 60] use a VQ tokenizer for discretizing video signals. Tab. 4 compares the impact of a continuous-domain tokenizer and sampler versus those of discrete VQ on FID (ImageNet), FVD (UCF-101), and VBench metrics (temporal flickering, motion smoothness). The continuous-domain tokenizer improves FID in image generation and shows more substantial gains in video metrics, enhancing FVD, temporal flickering, and motion smoothness by 64, \\(1.05\\%\\), and \\(0.82\\%\\), respectively. These demonstrate that continuous-domain sampling benefits both image and video"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 5. Impact of number \\( K \\) on ImageNet benchmark."
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| K | FID ↓ | IS ↑ | Latency (s) ↓ |
| 8 | 4.46 | 224.7 | 6.45 |
| 16 | 2.73 | 278.2 | 9.92 |
| 32 | 2.05 | 302.4 | 13.11 |
| 64 | 1.86 | 309.2 | 20.08 |
"
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+ "angle": 0,
+ "content": "generation, especially for video tasks."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Number of sets. We partition image patches into \\( K \\) sets, and predict each set simultaneously. Tab. 5 compares the effects of different \\( K \\) values on image generation. The inference speed is mainly controlled by \\( K \\), the number of sets. Smaller values, such as \\( K = 8 \\), reduce inference latency to 6.45 seconds but degrade the output quality. We choose \\( K = 32 \\) as a reasonable trade-off between performance and inference speed."
+ },
+ {
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+ "content": "6. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This paper introduces a unified continuous-domain autoregressive model for the image and video generation. Our method consists of two components: 1) an AR model predicting token distributions in the continuous domain. The SPP and TNP are introduced for partitioning image and video tokens, respectively. 2) A lightweight denoising sampler stochastically sampling tokens from the predicted distribution. In contrast to diffusion models jointly modeling all tokens, or prior AR methods with VQ tokenization and next-token prediction, our approach models the marginal distribution with continuous next-set prediction. Experiments show competitive FID, FVD, and IS scores to diffusion models on multiple benchmarks, with fewer than 1B parameters and a per-frame generation time of 1.1 seconds. VBench results and visualizations further validate the model's capability to generate subtle details and movements."
+ },
+ {
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+ }
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+ [
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Acknowledgement This work is supported in part by Grant No. 2023-JCJQ-LA-001-088, in part by Natural Science Foundation of China under Grant No. U20B2052, 61936011, in part by the Okawa Foundation Research Award, in part by Ant Group Research Intern Program, in part by the Ant Group Research Fund, and in part by the Kunpeng&Ascend Center of Excellence, Peking University."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "References"
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+# Unified Visual Generation via Next-Set Prediction in Continuous Domain
+
+Zhanzhou Feng $^{1\dagger}$ , Qingpei Guo $^{2}$ , Xinyu Xiao $^{2}$ , Ruihan Xu $^{1\dagger}$ , Ming Yang $^{2}$ , Shiliang Zhang $^{1}$
+
+$^{1}$ State Key Laboratory of Multimedia Information Processing, School of Computer Science, Peking University, Beijing, China.
+
+$^{2}$ Ant Group
+
+fengzz@stu.pku.edu.cn, smilexiao2020@gmail.com, {qingpei.gqp, m.yang}@antgroup.com,
+
+{xuruihan, slzhang.jdl}@pku.edu.cn
+
+# Abstract
+
+Existing video generation strategies can be categorized into two categories, i.e., the diffusion and autoregressive (AR) methods. While AR methods achieve high efficiency by predicting the next token based on known visual cues, they generally fall short of diffusion models in terms of video quality. To bridge this gap, this paper introduces a novel continuous-domain next-set prediction strategy. Our approach groups related tokens to be generated into one single set, and simultaneously predicts their probability distributions, thereby better exploiting their spatial and temporal dependencies. Specifically, we propose two token partitioning strategies: Spatial Progressive Partitioning for image tokens and Temporal Next-Frame Partitioning for video tokens. Additionally, we construct a denoising sampler to generate outputs from the token set distribution within a continuous domain. This method unifies image and video generation under a cohesive next-set prediction framework. Experimental results indicate that our method achieves video quality comparable to recent diffusion models, while significantly reducing inference costs. Notably, our method surpasses the recent token prediction approach Emu3, in video quality despite using approximately $90\%$ fewer parameters. Visualizations further confirm the effectiveness of our method in capturing intricate details and movements, such as water droplets and facial expressions.
+
+# 1. Introduction
+
+Over the last few years, video generation has made remarkable progress and shows huge potentials in films, television, advertising, and gaming industries. Recent advancements, such as Sora [5], Wan2.1 [53], Hunyuan [63], and Seaweed [33] have achieved impressive results in generating
+
+
+Figure 1. Illustration of diffusion model, AR model, and our method for video generation in (a), (b), and (c), respectively. The diffusion model such as SVD [3], jointly models the entire video distribution in a continuous domain. AR model like VideoPoet [25] predicts the next-token within a limited codebook space. Differently, our method presents continuous-domain next-set prediction, which leads to a comparable video quality to diffusion with significantly faster inference speed. FVD [56] is reported on UCF-101 [47] zero-shot setting.
+
+realistic visual signals and following precise text instructions [76]. Diffusion models and autoregressive models (AR) are two mainstream video generation methods. Diffusion models [22, 42, 77, 78] dominate continuous data generation by progressively adding and removing noise to match target distributions, enabling sampling in a continuous domain. Inspired by the success in language [1], code [1, 29], robotic [13] and comprehensive tasks [36], AR models are introduced to visual generation by quantizing image patches into discrete tokens.
+
+Diffusion and AR follow different intuitions to conduct 1) distribution prediction and 2) sampling, which are two key components in video generation. 1) For distribution prediction, diffusion model learns the joint distribution of the entire video, while AR model predicts the marginal probability of next token from visible tokens. This marginal probability in AR models is advantageous for aligning visual and language data in a shared discrete space, facilitating a unified framework for multimodal generation. 2) For the sampling, existing video generation works often couple model architecture with sampling methods, i.e., continuous sampling for diffusion and discrete sampling for AR models. VQ-based AR uses a finite codebook space, which causes quantization errors and sacrifices the continuity of generated content. Therefore, the overall video quality of AR models lags behind that of diffusion models. Fig. 1 illustrates two representative models SVD [3] for diffusion models and VideoPoet [25] for AR methods.
+
+This works aims to improve both the inference speed and generated visual quality of decoder-only AR method, as AR shows great potentials for flexible in-context learning and leveraging well-developed infrastructure for LLMs. As shown in Fig.1(c), instead of following the next-token prediction in pervious AR works, we group related tokens to be generated into the one single set, and predicts their probability distributions simultaneously. This next set prediction ensures better visual continuity by leveraging spatial and temporal dependencies among related tokens, and reduces the required inference iterations. We further combine the AR marginal probability modeling with continuous sampling. An Llama-like [55] AR Transformer is constructed to predict continuous distributions for a set of tokens at each step given certain conditions. This continuous sampling enhances the generated visual quality by reducing quantization errors.
+
+As for the implementation, we design the Spatial Progressive Partitioning (SPP) for image tokens partition and Temporal Next-Frame Partitioning (TNP) for video token partition to achieve token set generation. Token distributions are predicted jointly within each set, and new sets are predicted sequentially conditioned on previous sets. A small denoising model then samples stochastically from the predicted distribution, achieving diverse visual sampling following [31]. This next-set prediction unifies image and video distribution prediction into a single AR model, enabling fast inference and leveraging spatial knowledge to assist temporal modeling.
+
+There are many efforts attempting to improve VQ tokenizers to enhance the discrete space for video generation, such as 3D-VQ tokenizer [72], lookup-free quantization [73] and residual vector quantization [66]. Unlike previous AR video methods predicting discrete categorical distribution, this work predicts continuous proba
+
+bility distribution and proposes a novel next set prediction paradigm. Compared to recent works like MAR [31] and NOVA [11], which introduce continuous domain sampling into masked modeling, our approach adopts a decoder-only generation framework, compatible with the architecture of mainstream language models. This design is versatile and supports KV-cache [45] for acceleration. Experimental results show that the proposed method achieves significant improvements across FVD and VBench metrics, improving existing AR works in both generation fidelity and efficiency with smaller model sizes. For instance, it outperforms the EMU3 [60] in video quality with about $10\%$ of its parameter size. Visual comparisons in the appendix video demonstrate that our method achieves smoother motion and higher dynamic quality than recent works like NOVA [11]. This work also boosts the AR model performance to be comparable to that of diffusion models, with significantly higher efficiency.
+
+The contribution of this work can be summarized as a unified visual generation framework via next-set prediction in continuous domain. Our next-set prediction requires fewer inference steps, leading to substantially faster speed, compared to previous AR video generation methods that predict the next token. The introduction of continuous domain prediction allows the model to generate detailed contents and smooth transitions in images and videos. Our method also supports flexible in-context learning and enables unified image and video generation from text-based, image-based, and video-based inputs within a single framework. To the best of our knowledge, this is an original work to integrate the continuous domain sampling and unified next set prediction into decoder-only AR video generation. We will release all implementations to facilitate exploration of AR visual generation.
+
+# 2. Related works
+
+Video Generation in Discrete Domain. Though visual data are analog and continuous in nature, early works [51?] attempt to introduce discrete sampling. Large Language Models (LLM) based image generation methods can be categorized into autoregressive image generation works [9, 54, 71] and masked image modeling works [6, 7]. To leverage the power of LLM, VQ-VAE [57] and dVAE [41] quantize the image patches into discrete tokens to facilitate representing a categorical distribution. These tokens are fed into autoregressive models as if they were lexical words.
+
+In the field of video generation, some efforts attempt to improve VQ tokenizers tailored for video data. Some early works such as VideoGPT [68] and CogVideo [23] use an image pretrained 2D VQVAE for video tokenization. MAGVIT [72] expands the 2D convolutions in VQ tokenizer to 3D convolutions with a temporal axis. Building on this, MAGVIT-v2 [73] introduces a lookup-free
+
+quantization method that allows a much larger codebook thereby reducing quantization errors. VideoPoet [25] adopts MAGVIT-v2 [73] decoder and uses a cascade two-stage framework to generate video. VILA-U [66] utilizes an autoregressive next-token prediction framework and employs residual vector quantization across multiple depths to mitigate quantization errors. EMU3 [60] adopts next-token prediction to generate multiple modalities within a shared discrete space. Chameleon [52] pioneers a unified mixed-modal autoregressive framework that seamlessly integrates text and image understanding with generation. Though the previous AR works perform well in efficiency [15, 16] and in-context learning [6, 14], the overall generation quality is still inferior to that of continuous counterparts [42].
+
+Video Generation in Continuous Domain. Recent advancements in image and video generation have been largely led by diffusion models [3-5, 35, 38, 42, 59, 74]. Diffusion model is initially proposed in unconditional pixel generation task [22] and has demonstrated dominant performance in generating high-resolution image content [42]. The proposal of DiTs [38] has been shifting the backbone design from U-Net architecture to transformer-based architectures. Movie Gen [39] introduces a family of large-scale models for video, image and synchronized audio generation, achieving a state-of-the-art result and pushing the boundaries of multimodal generation. Some works [18, 32, 41, 49, 50] cascade AR models with a pretrained diffusion model, using two separate networks for text and visual generation, respectively. Although these pretrained models [42] are composable, they are not trained end-to-end in a unified framework, and the visual quality largely depends on diffusion model pretraining. Recently, MAR [31] and NOVA [11] introduce continuous generation to masked modeling built on encoder-decoder architectures which lack support for KV-Cache [45] and are not directly compatible with LLMs.
+
+In contrast to previous works, this paper proposes a next-set prediction framework equipping with continuous-domain sampling ability without relying on pretrained diffusion models. Experimental results show that the proposed method boosts the AR video generation performance to be competitive with diffusion models using lightweight framework and fast inference speed.
+
+# 3. Formulation
+
+Given a condition $C \coloneqq \{x\}$ consisting of tokens from prompt texts or images, image and video generation task can be consistently defined as generating a sequence of frames $\{\pmb{f}^t\}_{t=1:T}$ , where $T = 1$ for image generation, and $T > 1$ for video generation. We denote the $t$ -th frame $\pmb{f}^t \coloneqq \{x_n^t\}_{n=1:N}$ as a sequence of tokens $x_n^t \in \mathbb{R}^d$ , where $N$ is the number of tokens in this frame and $d$ is the dimension.
+
+In order to generate the sequence of $x_{n}^{t}$ , autoregressive model learns the probability distribution with a unidirectional dependency, where the probability distribution of next token is conditioned on prior generated ones. Using image generation as a simple illustration, the likelihood of typical decoder-only AR generation can be formulated as
+
+$$
+\mathrm {p} \left(\left\{x _ {n} \right\} _ {n = 1: N} \mid C\right) = \prod_ {n} ^ {N} \mathrm {p} \left(x _ {n} \mid x _ {< n}, C\right), \tag {1}
+$$
+
+where the frame ID $t$ is omitted for brevity. The above discrete next-token prediction is unable to effectively leverage the spatial and temporal dependencies among visual tokens.
+
+We thus group related tokens into one set, and perform next set prediction under the AR framework, to pursue better quality and speed. This can be conducted by dividing target token sequence $\{x_{n}\}_{n = 1:N}$ into $K$ sets $\{s^k\}_{k = 1:K}$ where each set $s^k$ consists of multiple tokens. Image generation via next set prediction can be denoted as,
+
+$$
+\mathrm {p} \left(\left\{\boldsymbol {s} ^ {k} \right\} _ {k = 1: K} \mid C\right) = \prod_ {k} ^ {K} \mathrm {p} \left(\boldsymbol {s} ^ {k} \mid \boldsymbol {s} ^ {< k}, C\right). \tag {2}
+$$
+
+Video can be generated in this pipeline by first generating the first frame $\pmb{f}^{1} = \{x_{n}^{1}\}_{n = 1:N}$ following Eq. (2), then generating the subsequent frames with $T - 1$ steps, i.e.,
+
+$$
+\mathrm {p} \left(\left\{\boldsymbol {f} ^ {t} \right\} _ {t = 1: T} | \boldsymbol {C}\right) = \prod_ {t} ^ {T} \mathrm {p} \left(\boldsymbol {f} ^ {t} \mid \boldsymbol {f} ^ {< t}, \boldsymbol {C}\right). \tag {3}
+$$
+
+The above strategy groups related tokens into one single set. By grouping visually similar tokens, or temporally related tokens, it essentially leverages the spatial-temporal dependency in images and videos to improve efficiency and quality.
+
+Proper strategy for partitioning tokens plays a crucial role in determining generation difficulty and quality. For image generation, we generate spatially adjacent image tokens as a set and iteratively increase the number of tokens in each set. For video generation, we take the tokens in the next frame as a set. The above intuitions lead to the SPP and TNP for image and video token partitions in Sec.4.2 and Sec.4.3, respectively. The next-set prediction largely reduces inference steps from the total number of tokens to the number of token sets, for example, reducing from sequence length $32 \times 16 \times 16 = 6272$ to $K = 63$ in our default image generation setting.
+
+Besides the next-set prediction, we further introduce a continuous domain sampler $\mathrm{D}(\cdot)$ to replace the discrete categorical sampling to preserve continuity of generated contents. In contrast to the previous decoder-only AR works [25, 60] that predict a discrete categorical distribution, we train a decoder-only autoregressive networks $\mathrm{G}_{\theta}(\cdot)$
+
+
+Figure 2. Overview of the video generation of our method. We take the 2nd frame generation as an example. Our method consists of two main components: the autoregressive generation model $\mathrm{G}_{\theta}$ and the continuous-domain sampler $\mathrm{D}$ . $\mathrm{G}_{\theta}$ predicts the probability distribution $z$ of the next-set tokens based on the given condition, while $\mathrm{D}$ performs stochastically sampling within the predicted continuous-domain distribution $z$ .
+
+in the continuous domain without vector quantization (VQ), where $\theta$ denotes trainable parameters. At the $k$ -th step of image generation, $\mathrm{G}_{\theta}$ is fed a set of special [mask] tokens $\{p\}$ added with position embeddings as input and predicts the next set of continuous probability distribution tokens $\{z\}$ . D then samples $s^k$ from distributions $\{z\}$ . This process can be formulated as
+
+$$
+\boldsymbol {s} ^ {k} = \mathrm {D} \left(\mathrm {G} _ {\theta} (\{p \} \mid \boldsymbol {s} ^ {< k})\right). \tag {4}
+$$
+
+$\mathrm{G}_{\theta}$ is a Llama-like [55] decoder-only AR model [48] consisting of multiple Transformer blocks, whose structure hyperparameters are given in Sec. 5.1. Notably, we use a single Transformer model as $\mathrm{G}_{\theta}$ for both image and video generation. The training objective aims to optimize the individual conditional probabilities of a known sequence at each step, which can be denoted as
+
+$$
+\mathcal {L} = - \sum_ {k} ^ {K} \sum_ {x \in \boldsymbol {s} ^ {k}} \mathcal {L} (x, \theta | \boldsymbol {s} ^ {< k}, C), \tag {5}
+$$
+
+where $x$ denotes a token included in the set $\pmb{s}^k$ .
+
+As shown in Fig. 2, the model $\mathrm{G}_{\theta}$ unifies image and video generation into the next set prediction autoregression. Next set prediction accelerates inference, while the continuous domain sampler enhances visual quality by alleviating quantization loss from VQ. Next section proceeds to introduce details of tokenization, token partition, and training.
+
+# 4. Methodology
+
+# 4.1. Tokenization
+
+Given text prompts or images as conditions, we first tokenize those inputs into the initial condition $C$ using visual and language tokenizers.
+
+Visual data are analog and continuous signal in nature. In contrast to VQ tokenizers used in previous AR works [25, 60], we adopt a variational autoencoder (VAE) [42] without VQ to map each image patch to continuous representations. Continuous features preserve the inherent visual continuity, and can enhance subtle details and motion cues for generation. We adopt a 2D VAE to bypass the need for 3D tokenizers [3] following [3], and feed the output of a 2D image-based VAE directly into the AR model. The 2D VAE is computation efficient, and provides faster speed compared to 3D VAEs. Formally, the tokenized representation $\{x\}$ can be computed as
+
+$$
+\{x \} = E (I), \tag {6}
+$$
+
+where $E(\cdot)$ is the VAE encoder, and $I$ denotes an image in the pixel space.
+
+The language modality is retained their natural discrete representation. A text prompt is encoded into a 1024-dimensions latent space using the popular CLIP [40] text encoder. Text embedding is not the primary focus of this work, thus we selected CLIP mainly for its lightweight model and efficiency, which reduces GPU memory usage and inference time.
+
+# 4.2. Spatial Progressive Partitioning (SPP)
+
+The intuition of SPP is to generate highly similar contents in parallel, thereby to reduce the required inference iterations. Visual content exhibits locality, where adjacent regions are related and share common cues. We thus partition neighboring tokens into one set to leverage such spatial dependency. Additionally, different generation stages present varying levels of difficulty. As few visual clues available at the start, generating too many tokens simultaneously may cause semantic conflicts between visual contents. Setting a small number of tokens in each set is beneficial for lowering generation difficulty and improving quality in the initial AR steps. We thus progressively increase the number of tokens in each set.
+
+Since it is not feasible to identify which tokens will be similar before generation, we leverage the spatial locality of images and group spatially adjacent tokens into a set. Following the raster-scan order, we first arrange image tokens into a sequence. Specifically, neighboring image tokens are grouped into one set, and the number of tokens in each set increases following a sine curve. A sine curve steadily increases the set size, also prevents generating too many tokens in later steps. The number of tokens in set $s^k$ is deter
+
+mined by
+
+$$
+m ^ {k} = \left\lfloor \alpha \cdot \sin \left(\frac {k \cdot \pi}{2 K}\right) \right\rfloor , \tag {7}
+$$
+
+where $\lfloor \cdot \rfloor$ denotes the floor function, and $\alpha$ is a constant determined by the number of tokens $N$ and the number of sets $K$ as
+
+$$
+\alpha = \frac {N}{\sum_ {k = 1} ^ {K} \sin \frac {k \cdot \pi}{2 K}}. \tag {8}
+$$
+
+Since $K$ is typically smaller than $N$ , e.g., $K = 32$ and $N = 196$ , this formulation ensures sine increasing trend and the sum of tokens across all sets equals to $N$ .
+
+The image sequence is surrounded with specific begin-of-image ([BOI]) and end-of-image ([EOI]) tokens. Once the [BOI] token along with subsequent mask tokens are fed into the network, the next-set masked image generation process begins. Similarly, the [EOI] token signifies the end of this process.
+
+# 4.3. Temporal Next-frame Partitioning (TNP)
+
+This part explains the partition of token sets for video generation. Human typically perceive the world in a linear temporal sequence, focusing on what happens next. Making token set prediction in chronological order aligns with how humans observe and predict physical world dynamics. Given frames $\pmb{f}^{| Model | Type | #params | FID ↓ | IS ↑ |
| MaskGIT [6] | Masked | 227M | 7.32 | 156.0 |
| RCG [30] | Masked | 502M | 3.49 | 215.5 |
| U-ViT-H[2] | Diff | 501M | 2.29 | 278.2 |
| DiT-XL[38] | Diff | 675M | 2.27 | 278.2 |
| ViTVQ [70] | AR | 1.7B | 4.17 | 175.1 |
| VAR-d24 [54] | AR | 1.0B | 2.09 | 312.09 |
| MAR-H [31] | AR | 943M | 1.55 | 303.7 |
| Ours | AR | 775M | 2.07 | 311.7 |
+
+# 5. Experiment
+
+# 5.1. Experiment Setup
+
+Dataset. For text-to-image training, we use 1.26M images from ImageNet-1K [12] with resolution of $512 \times 512$ , with description of class labels as captions. For text-to-video generation, the model is trained on approximately 6M higher-quality samples [26] from Pandas-70M [10] data, finetuned on high-quality in-house text-video pairs.
+
+Implementation details. The publicly available VAE tokenizers provided by LDM [42] is used to encode each image patch. The VAE encoder downsamples the image resolution by a factor of 16, generating a latent dimension of 16. Following DiT [38], we patchify latent representation using a patch size of $2 \times 2$ . The latent representation is then projected through a linear layer to match the dimension of the Transformer. We train a base model (343M) and a larger model (775M), which respectively consist of 24 and 36 Transformer blocks, with a width of 1024 and 1280. Their corresponding denoising samplers D consist of 6 or 12 MLPs blocks with a width of 1024 or 1536. Sampling process 100 and 1000 denoising steps for training and inference, respectively, following [31, 37]. Target video clip is provided at a size of $32 \times 512 \times 512$ . By default, the number of image sets $K$ is set to 32.
+
+Training is conducted on four nodes, each equipped with 8 NVIDIA H800 GPUs. To accelerate convergence, the model is first trained on text-to-image task using ImageNet-1K data for 800 epochs from scratch. We then transfer the weights for text-to-video training for 25 epochs. Across all experiments, the AdamW optimizer [34] is used with a weight decay of 0.02 and a base learning rate of 1e-4.
+
+Evaluation protocol includes widely used metrics such as Fréchet Image Distance (FID) [20] for image generation, and Fréchet Video Distance (FVD) [56], CLIP similarity score (CLIPSIM) [64], Inception Score (IS) [44], along with a comprehensive toolkit VBench [24] for evaluating video generation performance. We employ a zero-shot generation evaluation protocol, where the model has not been trained on the data of target benchmarks. Evaluation benchmark includes text-to-video generation on ImageNet
+
+
+Text condition: A red apple covered in water droplets on a dark background.
+
+
+
+
+
+
+
+
+Text condition: Underwater circular water wave appears in a clear sea.
+
+
+
+
+
+
+
+
+Text condition: Magnificent scenery of the dam.
+
+
+Figure 3. Text-to-image generation. For each text condition, we show four examples to show the diversity of output.
+
+
+
+
+
+1K [12] and text-to-video generation on MSR-VTT [67] and UCF-101 [47]. The results are reported with classifier-free guidance (CFG) [21]. Note that the higher CLIPSIM and IS (indicated as $\uparrow$ ) and lower FID and FVD (indicated as $\downarrow$ ) mean better performance.
+
+# 5.2. Main Results
+
+Image generation. Table 1 compares our method with Masked image modeling (MIM) [6, 30], diffusion models [2, 38] and autoregressive (AR) models [31, 54]. The results demonstrate that our method shows comparable performance with recent works in both visual quality and model compactness. Our approach also outperforms recent AR models such as VAR [54] in these two aspects.
+
+Video generation. We conduct a zero-shot comparison with recent open source and proprietary text-to-video models on widely used MSR-VTT [67] and UCF-101 [47] benchmarks in Table 2. As shown in the table, our method demonstrates highly competitive results compared to other diffusion models on FVD. Our method improves the AR model in both quality and efficiency. For example, compared to VideoPoet [25], we achieve better FVD scores (247 vs. 355 on UCF-101) with a much smaller model size (0.2B vs. 8B) and lower latency (1.1s vs. 2.0s per frame). Additionally, our method shows a significant advantage in IS (41.47 vs. 38.44), verifying that the continuous-domain sampler is capable of generating diverse video. Average frame generation latency is measured on a single NVIDIA A100 GPU with $32 \times 512 \times 512$ video size. The results show that our method generates better prediction distribution and enhances inference efficiency.
+
+Table 2. Video generation metrics on MSR-VTT [67] and UCF-101 [47] benchmarks. Latency is measure on a NVIDIA A100. † indicates that latency was measured using the official code. ↑ and ↓ denote higher or lower is better.
+
+| Model | Venue | MSR-VTT [67] | UCF-101 [47] | Type | #params | Latency ↓ (s/frame) |
| CLIPSIM ↑ | FVD ↓ | FVD ↓ | IS ↑ |
| Make-A-Video[46] | 2023 ICLR | 0.3049 | - | 367 | 33.00 | Diff | 9.6B | - |
| CogVideo[23] | 2023 ICLR | 0.2631 | 1294 | 702 | 25.27 | DIff | - | - |
| Video LDM[4] | 2023 CVPR | 0.2929 | - | 551 | 33.45 | DIff | - | - |
| SVD [3] | 2023 arxiv | - | - | 242 | - | Diff | 1521M | \( 1.9^{\dagger} \) |
| InternVid[62] | 2024 ICLR | 0.2951 | - | 617 | 21.04 | DIff | - | - |
| Videofactory[59] | 2024 Open. | 0.3005 | - | 410 | - | Diff | 1601M | - |
| Show-1[74] | 2024 IJCV | 0.3072 | 538 | 394 | 35.42 | Diff | - | - |
| NUWA [65] | 2022 ECCV | 0.2439 | - | - | - | AR | - | - |
| TATS [17] | 2022 ECCV | - | - | 420 | 57.63 | AR | - | - |
| VideoPoet [25] | 2024 ICML | 0.3049 | 213 | 355 | 38.44 | AR | 8B | 2.0 |
| Ours | 2025 ICCV | 0.2942 | 197 | 247 | 39.13 | AR | 343M | 1.1 |
| Ours | 2025 ICCV | 0.3092 | 182 | 204 | 41.47 | AR | 775M | 1.6 |
+
+Table 3. Comparison with recent text-to-video models on VBench [24]. Due to space limitations, we selected 9 out of the 16 evaluation dimensions. The horizontal line separates Diffusion models and AR models. Higher scores reflect better performance.
+
+| Models | Temporal Quality | Frame Quality | Condition Consist. | #params. | Average score |
| Motion smooth. | Dynamic degree | Subject consist. | Temporal flickering | Aesthetic quality | Image quality | Multiple objects | Human action | Object class |
| ModelScope [58] | 95.79 | 66.39 | 89.87 | 98.28 | 56.39 | 58.57 | 38.98 | 92.40 | 82.25 | 1.7B | 75.44 |
| LaVie [61] | 96.38 | 49.72 | 91.41 | 98.30 | 54.94 | 59.78 | 33.32 | 96.80 | 91.82 | 3B | 74.72 |
| Show-1 Zhang et al. [74] | 98.24 | 44.44 | 95.53 | 99.12 | 57.35 | 58.66 | 45.47 | 95.60 | 93.07 | 4B | 76.39 |
| OpenSora V1.2 [75] | 98.50 | 42.39 | 96.75 | 99.12 | 56.85 | 60.94 | 51.83 | 91.20 | 82.22 | 1B | 75.53 |
| AnimateDiff-V2 [19] | 97.76 | 40.83 | 95.30 | 98.75 | 67.16 | 70.10 | 36.88 | 92.60 | 90.90 | 1B | 76.70 |
| Gen-2 [43] | 99.58 | 18.89 | 97.61 | 99.56 | 66.96 | 67.42 | 55.47 | 89.20 | 90.92 | - | 76.18 |
| Pika [27] | 99.50 | 47.50 | 96.94 | 99.74 | 62.04 | 61.87 | 43.08 | 86.20 | 88.72 | - | 76.18 |
| VideoCrafter-2.0 [8] | 97.73 | 42.50 | 96.85 | 98.93 | 63.13 | 67.22 | 40.66 | 95.00 | 92.55 | 2B | 77.17 |
| T2V-Turbo (VC2) [28] | 97.34 | 49.17 | 96.28 | 97.48 | 63.04 | 72.47 | 54.65 | 95.20 | 93.96 | 2B | 79.95 |
| CogVideoX-2B [69] | 96.92 | 70.97 | 96.23 | 98.89 | 61.98 | 61.68 | 62.11 | 99.40 | 85.23 | 2B | 81.49 |
| Gen-3 [43] | 99.23 | 60.14 | 97.10 | 98.61 | 63.34 | 66.82 | 53.64 | 96.40 | 87.81 | - | 80.34 |
| Emu3 [60] | 98.93 | 79.27 | 95.32 | 98.57 | 59.64 | 62.63 | 44.64 | 77.71 | 86.17 | 8B | 78.10 |
| NOVA [11] | - | - | - | - | 54.52 | - | 73.46 | 91.20 | 91.36 | 0.6B | 78.48 |
| Ours | 98.67 | 54.21 | 96.73 | 98.92 | 63.93 | 67.76 | 52.19 | 93.86 | 89.57 | 0.8B | 79.54 |
+
+Following [60], we evaluate the text-to-video generation on VBench [24] across three key dimensions: temporal quality, frame quality, and condition consistency in Table 3. VBench provides a comprehensive toolkit for video generation assessment. Due to space constraints, we report 9 representative metrics and their average scores. For temporal quality, our method achieves scores of 98.67, 96.73, and 98.92 in motion smoothness, object consistency, and temporal flickering, respectively, matching the performance of state-of-the-art diffusion methods. In the dynamics degree metric, which measures the presence of large movements, our model obtains the score of 54.21, indicating sufficiently dynamic contents are generated. Compare to the larger EMU3 [25], our model demonstrates a strong performance-to-efficiency trade-off. It achieves comparable or better results than those of open-source diffusion models, with a smaller model size, i.e., 0.8B.
+
+Discussion. The above results indicate our model outperforms discrete AR models, and achieves competitive performance with diffusion models with fewer parameters and
+
+faster inference speed. This demonstrates that, with the proposed continuous-domain sampling and next-set generation strategies, AR methods have strong potentials for versatile in-context learning and unified language-visual generation.
+
+# 5.3. Qualitative Results
+
+High-quality image generation. Fig. 3 shows results of text-to-image generation. We generate four samples for each text condition. Our method produces diverse contents under the same prompt, such as both whole apple and close-up shots. The results highlight our method's ability to capture fine details, like water droplets on the apple and flowing waves in the $1^{st}$ and $2^{nd}$ cases. Additionally, our method can generate realistic lighting effects, such as the reflection of the sky on the water in the case of scenery of the dam.
+
+High-quality video generation. Fig. 4 shows the results for text-to-video and image-to-video generation tasks. Our method effectively models smooth temporal dependencies between frames. In text-to-video examples (a), the first aerial view sequence shows a yard gradually enlarging as
+
+
+Text condition: Aerial video of the lush greenery forest and the ranger yard.
+Text condition: The Cathedral is illuminated as fireworks explode overhead.
+Image condition
+
+
+Text condition: Man with a beard and black hat sits in room, speaking to the camera.
+
+
+(a) Text-to-video generation
+Figure 4. Generation results on text-to-video and image-to-video tasks.
+
+
+
+
+
+
+(b) Image-to-video generation
+
+Table 4. The effect of discrete and continuous-domain tokenizers. The tokenizers are provided by publicly available LDM [42].
+
+| Tokenizer | FID ↓ | FVD ↓ | Temporal flickering ↑ | Motion smoothness↑ |
| VQ-VAE [42] | 2.49 | 314 | 97.87 | 97.85 |
| VAE [42] | 2.05 | 247 | 98.92 | 98.67 |
+
+the camera zooms in until it exits the frame. The second example captures a smooth fireworks show from liftoff to explosion. The third showcases a man speaking to the camera with realistic facial expressions, accessories, and natural movements like blinking and head-turning. In imaged-to-video examples (b), key visual elements are consistently preserved, such as the animated panda's facial expressions, the Husky's head-turning motion, and the aerial view of a winter farmland.
+
+More generated videos and images, along with visual comparisons to related works, including OpenSora-1.1B [75], CogVideoX-2B [69], ModelScope-1.7B [58], and NOVA [11] are presented in the supplementary materials. These visual results demonstrate that our method generates high-quality contents and smooth motions under the AR framework.
+
+# 5.4. Ablation Study
+
+Compare to VQ tokenizer. Previous AR video generation methods [25, 60] use a VQ tokenizer for discretizing video signals. Tab. 4 compares the impact of a continuous-domain tokenizer and sampler versus those of discrete VQ on FID (ImageNet), FVD (UCF-101), and VBench metrics (temporal flickering, motion smoothness). The continuous-domain tokenizer improves FID in image generation and shows more substantial gains in video metrics, enhancing FVD, temporal flickering, and motion smoothness by 64, $1.05\%$ , and $0.82\%$ , respectively. These demonstrate that continuous-domain sampling benefits both image and video
+
+Table 5. Impact of number $K$ on ImageNet benchmark.
+
+| K | FID ↓ | IS ↑ | Latency (s) ↓ |
| 8 | 4.46 | 224.7 | 6.45 |
| 16 | 2.73 | 278.2 | 9.92 |
| 32 | 2.05 | 302.4 | 13.11 |
| 64 | 1.86 | 309.2 | 20.08 |
+
+generation, especially for video tasks.
+
+Number of sets. We partition image patches into $K$ sets, and predict each set simultaneously. Tab. 5 compares the effects of different $K$ values on image generation. The inference speed is mainly controlled by $K$ , the number of sets. Smaller values, such as $K = 8$ , reduce inference latency to 6.45 seconds but degrade the output quality. We choose $K = 32$ as a reasonable trade-off between performance and inference speed.
+
+# 6. Conclusion
+
+This paper introduces a unified continuous-domain autoregressive model for the image and video generation. Our method consists of two components: 1) an AR model predicting token distributions in the continuous domain. The SPP and TNP are introduced for partitioning image and video tokens, respectively. 2) A lightweight denoising sampler stochastically sampling tokens from the predicted distribution. In contrast to diffusion models jointly modeling all tokens, or prior AR methods with VQ tokenization and next-token prediction, our approach models the marginal distribution with continuous next-set prediction. Experiments show competitive FID, FVD, and IS scores to diffusion models on multiple benchmarks, with fewer than 1B parameters and a per-frame generation time of 1.1 seconds. VBench results and visualizations further validate the model's capability to generate subtle details and movements.
+
+Acknowledgement This work is supported in part by Grant No. 2023-JCJQ-LA-001-088, in part by Natural Science Foundation of China under Grant No. U20B2052, 61936011, in part by the Okawa Foundation Research Award, in part by Ant Group Research Intern Program, in part by the Ant Group Research Fund, and in part by the Kunpeng&Ascend Center of Excellence, Peking University.
+
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+ "content": " in our default image generation setting."
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| MaskGIT [6] | Masked | 227M | 7.32 | 156.0 |
| RCG [30] | Masked | 502M | 3.49 | 215.5 |
| U-ViT-H[2] | Diff | 501M | 2.29 | 278.2 |
| DiT-XL[38] | Diff | 675M | 2.27 | 278.2 |
| ViTVQ [70] | AR | 1.7B | 4.17 | 175.1 |
| VAR-d24 [54] | AR | 1.0B | 2.09 | 312.09 |
| MAR-H [31] | AR | 943M | 1.55 | 303.7 |
| Ours | AR | 775M | 2.07 | 311.7 |
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| CLIPSIM ↑ | FVD ↓ | FVD ↓ | IS ↑ |
| Make-A-Video[46] | 2023 ICLR | 0.3049 | - | 367 | 33.00 | Diff | 9.6B | - |
| CogVideo[23] | 2023 ICLR | 0.2631 | 1294 | 702 | 25.27 | DIff | - | - |
| Video LDM[4] | 2023 CVPR | 0.2929 | - | 551 | 33.45 | DIff | - | - |
| SVD [3] | 2023 arxiv | - | - | 242 | - | Diff | 1521M | \\( 1.9^{\\dagger} \\) |
| InternVid[62] | 2024 ICLR | 0.2951 | - | 617 | 21.04 | DIff | - | - |
| Videofactory[59] | 2024 Open. | 0.3005 | - | 410 | - | Diff | 1601M | - |
| Show-1[74] | 2024 IJCV | 0.3072 | 538 | 394 | 35.42 | Diff | - | - |
| NUWA [65] | 2022 ECCV | 0.2439 | - | - | - | AR | - | - |
| TATS [17] | 2022 ECCV | - | - | 420 | 57.63 | AR | - | - |
| VideoPoet [25] | 2024 ICML | 0.3049 | 213 | 355 | 38.44 | AR | 8B | 2.0 |
| Ours | 2025 ICCV | 0.2942 | 197 | 247 | 39.13 | AR | 343M | 1.1 |
| Ours | 2025 ICCV | 0.3092 | 182 | 204 | 41.47 | AR | 775M | 1.6 |
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| Motion smooth. | Dynamic degree | Subject consist. | Temporal flickering | Aesthetic quality | Image quality | Multiple objects | Human action | Object class |
| ModelScope [58] | 95.79 | 66.39 | 89.87 | 98.28 | 56.39 | 58.57 | 38.98 | 92.40 | 82.25 | 1.7B | 75.44 |
| LaVie [61] | 96.38 | 49.72 | 91.41 | 98.30 | 54.94 | 59.78 | 33.32 | 96.80 | 91.82 | 3B | 74.72 |
| Show-1 Zhang et al. [74] | 98.24 | 44.44 | 95.53 | 99.12 | 57.35 | 58.66 | 45.47 | 95.60 | 93.07 | 4B | 76.39 |
| OpenSora V1.2 [75] | 98.50 | 42.39 | 96.75 | 99.12 | 56.85 | 60.94 | 51.83 | 91.20 | 82.22 | 1B | 75.53 |
| AnimateDiff-V2 [19] | 97.76 | 40.83 | 95.30 | 98.75 | 67.16 | 70.10 | 36.88 | 92.60 | 90.90 | 1B | 76.70 |
| Gen-2 [43] | 99.58 | 18.89 | 97.61 | 99.56 | 66.96 | 67.42 | 55.47 | 89.20 | 90.92 | - | 76.18 |
| Pika [27] | 99.50 | 47.50 | 96.94 | 99.74 | 62.04 | 61.87 | 43.08 | 86.20 | 88.72 | - | 76.18 |
| VideoCrafter-2.0 [8] | 97.73 | 42.50 | 96.85 | 98.93 | 63.13 | 67.22 | 40.66 | 95.00 | 92.55 | 2B | 77.17 |
| T2V-Turbo (VC2) [28] | 97.34 | 49.17 | 96.28 | 97.48 | 63.04 | 72.47 | 54.65 | 95.20 | 93.96 | 2B | 79.95 |
| CogVideoX-2B [69] | 96.92 | 70.97 | 96.23 | 98.89 | 61.98 | 61.68 | 62.11 | 99.40 | 85.23 | 2B | 81.49 |
| Gen-3 [43] | 99.23 | 60.14 | 97.10 | 98.61 | 63.34 | 66.82 | 53.64 | 96.40 | 87.81 | - | 80.34 |
| Emu3 [60] | 98.93 | 79.27 | 95.32 | 98.57 | 59.64 | 62.63 | 44.64 | 77.71 | 86.17 | 8B | 78.10 |
| NOVA [11] | - | - | - | - | 54.52 | - | 73.46 | 91.20 | 91.36 | 0.6B | 78.48 |
| Ours | 98.67 | 54.21 | 96.73 | 98.92 | 63.93 | 67.76 | 52.19 | 93.86 | 89.57 | 0.8B | 79.54 |
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| VQ-VAE [42] | 2.49 | 314 | 97.87 | 97.85 |
| VAE [42] | 2.05 | 247 | 98.92 | 98.67 |
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| 8 | 4.46 | 224.7 | 6.45 |
| 16 | 2.73 | 278.2 | 9.92 |
| 32 | 2.05 | 302.4 | 13.11 |
| 64 | 1.86 | 309.2 | 20.08 |
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+ }
+ ]
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diff --git a/2025/UniversalBooth_ Model-Agnostic Personalized Text-to-Image Generation/5ed1061d-3c1f-4e57-b276-0976e7c57035_content_list.json b/2025/UniversalBooth_ Model-Agnostic Personalized Text-to-Image Generation/5ed1061d-3c1f-4e57-b276-0976e7c57035_content_list.json
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+ "text": "UniversalBooth: Model-Agnostic Personalized Text-to-Image Generation",
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+ "text": "Songhua Liu $^{12}$ , Ruonan Yu $^{1}$ , and Xinchao Wang $^{1*}$ $^{1}$ National University of Singapore $^{2}$ School of Artificial Intelligence, Shanghai Jiao Tong University \n{songhua.liu, ruonan}@u.nus.edu, xinchao@nus.edu.sg",
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+ "Figure 1. We propose a model-agnostic personalized text-to-image generation method termed UniversalBooth. Once trained, it can be applied to various diffusion models with different architectures and functionalities without any additional training. \"S\" is a virtual token referring to the input subject. The seen model during training is SD-v1.4, while the unseen models are Distilled SD [21], SD-XL [32], SD-v3-Medium [13], InstructPix2Pix [5], LaVie [46], and MVDream [40]."
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+ "text": "Given a source image, personalized text-to-image generation produces images preserving the identity and appearance while following the text prompts. Existing methods heavily rely on test-time optimization to achieve this customization. Although some recent works are dedicated to zero-shot personalization, they still require re-training when applied to different text-to-image diffusion models. In this paper, we instead propose a model-agnostic personalized method termed UniversalBooth. At the heart of our approach lies a novel cross-attention mechanism, where different blocks in the same diffusion scale share common square transformation matrices of key and value. In this way, the image encoder is decoupled from the diffusion architecture while maintaining its effectiveness. Moreover, the cross-attention performs hierarchically: the holistic attention first captures the global semantics of user inputs for textual combination with editing prompts, and the fine-grained attention divides the holistic attention scores",
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+ "text": "for various local patches to enhance appearance consistency. To improve the performance when deployed on unseen diffusion models, we further devise an optimal transport prior to the model and encourage the attention scores allocated by cross-attention to fulfill the optimal transport constraint. Experiments demonstrate that our personalized generation model can be generalized to unseen text-to-image diffusion models with a wide spectrum of architectures and functionalities without any additional optimization, while other methods cannot. Meanwhile, it achieves comparable zero-shot personalization performance on seen architectures with existing works.",
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+ "text": "1. Introduction",
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+ "text": "Although text-to-image diffusion models have advanced significantly in recent years due to their generative capabilities [11, 31, 36], they fall short in personalized image generation, also known as subject-driven image generation, where generated images adhere to text prompts while preserving specific identities and appearances from user-",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "provided images. Given the broad applicability in real-world scenarios, this customization has garnered attention from both academia and industry.",
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+ "text": "Personalized generation typically involves establishing correspondences between source images and textual space, allowing diffusion models to reconstruct images and generate variations based on text prompts. Early methods rely on test-time optimization [14] or fine-tuning the diffusion model [22, 37], which are computationally expensive and impractical for end users. Recent efforts aim to reduce this burden through offline learning, such as training a visual encoder for feed-forward textual correspondences [19, 24, 39, 44, 47, 52]. These methods achieve impressive zero-shot personalized text-to-image generation: once trained, the visual encoder can capture input concepts from subject images in real time.",
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+ "text": "However, flexibility remains an issue when applying these methods to various text-to-image models with unseen structures, which is a practical problem since real-world models can be updated or replaced frequently. Re-training the encoder for each model can take several days on multiple GPUs [44, 47], making it highly cumbersome if not impossible at all. Moreover, for some distilled models like LCM [28], it is even infeasible to conduct vanilla training directly as it requires a specific distillation objective concerning its teacher.",
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+ "text": "Focusing on this drawback, we aim at a model-agnostic approach termed UniversalBooth in this paper and expect a trained visual encoder to be generalized to other text-to-image backbones seamlessly. To this end, we first delve into the design intricacies of existing personalized generation methods without test-time optimization and reveal that the significant impediment to such generalization lies in the strong coupling between the visual encoder and the crossattention layers of the diffusion UNet, which are key modules for the diffusion model to interact with input conditions. Previous works largely ignore the variability in backbone text-to-image models. Consequently, their visual encoders are susceptible to overfitting the specific diffusion model seen in training.",
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+ "text": "In this paper, we tackle this challenge by introducing a novel cross-attention mechanism that decouples the visual subject encoder from the diffusion architecture. Unlike conventional approaches, our method utilizes a shared group of square mapping matrices for both key and value components across different blocks within the same diffusion scale. This design promotes flexibility across a range of diffusion models characterized by varying numbers of channels or blocks, all while ensuring consistent effectiveness in generating high-quality images.",
+ "bbox": [
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+ "type": "text",
+ "text": "Moreover, we devise a hierarchical cross-attention strategy. Specifically, the visual encoder first capsules global semantic features of user inputs into a virtual word, which",
+ "bbox": [
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+ "page_idx": 1
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+ "text": "is convenient for textual combination with editing prompts. To enhance appearance consistency, the cross-attention scores for this word are further divided by fine-grained attention considering local patches. Overall, this hierarchical approach ensures that the generated images not only align with textual prompts but also maintain coherence and fidelity to the visual subjects.",
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+ "text": "Notably, the fine-grained cross-attention in our approach is backed up with an optimal transport prior, which is achieved by regulating attention scores allocated by the cross-attention mechanism to fulfill optimal transport constraints. In this way, even when tested on unfamiliar novel diffusion architectures, our customization model can be guided by this prior knowledge acquired in training, which further bolsters cross-model generalizability.",
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+ "text": "We conduct extensive experiments to showcase the effectiveness and versatility of our approach. As shown in Fig. 1, results indicate that once trained, the proposed Universal-Booth can be generalized to unseen text-to-image diffusion models with a wide spectrum of architectures and functionalities without any additional training effort, while other methods cannot. Meanwhile, it yields on-par zero-shot personalized generation performance with existing works on seen diffusion backbones. Our contributions can be summarized as follows:",
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+ "list_items": [
+ "- We investigate a novel problem, namely model-agnostic personalized text-to-image generation. To the best of our knowledge, this is the first work dedicated to the cross-model generalization issue in this field.",
+ "- We tailor a novel cross-attention mechanism to address the problem. Specifically, it adopts shared key and value mappings among various blocks within the same scale, works in an innovative hierarchical manner, and is injected with optimal transport prior.",
+ "- Experiments suggest that UniversalBooth achieves superior cross-model personalized generation results to unseen diffusion models and comparable performance in the vanilla test setting on seen models."
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+ "text": "Personalized text-to-image generation refers to producing images according to the text prompts while preserving the identity and appearance of users' image inputs. One promising solution for this application is to learn the word embedding [14] or fine-tune the diffusion model [22, 37] specifically for one subject in an iterative optimization fashion, which exhibits limited flexibility. Recent studies have been dedicated to addressing this limitation and focused on an any-subject-one-model paradigm. The basic idea is to replace the optimization process with a single feedforward propagation: to learn a neural network and map the input images to the conditional space of the diffusion model [9, 16, 18, 24, 26, 29, 41, 43, 44, 47, 50, 52] in a one-",
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+ "type": "page_number",
+ "text": "18315",
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+ "type": "image",
+ "img_path": "images/22afc5f2c1ee1291b4fe7f3871355a4a34372e7038b88d689b044735c2f91060.jpg",
+ "image_caption": [
+ "Figure 2. (a) Overview of zero-shot personalized text-to-image generation solutions (text branch omitted). (b) Our approach learns square and shared key-value mappings in cross-attention layers, enabling flexible cross-diffusion-model generalization during inference without extra training.",
+ "Figure 3. Preliminary results of cross-model generalization by different operations on cross-attention. Images in (c), (d), (e), and (f) are generated with the prompt A photo of a S."
+ ],
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+ "type": "text",
+ "text": "stop manner. We provide a systematic summary of existing works in the appendix.",
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+ "text": "These methods typically focus on the subject-wise flexibility and have achieved remarkable performance simultaneously. Nevertheless, when the base diffusion model changes—a common and practical scenario given the rapid proliferation and advancement of large text-to-image diffusion models [3, 4, 10, 12, 13, 20, 21, 28-30, 32, 34, 34, 36, 38, 42, 44, 48]—they typically require adapting the subject mapper to the new architecture through an optimization process as well [35]. We thus offer a different perspective regarding the model-wise flexibility and introduce UniversalBooth in this paper, the first method specifically designed for the cross-model generalization problem in personalized generation. Unlike existing techniques, UniversalBooth enables zero-shot customized generation on unseen diffusion models without requiring any additional training.",
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+ "type": "text",
+ "text": "3. Methodology",
+ "text_level": 1,
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+ "type": "text",
+ "text": "3.1. Preliminary",
+ "text_level": 1,
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+ "text": "Different from early approaches [14, 22, 37] that obtain textual correspondences of subject images through test-time optimization, recent test-time fine-tuning-free personalized image generation methods learn a neural mapping from the visual space to the textual space so that the textual representations can be generated in a single forward propagation.",
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+ "text": "We illustrate the overall pipeline of some popular designs like ELITE [47] and IP-Adapter [50] in Fig. 2(a). Typically, given a subject image $x$ , these methods first adopt the CLIP image encoder [33], denoted as $\\phi(\\cdot)$ , for feature extraction. As CLIP has been trained on abundant text-image pairs to align corresponding features, it may serve as a valuable resource for learning text-aware vision representations. Subsequently, a learnable MLP denoted as $M$ is trained to convert CLIP vision features into virtual words in the textual embedding space. Additional cross-attention is incorporated into the cross-attention layers of the pre-trained diffusion UNet to enhance its adaptability to",
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+ "img_path": "images/18fbc14cb8312bcac5b30dbf98a7a51e9310dddb3af71857138fc0d2ebf1debb.jpg",
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+ "image_caption": [
+ "(a) Cosimine Similarity between Predicted and Optimal Mapping Matrices",
+ "(b) Subject Image"
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+ "image_caption": [
+ "(d) Square KV Mappings",
+ "(e) Square and Shap KV Mappings"
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+ "type": "image",
+ "img_path": "images/caec8dbf42ad9dcb74dfd9c6eec026918bcf06d99a8128ac889f5aafe132678c.jpg",
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+ "img_path": "images/5b28e56d390b01ca9479021d0012a52d53b7ac1286272f9ca6aafc880b8eca12.jpg",
+ "image_caption": [
+ "(f) wo KV Mappings"
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+ "type": "text",
+ "text": "conditions injected by subject images, which is crucial to the performance given the significant role of cross-attention (CA) in subject-driven text-to-image generation, as highlighted in [1, 15, 22]. The CA results for the subject branch are added to the original results:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\operatorname {O u t} \\leftarrow \\operatorname {O u t} + \\lambda \\operatorname {C A} (Q, (M \\circ \\phi (x)) \\hat {W} _ {k}, (M \\circ \\phi (x)) \\hat {W} _ {v}), \\tag {1}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where $Q$ is the query matrix mapped from features in the diffusion backbone, $\\hat{W}_k$ and $\\hat{W}_v$ are learnable key and value mappings respectively, and $\\lambda$ is a hyperparameter controlling the strength of subject injection.",
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+ "type": "text",
+ "text": "We assume that Stable Diffusion v1.5 [36] is adopted here. It first learns an auto-encoder $(\\mathcal{E}(\\cdot),\\mathcal{D}(\\cdot))$ , where the encoder $\\mathcal{E}(\\cdot)$ maps an image $x$ to a lower dimensional latent space: $z\\gets \\mathcal{E}(x)$ , and the decoder $\\mathcal{D}(\\cdot)$ learns to decode $z$ back to the image space $\\hat{x}\\gets \\mathcal{D}(z)$ such that $\\hat{x}$ is close to the original $x$ . Denoising is conducted in the latent space by a UNet $\\epsilon_{\\theta}(\\cdot)$ for noise prediction. With a pre-trained and frozen auto-encoder, text encoder, and UNet, the MLP and additional cross-attention layers are optimized using the vanilla noise prediction loss $\\mathcal{L}_{simple}$ [17, 31, 36]:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {s i m p l e}} = \\mathbb {E} _ {z, y, \\epsilon , t} [ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, \\tau (y), M \\circ \\phi (x)) \\| _ {2} ^ {2} ], \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "where $\\tau(\\cdot)$ represents the text encoder, $y$ denotes the text input, $t$ is the denoising step, and $z_{t}$ is the latent codes at step $t$ . Typically, the text $y$ is drawn from some templates, such as A photo of S, where S can be instantiated as virtual words [47] or the corresponding class name [50]. In the inference time, S can be flexibly composed with natural languages to achieve customization.",
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+ "type": "text",
+ "text": "3.2. Shared and Square KV Mapping Matrices",
+ "text_level": 1,
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+ "type": "text",
+ "text": "This paper aims at a plug-and-play customization model that enables users to utilize a diverse range of diffusion models with varying structures during testing. Achieving this goal necessitates ensuring that the customization encoder remains independent of the architecture of the diffusion UNet. However, recall the pipeline of existing techniques shown in Fig. 2(a), and we find that the encoder and the UNet are coupled in the cross-attention layers. When using a different architecture, the number of cross-attention layers and their dimensions do not necessarily match the seen model. Consequently, the trained customized model cannot be loaded into a novel diffusion model. To address this issue, instead of fine-tuning key and value mappings",
+ "bbox": [
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+ {
+ "type": "page_number",
+ "text": "18316",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "for cross-attention, we propose to learn additional square transformation matrices $T_{k}$ and $T_{v}$ for features after the image MLP, such that their shapes are only relevant to the image feature dimension, without any dependence on diffusion backbones. The key and value mappings used in the added cross-attention layers are obtained via linear transformation: $\\hat{W}_k\\gets T_kW_k$ and $\\hat{W}_v\\gets T_vW_v$ .",
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+ "type": "text",
+ "text": "We find that such a technique kills two birds with one stone: it not only resolves the issue of variability in the number of channels across various models, but also reduces the upper bound of generalized error even if their channel dimensions are consistent. Please refer to the theoretical analysis in the appendix, which indicates that our approach is less sensitive to the discrepancy of feature spaces between seen and unseen models. In Fig. 3(a), we validate this effect by comparing the cosine similarity between the estimated $\\hat{W}_k$ and $\\hat{W}_v$ in unseen architectures and their optimal counterparts that have been trained on these architectures and serve as oracles. As shown in Figs. 3(c) and (d), this design is essential for the model to produce meaningful results.",
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+ "type": "text",
+ "text": "At this point, the only unresolved issue is the variability in the number of cross-attention layers. To tackle the problem, it is crucial to discern between the invariant and variant factors across different target diffusion models. By ensuring that our method does not rely on variant factors, we can develop a solution that remains robust and adaptable across various diffusion models. In this paper, we capitalize on the multi-scale functionality inherent in diffusion UNets and introduce an innovative solution whereby the cross-attention layers within different blocks but the same resolution scale share a common set of $T_{k}$ and $T_{v}$ matrices. Formally, the cross-attention results for the $j$ -th block of the $i$ -th scale can be written as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\operatorname {C r o s s A t t n} \\left(Q ^ {i, j}, (M \\circ \\phi (x)) T _ {k} ^ {i} W _ {k} ^ {i, j}, (M \\circ \\phi (x)) T _ {v} ^ {i} W _ {v} ^ {i, j}\\right), \\tag {3}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where ${}^{i,j}$ specifies the indices of scale and block. The overall design is illustrated in Fig. 2(b). As shown in Figs. 3(d) and (e), this strategy further enhances the cross-model generalizability.",
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+ "type": "text",
+ "text": "One might wonder whether it is feasible to retain $T_{k}$ and $T_{v}$ as identity matrices and solely focus on learning the MLP part, yielding the simplest design. However, comparing Figs. 3(e) and (f), the method results in inferior identity preservation, underscoring the significance of adapting the textual condition space to the subject condition space. Please refer to the appendix for more explorations.",
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+ "type": "text",
+ "text": "3.3. Hierarchical Cross-Attention",
+ "text_level": 1,
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+ "type": "text",
+ "text": "To address the trade-off between appearance preservation and text prompt adherence, we devise a novel hierarchical cross-attention mechanism in this paper, where the holistic attention first captures the global semantics of subject images, and then the attention scores to the global semantics",
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+ {
+ "type": "image",
+ "img_path": "images/cc4a506724e961aef5846d74f4e90b559bd5bcdcd1fc7b0d0d70743d9c26377b.jpg",
+ "image_caption": [
+ "Figure 4. The proposed personalized text-to-image generation method is driven by holistic and fine-grained mappings. We devise a hierarchical cross-attention mechanism for the interaction between the two branches, which yields satisfactory text adherence and appearance preservation concurrently. An optimal transport constraint is applied here as prior knowledge guiding cross-model generalization."
+ ],
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+ "page_idx": 3
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+ {
+ "type": "text",
+ "text": "are divided according to the fine-grained attention. Similar to ELITE [47], we subsequently trained two mapping networks $M_{h}$ and $M_{f}$ to extract holistic and fine-grained features in the textual space for holistic and fine-grained cross-attention, respectively.",
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+ "type": "text",
+ "text": "Holistic Mapping: The designs of the holistic mapping network $M_h$ mainly follow the previous work BLIP-Diffusion [24], which extracts $n$ virtual words in the token embedding space of the CLIP text encoder via a Q-Former [25], taking as input features from a frozen pretrained image encoder. Denoting these virtual words as $S$ , the Q-Former is optimized to minimize a loss function $\\mathcal{L}_h$ consisting of $\\mathcal{L}_{simple}$ in Eq. 2 based on the text prompts like A photo of $S$ and an L1 regularization term for $S$ . Since the primary goal of holistic mapping is to extract virtual words that are compatible with real prompts, we omit $T_k$ and $T_v$ in Eq. 3, and instead directly use the native key-value parameters to process the textual conditions.",
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+ "type": "text",
+ "text": "Fine-Grained Mapping: The designs of the fine-grained mapping network $M_{f}$ mainly follow the previous work ELITE [47], where features of $n$ layers in the CLIP image encoder are separately mapped to $n$ virtual words in the token embedding space of the CLIP text encoder by $n$ learnable sub-mappers with two Linear-LayerNorm-LeakyReLU blocks. Following ELITE [47], we also apply subject masks here to filter out irrelevant backgrounds.",
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+ "type": "text",
+ "text": "Different from previous techniques that require adjusting the hyperparameter $\\lambda$ in Eq. 1 to balance the holistic and fine-grained attention, we propose a hierarchical approach. Denoting the query, key, and value after the projection of $W_{q}$ , $W_{k}$ , and $W_{v}$ in a holistic cross-attention layer as $Q \\in \\mathbb{R}^{s \\times c}$ and $K_{h}, V_{h} \\in \\mathbb{R}^{l_{h} \\times c}$ , respectively, where $s$ is the number of query tokens, i.e., the spatial dimensionality of current latent codes, $l_{h}$ is the number of textual tokens, and $c$ is the feature dimensionality of this layer, and assuming that the primary word is located at",
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+ "type": "page_number",
+ "text": "18317",
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+ {
+ "type": "table",
+ "img_path": "images/7003fac0485a51ba3e59ae129578b83eca500d356300d90a5e8c11439d7a4c63.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Method | Unseen Architecture |
| LCM | Base Diffusion | Small Diffusion | Tiny Diffusion | Seen Architecture |
| C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I |
| BLIP-Diffusion [24] | .282 | .589 | .201 | .275 | .680 | .201 | .266 | .652 | .360 | .281 | .565 | .181 | .300 | .771 | .583 |
| IP-Adapter [50] | .291 | .679 | .449 | .281 | .596 | .210 | .269 | .538 | .133 | .268 | .536 | .142 | .295 | .796 | .629 |
| ELITE [47] | .288 | .665 | .441 | .219 | .535 | .050 | .229 | .559 | .093 | .226 | .562 | .121 | .255 | .762 | .652 |
| Ours | .307 | .694 | .532 | .303 | .710 | .500 | .302 | .687 | .482 | .300 | .675 | .479 | .302 | .772 | .667 |
",
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+ "type": "text",
+ "text": "Table 1. Quantitative comparisons with state-of-the-art zero-shot text-to-image personalization methods and ablation studies. Best performance is marked in bold.",
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+ "type": "text",
+ "text": "the $p$ -th token, we first compute the holistic attention map $A_{h}$ with $A_{h} \\gets \\mathrm{Softmax}\\left(\\frac{QK_{h}^{\\top}}{\\sqrt{c}}\\right)$ , and extract the attention map corresponding to the primary word, i.e., the $p$ -th column of $A_{h}$ , denoted as $A_{h}^{:p} \\in \\mathbb{R}^{s \\times 1}$ . Then, denoting the post-projection key and value in the corresponding fine-grained cross-attention layer as $K_{f}, V_{f} \\in \\mathbb{R}^{l_{f} \\times c}$ , respectively, where $l_{f}$ is the number of fine-grained tokens, we further divide the column $A_{h}^{:p}$ into $l_{f}$ columns weighted by the fine-grained attention map $A_{f} \\gets \\mathrm{Softmax}\\left(\\frac{QK_{f}^{\\top}}{\\sqrt{c}}\\right)$ , i.e., replace the column $A_{h}^{:p}$ by $l_{f}$ columns $A_{h}^{:p} * A_{f}$ , with * representing element-wise multiplication allowing broadcast. Accordingly, the $p$ -th row in $V_{h}$ is substituted by the $l_{f}$ rows in $V_{f}$ . Denoting the updated attention map and value as $A'$ and $V'$ , respectively, the output of such hierarchical cross-attention is given by $\\mathrm{Out} \\gets A'V'$ , which is adopted to replace the original computational rule in Eq. 1 for all cross-attention layers. We offer an illustrative presentation of the workflow in Fig. 4.",
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+ "page_idx": 4
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+ {
+ "type": "text",
+ "text": "3.4. Optimal Transport Prior",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Without knowledge of unseen models, subject-driven models face challenges in achieving cross-model generalization. To mitigate this issue, we seek to imbue fine-grained attention with generic knowledge, guiding the cross-model customization process with priors to enhance performance. In this paper, we explore an optimal transport prior that encourages an even migration of visual patterns from subject images to customized results and penalizes one-to-many mappings [27]. Assume that $Q \\in \\mathbb{R}^{s \\times c}$ and $K_{f} \\in \\mathbb{R}^{lf \\times c}$ are two discrete distributions. The total mass in $K$ is defined as the total attention score to the primary word in the holistic attention, i.e., $\\sum A_{h}^{i,p}$ . Since we expect the mass in $K$ to be evenly transported into $Q$ , the mass of each point in $K$ should be $\\frac{\\sum A_{h}^{i,p}}{l_f}$ . We add the regularization of balanced total attention scores in each point of $K$ to Eq. 2. The loss function for the fine-grained mapping can be written as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {f} = \\mathcal {L} _ {\\text {s i m p l e}} + \\frac {\\alpha}{N} \\sum_ {j = 1} ^ {N} \\| \\sum A _ {f} ^ {:, j} - \\frac {\\sum A _ {h} ^ {: , p}}{l _ {f}} \\| _ {2} ^ {2}, \\tag {4}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "where $N$ denotes the total number of columns in all the fine-grained attention maps, and $\\alpha$ is a hyperparameter controlling the strength of this regularization.",
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+ {
+ "type": "text",
+ "text": "4. Experiments",
+ "text_level": 1,
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+ "page_idx": 4
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+ {
+ "type": "text",
+ "text": "4.1. Implementation Details",
+ "text_level": 1,
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+ "type": "text",
+ "text": "We build UniversalBooth on the open-source implementation of ELITE [47]. The architecture of the diffusion model in training is StableDiffusion v1.4 [36]. The test set of the OpenImages dataset [23], containing 120K images, is adopted to train the holistic mapping, while 47K of them with annotations of object masks are used to train the fine-grained mapping. The hyper-parameter $\\alpha$ in Eq. 4 is set as 0.01 empirically. We train the holistic and fine-grained mappings on 4 RTX 6000 Ada GPUs for 40,000 and 80,000 iterations, respectively. Other setups, including the diffusion sampler and the scale of classifier-free guidance, follow the default configurations if not mentioned specifically.",
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+ "type": "text",
+ "text": "The evaluation dataset is also consistent with ELITE [47] that adopts 2,500 test cases formed by a pairwise combination of 20 subject images, 25 text templates, and 5 random seeds. Following the convention of personalized text-to-image generation [22, 37, 47], we evaluate our method on 3 metrics, including CLIP-I (C-I) and DINO-I (D-I) for image consistency and CLIP-T (C-T) for text consistency. CLIP-I and DINO-I measure the cosine similarity between features of generated and source subject images in the CLIP image encoder [33] and the ViTS/16 DINO [6]. CLIP-T measures the cosine similarity between features of generated images in the CLIP image encoder and text prompts in the CLIP text encoder, where object class names of the subject images are used in the text templates.",
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+ "type": "text",
+ "text": "4.2. Cross-Architecture Generalization",
+ "text_level": 1,
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+ "table_body": "| Architecture | Method | CLIP-T | CLIP-I | DINO-I |
| SD-XL | ELITE | .317 | .650 | .336 |
| Ours | .294 | .766 | .580 |
| SD-3-Medium | ELITE | .316 | .691 | .446 |
| Ours | .319 | .750 | .581 |
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+ "text": "As a result, as shown in Fig. 5, without specific consideration of cross-model generalization, existing methods fail to produce plausible personalized text-to-image generation results. For BLIP-Diffusion, since it utilizes BLIP [25] as a pre-trained vision-language prior, the produced results can often convey aligned semantics. However, the colors and textures cannot match those in the original subject images. Even worse, when the architectural gap between the unseen and seen diffusion models is large, e.g., Tiny Diffusion, the content layouts tend to be out of control. For IP-Adapter and ELITE, suffering from misalignments of feature spaces in this setting, they are prone to messy and meaningless textures. Compared with them, our method successfully addresses these and exhibits better robustness to the architectural variations. Quantitatively, as reported in Tab. 1(left), our method outperforms existing ones in cross-architecture generalization by a large margin.",
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+ "text": "overall achieves comparable quantitative metrics with state-of-the-art methods. Specifically, it yields higher CLIP-T and DINO-I but slightly lower CLIP-I. We speculate that it is because the hierarchical cross-attention mechanism in this paper improves the trade-off between text alignment and the preservation of detailed local patterns, which may favor low-level metrics like DINO-I based on features of self-supervised learning compared with the high-level metric CLIP-T. Also, according to the ablation studies, the sharing of key and value mappings in cross-attention layers of the same scale inevitably sacrifices performance on seen architectures to some extent. In addition, compared with works like BLIP-Diffusion and IP-Adapter, the consumption of computational resources, including data, GPU cards, and training time, is significantly lower for our method, as demonstrated in the appendix. These are factors that UniversalBooth has not achieved significantly superior performance to the state-of-the-art methods on seen architectures.",
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+ "Figure 8. Existing methods like ELITE [47] require adjusting the hyperparameter $\\lambda$ to balance the text adherence and appearance preservation, whose optimal choices, marked by the stars, are case by case, while our method does not."
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+ "Figure 9. The optimal transport prior $\\mathcal{L}_{ot}$ helps cross-model generalization by regulating the layout of the generated subject."
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+ "text": "significant advantages in many cases. Specifically, methods like BLIP-Diffusion and IP-Adapter tend to preserve the major semantics while ignoring the local patterns, which leads to inferior appearance preservation, e.g., the cat, the bag, and the cat statue in the 1st, 4th, and 5th columns, respectively. ELITE struggles to deal with colors in text prompts by confusing colors of subjects and backgrounds, e.g., the dog in the 3rd column, and the bag in the 4th column. In comparison, our method handles these cases better.",
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+ "text": "In this part, we demonstrate the effectiveness of the proposed three components, including shared and square key and value mapping matrices, hierarchical cross-attention, and optimal transport prior, through ablation studies. Quantitatively, the impact of each component on the performance is shown in Tab. 3.",
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+ "text": "Shared and Square Key and Value Mapping Matrices: As demonstrated in Fig. 3, by decoupling the subject encoder from the number of channels and blocks in diffusion backbones, shared and square key and value mappings help align the subject feature space and the condition space shared by different diffusion models and play crucial roles in achieving cross-architecture generalization. We provide more supportive examples in the appendix.",
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+ "table_body": "| Setting | Unseen Architecture | Seen Architecture |
| Small Diffusion | Tiny Diffusion | C-T | C-I | D-I |
| C-T | C-I | D-I | C-T | C-I | D-I |
| w/o KV | .302 | .664 | .424 | .300 | .653 | .422 | .301 | .756 | .650 |
| w/o Shared KV | .283 | .650 | .365 | .232 | .556 | .163 | .300 | .785 | .683 |
| w/o HieraAttn | .289 | .614 | .291 | .288 | .613 | .305 | .297 | .768 | .629 |
| w/o Lot | .292 | .644 | .377 | .284 | .613 | .291 | .302 | .760 | .584 |
| Ours | .302 | .687 | .482 | .300 | .675 | .479 | .302 | .772 | .667 |
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+ "Figure 10. The design of shared and square key and value mappings enables UniversalBooth to be generalized to models with various functionalities like text-driven editing."
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+ "text": "In this paper, we present UniversalBooth, a model-agnostic framework for personalized text-to-image generation. Dedicated to the problem of cross-diffusion generalization, we mainly introduce three novel designs: (1) cross-attention with shared and square key and value mappings, which achieves cross-architecture zero-shot inference in functionality, (2) hierarchical cross-attention, which alleviates the trade-off between text adherence and appearance preservation, and (3) an optimal transport prior injected into the fine-grained attention, which guides the behavior of unseen models with generic knowledge and further improves the cross-model generalization performance. Experiments demonstrate that UniversalBooth is the first versatile model for personalized text-to-image generation that can be generalized to unseen diffusion backbones seamlessly without any additional training effort. It also achieves superior zero-shot personalization performance on seen architectures.",
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+ "type": "list",
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+ "angle": 0,
+ "content": "Given a source image, personalized text-to-image generation produces images preserving the identity and appearance while following the text prompts. Existing methods heavily rely on test-time optimization to achieve this customization. Although some recent works are dedicated to zero-shot personalization, they still require re-training when applied to different text-to-image diffusion models. In this paper, we instead propose a model-agnostic personalized method termed UniversalBooth. At the heart of our approach lies a novel cross-attention mechanism, where different blocks in the same diffusion scale share common square transformation matrices of key and value. In this way, the image encoder is decoupled from the diffusion architecture while maintaining its effectiveness. Moreover, the cross-attention performs hierarchically: the holistic attention first captures the global semantics of user inputs for textual combination with editing prompts, and the fine-grained attention divides the holistic attention scores"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.575,
+ 0.909,
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+ "angle": 0,
+ "content": "for various local patches to enhance appearance consistency. To improve the performance when deployed on unseen diffusion models, we further devise an optimal transport prior to the model and encourage the attention scores allocated by cross-attention to fulfill the optimal transport constraint. Experiments demonstrate that our personalized generation model can be generalized to unseen text-to-image diffusion models with a wide spectrum of architectures and functionalities without any additional optimization, while other methods cannot. Meanwhile, it achieves comparable zero-shot personalization performance on seen architectures with existing works."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Although text-to-image diffusion models have advanced significantly in recent years due to their generative capabilities [11, 31, 36], they fall short in personalized image generation, also known as subject-driven image generation, where generated images adhere to text prompts while preserving specific identities and appearances from user-"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "*Corresponding Author."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "18314"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.482,
+ 0.137
+ ],
+ "angle": 0,
+ "content": "provided images. Given the broad applicability in real-world scenarios, this customization has garnered attention from both academia and industry."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.139,
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+ ],
+ "angle": 0,
+ "content": "Personalized generation typically involves establishing correspondences between source images and textual space, allowing diffusion models to reconstruct images and generate variations based on text prompts. Early methods rely on test-time optimization [14] or fine-tuning the diffusion model [22, 37], which are computationally expensive and impractical for end users. Recent efforts aim to reduce this burden through offline learning, such as training a visual encoder for feed-forward textual correspondences [19, 24, 39, 44, 47, 52]. These methods achieve impressive zero-shot personalized text-to-image generation: once trained, the visual encoder can capture input concepts from subject images in real time."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "However, flexibility remains an issue when applying these methods to various text-to-image models with unseen structures, which is a practical problem since real-world models can be updated or replaced frequently. Re-training the encoder for each model can take several days on multiple GPUs [44, 47], making it highly cumbersome if not impossible at all. Moreover, for some distilled models like LCM [28], it is even infeasible to conduct vanilla training directly as it requires a specific distillation objective concerning its teacher."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Focusing on this drawback, we aim at a model-agnostic approach termed UniversalBooth in this paper and expect a trained visual encoder to be generalized to other text-to-image backbones seamlessly. To this end, we first delve into the design intricacies of existing personalized generation methods without test-time optimization and reveal that the significant impediment to such generalization lies in the strong coupling between the visual encoder and the crossattention layers of the diffusion UNet, which are key modules for the diffusion model to interact with input conditions. Previous works largely ignore the variability in backbone text-to-image models. Consequently, their visual encoders are susceptible to overfitting the specific diffusion model seen in training."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "In this paper, we tackle this challenge by introducing a novel cross-attention mechanism that decouples the visual subject encoder from the diffusion architecture. Unlike conventional approaches, our method utilizes a shared group of square mapping matrices for both key and value components across different blocks within the same diffusion scale. This design promotes flexibility across a range of diffusion models characterized by varying numbers of channels or blocks, all while ensuring consistent effectiveness in generating high-quality images."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.856,
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+ "angle": 0,
+ "content": "Moreover, we devise a hierarchical cross-attention strategy. Specifically, the visual encoder first capsules global semantic features of user inputs into a virtual word, which"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
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+ ],
+ "angle": 0,
+ "content": "is convenient for textual combination with editing prompts. To enhance appearance consistency, the cross-attention scores for this word are further divided by fine-grained attention considering local patches. Overall, this hierarchical approach ensures that the generated images not only align with textual prompts but also maintain coherence and fidelity to the visual subjects."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Notably, the fine-grained cross-attention in our approach is backed up with an optimal transport prior, which is achieved by regulating attention scores allocated by the cross-attention mechanism to fulfill optimal transport constraints. In this way, even when tested on unfamiliar novel diffusion architectures, our customization model can be guided by this prior knowledge acquired in training, which further bolsters cross-model generalizability."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We conduct extensive experiments to showcase the effectiveness and versatility of our approach. As shown in Fig. 1, results indicate that once trained, the proposed Universal-Booth can be generalized to unseen text-to-image diffusion models with a wide spectrum of architectures and functionalities without any additional training effort, while other methods cannot. Meanwhile, it yields on-par zero-shot personalized generation performance with existing works on seen diffusion backbones. Our contributions can be summarized as follows:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We investigate a novel problem, namely model-agnostic personalized text-to-image generation. To the best of our knowledge, this is the first work dedicated to the cross-model generalization issue in this field."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We tailor a novel cross-attention mechanism to address the problem. Specifically, it adopts shared key and value mappings among various blocks within the same scale, works in an innovative hierarchical manner, and is injected with optimal transport prior."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- Experiments suggest that UniversalBooth achieves superior cross-model personalized generation results to unseen diffusion models and comparable performance in the vanilla test setting on seen models."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "2. Related Works"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Personalized text-to-image generation refers to producing images according to the text prompts while preserving the identity and appearance of users' image inputs. One promising solution for this application is to learn the word embedding [14] or fine-tune the diffusion model [22, 37] specifically for one subject in an iterative optimization fashion, which exhibits limited flexibility. Recent studies have been dedicated to addressing this limitation and focused on an any-subject-one-model paradigm. The basic idea is to replace the optimization process with a single feedforward propagation: to learn a neural network and map the input images to the conditional space of the diffusion model [9, 16, 18, 24, 26, 29, 41, 43, 44, 47, 50, 52] in a one-"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "18315"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 2. (a) Overview of zero-shot personalized text-to-image generation solutions (text branch omitted). (b) Our approach learns square and shared key-value mappings in cross-attention layers, enabling flexible cross-diffusion-model generalization during inference without extra training."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "stop manner. We provide a systematic summary of existing works in the appendix."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "These methods typically focus on the subject-wise flexibility and have achieved remarkable performance simultaneously. Nevertheless, when the base diffusion model changes—a common and practical scenario given the rapid proliferation and advancement of large text-to-image diffusion models [3, 4, 10, 12, 13, 20, 21, 28-30, 32, 34, 34, 36, 38, 42, 44, 48]—they typically require adapting the subject mapper to the new architecture through an optimization process as well [35]. We thus offer a different perspective regarding the model-wise flexibility and introduce UniversalBooth in this paper, the first method specifically designed for the cross-model generalization problem in personalized generation. Unlike existing techniques, UniversalBooth enables zero-shot customized generation on unseen diffusion models without requiring any additional training."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3. Methodology"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3.1. Preliminary"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.628,
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+ ],
+ "angle": 0,
+ "content": "Different from early approaches [14, 22, 37] that obtain textual correspondences of subject images through test-time optimization, recent test-time fine-tuning-free personalized image generation methods learn a neural mapping from the visual space to the textual space so that the textual representations can be generated in a single forward propagation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We illustrate the overall pipeline of some popular designs like ELITE [47] and IP-Adapter [50] in Fig. 2(a). Typically, given a subject image \\( x \\), these methods first adopt the CLIP image encoder [33], denoted as \\( \\phi(\\cdot) \\), for feature extraction. As CLIP has been trained on abundant text-image pairs to align corresponding features, it may serve as a valuable resource for learning text-aware vision representations. Subsequently, a learnable MLP denoted as \\( M \\) is trained to convert CLIP vision features into virtual words in the textual embedding space. Additional cross-attention is incorporated into the cross-attention layers of the pre-trained diffusion UNet to enhance its adaptability to"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ 0.088,
+ 0.615,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.516,
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+ ],
+ "angle": 0,
+ "content": "(a) Cosimine Similarity between Predicted and Optimal Mapping Matrices"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(b) Subject Image"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.741,
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+ ],
+ "angle": 0,
+ "content": "(d) Square KV Mappings"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.788,
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(e) Square and Shap KV Mappings"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.847,
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.862,
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+ ],
+ "angle": 0,
+ "content": "(f) wo KV Mappings"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "Figure 3. Preliminary results of cross-model generalization by different operations on cross-attention. Images in (c), (d), (e), and (f) are generated with the prompt A photo of a S."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "conditions injected by subject images, which is crucial to the performance given the significant role of cross-attention (CA) in subject-driven text-to-image generation, as highlighted in [1, 15, 22]. The CA results for the subject branch are added to the original results:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.516,
+ 0.289,
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+ 0.32
+ ],
+ "angle": 0,
+ "content": "\\[\n\\operatorname {O u t} \\leftarrow \\operatorname {O u t} + \\lambda \\operatorname {C A} (Q, (M \\circ \\phi (x)) \\hat {W} _ {k}, (M \\circ \\phi (x)) \\hat {W} _ {v}), \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.321,
+ 0.905,
+ 0.381
+ ],
+ "angle": 0,
+ "content": "where \\(Q\\) is the query matrix mapped from features in the diffusion backbone, \\(\\hat{W}_k\\) and \\(\\hat{W}_v\\) are learnable key and value mappings respectively, and \\(\\lambda\\) is a hyperparameter controlling the strength of subject injection."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "We assume that Stable Diffusion v1.5 [36] is adopted here. It first learns an auto-encoder \\((\\mathcal{E}(\\cdot),\\mathcal{D}(\\cdot))\\), where the encoder \\(\\mathcal{E}(\\cdot)\\) maps an image \\(x\\) to a lower dimensional latent space: \\(z\\gets \\mathcal{E}(x)\\), and the decoder \\(\\mathcal{D}(\\cdot)\\) learns to decode \\(z\\) back to the image space \\(\\hat{x}\\gets \\mathcal{D}(z)\\) such that \\(\\hat{x}\\) is close to the original \\(x\\). Denoising is conducted in the latent space by a UNet \\(\\epsilon_{\\theta}(\\cdot)\\) for noise prediction. With a pre-trained and frozen auto-encoder, text encoder, and UNet, the MLP and additional cross-attention layers are optimized using the vanilla noise prediction loss \\(\\mathcal{L}_{simple}\\) [17, 31, 36]:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.524,
+ 0.542,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {s i m p l e}} = \\mathbb {E} _ {z, y, \\epsilon , t} [ \\| \\epsilon - \\epsilon_ {\\theta} (z _ {t}, t, \\tau (y), M \\circ \\phi (x)) \\| _ {2} ^ {2} ], \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.569,
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+ 0.675
+ ],
+ "angle": 0,
+ "content": "where \\(\\tau(\\cdot)\\) represents the text encoder, \\(y\\) denotes the text input, \\(t\\) is the denoising step, and \\(z_{t}\\) is the latent codes at step \\(t\\). Typically, the text \\(y\\) is drawn from some templates, such as A photo of S, where S can be instantiated as virtual words [47] or the corresponding class name [50]. In the inference time, S can be flexibly composed with natural languages to achieve customization."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.2. Shared and Square KV Mapping Matrices"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This paper aims at a plug-and-play customization model that enables users to utilize a diverse range of diffusion models with varying structures during testing. Achieving this goal necessitates ensuring that the customization encoder remains independent of the architecture of the diffusion UNet. However, recall the pipeline of existing techniques shown in Fig. 2(a), and we find that the encoder and the UNet are coupled in the cross-attention layers. When using a different architecture, the number of cross-attention layers and their dimensions do not necessarily match the seen model. Consequently, the trained customized model cannot be loaded into a novel diffusion model. To address this issue, instead of fine-tuning key and value mappings"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "18316"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
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+ ],
+ "angle": 0,
+ "content": "for cross-attention, we propose to learn additional square transformation matrices \\( T_{k} \\) and \\( T_{v} \\) for features after the image MLP, such that their shapes are only relevant to the image feature dimension, without any dependence on diffusion backbones. The key and value mappings used in the added cross-attention layers are obtained via linear transformation: \\( \\hat{W}_k\\gets T_kW_k \\) and \\( \\hat{W}_v\\gets T_vW_v \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "We find that such a technique kills two birds with one stone: it not only resolves the issue of variability in the number of channels across various models, but also reduces the upper bound of generalized error even if their channel dimensions are consistent. Please refer to the theoretical analysis in the appendix, which indicates that our approach is less sensitive to the discrepancy of feature spaces between seen and unseen models. In Fig. 3(a), we validate this effect by comparing the cosine similarity between the estimated \\(\\hat{W}_k\\) and \\(\\hat{W}_v\\) in unseen architectures and their optimal counterparts that have been trained on these architectures and serve as oracles. As shown in Figs. 3(c) and (d), this design is essential for the model to produce meaningful results."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "At this point, the only unresolved issue is the variability in the number of cross-attention layers. To tackle the problem, it is crucial to discern between the invariant and variant factors across different target diffusion models. By ensuring that our method does not rely on variant factors, we can develop a solution that remains robust and adaptable across various diffusion models. In this paper, we capitalize on the multi-scale functionality inherent in diffusion UNets and introduce an innovative solution whereby the cross-attention layers within different blocks but the same resolution scale share a common set of \\( T_{k} \\) and \\( T_{v} \\) matrices. Formally, the cross-attention results for the \\( j \\)-th block of the \\( i \\)-th scale can be written as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\operatorname {C r o s s A t t n} \\left(Q ^ {i, j}, (M \\circ \\phi (x)) T _ {k} ^ {i} W _ {k} ^ {i, j}, (M \\circ \\phi (x)) T _ {v} ^ {i} W _ {v} ^ {i, j}\\right), \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\( {}^{i,j} \\) specifies the indices of scale and block. The overall design is illustrated in Fig. 2(b). As shown in Figs. 3(d) and (e), this strategy further enhances the cross-model generalizability."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "One might wonder whether it is feasible to retain \\( T_{k} \\) and \\( T_{v} \\) as identity matrices and solely focus on learning the MLP part, yielding the simplest design. However, comparing Figs. 3(e) and (f), the method results in inferior identity preservation, underscoring the significance of adapting the textual condition space to the subject condition space. Please refer to the appendix for more explorations."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3.3. Hierarchical Cross-Attention"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "To address the trade-off between appearance preservation and text prompt adherence, we devise a novel hierarchical cross-attention mechanism in this paper, where the holistic attention first captures the global semantics of subject images, and then the attention scores to the global semantics"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 4. The proposed personalized text-to-image generation method is driven by holistic and fine-grained mappings. We devise a hierarchical cross-attention mechanism for the interaction between the two branches, which yields satisfactory text adherence and appearance preservation concurrently. An optimal transport constraint is applied here as prior knowledge guiding cross-model generalization."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.34,
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+ ],
+ "angle": 0,
+ "content": "are divided according to the fine-grained attention. Similar to ELITE [47], we subsequently trained two mapping networks \\(M_{h}\\) and \\(M_{f}\\) to extract holistic and fine-grained features in the textual space for holistic and fine-grained cross-attention, respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Holistic Mapping: The designs of the holistic mapping network \\( M_h \\) mainly follow the previous work BLIP-Diffusion [24], which extracts \\( n \\) virtual words in the token embedding space of the CLIP text encoder via a Q-Former [25], taking as input features from a frozen pretrained image encoder. Denoting these virtual words as \\( S \\), the Q-Former is optimized to minimize a loss function \\( \\mathcal{L}_h \\) consisting of \\( \\mathcal{L}_{simple} \\) in Eq. 2 based on the text prompts like A photo of \\( S \\) and an L1 regularization term for \\( S \\). Since the primary goal of holistic mapping is to extract virtual words that are compatible with real prompts, we omit \\( T_k \\) and \\( T_v \\) in Eq. 3, and instead directly use the native key-value parameters to process the textual conditions."
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+ "type": "text",
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+ "content": "Fine-Grained Mapping: The designs of the fine-grained mapping network \\( M_{f} \\) mainly follow the previous work ELITE [47], where features of \\( n \\) layers in the CLIP image encoder are separately mapped to \\( n \\) virtual words in the token embedding space of the CLIP text encoder by \\( n \\) learnable sub-mappers with two Linear-LayerNorm-LeakyReLU blocks. Following ELITE [47], we also apply subject masks here to filter out irrelevant backgrounds."
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+ "angle": 0,
+ "content": "Different from previous techniques that require adjusting the hyperparameter \\(\\lambda\\) in Eq. 1 to balance the holistic and fine-grained attention, we propose a hierarchical approach. Denoting the query, key, and value after the projection of \\(W_{q}\\), \\(W_{k}\\), and \\(W_{v}\\) in a holistic cross-attention layer as \\(Q \\in \\mathbb{R}^{s \\times c}\\) and \\(K_{h}, V_{h} \\in \\mathbb{R}^{l_{h} \\times c}\\), respectively, where \\(s\\) is the number of query tokens, i.e., the spatial dimensionality of current latent codes, \\(l_{h}\\) is the number of textual tokens, and \\(c\\) is the feature dimensionality of this layer, and assuming that the primary word is located at"
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+ [
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Method | Unseen Architecture |
| LCM | Base Diffusion | Small Diffusion | Tiny Diffusion | Seen Architecture |
| C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I |
| BLIP-Diffusion [24] | .282 | .589 | .201 | .275 | .680 | .201 | .266 | .652 | .360 | .281 | .565 | .181 | .300 | .771 | .583 |
| IP-Adapter [50] | .291 | .679 | .449 | .281 | .596 | .210 | .269 | .538 | .133 | .268 | .536 | .142 | .295 | .796 | .629 |
| ELITE [47] | .288 | .665 | .441 | .219 | .535 | .050 | .229 | .559 | .093 | .226 | .562 | .121 | .255 | .762 | .652 |
| Ours | .307 | .694 | .532 | .303 | .710 | .500 | .302 | .687 | .482 | .300 | .675 | .479 | .302 | .772 | .667 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. Quantitative comparisons with state-of-the-art zero-shot text-to-image personalization methods and ablation studies. Best performance is marked in bold."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.093,
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+ "angle": 0,
+ "content": "the \\(p\\)-th token, we first compute the holistic attention map \\(A_{h}\\) with \\(A_{h} \\gets \\mathrm{Softmax}\\left(\\frac{QK_{h}^{\\top}}{\\sqrt{c}}\\right)\\), and extract the attention map corresponding to the primary word, i.e., the \\(p\\)-th column of \\(A_{h}\\), denoted as \\(A_{h}^{:p} \\in \\mathbb{R}^{s \\times 1}\\). Then, denoting the post-projection key and value in the corresponding fine-grained cross-attention layer as \\(K_{f}, V_{f} \\in \\mathbb{R}^{l_{f} \\times c}\\), respectively, where \\(l_{f}\\) is the number of fine-grained tokens, we further divide the column \\(A_{h}^{:p}\\) into \\(l_{f}\\) columns weighted by the fine-grained attention map \\(A_{f} \\gets \\mathrm{Softmax}\\left(\\frac{QK_{f}^{\\top}}{\\sqrt{c}}\\right)\\), i.e., replace the column \\(A_{h}^{:p}\\) by \\(l_{f}\\) columns \\(A_{h}^{:p} * A_{f}\\), with * representing element-wise multiplication allowing broadcast. Accordingly, the \\(p\\)-th row in \\(V_{h}\\) is substituted by the \\(l_{f}\\) rows in \\(V_{f}\\). Denoting the updated attention map and value as \\(A'\\) and \\(V'\\), respectively, the output of such hierarchical cross-attention is given by \\(\\mathrm{Out} \\gets A'V'\\), which is adopted to replace the original computational rule in Eq. 1 for all cross-attention layers. We offer an illustrative presentation of the workflow in Fig. 4."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.4. Optimal Transport Prior"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Without knowledge of unseen models, subject-driven models face challenges in achieving cross-model generalization. To mitigate this issue, we seek to imbue fine-grained attention with generic knowledge, guiding the cross-model customization process with priors to enhance performance. In this paper, we explore an optimal transport prior that encourages an even migration of visual patterns from subject images to customized results and penalizes one-to-many mappings [27]. Assume that \\(Q \\in \\mathbb{R}^{s \\times c}\\) and \\(K_{f} \\in \\mathbb{R}^{lf \\times c}\\) are two discrete distributions. The total mass in \\(K\\) is defined as the total attention score to the primary word in the holistic attention, i.e., \\(\\sum A_{h}^{i,p}\\). Since we expect the mass in \\(K\\) to be evenly transported into \\(Q\\), the mass of each point in \\(K\\) should be \\(\\frac{\\sum A_{h}^{i,p}}{l_f}\\). We add the regularization of balanced total attention scores in each point of \\(K\\) to Eq. 2. The loss function for the fine-grained mapping can be written as:"
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+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {f} = \\mathcal {L} _ {\\text {s i m p l e}} + \\frac {\\alpha}{N} \\sum_ {j = 1} ^ {N} \\| \\sum A _ {f} ^ {:, j} - \\frac {\\sum A _ {h} ^ {: , p}}{l _ {f}} \\| _ {2} ^ {2}, \\tag {4}\n\\]"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(N\\) denotes the total number of columns in all the fine-grained attention maps, and \\(\\alpha\\) is a hyperparameter controlling the strength of this regularization."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.1. Implementation Details"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We build UniversalBooth on the open-source implementation of ELITE [47]. The architecture of the diffusion model in training is StableDiffusion v1.4 [36]. The test set of the OpenImages dataset [23], containing 120K images, is adopted to train the holistic mapping, while 47K of them with annotations of object masks are used to train the fine-grained mapping. The hyper-parameter \\(\\alpha\\) in Eq. 4 is set as 0.01 empirically. We train the holistic and fine-grained mappings on 4 RTX 6000 Ada GPUs for 40,000 and 80,000 iterations, respectively. Other setups, including the diffusion sampler and the scale of classifier-free guidance, follow the default configurations if not mentioned specifically."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The evaluation dataset is also consistent with ELITE [47] that adopts 2,500 test cases formed by a pairwise combination of 20 subject images, 25 text templates, and 5 random seeds. Following the convention of personalized text-to-image generation [22, 37, 47], we evaluate our method on 3 metrics, including CLIP-I (C-I) and DINO-I (D-I) for image consistency and CLIP-T (C-T) for text consistency. CLIP-I and DINO-I measure the cosine similarity between features of generated and source subject images in the CLIP image encoder [33] and the ViTS/16 DINO [6]. CLIP-T measures the cosine similarity between features of generated images in the CLIP image encoder and text prompts in the CLIP text encoder, where object class names of the subject images are used in the text templates."
+ },
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+ "angle": 0,
+ "content": "4.2. Cross-Architecture Generalization"
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "As our target in this paper is a model-agnostic personalized text-to-image generation method, we mainly evaluated the proposed UniversalBooth on diffusion models with unseen architectures in training. Specifically, we consider both cases of large-to-small and small-to-large cross-model generalization. For small architectures, we adopt two diffusion models distilled from Stable Diffusion in [21] for experiments, denoted as Small Diffusion and Tiny Diffusion. For large architectures, we consider two popular structures, i.e., StableDiffusion-XL [32] (SD-XL) and StableDiffusion-3-Medium [13] (SD-3). Although both seen and unseen involve CLIP for textual embedding, for SD-XL and SD"
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+ "angle": 0,
+ "content": "Figure 5. Results of large-to-small cross-architecture generalization comparing with state-of-the-art methods."
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+ "type": "text",
+ "bbox": [
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+ "content": "3, since the conditional spaces are constructed using multiple text encoders, they do not strictly satisfy the consistent condition space assumption required by the fine-grained encoder. Therefore, we use only the holistic encoder for them."
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+ "type": "text",
+ "bbox": [
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+ "content": "To demonstrate the unique superiority of our method in cross-architecture generalization, we compare Universal-Booth with three open-source and state-of-the-art personalized generation methods, including BLIP-Diffusion [24],"
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+ "angle": 0,
+ "content": "IP-Adapter [50], and ELITE [47]. These methods overlook the variability of diffusion models in the inference time and couple the subject encoder module with the diffusion UNet. For instance, BLIP-Diffusion requires fine-tuning both the whole diffusion UNet and the image-to-BLIP mapping module. IP-Adapter and ELITE fine-tune the crossattention layers in the original diffusion backbones, which makes the subject encoders overfit to the seen diffusion ar"
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+ "content": "a S on top of a purple rug in a forest"
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+ "angle": 0,
+ "content": "ELITE"
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 6. Results of small-to-large cross-architecture generalization. The seen architecture is StableDiffusion v1.4, while the unseen architectures are StableDiffusion-XL and StableDiffusion 3 Medium, respectively."
+ },
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+ "type": "table",
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+ "angle": 0,
+ "content": "| Architecture | Method | CLIP-T | CLIP-I | DINO-I |
| SD-XL | ELITE | .317 | .650 | .336 |
| Ours | .294 | .766 | .580 |
| SD-3-Medium | ELITE | .316 | .691 | .446 |
| Ours | .319 | .750 | .581 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Quantitative comparisons with the baseline method ELITE [47] on small-to-large cross-architecture generalization. Best performance is marked in bold."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "chitecture in training. To adapt them for cross-architecture generation, we only load the matched cross-attention layers in inference time and drop the extra layers."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "As a result, as shown in Fig. 5, without specific consideration of cross-model generalization, existing methods fail to produce plausible personalized text-to-image generation results. For BLIP-Diffusion, since it utilizes BLIP [25] as a pre-trained vision-language prior, the produced results can often convey aligned semantics. However, the colors and textures cannot match those in the original subject images. Even worse, when the architectural gap between the unseen and seen diffusion models is large, e.g., Tiny Diffusion, the content layouts tend to be out of control. For IP-Adapter and ELITE, suffering from misalignments of feature spaces in this setting, they are prone to messy and meaningless textures. Compared with them, our method successfully addresses these and exhibits better robustness to the architectural variations. Quantitatively, as reported in Tab. 1(left), our method outperforms existing ones in cross-architecture generalization by a large margin."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "For small-to-large generalization with SD-XL and SD-3, the qualitative and quantitative comparisons against the ELITE baseline [47] are shown in Fig. 6 and Tab. 2, respectively. Although ELITE can capture the overall semantics of subject images and textual prompts, the results largely overlook the detailed appearances. In contrast, our method exhibits superior cross-model generalization."
+ },
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.3. Comparisons on Seen Architectures"
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+ "content": "We also compare our method with existing ones on the seen architectures. As shown in Tab. 1(right), UniversalBooth"
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+ "content": "Subject Image Blip Diffusion"
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+ "content": "Figure 7. Results of personalized generation on seen architectures."
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+ "content": "overall achieves comparable quantitative metrics with state-of-the-art methods. Specifically, it yields higher CLIP-T and DINO-I but slightly lower CLIP-I. We speculate that it is because the hierarchical cross-attention mechanism in this paper improves the trade-off between text alignment and the preservation of detailed local patterns, which may favor low-level metrics like DINO-I based on features of self-supervised learning compared with the high-level metric CLIP-T. Also, according to the ablation studies, the sharing of key and value mappings in cross-attention layers of the same scale inevitably sacrifices performance on seen architectures to some extent. In addition, compared with works like BLIP-Diffusion and IP-Adapter, the consumption of computational resources, including data, GPU cards, and training time, is significantly lower for our method, as demonstrated in the appendix. These are factors that UniversalBooth has not achieved significantly superior performance to the state-of-the-art methods on seen architectures."
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+ "content": "Nevertheless, as shown in Fig. 7, our method indeed has"
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+ "content": "Figure 8. Existing methods like ELITE [47] require adjusting the hyperparameter \\(\\lambda\\) to balance the text adherence and appearance preservation, whose optimal choices, marked by the stars, are case by case, while our method does not."
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+ "content": "Figure 9. The optimal transport prior \\(\\mathcal{L}_{ot}\\) helps cross-model generalization by regulating the layout of the generated subject."
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+ "content": "significant advantages in many cases. Specifically, methods like BLIP-Diffusion and IP-Adapter tend to preserve the major semantics while ignoring the local patterns, which leads to inferior appearance preservation, e.g., the cat, the bag, and the cat statue in the 1st, 4th, and 5th columns, respectively. ELITE struggles to deal with colors in text prompts by confusing colors of subjects and backgrounds, e.g., the dog in the 3rd column, and the bag in the 4th column. In comparison, our method handles these cases better."
+ },
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+ "content": "4.4. Ablation Studies"
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+ "content": "In this part, we demonstrate the effectiveness of the proposed three components, including shared and square key and value mapping matrices, hierarchical cross-attention, and optimal transport prior, through ablation studies. Quantitatively, the impact of each component on the performance is shown in Tab. 3."
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+ "content": "Shared and Square Key and Value Mapping Matrices: As demonstrated in Fig. 3, by decoupling the subject encoder from the number of channels and blocks in diffusion backbones, shared and square key and value mappings help align the subject feature space and the condition space shared by different diffusion models and play crucial roles in achieving cross-architecture generalization. We provide more supportive examples in the appendix."
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+ "content": "Hierarchical Cross-Attention: Previous methods like IP-Adapter and ELITE achieve the trade-off between text prompt adherence and appearance preservation by adjusting the weight of the subject condition, which is not robust in practice. As shown in Fig. 8, in different cases, the optimal choice of this hyperparameter can also be different. Compared with these methods, the hierarchical cross-attention proposed in this paper can balance the two worlds better without deliberate adjustment."
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+ "content": "| Setting | Unseen Architecture | Seen Architecture |
| Small Diffusion | Tiny Diffusion | C-T | C-I | D-I |
| C-T | C-I | D-I | C-T | C-I | D-I |
| w/o KV | .302 | .664 | .424 | .300 | .653 | .422 | .301 | .756 | .650 |
| w/o Shared KV | .283 | .650 | .365 | .232 | .556 | .163 | .300 | .785 | .683 |
| w/o HieraAttn | .289 | .614 | .291 | .288 | .613 | .305 | .297 | .768 | .629 |
| w/o Lot | .292 | .644 | .377 | .284 | .613 | .291 | .302 | .760 | .584 |
| Ours | .302 | .687 | .482 | .300 | .675 | .479 | .302 | .772 | .667 |
"
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+ "content": "Table 3. Ablation studies for various technical designs introduced in this paper. HieraAttn denotes the hierarchical attention. Best performance is marked in bold."
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+ "content": "Figure 10. The design of shared and square key and value mappings enables UniversalBooth to be generalized to models with various functionalities like text-driven editing."
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+ "content": "Optimal Transport Prior: The optimal transport prior is useful to regulate the semantic layout of the generated results by penalizing one-to-many mappings. We illustrate this effect in Fig. 9. Quantitative measurements on the test cases also validate that adding the regularization \\(\\mathcal{L}_{ot}\\) in training would lead to lower \\(\\mathcal{L}_{ot}\\) in cross-model inference."
+ },
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+ "content": "4.5. Further Extension"
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+ "content": "Interestingly, we find that the proposed UniversalBooth is also compatible with other text-to-image models with different functionalities, like InstructPix2Pix [5] for text-driven image editing, thanks to the universal subject space resulting from the shared and square key and value mapping matrices. As shown in Fig. 10, the model would migrate incorrect or insufficient subject patterns if square mappings or shared mappings are removed."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "5. Conclusions"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this paper, we present UniversalBooth, a model-agnostic framework for personalized text-to-image generation. Dedicated to the problem of cross-diffusion generalization, we mainly introduce three novel designs: (1) cross-attention with shared and square key and value mappings, which achieves cross-architecture zero-shot inference in functionality, (2) hierarchical cross-attention, which alleviates the trade-off between text adherence and appearance preservation, and (3) an optimal transport prior injected into the fine-grained attention, which guides the behavior of unseen models with generic knowledge and further improves the cross-model generalization performance. Experiments demonstrate that UniversalBooth is the first versatile model for personalized text-to-image generation that can be generalized to unseen diffusion backbones seamlessly without any additional training effort. It also achieves superior zero-shot personalization performance on seen architectures."
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+ "content": "Acknowledgments"
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+ "type": "text",
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+ "angle": 0,
+ "content": "This project is supported by the Ministry of Education, Singapore, under its Academic Research Fund Tier 2 (Award Number: MOE-T2EP20122-0006)."
+ },
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+ "content": "References"
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+# UniversalBooth: Model-Agnostic Personalized Text-to-Image Generation
+
+Songhua Liu $^{12}$ , Ruonan Yu $^{1}$ , and Xinchao Wang $^{1*}$ $^{1}$ National University of Singapore $^{2}$ School of Artificial Intelligence, Shanghai Jiao Tong University
+{songhua.liu, ruonan}@u.nus.edu, xinchao@nus.edu.sg
+
+
+Personalized Image Generation
+
+
+
+
+Figure 1. We propose a model-agnostic personalized text-to-image generation method termed UniversalBooth. Once trained, it can be applied to various diffusion models with different architectures and functionalities without any additional training. "S" is a virtual token referring to the input subject. The seen model during training is SD-v1.4, while the unseen models are Distilled SD [21], SD-XL [32], SD-v3-Medium [13], InstructPix2Pix [5], LaVie [46], and MVDream [40].
+
+
+Cross-Architecture
+Cross-Functionality
+
+
+
+# Abstract
+
+Given a source image, personalized text-to-image generation produces images preserving the identity and appearance while following the text prompts. Existing methods heavily rely on test-time optimization to achieve this customization. Although some recent works are dedicated to zero-shot personalization, they still require re-training when applied to different text-to-image diffusion models. In this paper, we instead propose a model-agnostic personalized method termed UniversalBooth. At the heart of our approach lies a novel cross-attention mechanism, where different blocks in the same diffusion scale share common square transformation matrices of key and value. In this way, the image encoder is decoupled from the diffusion architecture while maintaining its effectiveness. Moreover, the cross-attention performs hierarchically: the holistic attention first captures the global semantics of user inputs for textual combination with editing prompts, and the fine-grained attention divides the holistic attention scores
+
+for various local patches to enhance appearance consistency. To improve the performance when deployed on unseen diffusion models, we further devise an optimal transport prior to the model and encourage the attention scores allocated by cross-attention to fulfill the optimal transport constraint. Experiments demonstrate that our personalized generation model can be generalized to unseen text-to-image diffusion models with a wide spectrum of architectures and functionalities without any additional optimization, while other methods cannot. Meanwhile, it achieves comparable zero-shot personalization performance on seen architectures with existing works.
+
+# 1. Introduction
+
+Although text-to-image diffusion models have advanced significantly in recent years due to their generative capabilities [11, 31, 36], they fall short in personalized image generation, also known as subject-driven image generation, where generated images adhere to text prompts while preserving specific identities and appearances from user-
+
+provided images. Given the broad applicability in real-world scenarios, this customization has garnered attention from both academia and industry.
+
+Personalized generation typically involves establishing correspondences between source images and textual space, allowing diffusion models to reconstruct images and generate variations based on text prompts. Early methods rely on test-time optimization [14] or fine-tuning the diffusion model [22, 37], which are computationally expensive and impractical for end users. Recent efforts aim to reduce this burden through offline learning, such as training a visual encoder for feed-forward textual correspondences [19, 24, 39, 44, 47, 52]. These methods achieve impressive zero-shot personalized text-to-image generation: once trained, the visual encoder can capture input concepts from subject images in real time.
+
+However, flexibility remains an issue when applying these methods to various text-to-image models with unseen structures, which is a practical problem since real-world models can be updated or replaced frequently. Re-training the encoder for each model can take several days on multiple GPUs [44, 47], making it highly cumbersome if not impossible at all. Moreover, for some distilled models like LCM [28], it is even infeasible to conduct vanilla training directly as it requires a specific distillation objective concerning its teacher.
+
+Focusing on this drawback, we aim at a model-agnostic approach termed UniversalBooth in this paper and expect a trained visual encoder to be generalized to other text-to-image backbones seamlessly. To this end, we first delve into the design intricacies of existing personalized generation methods without test-time optimization and reveal that the significant impediment to such generalization lies in the strong coupling between the visual encoder and the crossattention layers of the diffusion UNet, which are key modules for the diffusion model to interact with input conditions. Previous works largely ignore the variability in backbone text-to-image models. Consequently, their visual encoders are susceptible to overfitting the specific diffusion model seen in training.
+
+In this paper, we tackle this challenge by introducing a novel cross-attention mechanism that decouples the visual subject encoder from the diffusion architecture. Unlike conventional approaches, our method utilizes a shared group of square mapping matrices for both key and value components across different blocks within the same diffusion scale. This design promotes flexibility across a range of diffusion models characterized by varying numbers of channels or blocks, all while ensuring consistent effectiveness in generating high-quality images.
+
+Moreover, we devise a hierarchical cross-attention strategy. Specifically, the visual encoder first capsules global semantic features of user inputs into a virtual word, which
+
+is convenient for textual combination with editing prompts. To enhance appearance consistency, the cross-attention scores for this word are further divided by fine-grained attention considering local patches. Overall, this hierarchical approach ensures that the generated images not only align with textual prompts but also maintain coherence and fidelity to the visual subjects.
+
+Notably, the fine-grained cross-attention in our approach is backed up with an optimal transport prior, which is achieved by regulating attention scores allocated by the cross-attention mechanism to fulfill optimal transport constraints. In this way, even when tested on unfamiliar novel diffusion architectures, our customization model can be guided by this prior knowledge acquired in training, which further bolsters cross-model generalizability.
+
+We conduct extensive experiments to showcase the effectiveness and versatility of our approach. As shown in Fig. 1, results indicate that once trained, the proposed Universal-Booth can be generalized to unseen text-to-image diffusion models with a wide spectrum of architectures and functionalities without any additional training effort, while other methods cannot. Meanwhile, it yields on-par zero-shot personalized generation performance with existing works on seen diffusion backbones. Our contributions can be summarized as follows:
+
+- We investigate a novel problem, namely model-agnostic personalized text-to-image generation. To the best of our knowledge, this is the first work dedicated to the cross-model generalization issue in this field.
+- We tailor a novel cross-attention mechanism to address the problem. Specifically, it adopts shared key and value mappings among various blocks within the same scale, works in an innovative hierarchical manner, and is injected with optimal transport prior.
+- Experiments suggest that UniversalBooth achieves superior cross-model personalized generation results to unseen diffusion models and comparable performance in the vanilla test setting on seen models.
+
+# 2. Related Works
+
+Personalized text-to-image generation refers to producing images according to the text prompts while preserving the identity and appearance of users' image inputs. One promising solution for this application is to learn the word embedding [14] or fine-tune the diffusion model [22, 37] specifically for one subject in an iterative optimization fashion, which exhibits limited flexibility. Recent studies have been dedicated to addressing this limitation and focused on an any-subject-one-model paradigm. The basic idea is to replace the optimization process with a single feedforward propagation: to learn a neural network and map the input images to the conditional space of the diffusion model [9, 16, 18, 24, 26, 29, 41, 43, 44, 47, 50, 52] in a one-
+
+
+Figure 2. (a) Overview of zero-shot personalized text-to-image generation solutions (text branch omitted). (b) Our approach learns square and shared key-value mappings in cross-attention layers, enabling flexible cross-diffusion-model generalization during inference without extra training.
+Figure 3. Preliminary results of cross-model generalization by different operations on cross-attention. Images in (c), (d), (e), and (f) are generated with the prompt A photo of a S.
+
+stop manner. We provide a systematic summary of existing works in the appendix.
+
+These methods typically focus on the subject-wise flexibility and have achieved remarkable performance simultaneously. Nevertheless, when the base diffusion model changes—a common and practical scenario given the rapid proliferation and advancement of large text-to-image diffusion models [3, 4, 10, 12, 13, 20, 21, 28-30, 32, 34, 34, 36, 38, 42, 44, 48]—they typically require adapting the subject mapper to the new architecture through an optimization process as well [35]. We thus offer a different perspective regarding the model-wise flexibility and introduce UniversalBooth in this paper, the first method specifically designed for the cross-model generalization problem in personalized generation. Unlike existing techniques, UniversalBooth enables zero-shot customized generation on unseen diffusion models without requiring any additional training.
+
+# 3. Methodology
+
+# 3.1. Preliminary
+
+Different from early approaches [14, 22, 37] that obtain textual correspondences of subject images through test-time optimization, recent test-time fine-tuning-free personalized image generation methods learn a neural mapping from the visual space to the textual space so that the textual representations can be generated in a single forward propagation.
+
+We illustrate the overall pipeline of some popular designs like ELITE [47] and IP-Adapter [50] in Fig. 2(a). Typically, given a subject image $x$ , these methods first adopt the CLIP image encoder [33], denoted as $\phi(\cdot)$ , for feature extraction. As CLIP has been trained on abundant text-image pairs to align corresponding features, it may serve as a valuable resource for learning text-aware vision representations. Subsequently, a learnable MLP denoted as $M$ is trained to convert CLIP vision features into virtual words in the textual embedding space. Additional cross-attention is incorporated into the cross-attention layers of the pre-trained diffusion UNet to enhance its adaptability to
+
+
+
+
+(a) Cosimine Similarity between Predicted and Optimal Mapping Matrices
+(b) Subject Image
+
+
+(d) Square KV Mappings
+(e) Square and Shap KV Mappings
+
+
+
+
+(f) wo KV Mappings
+
+conditions injected by subject images, which is crucial to the performance given the significant role of cross-attention (CA) in subject-driven text-to-image generation, as highlighted in [1, 15, 22]. The CA results for the subject branch are added to the original results:
+
+$$
+\operatorname {O u t} \leftarrow \operatorname {O u t} + \lambda \operatorname {C A} (Q, (M \circ \phi (x)) \hat {W} _ {k}, (M \circ \phi (x)) \hat {W} _ {v}), \tag {1}
+$$
+
+where $Q$ is the query matrix mapped from features in the diffusion backbone, $\hat{W}_k$ and $\hat{W}_v$ are learnable key and value mappings respectively, and $\lambda$ is a hyperparameter controlling the strength of subject injection.
+
+We assume that Stable Diffusion v1.5 [36] is adopted here. It first learns an auto-encoder $(\mathcal{E}(\cdot),\mathcal{D}(\cdot))$ , where the encoder $\mathcal{E}(\cdot)$ maps an image $x$ to a lower dimensional latent space: $z\gets \mathcal{E}(x)$ , and the decoder $\mathcal{D}(\cdot)$ learns to decode $z$ back to the image space $\hat{x}\gets \mathcal{D}(z)$ such that $\hat{x}$ is close to the original $x$ . Denoising is conducted in the latent space by a UNet $\epsilon_{\theta}(\cdot)$ for noise prediction. With a pre-trained and frozen auto-encoder, text encoder, and UNet, the MLP and additional cross-attention layers are optimized using the vanilla noise prediction loss $\mathcal{L}_{simple}$ [17, 31, 36]:
+
+$$
+\mathcal {L} _ {\text {s i m p l e}} = \mathbb {E} _ {z, y, \epsilon , t} [ \| \epsilon - \epsilon_ {\theta} (z _ {t}, t, \tau (y), M \circ \phi (x)) \| _ {2} ^ {2} ], \tag {2}
+$$
+
+where $\tau(\cdot)$ represents the text encoder, $y$ denotes the text input, $t$ is the denoising step, and $z_{t}$ is the latent codes at step $t$ . Typically, the text $y$ is drawn from some templates, such as A photo of S, where S can be instantiated as virtual words [47] or the corresponding class name [50]. In the inference time, S can be flexibly composed with natural languages to achieve customization.
+
+# 3.2. Shared and Square KV Mapping Matrices
+
+This paper aims at a plug-and-play customization model that enables users to utilize a diverse range of diffusion models with varying structures during testing. Achieving this goal necessitates ensuring that the customization encoder remains independent of the architecture of the diffusion UNet. However, recall the pipeline of existing techniques shown in Fig. 2(a), and we find that the encoder and the UNet are coupled in the cross-attention layers. When using a different architecture, the number of cross-attention layers and their dimensions do not necessarily match the seen model. Consequently, the trained customized model cannot be loaded into a novel diffusion model. To address this issue, instead of fine-tuning key and value mappings
+
+for cross-attention, we propose to learn additional square transformation matrices $T_{k}$ and $T_{v}$ for features after the image MLP, such that their shapes are only relevant to the image feature dimension, without any dependence on diffusion backbones. The key and value mappings used in the added cross-attention layers are obtained via linear transformation: $\hat{W}_k\gets T_kW_k$ and $\hat{W}_v\gets T_vW_v$ .
+
+We find that such a technique kills two birds with one stone: it not only resolves the issue of variability in the number of channels across various models, but also reduces the upper bound of generalized error even if their channel dimensions are consistent. Please refer to the theoretical analysis in the appendix, which indicates that our approach is less sensitive to the discrepancy of feature spaces between seen and unseen models. In Fig. 3(a), we validate this effect by comparing the cosine similarity between the estimated $\hat{W}_k$ and $\hat{W}_v$ in unseen architectures and their optimal counterparts that have been trained on these architectures and serve as oracles. As shown in Figs. 3(c) and (d), this design is essential for the model to produce meaningful results.
+
+At this point, the only unresolved issue is the variability in the number of cross-attention layers. To tackle the problem, it is crucial to discern between the invariant and variant factors across different target diffusion models. By ensuring that our method does not rely on variant factors, we can develop a solution that remains robust and adaptable across various diffusion models. In this paper, we capitalize on the multi-scale functionality inherent in diffusion UNets and introduce an innovative solution whereby the cross-attention layers within different blocks but the same resolution scale share a common set of $T_{k}$ and $T_{v}$ matrices. Formally, the cross-attention results for the $j$ -th block of the $i$ -th scale can be written as:
+
+$$
+\operatorname {C r o s s A t t n} \left(Q ^ {i, j}, (M \circ \phi (x)) T _ {k} ^ {i} W _ {k} ^ {i, j}, (M \circ \phi (x)) T _ {v} ^ {i} W _ {v} ^ {i, j}\right), \tag {3}
+$$
+
+where ${}^{i,j}$ specifies the indices of scale and block. The overall design is illustrated in Fig. 2(b). As shown in Figs. 3(d) and (e), this strategy further enhances the cross-model generalizability.
+
+One might wonder whether it is feasible to retain $T_{k}$ and $T_{v}$ as identity matrices and solely focus on learning the MLP part, yielding the simplest design. However, comparing Figs. 3(e) and (f), the method results in inferior identity preservation, underscoring the significance of adapting the textual condition space to the subject condition space. Please refer to the appendix for more explorations.
+
+# 3.3. Hierarchical Cross-Attention
+
+To address the trade-off between appearance preservation and text prompt adherence, we devise a novel hierarchical cross-attention mechanism in this paper, where the holistic attention first captures the global semantics of subject images, and then the attention scores to the global semantics
+
+
+Figure 4. The proposed personalized text-to-image generation method is driven by holistic and fine-grained mappings. We devise a hierarchical cross-attention mechanism for the interaction between the two branches, which yields satisfactory text adherence and appearance preservation concurrently. An optimal transport constraint is applied here as prior knowledge guiding cross-model generalization.
+
+are divided according to the fine-grained attention. Similar to ELITE [47], we subsequently trained two mapping networks $M_{h}$ and $M_{f}$ to extract holistic and fine-grained features in the textual space for holistic and fine-grained cross-attention, respectively.
+
+Holistic Mapping: The designs of the holistic mapping network $M_h$ mainly follow the previous work BLIP-Diffusion [24], which extracts $n$ virtual words in the token embedding space of the CLIP text encoder via a Q-Former [25], taking as input features from a frozen pretrained image encoder. Denoting these virtual words as $S$ , the Q-Former is optimized to minimize a loss function $\mathcal{L}_h$ consisting of $\mathcal{L}_{simple}$ in Eq. 2 based on the text prompts like A photo of $S$ and an L1 regularization term for $S$ . Since the primary goal of holistic mapping is to extract virtual words that are compatible with real prompts, we omit $T_k$ and $T_v$ in Eq. 3, and instead directly use the native key-value parameters to process the textual conditions.
+
+Fine-Grained Mapping: The designs of the fine-grained mapping network $M_{f}$ mainly follow the previous work ELITE [47], where features of $n$ layers in the CLIP image encoder are separately mapped to $n$ virtual words in the token embedding space of the CLIP text encoder by $n$ learnable sub-mappers with two Linear-LayerNorm-LeakyReLU blocks. Following ELITE [47], we also apply subject masks here to filter out irrelevant backgrounds.
+
+Different from previous techniques that require adjusting the hyperparameter $\lambda$ in Eq. 1 to balance the holistic and fine-grained attention, we propose a hierarchical approach. Denoting the query, key, and value after the projection of $W_{q}$ , $W_{k}$ , and $W_{v}$ in a holistic cross-attention layer as $Q \in \mathbb{R}^{s \times c}$ and $K_{h}, V_{h} \in \mathbb{R}^{l_{h} \times c}$ , respectively, where $s$ is the number of query tokens, i.e., the spatial dimensionality of current latent codes, $l_{h}$ is the number of textual tokens, and $c$ is the feature dimensionality of this layer, and assuming that the primary word is located at
+
+| Method | Unseen Architecture |
| LCM | Base Diffusion | Small Diffusion | Tiny Diffusion | Seen Architecture |
| C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I |
| BLIP-Diffusion [24] | .282 | .589 | .201 | .275 | .680 | .201 | .266 | .652 | .360 | .281 | .565 | .181 | .300 | .771 | .583 |
| IP-Adapter [50] | .291 | .679 | .449 | .281 | .596 | .210 | .269 | .538 | .133 | .268 | .536 | .142 | .295 | .796 | .629 |
| ELITE [47] | .288 | .665 | .441 | .219 | .535 | .050 | .229 | .559 | .093 | .226 | .562 | .121 | .255 | .762 | .652 |
| Ours | .307 | .694 | .532 | .303 | .710 | .500 | .302 | .687 | .482 | .300 | .675 | .479 | .302 | .772 | .667 |
+
+Table 1. Quantitative comparisons with state-of-the-art zero-shot text-to-image personalization methods and ablation studies. Best performance is marked in bold.
+
+the $p$ -th token, we first compute the holistic attention map $A_{h}$ with $A_{h} \gets \mathrm{Softmax}\left(\frac{QK_{h}^{\top}}{\sqrt{c}}\right)$ , and extract the attention map corresponding to the primary word, i.e., the $p$ -th column of $A_{h}$ , denoted as $A_{h}^{:p} \in \mathbb{R}^{s \times 1}$ . Then, denoting the post-projection key and value in the corresponding fine-grained cross-attention layer as $K_{f}, V_{f} \in \mathbb{R}^{l_{f} \times c}$ , respectively, where $l_{f}$ is the number of fine-grained tokens, we further divide the column $A_{h}^{:p}$ into $l_{f}$ columns weighted by the fine-grained attention map $A_{f} \gets \mathrm{Softmax}\left(\frac{QK_{f}^{\top}}{\sqrt{c}}\right)$ , i.e., replace the column $A_{h}^{:p}$ by $l_{f}$ columns $A_{h}^{:p} * A_{f}$ , with * representing element-wise multiplication allowing broadcast. Accordingly, the $p$ -th row in $V_{h}$ is substituted by the $l_{f}$ rows in $V_{f}$ . Denoting the updated attention map and value as $A'$ and $V'$ , respectively, the output of such hierarchical cross-attention is given by $\mathrm{Out} \gets A'V'$ , which is adopted to replace the original computational rule in Eq. 1 for all cross-attention layers. We offer an illustrative presentation of the workflow in Fig. 4.
+
+# 3.4. Optimal Transport Prior
+
+Without knowledge of unseen models, subject-driven models face challenges in achieving cross-model generalization. To mitigate this issue, we seek to imbue fine-grained attention with generic knowledge, guiding the cross-model customization process with priors to enhance performance. In this paper, we explore an optimal transport prior that encourages an even migration of visual patterns from subject images to customized results and penalizes one-to-many mappings [27]. Assume that $Q \in \mathbb{R}^{s \times c}$ and $K_{f} \in \mathbb{R}^{lf \times c}$ are two discrete distributions. The total mass in $K$ is defined as the total attention score to the primary word in the holistic attention, i.e., $\sum A_{h}^{i,p}$ . Since we expect the mass in $K$ to be evenly transported into $Q$ , the mass of each point in $K$ should be $\frac{\sum A_{h}^{i,p}}{l_f}$ . We add the regularization of balanced total attention scores in each point of $K$ to Eq. 2. The loss function for the fine-grained mapping can be written as:
+
+$$
+\mathcal {L} _ {f} = \mathcal {L} _ {\text {s i m p l e}} + \frac {\alpha}{N} \sum_ {j = 1} ^ {N} \| \sum A _ {f} ^ {:, j} - \frac {\sum A _ {h} ^ {: , p}}{l _ {f}} \| _ {2} ^ {2}, \tag {4}
+$$
+
+where $N$ denotes the total number of columns in all the fine-grained attention maps, and $\alpha$ is a hyperparameter controlling the strength of this regularization.
+
+# 4. Experiments
+
+# 4.1. Implementation Details
+
+We build UniversalBooth on the open-source implementation of ELITE [47]. The architecture of the diffusion model in training is StableDiffusion v1.4 [36]. The test set of the OpenImages dataset [23], containing 120K images, is adopted to train the holistic mapping, while 47K of them with annotations of object masks are used to train the fine-grained mapping. The hyper-parameter $\alpha$ in Eq. 4 is set as 0.01 empirically. We train the holistic and fine-grained mappings on 4 RTX 6000 Ada GPUs for 40,000 and 80,000 iterations, respectively. Other setups, including the diffusion sampler and the scale of classifier-free guidance, follow the default configurations if not mentioned specifically.
+
+The evaluation dataset is also consistent with ELITE [47] that adopts 2,500 test cases formed by a pairwise combination of 20 subject images, 25 text templates, and 5 random seeds. Following the convention of personalized text-to-image generation [22, 37, 47], we evaluate our method on 3 metrics, including CLIP-I (C-I) and DINO-I (D-I) for image consistency and CLIP-T (C-T) for text consistency. CLIP-I and DINO-I measure the cosine similarity between features of generated and source subject images in the CLIP image encoder [33] and the ViTS/16 DINO [6]. CLIP-T measures the cosine similarity between features of generated images in the CLIP image encoder and text prompts in the CLIP text encoder, where object class names of the subject images are used in the text templates.
+
+# 4.2. Cross-Architecture Generalization
+
+As our target in this paper is a model-agnostic personalized text-to-image generation method, we mainly evaluated the proposed UniversalBooth on diffusion models with unseen architectures in training. Specifically, we consider both cases of large-to-small and small-to-large cross-model generalization. For small architectures, we adopt two diffusion models distilled from Stable Diffusion in [21] for experiments, denoted as Small Diffusion and Tiny Diffusion. For large architectures, we consider two popular structures, i.e., StableDiffusion-XL [32] (SD-XL) and StableDiffusion-3-Medium [13] (SD-3). Although both seen and unseen involve CLIP for textual embedding, for SD-XL and SD
+
+
+Figure 5. Results of large-to-small cross-architecture generalization comparing with state-of-the-art methods.
+
+3, since the conditional spaces are constructed using multiple text encoders, they do not strictly satisfy the consistent condition space assumption required by the fine-grained encoder. Therefore, we use only the holistic encoder for them.
+
+To demonstrate the unique superiority of our method in cross-architecture generalization, we compare Universal-Booth with three open-source and state-of-the-art personalized generation methods, including BLIP-Diffusion [24],
+
+IP-Adapter [50], and ELITE [47]. These methods overlook the variability of diffusion models in the inference time and couple the subject encoder module with the diffusion UNet. For instance, BLIP-Diffusion requires fine-tuning both the whole diffusion UNet and the image-to-BLIP mapping module. IP-Adapter and ELITE fine-tune the crossattention layers in the original diffusion backbones, which makes the subject encoders overfit to the seen diffusion ar
+
+a S on top of a purple rug in a forest
+
+
+sS
+
+
+
+
+
+
+s-3
+Subject
+
+
+Ours
+
+
+ELITE
+
+
+a S floating on top of water
+
+
+
+
+
+
+
+
+Ours
+
+
+ELITE
+
+
+
+
+a cube shaped S
+
+
+
+
+
+
+Ours
+
+
+ELITE
+
+| Architecture | Method | CLIP-T | CLIP-I | DINO-I |
| SD-XL | ELITE | .317 | .650 | .336 |
| Ours | .294 | .766 | .580 |
| SD-3-Medium | ELITE | .316 | .691 | .446 |
| Ours | .319 | .750 | .581 |
+
+Table 2. Quantitative comparisons with the baseline method ELITE [47] on small-to-large cross-architecture generalization. Best performance is marked in bold.
+
+chitecture in training. To adapt them for cross-architecture generation, we only load the matched cross-attention layers in inference time and drop the extra layers.
+
+As a result, as shown in Fig. 5, without specific consideration of cross-model generalization, existing methods fail to produce plausible personalized text-to-image generation results. For BLIP-Diffusion, since it utilizes BLIP [25] as a pre-trained vision-language prior, the produced results can often convey aligned semantics. However, the colors and textures cannot match those in the original subject images. Even worse, when the architectural gap between the unseen and seen diffusion models is large, e.g., Tiny Diffusion, the content layouts tend to be out of control. For IP-Adapter and ELITE, suffering from misalignments of feature spaces in this setting, they are prone to messy and meaningless textures. Compared with them, our method successfully addresses these and exhibits better robustness to the architectural variations. Quantitatively, as reported in Tab. 1(left), our method outperforms existing ones in cross-architecture generalization by a large margin.
+
+For small-to-large generalization with SD-XL and SD-3, the qualitative and quantitative comparisons against the ELITE baseline [47] are shown in Fig. 6 and Tab. 2, respectively. Although ELITE can capture the overall semantics of subject images and textual prompts, the results largely overlook the detailed appearances. In contrast, our method exhibits superior cross-model generalization.
+
+# 4.3. Comparisons on Seen Architectures
+
+We also compare our method with existing ones on the seen architectures. As shown in Tab. 1(right), UniversalBooth
+
+
+Subject Image Blip Diffusion
+
+
+Figure 6. Results of small-to-large cross-architecture generalization. The seen architecture is StableDiffusion v1.4, while the unseen architectures are StableDiffusion-XL and StableDiffusion 3 Medium, respectively.
+
+
+
+
+
+
+
+
+PAdaptor
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+wearing pink glasses
+Figure 7. Results of personalized generation on seen architectures.
+
+
+wearing a sarta hat
+
+
+wearing a yellow shirt
+
+
+with a blue house in the background
+
+
+with a city in the background
+
+overall achieves comparable quantitative metrics with state-of-the-art methods. Specifically, it yields higher CLIP-T and DINO-I but slightly lower CLIP-I. We speculate that it is because the hierarchical cross-attention mechanism in this paper improves the trade-off between text alignment and the preservation of detailed local patterns, which may favor low-level metrics like DINO-I based on features of self-supervised learning compared with the high-level metric CLIP-T. Also, according to the ablation studies, the sharing of key and value mappings in cross-attention layers of the same scale inevitably sacrifices performance on seen architectures to some extent. In addition, compared with works like BLIP-Diffusion and IP-Adapter, the consumption of computational resources, including data, GPU cards, and training time, is significantly lower for our method, as demonstrated in the appendix. These are factors that UniversalBooth has not achieved significantly superior performance to the state-of-the-art methods on seen architectures.
+
+Nevertheless, as shown in Fig. 7, our method indeed has
+
+
+Figure 8. Existing methods like ELITE [47] require adjusting the hyperparameter $\lambda$ to balance the text adherence and appearance preservation, whose optimal choices, marked by the stars, are case by case, while our method does not.
+
+
+Figure 9. The optimal transport prior $\mathcal{L}_{ot}$ helps cross-model generalization by regulating the layout of the generated subject.
+
+significant advantages in many cases. Specifically, methods like BLIP-Diffusion and IP-Adapter tend to preserve the major semantics while ignoring the local patterns, which leads to inferior appearance preservation, e.g., the cat, the bag, and the cat statue in the 1st, 4th, and 5th columns, respectively. ELITE struggles to deal with colors in text prompts by confusing colors of subjects and backgrounds, e.g., the dog in the 3rd column, and the bag in the 4th column. In comparison, our method handles these cases better.
+
+# 4.4. Ablation Studies
+
+In this part, we demonstrate the effectiveness of the proposed three components, including shared and square key and value mapping matrices, hierarchical cross-attention, and optimal transport prior, through ablation studies. Quantitatively, the impact of each component on the performance is shown in Tab. 3.
+
+Shared and Square Key and Value Mapping Matrices: As demonstrated in Fig. 3, by decoupling the subject encoder from the number of channels and blocks in diffusion backbones, shared and square key and value mappings help align the subject feature space and the condition space shared by different diffusion models and play crucial roles in achieving cross-architecture generalization. We provide more supportive examples in the appendix.
+
+Hierarchical Cross-Attention: Previous methods like IP-Adapter and ELITE achieve the trade-off between text prompt adherence and appearance preservation by adjusting the weight of the subject condition, which is not robust in practice. As shown in Fig. 8, in different cases, the optimal choice of this hyperparameter can also be different. Compared with these methods, the hierarchical cross-attention proposed in this paper can balance the two worlds better without deliberate adjustment.
+
+| Setting | Unseen Architecture | Seen Architecture |
| Small Diffusion | Tiny Diffusion | C-T | C-I | D-I |
| C-T | C-I | D-I | C-T | C-I | D-I |
| w/o KV | .302 | .664 | .424 | .300 | .653 | .422 | .301 | .756 | .650 |
| w/o Shared KV | .283 | .650 | .365 | .232 | .556 | .163 | .300 | .785 | .683 |
| w/o HieraAttn | .289 | .614 | .291 | .288 | .613 | .305 | .297 | .768 | .629 |
| w/o Lot | .292 | .644 | .377 | .284 | .613 | .291 | .302 | .760 | .584 |
| Ours | .302 | .687 | .482 | .300 | .675 | .479 | .302 | .772 | .667 |
+
+Table 3. Ablation studies for various technical designs introduced in this paper. HieraAttn denotes the hierarchical attention. Best performance is marked in bold.
+
+
+Figure 10. The design of shared and square key and value mappings enables UniversalBooth to be generalized to models with various functionalities like text-driven editing.
+
+Optimal Transport Prior: The optimal transport prior is useful to regulate the semantic layout of the generated results by penalizing one-to-many mappings. We illustrate this effect in Fig. 9. Quantitative measurements on the test cases also validate that adding the regularization $\mathcal{L}_{ot}$ in training would lead to lower $\mathcal{L}_{ot}$ in cross-model inference.
+
+# 4.5. Further Extension
+
+Interestingly, we find that the proposed UniversalBooth is also compatible with other text-to-image models with different functionalities, like InstructPix2Pix [5] for text-driven image editing, thanks to the universal subject space resulting from the shared and square key and value mapping matrices. As shown in Fig. 10, the model would migrate incorrect or insufficient subject patterns if square mappings or shared mappings are removed.
+
+# 5. Conclusions
+
+In this paper, we present UniversalBooth, a model-agnostic framework for personalized text-to-image generation. Dedicated to the problem of cross-diffusion generalization, we mainly introduce three novel designs: (1) cross-attention with shared and square key and value mappings, which achieves cross-architecture zero-shot inference in functionality, (2) hierarchical cross-attention, which alleviates the trade-off between text adherence and appearance preservation, and (3) an optimal transport prior injected into the fine-grained attention, which guides the behavior of unseen models with generic knowledge and further improves the cross-model generalization performance. Experiments demonstrate that UniversalBooth is the first versatile model for personalized text-to-image generation that can be generalized to unseen diffusion backbones seamlessly without any additional training effort. It also achieves superior zero-shot personalization performance on seen architectures.
+
+# Acknowledgments
+
+# References
+
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| LCM | Base Diffusion | Small Diffusion | Tiny Diffusion | Seen Architecture |
| C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I | C-T | C-I | D-I |
| BLIP-Diffusion [24] | .282 | .589 | .201 | .275 | .680 | .201 | .266 | .652 | .360 | .281 | .565 | .181 | .300 | .771 | .583 |
| IP-Adapter [50] | .291 | .679 | .449 | .281 | .596 | .210 | .269 | .538 | .133 | .268 | .536 | .142 | .295 | .796 | .629 |
| ELITE [47] | .288 | .665 | .441 | .219 | .535 | .050 | .229 | .559 | .093 | .226 | .562 | .121 | .255 | .762 | .652 |
| Ours | .307 | .694 | .532 | .303 | .710 | .500 | .302 | .687 | .482 | .300 | .675 | .479 | .302 | .772 | .667 |
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| Small Diffusion | Tiny Diffusion | C-T | C-I | D-I |
| C-T | C-I | D-I | C-T | C-I | D-I |
| w/o KV | .302 | .664 | .424 | .300 | .653 | .422 | .301 | .756 | .650 |
| w/o Shared KV | .283 | .650 | .365 | .232 | .556 | .163 | .300 | .785 | .683 |
| w/o HieraAttn | .289 | .614 | .291 | .288 | .613 | .305 | .297 | .768 | .629 |
| w/o Lot | .292 | .644 | .377 | .284 | .613 | .291 | .302 | .760 | .584 |
| Ours | .302 | .687 | .482 | .300 | .675 | .479 | .302 | .772 | .667 |
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diff --git a/2025/Unknown Text Learning for CLIP-based Few-Shot Open-set Recognition/8df0b349-1f30-4db7-a5dd-d902f9f32a3f_content_list.json b/2025/Unknown Text Learning for CLIP-based Few-Shot Open-set Recognition/8df0b349-1f30-4db7-a5dd-d902f9f32a3f_content_list.json
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+ "type": "text",
+ "text": "Unknown Text Learning for CLIP-based Few-shot Open-Set Recognition",
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+ "text": "Rui Ma, Qilong Wang\\*, Bing Cao, Qinghua Hu, Yahong Han Tianjin University, China",
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+ "text": "{miracle0205, qlwang, caobing, huqinghua, yahong}@tju.edu.cn",
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+ "text": "Recently, vision-language models (e.g., CLIP) with prompt learning have shown great potential in few-shot learning. However, an open issue remains for the effective extension of CLIP-based models to few-shot open-set recognition (FSOR), which requires classifying known classes and detecting unknown samples using a few known samples. The core challenge is that unknown samples and their textual descriptions are unavailable. To address this, we propose an Unknown Text Learning (UTL) method for CLIP-based FSOR tasks with only known samples. Specifically, UTL involves two key components, i.e., universal unknown words optimization $(U^2 WO)$ and unknown label smoothing (ULS). Specifically, $U^2 WO$ constructs the universal space of unknown words with basis vectors and characterizes unknown text based on a linear combination of those basis vectors. To efficiently learn unknown text without unknown samples, ULS is presented to perform contrast learning between unknown text and known samples by regulating the label of unknown classes to a small constant, which flexibly empowers unknown text to be non-matching and confused with known visual samples. In addition, our UTL incorporates an additional context for known classes to mitigate conflicts of context optimization between known and unknown classes. UTL effectively regularizes the predicted probability by integrating learnable unknown text. Experimental results on various benchmarks show that our UTL is superior to its counterparts while achieving state-of-the-art performance.",
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+ "type": "text",
+ "text": "1. Introduction",
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+ "type": "text",
+ "text": "Test samples in real-world scenarios often belong to classes not encountered during training, posing a critical challenge for recognition systems. Additionally, the high cost of data annotation and privacy concerns limit access to large-scale, high-quality datasets, further exacerbating the problem. To address this, Few-Shot Open-Set Recognition (FSOR) [20] has been proposed to enable recognition systems to classify predefined known classes while identifying unknown",
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+ "image_caption": [
+ "(a)",
+ "Figure 1. (a) Comparison of our UTL with its counterparts in terms of prompt. Specifically, CoOp [54] and M-Tuning [19] learn only context prompt. In contrast, our UTL learns context prompts and unknown text more flexibly under various open-set scenarios. (b) Density distribution of confidence score (maximum predicted probability) with the proposed UTL and CoOp. The gap between the mean scores of known and unknown samples indicates the method's ability to distinguish open-set instances."
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+ "(b)"
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+ "text": "samples under data-limited conditions. This problem has gained significant attention, inspiring research efforts to extend few-shot learning methods to open-set settings [11, 12, 20, 42]. Recently, vision-language models (e.g., CLIP [32]) with prompt learning [13, 45, 46, 50, 54, 55] have demonstrated remarkable performance in few-shot classification by learning textual prompts from training samples. That inspires us to explore the potential of prompt learning for FSOR. As shown in Fig. 1(a), CLIP constructs prompts with context and class names. However, in FSOR, the class names of unknown samples are unavailable. The absence of unknown class names imposes a closed-set assumption, making CLIP vulnerable to open-set conditions [25]. Prompt learning methods like CoOp [54] attempt to learn contextual prompts directly from image features, but they still rely on a closed-set assumption and cannot be extended to unknown text due to the absence of unknown samples. As a result, the effectiveness of prompt learning in FSOR remains fundamentally limited, as the core challenge lies in the absence of unknown samples and their corresponding textual descriptions.",
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+ "type": "header",
+ "text": "CVF",
+ "bbox": [
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+ },
+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "*Corresponding author",
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+ "img_path": "images/848a6fba86e434bb591992c487f46475cafe7479308e42ebcd89515f82807547.jpg",
+ "image_caption": [
+ "Figure 2. Overview of our proposed UTL method for CLIP-based few-shot open set recognition. First, $\\mathrm{U}^2\\mathrm{WO}$ is developed to characterize unknown words based on a linear combination of a universal, learnable word basis, which is jointly optimized with context prompt to avoid the specialized generation of unknown words. Then, our ULS is presented to perform contrast learning between unknown text and known samples by regulating labels of all unknown classes to a small constant, efficiently learning unknown text free of unknown samples."
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+ {
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+ "text": "A natural solution is to generate unknown samples along with their textual descriptions. LMC [31] represents a pioneering effort in this direction, leveraging large pre-trained models (e.g., ChatGPT [4], DALL-E [33], CLIP [32]) to generate unknown samples and their corresponding virtual class names simultaneously. However, this approach is unstable when handling diverse class compositions and struggles to produce high-quality image-text pairs, limiting its generalization. To better explore the text processing ability of CLIP for the open set setting, as shown in Fig. 1(a), M-Tuning [19] manually selects specialized words, referred to as open words, from WordNet [26] and incorporates them into context templates to construct unknown prompts. The model then learns context prompts following CoOp [54] while regularizing known-class predictions. However, selecting the specialized words as unknown text is potentially inflexible to various scenarios and is sensitive to the number of known classes. As discussed above, generating imagetext pairs and specialized word selection are insufficiently flexible and stable to cope with different scenarios. Consequently, a critical challenge persists: effectively extending CLIP-based models to FSOR while addressing the absence of unknown samples and their textual descriptions.",
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+ "type": "text",
+ "text": "To overcome the above challenge, we propose a novel Unknown Text Learning (UTL) method, which simultaneously learns the unknown text and context prompt using a few known samples. The core components of UTL involve a universal unknown words optimization $(\\mathrm{U}^2\\mathrm{WO})$ and an unknown label smoothing (ULS) for effectively characterizing and efficiently optimizing the unknown text, respectively. Specifically, our $\\mathrm{U}^2\\mathrm{WO}$ first constructs a universal space of unknown words based on the label name of the base classes. We perform a principal component analysis (PCA) of their",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "embedding token vectors, utilizing the top- $k$ principal components to form the universal space of unknown words. Subsequently, the unknown text is characterized based on a linear combination of these basis vectors. As such, our $\\mathrm{U}^2\\mathrm{WO}$ avoids the specialized word selection and provides a space constraint on unknown text learning. To efficiently learn unknown text, our ULS regulates the labels of all unknown classes to a small constant and then performs contrast learning between unknown text and known samples. As such, ULS can learn the unknown text by avoiding the requirement of unknown samples. Based on the proposed $\\mathrm{U}^2\\mathrm{WO}$ and ULS modules, our UTL can realize effective prompt learning for CLIP-based FSOR with no need for unknown samples and the corresponding specialized text descriptions. As illustrated in Fig. 1 (a), our UTL method learns context prompts and unknown text, giving UTL more flexibility than M-Tuning and CoOp, which focus only on prompt context. In addition, our UTL incorporates an additional context for known classes to mitigate conflicts of context optimization between known and unknown classes. As shown in Fig. 4, our UTL can effectively handle the context conflict, achieving stable performance. As illustrated in Fig. 1(b), our UTL effectively regularizes the predicted probability by incorporating learnable unknown text. Notably, UTL significantly reduces the confidence of unknown samples (from approximately 0.8 to 0.2) and slightly lowers known samples, substantially widening the confidence gap between known and unknown samples and improving the performance of unknown detection. The overview of our proposed UTL is illustrated in Fig. 2. To verify the effectiveness of our UTL method, we conduct experiments on various benchmarks [16, 17, 24, 27, 34, 39-41, 43]. The contributions of our work are summarized as follows:",
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+ "- In this paper, we propose a novel Unknown Text Learning (UTL) method to explore the potential of CLIP for FSOR tasks. Our UTL makes the first attempt to simultaneously learn context prompts and unknown text using only known samples, without extra datasets and large models.",
+ "- To this end, our UTL respectively presents a universal unknown words optimization (U²WO) and an unknown label smoothing (ULS) to characterize and optimize the unknown text, realizing effective and efficient prompt learning for CLIP-based FSOR. Furthermore, a dual-context strategy is introduced to avoid context conflict.",
+ "- Extensive experiments are conducted on various benchmarks using different backbone models, and the results show that our UTL significantly outperforms its counterparts while achieving state-of-the-art performance."
+ ],
+ "bbox": [
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+ "text": "2. Related Work",
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+ "text": "Prompt Learning. Recently, prompt learning has demonstrated its effectiveness in adapting large vision-language (VL) pre-trained models to few-shot downstream vision tasks. Researchers contributed a great deal of effort to explore diverse techniques for the generalization issue [10, 13, 45, 46, 50, 54, 55]. CoOp [54] introduces continuous context optimization. As an extension of CoOp, CoCoOp [13] enhances the performance by incorporating a lightweight neural network to generate dynamic input-conditional tokens for each image. However, these methods developed under a closed-set assumption are unsuitable for FSOR. In recent works, synthesizing image-text pairs [22, 37, 38, 44] to improve the performance of vision-language models has been proposed for closed-set tasks. These methods strive to present more accurate image-text pairs in the embedding space but do not provide solutions for unknown image-text pairs that represent negation semantics. Unlike them, our UTL can learn unknown text for CLIP while achieving better FSOR performance (see Sec. 4.2).",
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+ "text": "Few-Shot Open-Set Recognition. Few-shot open-set recognition (FSOR) is proposed to generalize open-set recognition (OSR) [2, 30, 36, 40, 48, 49, 53] to the data-limited task. Current methods usually extend few-shot methods to the open-set setting, which can be mainly categorized into metric-based methods [3, 11, 12, 20, 29, 42, 51] and CLIP-based methods [19]. We focus on the generalization of CLIP-based methods to OSR. Existing CLIP-based methods regularize the predicted probability with generated unknown samples and text to enhance the models' ability to open settings. LMC [31] first simulates text with ChatGPT [4], generates the aligned images with DALL-E [33], and acess the alignment using CLIP [32]. To further explore the text processability, M-Tuning [19] provides select open words from WordNet as unknown words, which can easily get texts from non-target class names. Prompt methods are also proposed in out-of-distribution (OOD)",
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+ "text": "detection. ID-like [1] learns the unknown prompts based on low-similarity samples selected from the augmentations of in-distribution images. The similarity-based selection is preprocessed with CLIP. However, the quality of selected images constrains the models' performance. NegPrompt [18] is designed to learn a set of negative context prompts, which can be explained as \"a photo of not a\". However, the negative context learning batch makes unknown prompts easily redundant for downstream tasks. Meanwhile, it leads to a linear increase in the number of prompts, which is not friendly to large-scale settings. Unlike previous works [1, 18, 28], our UTL leverages the capabilities of CLIP without requiring additional large models or simulation processes, which learn both context and unknown text with only known samples efficiently.",
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+ "type": "text",
+ "text": "3. Method",
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+ "type": "text",
+ "text": "3.1. Preliminaries",
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+ "text": "CLIP with Prompt Learning. CLIP [32] comprises a text encoder $\\mathcal{T}:t\\to \\mathbb{R}^d$ and an image encoder $\\mathcal{I}:x\\rightarrow$ $\\mathbb{R}^d$ , designed to map textual prompts $t$ and images $\\pmb{x}$ into a shared alignment space, respectively. Given $K$ predefined class names, the $k$ -th textual prompt $t_k$ can be constructed in the form \"a photo of a $[\\mathrm{CLASS}_k]$ .\", \"[CLASSk]\" is the $k$ -th class name. With these prompts, CLIP can easily generalize to downstream $K$ -class classification tasks by computing the similarity of image features relative to all corresponding text features as $s_k(x) =$ $\\sin (\\mathcal{T}(t_k),\\mathcal{I}(\\boldsymbol {x}))$ , where $\\sin (\\cdot ,\\cdot)$ denotes the cosine similarity and $k\\in [1,K]$ . The predicted probability $p_k^C (x)$ in the close-set setting can be expressed as",
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+ "type": "equation",
+ "text": "\n$$\np _ {k} ^ {C} (\\boldsymbol {x}) = \\frac {\\exp \\left(\\operatorname {s i m} \\left(\\mathcal {T} \\left(\\boldsymbol {t} _ {\\boldsymbol {k}}\\right) , \\mathcal {I} (\\boldsymbol {x})\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(\\operatorname {s i m} \\left(\\mathcal {T} \\left(\\boldsymbol {t} _ {\\boldsymbol {j}}\\right) , \\mathcal {I} (\\boldsymbol {x})\\right) / \\tau\\right)}, \\tag {1}\n$$\n",
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+ "text": "where $\\tau$ is the temperature parameter. To avoid manual prompt tuning, CoOp [54] introduces a learnable context prompt by modeling context words with continuous vectors, the learnable prompt could be $t = [\\mathrm{V}]_1[\\mathrm{V}]_2\\ldots [\\mathrm{V}]_L[\\mathrm{CLASS}]$ , where each $[\\mathrm{V}]_l$ ( $l \\in \\{1,\\dots,L\\}$ ) is a vector with the same dimension as word embeddings and $L$ is the length of context tokens.",
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+ "text": "Unknown detection in Open Set Recognition (OSR). An intuitive way to detect unknown samples is thresholding on the confidence score. Taking the maximum softmax probability (MSP) across known classes as a confidence score. The $K$ -class classifier to detect unknown samples can be extended as:",
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+ "text": "\n$$\n\\hat {y} = \\left\\{ \\begin{array}{l l} \\underset {k \\in [ 1, K ]} {\\arg \\max } p _ {k} ^ {C} (\\boldsymbol {x}), & \\text {i f} \\underset {k \\in [ 1, K ]} {\\max } p _ {k} ^ {C} (\\boldsymbol {x}) \\geq \\theta , \\\\ \\text {u n k n o w n}, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {2}\n$$\n",
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+ "text": "where $\\theta$ is the preset threshold.",
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+ "type": "text",
+ "text": "3.2. Overview of Unknown Text Learning (UTL)",
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+ "text": "In an open-set scenario, the absence of prompts for unknown classes forces the model to classify all test samples into one of the known categories with high confidence. To address this issue, we propose a novel Unknown Text Learning (UTL) method to integrate the learning of unknown text with context optimization, aiming to extend the principle of prompt learning to the open-set setting. The overview of our proposed UTL is shown in Fig. 2. UTL involves a universal unknown words optimization $(\\mathrm{U}^2\\mathrm{WO})$ and an unknown label smoothing (ULS). Specifically, our UTL models each unknown text with continuous vectors $U = [u_{1}][u_{2}]\\ldots [u_{M}]$ . Each $[u_m]$ ( $m\\in \\{1,\\dots ,M\\}$ ) is a vector with the same dimension as word embeddings, while $M$ is the length of unknown text tokens. $\\mathrm{U}^2\\mathrm{WO}$ constructs the universal unknown words space with a group of basis vectors denoted as $[Q_1,Q_2,\\dots ,Q_F]$ , where $Q_{f}$ ( $f\\in \\{1,\\dots ,F\\}$ ) is a basis vector and $F$ is the number of basis vectors. Then the unknown text $U_{k}$ can be calculated by a linear combination of these basis vectors as",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\boldsymbol {U} _ {k} = w ^ {1} \\boldsymbol {Q} _ {1} + w ^ {2} \\boldsymbol {Q} _ {2} + \\dots + w ^ {F} \\boldsymbol {Q} _ {F}, \\tag {3} \\\\ k \\in \\{K + 1, \\dots , K + N \\}, \\\\ \\end{array}\n$$\n",
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+ "text": "where $\\mathbf{W} = \\{w^{1},\\dots ,w^{F}\\}$ indicates the weights of combination. To efficiently learn the weights $\\mathbf{W}$ , unknown label smoothing (ULS) is presented to perform contrast learning between unknown text and known samples by regulating the label of all unknown classes to a small constant $\\varepsilon$ . As such, our UTL with $\\mathrm{U^2WO}$ and ULS can effectively learn unknown text for CLIP-based FSOR without unknown samples and the corresponding precise text descriptions.",
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+ "text": "Consider the $K$ -class classification task, UTL add additional $N$ unknown text, $[U_{K + 1}, U_{K + 2}, \\ldots, U_{K + N}]$ , as the textual description for the last $N$ unknown classes. Let the context prompt $\\mathbf{V} = [\\mathrm{V}]_1[\\mathrm{V}]_2 \\ldots [\\mathrm{V}]_L$ , the unknown prompt incorporating unknown text and context prompt can be formulated as $\\pmb{t}_k = [V, U_k]$ , where $k \\in \\{K + 1, \\ldots, K + N\\}$ . For the $K$ known classes, let known class name as $[C_1, C_2, \\ldots, C_K]$ , the prompt for $k$ -th known class can be formulated as $\\pmb{t}_k = [V, C_k]$ , $k \\in \\{1, \\ldots, K\\}$ . Incorporating the prompts for known classes and unknown classes, the predicted probability for the $k$ -th known class under the open setting is calculated as",
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+ {
+ "type": "equation",
+ "text": "\n$$\np _ {k} ^ {O} (\\boldsymbol {x}) = \\frac {\\exp \\left(s _ {k} ^ {C} / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(s _ {j} ^ {C} / \\tau\\right) + \\sum_ {j = K + 1} ^ {K + N} \\exp \\left(s _ {j} ^ {O} / \\tau\\right)}, \\tag {4}\n$$\n",
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+ "text": "where $s_k^C = \\mathrm{sim}(\\mathcal{T}([V,C_k]),\\mathcal{I}(\\pmb {x}))$ $k\\in \\{1,\\dots ,K\\}$ $s_k^O = \\mathrm{sim}(\\mathcal{T}([V,U_k]),\\mathcal{I}(\\pmb {x}))$ $k\\in \\{K + 1,\\ldots ,K + N\\}$ From Eq. (1) and Eq. (4), we can observe that our UTL introduces learning unknown text to regularize the predicted probability, enhancing the models' ability to detect un",
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+ "type": "text",
+ "text": "known samples by thresholding on the maximum softmax probability over known classes.",
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+ "type": "text",
+ "text": "3.3. Universal Unknown Words Optimization",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Intuitively, the unknown text can be learned from scratch without any constraints, as CoOp [54]. However, the text space is ample, and direct learning tends to overfit [9]. The textual descriptions for unknown classes may be uncertain, but they still belong to a subset of the word embedding space of CLIP. Inspired by the visual learning based on a universal dictionary [52], we construct space constraints to characterize the unknown text. As a subset of the word embedding space of CLIP, we construct the Universal Unknown Words Space based on the word embedding of the text description. Specifically, we first gather 1000 label names from base classes. Particularly, we use known classes and outlier text as the base classes. To ensure the quality of outlier text, we rigorously filter outlier text based on its corresponding Synset IDs, explicitly excluding names associated with unknown classes that may appear in downstream tasks. Next, the collected label names are processed through the CLIP text encoder to extract word embeddings. Finally, this study employs a simple principal component analysis (PCA) on these embedding vectors to obtain the universal basis vectors. Detailed criteria for space construction and base class selection are provided in Sup. S1.",
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+ "type": "text",
+ "text": "3.4. Unknown Label Smoothing",
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+ "text": "Existing studies [1, 18] have typically framed unknowns as samples residing far from the known space or situated in the vicinity of known samples. These unknown samples tend to exhibit lower probabilities when associated with known classes. Alternatively, we can invert this perspective, considering known samples as prone to acquiring lower probabilities when related to unknown classes. Building upon this rethinking, we introduce Unknown Label Smoothing (ULS) regularization. The core idea of ULS is to constrain a random small constant $\\varepsilon$ between known samples and unknown prompts for contrastive learning. Specifically, for an image of a known class where $y_{t}$ represents the ground truth class label, the final ground truth distribution $q(k)$ can be defined as follows,",
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+ "text": "\n$$\nq (k) = \\left\\{ \\begin{array}{l l} 1 & k = y _ {t}, k \\in [ 1, K ], \\\\ 0 & k \\neq y _ {t}, k \\in [ 1, K ], \\\\ \\varepsilon & k \\in [ K + 1, K + N ]. \\end{array} \\right. \\tag {5}\n$$\n",
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+ "type": "text",
+ "text": "Therefore, we can rewrite the cross-entropy loss as:",
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+ "text": "\n$$\nl _ {O} = - \\log \\left(p _ {y _ {t}} ^ {O} (\\boldsymbol {x})\\right) - \\varepsilon \\sum_ {k = K + 1} ^ {K + N} \\log \\left(p _ {k} ^ {U} (k)\\right), \\tag {6}\n$$\n",
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+ "text": "660",
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+ {
+ "type": "image",
+ "img_path": "images/65e14a7f2ad6e551f89830e1faf49be7f86937514e460d60aa7fb0a34d038cd4.jpg",
+ "image_caption": [
+ "Figure 3. Unified Context (UC) vs. Dual Context (DC)."
+ ],
+ "image_footnote": [],
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+ "page_idx": 4
+ },
+ {
+ "type": "image",
+ "img_path": "images/4901275dfdc4874fb82ff96d3744d4509e53db5f04772679009e9fee709972c3.jpg",
+ "image_caption": [
+ "Figure 4. Performance of UC vs. DC with various $\\varepsilon$ ."
+ ],
+ "image_footnote": [],
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\np _ {k} ^ {U} (\\boldsymbol {x}) = \\frac {\\exp \\left(s _ {k} ^ {O} / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(s _ {j} ^ {C} / \\tau\\right) + \\sum_ {j = K + 1} ^ {K + N} \\exp \\left(s _ {j} ^ {O} / \\tau\\right)}, \\tag {7}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where $k \\in [K + 1, K + N]$ .",
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+ "type": "text",
+ "text": "Note that $\\varepsilon$ may vary for different classes, but it is hard to decide $\\varepsilon$ optimally. So, we use the same $\\varepsilon$ for all cases for efficiency. From an optimization perspective, $\\varepsilon > 0$ distinguishes unknown classes from other known ones, avoiding overfitting to known classes. $\\varepsilon = 0$ returns back CoOp, losing the effect of regularization.",
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+ "type": "text",
+ "text": "3.5. Dual-Context Strategy",
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+ "type": "text",
+ "text": "UTL performs contrastive learning between the unknown text and known samples by assigning a uniform small value to the label truth of all unknown classes. Since different known-class samples share the same expected value, the context prompt learning for unknown classes lacks discriminability among different known classes, especially when the assigned value is not sufficiently small. This discrepancy conflicts with the context prompt learning of known classes, which requires higher discriminability. As shown in Fig. 4, we empirically observe opposite trends in performance between ACC, which represents the performance of known-class classification, and AUROC (Area Under the Receiver-Operator Curve), which evaluates the performance of unknown detection, with various $\\varepsilon$ under a unified context prompt. Therefore, we introduce a dual-context strategy for UTL to mitigate conflicts within context learning between known and unknown classes. As illustrated in Fig. 3, the unified context version for our UTL, in which known classes and unknown classes tend to learn the unified context based on known samples, while the dual-context",
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+ "type": "text",
+ "text": "strategy introduces an additional context for known classes. UTL performs contrastive learning with a combined loss:",
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+ "type": "equation",
+ "text": "\n$$\nl = (1 - \\lambda) \\cdot \\left(- \\log \\left(p _ {y ^ {t}} ^ {C} (\\boldsymbol {x})\\right)\\right) + \\lambda \\cdot l _ {O}. \\tag {8}\n$$\n",
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+ "type": "text",
+ "text": "where $\\lambda$ is a balancing coefficient.",
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+ "type": "text",
+ "text": "Inference. When performing the classification task, we use additional context prompts only for known classes and compute their predicted probability $p_k^C$ . For unknown detection, we threshold the maximum softmax probability (MSP) of $p_k^O$ as a confidence score.",
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+ "type": "text",
+ "text": "4. Experiments",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "4.1. Experimental Setup",
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+ "type": "text",
+ "text": "Datasets. We conduct experiments on various benchmarks for FSOR. Following the previous works [3, 5, 6, 15, 24, 27, 40, 42, 47, 53], we construct the standard benchmarks following the traditional OSR setting including CIFAR10 (C10) [16], CIFAR10 + 10 (C10 + 10) [16], CIFAR10 + 50 (C10 + 50) [16], CIFAR100 (C100) [16], TinyImageNet (TINY) [17], TinyImageNet-Hard (TINY-H) [17]. Then, we construct two benchmarks with the two widely used datasets in FSOR involved in MiniImageNet (MiniIN) [41] and TieredImageNet (TieredIN) [34]. Finally, we employ the more challenging large-scale benchmark datasets, such as ImageNet-200 (IN-200) [43], iNaturalist (iNa) [39], Places [23], ImageNet-Easy (IN-Easy) [40], ImageNet-Hard (IN-Hard) [40], ImageNet-LT (IN-LT) [24]. Details of datasets and splits are presented in Sup. S2.",
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+ {
+ "type": "text",
+ "text": "Evaluation Metrics. AUROC (Area Under the Receiver-Operator Curve) and ACC are used for the evaluation. We also reported the OSCR (Open Set Classification Rate) [8] results. All results on the six traditional benchmarks are reported over five random splits on average.",
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+ "text": "Implementation Details. In our experiments, we employ the available vision backbones in CLIP, including RN50 and ViT-B/16. The \"[CLASS]\" is placed at the end of the prompts. The length of the unknown text $(M)$ is set to 30, and the number of context tokens $(P)$ is set to 16. The number of basis vectors $(F)$ is set to 100. $\\lambda$ is set to 0.9. The $\\varepsilon$ is set to 0.1 for most benchmarks, except the IN-Hard and IN-LT, where it is set to 0.001. Similarly, the number of unknown text $N$ is set to 5 for most benchmarks, with the same exceptions (IN-Hard(30) and IN-LT(60)). The weights matrix $W$ is initialized with random values drawn from a zero-mean Gaussian distribution with a standard deviation of 0.02. We employ the SGD optimizer with an initial learning rate of 0.002, decayed according to the cosine annealing rule, following the default setup in CoOp. The maximum number of epochs is set to 50, and the batch size is set to 32. All experiments are conducted on",
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+ "type": "page_number",
+ "text": "661",
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+ {
+ "type": "table",
+ "img_path": "images/3d184df38ea66a581cdfc2f2aa0365206922507c84a793e6a4fc0452b7858ec7.jpg",
+ "table_caption": [
+ "Table 1. Comparison (%) of our UTL with different methods on various benchmarks in terms of open-set performance (AUROC). The best and second-best results are highlighted in bold and underline, respectively."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods(ViT-B/16) | C10 | C10+10 | C10+50 | C100 | TINY | TINY-H | Average |
| Training-free |
| CLIP [32] | 92.51±3.37 | 92.42±2.73 | 93.14±1.66 | 81.94±3.26 | 85.20±1.58 | 81.17±1.93 | 87.73 |
| CLIP-PE [32] | 93.43±3.43 | 94.77±2.45 | 94.83±1.56 | 81.82±3.29 | 86.07±1.42 | 81.90±1.55 | 88.80 |
| LMC [31] | 96.60±0.30 | 98.90±0.70 | 98.50±0.40 | - | 86.70±1.40 | - | - |
| Few-shot close-set methods |
| CoOp (16-shot setting) [54] | 91.66±2.43 | 97.07±0.91 | 94.97±1.64 | 80.20±3.14 | 85.88±2.44 | 82.28±1.42 | 88.68 |
| CoCoOp (16-shot setting) [13] | 94.08±1.70 | 96.13±2.30 | 94.77±2.30 | 80.46±3.66 | 86.93±1.41 | 82.83±1.40 | 89.20 |
| Few-shot OOD methods |
| ID-like (16-shot setting) [1] | 90.56±2.89 | 91.51±2.80 | 90.73±3.02 | 71.58±4.76 | 47.88±1.10 | 49.85±1.31 | 73.69 |
| NegPrompt (16-shot setting) [18] | 83.43±2.21 | 88.13±7.75 | 84.74±9.59 | 69.51±3.35 | 83.21±2.01 | 77.53±0.94 | 81.09 |
| Few-shot OSR methods |
| M-Tuning (16-shot setting) [19] | 92.82±1.79 | 97.83±1.03 | 96.04±1.58 | 81.14±2.88 | 86.61±2.05 | 82.96±1.76 | 89.57 |
| UTL (16-shot setting) (Ours) | 97.39±0.85 | 99.33±0.55 | 97.69±1.42 | 87.82±2.48 | 90.64±0.83 | 87.17±1.39 | 93.34 |
",
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+ "img_path": "images/11a05d1f6b0cf49cc3eeb482cd3841d3d52caa907278b209918972754c0519b3.jpg",
+ "table_caption": [
+ "Table 2. Comparison (%) of different methods on standard FSOR benchmark datasets in terms of close-set performance (ACC). The best and second-best results are highlighted in bold and underline, respectively."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods(ViT-B/16) | C10 | C10+10 | C10+50 | C100 | TINY | TINY-H | Average |
| CLIP [32] | 93.02±1.08 | 94.70±0.74 | 94.70±0.74 | 82.20±4.09 | 88.30±2.59 | 80.96±3.17 | 88.98 |
| CLIP-PE [32] | 94.10±1.14 | 95.88±0.70 | 95.88±0.70 | 82.28±4.37 | 89.30±2.45 | 83.20±3.01 | 90.11 |
| CoOp (16-shot setting) [54] | 95.54±1.18 | 97.32±0.70 | 97.32±0.70 | 85.50±2.87 | 91.07±2.02 | 85.69±1.94 | 92.07 |
| CoCoOp (16-shot setting) [13] | 94.94±2.33 | 96.77±0.91 | 96.77±0.91 | 85.44±2.81 | 91.17±1.96 | 85.72±1.92 | 91.80 |
| M-Tuning (16-shot setting) [19] | 95.50±1.05 | 97.27±2.55 | 97.27±2.55 | 85.66±2.72 | 90.69±2.27 | 85.57±1.97 | 91.99 |
| UTL (16-shot setting) (Our) | 95.54±1.06 | 97.36±0.83 | 97.36±0.83 | 85.77±2.95 | 91.18±2.33 | 85.77±1.96 | 92.16 |
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+ "type": "text",
+ "text": "a single NVIDIA Tesla V100 GPU. Our code is available at: https://github.com/miracle0205/UTL_FSOR.",
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+ "text": "4.2. Comparison with SOTA Methods",
+ "text_level": 1,
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+ "text": "Compared Methods. As the limitation of the available vision backbone of CLIP-based models, we reconstruct some baselines for comparison, including CLIP [32], CLIP with Prompt Engineering (CLIP-PE) [32], LMC [31], CoOp [54] and CoCoOp [13], M-Tuning [19], ID-like [1], LoCoOp [28], NegPrompt [18]. These methods are compared under a few-shot setting. For fairness, all methods are trained using the same pre-trained model (CLIP/ViT-B/16), and we reproduce results from M-Tuning [19], ID-like [1], LoCoOp [28], NegPrompt [18]. We also compared UTL with OSR methods in all-data settings. The implementation details for all compared methods are in the Sup. S3.",
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+ "text": "Results on Standard and Challenging Benchmarks. To evaluate the effectiveness of our UTL, we compared several CLIP-based methods with the backbone of ViT-B/16 on standard FSOR benchmarks under the 16-shot setting. As shown in Tab. 1, UTL achieves the best average results, outperforming CLIP and CLIP-PE by $5.61\\%$ and $4.54\\%$ , respectively. It also surpassed CoOp and CoCoOp by $4.66\\%$",
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+ "type": "text",
+ "text": "and $4.14\\%$ . CoOp performs similarly to CLIP, indicating that prompt learning following a closed-set assumption cannot benefit open-set performance. Compared to M-Tuning, UTL achieves a $3.77\\%$ improvement, demonstrating its superiority in learning effective unknown text compared to manually selected alternatives. Additionally, UTL outperforms the ID-like by $19.65\\%$ on average, demonstrating the stability of our prompt learning without unknown samples. In contrast to NegPrompt, UTL achieves an average gain of $12.25\\%$ , indicating that unknown text learning is more flexible and effective than context learning in the open setting, especially on small benchmarks. For closed-set classification, Tab. 2 shows that UTL achieves the highest average accuracy among all methods in the 16-shot setting. The OSCR results are presented in Sup. S4. To further assess UTL's effectiveness, we extend our evaluation to more challenging benchmarks. As described in Tab. 3, our UTL model outperformed all CLIP-based methods in the 16-shot setting in open-set performance. Specifically, UTL improves CoOp, CoCoOp, and M-tuning by $11.11\\%$ , $10.27\\%$ , and $8.58\\%$ on average, respectively. Notably, UTL outperforms the second-best method by $4.59\\%$ , $9.5\\%$ , and $10.11\\%$ on iNa, IN-Hard, and IN-LT, respectively. These results indicate",
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+ "img_path": "images/a6a513987e6af64a42b92a9292bb5f503eb9855b40686fe65fbe4192e0f35180.jpg",
+ "image_caption": [
+ "(a) AUROC of three methods with various numbers of shots on IN-Easy and IN-LT."
+ ],
+ "image_footnote": [],
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+ "image_caption": [
+ "(b) AUROC of three methods with various numbers of shots on IN-Hard and iNa."
+ ],
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+ {
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+ "img_path": "images/6577e76e502a4cf56320e627a17c2b4f5991a6b2dc54d74bd10fc13d679da9f7.jpg",
+ "image_caption": [
+ "(c) ACC of three methods with various numbers of shots on ImageNet.",
+ "Figure 5. Comparison $(\\%)$ of different methods under various few-shot settings on four challenging benchmarks."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ },
+ {
+ "type": "table",
+ "img_path": "images/732e66940ce033dd1776e6ea6d2462d2a358a96e3a013173353df4844c7f1790.jpg",
+ "table_caption": [
+ "Table 3. Comparison (%) of our UTL with different methods on challenging benchmarks in terms of open-set performance (AUROC). The best and second-best results are highlighted in bold and underline, respectively."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods(ViT-B/16) | Mini-IN | Tiered-IN | IN200 | iNa | Places | IN-Easy | IN-Hard | IN-LT | Average |
| Training-free |
| CLIP [32] | 86.82 | 82.06 | 90.77 | 63.01 | 60.99 | 73.30 | 62.21 | 76.24 | 74.42 |
| CLIP-PE [32] | 87.99 | 81.43 | 89.43 | 61.75 | 67.26 | 73.08 | 61.23 | 72.64 | 74.35 |
| Few-shot close-set methods |
| CoOp (16-shot setting) [54] | 88.07 | 79.53 | 88.79 | 64.81 | 65.14 | 72.80 | 62.19 | 72.06 | 74.17 |
| CoCoOp (16-shot setting) [13] | 88.65 | 80.27 | 90.80 | 62.85 | 65.90 | 74.03 | 63.11 | 74.51 | 75.01 |
| Few-shot OOD methods |
| LoCoOp (16-shot setting) [28] | 89.40 | 89.73 | 95.72 | 69.55 | 67.92 | 81.74 | 67.38 | 83.35 | 80.60 |
| ID-like (16-shot setting) [1] | 53.95 | 50.52 | 92.91 | 53.44 | 61.34 | 70.53 | 58.28 | 73.94 | 64.36 |
| Few-shot OSR methods (16-shot setting) |
| M-Tuning (16-shot setting) [19] | 88.29 | 79.65 | 97.27 | 64.94 | 65.11 | 73.33 | 63.53 | 81.51 | 76.70 |
| UTL (16-shot setting) (Our) | 92.28 | 92.82 | 98.22 | 74.14 | 70.91 | 82.97 | 76.88 | 93.46 | 85.28 |
",
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+ {
+ "type": "text",
+ "text": "that UTL demonstrates more significant improvements in more challenging settings. In addition, UTL also achieves competitive ACC and OSCR performance on challenging benchmarks, which are provided in Sup. S4.",
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+ "text": "Results of Different Shot Settings. To further verify the effectiveness of our UTL method, we conducted a broader evaluation of both closed-set and open-set performance across different shot settings on IN-LT, IN-Easy, IN-Hard, and iNa. The results are shown in Fig. 5. Our UTL outperforms CoOp by a significant margin in AUROC and exhibits a consistent upward trend across all settings. As illustrated in Fig. 5(a), the AUROC of UTL on IN-LT increases rapidly with the number of shots while performance on IN-Easy is relatively stable. Similarly, the AUROC of UTL on IN-Hard and iNa also improves with more shot settings, as depicted in Fig. 5(b). That indicates that our UTL benefits from having more known samples in more challenging settings. Meanwhile, Fig. 5(c) shows that the closed-set performance of UTL is similar to CoOp on various benchmarks across different shot settings. Additionally, our UTL also achieves competitive performance in all data settings, as referred to in Sup. S5. Our UTL boosts the performance",
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+ {
+ "type": "text",
+ "text": "in both the closed-set and open-set settings, along with various shots of training samples.",
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+ "text": "4.3. Ablation Study",
+ "text_level": 1,
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+ "text": "In this subsection, we conduct an ablation study to evaluate the impact of the core components $\\mathrm{U}^2\\mathrm{WO}$ and ULS on the performance of our UTL using ViT-B/16 as the backbone.",
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+ "text": "Effect of $\\mathrm{U}^2\\mathrm{WO}$ . To evaluate the effect of our $\\mathrm{U}^2\\mathrm{WO}$ , we compare it with variants: 1) Directly learning without $\\mathrm{U}^2\\mathrm{WO}$ (DLU): the unknown text is learned based on the vectors with the random initialization as CoOp; 2) $\\mathrm{U}^2\\mathrm{WO}$ with Known Basis (UKB): Base class names come from known classes; 3) $\\mathrm{U}^2\\mathrm{WO}$ with Open Basis (UOB): the base class name is from the Outlier text (as detailed in Sup. S1). The experiments are conducted on the IN-Easy and IN-Hard datasets. The AUROC results are compared in Tab. 4, where we can observe that UKB and UOB achieve clear improvement over DLU methods, demonstrating the importance of our $\\mathrm{U}^2\\mathrm{WO}$ and the effectiveness of our $\\mathrm{U}^2\\mathrm{WO}$ in constructing the basis. In addition, the UKB performs similarly with UOB, indicating the robustness of our $\\mathrm{U}^2\\mathrm{WO}$ to the base class names. Significantly, the effectiveness of the",
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+ "text": "663",
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+ "img_path": "images/24741fa321685defa429f82a79f0306b28c34140ab46cf80b68b5fd6dee78fd7.jpg",
+ "image_caption": [
+ "(a) Results vary with $\\varepsilon$ on C10 and TINY."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 7
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+ {
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+ "img_path": "images/90f88f2501798d502511885ec1914db759bb9f1320f0b1263bffff3c0242f78a.jpg",
+ "image_caption": [
+ "(b) Results vary with $\\varepsilon$ on IN-Easy and IN-Hard."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 7
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+ {
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+ "img_path": "images/6599ecb9e76c8eee0191085d8e43ed8c5d24cf9b72569dc06e0c93e309c2e491.jpg",
+ "image_caption": [
+ "(c) Results vary with $N$ on IN-Easy and IN-hard.",
+ "Figure 6. Ablation results $(\\%)$ of our UTL with various $\\varepsilon$ and $N$ ."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "img_path": "images/c3a52bbf85c1f44876a09d4d725d9cea90cf991a5ee34769241b9f01de0116b8.jpg",
+ "table_caption": [
+ "Table 4. Comparison of ${\\mathrm{U}}^{2}\\mathrm{{WO}}$ with its variants (AUROC)."
+ ],
+ "table_footnote": [],
+ "table_body": "| ViT-B/16 | DLU | UKB | UOB |
| IN-Easy | 81.69 | 82.72 | 82.97 |
| IN-Hard | 75.54 | 76.88 | 76.29 |
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+ "img_path": "images/7895886af222a8b5122d759a36a8ce4eef79faedb0ef5fb42dc4cb49c4562a93.jpg",
+ "table_caption": [
+ "Table 5. AUROC of UTL vary with $N$ on TINY."
+ ],
+ "table_footnote": [],
+ "table_body": "| N | 1 | 2 | 5 | 7 | 10 | 20 |
| AUROC | 90.46 | 90.64 | 90.75 | 90.22 | 89.94 | 89.74 |
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+ {
+ "type": "text",
+ "text": "known basis in UKB shows that our UTL effectively learns unknown text when provided with sufficient known class names.",
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+ "text": "Effect of $\\varepsilon$ on ULS. To evaluate the effect of ULS, we conducted an ablation study by varying $\\varepsilon$ across different benchmarks. The selection of $\\varepsilon$ was guided by the number of known classes $K$ , where a larger $K$ necessitates a smaller $\\varepsilon$ to ensure sufficient discriminability of unknown text. Specifically, for C10 ( $K = 4$ ) and TINY ( $K = 20$ ), we set $\\varepsilon$ with the range of [0.001, 0.5] with $N$ at 5. For IN-Easy and IN-Hard ( $K = 1000$ ), we selected $\\varepsilon \\in \\{0.1, 0.01, 0.001, 0.0001\\}$ , with $N = 5$ for IN-Easy and $N = 30$ for IN-Hard. As shown in Fig. 6(a), AUROC improves with increasing $\\varepsilon$ but experiences a slight decline beyond 0.3 for C10 and 0.2 for TINY. The results for IN-Easy and IN-Hard are illustrated in Fig. 6(b), where performance peaks at $\\varepsilon = 0.001$ before decreasing. Based on the AUROC results across the four datasets, we can derive 1) As the $K$ increases, the sensitivity to $\\varepsilon$ rises, leading to a narrower stable range and greater performance fluctuations. 2) The optimal value decreases as $K$ increases. In our experiments, we set $\\varepsilon = 0.1$ for most benchmarks and set $\\varepsilon = 0.001$ for IN-Easy, IN-Hard, and IN-LT. All that indicates our ULS consistently achieves stable improvement on most benchmarks and can achieve the best performance on the more challenging benchmarks. However, on more challenging datasets, performance instability persists, which we attribute to the uniform constraint imposed by ULS, suggesting potential areas for improvement.",
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+ {
+ "type": "text",
+ "text": "Number of Unknown Words $N$ . To evaluate the effect of",
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+ },
+ {
+ "type": "text",
+ "text": "the number of unknown text $N$ , we conduct experiments by varying $N$ on TINY, IN-Easy, and IN-Hard. The AUROC results on TINY are illustrated in Tab. 5. The AUROC results have declined slightly along with the increase of $N$ on the TINY dataset. As shown in Fig. 6(c), UTL performs stably against $N$ on IN-Easy and IN-Hard. As such, UTL tends to choose a small amount of $N$ and increase the amount of $N$ with a large number of known classes. Meanwhile, UTL is insensitive to $N$ under the large-scale setting, suggesting that our method is potentially scalable to various tasks.",
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+ "text": "Unified-Context vs Dual-Context. As illustrated in Fig. 4, our Dual-Context strategy can effectively handle the conflict of context optimization between the known and unknown classes, achieving stable performance. Intuitively, adding a context prompt introduces additional learnable parameters. However, we implement a unified prompt for each task, and the extra parameters amount to only about 8K. Regarding training speed, the total training times for dual-context and unified-context on TINY are 88.27 seconds and 73.67 seconds, respectively. Overall, we can conclude that the Dual Context strategy provides stable performance benefits while adding minimal computational overhead.",
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+ "type": "text",
+ "text": "5. Conclusions",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "This paper has proposed an Unknown Text Learning (UTL) method for effective extension of vision-language models (i.e., CLIP) to the FSOR task. The core of UTL is to simultaneously learn context prompt and unknown words for CLIP with free of unknown samples and the corresponding precise text descriptions. To this end, UTL develops an effective universal unknown words optimization $(\\mathrm{U}^2\\mathrm{WO})$ and an efficient unknown label smoothing (ULS) to characterize and optimize the unknown text, respectively. Going beyond UTL, a decoupled prompt strategy is presented to achieve a better performance trade-off between known classification and unknown detection tasks. Extensive experiments on both traditional FSOR benchmarks and challenge datasets clearly demonstrate the effectiveness of our UTL method. We hope our proposed UTL could encourage more work on effective prompt learning for the FSOR task.",
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+ "text": "664",
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+ {
+ "type": "text",
+ "text": "Acknowledgments",
+ "text_level": 1,
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+ },
+ {
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+ "text": "This work was supported in part by the National Natural Science Foundation of China under Grant 62276186, U23B2049, 62476198, and 62376186.",
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+ {
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+ "text": "References",
+ "text_level": 1,
+ "bbox": [
+ 102,
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+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "list",
+ "sub_type": "ref_text",
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diff --git a/2025/Unknown Text Learning for CLIP-based Few-Shot Open-set Recognition/8df0b349-1f30-4db7-a5dd-d902f9f32a3f_model.json b/2025/Unknown Text Learning for CLIP-based Few-Shot Open-set Recognition/8df0b349-1f30-4db7-a5dd-d902f9f32a3f_model.json
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+ "content": "{miracle0205, qlwang, caobing, huqinghua, yahong}@tju.edu.cn"
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+ "content": "Recently, vision-language models (e.g., CLIP) with prompt learning have shown great potential in few-shot learning. However, an open issue remains for the effective extension of CLIP-based models to few-shot open-set recognition (FSOR), which requires classifying known classes and detecting unknown samples using a few known samples. The core challenge is that unknown samples and their textual descriptions are unavailable. To address this, we propose an Unknown Text Learning (UTL) method for CLIP-based FSOR tasks with only known samples. Specifically, UTL involves two key components, i.e., universal unknown words optimization \\((U^2 WO)\\) and unknown label smoothing (ULS). Specifically, \\(U^2 WO\\) constructs the universal space of unknown words with basis vectors and characterizes unknown text based on a linear combination of those basis vectors. To efficiently learn unknown text without unknown samples, ULS is presented to perform contrast learning between unknown text and known samples by regulating the label of unknown classes to a small constant, which flexibly empowers unknown text to be non-matching and confused with known visual samples. In addition, our UTL incorporates an additional context for known classes to mitigate conflicts of context optimization between known and unknown classes. UTL effectively regularizes the predicted probability by integrating learnable unknown text. Experimental results on various benchmarks show that our UTL is superior to its counterparts while achieving state-of-the-art performance."
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+ "content": "Test samples in real-world scenarios often belong to classes not encountered during training, posing a critical challenge for recognition systems. Additionally, the high cost of data annotation and privacy concerns limit access to large-scale, high-quality datasets, further exacerbating the problem. To address this, Few-Shot Open-Set Recognition (FSOR) [20] has been proposed to enable recognition systems to classify predefined known classes while identifying unknown"
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+ "content": "Figure 1. (a) Comparison of our UTL with its counterparts in terms of prompt. Specifically, CoOp [54] and M-Tuning [19] learn only context prompt. In contrast, our UTL learns context prompts and unknown text more flexibly under various open-set scenarios. (b) Density distribution of confidence score (maximum predicted probability) with the proposed UTL and CoOp. The gap between the mean scores of known and unknown samples indicates the method's ability to distinguish open-set instances."
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+ "content": "samples under data-limited conditions. This problem has gained significant attention, inspiring research efforts to extend few-shot learning methods to open-set settings [11, 12, 20, 42]. Recently, vision-language models (e.g., CLIP [32]) with prompt learning [13, 45, 46, 50, 54, 55] have demonstrated remarkable performance in few-shot classification by learning textual prompts from training samples. That inspires us to explore the potential of prompt learning for FSOR. As shown in Fig. 1(a), CLIP constructs prompts with context and class names. However, in FSOR, the class names of unknown samples are unavailable. The absence of unknown class names imposes a closed-set assumption, making CLIP vulnerable to open-set conditions [25]. Prompt learning methods like CoOp [54] attempt to learn contextual prompts directly from image features, but they still rely on a closed-set assumption and cannot be extended to unknown text due to the absence of unknown samples. As a result, the effectiveness of prompt learning in FSOR remains fundamentally limited, as the core challenge lies in the absence of unknown samples and their corresponding textual descriptions."
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+ "content": "*Corresponding author"
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+ "content": "Figure 2. Overview of our proposed UTL method for CLIP-based few-shot open set recognition. First, \\(\\mathrm{U}^2\\mathrm{WO}\\) is developed to characterize unknown words based on a linear combination of a universal, learnable word basis, which is jointly optimized with context prompt to avoid the specialized generation of unknown words. Then, our ULS is presented to perform contrast learning between unknown text and known samples by regulating labels of all unknown classes to a small constant, efficiently learning unknown text free of unknown samples."
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+ "content": "A natural solution is to generate unknown samples along with their textual descriptions. LMC [31] represents a pioneering effort in this direction, leveraging large pre-trained models (e.g., ChatGPT [4], DALL-E [33], CLIP [32]) to generate unknown samples and their corresponding virtual class names simultaneously. However, this approach is unstable when handling diverse class compositions and struggles to produce high-quality image-text pairs, limiting its generalization. To better explore the text processing ability of CLIP for the open set setting, as shown in Fig. 1(a), M-Tuning [19] manually selects specialized words, referred to as open words, from WordNet [26] and incorporates them into context templates to construct unknown prompts. The model then learns context prompts following CoOp [54] while regularizing known-class predictions. However, selecting the specialized words as unknown text is potentially inflexible to various scenarios and is sensitive to the number of known classes. As discussed above, generating imagetext pairs and specialized word selection are insufficiently flexible and stable to cope with different scenarios. Consequently, a critical challenge persists: effectively extending CLIP-based models to FSOR while addressing the absence of unknown samples and their textual descriptions."
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+ "content": "To overcome the above challenge, we propose a novel Unknown Text Learning (UTL) method, which simultaneously learns the unknown text and context prompt using a few known samples. The core components of UTL involve a universal unknown words optimization \\((\\mathrm{U}^2\\mathrm{WO})\\) and an unknown label smoothing (ULS) for effectively characterizing and efficiently optimizing the unknown text, respectively. Specifically, our \\(\\mathrm{U}^2\\mathrm{WO}\\) first constructs a universal space of unknown words based on the label name of the base classes. We perform a principal component analysis (PCA) of their"
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+ "content": "embedding token vectors, utilizing the top-\\(k\\) principal components to form the universal space of unknown words. Subsequently, the unknown text is characterized based on a linear combination of these basis vectors. As such, our \\(\\mathrm{U}^2\\mathrm{WO}\\) avoids the specialized word selection and provides a space constraint on unknown text learning. To efficiently learn unknown text, our ULS regulates the labels of all unknown classes to a small constant and then performs contrast learning between unknown text and known samples. As such, ULS can learn the unknown text by avoiding the requirement of unknown samples. Based on the proposed \\(\\mathrm{U}^2\\mathrm{WO}\\) and ULS modules, our UTL can realize effective prompt learning for CLIP-based FSOR with no need for unknown samples and the corresponding specialized text descriptions. As illustrated in Fig. 1 (a), our UTL method learns context prompts and unknown text, giving UTL more flexibility than M-Tuning and CoOp, which focus only on prompt context. In addition, our UTL incorporates an additional context for known classes to mitigate conflicts of context optimization between known and unknown classes. As shown in Fig. 4, our UTL can effectively handle the context conflict, achieving stable performance. As illustrated in Fig. 1(b), our UTL effectively regularizes the predicted probability by incorporating learnable unknown text. Notably, UTL significantly reduces the confidence of unknown samples (from approximately 0.8 to 0.2) and slightly lowers known samples, substantially widening the confidence gap between known and unknown samples and improving the performance of unknown detection. The overview of our proposed UTL is illustrated in Fig. 2. To verify the effectiveness of our UTL method, we conduct experiments on various benchmarks [16, 17, 24, 27, 34, 39-41, 43]. The contributions of our work are summarized as follows:"
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+ "content": "- In this paper, we propose a novel Unknown Text Learning (UTL) method to explore the potential of CLIP for FSOR tasks. Our UTL makes the first attempt to simultaneously learn context prompts and unknown text using only known samples, without extra datasets and large models."
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+ "content": "- To this end, our UTL respectively presents a universal unknown words optimization (U²WO) and an unknown label smoothing (ULS) to characterize and optimize the unknown text, realizing effective and efficient prompt learning for CLIP-based FSOR. Furthermore, a dual-context strategy is introduced to avoid context conflict."
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+ "content": "- Extensive experiments are conducted on various benchmarks using different backbone models, and the results show that our UTL significantly outperforms its counterparts while achieving state-of-the-art performance."
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+ "content": "2. Related Work"
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+ "content": "Prompt Learning. Recently, prompt learning has demonstrated its effectiveness in adapting large vision-language (VL) pre-trained models to few-shot downstream vision tasks. Researchers contributed a great deal of effort to explore diverse techniques for the generalization issue [10, 13, 45, 46, 50, 54, 55]. CoOp [54] introduces continuous context optimization. As an extension of CoOp, CoCoOp [13] enhances the performance by incorporating a lightweight neural network to generate dynamic input-conditional tokens for each image. However, these methods developed under a closed-set assumption are unsuitable for FSOR. In recent works, synthesizing image-text pairs [22, 37, 38, 44] to improve the performance of vision-language models has been proposed for closed-set tasks. These methods strive to present more accurate image-text pairs in the embedding space but do not provide solutions for unknown image-text pairs that represent negation semantics. Unlike them, our UTL can learn unknown text for CLIP while achieving better FSOR performance (see Sec. 4.2)."
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+ "content": "Few-Shot Open-Set Recognition. Few-shot open-set recognition (FSOR) is proposed to generalize open-set recognition (OSR) [2, 30, 36, 40, 48, 49, 53] to the data-limited task. Current methods usually extend few-shot methods to the open-set setting, which can be mainly categorized into metric-based methods [3, 11, 12, 20, 29, 42, 51] and CLIP-based methods [19]. We focus on the generalization of CLIP-based methods to OSR. Existing CLIP-based methods regularize the predicted probability with generated unknown samples and text to enhance the models' ability to open settings. LMC [31] first simulates text with ChatGPT [4], generates the aligned images with DALL-E [33], and acess the alignment using CLIP [32]. To further explore the text processability, M-Tuning [19] provides select open words from WordNet as unknown words, which can easily get texts from non-target class names. Prompt methods are also proposed in out-of-distribution (OOD)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.103,
+ 0.895,
+ 0.324
+ ],
+ "angle": 0,
+ "content": "detection. ID-like [1] learns the unknown prompts based on low-similarity samples selected from the augmentations of in-distribution images. The similarity-based selection is preprocessed with CLIP. However, the quality of selected images constrains the models' performance. NegPrompt [18] is designed to learn a set of negative context prompts, which can be explained as \"a photo of not a\". However, the negative context learning batch makes unknown prompts easily redundant for downstream tasks. Meanwhile, it leads to a linear increase in the number of prompts, which is not friendly to large-scale settings. Unlike previous works [1, 18, 28], our UTL leverages the capabilities of CLIP without requiring additional large models or simulation processes, which learn both context and unknown text with only known samples efficiently."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.335,
+ 0.602,
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+ ],
+ "angle": 0,
+ "content": "3. Method"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.359,
+ 0.65,
+ 0.373
+ ],
+ "angle": 0,
+ "content": "3.1. Preliminaries"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.38,
+ 0.895,
+ 0.572
+ ],
+ "angle": 0,
+ "content": "CLIP with Prompt Learning. CLIP [32] comprises a text encoder \\(\\mathcal{T}:t\\to \\mathbb{R}^d\\) and an image encoder \\(\\mathcal{I}:x\\rightarrow\\) \\(\\mathbb{R}^d\\) , designed to map textual prompts \\(t\\) and images \\(\\pmb{x}\\) into a shared alignment space, respectively. Given \\(K\\) predefined class names, the \\(k\\) -th textual prompt \\(t_k\\) can be constructed in the form \"a photo of a \\([\\mathrm{CLASS}_k]\\) .\", \"[CLASSk]\" is the \\(k\\) -th class name. With these prompts, CLIP can easily generalize to downstream \\(K\\) -class classification tasks by computing the similarity of image features relative to all corresponding text features as \\(s_k(x) =\\) \\(\\sin (\\mathcal{T}(t_k),\\mathcal{I}(\\boldsymbol {x}))\\) , where \\(\\sin (\\cdot ,\\cdot)\\) denotes the cosine similarity and \\(k\\in [1,K]\\) . The predicted probability \\(p_k^C (x)\\) in the close-set setting can be expressed as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.553,
+ 0.58,
+ 0.894,
+ 0.617
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {k} ^ {C} (\\boldsymbol {x}) = \\frac {\\exp \\left(\\operatorname {s i m} \\left(\\mathcal {T} \\left(\\boldsymbol {t} _ {\\boldsymbol {k}}\\right) , \\mathcal {I} (\\boldsymbol {x})\\right) / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(\\operatorname {s i m} \\left(\\mathcal {T} \\left(\\boldsymbol {t} _ {\\boldsymbol {j}}\\right) , \\mathcal {I} (\\boldsymbol {x})\\right) / \\tau\\right)}, \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.624,
+ 0.894,
+ 0.726
+ ],
+ "angle": 0,
+ "content": "where \\(\\tau\\) is the temperature parameter. To avoid manual prompt tuning, CoOp [54] introduces a learnable context prompt by modeling context words with continuous vectors, the learnable prompt could be \\(t = [\\mathrm{V}]_1[\\mathrm{V}]_2\\ldots [\\mathrm{V}]_L[\\mathrm{CLASS}]\\), where each \\([\\mathrm{V}]_l\\) (\\(l \\in \\{1,\\dots,L\\}\\)) is a vector with the same dimension as word embeddings and \\(L\\) is the length of context tokens."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.727,
+ 0.894,
+ 0.813
+ ],
+ "angle": 0,
+ "content": "Unknown detection in Open Set Recognition (OSR). An intuitive way to detect unknown samples is thresholding on the confidence score. Taking the maximum softmax probability (MSP) across known classes as a confidence score. The \\(K\\)-class classifier to detect unknown samples can be extended as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.552,
+ 0.821,
+ 0.894,
+ 0.868
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {y} = \\left\\{ \\begin{array}{l l} \\underset {k \\in [ 1, K ]} {\\arg \\max } p _ {k} ^ {C} (\\boldsymbol {x}), & \\text {i f} \\underset {k \\in [ 1, K ]} {\\max } p _ {k} ^ {C} (\\boldsymbol {x}) \\geq \\theta , \\\\ \\text {u n k n o w n}, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.875,
+ 0.716,
+ 0.89
+ ],
+ "angle": 0,
+ "content": "where \\(\\theta\\) is the preset threshold."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.487,
+ 0.929,
+ 0.511,
+ 0.939
+ ],
+ "angle": 0,
+ "content": "659"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3.2. Overview of Unknown Text Learning (UTL)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.101,
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+ ],
+ "angle": 0,
+ "content": "In an open-set scenario, the absence of prompts for unknown classes forces the model to classify all test samples into one of the known categories with high confidence. To address this issue, we propose a novel Unknown Text Learning (UTL) method to integrate the learning of unknown text with context optimization, aiming to extend the principle of prompt learning to the open-set setting. The overview of our proposed UTL is shown in Fig. 2. UTL involves a universal unknown words optimization \\((\\mathrm{U}^2\\mathrm{WO})\\) and an unknown label smoothing (ULS). Specifically, our UTL models each unknown text with continuous vectors \\(U = [u_{1}][u_{2}]\\ldots [u_{M}]\\). Each \\([u_m]\\) (\\(m\\in \\{1,\\dots ,M\\}\\)) is a vector with the same dimension as word embeddings, while \\(M\\) is the length of unknown text tokens. \\(\\mathrm{U}^2\\mathrm{WO}\\) constructs the universal unknown words space with a group of basis vectors denoted as \\([Q_1,Q_2,\\dots ,Q_F]\\), where \\(Q_{f}\\) (\\(f\\in \\{1,\\dots ,F\\}\\)) is a basis vector and \\(F\\) is the number of basis vectors. Then the unknown text \\(U_{k}\\) can be calculated by a linear combination of these basis vectors as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.164,
+ 0.413,
+ 0.482,
+ 0.449
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\boldsymbol {U} _ {k} = w ^ {1} \\boldsymbol {Q} _ {1} + w ^ {2} \\boldsymbol {Q} _ {2} + \\dots + w ^ {F} \\boldsymbol {Q} _ {F}, \\tag {3} \\\\ k \\in \\{K + 1, \\dots , K + N \\}, \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.101,
+ 0.461,
+ 0.484,
+ 0.578
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbf{W} = \\{w^{1},\\dots ,w^{F}\\}\\) indicates the weights of combination. To efficiently learn the weights \\(\\mathbf{W}\\), unknown label smoothing (ULS) is presented to perform contrast learning between unknown text and known samples by regulating the label of all unknown classes to a small constant \\(\\varepsilon\\). As such, our UTL with \\(\\mathrm{U^2WO}\\) and ULS can effectively learn unknown text for CLIP-based FSOR without unknown samples and the corresponding precise text descriptions."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.101,
+ 0.579,
+ 0.484,
+ 0.755
+ ],
+ "angle": 0,
+ "content": "Consider the \\(K\\)-class classification task, UTL add additional \\(N\\) unknown text, \\([U_{K + 1}, U_{K + 2}, \\ldots, U_{K + N}]\\), as the textual description for the last \\(N\\) unknown classes. Let the context prompt \\(\\mathbf{V} = [\\mathrm{V}]_1[\\mathrm{V}]_2 \\ldots [\\mathrm{V}]_L\\), the unknown prompt incorporating unknown text and context prompt can be formulated as \\(\\pmb{t}_k = [V, U_k]\\), where \\(k \\in \\{K + 1, \\ldots, K + N\\}\\). For the \\(K\\) known classes, let known class name as \\([C_1, C_2, \\ldots, C_K]\\), the prompt for \\(k\\)-th known class can be formulated as \\(\\pmb{t}_k = [V, C_k]\\), \\(k \\in \\{1, \\ldots, K\\}\\). Incorporating the prompts for known classes and unknown classes, the predicted probability for the \\(k\\)-th known class under the open setting is calculated as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.114,
+ 0.765,
+ 0.484,
+ 0.814
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {k} ^ {O} (\\boldsymbol {x}) = \\frac {\\exp \\left(s _ {k} ^ {C} / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(s _ {j} ^ {C} / \\tau\\right) + \\sum_ {j = K + 1} ^ {K + N} \\exp \\left(s _ {j} ^ {O} / \\tau\\right)}, \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.101,
+ 0.816,
+ 0.484,
+ 0.892
+ ],
+ "angle": 0,
+ "content": "where \\(s_k^C = \\mathrm{sim}(\\mathcal{T}([V,C_k]),\\mathcal{I}(\\pmb {x}))\\) \\(k\\in \\{1,\\dots ,K\\}\\) \\(s_k^O = \\mathrm{sim}(\\mathcal{T}([V,U_k]),\\mathcal{I}(\\pmb {x}))\\) \\(k\\in \\{K + 1,\\ldots ,K + N\\}\\) From Eq. (1) and Eq. (4), we can observe that our UTL introduces learning unknown text to regularize the predicted probability, enhancing the models' ability to detect un"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.103,
+ 0.894,
+ 0.133
+ ],
+ "angle": 0,
+ "content": "known samples by thresholding on the maximum softmax probability over known classes."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.147,
+ 0.854,
+ 0.164
+ ],
+ "angle": 0,
+ "content": "3.3. Universal Unknown Words Optimization"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.171,
+ 0.896,
+ 0.495
+ ],
+ "angle": 0,
+ "content": "Intuitively, the unknown text can be learned from scratch without any constraints, as CoOp [54]. However, the text space is ample, and direct learning tends to overfit [9]. The textual descriptions for unknown classes may be uncertain, but they still belong to a subset of the word embedding space of CLIP. Inspired by the visual learning based on a universal dictionary [52], we construct space constraints to characterize the unknown text. As a subset of the word embedding space of CLIP, we construct the Universal Unknown Words Space based on the word embedding of the text description. Specifically, we first gather 1000 label names from base classes. Particularly, we use known classes and outlier text as the base classes. To ensure the quality of outlier text, we rigorously filter outlier text based on its corresponding Synset IDs, explicitly excluding names associated with unknown classes that may appear in downstream tasks. Next, the collected label names are processed through the CLIP text encoder to extract word embeddings. Finally, this study employs a simple principal component analysis (PCA) on these embedding vectors to obtain the universal basis vectors. Detailed criteria for space construction and base class selection are provided in Sup. S1."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.509,
+ 0.755,
+ 0.526
+ ],
+ "angle": 0,
+ "content": "3.4. Unknown Label Smoothing"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.533,
+ 0.895,
+ 0.738
+ ],
+ "angle": 0,
+ "content": "Existing studies [1, 18] have typically framed unknowns as samples residing far from the known space or situated in the vicinity of known samples. These unknown samples tend to exhibit lower probabilities when associated with known classes. Alternatively, we can invert this perspective, considering known samples as prone to acquiring lower probabilities when related to unknown classes. Building upon this rethinking, we introduce Unknown Label Smoothing (ULS) regularization. The core idea of ULS is to constrain a random small constant \\(\\varepsilon\\) between known samples and unknown prompts for contrastive learning. Specifically, for an image of a known class where \\(y_{t}\\) represents the ground truth class label, the final ground truth distribution \\(q(k)\\) can be defined as follows,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.585,
+ 0.753,
+ 0.895,
+ 0.808
+ ],
+ "angle": 0,
+ "content": "\\[\nq (k) = \\left\\{ \\begin{array}{l l} 1 & k = y _ {t}, k \\in [ 1, K ], \\\\ 0 & k \\neq y _ {t}, k \\in [ 1, K ], \\\\ \\varepsilon & k \\in [ K + 1, K + N ]. \\end{array} \\right. \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.822,
+ 0.847,
+ 0.837
+ ],
+ "angle": 0,
+ "content": "Therefore, we can rewrite the cross-entropy loss as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.56,
+ 0.851,
+ 0.895,
+ 0.893
+ ],
+ "angle": 0,
+ "content": "\\[\nl _ {O} = - \\log \\left(p _ {y _ {t}} ^ {O} (\\boldsymbol {x})\\right) - \\varepsilon \\sum_ {k = K + 1} ^ {K + N} \\log \\left(p _ {k} ^ {U} (k)\\right), \\tag {6}\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.487,
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+ ],
+ "angle": 0,
+ "content": "660"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.135,
+ 0.101,
+ 0.454,
+ 0.194
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.131,
+ 0.199,
+ 0.454,
+ 0.213
+ ],
+ "angle": 0,
+ "content": "Figure 3. Unified Context (UC) vs. Dual Context (DC)."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.172,
+ 0.227,
+ 0.41,
+ 0.37
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.14,
+ 0.381,
+ 0.444,
+ 0.395
+ ],
+ "angle": 0,
+ "content": "Figure 4. Performance of UC vs. DC with various \\(\\varepsilon\\)."
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.115,
+ 0.407,
+ 0.483,
+ 0.457
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {k} ^ {U} (\\boldsymbol {x}) = \\frac {\\exp \\left(s _ {k} ^ {O} / \\tau\\right)}{\\sum_ {j = 1} ^ {K} \\exp \\left(s _ {j} ^ {C} / \\tau\\right) + \\sum_ {j = K + 1} ^ {K + N} \\exp \\left(s _ {j} ^ {O} / \\tau\\right)}, \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.102,
+ 0.458,
+ 0.288,
+ 0.473
+ ],
+ "angle": 0,
+ "content": "where \\( k \\in [K + 1, K + N] \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.101,
+ 0.474,
+ 0.484,
+ 0.562
+ ],
+ "angle": 0,
+ "content": "Note that \\(\\varepsilon\\) may vary for different classes, but it is hard to decide \\(\\varepsilon\\) optimally. So, we use the same \\(\\varepsilon\\) for all cases for efficiency. From an optimization perspective, \\(\\varepsilon > 0\\) distinguishes unknown classes from other known ones, avoiding overfitting to known classes. \\(\\varepsilon = 0\\) returns back CoOp, losing the effect of regularization."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.102,
+ 0.574,
+ 0.307,
+ 0.59
+ ],
+ "angle": 0,
+ "content": "3.5. Dual-Context Strategy"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.101,
+ 0.596,
+ 0.484,
+ 0.89
+ ],
+ "angle": 0,
+ "content": "UTL performs contrastive learning between the unknown text and known samples by assigning a uniform small value to the label truth of all unknown classes. Since different known-class samples share the same expected value, the context prompt learning for unknown classes lacks discriminability among different known classes, especially when the assigned value is not sufficiently small. This discrepancy conflicts with the context prompt learning of known classes, which requires higher discriminability. As shown in Fig. 4, we empirically observe opposite trends in performance between ACC, which represents the performance of known-class classification, and AUROC (Area Under the Receiver-Operator Curve), which evaluates the performance of unknown detection, with various \\(\\varepsilon\\) under a unified context prompt. Therefore, we introduce a dual-context strategy for UTL to mitigate conflicts within context learning between known and unknown classes. As illustrated in Fig. 3, the unified context version for our UTL, in which known classes and unknown classes tend to learn the unified context based on known samples, while the dual-context"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.103,
+ 0.893,
+ 0.133
+ ],
+ "angle": 0,
+ "content": "strategy introduces an additional context for known classes. UTL performs contrastive learning with a combined loss:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.575,
+ 0.16,
+ 0.894,
+ 0.18
+ ],
+ "angle": 0,
+ "content": "\\[\nl = (1 - \\lambda) \\cdot \\left(- \\log \\left(p _ {y ^ {t}} ^ {C} (\\boldsymbol {x})\\right)\\right) + \\lambda \\cdot l _ {O}. \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.191,
+ 0.736,
+ 0.206
+ ],
+ "angle": 0,
+ "content": "where \\(\\lambda\\) is a balancing coefficient."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.207,
+ 0.895,
+ 0.281
+ ],
+ "angle": 0,
+ "content": "Inference. When performing the classification task, we use additional context prompts only for known classes and compute their predicted probability \\( p_k^C \\). For unknown detection, we threshold the maximum softmax probability (MSP) of \\( p_k^O \\) as a confidence score."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.297,
+ 0.642,
+ 0.314
+ ],
+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.322,
+ 0.698,
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+ ],
+ "angle": 0,
+ "content": "4.1. Experimental Setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.344,
+ 0.895,
+ 0.565
+ ],
+ "angle": 0,
+ "content": "Datasets. We conduct experiments on various benchmarks for FSOR. Following the previous works [3, 5, 6, 15, 24, 27, 40, 42, 47, 53], we construct the standard benchmarks following the traditional OSR setting including CIFAR10 (C10) [16], CIFAR10 + 10 (C10 + 10) [16], CIFAR10 + 50 (C10 + 50) [16], CIFAR100 (C100) [16], TinyImageNet (TINY) [17], TinyImageNet-Hard (TINY-H) [17]. Then, we construct two benchmarks with the two widely used datasets in FSOR involved in MiniImageNet (MiniIN) [41] and TieredImageNet (TieredIN) [34]. Finally, we employ the more challenging large-scale benchmark datasets, such as ImageNet-200 (IN-200) [43], iNaturalist (iNa) [39], Places [23], ImageNet-Easy (IN-Easy) [40], ImageNet-Hard (IN-Hard) [40], ImageNet-LT (IN-LT) [24]. Details of datasets and splits are presented in Sup. S2."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.566,
+ 0.894,
+ 0.639
+ ],
+ "angle": 0,
+ "content": "Evaluation Metrics. AUROC (Area Under the Receiver-Operator Curve) and ACC are used for the evaluation. We also reported the OSCR (Open Set Classification Rate) [8] results. All results on the six traditional benchmarks are reported over five random splits on average."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.641,
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+ ],
+ "angle": 0,
+ "content": "Implementation Details. In our experiments, we employ the available vision backbones in CLIP, including RN50 and ViT-B/16. The \"[CLASS]\" is placed at the end of the prompts. The length of the unknown text \\((M)\\) is set to 30, and the number of context tokens \\((P)\\) is set to 16. The number of basis vectors \\((F)\\) is set to 100. \\(\\lambda\\) is set to 0.9. The \\(\\varepsilon\\) is set to 0.1 for most benchmarks, except the IN-Hard and IN-LT, where it is set to 0.001. Similarly, the number of unknown text \\(N\\) is set to 5 for most benchmarks, with the same exceptions (IN-Hard(30) and IN-LT(60)). The weights matrix \\(W\\) is initialized with random values drawn from a zero-mean Gaussian distribution with a standard deviation of 0.02. We employ the SGD optimizer with an initial learning rate of 0.002, decayed according to the cosine annealing rule, following the default setup in CoOp. The maximum number of epochs is set to 50, and the batch size is set to 32. All experiments are conducted on"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "661"
+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.101,
+ 0.1,
+ 0.897,
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+ ],
+ "angle": 0,
+ "content": "Table 1. Comparison (%) of our UTL with different methods on various benchmarks in terms of open-set performance (AUROC). The best and second-best results are highlighted in bold and underline, respectively."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.1,
+ 0.135,
+ 0.897,
+ 0.365
+ ],
+ "angle": 0,
+ "content": "| Methods(ViT-B/16) | C10 | C10+10 | C10+50 | C100 | TINY | TINY-H | Average |
| Training-free |
| CLIP [32] | 92.51±3.37 | 92.42±2.73 | 93.14±1.66 | 81.94±3.26 | 85.20±1.58 | 81.17±1.93 | 87.73 |
| CLIP-PE [32] | 93.43±3.43 | 94.77±2.45 | 94.83±1.56 | 81.82±3.29 | 86.07±1.42 | 81.90±1.55 | 88.80 |
| LMC [31] | 96.60±0.30 | 98.90±0.70 | 98.50±0.40 | - | 86.70±1.40 | - | - |
| Few-shot close-set methods |
| CoOp (16-shot setting) [54] | 91.66±2.43 | 97.07±0.91 | 94.97±1.64 | 80.20±3.14 | 85.88±2.44 | 82.28±1.42 | 88.68 |
| CoCoOp (16-shot setting) [13] | 94.08±1.70 | 96.13±2.30 | 94.77±2.30 | 80.46±3.66 | 86.93±1.41 | 82.83±1.40 | 89.20 |
| Few-shot OOD methods |
| ID-like (16-shot setting) [1] | 90.56±2.89 | 91.51±2.80 | 90.73±3.02 | 71.58±4.76 | 47.88±1.10 | 49.85±1.31 | 73.69 |
| NegPrompt (16-shot setting) [18] | 83.43±2.21 | 88.13±7.75 | 84.74±9.59 | 69.51±3.35 | 83.21±2.01 | 77.53±0.94 | 81.09 |
| Few-shot OSR methods |
| M-Tuning (16-shot setting) [19] | 92.82±1.79 | 97.83±1.03 | 96.04±1.58 | 81.14±2.88 | 86.61±2.05 | 82.96±1.76 | 89.57 |
| UTL (16-shot setting) (Ours) | 97.39±0.85 | 99.33±0.55 | 97.69±1.42 | 87.82±2.48 | 90.64±0.83 | 87.17±1.39 | 93.34 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Comparison (%) of different methods on standard FSOR benchmark datasets in terms of close-set performance (ACC). The best and second-best results are highlighted in bold and underline, respectively."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Methods(ViT-B/16) | C10 | C10+10 | C10+50 | C100 | TINY | TINY-H | Average |
| CLIP [32] | 93.02±1.08 | 94.70±0.74 | 94.70±0.74 | 82.20±4.09 | 88.30±2.59 | 80.96±3.17 | 88.98 |
| CLIP-PE [32] | 94.10±1.14 | 95.88±0.70 | 95.88±0.70 | 82.28±4.37 | 89.30±2.45 | 83.20±3.01 | 90.11 |
| CoOp (16-shot setting) [54] | 95.54±1.18 | 97.32±0.70 | 97.32±0.70 | 85.50±2.87 | 91.07±2.02 | 85.69±1.94 | 92.07 |
| CoCoOp (16-shot setting) [13] | 94.94±2.33 | 96.77±0.91 | 96.77±0.91 | 85.44±2.81 | 91.17±1.96 | 85.72±1.92 | 91.80 |
| M-Tuning (16-shot setting) [19] | 95.50±1.05 | 97.27±2.55 | 97.27±2.55 | 85.66±2.72 | 90.69±2.27 | 85.57±1.97 | 91.99 |
| UTL (16-shot setting) (Our) | 95.54±1.06 | 97.36±0.83 | 97.36±0.83 | 85.77±2.95 | 91.18±2.33 | 85.77±1.96 | 92.16 |
"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "a single NVIDIA Tesla V100 GPU. Our code is available at: https://github.com/miracle0205/UTL_FSOR."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "content": "4.2. Comparison with SOTA Methods"
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+ "content": "Compared Methods. As the limitation of the available vision backbone of CLIP-based models, we reconstruct some baselines for comparison, including CLIP [32], CLIP with Prompt Engineering (CLIP-PE) [32], LMC [31], CoOp [54] and CoCoOp [13], M-Tuning [19], ID-like [1], LoCoOp [28], NegPrompt [18]. These methods are compared under a few-shot setting. For fairness, all methods are trained using the same pre-trained model (CLIP/ViT-B/16), and we reproduce results from M-Tuning [19], ID-like [1], LoCoOp [28], NegPrompt [18]. We also compared UTL with OSR methods in all-data settings. The implementation details for all compared methods are in the Sup. S3."
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+ "type": "text",
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+ "content": "Results on Standard and Challenging Benchmarks. To evaluate the effectiveness of our UTL, we compared several CLIP-based methods with the backbone of ViT-B/16 on standard FSOR benchmarks under the 16-shot setting. As shown in Tab. 1, UTL achieves the best average results, outperforming CLIP and CLIP-PE by \\(5.61\\%\\) and \\(4.54\\%\\), respectively. It also surpassed CoOp and CoCoOp by \\(4.66\\%\\)"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "and \\(4.14\\%\\). CoOp performs similarly to CLIP, indicating that prompt learning following a closed-set assumption cannot benefit open-set performance. Compared to M-Tuning, UTL achieves a \\(3.77\\%\\) improvement, demonstrating its superiority in learning effective unknown text compared to manually selected alternatives. Additionally, UTL outperforms the ID-like by \\(19.65\\%\\) on average, demonstrating the stability of our prompt learning without unknown samples. In contrast to NegPrompt, UTL achieves an average gain of \\(12.25\\%\\), indicating that unknown text learning is more flexible and effective than context learning in the open setting, especially on small benchmarks. For closed-set classification, Tab. 2 shows that UTL achieves the highest average accuracy among all methods in the 16-shot setting. The OSCR results are presented in Sup. S4. To further assess UTL's effectiveness, we extend our evaluation to more challenging benchmarks. As described in Tab. 3, our UTL model outperformed all CLIP-based methods in the 16-shot setting in open-set performance. Specifically, UTL improves CoOp, CoCoOp, and M-tuning by \\(11.11\\%\\), \\(10.27\\%\\), and \\(8.58\\%\\) on average, respectively. Notably, UTL outperforms the second-best method by \\(4.59\\%\\), \\(9.5\\%\\), and \\(10.11\\%\\) on iNa, IN-Hard, and IN-LT, respectively. These results indicate"
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+ "content": "(a) AUROC of three methods with various numbers of shots on IN-Easy and IN-LT."
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+ "content": "(c) ACC of three methods with various numbers of shots on ImageNet."
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. Comparison \\((\\%)\\) of different methods under various few-shot settings on four challenging benchmarks."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Comparison (%) of our UTL with different methods on challenging benchmarks in terms of open-set performance (AUROC). The best and second-best results are highlighted in bold and underline, respectively."
+ },
+ {
+ "type": "table",
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+ "angle": 0,
+ "content": "| Methods(ViT-B/16) | Mini-IN | Tiered-IN | IN200 | iNa | Places | IN-Easy | IN-Hard | IN-LT | Average |
| Training-free |
| CLIP [32] | 86.82 | 82.06 | 90.77 | 63.01 | 60.99 | 73.30 | 62.21 | 76.24 | 74.42 |
| CLIP-PE [32] | 87.99 | 81.43 | 89.43 | 61.75 | 67.26 | 73.08 | 61.23 | 72.64 | 74.35 |
| Few-shot close-set methods |
| CoOp (16-shot setting) [54] | 88.07 | 79.53 | 88.79 | 64.81 | 65.14 | 72.80 | 62.19 | 72.06 | 74.17 |
| CoCoOp (16-shot setting) [13] | 88.65 | 80.27 | 90.80 | 62.85 | 65.90 | 74.03 | 63.11 | 74.51 | 75.01 |
| Few-shot OOD methods |
| LoCoOp (16-shot setting) [28] | 89.40 | 89.73 | 95.72 | 69.55 | 67.92 | 81.74 | 67.38 | 83.35 | 80.60 |
| ID-like (16-shot setting) [1] | 53.95 | 50.52 | 92.91 | 53.44 | 61.34 | 70.53 | 58.28 | 73.94 | 64.36 |
| Few-shot OSR methods (16-shot setting) |
| M-Tuning (16-shot setting) [19] | 88.29 | 79.65 | 97.27 | 64.94 | 65.11 | 73.33 | 63.53 | 81.51 | 76.70 |
| UTL (16-shot setting) (Our) | 92.28 | 92.82 | 98.22 | 74.14 | 70.91 | 82.97 | 76.88 | 93.46 | 85.28 |
"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "that UTL demonstrates more significant improvements in more challenging settings. In addition, UTL also achieves competitive ACC and OSCR performance on challenging benchmarks, which are provided in Sup. S4."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Results of Different Shot Settings. To further verify the effectiveness of our UTL method, we conducted a broader evaluation of both closed-set and open-set performance across different shot settings on IN-LT, IN-Easy, IN-Hard, and iNa. The results are shown in Fig. 5. Our UTL outperforms CoOp by a significant margin in AUROC and exhibits a consistent upward trend across all settings. As illustrated in Fig. 5(a), the AUROC of UTL on IN-LT increases rapidly with the number of shots while performance on IN-Easy is relatively stable. Similarly, the AUROC of UTL on IN-Hard and iNa also improves with more shot settings, as depicted in Fig. 5(b). That indicates that our UTL benefits from having more known samples in more challenging settings. Meanwhile, Fig. 5(c) shows that the closed-set performance of UTL is similar to CoOp on various benchmarks across different shot settings. Additionally, our UTL also achieves competitive performance in all data settings, as referred to in Sup. S5. Our UTL boosts the performance"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "in both the closed-set and open-set settings, along with various shots of training samples."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "content": "4.3. Ablation Study"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this subsection, we conduct an ablation study to evaluate the impact of the core components \\(\\mathrm{U}^2\\mathrm{WO}\\) and ULS on the performance of our UTL using ViT-B/16 as the backbone."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Effect of \\(\\mathrm{U}^2\\mathrm{WO}\\). To evaluate the effect of our \\(\\mathrm{U}^2\\mathrm{WO}\\), we compare it with variants: 1) Directly learning without \\(\\mathrm{U}^2\\mathrm{WO}\\) (DLU): the unknown text is learned based on the vectors with the random initialization as CoOp; 2) \\(\\mathrm{U}^2\\mathrm{WO}\\) with Known Basis (UKB): Base class names come from known classes; 3) \\(\\mathrm{U}^2\\mathrm{WO}\\) with Open Basis (UOB): the base class name is from the Outlier text (as detailed in Sup. S1). The experiments are conducted on the IN-Easy and IN-Hard datasets. The AUROC results are compared in Tab. 4, where we can observe that UKB and UOB achieve clear improvement over DLU methods, demonstrating the importance of our \\(\\mathrm{U}^2\\mathrm{WO}\\) and the effectiveness of our \\(\\mathrm{U}^2\\mathrm{WO}\\) in constructing the basis. In addition, the UKB performs similarly with UOB, indicating the robustness of our \\(\\mathrm{U}^2\\mathrm{WO}\\) to the base class names. Significantly, the effectiveness of the"
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+ [
+ {
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+ "bbox": [
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+ "angle": 0,
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(a) Results vary with \\(\\varepsilon\\) on C10 and TINY."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "(b) Results vary with \\(\\varepsilon\\) on IN-Easy and IN-Hard."
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+ "bbox": [
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+ "bbox": [
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+ "angle": 0,
+ "content": "(c) Results vary with \\(N\\) on IN-Easy and IN-hard."
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 6. Ablation results \\((\\%)\\) of our UTL with various \\(\\varepsilon\\) and \\(N\\)."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Comparison of \\( {\\mathrm{U}}^{2}\\mathrm{{WO}} \\) with its variants (AUROC)."
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| ViT-B/16 | DLU | UKB | UOB |
| IN-Easy | 81.69 | 82.72 | 82.97 |
| IN-Hard | 75.54 | 76.88 | 76.29 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 5. AUROC of UTL vary with \\(N\\) on TINY."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ 0.397,
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+ "angle": 0,
+ "content": "| N | 1 | 2 | 5 | 7 | 10 | 20 |
| AUROC | 90.46 | 90.64 | 90.75 | 90.22 | 89.94 | 89.74 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "known basis in UKB shows that our UTL effectively learns unknown text when provided with sufficient known class names."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Effect of \\(\\varepsilon\\) on ULS. To evaluate the effect of ULS, we conducted an ablation study by varying \\(\\varepsilon\\) across different benchmarks. The selection of \\(\\varepsilon\\) was guided by the number of known classes \\(K\\), where a larger \\(K\\) necessitates a smaller \\(\\varepsilon\\) to ensure sufficient discriminability of unknown text. Specifically, for C10 (\\(K = 4\\)) and TINY (\\(K = 20\\)), we set \\(\\varepsilon\\) with the range of [0.001, 0.5] with \\(N\\) at 5. For IN-Easy and IN-Hard (\\(K = 1000\\)), we selected \\(\\varepsilon \\in \\{0.1, 0.01, 0.001, 0.0001\\}\\), with \\(N = 5\\) for IN-Easy and \\(N = 30\\) for IN-Hard. As shown in Fig. 6(a), AUROC improves with increasing \\(\\varepsilon\\) but experiences a slight decline beyond 0.3 for C10 and 0.2 for TINY. The results for IN-Easy and IN-Hard are illustrated in Fig. 6(b), where performance peaks at \\(\\varepsilon = 0.001\\) before decreasing. Based on the AUROC results across the four datasets, we can derive 1) As the \\(K\\) increases, the sensitivity to \\(\\varepsilon\\) rises, leading to a narrower stable range and greater performance fluctuations. 2) The optimal value decreases as \\(K\\) increases. In our experiments, we set \\(\\varepsilon = 0.1\\) for most benchmarks and set \\(\\varepsilon = 0.001\\) for IN-Easy, IN-Hard, and IN-LT. All that indicates our ULS consistently achieves stable improvement on most benchmarks and can achieve the best performance on the more challenging benchmarks. However, on more challenging datasets, performance instability persists, which we attribute to the uniform constraint imposed by ULS, suggesting potential areas for improvement."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.102,
+ 0.875,
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+ "angle": 0,
+ "content": "Number of Unknown Words \\(N\\). To evaluate the effect of"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.279,
+ 0.895,
+ 0.426
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+ "angle": 0,
+ "content": "the number of unknown text \\(N\\), we conduct experiments by varying \\(N\\) on TINY, IN-Easy, and IN-Hard. The AUROC results on TINY are illustrated in Tab. 5. The AUROC results have declined slightly along with the increase of \\(N\\) on the TINY dataset. As shown in Fig. 6(c), UTL performs stably against \\(N\\) on IN-Easy and IN-Hard. As such, UTL tends to choose a small amount of \\(N\\) and increase the amount of \\(N\\) with a large number of known classes. Meanwhile, UTL is insensitive to \\(N\\) under the large-scale setting, suggesting that our method is potentially scalable to various tasks."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.429,
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+ ],
+ "angle": 0,
+ "content": "Unified-Context vs Dual-Context. As illustrated in Fig. 4, our Dual-Context strategy can effectively handle the conflict of context optimization between the known and unknown classes, achieving stable performance. Intuitively, adding a context prompt introduces additional learnable parameters. However, we implement a unified prompt for each task, and the extra parameters amount to only about 8K. Regarding training speed, the total training times for dual-context and unified-context on TINY are 88.27 seconds and 73.67 seconds, respectively. Overall, we can conclude that the Dual Context strategy provides stable performance benefits while adding minimal computational overhead."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Conclusions"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.511,
+ 0.655,
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+ ],
+ "angle": 0,
+ "content": "This paper has proposed an Unknown Text Learning (UTL) method for effective extension of vision-language models (i.e., CLIP) to the FSOR task. The core of UTL is to simultaneously learn context prompt and unknown words for CLIP with free of unknown samples and the corresponding precise text descriptions. To this end, UTL develops an effective universal unknown words optimization \\((\\mathrm{U}^2\\mathrm{WO})\\) and an efficient unknown label smoothing (ULS) to characterize and optimize the unknown text, respectively. Going beyond UTL, a decoupled prompt strategy is presented to achieve a better performance trade-off between known classification and unknown detection tasks. Extensive experiments on both traditional FSOR benchmarks and challenge datasets clearly demonstrate the effectiveness of our UTL method. We hope our proposed UTL could encourage more work on effective prompt learning for the FSOR task."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "664"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.103,
+ 0.102,
+ 0.257,
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+ ],
+ "angle": 0,
+ "content": "Acknowledgments"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.102,
+ 0.127,
+ 0.484,
+ 0.171
+ ],
+ "angle": 0,
+ "content": "This work was supported in part by the National Natural Science Foundation of China under Grant 62276186, U23B2049, 62476198, and 62376186."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.104,
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+ 0.197,
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+ "angle": 0,
+ "content": "References"
+ },
+ {
+ "type": "ref_text",
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+ 0.278
+ ],
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+# Unknown Text Learning for CLIP-based Few-shot Open-Set Recognition
+
+Rui Ma, Qilong Wang\*, Bing Cao, Qinghua Hu, Yahong Han Tianjin University, China
+
+{miracle0205, qlwang, caobing, huqinghua, yahong}@tju.edu.cn
+
+# Abstract
+
+Recently, vision-language models (e.g., CLIP) with prompt learning have shown great potential in few-shot learning. However, an open issue remains for the effective extension of CLIP-based models to few-shot open-set recognition (FSOR), which requires classifying known classes and detecting unknown samples using a few known samples. The core challenge is that unknown samples and their textual descriptions are unavailable. To address this, we propose an Unknown Text Learning (UTL) method for CLIP-based FSOR tasks with only known samples. Specifically, UTL involves two key components, i.e., universal unknown words optimization $(U^2 WO)$ and unknown label smoothing (ULS). Specifically, $U^2 WO$ constructs the universal space of unknown words with basis vectors and characterizes unknown text based on a linear combination of those basis vectors. To efficiently learn unknown text without unknown samples, ULS is presented to perform contrast learning between unknown text and known samples by regulating the label of unknown classes to a small constant, which flexibly empowers unknown text to be non-matching and confused with known visual samples. In addition, our UTL incorporates an additional context for known classes to mitigate conflicts of context optimization between known and unknown classes. UTL effectively regularizes the predicted probability by integrating learnable unknown text. Experimental results on various benchmarks show that our UTL is superior to its counterparts while achieving state-of-the-art performance.
+
+# 1. Introduction
+
+Test samples in real-world scenarios often belong to classes not encountered during training, posing a critical challenge for recognition systems. Additionally, the high cost of data annotation and privacy concerns limit access to large-scale, high-quality datasets, further exacerbating the problem. To address this, Few-Shot Open-Set Recognition (FSOR) [20] has been proposed to enable recognition systems to classify predefined known classes while identifying unknown
+
+
+(a)
+Figure 1. (a) Comparison of our UTL with its counterparts in terms of prompt. Specifically, CoOp [54] and M-Tuning [19] learn only context prompt. In contrast, our UTL learns context prompts and unknown text more flexibly under various open-set scenarios. (b) Density distribution of confidence score (maximum predicted probability) with the proposed UTL and CoOp. The gap between the mean scores of known and unknown samples indicates the method's ability to distinguish open-set instances.
+
+
+(b)
+
+samples under data-limited conditions. This problem has gained significant attention, inspiring research efforts to extend few-shot learning methods to open-set settings [11, 12, 20, 42]. Recently, vision-language models (e.g., CLIP [32]) with prompt learning [13, 45, 46, 50, 54, 55] have demonstrated remarkable performance in few-shot classification by learning textual prompts from training samples. That inspires us to explore the potential of prompt learning for FSOR. As shown in Fig. 1(a), CLIP constructs prompts with context and class names. However, in FSOR, the class names of unknown samples are unavailable. The absence of unknown class names imposes a closed-set assumption, making CLIP vulnerable to open-set conditions [25]. Prompt learning methods like CoOp [54] attempt to learn contextual prompts directly from image features, but they still rely on a closed-set assumption and cannot be extended to unknown text due to the absence of unknown samples. As a result, the effectiveness of prompt learning in FSOR remains fundamentally limited, as the core challenge lies in the absence of unknown samples and their corresponding textual descriptions.
+
+
+Figure 2. Overview of our proposed UTL method for CLIP-based few-shot open set recognition. First, $\mathrm{U}^2\mathrm{WO}$ is developed to characterize unknown words based on a linear combination of a universal, learnable word basis, which is jointly optimized with context prompt to avoid the specialized generation of unknown words. Then, our ULS is presented to perform contrast learning between unknown text and known samples by regulating labels of all unknown classes to a small constant, efficiently learning unknown text free of unknown samples.
+
+A natural solution is to generate unknown samples along with their textual descriptions. LMC [31] represents a pioneering effort in this direction, leveraging large pre-trained models (e.g., ChatGPT [4], DALL-E [33], CLIP [32]) to generate unknown samples and their corresponding virtual class names simultaneously. However, this approach is unstable when handling diverse class compositions and struggles to produce high-quality image-text pairs, limiting its generalization. To better explore the text processing ability of CLIP for the open set setting, as shown in Fig. 1(a), M-Tuning [19] manually selects specialized words, referred to as open words, from WordNet [26] and incorporates them into context templates to construct unknown prompts. The model then learns context prompts following CoOp [54] while regularizing known-class predictions. However, selecting the specialized words as unknown text is potentially inflexible to various scenarios and is sensitive to the number of known classes. As discussed above, generating imagetext pairs and specialized word selection are insufficiently flexible and stable to cope with different scenarios. Consequently, a critical challenge persists: effectively extending CLIP-based models to FSOR while addressing the absence of unknown samples and their textual descriptions.
+
+To overcome the above challenge, we propose a novel Unknown Text Learning (UTL) method, which simultaneously learns the unknown text and context prompt using a few known samples. The core components of UTL involve a universal unknown words optimization $(\mathrm{U}^2\mathrm{WO})$ and an unknown label smoothing (ULS) for effectively characterizing and efficiently optimizing the unknown text, respectively. Specifically, our $\mathrm{U}^2\mathrm{WO}$ first constructs a universal space of unknown words based on the label name of the base classes. We perform a principal component analysis (PCA) of their
+
+embedding token vectors, utilizing the top- $k$ principal components to form the universal space of unknown words. Subsequently, the unknown text is characterized based on a linear combination of these basis vectors. As such, our $\mathrm{U}^2\mathrm{WO}$ avoids the specialized word selection and provides a space constraint on unknown text learning. To efficiently learn unknown text, our ULS regulates the labels of all unknown classes to a small constant and then performs contrast learning between unknown text and known samples. As such, ULS can learn the unknown text by avoiding the requirement of unknown samples. Based on the proposed $\mathrm{U}^2\mathrm{WO}$ and ULS modules, our UTL can realize effective prompt learning for CLIP-based FSOR with no need for unknown samples and the corresponding specialized text descriptions. As illustrated in Fig. 1 (a), our UTL method learns context prompts and unknown text, giving UTL more flexibility than M-Tuning and CoOp, which focus only on prompt context. In addition, our UTL incorporates an additional context for known classes to mitigate conflicts of context optimization between known and unknown classes. As shown in Fig. 4, our UTL can effectively handle the context conflict, achieving stable performance. As illustrated in Fig. 1(b), our UTL effectively regularizes the predicted probability by incorporating learnable unknown text. Notably, UTL significantly reduces the confidence of unknown samples (from approximately 0.8 to 0.2) and slightly lowers known samples, substantially widening the confidence gap between known and unknown samples and improving the performance of unknown detection. The overview of our proposed UTL is illustrated in Fig. 2. To verify the effectiveness of our UTL method, we conduct experiments on various benchmarks [16, 17, 24, 27, 34, 39-41, 43]. The contributions of our work are summarized as follows:
+
+- In this paper, we propose a novel Unknown Text Learning (UTL) method to explore the potential of CLIP for FSOR tasks. Our UTL makes the first attempt to simultaneously learn context prompts and unknown text using only known samples, without extra datasets and large models.
+- To this end, our UTL respectively presents a universal unknown words optimization (U²WO) and an unknown label smoothing (ULS) to characterize and optimize the unknown text, realizing effective and efficient prompt learning for CLIP-based FSOR. Furthermore, a dual-context strategy is introduced to avoid context conflict.
+- Extensive experiments are conducted on various benchmarks using different backbone models, and the results show that our UTL significantly outperforms its counterparts while achieving state-of-the-art performance.
+
+# 2. Related Work
+
+Prompt Learning. Recently, prompt learning has demonstrated its effectiveness in adapting large vision-language (VL) pre-trained models to few-shot downstream vision tasks. Researchers contributed a great deal of effort to explore diverse techniques for the generalization issue [10, 13, 45, 46, 50, 54, 55]. CoOp [54] introduces continuous context optimization. As an extension of CoOp, CoCoOp [13] enhances the performance by incorporating a lightweight neural network to generate dynamic input-conditional tokens for each image. However, these methods developed under a closed-set assumption are unsuitable for FSOR. In recent works, synthesizing image-text pairs [22, 37, 38, 44] to improve the performance of vision-language models has been proposed for closed-set tasks. These methods strive to present more accurate image-text pairs in the embedding space but do not provide solutions for unknown image-text pairs that represent negation semantics. Unlike them, our UTL can learn unknown text for CLIP while achieving better FSOR performance (see Sec. 4.2).
+
+Few-Shot Open-Set Recognition. Few-shot open-set recognition (FSOR) is proposed to generalize open-set recognition (OSR) [2, 30, 36, 40, 48, 49, 53] to the data-limited task. Current methods usually extend few-shot methods to the open-set setting, which can be mainly categorized into metric-based methods [3, 11, 12, 20, 29, 42, 51] and CLIP-based methods [19]. We focus on the generalization of CLIP-based methods to OSR. Existing CLIP-based methods regularize the predicted probability with generated unknown samples and text to enhance the models' ability to open settings. LMC [31] first simulates text with ChatGPT [4], generates the aligned images with DALL-E [33], and acess the alignment using CLIP [32]. To further explore the text processability, M-Tuning [19] provides select open words from WordNet as unknown words, which can easily get texts from non-target class names. Prompt methods are also proposed in out-of-distribution (OOD)
+
+detection. ID-like [1] learns the unknown prompts based on low-similarity samples selected from the augmentations of in-distribution images. The similarity-based selection is preprocessed with CLIP. However, the quality of selected images constrains the models' performance. NegPrompt [18] is designed to learn a set of negative context prompts, which can be explained as "a photo of not a". However, the negative context learning batch makes unknown prompts easily redundant for downstream tasks. Meanwhile, it leads to a linear increase in the number of prompts, which is not friendly to large-scale settings. Unlike previous works [1, 18, 28], our UTL leverages the capabilities of CLIP without requiring additional large models or simulation processes, which learn both context and unknown text with only known samples efficiently.
+
+# 3. Method
+
+# 3.1. Preliminaries
+
+CLIP with Prompt Learning. CLIP [32] comprises a text encoder $\mathcal{T}:t\to \mathbb{R}^d$ and an image encoder $\mathcal{I}:x\rightarrow$ $\mathbb{R}^d$ , designed to map textual prompts $t$ and images $\pmb{x}$ into a shared alignment space, respectively. Given $K$ predefined class names, the $k$ -th textual prompt $t_k$ can be constructed in the form "a photo of a $[\mathrm{CLASS}_k]$ .", "[CLASSk]" is the $k$ -th class name. With these prompts, CLIP can easily generalize to downstream $K$ -class classification tasks by computing the similarity of image features relative to all corresponding text features as $s_k(x) =$ $\sin (\mathcal{T}(t_k),\mathcal{I}(\boldsymbol {x}))$ , where $\sin (\cdot ,\cdot)$ denotes the cosine similarity and $k\in [1,K]$ . The predicted probability $p_k^C (x)$ in the close-set setting can be expressed as
+
+$$
+p _ {k} ^ {C} (\boldsymbol {x}) = \frac {\exp \left(\operatorname {s i m} \left(\mathcal {T} \left(\boldsymbol {t} _ {\boldsymbol {k}}\right) , \mathcal {I} (\boldsymbol {x})\right) / \tau\right)}{\sum_ {j = 1} ^ {K} \exp \left(\operatorname {s i m} \left(\mathcal {T} \left(\boldsymbol {t} _ {\boldsymbol {j}}\right) , \mathcal {I} (\boldsymbol {x})\right) / \tau\right)}, \tag {1}
+$$
+
+where $\tau$ is the temperature parameter. To avoid manual prompt tuning, CoOp [54] introduces a learnable context prompt by modeling context words with continuous vectors, the learnable prompt could be $t = [\mathrm{V}]_1[\mathrm{V}]_2\ldots [\mathrm{V}]_L[\mathrm{CLASS}]$ , where each $[\mathrm{V}]_l$ ( $l \in \{1,\dots,L\}$ ) is a vector with the same dimension as word embeddings and $L$ is the length of context tokens.
+
+Unknown detection in Open Set Recognition (OSR). An intuitive way to detect unknown samples is thresholding on the confidence score. Taking the maximum softmax probability (MSP) across known classes as a confidence score. The $K$ -class classifier to detect unknown samples can be extended as:
+
+$$
+\hat {y} = \left\{ \begin{array}{l l} \underset {k \in [ 1, K ]} {\arg \max } p _ {k} ^ {C} (\boldsymbol {x}), & \text {i f} \underset {k \in [ 1, K ]} {\max } p _ {k} ^ {C} (\boldsymbol {x}) \geq \theta , \\ \text {u n k n o w n}, & \text {o t h e r w i s e}, \end{array} \right. \tag {2}
+$$
+
+where $\theta$ is the preset threshold.
+
+# 3.2. Overview of Unknown Text Learning (UTL)
+
+In an open-set scenario, the absence of prompts for unknown classes forces the model to classify all test samples into one of the known categories with high confidence. To address this issue, we propose a novel Unknown Text Learning (UTL) method to integrate the learning of unknown text with context optimization, aiming to extend the principle of prompt learning to the open-set setting. The overview of our proposed UTL is shown in Fig. 2. UTL involves a universal unknown words optimization $(\mathrm{U}^2\mathrm{WO})$ and an unknown label smoothing (ULS). Specifically, our UTL models each unknown text with continuous vectors $U = [u_{1}][u_{2}]\ldots [u_{M}]$ . Each $[u_m]$ ( $m\in \{1,\dots ,M\}$ ) is a vector with the same dimension as word embeddings, while $M$ is the length of unknown text tokens. $\mathrm{U}^2\mathrm{WO}$ constructs the universal unknown words space with a group of basis vectors denoted as $[Q_1,Q_2,\dots ,Q_F]$ , where $Q_{f}$ ( $f\in \{1,\dots ,F\}$ ) is a basis vector and $F$ is the number of basis vectors. Then the unknown text $U_{k}$ can be calculated by a linear combination of these basis vectors as
+
+$$
+\begin{array}{l} \boldsymbol {U} _ {k} = w ^ {1} \boldsymbol {Q} _ {1} + w ^ {2} \boldsymbol {Q} _ {2} + \dots + w ^ {F} \boldsymbol {Q} _ {F}, \tag {3} \\ k \in \{K + 1, \dots , K + N \}, \\ \end{array}
+$$
+
+where $\mathbf{W} = \{w^{1},\dots ,w^{F}\}$ indicates the weights of combination. To efficiently learn the weights $\mathbf{W}$ , unknown label smoothing (ULS) is presented to perform contrast learning between unknown text and known samples by regulating the label of all unknown classes to a small constant $\varepsilon$ . As such, our UTL with $\mathrm{U^2WO}$ and ULS can effectively learn unknown text for CLIP-based FSOR without unknown samples and the corresponding precise text descriptions.
+
+Consider the $K$ -class classification task, UTL add additional $N$ unknown text, $[U_{K + 1}, U_{K + 2}, \ldots, U_{K + N}]$ , as the textual description for the last $N$ unknown classes. Let the context prompt $\mathbf{V} = [\mathrm{V}]_1[\mathrm{V}]_2 \ldots [\mathrm{V}]_L$ , the unknown prompt incorporating unknown text and context prompt can be formulated as $\pmb{t}_k = [V, U_k]$ , where $k \in \{K + 1, \ldots, K + N\}$ . For the $K$ known classes, let known class name as $[C_1, C_2, \ldots, C_K]$ , the prompt for $k$ -th known class can be formulated as $\pmb{t}_k = [V, C_k]$ , $k \in \{1, \ldots, K\}$ . Incorporating the prompts for known classes and unknown classes, the predicted probability for the $k$ -th known class under the open setting is calculated as
+
+$$
+p _ {k} ^ {O} (\boldsymbol {x}) = \frac {\exp \left(s _ {k} ^ {C} / \tau\right)}{\sum_ {j = 1} ^ {K} \exp \left(s _ {j} ^ {C} / \tau\right) + \sum_ {j = K + 1} ^ {K + N} \exp \left(s _ {j} ^ {O} / \tau\right)}, \tag {4}
+$$
+
+where $s_k^C = \mathrm{sim}(\mathcal{T}([V,C_k]),\mathcal{I}(\pmb {x}))$ $k\in \{1,\dots ,K\}$ $s_k^O = \mathrm{sim}(\mathcal{T}([V,U_k]),\mathcal{I}(\pmb {x}))$ $k\in \{K + 1,\ldots ,K + N\}$ From Eq. (1) and Eq. (4), we can observe that our UTL introduces learning unknown text to regularize the predicted probability, enhancing the models' ability to detect un
+
+known samples by thresholding on the maximum softmax probability over known classes.
+
+# 3.3. Universal Unknown Words Optimization
+
+Intuitively, the unknown text can be learned from scratch without any constraints, as CoOp [54]. However, the text space is ample, and direct learning tends to overfit [9]. The textual descriptions for unknown classes may be uncertain, but they still belong to a subset of the word embedding space of CLIP. Inspired by the visual learning based on a universal dictionary [52], we construct space constraints to characterize the unknown text. As a subset of the word embedding space of CLIP, we construct the Universal Unknown Words Space based on the word embedding of the text description. Specifically, we first gather 1000 label names from base classes. Particularly, we use known classes and outlier text as the base classes. To ensure the quality of outlier text, we rigorously filter outlier text based on its corresponding Synset IDs, explicitly excluding names associated with unknown classes that may appear in downstream tasks. Next, the collected label names are processed through the CLIP text encoder to extract word embeddings. Finally, this study employs a simple principal component analysis (PCA) on these embedding vectors to obtain the universal basis vectors. Detailed criteria for space construction and base class selection are provided in Sup. S1.
+
+# 3.4. Unknown Label Smoothing
+
+Existing studies [1, 18] have typically framed unknowns as samples residing far from the known space or situated in the vicinity of known samples. These unknown samples tend to exhibit lower probabilities when associated with known classes. Alternatively, we can invert this perspective, considering known samples as prone to acquiring lower probabilities when related to unknown classes. Building upon this rethinking, we introduce Unknown Label Smoothing (ULS) regularization. The core idea of ULS is to constrain a random small constant $\varepsilon$ between known samples and unknown prompts for contrastive learning. Specifically, for an image of a known class where $y_{t}$ represents the ground truth class label, the final ground truth distribution $q(k)$ can be defined as follows,
+
+$$
+q (k) = \left\{ \begin{array}{l l} 1 & k = y _ {t}, k \in [ 1, K ], \\ 0 & k \neq y _ {t}, k \in [ 1, K ], \\ \varepsilon & k \in [ K + 1, K + N ]. \end{array} \right. \tag {5}
+$$
+
+Therefore, we can rewrite the cross-entropy loss as:
+
+$$
+l _ {O} = - \log \left(p _ {y _ {t}} ^ {O} (\boldsymbol {x})\right) - \varepsilon \sum_ {k = K + 1} ^ {K + N} \log \left(p _ {k} ^ {U} (k)\right), \tag {6}
+$$
+
+
+Figure 3. Unified Context (UC) vs. Dual Context (DC).
+
+
+Figure 4. Performance of UC vs. DC with various $\varepsilon$ .
+
+$$
+p _ {k} ^ {U} (\boldsymbol {x}) = \frac {\exp \left(s _ {k} ^ {O} / \tau\right)}{\sum_ {j = 1} ^ {K} \exp \left(s _ {j} ^ {C} / \tau\right) + \sum_ {j = K + 1} ^ {K + N} \exp \left(s _ {j} ^ {O} / \tau\right)}, \tag {7}
+$$
+
+where $k \in [K + 1, K + N]$ .
+
+Note that $\varepsilon$ may vary for different classes, but it is hard to decide $\varepsilon$ optimally. So, we use the same $\varepsilon$ for all cases for efficiency. From an optimization perspective, $\varepsilon > 0$ distinguishes unknown classes from other known ones, avoiding overfitting to known classes. $\varepsilon = 0$ returns back CoOp, losing the effect of regularization.
+
+# 3.5. Dual-Context Strategy
+
+UTL performs contrastive learning between the unknown text and known samples by assigning a uniform small value to the label truth of all unknown classes. Since different known-class samples share the same expected value, the context prompt learning for unknown classes lacks discriminability among different known classes, especially when the assigned value is not sufficiently small. This discrepancy conflicts with the context prompt learning of known classes, which requires higher discriminability. As shown in Fig. 4, we empirically observe opposite trends in performance between ACC, which represents the performance of known-class classification, and AUROC (Area Under the Receiver-Operator Curve), which evaluates the performance of unknown detection, with various $\varepsilon$ under a unified context prompt. Therefore, we introduce a dual-context strategy for UTL to mitigate conflicts within context learning between known and unknown classes. As illustrated in Fig. 3, the unified context version for our UTL, in which known classes and unknown classes tend to learn the unified context based on known samples, while the dual-context
+
+strategy introduces an additional context for known classes. UTL performs contrastive learning with a combined loss:
+
+$$
+l = (1 - \lambda) \cdot \left(- \log \left(p _ {y ^ {t}} ^ {C} (\boldsymbol {x})\right)\right) + \lambda \cdot l _ {O}. \tag {8}
+$$
+
+where $\lambda$ is a balancing coefficient.
+
+Inference. When performing the classification task, we use additional context prompts only for known classes and compute their predicted probability $p_k^C$ . For unknown detection, we threshold the maximum softmax probability (MSP) of $p_k^O$ as a confidence score.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Datasets. We conduct experiments on various benchmarks for FSOR. Following the previous works [3, 5, 6, 15, 24, 27, 40, 42, 47, 53], we construct the standard benchmarks following the traditional OSR setting including CIFAR10 (C10) [16], CIFAR10 + 10 (C10 + 10) [16], CIFAR10 + 50 (C10 + 50) [16], CIFAR100 (C100) [16], TinyImageNet (TINY) [17], TinyImageNet-Hard (TINY-H) [17]. Then, we construct two benchmarks with the two widely used datasets in FSOR involved in MiniImageNet (MiniIN) [41] and TieredImageNet (TieredIN) [34]. Finally, we employ the more challenging large-scale benchmark datasets, such as ImageNet-200 (IN-200) [43], iNaturalist (iNa) [39], Places [23], ImageNet-Easy (IN-Easy) [40], ImageNet-Hard (IN-Hard) [40], ImageNet-LT (IN-LT) [24]. Details of datasets and splits are presented in Sup. S2.
+
+Evaluation Metrics. AUROC (Area Under the Receiver-Operator Curve) and ACC are used for the evaluation. We also reported the OSCR (Open Set Classification Rate) [8] results. All results on the six traditional benchmarks are reported over five random splits on average.
+
+Implementation Details. In our experiments, we employ the available vision backbones in CLIP, including RN50 and ViT-B/16. The "[CLASS]" is placed at the end of the prompts. The length of the unknown text $(M)$ is set to 30, and the number of context tokens $(P)$ is set to 16. The number of basis vectors $(F)$ is set to 100. $\lambda$ is set to 0.9. The $\varepsilon$ is set to 0.1 for most benchmarks, except the IN-Hard and IN-LT, where it is set to 0.001. Similarly, the number of unknown text $N$ is set to 5 for most benchmarks, with the same exceptions (IN-Hard(30) and IN-LT(60)). The weights matrix $W$ is initialized with random values drawn from a zero-mean Gaussian distribution with a standard deviation of 0.02. We employ the SGD optimizer with an initial learning rate of 0.002, decayed according to the cosine annealing rule, following the default setup in CoOp. The maximum number of epochs is set to 50, and the batch size is set to 32. All experiments are conducted on
+
+Table 1. Comparison (%) of our UTL with different methods on various benchmarks in terms of open-set performance (AUROC). The best and second-best results are highlighted in bold and underline, respectively.
+
+| Methods(ViT-B/16) | C10 | C10+10 | C10+50 | C100 | TINY | TINY-H | Average |
| Training-free |
| CLIP [32] | 92.51±3.37 | 92.42±2.73 | 93.14±1.66 | 81.94±3.26 | 85.20±1.58 | 81.17±1.93 | 87.73 |
| CLIP-PE [32] | 93.43±3.43 | 94.77±2.45 | 94.83±1.56 | 81.82±3.29 | 86.07±1.42 | 81.90±1.55 | 88.80 |
| LMC [31] | 96.60±0.30 | 98.90±0.70 | 98.50±0.40 | - | 86.70±1.40 | - | - |
| Few-shot close-set methods |
| CoOp (16-shot setting) [54] | 91.66±2.43 | 97.07±0.91 | 94.97±1.64 | 80.20±3.14 | 85.88±2.44 | 82.28±1.42 | 88.68 |
| CoCoOp (16-shot setting) [13] | 94.08±1.70 | 96.13±2.30 | 94.77±2.30 | 80.46±3.66 | 86.93±1.41 | 82.83±1.40 | 89.20 |
| Few-shot OOD methods |
| ID-like (16-shot setting) [1] | 90.56±2.89 | 91.51±2.80 | 90.73±3.02 | 71.58±4.76 | 47.88±1.10 | 49.85±1.31 | 73.69 |
| NegPrompt (16-shot setting) [18] | 83.43±2.21 | 88.13±7.75 | 84.74±9.59 | 69.51±3.35 | 83.21±2.01 | 77.53±0.94 | 81.09 |
| Few-shot OSR methods |
| M-Tuning (16-shot setting) [19] | 92.82±1.79 | 97.83±1.03 | 96.04±1.58 | 81.14±2.88 | 86.61±2.05 | 82.96±1.76 | 89.57 |
| UTL (16-shot setting) (Ours) | 97.39±0.85 | 99.33±0.55 | 97.69±1.42 | 87.82±2.48 | 90.64±0.83 | 87.17±1.39 | 93.34 |
+
+Table 2. Comparison (%) of different methods on standard FSOR benchmark datasets in terms of close-set performance (ACC). The best and second-best results are highlighted in bold and underline, respectively.
+
+| Methods(ViT-B/16) | C10 | C10+10 | C10+50 | C100 | TINY | TINY-H | Average |
| CLIP [32] | 93.02±1.08 | 94.70±0.74 | 94.70±0.74 | 82.20±4.09 | 88.30±2.59 | 80.96±3.17 | 88.98 |
| CLIP-PE [32] | 94.10±1.14 | 95.88±0.70 | 95.88±0.70 | 82.28±4.37 | 89.30±2.45 | 83.20±3.01 | 90.11 |
| CoOp (16-shot setting) [54] | 95.54±1.18 | 97.32±0.70 | 97.32±0.70 | 85.50±2.87 | 91.07±2.02 | 85.69±1.94 | 92.07 |
| CoCoOp (16-shot setting) [13] | 94.94±2.33 | 96.77±0.91 | 96.77±0.91 | 85.44±2.81 | 91.17±1.96 | 85.72±1.92 | 91.80 |
| M-Tuning (16-shot setting) [19] | 95.50±1.05 | 97.27±2.55 | 97.27±2.55 | 85.66±2.72 | 90.69±2.27 | 85.57±1.97 | 91.99 |
| UTL (16-shot setting) (Our) | 95.54±1.06 | 97.36±0.83 | 97.36±0.83 | 85.77±2.95 | 91.18±2.33 | 85.77±1.96 | 92.16 |
+
+a single NVIDIA Tesla V100 GPU. Our code is available at: https://github.com/miracle0205/UTL_FSOR.
+
+# 4.2. Comparison with SOTA Methods
+
+Compared Methods. As the limitation of the available vision backbone of CLIP-based models, we reconstruct some baselines for comparison, including CLIP [32], CLIP with Prompt Engineering (CLIP-PE) [32], LMC [31], CoOp [54] and CoCoOp [13], M-Tuning [19], ID-like [1], LoCoOp [28], NegPrompt [18]. These methods are compared under a few-shot setting. For fairness, all methods are trained using the same pre-trained model (CLIP/ViT-B/16), and we reproduce results from M-Tuning [19], ID-like [1], LoCoOp [28], NegPrompt [18]. We also compared UTL with OSR methods in all-data settings. The implementation details for all compared methods are in the Sup. S3.
+
+Results on Standard and Challenging Benchmarks. To evaluate the effectiveness of our UTL, we compared several CLIP-based methods with the backbone of ViT-B/16 on standard FSOR benchmarks under the 16-shot setting. As shown in Tab. 1, UTL achieves the best average results, outperforming CLIP and CLIP-PE by $5.61\%$ and $4.54\%$ , respectively. It also surpassed CoOp and CoCoOp by $4.66\%$
+
+and $4.14\%$ . CoOp performs similarly to CLIP, indicating that prompt learning following a closed-set assumption cannot benefit open-set performance. Compared to M-Tuning, UTL achieves a $3.77\%$ improvement, demonstrating its superiority in learning effective unknown text compared to manually selected alternatives. Additionally, UTL outperforms the ID-like by $19.65\%$ on average, demonstrating the stability of our prompt learning without unknown samples. In contrast to NegPrompt, UTL achieves an average gain of $12.25\%$ , indicating that unknown text learning is more flexible and effective than context learning in the open setting, especially on small benchmarks. For closed-set classification, Tab. 2 shows that UTL achieves the highest average accuracy among all methods in the 16-shot setting. The OSCR results are presented in Sup. S4. To further assess UTL's effectiveness, we extend our evaluation to more challenging benchmarks. As described in Tab. 3, our UTL model outperformed all CLIP-based methods in the 16-shot setting in open-set performance. Specifically, UTL improves CoOp, CoCoOp, and M-tuning by $11.11\%$ , $10.27\%$ , and $8.58\%$ on average, respectively. Notably, UTL outperforms the second-best method by $4.59\%$ , $9.5\%$ , and $10.11\%$ on iNa, IN-Hard, and IN-LT, respectively. These results indicate
+
+
+(a) AUROC of three methods with various numbers of shots on IN-Easy and IN-LT.
+
+
+(b) AUROC of three methods with various numbers of shots on IN-Hard and iNa.
+
+
+(c) ACC of three methods with various numbers of shots on ImageNet.
+Figure 5. Comparison $(\%)$ of different methods under various few-shot settings on four challenging benchmarks.
+
+Table 3. Comparison (%) of our UTL with different methods on challenging benchmarks in terms of open-set performance (AUROC). The best and second-best results are highlighted in bold and underline, respectively.
+
+| Methods(ViT-B/16) | Mini-IN | Tiered-IN | IN200 | iNa | Places | IN-Easy | IN-Hard | IN-LT | Average |
| Training-free |
| CLIP [32] | 86.82 | 82.06 | 90.77 | 63.01 | 60.99 | 73.30 | 62.21 | 76.24 | 74.42 |
| CLIP-PE [32] | 87.99 | 81.43 | 89.43 | 61.75 | 67.26 | 73.08 | 61.23 | 72.64 | 74.35 |
| Few-shot close-set methods |
| CoOp (16-shot setting) [54] | 88.07 | 79.53 | 88.79 | 64.81 | 65.14 | 72.80 | 62.19 | 72.06 | 74.17 |
| CoCoOp (16-shot setting) [13] | 88.65 | 80.27 | 90.80 | 62.85 | 65.90 | 74.03 | 63.11 | 74.51 | 75.01 |
| Few-shot OOD methods |
| LoCoOp (16-shot setting) [28] | 89.40 | 89.73 | 95.72 | 69.55 | 67.92 | 81.74 | 67.38 | 83.35 | 80.60 |
| ID-like (16-shot setting) [1] | 53.95 | 50.52 | 92.91 | 53.44 | 61.34 | 70.53 | 58.28 | 73.94 | 64.36 |
| Few-shot OSR methods (16-shot setting) |
| M-Tuning (16-shot setting) [19] | 88.29 | 79.65 | 97.27 | 64.94 | 65.11 | 73.33 | 63.53 | 81.51 | 76.70 |
| UTL (16-shot setting) (Our) | 92.28 | 92.82 | 98.22 | 74.14 | 70.91 | 82.97 | 76.88 | 93.46 | 85.28 |
+
+that UTL demonstrates more significant improvements in more challenging settings. In addition, UTL also achieves competitive ACC and OSCR performance on challenging benchmarks, which are provided in Sup. S4.
+
+Results of Different Shot Settings. To further verify the effectiveness of our UTL method, we conducted a broader evaluation of both closed-set and open-set performance across different shot settings on IN-LT, IN-Easy, IN-Hard, and iNa. The results are shown in Fig. 5. Our UTL outperforms CoOp by a significant margin in AUROC and exhibits a consistent upward trend across all settings. As illustrated in Fig. 5(a), the AUROC of UTL on IN-LT increases rapidly with the number of shots while performance on IN-Easy is relatively stable. Similarly, the AUROC of UTL on IN-Hard and iNa also improves with more shot settings, as depicted in Fig. 5(b). That indicates that our UTL benefits from having more known samples in more challenging settings. Meanwhile, Fig. 5(c) shows that the closed-set performance of UTL is similar to CoOp on various benchmarks across different shot settings. Additionally, our UTL also achieves competitive performance in all data settings, as referred to in Sup. S5. Our UTL boosts the performance
+
+in both the closed-set and open-set settings, along with various shots of training samples.
+
+# 4.3. Ablation Study
+
+In this subsection, we conduct an ablation study to evaluate the impact of the core components $\mathrm{U}^2\mathrm{WO}$ and ULS on the performance of our UTL using ViT-B/16 as the backbone.
+
+Effect of $\mathrm{U}^2\mathrm{WO}$ . To evaluate the effect of our $\mathrm{U}^2\mathrm{WO}$ , we compare it with variants: 1) Directly learning without $\mathrm{U}^2\mathrm{WO}$ (DLU): the unknown text is learned based on the vectors with the random initialization as CoOp; 2) $\mathrm{U}^2\mathrm{WO}$ with Known Basis (UKB): Base class names come from known classes; 3) $\mathrm{U}^2\mathrm{WO}$ with Open Basis (UOB): the base class name is from the Outlier text (as detailed in Sup. S1). The experiments are conducted on the IN-Easy and IN-Hard datasets. The AUROC results are compared in Tab. 4, where we can observe that UKB and UOB achieve clear improvement over DLU methods, demonstrating the importance of our $\mathrm{U}^2\mathrm{WO}$ and the effectiveness of our $\mathrm{U}^2\mathrm{WO}$ in constructing the basis. In addition, the UKB performs similarly with UOB, indicating the robustness of our $\mathrm{U}^2\mathrm{WO}$ to the base class names. Significantly, the effectiveness of the
+
+
+(a) Results vary with $\varepsilon$ on C10 and TINY.
+
+
+(b) Results vary with $\varepsilon$ on IN-Easy and IN-Hard.
+
+
+(c) Results vary with $N$ on IN-Easy and IN-hard.
+Figure 6. Ablation results $(\%)$ of our UTL with various $\varepsilon$ and $N$ .
+
+Table 4. Comparison of ${\mathrm{U}}^{2}\mathrm{{WO}}$ with its variants (AUROC).
+
+| ViT-B/16 | DLU | UKB | UOB |
| IN-Easy | 81.69 | 82.72 | 82.97 |
| IN-Hard | 75.54 | 76.88 | 76.29 |
+
+Table 5. AUROC of UTL vary with $N$ on TINY.
+
+| N | 1 | 2 | 5 | 7 | 10 | 20 |
| AUROC | 90.46 | 90.64 | 90.75 | 90.22 | 89.94 | 89.74 |
+
+known basis in UKB shows that our UTL effectively learns unknown text when provided with sufficient known class names.
+
+Effect of $\varepsilon$ on ULS. To evaluate the effect of ULS, we conducted an ablation study by varying $\varepsilon$ across different benchmarks. The selection of $\varepsilon$ was guided by the number of known classes $K$ , where a larger $K$ necessitates a smaller $\varepsilon$ to ensure sufficient discriminability of unknown text. Specifically, for C10 ( $K = 4$ ) and TINY ( $K = 20$ ), we set $\varepsilon$ with the range of [0.001, 0.5] with $N$ at 5. For IN-Easy and IN-Hard ( $K = 1000$ ), we selected $\varepsilon \in \{0.1, 0.01, 0.001, 0.0001\}$ , with $N = 5$ for IN-Easy and $N = 30$ for IN-Hard. As shown in Fig. 6(a), AUROC improves with increasing $\varepsilon$ but experiences a slight decline beyond 0.3 for C10 and 0.2 for TINY. The results for IN-Easy and IN-Hard are illustrated in Fig. 6(b), where performance peaks at $\varepsilon = 0.001$ before decreasing. Based on the AUROC results across the four datasets, we can derive 1) As the $K$ increases, the sensitivity to $\varepsilon$ rises, leading to a narrower stable range and greater performance fluctuations. 2) The optimal value decreases as $K$ increases. In our experiments, we set $\varepsilon = 0.1$ for most benchmarks and set $\varepsilon = 0.001$ for IN-Easy, IN-Hard, and IN-LT. All that indicates our ULS consistently achieves stable improvement on most benchmarks and can achieve the best performance on the more challenging benchmarks. However, on more challenging datasets, performance instability persists, which we attribute to the uniform constraint imposed by ULS, suggesting potential areas for improvement.
+
+Number of Unknown Words $N$ . To evaluate the effect of
+
+the number of unknown text $N$ , we conduct experiments by varying $N$ on TINY, IN-Easy, and IN-Hard. The AUROC results on TINY are illustrated in Tab. 5. The AUROC results have declined slightly along with the increase of $N$ on the TINY dataset. As shown in Fig. 6(c), UTL performs stably against $N$ on IN-Easy and IN-Hard. As such, UTL tends to choose a small amount of $N$ and increase the amount of $N$ with a large number of known classes. Meanwhile, UTL is insensitive to $N$ under the large-scale setting, suggesting that our method is potentially scalable to various tasks.
+
+Unified-Context vs Dual-Context. As illustrated in Fig. 4, our Dual-Context strategy can effectively handle the conflict of context optimization between the known and unknown classes, achieving stable performance. Intuitively, adding a context prompt introduces additional learnable parameters. However, we implement a unified prompt for each task, and the extra parameters amount to only about 8K. Regarding training speed, the total training times for dual-context and unified-context on TINY are 88.27 seconds and 73.67 seconds, respectively. Overall, we can conclude that the Dual Context strategy provides stable performance benefits while adding minimal computational overhead.
+
+# 5. Conclusions
+
+This paper has proposed an Unknown Text Learning (UTL) method for effective extension of vision-language models (i.e., CLIP) to the FSOR task. The core of UTL is to simultaneously learn context prompt and unknown words for CLIP with free of unknown samples and the corresponding precise text descriptions. To this end, UTL develops an effective universal unknown words optimization $(\mathrm{U}^2\mathrm{WO})$ and an efficient unknown label smoothing (ULS) to characterize and optimize the unknown text, respectively. Going beyond UTL, a decoupled prompt strategy is presented to achieve a better performance trade-off between known classification and unknown detection tasks. Extensive experiments on both traditional FSOR benchmarks and challenge datasets clearly demonstrate the effectiveness of our UTL method. We hope our proposed UTL could encourage more work on effective prompt learning for the FSOR task.
+
+# Acknowledgments
+
+This work was supported in part by the National Natural Science Foundation of China under Grant 62276186, U23B2049, 62476198, and 62376186.
+
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\ No newline at end of file
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+ "content": " constructs the universal space of unknown words with basis vectors and characterizes unknown text based on a linear combination of those basis vectors. To efficiently learn unknown text without unknown samples, ULS is presented to perform contrast learning between unknown text and known samples by regulating the label of unknown classes to a small constant, which flexibly empowers unknown text to be non-matching and confused with known visual samples. In addition, our UTL incorporates an additional context for known classes to mitigate conflicts of context optimization between known and unknown classes. UTL effectively regularizes the predicted probability by integrating learnable unknown text. Experimental results on various benchmarks show that our UTL is superior to its counterparts while achieving state-of-the-art performance."
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+ "content": " and ULS modules, our UTL can realize effective prompt learning for CLIP-based FSOR with no need for unknown samples and the corresponding specialized text descriptions. As illustrated in Fig. 1 (a), our UTL method learns context prompts and unknown text, giving UTL more flexibility than M-Tuning and CoOp, which focus only on prompt context. In addition, our UTL incorporates an additional context for known classes to mitigate conflicts of context optimization between known and unknown classes. As shown in Fig. 4, our UTL can effectively handle the context conflict, achieving stable performance. As illustrated in Fig. 1(b), our UTL effectively regularizes the predicted probability by incorporating learnable unknown text. Notably, UTL significantly reduces the confidence of unknown samples (from approximately 0.8 to 0.2) and slightly lowers known samples, substantially widening the confidence gap between known and unknown samples and improving the performance of unknown detection. The overview of our proposed UTL is illustrated in Fig. 2. To verify the effectiveness of our UTL method, we conduct experiments on various benchmarks [16, 17, 24, 27, 34, 39-41, 43]. The contributions of our work are summarized as follows:"
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| Training-free |
| CLIP [32] | 92.51±3.37 | 92.42±2.73 | 93.14±1.66 | 81.94±3.26 | 85.20±1.58 | 81.17±1.93 | 87.73 |
| CLIP-PE [32] | 93.43±3.43 | 94.77±2.45 | 94.83±1.56 | 81.82±3.29 | 86.07±1.42 | 81.90±1.55 | 88.80 |
| LMC [31] | 96.60±0.30 | 98.90±0.70 | 98.50±0.40 | - | 86.70±1.40 | - | - |
| Few-shot close-set methods |
| CoOp (16-shot setting) [54] | 91.66±2.43 | 97.07±0.91 | 94.97±1.64 | 80.20±3.14 | 85.88±2.44 | 82.28±1.42 | 88.68 |
| CoCoOp (16-shot setting) [13] | 94.08±1.70 | 96.13±2.30 | 94.77±2.30 | 80.46±3.66 | 86.93±1.41 | 82.83±1.40 | 89.20 |
| Few-shot OOD methods |
| ID-like (16-shot setting) [1] | 90.56±2.89 | 91.51±2.80 | 90.73±3.02 | 71.58±4.76 | 47.88±1.10 | 49.85±1.31 | 73.69 |
| NegPrompt (16-shot setting) [18] | 83.43±2.21 | 88.13±7.75 | 84.74±9.59 | 69.51±3.35 | 83.21±2.01 | 77.53±0.94 | 81.09 |
| Few-shot OSR methods |
| M-Tuning (16-shot setting) [19] | 92.82±1.79 | 97.83±1.03 | 96.04±1.58 | 81.14±2.88 | 86.61±2.05 | 82.96±1.76 | 89.57 |
| UTL (16-shot setting) (Ours) | 97.39±0.85 | 99.33±0.55 | 97.69±1.42 | 87.82±2.48 | 90.64±0.83 | 87.17±1.39 | 93.34 |
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| CLIP [32] | 93.02±1.08 | 94.70±0.74 | 94.70±0.74 | 82.20±4.09 | 88.30±2.59 | 80.96±3.17 | 88.98 |
| CLIP-PE [32] | 94.10±1.14 | 95.88±0.70 | 95.88±0.70 | 82.28±4.37 | 89.30±2.45 | 83.20±3.01 | 90.11 |
| CoOp (16-shot setting) [54] | 95.54±1.18 | 97.32±0.70 | 97.32±0.70 | 85.50±2.87 | 91.07±2.02 | 85.69±1.94 | 92.07 |
| CoCoOp (16-shot setting) [13] | 94.94±2.33 | 96.77±0.91 | 96.77±0.91 | 85.44±2.81 | 91.17±1.96 | 85.72±1.92 | 91.80 |
| M-Tuning (16-shot setting) [19] | 95.50±1.05 | 97.27±2.55 | 97.27±2.55 | 85.66±2.72 | 90.69±2.27 | 85.57±1.97 | 91.99 |
| UTL (16-shot setting) (Our) | 95.54±1.06 | 97.36±0.83 | 97.36±0.83 | 85.77±2.95 | 91.18±2.33 | 85.77±1.96 | 92.16 |
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+ "html": "| Methods(ViT-B/16) | Mini-IN | Tiered-IN | IN200 | iNa | Places | IN-Easy | IN-Hard | IN-LT | Average |
| Training-free |
| CLIP [32] | 86.82 | 82.06 | 90.77 | 63.01 | 60.99 | 73.30 | 62.21 | 76.24 | 74.42 |
| CLIP-PE [32] | 87.99 | 81.43 | 89.43 | 61.75 | 67.26 | 73.08 | 61.23 | 72.64 | 74.35 |
| Few-shot close-set methods |
| CoOp (16-shot setting) [54] | 88.07 | 79.53 | 88.79 | 64.81 | 65.14 | 72.80 | 62.19 | 72.06 | 74.17 |
| CoCoOp (16-shot setting) [13] | 88.65 | 80.27 | 90.80 | 62.85 | 65.90 | 74.03 | 63.11 | 74.51 | 75.01 |
| Few-shot OOD methods |
| LoCoOp (16-shot setting) [28] | 89.40 | 89.73 | 95.72 | 69.55 | 67.92 | 81.74 | 67.38 | 83.35 | 80.60 |
| ID-like (16-shot setting) [1] | 53.95 | 50.52 | 92.91 | 53.44 | 61.34 | 70.53 | 58.28 | 73.94 | 64.36 |
| Few-shot OSR methods (16-shot setting) |
| M-Tuning (16-shot setting) [19] | 88.29 | 79.65 | 97.27 | 64.94 | 65.11 | 73.33 | 63.53 | 81.51 | 76.70 |
| UTL (16-shot setting) (Our) | 92.28 | 92.82 | 98.22 | 74.14 | 70.91 | 82.97 | 76.88 | 93.46 | 85.28 |
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| AUROC | 90.46 | 90.64 | 90.75 | 90.22 | 89.94 | 89.74 |
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+ "content": "This paper has proposed an Unknown Text Learning (UTL) method for effective extension of vision-language models (i.e., CLIP) to the FSOR task. The core of UTL is to simultaneously learn context prompt and unknown words for CLIP with free of unknown samples and the corresponding precise text descriptions. To this end, UTL develops an effective universal unknown words optimization "
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+ {
+ "type": "text",
+ "text": "Unlearning the Noisy Correspondence Makes CLIP More Robust",
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+ "text": "Haochen Han1, Alex Jinpeng Wang12†, Peijun Ye1, Fangming Liu1† \n1 Peng Cheng Laboratory 2 Central South University",
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+ {
+ "type": "text",
+ "text": "Abstract",
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+ "text": "The data appetite for Vision-Language Models (VLMs) has continuously scaled up from the early millions to billions today, which faces an untenable trade-off with data quality and inevitably introduces Noisy Correspondence (NC) samples. Undoubtedly, such semantically unrelated data significantly impairs the performance of VLMs. Previous efforts mainly address this challenge by estimating refined alignment for more precise guidance. However, such resource-intensive pipelines that train VLMs from scratch struggle to meet realistic data demands. In this paper, we present a brand new perspective that seeks to directly eliminate the harmful effects of NC in pre-trained VLMs. Specifically, we propose NCU, a Noisy Correspondence Unlearning fine-tuning framework that efficiently enhances VLMs' robustness by forgetting learned noisy knowledge. The key to NCU is learning the hardest negative information, which can provide explicit unlearning direction for both false positives and false negatives. Such twin goals unlearning process can be formalized into one unified optimal transport objective for fast fine-tuning. We validate our approach with the prevailing CLIP model over various downstream tasks. Remarkably, NCU surpasses the robust pre-trained method on zero-shot transfer while with lower computational overhead. The code is available at https://github.com/hhc1997/NCU.",
+ "bbox": [
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+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
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+ "type": "text",
+ "text": "The pursuit of general intelligence has driven progress in multimodal learning, which seeks to integrate and understand multiple sensory modalities like humans. Large-scale vision-language training, exemplified by CLIP [37], is seen as a key milestone in multimodal learning due to its remarkable transfer capabilities in real-world applications, such as image-text retrieval [13, 22, 34] and robotics control [41].",
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+ {
+ "type": "text",
+ "text": "However, much of their success can be attributed to scaling laws enabled by massive training data. As every coin has two sides, the insatiable demand for data forces a",
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+ "img_path": "images/afd3298f3cb7c792dd569209496c2d0eb1a1c07bf52bbebbe9ca5dfa94054ef7.jpg",
+ "image_caption": [
+ "$\\Delta$ Image",
+ "$\\bigcirc$ Text"
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+ "image_caption": [
+ "#",
+ "Hardest Negative Text",
+ "Figure 1. Illustration on the core concept of NCU. The twin goals unlearning process is guided by the learned hardest negative information. For the FP, $t_i^{Neg}$ directly pulls $v_i$ away from the mismatched $t_i$ . While for the FN, $t_i^{Neg}$ acts as a distance upper bound to facilitate modeling many-to-many relations."
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+ "type": "text",
+ "text": "difficult trade-off between quantity and quality, which inevitably introduces noisy correspondence into the training set. Taking the CC3M dataset [39] as an example, despite being filtered from 500 million images, it still contains at least $3\\%$ [20] unrelated image-text pairs, i.e., false positive. To make matters worse, training on massive data necessitates larger batch sizes (32K used in CLIP), which increases the likelihood of unpaired samples sharing semantic similarities, i.e., false negative. Undoubtedly, such two-aspects noisy correspondence can significantly impair the performance of vision-language models.",
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+ "type": "text",
+ "text": "To endow robustness against NC, one natural direction is to revise the pre-training paradigm [1, 3, 11, 12, 21] that supervises VLMs with refined alignment. However, existing methods require training from scratch and may rely on guidance from external large models [3, 11]. Such resource-intensive pipelines obviously struggle to face the realistic demand, especially with today's billion-scale datasets [38]. Hence, it is necessary to address the NC problem in vision-language training with a cost-effective method.",
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+ "type": "text",
+ "text": "In this paper, we think outside the box of robust pretraining and pose an important question: Can we directly",
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+ "type": "header",
+ "text": "CVF",
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+ },
+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "type": "page_footnote",
+ "text": "† Co-corresponding authors.",
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+ "type": "page_number",
+ "text": "4518",
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+ "text": "To answer this question, we resort to machine unlearning [2] and present NCU, a Noisy Correspondence Unlearning fine-tuning framework that improves the robustness of CLIP by erasing learned noisy knowledge. Machine unlearning is a reversed learning process that aims to delete the influence of specific training samples from trained models. Despite its promise in widespread tasks [7, 9], unlearning the NC in VLMs remains unexplored due to a key challenge: the ambiguous forgetting direction would corrupt the learned semantic structure in the feature space. To address this, we propose to learn the hardest negative information that can provide explicit unlearning direction. As illustrated in Fig. 1, on the one hand, the negative information would directly serve as reliable supervision for forgetting false positives. On the other hand, it would facilitate the modeling of many-to-many relationships among unpaired data for forgetting false negatives. Then, we show that such twin goals unlearning process can be formalized as one unified optimal transport problem, which efficiently fine-tunes CLIP to resist both FP and FN.",
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+ {
+ "type": "text",
+ "text": "Our main contributions are highlighted below:",
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+ "list_items": [
+ "- To the best of our knowledge, this work could be the first study to eliminate the harmful effects of noisy correspondence from pre-trained CLIP.",
+ "- We propose the NCU framework, which efficiently unlearns FP and FN with explicit direction derived from the hardest negative information.",
+ "- We demonstrate that NCU achieves significant improvements over CLIP on several downstream tasks and surpasses the previous robust pre-training method with lower computational overhead."
+ ],
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+ "type": "text",
+ "text": "2. Related Work",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "Noisy Correspondence Learning. Noisy correspondence refers to the alignment error presented in multimodal data. The false positive is a typical NC problem, where irrelevant multimodal pairs are wrongly treated as matched. To alleviate this, several techniques have been developed in various multimodal applications, including cross-modal retrieval [16, 18, 20, 36], video temporal learning [17, 30], multimodal person re-identification [35, 47], question answering [23], and image captioning [10, 24]. In more complex scenarios, e.g., vision-language pre-training [19, 21], models also suffer from false negatives caused by the training paradigm [12], where similar unpaired samples are forced to be distant. Considering the computational burden of large VLMs, this work presents a low-carbon solution to directly improve the robustness of pre-trained VLMs.",
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "Contrastive Vision Language Models. Contrastive vision language models (VLMs) [8, 13, 14, 33, 44, 48] aim to learn visual representations by the corresponding textual",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "supervision, which have attracted significant attention due to their simplicity and powerful representation capability. Pioneering works CLIP [37] and ALIGN [22] have shown great success via learning from massive image-text pairs. However, such web-crawled data are noisy [38, 42] and inevitably harm the efficacy of existing VLMs. To tackle this issue, a series of works attempted to train the VLM with refined soft image-text alignments by label smoothing [12], knowledge distillation [1], fine-grained intra-modal guidance [11], text rewriting [3], or positive-negative contrastive loss [21]. Besides, OT-based methods[40, 46] have also emerged as they naturally model such matching problems. Despite the success, previous works focus on training robust VLMs from scratch, which overlooks readily available pre-trained models and incurs unnecessary computational costs. To this end, this paper pioneers an efficient approach to enhance model robustness by unlearning noisy information from pre-trained models.",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "Machine Unlearning. Recent advances in MU mainly focus on practical approximate unlearning, which seeks to mimic the behavior of a model re-trained from scratch. Driven by privacy concerns, existing MU works [7, 9, 32] in computer vision focus on image classification that attempts to forget specific classes. In parallel, MU has also become a popular topic in large language models due to its capability to eliminate harmful responses [31, 50]. However, multimodal forgetting remains under-explored in the literature. Pioneering works [26, 27] studied data-free class removal for CLIP's downstream image classification. To date, none of the existing MU methods has explored the unlearning of noisy concepts from VLMs.",
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+ "type": "text",
+ "text": "3. Preliminaries",
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+ "type": "text",
+ "text": "3.1. Contrastive Language-Image Pre-training",
+ "text_level": 1,
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+ "text": "CLIP is a vision-language model trained on millions of web-harvested image-text pairs. We consider a batch of $N$ image-text pairs $\\{v_{i},t_{i}\\}_{i = 1}^{N}$ sampled from a cross-modal dataset $\\mathbb{D}$ , where $v_{i}$ and $t_i$ represent the raw image and corresponding text, respectively. The goal of CLIP is to train two modality-specific encoders that bring matched pairs closer while pushing unmatched ones apart. Specifically, image embedding $\\pmb {v}_i\\in \\mathbb{R}^d$ and text embedding $t_i\\in \\mathbb{R}^d$ are obtained by passing $v_{i}$ and $t_i$ through the image encoder $f_{v}$ and text encoder $f_{t}$ , respectively, where $d$ is the embedding dimension. The encoded $l_{2}$ normalized embeddings are then aligned in the feature space by minimizing the contrastive objective, i.e., InfoNCE loss:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {v \\rightarrow t} ^ {C L} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\log \\frac {\\exp \\left(\\langle \\boldsymbol {v} _ {i} , \\boldsymbol {t} _ {i} \\rangle / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\langle \\boldsymbol {v} _ {i} , \\boldsymbol {t} _ {j} \\rangle / \\tau\\right)}, \\tag {1}\n$$\n",
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+ {
+ "type": "page_number",
+ "text": "4519",
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+ },
+ {
+ "type": "text",
+ "text": "where $\\langle \\cdot \\rangle$ represents the inner product and $\\tau$ is a trainable temperature parameter. As InfoNCE loss is symmetric, we can define $\\mathcal{L}_{t\\to v}^{CL}$ similarly. The complete CLIP training objective is formulated as: $\\mathcal{L}_{CLIP} = \\mathcal{L}_{v\\rightarrow t}^{CL} + \\mathcal{L}_{t\\rightarrow v}^{CL}$ .",
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "Despite its promising performance, the standard contrastive learning can suffer from the noisy correspondence problem in two aspects. First, the web-collected pairs inevitably contain an unknown portion of mismatched data, i.e., false positives. Second, hard target alignment neglects the potential semantic similarity among unpaired samples, i.e., false negatives, especially under large batch settings.",
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+ "type": "text",
+ "text": "3.2. Machine Unlearning",
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "Given a CLIP model (also named reference model) $\\{f_v, f_t\\}$ that is already trained on a cross-modal dataset $\\mathbb{D}$ , machine unlearning aims to fine-tune the model to forget a specific subset $\\mathbb{D}_{FG} \\subseteq \\mathbb{D}$ while maintaining effectiveness on the retained set $\\mathbb{D}_{RT} = \\mathbb{D} \\setminus \\mathbb{D}_{FG}$ . Ideally, the model should behave as if it were trained without any sample from $\\mathbb{D}_{FG}$ . In principle, re-training the model from scratch on $\\mathbb{D}_{RT}$ would serve as the gold standard. However, since CLIP is trained on massive-scale data, it is unrealistic to obtain a forget set that includes all noisy information, especially when some data are not publicly accessible. Therefore, we focus on an approximate unlearning approach in which $\\mathbb{D} = \\mathbb{D}_{FG} \\cup \\mathbb{D}_{RT}$ does not need to contain all training pairs, making the unlearning process more practical for real-world scenarios.",
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+ {
+ "type": "text",
+ "text": "The most straightforward method to unlearn is gradient ascent or its variants, which optimizes the negative prediction loss over the forget set. Another typical approach is performing forget loss that encourages the model to relearn the modified form of undesired data. For example, we can update CLIP by minimizing InfoNCE loss in pair $\\{v_i,\\tilde{t}_i\\} \\sim \\mathbb{D}_{FG}$ to forget the relation between $v_{i}$ and $t_i$ where $\\tilde{t}_i\\neq t_i$ could be random or hand-crafted text to replace the original. Based on these, existing MU methods have shown promising progress in class forgetting and LLM privacy protection. However, applying these strategies to CLIP unlearning poses a key challenge: the ambiguous forgetting direction would corrupt the learned semantic structure in the feature space. In other words, the model forgets the undesired data by learning other meaningless patterns.",
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+ "type": "text",
+ "text": "4. Methodology",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "To tackle the above issues, we introduce the Noisy Correspondence Unlearning (NCU) framework. In the following, we first introduce the division of forget and retained sets in Sec 4.1. Subsequently, we elaborate on learning the hardest negative information in Sec 4.2 and explain how to formalize the twin goals unlearning process into an optimal transport object for efficiently fine-tuning in Sec 2. The overall training pseudo-code is shown in Supplementary A.",
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+ {
+ "type": "text",
+ "text": "4.1. Identifying the Forget Set",
+ "text_level": 1,
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "Unlike standard MU tasks with a predefined forget set, we need to manually identify mismatched samples from CLIP's training data to construct it. As pre-trained CLIP has shown strong representation capability, we propose using the basic similarity score to obtain $\\mathbb{D}_{FG}$ and $\\mathbb{D}_{RT}$ , i.e.,",
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+ "page_idx": 2
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\omega_ {i} = \\frac {1}{2} \\left[ \\frac {\\exp \\left(\\left\\langle \\boldsymbol {v} _ {i} , \\boldsymbol {t} _ {i} \\right\\rangle / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\left\\langle \\boldsymbol {v} _ {i} , \\boldsymbol {t} _ {j} \\right\\rangle / \\tau\\right)} + \\frac {\\exp \\left(\\left\\langle \\boldsymbol {t} _ {i} , \\boldsymbol {v} _ {i} \\right\\rangle / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\left\\langle \\boldsymbol {t} _ {i} , \\boldsymbol {v} _ {j} \\right\\rangle / \\tau\\right)} \\right]. \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "By comparing $(v_{i},t_{i})$ with other cross-modal samples in the batch, $\\omega_{i}$ serves as a clean confidence that measures the extent of semantic match. Then, we select pairs with the lowest $P\\%$ of $\\omega_{i}$ within the batch as false positives to construct the forget set $\\mathbb{D}_{FG}$ , while treating the remaining in-batch pairs as the retained set $\\mathbb{D}_{RT}$ .",
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+ "type": "text",
+ "text": "Note that $\\mathbb{D}_{FG}$ and $\\mathbb{D}_{RT}$ are dynamically selected at each batch, which enjoys two merits: 1) CLIP could be efficiently updated with one intra-batch optimization; 2) The forget-retain ratio could be flexibly adjusted through the predefined parameter $P$ .",
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+ "text": "4.2. Learning Hardest Negative Semantics",
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+ "type": "text",
+ "text": "To guide CLIP with an explicit unlearning direction, we aim to learn the hardest negative semantics as supervision. Intuitionally, for an irrelevant pair $(v_{i},t_{i})$ that misleads the model with $v_{i}$ and $t_i$ are matched', we encourage the model to forget this information by relearning that $v_{i}$ and $t_i$ are not matched'. From a data utilization viewpoint, this paradigm is similar to negative learning[25] that supervises the model with complementary information [18], i.e., pushing the candidate away from other unpaired samples. Differently, our method seeks the hardest negative information to avoid uncertain optimization directions.",
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+ "text": "To achieve this, we incorporate a set of learnable vectors to represent the textual negative semantics inspired by prompt learning [51]. Specifically, for any training pair $(v_{i},t_{i})$ , the token features of $t_i$ are combined with $m$ shared prompt vectors to present the corresponding negative semantics $t_i^{Neg}$ in the feature space. While such prompt-driven semantic negation of CLIP has demonstrated success in out-of-distribution detection [29, 43], existing methods are confined to closed-set downstream tasks with limited category concepts. In contrast, our challenge lies in extending the semantic opposite operation into the open-set knowledge that CLIP pre-trained.",
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+ "text": "Intuitively, the hardest negative satisfies two constraints in the feature space: 1) $t_i^{Neg}$ needs to maximize its distance from $v_i$ and $t_i$ ; 2) $t_i^{Neg}$ should maintain certain similarity to those unpaired images, as it is not a wrong description [43] despite being semantically irrelevant to $v_j$ . Furthermore, we only use $\\mathbb{D}_{RT}$ to learn the prompt tokens to avoid overfitting caused by noisy correspondence. For notation simplicity,",
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+ "(a). Maximize $L_{2}$ -distance"
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+ "image_caption": [
+ "(b). Similarity Bound",
+ "Figure 2. Illustration of the optimization objective to learn the hardest negative semantics. (a) Previous attempts that directly maximize the $L_{2}$ distance prevent $\\pmb{t}_{i}^{Neg}$ from providing certain guidance for unpaired images, e.g., $\\pmb{v}_{k}$ . (b) We bound the similarity with margins for a more relaxed semantic separation, but it may lead to uncertain targets, e.g., $\\pmb{t}_{i}^{Neg}$ and $\\pmb{t}_{i}^{Neg'}$ . (c) We further preserve relation structures for precise objectives. The intuition is that the opposite text should also maintain semantic relationships, e.g., $\\langle \\pmb{t}_i,\\pmb{t}_j^{Neg}\\rangle \\approx \\langle \\pmb{t}_j,\\pmb{t}_i^{Neg}\\rangle$"
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+ "(c). Relation Opposite"
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+ "text": "we denote $\\tilde{N}$ as the size of $\\mathbb{D}_{RT}$ within each batch. Based on the above insights, we propose the following intra-modal and cross-modal training objectives.",
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+ "text": "Text Relation Opposite. It encourages semantic separation between the embeddings of negative text and its original. Most previous works [29, 43] typically reduce the per-instance similarity gap among textual pairs, e.g., $\\| t_i - t_i^{Neg}\\| _2\\to 2$ [43] to directly maximize its $L_{2}$ distance. However, such rigid constraint incurs a crucial limitation in the open-set semantic space—enforcing maximal distance pushes $t_i^{Neg}$ away from unpaired images (Fig. 2(a)), which is contrary to our objective. To this end, we propose a relaxed similarity bound to constrain the semantic separation:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} ^ {s e p} = \\frac {1}{\\tilde {N}} \\sum_ {i = 1} ^ {\\tilde {N}} \\left(\\left[ \\alpha - \\langle \\boldsymbol {t} _ {i}, \\boldsymbol {t} _ {i} ^ {N e g} \\rangle \\right] _ {+} + \\left[ \\langle \\boldsymbol {t} _ {i}, \\boldsymbol {t} _ {i} ^ {N e g} \\rangle - \\beta \\right] _ {+}\\right), \\tag {3}\n$$\n",
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+ "type": "text",
+ "text": "where $\\alpha < 0$ and $\\beta < 0$ are the margin parameters to locate $\\langle t_i, t_i^{Neg} \\rangle \\in [\\alpha, \\beta]$ , and $[x]_+ = \\max(x, 0)$ is the hinge function. As illustrated in Fig. 2(b), although minimizing Eq.(3) enables $t_i^{Neg}$ to be distant from $t_i$ while remaining relatively similar to unpaired images, the broad range of variations makes training convergence difficult. To address this issue, we propose to perform semantic opposite at the relation level instead of the instance level, which is achieved by preserving the geometrical structures among all negative and original text within the batch:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} ^ {r e l} = \\frac {1}{\\tilde {N}} \\sum_ {i = 1} ^ {\\tilde {N}} \\sum_ {j = 1} ^ {\\tilde {N}} \\left(\\left\\langle \\boldsymbol {t} _ {i}, \\boldsymbol {t} _ {j} ^ {N e g} \\right\\rangle - \\left\\langle \\boldsymbol {t} _ {j}, \\boldsymbol {t} _ {i} ^ {N e g} \\right\\rangle\\right) ^ {2}. \\tag {4}\n$$\n",
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+ "type": "text",
+ "text": "As shown in Fig. 2(c), regularizing the negative-original relation consistency can guide $t_i^{Neg}$ toward a precise location in the feature space.",
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+ "type": "text",
+ "text": "Image-text Matching Opposite. It aims to model the alignment between the embeddings of negative text and images. As discussed, $t_i^{Neg}$ provides positive supervision to unpaired images while separating from its paired image, which presents opposite matching patterns to the normal contrastive objective. To achieve this, we take inspiration from Sigmoid loss [49] that efficiently supports such multi-positive alignment. Specifically, it guides per cross-modal pair independently by the binary matching target:",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\mathcal {L} ^ {i t m} = \\frac {1}{\\tilde {N}} \\sum_ {i = 1} ^ {\\tilde {N}} \\sum_ {j = 1} ^ {\\tilde {N}} \\left(\\log \\frac {1}{1 + \\exp \\left(m _ {i j} \\left(- \\langle \\boldsymbol {t} _ {i} , \\boldsymbol {v} _ {j} \\rangle / \\tau\\right)\\right)} \\right. \\tag {5} \\\\ + \\log \\frac {1}{1 + \\exp (- m _ {i j} (- \\langle \\pmb {t} _ {i} ^ {N e g} , \\pmb {v} _ {j} \\rangle / \\tau))}, \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "where $m_{ij}$ equals 1 for $i = j$ and $-1$ for $i\\neq j$ . In Eq.(5), the first part follows the standard one-to-one matching to retain the original CLIP knowledge, while the second part utilizes the opposite binary target, i.e., $-m_{ij}$ , to bring $t_i^{Neg}$ closer to multiple images.",
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+ "type": "text",
+ "text": "With the visual encoder frozen, the overall loss for learning the hardest negative semantics is balanced by a scaling factor $\\lambda$ and given by:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} ^ {H N} = \\lambda \\left(\\mathcal {L} ^ {s e p} + \\mathcal {L} ^ {r e l}\\right) + \\mathcal {L} ^ {i t m}. \\tag {6}\n$$\n",
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+ "type": "text",
+ "text": "4.3. Hardest-Negative Guided Noise Unlearning",
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+ "text": "The hardest negative semantics serve dual purposes in erasing the learned noisy correspondence: 1) guide CLIP to unlearn the false positive pair $(v_{i},t_{i})$ by matching $v_{i}$ with $t_i^{Neg}$ . 2) While for the well-matched pair $(v_{i},t_{i})$ , $t_i^{Neg}$ assists in inferring the soft alignment among unpaired data to unlearn the false negative pattern. To efficiently fine-tune CLIP, we formalize such twin goals unlearning process into one unified Optimal Transport problem.",
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+ "type": "text",
+ "text": "Optimal Transport. OT seeks to establish a flexible alignment between images and captions by computing a",
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+ "text": "4521",
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+ "Figure 3. Overview of the Noisy Correspondence Unlearning process. With the learned negative prompt frozen, we formulate an optimal transport problem guided by the hardest negative and then use the solved transport plan to robustly fine-tune the model $f_{t}$ and $f_{v}$ ."
+ ],
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+ "text": "minimal-cost transport plan, where the cost refers to the expense of transporting mass from source to target distribution and is generally set to a distance measure [15]. Let $\\mathbf{C} \\in \\mathbb{R}_{+}^{N \\times N}$ denotes the cost matrix for the mini-batch, where $[\\mathbf{C}]_{i,j} = 1 - \\langle \\mathbf{v}_i, \\mathbf{t}_j \\rangle$ is the cosine distance of $v_i$ and $t_j$ . $\\Gamma \\in \\mathbb{R}_{+}^{N \\times N}$ denotes the corresponding transport plan that $[\\Gamma]_{i,j}$ represents the alignment probability between $v_i$ and $t_j$ . Formally, the objective of OT is defined as follows:",
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+ "type": "equation",
+ "text": "\n$$\n\\min _ {\\Gamma \\in \\Pi (\\pmb {\\mu}, \\pmb {\\nu})} \\langle \\Gamma , \\pmb {C} \\rangle - \\epsilon H (\\Gamma)\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathrm {s . t .} \\Pi (\\boldsymbol {\\mu}, \\boldsymbol {\\nu}) = \\left\\{\\boldsymbol {\\Gamma} \\in \\mathbb {R} _ {+} ^ {N \\times N} \\mid \\boldsymbol {\\Gamma} \\mathbb {1} _ {N} = \\boldsymbol {\\mu}, \\boldsymbol {\\Gamma} ^ {\\top} \\mathbb {1} _ {N} = \\boldsymbol {\\nu} \\right\\},\n$$\n",
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+ "type": "text",
+ "text": "where $\\mathbb{1}_N$ denotes a $N$ -dimensional all-one vector, $\\mu, \\nu \\in \\mathbb{R}^N$ are probability measures representing the relative importance of each image and caption. Without prior knowledge, $\\mu = \\frac{1}{N}\\mathbb{1}_N$ and $\\nu = \\frac{1}{N}\\mathbb{1}_N$ are considered to be uniformly distributed since each pair is sampled independently. $H(\\Gamma)$ is an additional entropy regularizer controlled by the smooth parameter $\\epsilon$ , which enables the OT objective to be solved by the rapid Sinkhorn-Knopp algorithm [6].",
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+ "type": "text",
+ "text": "Boosting OT via Hardest Negatives. To endow the transport plan with dual forgetting purposes, we reformulate Eq.(7) by imposing guidance from the hardest negative information. Specifically, for each image $v_{i}$ , we extend its transport target from $\\{t_i\\}_{i = 1}^N$ to include its paired negative text $t_i^{Neg}$ . As shown in Fig. 3, the negative text composes a new alignable column for the transport objective, which append the cost matrix $C$ to $\\bar{C} \\in \\mathbb{R}_+^{N\\times (N + 1)}$ , i.e.,",
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+ {
+ "type": "equation",
+ "text": "\n$$\n[ \\bar {\\boldsymbol {C}} ] _ {i, N + 1} = 1 - \\langle \\pmb {v} _ {i}, \\pmb {t} _ {i} ^ {N e g} \\rangle , [ \\bar {\\boldsymbol {C}} ] _ {i, j} = [ \\pmb {C} ] _ {i, j}, \\forall i, j \\in [ 1, N ].\n$$\n",
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+ "type": "text",
+ "text": "For the two parts $\\mathbb{D}_{FG}$ and $\\mathbb{D}_{RT}$ within each batch, the hardest negative should impose different guidance for distinct unlearning goals. To this end, we propose a maskbase constraint to the corresponding transport plan $\\bar{\\Gamma}$ that regulates the effect of $t_i^{Neg}$ . Specifically, the mask matrix",
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+ "type": "text",
+ "text": "$M\\in \\mathbb{R}_{+}^{N\\times (N + 1)}$ satisfies that",
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+ "type": "equation",
+ "text": "\n$$\n[ M ] _ {i, j} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} (v _ {i}, t _ {i}) \\in \\mathbb {D} _ {F G} \\text {a n d} j = i, \\\\ 0, & \\text {i f} (v _ {i}, t _ {i}) \\in \\mathbb {D} _ {R T} \\text {a n d} j = N + 1, \\\\ 1, & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {8}\n$$\n",
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+ "type": "text",
+ "text": "For the toy example illustrated in Fig. 3, if the pair is considered to be mismatched, the transport mass between $v_{i}$ and $t_{i}$ should be constrained to zero. Conversely, for the well-matched pair, $t_{i}^{Neg}$ acts as a lower limit where the transport mass between $v_{i}$ and $t_{j}$ should be higher than it. Following the solver from [15], we model the mask constraint as the Hadamard product form that $\\hat{\\Gamma} = M \\odot \\bar{\\Gamma}$ , and the optimal alignment is formulated as (detailed Sinkhorn solution is presented in Supplementary B):",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\hat {\\Gamma} ^ {*} = \\underset {\\hat {\\Gamma} \\in \\Pi (\\mu , \\bar {\\nu})} {\\arg \\min } \\left\\langle \\hat {\\Gamma}, \\bar {C} \\right\\rangle - \\epsilon H (\\hat {\\Gamma}), \\tag {9}\n$$\n",
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+ "type": "text",
+ "text": "where $\\bar{\\nu} = \\frac{1}{N + 1}\\mathbb{1}_{N + 1}$ to satisfy the additional column.",
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+ "type": "text",
+ "text": "The Unlearning Objective. Although $\\hat{\\Gamma}^*$ provides the more refined alignment, we suggest further incorporating an identity-like matrix $\\pmb{I}$ for two merits. First, diagonal elements are set as 1 for true positives to retain the initial alignment. Second, $[I]_{i,N + 1} = 1$ to enhance the unlearning for the possible false positive $(v_{i},t_{i})\\in \\mathbb{D}_{FG}$ . Thus, the overall alignment balanced by the factor $\\gamma$ is defined as:",
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+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {T} = \\gamma \\hat {\\boldsymbol {\\Gamma}} ^ {*} + (1 - \\gamma) \\boldsymbol {I}. \\tag {10}\n$$\n",
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+ "type": "text",
+ "text": "To fine-tune CLIP with this soft alignment, we use the KL divergence to optimize the matching distribution. Formally, we denote the batched similarity matrix as $\\pmb{P} \\in \\mathbb{R}^{N \\times (N + 1)}$ where $P_{i} = [\\langle v_{i}, t_{1} \\rangle, \\dots, \\langle v_{i}, t_{N} \\rangle, \\langle v_{i}, t_{i}^{Neg} \\rangle]^{\\top}$ . We obtain $P_{i}^{v2t}$ and $P_{i}^{t2v}$ by applying row-wise and column-wise softmax operation to $P$ , respectively. Correspondingly, let $T_{i}^{v2t}$ and $T_{i}^{t2v}$ be the row-wise and column-wise normalized refined alignment for the $i$ -th sample, respectively. The",
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+ "text": "4522",
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+ "text": "OT-guided re-aligning is defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} ^ {o t r} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {K L} \\left(\\boldsymbol {T} _ {i} ^ {v 2 t} \\| \\boldsymbol {P} _ {i} ^ {v 2 t}\\right) + \\frac {1}{N + 1} \\sum_ {i = 1} ^ {N + 1} \\mathrm {K L} \\left(\\boldsymbol {T} _ {i} ^ {t 2 v} \\| \\boldsymbol {P} _ {i} ^ {t 2 v}\\right). \\tag {11}\n$$\n",
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+ "type": "text",
+ "text": "Moreover, we empirically observe that preserving the textual semantic separation term can make the unlearning more stable. Thus, the final unlearning objective is defined as:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} ^ {U L} = \\mathcal {L} ^ {o t r} + \\mathcal {L} ^ {s e p}. \\tag {12}\n$$\n",
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+ "type": "text",
+ "text": "5. Experiment",
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+ "type": "text",
+ "text": "In this section, we experimentally analyze the effectiveness of NCU in unlearning the NC knowledge from CLIP.",
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+ "type": "text",
+ "text": "5.1. Setup",
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+ "type": "text",
+ "text": "Datasets. Our experiments are conducted on three vision-language datasets at different scales and noise: Conceptual Captions 3M (CC3M) [39], Conceptual Captions 12M (CC12M) [4], and YFCC15M-R (provided by [14], an LLM-recaptioned subset from the YFCC100M [42]). All datasets are web-crawled and contain an unknown portion of NC pairs, e.g., CC3M is estimated to include at least $3\\%$ false positives. We evaluate NCU on ImageNet and 15 common downstream datasets for classification performance and on MSCOCO and Flickr30K for retrieval capability. Details for datasets are shown in Supplementary C.",
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+ "type": "text",
+ "text": "Unlearning Details. Following CLIP, we consider two architectures for the image encoder, i.e., ViT/B16 and ViT/B32, while the text encoder adopts the transformer architecture. We consider a CLIP pre-trained on dataset $\\mathbb{D}$ , e.g., CC3M, CC12M, or YFCC15M-R, as our reference model, then we perform the NC unlearning on $\\mathbb{D}$ or its subset to enhance CLIP's robustness. For all experiments, we allocate 2 epochs for learning negative semantics and 8 epochs for noise unlearning. All models are trained with a batch size of 2,048 on 16 NVIDIA V100 GPUs. Detailed training settings are presented in Supplementary D.",
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+ "type": "text",
+ "text": "Evaluation Protocol. We evaluate NCU's transferability with Zero-Shot (ZS) classification accuracy and Linear Probing (LP) accuracy. For ZS classification, we follow CLIP's [37] prompt templates to compute distances between class text embeddings and image features. For LP, we follow the mainstream setting [8, 37] that trains a linear classifier using L-BFGS on features extracted from the frozen image encoder. Besides, we evaluate the retrieval performance with the Recall at rank K (R@K) metric.",
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+ "type": "text",
+ "text": "5.2. Evaluation on Diverse Downstream Tasks",
+ "text_level": 1,
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+ "type": "text",
+ "text": "To verify the generalization of NCU, we compare it with CLIP on three different types of downstream tasks.",
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+ "text": "Zero-Shot Transfer. We compare the zero-shot performance of CLIP and NCU on 16 popular image classification datasets. We follow the prompt templates suggested in the CLIP paper [37] to form each class name into a natural sentence. As demonstrated in Tab. 1, our NCU approach significantly outperforms the baseline CLIP model on both ImageNet and other downstream datasets. Specifically, across all fine-tuning datasets and all model architectures, NCU gains in the range of $2.8\\% \\sim 4.1\\%$ in top-1 accuracy on ImageNet and $2.5\\% \\sim 4.0\\%$ on average over the other downstream datasets. This reveals that NCU can successfully eliminate the impact of NC on CLIP by robust fine-tuning with the same dataset.",
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+ "text": "Image-Text Retrieval. We present the zero-shot cross-modal retrieval performance on the testing set of Flickr30K (1K) and MSCOCO (5K) in Tab. 2. Our method considerably outperforms the vanilla CLIP in almost all cases. For instance, when fine-tuning CLIP (ViT-B/32) pre-trained on the CC3M dataset, our NCU method achieves a $7.7\\%$ improvement in average recall scores on Flickr30K and $4.8\\%$ improvement in average recall scores on MSCOCO. This finding indicates that NCU can remarkably enhance the alignment of images and text in the embedding space.",
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+ "type": "text",
+ "text": "Linear Probing. Tab. 3 reports the linear probing performance on 4 representative downstream datasets. Our NCU consistently surpasses CLIP in the vast majority of cases, suggesting that the visual embeddings learned by our NCU are more effective and transferable than CLIP.",
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+ "type": "text",
+ "text": "5.3. Compared to Robust Methods",
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+ "text": "In this section, we compare NCU with other robust-designed techniques against NC on zero-shot ImageNet1K classification task, i.e., gradient ascent (GA), and SoftCLIP [11]. Specifically, we evaluate GA as a standalone method, where $-\\mathcal{L}_{CLIP}$ is performed on $\\mathbb{D}_{FG}$ for handling FPs and $\\mathcal{L}_{CLIP}$ with label smoothing is performed on $\\mathbb{D}_{RT}$ for FNs. SoftCLIP is a noise-robust SOTA method that trains CLIP from scratch by additional intra-modal guided alignment, i.e., ROI features. As shown in Tab. 4, although GA is a naive unlearning strategy, it still achieves observable performance gains. Meanwhile, SoftCLIP's self-similarity modeling fails to excavate supervision from false positives, which may explain why it performs worse than GA in some cases, e.g., CC12M with ViT-B/32. By contrast, our NCU achieves solid improvements by forgetting both false positives and false negatives, outperforming SoftCLIP by $1.1\\% \\sim 2.3\\%$ without external guidance.",
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+ "type": "text",
+ "text": "5.4. Ablation Study",
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+ "text": "To investigate the effectiveness of specific components in our method, we carry out some ablation studies on Ima-",
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+ "type": "table",
+ "img_path": "images/3ac21aa4c8a1a72c2451667d83c0d61dcabf3f26ecab98554380c5db5dc09fa3.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Dataset | Model | Caltech101 | CIFAR-10 | CIFAR-100 | DTD | Aircraft | SST2 | Flowers102 | Food101 | GTSRB | OxfordPeds | RESISC45 | SUN397 | EuroSAT | StanfordCars | STL10 | Average | ImageNet1K |
| Model Architecture: ViT-B/16 |
| CC3M | CLIP | 52.3 | 55.2 | 24.1 | 10.9 | 1.0 | 50.1 | 11.9 | 11.1 | 6.9 | 12.9 | 19.5 | 25.0 | 13.5 | 0.8 | 81.7 | 25.1 | 16.0 |
| NCU | 59.1 | 54.3 | 28.8 | 12.3 | 1.1 | 50.1 | 14.1 | 14.8 | 7.4 | 16.3 | 22.8 | 32.3 | 21.7 | 1.5 | 86.3 | 28.2↑3.1 | 20.0↑4.0 |
| CC12M | CLIP | 77.0 | 66.5 | 38.3 | 21.2 | 2.5 | 47.7 | 33.4 | 51.9 | 7.3 | 64.2 | 39.0 | 44.7 | 21.2 | 25.5 | 91.4 | 42.1 | 40.6 |
| NCU | 80.9 | 79.3 | 49.1 | 23.2 | 2.7 | 48.0 | 31.7 | 52.7 | 10.1 | 66.5 | 41.9 | 52.6 | 28.6 | 29.0 | 93.2 | 46.0↑3.9 | 43.4↑2.8 |
| Model Architecture: ViT-B/32 |
| CC3M | CLIP | 47.7 | 54.2 | 18.0 | 7.6 | 1.2 | 50.1 | 9.3 | 9.1 | 6.0 | 7.4 | 16.2 | 16.0 | 15.5 | 0.8 | 77.7 | 22.5 | 11.8 |
| NCU | 53.0 | 56.7 | 25.9 | 10.4 | 1.7 | 50.1 | 10.2 | 10.5 | 6.5 | 10.5 | 19.0 | 22.2 | 16.7 | 1.4 | 80.1 | 25.0↑2.5 | 14.6↑2.8 |
| CC12M | CLIP | 76.3 | 68.2 | 35.2 | 16.1 | 2.8 | 50.1 | 29.3 | 37.6 | 6.4 | 54.1 | 30.1 | 39.2 | 22.5 | 14.8 | 90.8 | 38.2 | 33.8 |
| NCU | 80.4 | 68.5 | 41.4 | 19.3 | 2.6 | 52.8 | 28.6 | 43.4 | 7.2 | 62.4 | 35.7 | 48.3 | 31.3 | 18.1 | 92.5 | 42.2↑4.0 | 36.7↑2.9 |
| YFCC15M-R | CLIP | 53.7 | 67.0 | 34.4 | 13.1 | 1.1 | 49.3 | 22.1 | 18.6 | 11.0 | 13.5 | 20.3 | 29.3 | 23.0 | 1.7 | 83.7 | 29.5 | 17.8 |
| NCU | 58.2 | 69.5 | 37.8 | 15.3 | 1.8 | 49.9 | 29.2 | 23.7 | 11.2 | 16.1 | 23.1 | 34.0 | 23.3 | 1.8 | 86.7 | 32.1↑2.6 | 21.9↑4.1 |
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+ "img_path": "images/d5cb8446e6a2a3e7099d1fb6db2ca304530f5daf9034e074ce61c55aed95fc51.jpg",
+ "table_caption": [
+ "Table 1. Zero-shot transfer evaluation of different models."
+ ],
+ "table_footnote": [],
+ "table_body": "| Dataset | Architecture | Model | Flickr30K 1K Testing | MSCOCO 5K Testing |
| Image-to-Text | Text-to-Image | Average | Image-to-Text | Text-to-Image | Average | |
| R@1 | R@5 | R@10 | R@1 | R@5 | R@10 | R@1 | R@5 | R@10 | R@1 | R@5 | R@10 | |
| CC3M | ViT-B/16 | CLIP | 27.6 | 54.2 | 65.8 | 19.0 | 40.5 | 51.3 | 43.1 | 12.8 | 30.9 | 42.7 | 9.7 | 25.4 | 35.2 | 26.1 | |
| NCU | 32.1 | 60.7 | 71.9 | 25.2 | 49.5 | 61.0 | 50.1↑7.0 | 15.8 | 36.9 | 48.4 | 12.1 | 29.7 | 40.1 | 30.5↑4.4 | |
| ViT-B/32 | CLIP | 14.0 | 35.2 | 47.7 | 11.5 | 27.9 | 37.8 | 29.0 | 7.0 | 20.1 | 28.9 | 6.0 | 16.7 | 24.0 | 17.1 | |
| NCU | 21.3 | 44.5 | 55.7 | 15.7 | 36.3 | 46.4 | 36.7↑7.7 | 10.7 | 25.7 | 35.4 | 8.1 | 21.3 | 30.2 | 21.9↑4.8 | |
| CC12M | ViT-B/32 | CLIP | 50.3 | 77.2 | 85.9 | 37.9 | 64.8 | 74.2 | 65.1 | 26.8 | 54.0 | 65.9 | 20.0 | 42.4 | 54.2 | 43.9 | |
| NCU | 53.0 | 77.3 | 85.0 | 38.4 | 66.6 | 76.7 | 66.2↑1.1 | 28.2 | 54.7 | 66.7 | 20.0 | 42.8 | 54.3 | 44.5↑0.6 | |
| YFCC15M-R | ViT-B/32 | CLIP | 57.4 | 81.6 | 89.1 | 40.8 | 66.4 | 75.4 | 68.5 | 35.0 | 60.9 | 71.8 | 22.6 | 46.0 | 58.0 | 49.1 | |
| NCU | 58.0 | 83.2 | 89.7 | 42.5 | 69.9 | 78.8 | 70.4↑1.9 | 34.3 | 62.0 | 73.5 | 24.6 | 49.0 | 60.8 | 50.7↑1.6 | |
",
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+ "type": "table",
+ "img_path": "images/520a23d3dfe373dafd76d3dde08907497d93a9221bca8f3da771f68a24efa1d1.jpg",
+ "table_caption": [
+ "Table 2. Zero-shot cross-modal retrieval evaluation of different models."
+ ],
+ "table_footnote": [],
+ "table_body": "| Dataset | Architecture | Model | SUN397 | OxfordPeds | Food101 | ImageNet |
| CC3M | ViT-B/16 | CLIP | 54.38 | 62.20 | 54.36 | 48.13 |
| NCU | 55.60 | 62.85 | 54.74 | 49.90 |
| ViT-B/32 | CLIP | 46.96 | 52.30 | 46.96 | 40.20 |
| NCU | 48.20 | 52.82 | 46.85 | 41.49 |
| CC12M | ViT-B/16 | CLIP | 70.94 | 82.83 | 78.99 | 66.70 |
| NCU | 71.36 | 84.76 | 79.18 | 66.65 |
| ViT-B/32 | CLIP | 66.05 | 78.41 | 70.12 | 59.19 |
| NCU | 66.63 | 78.63 | 70.76 | 60.34 |
| YFCC15M-R | ViT-B/32 | CLIP | 60.46 | 61.90 | 59.09 | 51.07 |
| NCU | 60.75 | 62.85 | 60.46 | 52.29 |
",
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+ {
+ "type": "text",
+ "text": "geNet1K with models unlearned on CC3M. We first ablate the contributions of two key components of NCU, i.e., negative prompt and text relation opposite. Specifically, in the variant $\\nu_{1}$ , we replace the learnable prompt tokens by preponding some textual negative prefixes to raw captions, e.g., 'the image has no' or 'this picture lacks'. In the variant $\\nu_{2}$ , we use maximal $L_{2}$ distance loss [43] as a substitute for our text relation opposite. Besides, we validate the impact of different NC unlearning by intervening with the refined",
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+ "img_path": "images/78f4d4fb37f0e134362ae4ff4d46faf3f60a605c0c0056c54fcd46455476bd1b.jpg",
+ "table_caption": [
+ "Table 3. Linear probing comparison of different models."
+ ],
+ "table_footnote": [],
+ "table_body": "| Dataset | Model | Model Architecture | ImageNet1K ZS top-1 |
| CC3M | CLIP | ViT-B/16 | 16.0 |
| Gradient Ascent | 16.7 ↑0.7 |
| SoftCLIP | 18.9 ↑2.9 |
| NCU | 20.0 ↑4.0 |
| CC3M | CLIP | ViT-B/32 | 11.8 |
| Gradient Ascent | 12.1 ↑0.3 |
| SoftCLIP | 13.3 ↑1.5 |
| NCU | 14.6 ↑2.8 |
| CC12M | CLIP | ViT-B/16 | 40.6 |
| Gradient Ascent | 41.6 ↑1.0 |
| SoftCLIP | 42.1 ↑1.5 |
| NCU | 43.4 ↑2.8 |
| CC12M | CLIP | ViT-B/32 | 33.8 |
| Gradient Ascent | 35.1 ↑1.3 |
| SoftCLIP | 34.4 ↑0.6 |
| NCU | 36.7 ↑2.9 |
",
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+ {
+ "type": "text",
+ "text": "Table 4. Zero-shot top-1 performance on ImageNet1K.",
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+ },
+ {
+ "type": "text",
+ "text": "alignment, i.e., $\\mathcal{V}_3$ and $\\mathcal{V}_4$ . As shown in Tab. 5, we observe that: 1) Using negative textual prefixes also shows competitive results, demonstrating the generalization of our method. However, we argue that the learnable prompt is preferable, except for performance gains, operating to features makes",
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+ "text": "4524",
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+ "img_path": "images/e48d1a31d0394052e2aa940d194db7ed2f86ec4dc0b9afdfff606ebef029b7f3.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Model | ImageNet1K ZS top-1 |
| ViT-B/16 | ViT-B/32 |
| NCU | 20.0 | 14.6 |
| V1 (w/o Hardest Negative Prompts) | 19.3 ↓0.7 | 14.4 ↓0.2 |
| V2 (w/o Text Relation Opposite) | 18.8 ↓1.2 | 13.9 ↓0.7 |
| V3 (w only False Negatives Unlearning) | 17.7 ↓2.3 | 13.5 ↓1.1 |
| V4 (w only False Positives Unlearning) | 19.2 ↓0.8 | 14.3 ↓0.3 |
",
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+ },
+ {
+ "type": "text",
+ "text": "Table 5. Ablation studies on zero-shot transfer task (ImageNet1K) of models unlearned on CC3M.",
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "it possible for NCU to extend to modalities beyond text. 2) Simply maximizing the distance between negative and original text embeddings leads to suboptimal performance, which aligns with our analysis in Fig. 2. 3) Both types of NC impair CLIP's performance, among which the false positive causes a more severe impact. While NCU achieves the best performance by forgetting such noisy knowledge.",
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+ {
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+ "img_path": "images/68310a3d17ae003570f4382b36760c51e8bf521eb8ec24afef543d13ad824a9a.jpg",
+ "image_caption": [
+ "Figure 4. Effect of NCU with varying fine-tuning dataset sizes on zero-shot image classification and cross-modal retrieval."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "5.5. NC Unlearning with Partial Data",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "In this section, we conduct an interesting study to verify whether CLIP can improve robustness by only unlearning NC with a portion of the pre-trained data. To this end, given a CLIP pre-trained on CC3M as the reference model, we evaluate NCU using different data portions ranging from 0.5 million to 3 million image-text pairs. Fig. 4 plots the ZS top-1 accuracy on ImageNet1K and the average of recalls on MSCOCO 5K. Remarkably, even when unlearning on less than $20\\%$ of the original data (0.5M), NCU achieves significant performance gains while preserving overall knowledge learned in CC3M. With the accessible data increasing, NCU shows consistent improvements on both zero-shot downstream tasks. This phenomenon indicates NCU's flexibility in enhancing the robustness of models with limited data, which is valuable to handling VLMs pre-trained with partially private or proprietary data.",
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+ {
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+ "img_path": "images/7c80b87e512da062ca54ecf34ca1f00d91ae2880e3f2426c9e046649a7d85dcf.jpg",
+ "image_caption": [
+ "(a) NCU",
+ "Figure 5. Similarity scores distribution of positive and negative pairs from CLIP and NCU. Both models are based on ViT/B16 and learning from the CC3M training set."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ },
+ {
+ "type": "image",
+ "img_path": "images/0662380555a74c2e2a59559050d36ddf45ef649867a465468052cdc2120e9e90.jpg",
+ "image_caption": [
+ "(b) CLIP"
+ ],
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+ },
+ {
+ "type": "text",
+ "text": "5.6. Visualization and Analysis",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "To intuitively show the robust embedding space that is refined by our approach, we plot the distribution of normalized similarity for CLIP and NCU on the validation set of CC3M. In Fig. 5, we illustrate similarity scores for positive pairs, mean of negative pairs, and top $5\\%$ maximum of negative pairs. First, we observe that NCU produces a wider distribution of positive similarity scores, capturing more fine-grained matching degrees among positive pairs. Second, NCU improves the feature discrimination, which leads to a more significant separation between positive and negative pairs. Lastly, NCU provides more appropriate measures for hard negatives, which maintains separation from both positive and other negative pairs.",
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+ {
+ "type": "text",
+ "text": "6. Limitations and Future Works",
+ "text_level": 1,
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+ "text": "Our work still has certain limitations due to the finite computing capability, including 1) This work only uses CLIP to explore the efficacy of NCU. Further research is needed to confirm its applicability in other VLMs, such as BLIP-2 [28], and even larger VLMs like VisionLLM [45] or InternVL [5]. 2) The current experiments are mainly conducted on million-scale data, and we plan to extend it to larger-scale datasets to verify NCU's generalization.",
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+ "type": "text",
+ "text": "7. Conclusion",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "This work provides a new thinking in robust vision-language learning. Instead of re-training models from scratch, we suggest eliminating the harmful effects of noisy correspondence from pre-trained models. To this end, we propose NCU, a robust fine-tuning framework that efficiently unlearns noisy correspondence in CLIP. Our key concept is to learn the hardest negative information that can provide explicit unlearning direction to resist both FP and FN. We formalize such twin goals unlearning process into one unified OT problem for fast fine-tuning. Extensive experiments are conducted to verify that NCU can endow CLIP with strong robustness against noisy correspondence.",
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+ {
+ "type": "page_number",
+ "text": "4525",
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+ {
+ "type": "text",
+ "text": "Acknowledgments",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "This work was supported in part by the Major Key Project of PCL under Grant PCL2025AS10 and PCL2024A06, and in part by the Shenzhen Science and Technology Program under Grant RCJC20231211085918010.",
+ "bbox": [
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+ {
+ "type": "text",
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+ "[51] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Learning to prompt for vision-language models. International Journal of Computer Vision, 130(9):2337-2348, 2022. 3"
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+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
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+ "type": "title",
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+ "content": "Unlearning the Noisy Correspondence Makes CLIP More Robust"
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+ "content": "Haochen Han1, Alex Jinpeng Wang12†, Peijun Ye1, Fangming Liu1† \n1 Peng Cheng Laboratory 2 Central South University"
+ },
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+ "type": "title",
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+ "content": "The data appetite for Vision-Language Models (VLMs) has continuously scaled up from the early millions to billions today, which faces an untenable trade-off with data quality and inevitably introduces Noisy Correspondence (NC) samples. Undoubtedly, such semantically unrelated data significantly impairs the performance of VLMs. Previous efforts mainly address this challenge by estimating refined alignment for more precise guidance. However, such resource-intensive pipelines that train VLMs from scratch struggle to meet realistic data demands. In this paper, we present a brand new perspective that seeks to directly eliminate the harmful effects of NC in pre-trained VLMs. Specifically, we propose NCU, a Noisy Correspondence Unlearning fine-tuning framework that efficiently enhances VLMs' robustness by forgetting learned noisy knowledge. The key to NCU is learning the hardest negative information, which can provide explicit unlearning direction for both false positives and false negatives. Such twin goals unlearning process can be formalized into one unified optimal transport objective for fast fine-tuning. We validate our approach with the prevailing CLIP model over various downstream tasks. Remarkably, NCU surpasses the robust pre-trained method on zero-shot transfer while with lower computational overhead. The code is available at https://github.com/hhc1997/NCU."
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+ "type": "title",
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+ "content": "1. Introduction"
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+ "content": "The pursuit of general intelligence has driven progress in multimodal learning, which seeks to integrate and understand multiple sensory modalities like humans. Large-scale vision-language training, exemplified by CLIP [37], is seen as a key milestone in multimodal learning due to its remarkable transfer capabilities in real-world applications, such as image-text retrieval [13, 22, 34] and robotics control [41]."
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+ "content": "However, much of their success can be attributed to scaling laws enabled by massive training data. As every coin has two sides, the insatiable demand for data forces a"
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+ "content": "Figure 1. Illustration on the core concept of NCU. The twin goals unlearning process is guided by the learned hardest negative information. For the FP, \\( t_i^{Neg} \\) directly pulls \\( v_i \\) away from the mismatched \\( t_i \\). While for the FN, \\( t_i^{Neg} \\) acts as a distance upper bound to facilitate modeling many-to-many relations."
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+ "content": "difficult trade-off between quantity and quality, which inevitably introduces noisy correspondence into the training set. Taking the CC3M dataset [39] as an example, despite being filtered from 500 million images, it still contains at least \\(3\\%\\) [20] unrelated image-text pairs, i.e., false positive. To make matters worse, training on massive data necessitates larger batch sizes (32K used in CLIP), which increases the likelihood of unpaired samples sharing semantic similarities, i.e., false negative. Undoubtedly, such two-aspects noisy correspondence can significantly impair the performance of vision-language models."
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+ "content": "To endow robustness against NC, one natural direction is to revise the pre-training paradigm [1, 3, 11, 12, 21] that supervises VLMs with refined alignment. However, existing methods require training from scratch and may rely on guidance from external large models [3, 11]. Such resource-intensive pipelines obviously struggle to face the realistic demand, especially with today's billion-scale datasets [38]. Hence, it is necessary to address the NC problem in vision-language training with a cost-effective method."
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+ "content": "In this paper, we think outside the box of robust pretraining and pose an important question: Can we directly"
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+ "content": "† Co-corresponding authors."
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+ "content": "To answer this question, we resort to machine unlearning [2] and present NCU, a Noisy Correspondence Unlearning fine-tuning framework that improves the robustness of CLIP by erasing learned noisy knowledge. Machine unlearning is a reversed learning process that aims to delete the influence of specific training samples from trained models. Despite its promise in widespread tasks [7, 9], unlearning the NC in VLMs remains unexplored due to a key challenge: the ambiguous forgetting direction would corrupt the learned semantic structure in the feature space. To address this, we propose to learn the hardest negative information that can provide explicit unlearning direction. As illustrated in Fig. 1, on the one hand, the negative information would directly serve as reliable supervision for forgetting false positives. On the other hand, it would facilitate the modeling of many-to-many relationships among unpaired data for forgetting false negatives. Then, we show that such twin goals unlearning process can be formalized as one unified optimal transport problem, which efficiently fine-tunes CLIP to resist both FP and FN."
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+ "content": "Our main contributions are highlighted below:"
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+ "content": "- To the best of our knowledge, this work could be the first study to eliminate the harmful effects of noisy correspondence from pre-trained CLIP."
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+ "content": "- We propose the NCU framework, which efficiently unlearns FP and FN with explicit direction derived from the hardest negative information."
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+ "content": "- We demonstrate that NCU achieves significant improvements over CLIP on several downstream tasks and surpasses the previous robust pre-training method with lower computational overhead."
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+ "content": "2. Related Work"
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+ "content": "Noisy Correspondence Learning. Noisy correspondence refers to the alignment error presented in multimodal data. The false positive is a typical NC problem, where irrelevant multimodal pairs are wrongly treated as matched. To alleviate this, several techniques have been developed in various multimodal applications, including cross-modal retrieval [16, 18, 20, 36], video temporal learning [17, 30], multimodal person re-identification [35, 47], question answering [23], and image captioning [10, 24]. In more complex scenarios, e.g., vision-language pre-training [19, 21], models also suffer from false negatives caused by the training paradigm [12], where similar unpaired samples are forced to be distant. Considering the computational burden of large VLMs, this work presents a low-carbon solution to directly improve the robustness of pre-trained VLMs."
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+ "content": "Contrastive Vision Language Models. Contrastive vision language models (VLMs) [8, 13, 14, 33, 44, 48] aim to learn visual representations by the corresponding textual"
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+ "content": "supervision, which have attracted significant attention due to their simplicity and powerful representation capability. Pioneering works CLIP [37] and ALIGN [22] have shown great success via learning from massive image-text pairs. However, such web-crawled data are noisy [38, 42] and inevitably harm the efficacy of existing VLMs. To tackle this issue, a series of works attempted to train the VLM with refined soft image-text alignments by label smoothing [12], knowledge distillation [1], fine-grained intra-modal guidance [11], text rewriting [3], or positive-negative contrastive loss [21]. Besides, OT-based methods[40, 46] have also emerged as they naturally model such matching problems. Despite the success, previous works focus on training robust VLMs from scratch, which overlooks readily available pre-trained models and incurs unnecessary computational costs. To this end, this paper pioneers an efficient approach to enhance model robustness by unlearning noisy information from pre-trained models."
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+ "content": "Machine Unlearning. Recent advances in MU mainly focus on practical approximate unlearning, which seeks to mimic the behavior of a model re-trained from scratch. Driven by privacy concerns, existing MU works [7, 9, 32] in computer vision focus on image classification that attempts to forget specific classes. In parallel, MU has also become a popular topic in large language models due to its capability to eliminate harmful responses [31, 50]. However, multimodal forgetting remains under-explored in the literature. Pioneering works [26, 27] studied data-free class removal for CLIP's downstream image classification. To date, none of the existing MU methods has explored the unlearning of noisy concepts from VLMs."
+ },
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+ "content": "3.1. Contrastive Language-Image Pre-training"
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+ "content": "CLIP is a vision-language model trained on millions of web-harvested image-text pairs. We consider a batch of \\(N\\) image-text pairs \\(\\{v_{i},t_{i}\\}_{i = 1}^{N}\\) sampled from a cross-modal dataset \\(\\mathbb{D}\\), where \\(v_{i}\\) and \\(t_i\\) represent the raw image and corresponding text, respectively. The goal of CLIP is to train two modality-specific encoders that bring matched pairs closer while pushing unmatched ones apart. Specifically, image embedding \\(\\pmb {v}_i\\in \\mathbb{R}^d\\) and text embedding \\(t_i\\in \\mathbb{R}^d\\) are obtained by passing \\(v_{i}\\) and \\(t_i\\) through the image encoder \\(f_{v}\\) and text encoder \\(f_{t}\\), respectively, where \\(d\\) is the embedding dimension. The encoded \\(l_{2}\\) normalized embeddings are then aligned in the feature space by minimizing the contrastive objective, i.e., InfoNCE loss:"
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+ "content": "\\[\n\\mathcal {L} _ {v \\rightarrow t} ^ {C L} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\log \\frac {\\exp \\left(\\langle \\boldsymbol {v} _ {i} , \\boldsymbol {t} _ {i} \\rangle / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\langle \\boldsymbol {v} _ {i} , \\boldsymbol {t} _ {j} \\rangle / \\tau\\right)}, \\tag {1}\n\\]"
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+ "content": "where \\(\\langle \\cdot \\rangle\\) represents the inner product and \\(\\tau\\) is a trainable temperature parameter. As InfoNCE loss is symmetric, we can define \\(\\mathcal{L}_{t\\to v}^{CL}\\) similarly. The complete CLIP training objective is formulated as: \\(\\mathcal{L}_{CLIP} = \\mathcal{L}_{v\\rightarrow t}^{CL} + \\mathcal{L}_{t\\rightarrow v}^{CL}\\)."
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+ "content": "Despite its promising performance, the standard contrastive learning can suffer from the noisy correspondence problem in two aspects. First, the web-collected pairs inevitably contain an unknown portion of mismatched data, i.e., false positives. Second, hard target alignment neglects the potential semantic similarity among unpaired samples, i.e., false negatives, especially under large batch settings."
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+ "content": "3.2. Machine Unlearning"
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+ "content": "Given a CLIP model (also named reference model) \\(\\{f_v, f_t\\}\\) that is already trained on a cross-modal dataset \\(\\mathbb{D}\\), machine unlearning aims to fine-tune the model to forget a specific subset \\(\\mathbb{D}_{FG} \\subseteq \\mathbb{D}\\) while maintaining effectiveness on the retained set \\(\\mathbb{D}_{RT} = \\mathbb{D} \\setminus \\mathbb{D}_{FG}\\). Ideally, the model should behave as if it were trained without any sample from \\(\\mathbb{D}_{FG}\\). In principle, re-training the model from scratch on \\(\\mathbb{D}_{RT}\\) would serve as the gold standard. However, since CLIP is trained on massive-scale data, it is unrealistic to obtain a forget set that includes all noisy information, especially when some data are not publicly accessible. Therefore, we focus on an approximate unlearning approach in which \\(\\mathbb{D} = \\mathbb{D}_{FG} \\cup \\mathbb{D}_{RT}\\) does not need to contain all training pairs, making the unlearning process more practical for real-world scenarios."
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+ "angle": 0,
+ "content": "The most straightforward method to unlearn is gradient ascent or its variants, which optimizes the negative prediction loss over the forget set. Another typical approach is performing forget loss that encourages the model to relearn the modified form of undesired data. For example, we can update CLIP by minimizing InfoNCE loss in pair \\(\\{v_i,\\tilde{t}_i\\} \\sim \\mathbb{D}_{FG}\\) to forget the relation between \\(v_{i}\\) and \\(t_i\\) where \\(\\tilde{t}_i\\neq t_i\\) could be random or hand-crafted text to replace the original. Based on these, existing MU methods have shown promising progress in class forgetting and LLM privacy protection. However, applying these strategies to CLIP unlearning poses a key challenge: the ambiguous forgetting direction would corrupt the learned semantic structure in the feature space. In other words, the model forgets the undesired data by learning other meaningless patterns."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.755,
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+ ],
+ "angle": 0,
+ "content": "4. Methodology"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.78,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "To tackle the above issues, we introduce the Noisy Correspondence Unlearning (NCU) framework. In the following, we first introduce the division of forget and retained sets in Sec 4.1. Subsequently, we elaborate on learning the hardest negative information in Sec 4.2 and explain how to formalize the twin goals unlearning process into an optimal transport object for efficiently fine-tuning in Sec 2. The overall training pseudo-code is shown in Supplementary A."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
+ 0.091,
+ 0.747,
+ 0.108
+ ],
+ "angle": 0,
+ "content": "4.1. Identifying the Forget Set"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.113,
+ 0.905,
+ 0.189
+ ],
+ "angle": 0,
+ "content": "Unlike standard MU tasks with a predefined forget set, we need to manually identify mismatched samples from CLIP's training data to construct it. As pre-trained CLIP has shown strong representation capability, we propose using the basic similarity score to obtain \\(\\mathbb{D}_{FG}\\) and \\(\\mathbb{D}_{RT}\\), i.e.,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.515,
+ 0.198,
+ 0.905,
+ 0.246
+ ],
+ "angle": 0,
+ "content": "\\[\n\\omega_ {i} = \\frac {1}{2} \\left[ \\frac {\\exp \\left(\\left\\langle \\boldsymbol {v} _ {i} , \\boldsymbol {t} _ {i} \\right\\rangle / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\left\\langle \\boldsymbol {v} _ {i} , \\boldsymbol {t} _ {j} \\right\\rangle / \\tau\\right)} + \\frac {\\exp \\left(\\left\\langle \\boldsymbol {t} _ {i} , \\boldsymbol {v} _ {i} \\right\\rangle / \\tau\\right)}{\\sum_ {j = 1} ^ {N} \\exp \\left(\\left\\langle \\boldsymbol {t} _ {i} , \\boldsymbol {v} _ {j} \\right\\rangle / \\tau\\right)} \\right]. \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.248,
+ 0.905,
+ 0.337
+ ],
+ "angle": 0,
+ "content": "By comparing \\((v_{i},t_{i})\\) with other cross-modal samples in the batch, \\(\\omega_{i}\\) serves as a clean confidence that measures the extent of semantic match. Then, we select pairs with the lowest \\(P\\%\\) of \\(\\omega_{i}\\) within the batch as false positives to construct the forget set \\(\\mathbb{D}_{FG}\\), while treating the remaining in-batch pairs as the retained set \\(\\mathbb{D}_{RT}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.339,
+ 0.905,
+ 0.414
+ ],
+ "angle": 0,
+ "content": "Note that \\(\\mathbb{D}_{FG}\\) and \\(\\mathbb{D}_{RT}\\) are dynamically selected at each batch, which enjoys two merits: 1) CLIP could be efficiently updated with one intra-batch optimization; 2) The forget-retain ratio could be flexibly adjusted through the predefined parameter \\(P\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.424,
+ 0.842,
+ 0.439
+ ],
+ "angle": 0,
+ "content": "4.2. Learning Hardest Negative Semantics"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.446,
+ 0.907,
+ 0.611
+ ],
+ "angle": 0,
+ "content": "To guide CLIP with an explicit unlearning direction, we aim to learn the hardest negative semantics as supervision. Intuitionally, for an irrelevant pair \\((v_{i},t_{i})\\) that misleads the model with \\(v_{i}\\) and \\(t_i\\) are matched', we encourage the model to forget this information by relearning that \\(v_{i}\\) and \\(t_i\\) are not matched'. From a data utilization viewpoint, this paradigm is similar to negative learning[25] that supervises the model with complementary information [18], i.e., pushing the candidate away from other unpaired samples. Differently, our method seeks the hardest negative information to avoid uncertain optimization directions."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.612,
+ 0.906,
+ 0.793
+ ],
+ "angle": 0,
+ "content": "To achieve this, we incorporate a set of learnable vectors to represent the textual negative semantics inspired by prompt learning [51]. Specifically, for any training pair \\((v_{i},t_{i})\\), the token features of \\(t_i\\) are combined with \\(m\\) shared prompt vectors to present the corresponding negative semantics \\(t_i^{Neg}\\) in the feature space. While such prompt-driven semantic negation of CLIP has demonstrated success in out-of-distribution detection [29, 43], existing methods are confined to closed-set downstream tasks with limited category concepts. In contrast, our challenge lies in extending the semantic opposite operation into the open-set knowledge that CLIP pre-trained."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.794,
+ 0.906,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Intuitively, the hardest negative satisfies two constraints in the feature space: 1) \\( t_i^{Neg} \\) needs to maximize its distance from \\( v_i \\) and \\( t_i \\); 2) \\( t_i^{Neg} \\) should maintain certain similarity to those unpaired images, as it is not a wrong description [43] despite being semantically irrelevant to \\( v_j \\). Furthermore, we only use \\( \\mathbb{D}_{RT} \\) to learn the prompt tokens to avoid overfitting caused by noisy correspondence. For notation simplicity,"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.482,
+ 0.945,
+ 0.516,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "4520"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.161,
+ 0.087,
+ 0.35,
+ 0.213
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.159,
+ 0.216,
+ 0.334,
+ 0.232
+ ],
+ "angle": 0,
+ "content": "(a). Maximize \\(L_{2}\\) -distance"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.414,
+ 0.087,
+ 0.621,
+ 0.216
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.427,
+ 0.217,
+ 0.569,
+ 0.232
+ ],
+ "angle": 0,
+ "content": "(b). Similarity Bound"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.652,
+ 0.087,
+ 0.862,
+ 0.217
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.676,
+ 0.217,
+ 0.824,
+ 0.232
+ ],
+ "angle": 0,
+ "content": "(c). Relation Opposite"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
+ 0.243,
+ 0.907,
+ 0.302
+ ],
+ "angle": 0,
+ "content": "Figure 2. Illustration of the optimization objective to learn the hardest negative semantics. (a) Previous attempts that directly maximize the \\(L_{2}\\) distance prevent \\(\\pmb{t}_{i}^{Neg}\\) from providing certain guidance for unpaired images, e.g., \\(\\pmb{v}_{k}\\). (b) We bound the similarity with margins for a more relaxed semantic separation, but it may lead to uncertain targets, e.g., \\(\\pmb{t}_{i}^{Neg}\\) and \\(\\pmb{t}_{i}^{Neg'}\\). (c) We further preserve relation structures for precise objectives. The intuition is that the opposite text should also maintain semantic relationships, e.g., \\(\\langle \\pmb{t}_i,\\pmb{t}_j^{Neg}\\rangle \\approx \\langle \\pmb{t}_j,\\pmb{t}_i^{Neg}\\rangle\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.326,
+ 0.484,
+ 0.372
+ ],
+ "angle": 0,
+ "content": "we denote \\(\\tilde{N}\\) as the size of \\(\\mathbb{D}_{RT}\\) within each batch. Based on the above insights, we propose the following intra-modal and cross-modal training objectives."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.398,
+ 0.484,
+ 0.55
+ ],
+ "angle": 0,
+ "content": "Text Relation Opposite. It encourages semantic separation between the embeddings of negative text and its original. Most previous works [29, 43] typically reduce the per-instance similarity gap among textual pairs, e.g., \\(\\| t_i - t_i^{Neg}\\| _2\\to 2\\) [43] to directly maximize its \\(L_{2}\\) distance. However, such rigid constraint incurs a crucial limitation in the open-set semantic space—enforcing maximal distance pushes \\(t_i^{Neg}\\) away from unpaired images (Fig. 2(a)), which is contrary to our objective. To this end, we propose a relaxed similarity bound to constrain the semantic separation:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.1,
+ 0.576,
+ 0.483,
+ 0.62
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} ^ {s e p} = \\frac {1}{\\tilde {N}} \\sum_ {i = 1} ^ {\\tilde {N}} \\left(\\left[ \\alpha - \\langle \\boldsymbol {t} _ {i}, \\boldsymbol {t} _ {i} ^ {N e g} \\rangle \\right] _ {+} + \\left[ \\langle \\boldsymbol {t} _ {i}, \\boldsymbol {t} _ {i} ^ {N e g} \\rangle - \\beta \\right] _ {+}\\right), \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.632,
+ 0.484,
+ 0.784
+ ],
+ "angle": 0,
+ "content": "where \\(\\alpha < 0\\) and \\(\\beta < 0\\) are the margin parameters to locate \\(\\langle t_i, t_i^{Neg} \\rangle \\in [\\alpha, \\beta]\\), and \\([x]_+ = \\max(x, 0)\\) is the hinge function. As illustrated in Fig. 2(b), although minimizing Eq.(3) enables \\(t_i^{Neg}\\) to be distant from \\(t_i\\) while remaining relatively similar to unpaired images, the broad range of variations makes training convergence difficult. To address this issue, we propose to perform semantic opposite at the relation level instead of the instance level, which is achieved by preserving the geometrical structures among all negative and original text within the batch:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.134,
+ 0.798,
+ 0.483,
+ 0.843
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} ^ {r e l} = \\frac {1}{\\tilde {N}} \\sum_ {i = 1} ^ {\\tilde {N}} \\sum_ {j = 1} ^ {\\tilde {N}} \\left(\\left\\langle \\boldsymbol {t} _ {i}, \\boldsymbol {t} _ {j} ^ {N e g} \\right\\rangle - \\left\\langle \\boldsymbol {t} _ {j}, \\boldsymbol {t} _ {i} ^ {N e g} \\right\\rangle\\right) ^ {2}. \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.856,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "As shown in Fig. 2(c), regularizing the negative-original relation consistency can guide \\( t_i^{Neg} \\) toward a precise location in the feature space."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.326,
+ 0.907,
+ 0.463
+ ],
+ "angle": 0,
+ "content": "Image-text Matching Opposite. It aims to model the alignment between the embeddings of negative text and images. As discussed, \\( t_i^{Neg} \\) provides positive supervision to unpaired images while separating from its paired image, which presents opposite matching patterns to the normal contrastive objective. To achieve this, we take inspiration from Sigmoid loss [49] that efficiently supports such multi-positive alignment. Specifically, it guides per cross-modal pair independently by the binary matching target:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.525,
+ 0.47,
+ 0.906,
+ 0.552
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathcal {L} ^ {i t m} = \\frac {1}{\\tilde {N}} \\sum_ {i = 1} ^ {\\tilde {N}} \\sum_ {j = 1} ^ {\\tilde {N}} \\left(\\log \\frac {1}{1 + \\exp \\left(m _ {i j} \\left(- \\langle \\boldsymbol {t} _ {i} , \\boldsymbol {v} _ {j} \\rangle / \\tau\\right)\\right)} \\right. \\tag {5} \\\\ + \\log \\frac {1}{1 + \\exp (- m _ {i j} (- \\langle \\pmb {t} _ {i} ^ {N e g} , \\pmb {v} _ {j} \\rangle / \\tau))}, \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.557,
+ 0.906,
+ 0.632
+ ],
+ "angle": 0,
+ "content": "where \\(m_{ij}\\) equals 1 for \\(i = j\\) and \\(-1\\) for \\(i\\neq j\\). In Eq.(5), the first part follows the standard one-to-one matching to retain the original CLIP knowledge, while the second part utilizes the opposite binary target, i.e., \\(-m_{ij}\\), to bring \\(t_i^{Neg}\\) closer to multiple images."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.632,
+ 0.906,
+ 0.678
+ ],
+ "angle": 0,
+ "content": "With the visual encoder frozen, the overall loss for learning the hardest negative semantics is balanced by a scaling factor \\(\\lambda\\) and given by:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.599,
+ 0.684,
+ 0.905,
+ 0.703
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} ^ {H N} = \\lambda \\left(\\mathcal {L} ^ {s e p} + \\mathcal {L} ^ {r e l}\\right) + \\mathcal {L} ^ {i t m}. \\tag {6}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.709,
+ 0.885,
+ 0.726
+ ],
+ "angle": 0,
+ "content": "4.3. Hardest-Negative Guided Noise Unlearning"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.731,
+ 0.907,
+ 0.854
+ ],
+ "angle": 0,
+ "content": "The hardest negative semantics serve dual purposes in erasing the learned noisy correspondence: 1) guide CLIP to unlearn the false positive pair \\((v_{i},t_{i})\\) by matching \\(v_{i}\\) with \\(t_i^{Neg}\\). 2) While for the well-matched pair \\((v_{i},t_{i})\\), \\(t_i^{Neg}\\) assists in inferring the soft alignment among unpaired data to unlearn the false negative pattern. To efficiently fine-tune CLIP, we formalize such twin goals unlearning process into one unified Optimal Transport problem."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.871,
+ 0.907,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Optimal Transport. OT seeks to establish a flexible alignment between images and captions by computing a"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
+ 0.945,
+ 0.514,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "4521"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.094,
+ 0.089,
+ 0.905,
+ 0.241
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
+ 0.252,
+ 0.908,
+ 0.283
+ ],
+ "angle": 0,
+ "content": "Figure 3. Overview of the Noisy Correspondence Unlearning process. With the learned negative prompt frozen, we formulate an optimal transport problem guided by the hardest negative and then use the solved transport plan to robustly fine-tune the model \\( f_{t} \\) and \\( f_{v} \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.307,
+ 0.485,
+ 0.43
+ ],
+ "angle": 0,
+ "content": "minimal-cost transport plan, where the cost refers to the expense of transporting mass from source to target distribution and is generally set to a distance measure [15]. Let \\( \\mathbf{C} \\in \\mathbb{R}_{+}^{N \\times N} \\) denotes the cost matrix for the mini-batch, where \\( [\\mathbf{C}]_{i,j} = 1 - \\langle \\mathbf{v}_i, \\mathbf{t}_j \\rangle \\) is the cosine distance of \\( v_i \\) and \\( t_j \\). \\( \\Gamma \\in \\mathbb{R}_{+}^{N \\times N} \\) denotes the corresponding transport plan that \\( [\\Gamma]_{i,j} \\) represents the alignment probability between \\( v_i \\) and \\( t_j \\). Formally, the objective of OT is defined as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.184,
+ 0.443,
+ 0.36,
+ 0.472
+ ],
+ "angle": 0,
+ "content": "\\[\n\\min _ {\\Gamma \\in \\Pi (\\pmb {\\mu}, \\pmb {\\nu})} \\langle \\Gamma , \\pmb {C} \\rangle - \\epsilon H (\\Gamma)\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.108,
+ 0.471,
+ 0.453,
+ 0.49
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {s . t .} \\Pi (\\boldsymbol {\\mu}, \\boldsymbol {\\nu}) = \\left\\{\\boldsymbol {\\Gamma} \\in \\mathbb {R} _ {+} ^ {N \\times N} \\mid \\boldsymbol {\\Gamma} \\mathbb {1} _ {N} = \\boldsymbol {\\mu}, \\boldsymbol {\\Gamma} ^ {\\top} \\mathbb {1} _ {N} = \\boldsymbol {\\nu} \\right\\},\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.503,
+ 0.484,
+ 0.625
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbb{1}_N\\) denotes a \\(N\\)-dimensional all-one vector, \\(\\mu, \\nu \\in \\mathbb{R}^N\\) are probability measures representing the relative importance of each image and caption. Without prior knowledge, \\(\\mu = \\frac{1}{N}\\mathbb{1}_N\\) and \\(\\nu = \\frac{1}{N}\\mathbb{1}_N\\) are considered to be uniformly distributed since each pair is sampled independently. \\(H(\\Gamma)\\) is an additional entropy regularizer controlled by the smooth parameter \\(\\epsilon\\), which enables the OT objective to be solved by the rapid Sinkhorn-Knopp algorithm [6]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.652,
+ 0.484,
+ 0.779
+ ],
+ "angle": 0,
+ "content": "Boosting OT via Hardest Negatives. To endow the transport plan with dual forgetting purposes, we reformulate Eq.(7) by imposing guidance from the hardest negative information. Specifically, for each image \\( v_{i} \\), we extend its transport target from \\( \\{t_i\\}_{i = 1}^N \\) to include its paired negative text \\( t_i^{Neg} \\). As shown in Fig. 3, the negative text composes a new alignable column for the transport objective, which append the cost matrix \\( C \\) to \\( \\bar{C} \\in \\mathbb{R}_+^{N\\times (N + 1)} \\), i.e.,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.092,
+ 0.792,
+ 0.483,
+ 0.813
+ ],
+ "angle": 0,
+ "content": "\\[\n[ \\bar {\\boldsymbol {C}} ] _ {i, N + 1} = 1 - \\langle \\pmb {v} _ {i}, \\pmb {t} _ {i} ^ {N e g} \\rangle , [ \\bar {\\boldsymbol {C}} ] _ {i, j} = [ \\pmb {C} ] _ {i, j}, \\forall i, j \\in [ 1, N ].\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.825,
+ 0.484,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "For the two parts \\(\\mathbb{D}_{FG}\\) and \\(\\mathbb{D}_{RT}\\) within each batch, the hardest negative should impose different guidance for distinct unlearning goals. To this end, we propose a maskbase constraint to the corresponding transport plan \\(\\bar{\\Gamma}\\) that regulates the effect of \\(t_i^{Neg}\\). Specifically, the mask matrix"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.515,
+ 0.304,
+ 0.719,
+ 0.325
+ ],
+ "angle": 0,
+ "content": "\\(M\\in \\mathbb{R}_{+}^{N\\times (N + 1)}\\) satisfies that"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.53,
+ 0.337,
+ 0.907,
+ 0.392
+ ],
+ "angle": 0,
+ "content": "\\[\n[ M ] _ {i, j} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} (v _ {i}, t _ {i}) \\in \\mathbb {D} _ {F G} \\text {a n d} j = i, \\\\ 0, & \\text {i f} (v _ {i}, t _ {i}) \\in \\mathbb {D} _ {R T} \\text {a n d} j = N + 1, \\\\ 1, & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.403,
+ 0.907,
+ 0.541
+ ],
+ "angle": 0,
+ "content": "For the toy example illustrated in Fig. 3, if the pair is considered to be mismatched, the transport mass between \\( v_{i} \\) and \\( t_{i} \\) should be constrained to zero. Conversely, for the well-matched pair, \\( t_{i}^{Neg} \\) acts as a lower limit where the transport mass between \\( v_{i} \\) and \\( t_{j} \\) should be higher than it. Following the solver from [15], we model the mask constraint as the Hadamard product form that \\( \\hat{\\Gamma} = M \\odot \\bar{\\Gamma} \\), and the optimal alignment is formulated as (detailed Sinkhorn solution is presented in Supplementary B):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.599,
+ 0.55,
+ 0.907,
+ 0.581
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\Gamma} ^ {*} = \\underset {\\hat {\\Gamma} \\in \\Pi (\\mu , \\bar {\\nu})} {\\arg \\min } \\left\\langle \\hat {\\Gamma}, \\bar {C} \\right\\rangle - \\epsilon H (\\hat {\\Gamma}), \\tag {9}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.593,
+ 0.88,
+ 0.613
+ ],
+ "angle": 0,
+ "content": "where \\(\\bar{\\nu} = \\frac{1}{N + 1}\\mathbb{1}_{N + 1}\\) to satisfy the additional column."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.632,
+ 0.907,
+ 0.74
+ ],
+ "angle": 0,
+ "content": "The Unlearning Objective. Although \\(\\hat{\\Gamma}^*\\) provides the more refined alignment, we suggest further incorporating an identity-like matrix \\(\\pmb{I}\\) for two merits. First, diagonal elements are set as 1 for true positives to retain the initial alignment. Second, \\([I]_{i,N + 1} = 1\\) to enhance the unlearning for the possible false positive \\((v_{i},t_{i})\\in \\mathbb{D}_{FG}\\). Thus, the overall alignment balanced by the factor \\(\\gamma\\) is defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.633,
+ 0.751,
+ 0.907,
+ 0.769
+ ],
+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {T} = \\gamma \\hat {\\boldsymbol {\\Gamma}} ^ {*} + (1 - \\gamma) \\boldsymbol {I}. \\tag {10}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.78,
+ 0.909,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "To fine-tune CLIP with this soft alignment, we use the KL divergence to optimize the matching distribution. Formally, we denote the batched similarity matrix as \\( \\pmb{P} \\in \\mathbb{R}^{N \\times (N + 1)} \\) where \\( P_{i} = [\\langle v_{i}, t_{1} \\rangle, \\dots, \\langle v_{i}, t_{N} \\rangle, \\langle v_{i}, t_{i}^{Neg} \\rangle]^{\\top} \\). We obtain \\( P_{i}^{v2t} \\) and \\( P_{i}^{t2v} \\) by applying row-wise and column-wise softmax operation to \\( P \\), respectively. Correspondingly, let \\( T_{i}^{v2t} \\) and \\( T_{i}^{t2v} \\) be the row-wise and column-wise normalized refined alignment for the \\( i \\)-th sample, respectively. The"
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+ "type": "page_number",
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+ "content": "4522"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "OT-guided re-aligning is defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.091,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} ^ {o t r} = \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\mathrm {K L} \\left(\\boldsymbol {T} _ {i} ^ {v 2 t} \\| \\boldsymbol {P} _ {i} ^ {v 2 t}\\right) + \\frac {1}{N + 1} \\sum_ {i = 1} ^ {N + 1} \\mathrm {K L} \\left(\\boldsymbol {T} _ {i} ^ {t 2 v} \\| \\boldsymbol {P} _ {i} ^ {t 2 v}\\right). \\tag {11}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Moreover, we empirically observe that preserving the textual semantic separation term can make the unlearning more stable. Thus, the final unlearning objective is defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} ^ {U L} = \\mathcal {L} ^ {o t r} + \\mathcal {L} ^ {s e p}. \\tag {12}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Experiment"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this section, we experimentally analyze the effectiveness of NCU in unlearning the NC knowledge from CLIP."
+ },
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5.1. Setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Datasets. Our experiments are conducted on three vision-language datasets at different scales and noise: Conceptual Captions 3M (CC3M) [39], Conceptual Captions 12M (CC12M) [4], and YFCC15M-R (provided by [14], an LLM-recaptioned subset from the YFCC100M [42]). All datasets are web-crawled and contain an unknown portion of NC pairs, e.g., CC3M is estimated to include at least \\(3\\%\\) false positives. We evaluate NCU on ImageNet and 15 common downstream datasets for classification performance and on MSCOCO and Flickr30K for retrieval capability. Details for datasets are shown in Supplementary C."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Unlearning Details. Following CLIP, we consider two architectures for the image encoder, i.e., ViT/B16 and ViT/B32, while the text encoder adopts the transformer architecture. We consider a CLIP pre-trained on dataset \\(\\mathbb{D}\\), e.g., CC3M, CC12M, or YFCC15M-R, as our reference model, then we perform the NC unlearning on \\(\\mathbb{D}\\) or its subset to enhance CLIP's robustness. For all experiments, we allocate 2 epochs for learning negative semantics and 8 epochs for noise unlearning. All models are trained with a batch size of 2,048 on 16 NVIDIA V100 GPUs. Detailed training settings are presented in Supplementary D."
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+ "type": "text",
+ "bbox": [
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+ "content": "Evaluation Protocol. We evaluate NCU's transferability with Zero-Shot (ZS) classification accuracy and Linear Probing (LP) accuracy. For ZS classification, we follow CLIP's [37] prompt templates to compute distances between class text embeddings and image features. For LP, we follow the mainstream setting [8, 37] that trains a linear classifier using L-BFGS on features extracted from the frozen image encoder. Besides, we evaluate the retrieval performance with the Recall at rank K (R@K) metric."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5.2. Evaluation on Diverse Downstream Tasks"
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "To verify the generalization of NCU, we compare it with CLIP on three different types of downstream tasks."
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+ "type": "text",
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+ "content": "Zero-Shot Transfer. We compare the zero-shot performance of CLIP and NCU on 16 popular image classification datasets. We follow the prompt templates suggested in the CLIP paper [37] to form each class name into a natural sentence. As demonstrated in Tab. 1, our NCU approach significantly outperforms the baseline CLIP model on both ImageNet and other downstream datasets. Specifically, across all fine-tuning datasets and all model architectures, NCU gains in the range of \\(2.8\\% \\sim 4.1\\%\\) in top-1 accuracy on ImageNet and \\(2.5\\% \\sim 4.0\\%\\) on average over the other downstream datasets. This reveals that NCU can successfully eliminate the impact of NC on CLIP by robust fine-tuning with the same dataset."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Image-Text Retrieval. We present the zero-shot cross-modal retrieval performance on the testing set of Flickr30K (1K) and MSCOCO (5K) in Tab. 2. Our method considerably outperforms the vanilla CLIP in almost all cases. For instance, when fine-tuning CLIP (ViT-B/32) pre-trained on the CC3M dataset, our NCU method achieves a \\(7.7\\%\\) improvement in average recall scores on Flickr30K and \\(4.8\\%\\) improvement in average recall scores on MSCOCO. This finding indicates that NCU can remarkably enhance the alignment of images and text in the embedding space."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Linear Probing. Tab. 3 reports the linear probing performance on 4 representative downstream datasets. Our NCU consistently surpasses CLIP in the vast majority of cases, suggesting that the visual embeddings learned by our NCU are more effective and transferable than CLIP."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5.3. Compared to Robust Methods"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "In this section, we compare NCU with other robust-designed techniques against NC on zero-shot ImageNet1K classification task, i.e., gradient ascent (GA), and SoftCLIP [11]. Specifically, we evaluate GA as a standalone method, where \\(-\\mathcal{L}_{CLIP}\\) is performed on \\(\\mathbb{D}_{FG}\\) for handling FPs and \\(\\mathcal{L}_{CLIP}\\) with label smoothing is performed on \\(\\mathbb{D}_{RT}\\) for FNs. SoftCLIP is a noise-robust SOTA method that trains CLIP from scratch by additional intra-modal guided alignment, i.e., ROI features. As shown in Tab. 4, although GA is a naive unlearning strategy, it still achieves observable performance gains. Meanwhile, SoftCLIP's self-similarity modeling fails to excavate supervision from false positives, which may explain why it performs worse than GA in some cases, e.g., CC12M with ViT-B/32. By contrast, our NCU achieves solid improvements by forgetting both false positives and false negatives, outperforming SoftCLIP by \\(1.1\\% \\sim 2.3\\%\\) without external guidance."
+ },
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+ "content": "5.4. Ablation Study"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To investigate the effectiveness of specific components in our method, we carry out some ablation studies on Ima-"
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+ "angle": 0,
+ "content": "| Dataset | Model | Caltech101 | CIFAR-10 | CIFAR-100 | DTD | Aircraft | SST2 | Flowers102 | Food101 | GTSRB | OxfordPeds | RESISC45 | SUN397 | EuroSAT | StanfordCars | STL10 | Average | ImageNet1K |
| Model Architecture: ViT-B/16 |
| CC3M | CLIP | 52.3 | 55.2 | 24.1 | 10.9 | 1.0 | 50.1 | 11.9 | 11.1 | 6.9 | 12.9 | 19.5 | 25.0 | 13.5 | 0.8 | 81.7 | 25.1 | 16.0 |
| NCU | 59.1 | 54.3 | 28.8 | 12.3 | 1.1 | 50.1 | 14.1 | 14.8 | 7.4 | 16.3 | 22.8 | 32.3 | 21.7 | 1.5 | 86.3 | 28.2↑3.1 | 20.0↑4.0 |
| CC12M | CLIP | 77.0 | 66.5 | 38.3 | 21.2 | 2.5 | 47.7 | 33.4 | 51.9 | 7.3 | 64.2 | 39.0 | 44.7 | 21.2 | 25.5 | 91.4 | 42.1 | 40.6 |
| NCU | 80.9 | 79.3 | 49.1 | 23.2 | 2.7 | 48.0 | 31.7 | 52.7 | 10.1 | 66.5 | 41.9 | 52.6 | 28.6 | 29.0 | 93.2 | 46.0↑3.9 | 43.4↑2.8 |
| Model Architecture: ViT-B/32 |
| CC3M | CLIP | 47.7 | 54.2 | 18.0 | 7.6 | 1.2 | 50.1 | 9.3 | 9.1 | 6.0 | 7.4 | 16.2 | 16.0 | 15.5 | 0.8 | 77.7 | 22.5 | 11.8 |
| NCU | 53.0 | 56.7 | 25.9 | 10.4 | 1.7 | 50.1 | 10.2 | 10.5 | 6.5 | 10.5 | 19.0 | 22.2 | 16.7 | 1.4 | 80.1 | 25.0↑2.5 | 14.6↑2.8 |
| CC12M | CLIP | 76.3 | 68.2 | 35.2 | 16.1 | 2.8 | 50.1 | 29.3 | 37.6 | 6.4 | 54.1 | 30.1 | 39.2 | 22.5 | 14.8 | 90.8 | 38.2 | 33.8 |
| NCU | 80.4 | 68.5 | 41.4 | 19.3 | 2.6 | 52.8 | 28.6 | 43.4 | 7.2 | 62.4 | 35.7 | 48.3 | 31.3 | 18.1 | 92.5 | 42.2↑4.0 | 36.7↑2.9 |
| YFCC15M-R | CLIP | 53.7 | 67.0 | 34.4 | 13.1 | 1.1 | 49.3 | 22.1 | 18.6 | 11.0 | 13.5 | 20.3 | 29.3 | 23.0 | 1.7 | 83.7 | 29.5 | 17.8 |
| NCU | 58.2 | 69.5 | 37.8 | 15.3 | 1.8 | 49.9 | 29.2 | 23.7 | 11.2 | 16.1 | 23.1 | 34.0 | 23.3 | 1.8 | 86.7 | 32.1↑2.6 | 21.9↑4.1 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. Zero-shot transfer evaluation of different models."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "| Dataset | Architecture | Model | Flickr30K 1K Testing | MSCOCO 5K Testing |
| Image-to-Text | Text-to-Image | Average | Image-to-Text | Text-to-Image | Average | |
| R@1 | R@5 | R@10 | R@1 | R@5 | R@10 | R@1 | R@5 | R@10 | R@1 | R@5 | R@10 | |
| CC3M | ViT-B/16 | CLIP | 27.6 | 54.2 | 65.8 | 19.0 | 40.5 | 51.3 | 43.1 | 12.8 | 30.9 | 42.7 | 9.7 | 25.4 | 35.2 | 26.1 | |
| NCU | 32.1 | 60.7 | 71.9 | 25.2 | 49.5 | 61.0 | 50.1↑7.0 | 15.8 | 36.9 | 48.4 | 12.1 | 29.7 | 40.1 | 30.5↑4.4 | |
| ViT-B/32 | CLIP | 14.0 | 35.2 | 47.7 | 11.5 | 27.9 | 37.8 | 29.0 | 7.0 | 20.1 | 28.9 | 6.0 | 16.7 | 24.0 | 17.1 | |
| NCU | 21.3 | 44.5 | 55.7 | 15.7 | 36.3 | 46.4 | 36.7↑7.7 | 10.7 | 25.7 | 35.4 | 8.1 | 21.3 | 30.2 | 21.9↑4.8 | |
| CC12M | ViT-B/32 | CLIP | 50.3 | 77.2 | 85.9 | 37.9 | 64.8 | 74.2 | 65.1 | 26.8 | 54.0 | 65.9 | 20.0 | 42.4 | 54.2 | 43.9 | |
| NCU | 53.0 | 77.3 | 85.0 | 38.4 | 66.6 | 76.7 | 66.2↑1.1 | 28.2 | 54.7 | 66.7 | 20.0 | 42.8 | 54.3 | 44.5↑0.6 | |
| YFCC15M-R | ViT-B/32 | CLIP | 57.4 | 81.6 | 89.1 | 40.8 | 66.4 | 75.4 | 68.5 | 35.0 | 60.9 | 71.8 | 22.6 | 46.0 | 58.0 | 49.1 | |
| NCU | 58.0 | 83.2 | 89.7 | 42.5 | 69.9 | 78.8 | 70.4↑1.9 | 34.3 | 62.0 | 73.5 | 24.6 | 49.0 | 60.8 | 50.7↑1.6 | |
"
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+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Zero-shot cross-modal retrieval evaluation of different models."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ 0.485,
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+ ],
+ "angle": 0,
+ "content": "| Dataset | Architecture | Model | SUN397 | OxfordPeds | Food101 | ImageNet |
| CC3M | ViT-B/16 | CLIP | 54.38 | 62.20 | 54.36 | 48.13 |
| NCU | 55.60 | 62.85 | 54.74 | 49.90 |
| ViT-B/32 | CLIP | 46.96 | 52.30 | 46.96 | 40.20 |
| NCU | 48.20 | 52.82 | 46.85 | 41.49 |
| CC12M | ViT-B/16 | CLIP | 70.94 | 82.83 | 78.99 | 66.70 |
| NCU | 71.36 | 84.76 | 79.18 | 66.65 |
| ViT-B/32 | CLIP | 66.05 | 78.41 | 70.12 | 59.19 |
| NCU | 66.63 | 78.63 | 70.76 | 60.34 |
| YFCC15M-R | ViT-B/32 | CLIP | 60.46 | 61.90 | 59.09 | 51.07 |
| NCU | 60.75 | 62.85 | 60.46 | 52.29 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.119,
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+ 0.73
+ ],
+ "angle": 0,
+ "content": "Table 3. Linear probing comparison of different models."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "geNet1K with models unlearned on CC3M. We first ablate the contributions of two key components of NCU, i.e., negative prompt and text relation opposite. Specifically, in the variant \\(\\nu_{1}\\), we replace the learnable prompt tokens by preponding some textual negative prefixes to raw captions, e.g., 'the image has no' or 'this picture lacks'. In the variant \\(\\nu_{2}\\), we use maximal \\(L_{2}\\) distance loss [43] as a substitute for our text relation opposite. Besides, we validate the impact of different NC unlearning by intervening with the refined"
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "| Dataset | Model | Model Architecture | ImageNet1K ZS top-1 |
| CC3M | CLIP | ViT-B/16 | 16.0 |
| Gradient Ascent | 16.7 ↑0.7 |
| SoftCLIP | 18.9 ↑2.9 |
| NCU | 20.0 ↑4.0 |
| CC3M | CLIP | ViT-B/32 | 11.8 |
| Gradient Ascent | 12.1 ↑0.3 |
| SoftCLIP | 13.3 ↑1.5 |
| NCU | 14.6 ↑2.8 |
| CC12M | CLIP | ViT-B/16 | 40.6 |
| Gradient Ascent | 41.6 ↑1.0 |
| SoftCLIP | 42.1 ↑1.5 |
| NCU | 43.4 ↑2.8 |
| CC12M | CLIP | ViT-B/32 | 33.8 |
| Gradient Ascent | 35.1 ↑1.3 |
| SoftCLIP | 34.4 ↑0.6 |
| NCU | 36.7 ↑2.9 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.546,
+ 0.779,
+ 0.874,
+ 0.793
+ ],
+ "angle": 0,
+ "content": "Table 4. Zero-shot top-1 performance on ImageNet1K."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "alignment, i.e., \\(\\mathcal{V}_3\\) and \\(\\mathcal{V}_4\\). As shown in Tab. 5, we observe that: 1) Using negative textual prefixes also shows competitive results, demonstrating the generalization of our method. However, we argue that the learnable prompt is preferable, except for performance gains, operating to features makes"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "4524"
+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
+ 0.102,
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+ 0.183
+ ],
+ "angle": 0,
+ "content": "| Model | ImageNet1K ZS top-1 |
| ViT-B/16 | ViT-B/32 |
| NCU | 20.0 | 14.6 |
| V1 (w/o Hardest Negative Prompts) | 19.3 ↓0.7 | 14.4 ↓0.2 |
| V2 (w/o Text Relation Opposite) | 18.8 ↓1.2 | 13.9 ↓0.7 |
| V3 (w only False Negatives Unlearning) | 17.7 ↓2.3 | 13.5 ↓1.1 |
| V4 (w only False Positives Unlearning) | 19.2 ↓0.8 | 14.3 ↓0.3 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Table 5. Ablation studies on zero-shot transfer task (ImageNet1K) of models unlearned on CC3M."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.242,
+ 0.485,
+ 0.35
+ ],
+ "angle": 0,
+ "content": "it possible for NCU to extend to modalities beyond text. 2) Simply maximizing the distance between negative and original text embeddings leads to suboptimal performance, which aligns with our analysis in Fig. 2. 3) Both types of NC impair CLIP's performance, among which the false positive causes a more severe impact. While NCU achieves the best performance by forgetting such noisy knowledge."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.092,
+ 0.374,
+ 0.485,
+ 0.556
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.565,
+ 0.483,
+ 0.594
+ ],
+ "angle": 0,
+ "content": "Figure 4. Effect of NCU with varying fine-tuning dataset sizes on zero-shot image classification and cross-modal retrieval."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.09,
+ 0.634,
+ 0.383,
+ 0.65
+ ],
+ "angle": 0,
+ "content": "5.5. NC Unlearning with Partial Data"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.659,
+ 0.483,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "In this section, we conduct an interesting study to verify whether CLIP can improve robustness by only unlearning NC with a portion of the pre-trained data. To this end, given a CLIP pre-trained on CC3M as the reference model, we evaluate NCU using different data portions ranging from 0.5 million to 3 million image-text pairs. Fig. 4 plots the ZS top-1 accuracy on ImageNet1K and the average of recalls on MSCOCO 5K. Remarkably, even when unlearning on less than \\(20\\%\\) of the original data (0.5M), NCU achieves significant performance gains while preserving overall knowledge learned in CC3M. With the accessible data increasing, NCU shows consistent improvements on both zero-shot downstream tasks. This phenomenon indicates NCU's flexibility in enhancing the robustness of models with limited data, which is valuable to handling VLMs pre-trained with partially private or proprietary data."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.515,
+ 0.087,
+ 0.712,
+ 0.206
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.59,
+ 0.207,
+ 0.638,
+ 0.22
+ ],
+ "angle": 0,
+ "content": "(a) NCU"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.712,
+ 0.087,
+ 0.906,
+ 0.206
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.782,
+ 0.207,
+ 0.832,
+ 0.22
+ ],
+ "angle": 0,
+ "content": "(b) CLIP"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.512,
+ 0.232,
+ 0.907,
+ 0.275
+ ],
+ "angle": 0,
+ "content": "Figure 5. Similarity scores distribution of positive and negative pairs from CLIP and NCU. Both models are based on ViT/B16 and learning from the CC3M training set."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.295,
+ 0.755,
+ 0.311
+ ],
+ "angle": 0,
+ "content": "5.6. Visualization and Analysis"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.318,
+ 0.907,
+ 0.515
+ ],
+ "angle": 0,
+ "content": "To intuitively show the robust embedding space that is refined by our approach, we plot the distribution of normalized similarity for CLIP and NCU on the validation set of CC3M. In Fig. 5, we illustrate similarity scores for positive pairs, mean of negative pairs, and top \\(5\\%\\) maximum of negative pairs. First, we observe that NCU produces a wider distribution of positive similarity scores, capturing more fine-grained matching degrees among positive pairs. Second, NCU improves the feature discrimination, which leads to a more significant separation between positive and negative pairs. Lastly, NCU provides more appropriate measures for hard negatives, which maintains separation from both positive and other negative pairs."
+ },
+ {
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+ "content": "6. Limitations and Future Works"
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+ "content": "Our work still has certain limitations due to the finite computing capability, including 1) This work only uses CLIP to explore the efficacy of NCU. Further research is needed to confirm its applicability in other VLMs, such as BLIP-2 [28], and even larger VLMs like VisionLLM [45] or InternVL [5]. 2) The current experiments are mainly conducted on million-scale data, and we plan to extend it to larger-scale datasets to verify NCU's generalization."
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+ "content": "7. Conclusion"
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+ "content": "This work provides a new thinking in robust vision-language learning. Instead of re-training models from scratch, we suggest eliminating the harmful effects of noisy correspondence from pre-trained models. To this end, we propose NCU, a robust fine-tuning framework that efficiently unlearns noisy correspondence in CLIP. Our key concept is to learn the hardest negative information that can provide explicit unlearning direction to resist both FP and FN. We formalize such twin goals unlearning process into one unified OT problem for fast fine-tuning. Extensive experiments are conducted to verify that NCU can endow CLIP with strong robustness against noisy correspondence."
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+ "content": "Acknowledgments"
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+ "content": "This work was supported in part by the Major Key Project of PCL under Grant PCL2025AS10 and PCL2024A06, and in part by the Shenzhen Science and Technology Program under Grant RCJC20231211085918010."
+ },
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+# Unlearning the Noisy Correspondence Makes CLIP More Robust
+
+Haochen Han1, Alex Jinpeng Wang12†, Peijun Ye1, Fangming Liu1†
+1 Peng Cheng Laboratory 2 Central South University
+
+# Abstract
+
+The data appetite for Vision-Language Models (VLMs) has continuously scaled up from the early millions to billions today, which faces an untenable trade-off with data quality and inevitably introduces Noisy Correspondence (NC) samples. Undoubtedly, such semantically unrelated data significantly impairs the performance of VLMs. Previous efforts mainly address this challenge by estimating refined alignment for more precise guidance. However, such resource-intensive pipelines that train VLMs from scratch struggle to meet realistic data demands. In this paper, we present a brand new perspective that seeks to directly eliminate the harmful effects of NC in pre-trained VLMs. Specifically, we propose NCU, a Noisy Correspondence Unlearning fine-tuning framework that efficiently enhances VLMs' robustness by forgetting learned noisy knowledge. The key to NCU is learning the hardest negative information, which can provide explicit unlearning direction for both false positives and false negatives. Such twin goals unlearning process can be formalized into one unified optimal transport objective for fast fine-tuning. We validate our approach with the prevailing CLIP model over various downstream tasks. Remarkably, NCU surpasses the robust pre-trained method on zero-shot transfer while with lower computational overhead. The code is available at https://github.com/hhc1997/NCU.
+
+# 1. Introduction
+
+The pursuit of general intelligence has driven progress in multimodal learning, which seeks to integrate and understand multiple sensory modalities like humans. Large-scale vision-language training, exemplified by CLIP [37], is seen as a key milestone in multimodal learning due to its remarkable transfer capabilities in real-world applications, such as image-text retrieval [13, 22, 34] and robotics control [41].
+
+However, much of their success can be attributed to scaling laws enabled by massive training data. As every coin has two sides, the insatiable demand for data forces a
+
+
+
+
+
+
+$\Delta$ Image
+$\bigcirc$ Text
+
+
+#
+Hardest Negative Text
+Figure 1. Illustration on the core concept of NCU. The twin goals unlearning process is guided by the learned hardest negative information. For the FP, $t_i^{Neg}$ directly pulls $v_i$ away from the mismatched $t_i$ . While for the FN, $t_i^{Neg}$ acts as a distance upper bound to facilitate modeling many-to-many relations.
+
+difficult trade-off between quantity and quality, which inevitably introduces noisy correspondence into the training set. Taking the CC3M dataset [39] as an example, despite being filtered from 500 million images, it still contains at least $3\%$ [20] unrelated image-text pairs, i.e., false positive. To make matters worse, training on massive data necessitates larger batch sizes (32K used in CLIP), which increases the likelihood of unpaired samples sharing semantic similarities, i.e., false negative. Undoubtedly, such two-aspects noisy correspondence can significantly impair the performance of vision-language models.
+
+To endow robustness against NC, one natural direction is to revise the pre-training paradigm [1, 3, 11, 12, 21] that supervises VLMs with refined alignment. However, existing methods require training from scratch and may rely on guidance from external large models [3, 11]. Such resource-intensive pipelines obviously struggle to face the realistic demand, especially with today's billion-scale datasets [38]. Hence, it is necessary to address the NC problem in vision-language training with a cost-effective method.
+
+In this paper, we think outside the box of robust pretraining and pose an important question: Can we directly
+
+To answer this question, we resort to machine unlearning [2] and present NCU, a Noisy Correspondence Unlearning fine-tuning framework that improves the robustness of CLIP by erasing learned noisy knowledge. Machine unlearning is a reversed learning process that aims to delete the influence of specific training samples from trained models. Despite its promise in widespread tasks [7, 9], unlearning the NC in VLMs remains unexplored due to a key challenge: the ambiguous forgetting direction would corrupt the learned semantic structure in the feature space. To address this, we propose to learn the hardest negative information that can provide explicit unlearning direction. As illustrated in Fig. 1, on the one hand, the negative information would directly serve as reliable supervision for forgetting false positives. On the other hand, it would facilitate the modeling of many-to-many relationships among unpaired data for forgetting false negatives. Then, we show that such twin goals unlearning process can be formalized as one unified optimal transport problem, which efficiently fine-tunes CLIP to resist both FP and FN.
+
+Our main contributions are highlighted below:
+
+- To the best of our knowledge, this work could be the first study to eliminate the harmful effects of noisy correspondence from pre-trained CLIP.
+- We propose the NCU framework, which efficiently unlearns FP and FN with explicit direction derived from the hardest negative information.
+- We demonstrate that NCU achieves significant improvements over CLIP on several downstream tasks and surpasses the previous robust pre-training method with lower computational overhead.
+
+# 2. Related Work
+
+Noisy Correspondence Learning. Noisy correspondence refers to the alignment error presented in multimodal data. The false positive is a typical NC problem, where irrelevant multimodal pairs are wrongly treated as matched. To alleviate this, several techniques have been developed in various multimodal applications, including cross-modal retrieval [16, 18, 20, 36], video temporal learning [17, 30], multimodal person re-identification [35, 47], question answering [23], and image captioning [10, 24]. In more complex scenarios, e.g., vision-language pre-training [19, 21], models also suffer from false negatives caused by the training paradigm [12], where similar unpaired samples are forced to be distant. Considering the computational burden of large VLMs, this work presents a low-carbon solution to directly improve the robustness of pre-trained VLMs.
+
+Contrastive Vision Language Models. Contrastive vision language models (VLMs) [8, 13, 14, 33, 44, 48] aim to learn visual representations by the corresponding textual
+
+supervision, which have attracted significant attention due to their simplicity and powerful representation capability. Pioneering works CLIP [37] and ALIGN [22] have shown great success via learning from massive image-text pairs. However, such web-crawled data are noisy [38, 42] and inevitably harm the efficacy of existing VLMs. To tackle this issue, a series of works attempted to train the VLM with refined soft image-text alignments by label smoothing [12], knowledge distillation [1], fine-grained intra-modal guidance [11], text rewriting [3], or positive-negative contrastive loss [21]. Besides, OT-based methods[40, 46] have also emerged as they naturally model such matching problems. Despite the success, previous works focus on training robust VLMs from scratch, which overlooks readily available pre-trained models and incurs unnecessary computational costs. To this end, this paper pioneers an efficient approach to enhance model robustness by unlearning noisy information from pre-trained models.
+
+Machine Unlearning. Recent advances in MU mainly focus on practical approximate unlearning, which seeks to mimic the behavior of a model re-trained from scratch. Driven by privacy concerns, existing MU works [7, 9, 32] in computer vision focus on image classification that attempts to forget specific classes. In parallel, MU has also become a popular topic in large language models due to its capability to eliminate harmful responses [31, 50]. However, multimodal forgetting remains under-explored in the literature. Pioneering works [26, 27] studied data-free class removal for CLIP's downstream image classification. To date, none of the existing MU methods has explored the unlearning of noisy concepts from VLMs.
+
+# 3. Preliminaries
+
+# 3.1. Contrastive Language-Image Pre-training
+
+CLIP is a vision-language model trained on millions of web-harvested image-text pairs. We consider a batch of $N$ image-text pairs $\{v_{i},t_{i}\}_{i = 1}^{N}$ sampled from a cross-modal dataset $\mathbb{D}$ , where $v_{i}$ and $t_i$ represent the raw image and corresponding text, respectively. The goal of CLIP is to train two modality-specific encoders that bring matched pairs closer while pushing unmatched ones apart. Specifically, image embedding $\pmb {v}_i\in \mathbb{R}^d$ and text embedding $t_i\in \mathbb{R}^d$ are obtained by passing $v_{i}$ and $t_i$ through the image encoder $f_{v}$ and text encoder $f_{t}$ , respectively, where $d$ is the embedding dimension. The encoded $l_{2}$ normalized embeddings are then aligned in the feature space by minimizing the contrastive objective, i.e., InfoNCE loss:
+
+$$
+\mathcal {L} _ {v \rightarrow t} ^ {C L} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \log \frac {\exp \left(\langle \boldsymbol {v} _ {i} , \boldsymbol {t} _ {i} \rangle / \tau\right)}{\sum_ {j = 1} ^ {N} \exp \left(\langle \boldsymbol {v} _ {i} , \boldsymbol {t} _ {j} \rangle / \tau\right)}, \tag {1}
+$$
+
+where $\langle \cdot \rangle$ represents the inner product and $\tau$ is a trainable temperature parameter. As InfoNCE loss is symmetric, we can define $\mathcal{L}_{t\to v}^{CL}$ similarly. The complete CLIP training objective is formulated as: $\mathcal{L}_{CLIP} = \mathcal{L}_{v\rightarrow t}^{CL} + \mathcal{L}_{t\rightarrow v}^{CL}$ .
+
+Despite its promising performance, the standard contrastive learning can suffer from the noisy correspondence problem in two aspects. First, the web-collected pairs inevitably contain an unknown portion of mismatched data, i.e., false positives. Second, hard target alignment neglects the potential semantic similarity among unpaired samples, i.e., false negatives, especially under large batch settings.
+
+# 3.2. Machine Unlearning
+
+Given a CLIP model (also named reference model) $\{f_v, f_t\}$ that is already trained on a cross-modal dataset $\mathbb{D}$ , machine unlearning aims to fine-tune the model to forget a specific subset $\mathbb{D}_{FG} \subseteq \mathbb{D}$ while maintaining effectiveness on the retained set $\mathbb{D}_{RT} = \mathbb{D} \setminus \mathbb{D}_{FG}$ . Ideally, the model should behave as if it were trained without any sample from $\mathbb{D}_{FG}$ . In principle, re-training the model from scratch on $\mathbb{D}_{RT}$ would serve as the gold standard. However, since CLIP is trained on massive-scale data, it is unrealistic to obtain a forget set that includes all noisy information, especially when some data are not publicly accessible. Therefore, we focus on an approximate unlearning approach in which $\mathbb{D} = \mathbb{D}_{FG} \cup \mathbb{D}_{RT}$ does not need to contain all training pairs, making the unlearning process more practical for real-world scenarios.
+
+The most straightforward method to unlearn is gradient ascent or its variants, which optimizes the negative prediction loss over the forget set. Another typical approach is performing forget loss that encourages the model to relearn the modified form of undesired data. For example, we can update CLIP by minimizing InfoNCE loss in pair $\{v_i,\tilde{t}_i\} \sim \mathbb{D}_{FG}$ to forget the relation between $v_{i}$ and $t_i$ where $\tilde{t}_i\neq t_i$ could be random or hand-crafted text to replace the original. Based on these, existing MU methods have shown promising progress in class forgetting and LLM privacy protection. However, applying these strategies to CLIP unlearning poses a key challenge: the ambiguous forgetting direction would corrupt the learned semantic structure in the feature space. In other words, the model forgets the undesired data by learning other meaningless patterns.
+
+# 4. Methodology
+
+To tackle the above issues, we introduce the Noisy Correspondence Unlearning (NCU) framework. In the following, we first introduce the division of forget and retained sets in Sec 4.1. Subsequently, we elaborate on learning the hardest negative information in Sec 4.2 and explain how to formalize the twin goals unlearning process into an optimal transport object for efficiently fine-tuning in Sec 2. The overall training pseudo-code is shown in Supplementary A.
+
+# 4.1. Identifying the Forget Set
+
+Unlike standard MU tasks with a predefined forget set, we need to manually identify mismatched samples from CLIP's training data to construct it. As pre-trained CLIP has shown strong representation capability, we propose using the basic similarity score to obtain $\mathbb{D}_{FG}$ and $\mathbb{D}_{RT}$ , i.e.,
+
+$$
+\omega_ {i} = \frac {1}{2} \left[ \frac {\exp \left(\left\langle \boldsymbol {v} _ {i} , \boldsymbol {t} _ {i} \right\rangle / \tau\right)}{\sum_ {j = 1} ^ {N} \exp \left(\left\langle \boldsymbol {v} _ {i} , \boldsymbol {t} _ {j} \right\rangle / \tau\right)} + \frac {\exp \left(\left\langle \boldsymbol {t} _ {i} , \boldsymbol {v} _ {i} \right\rangle / \tau\right)}{\sum_ {j = 1} ^ {N} \exp \left(\left\langle \boldsymbol {t} _ {i} , \boldsymbol {v} _ {j} \right\rangle / \tau\right)} \right]. \tag {2}
+$$
+
+By comparing $(v_{i},t_{i})$ with other cross-modal samples in the batch, $\omega_{i}$ serves as a clean confidence that measures the extent of semantic match. Then, we select pairs with the lowest $P\%$ of $\omega_{i}$ within the batch as false positives to construct the forget set $\mathbb{D}_{FG}$ , while treating the remaining in-batch pairs as the retained set $\mathbb{D}_{RT}$ .
+
+Note that $\mathbb{D}_{FG}$ and $\mathbb{D}_{RT}$ are dynamically selected at each batch, which enjoys two merits: 1) CLIP could be efficiently updated with one intra-batch optimization; 2) The forget-retain ratio could be flexibly adjusted through the predefined parameter $P$ .
+
+# 4.2. Learning Hardest Negative Semantics
+
+To guide CLIP with an explicit unlearning direction, we aim to learn the hardest negative semantics as supervision. Intuitionally, for an irrelevant pair $(v_{i},t_{i})$ that misleads the model with $v_{i}$ and $t_i$ are matched', we encourage the model to forget this information by relearning that $v_{i}$ and $t_i$ are not matched'. From a data utilization viewpoint, this paradigm is similar to negative learning[25] that supervises the model with complementary information [18], i.e., pushing the candidate away from other unpaired samples. Differently, our method seeks the hardest negative information to avoid uncertain optimization directions.
+
+To achieve this, we incorporate a set of learnable vectors to represent the textual negative semantics inspired by prompt learning [51]. Specifically, for any training pair $(v_{i},t_{i})$ , the token features of $t_i$ are combined with $m$ shared prompt vectors to present the corresponding negative semantics $t_i^{Neg}$ in the feature space. While such prompt-driven semantic negation of CLIP has demonstrated success in out-of-distribution detection [29, 43], existing methods are confined to closed-set downstream tasks with limited category concepts. In contrast, our challenge lies in extending the semantic opposite operation into the open-set knowledge that CLIP pre-trained.
+
+Intuitively, the hardest negative satisfies two constraints in the feature space: 1) $t_i^{Neg}$ needs to maximize its distance from $v_i$ and $t_i$ ; 2) $t_i^{Neg}$ should maintain certain similarity to those unpaired images, as it is not a wrong description [43] despite being semantically irrelevant to $v_j$ . Furthermore, we only use $\mathbb{D}_{RT}$ to learn the prompt tokens to avoid overfitting caused by noisy correspondence. For notation simplicity,
+
+
+(a). Maximize $L_{2}$ -distance
+
+
+(b). Similarity Bound
+Figure 2. Illustration of the optimization objective to learn the hardest negative semantics. (a) Previous attempts that directly maximize the $L_{2}$ distance prevent $\pmb{t}_{i}^{Neg}$ from providing certain guidance for unpaired images, e.g., $\pmb{v}_{k}$ . (b) We bound the similarity with margins for a more relaxed semantic separation, but it may lead to uncertain targets, e.g., $\pmb{t}_{i}^{Neg}$ and $\pmb{t}_{i}^{Neg'}$ . (c) We further preserve relation structures for precise objectives. The intuition is that the opposite text should also maintain semantic relationships, e.g., $\langle \pmb{t}_i,\pmb{t}_j^{Neg}\rangle \approx \langle \pmb{t}_j,\pmb{t}_i^{Neg}\rangle$
+
+
+(c). Relation Opposite
+
+we denote $\tilde{N}$ as the size of $\mathbb{D}_{RT}$ within each batch. Based on the above insights, we propose the following intra-modal and cross-modal training objectives.
+
+Text Relation Opposite. It encourages semantic separation between the embeddings of negative text and its original. Most previous works [29, 43] typically reduce the per-instance similarity gap among textual pairs, e.g., $\| t_i - t_i^{Neg}\| _2\to 2$ [43] to directly maximize its $L_{2}$ distance. However, such rigid constraint incurs a crucial limitation in the open-set semantic space—enforcing maximal distance pushes $t_i^{Neg}$ away from unpaired images (Fig. 2(a)), which is contrary to our objective. To this end, we propose a relaxed similarity bound to constrain the semantic separation:
+
+$$
+\mathcal {L} ^ {s e p} = \frac {1}{\tilde {N}} \sum_ {i = 1} ^ {\tilde {N}} \left(\left[ \alpha - \langle \boldsymbol {t} _ {i}, \boldsymbol {t} _ {i} ^ {N e g} \rangle \right] _ {+} + \left[ \langle \boldsymbol {t} _ {i}, \boldsymbol {t} _ {i} ^ {N e g} \rangle - \beta \right] _ {+}\right), \tag {3}
+$$
+
+where $\alpha < 0$ and $\beta < 0$ are the margin parameters to locate $\langle t_i, t_i^{Neg} \rangle \in [\alpha, \beta]$ , and $[x]_+ = \max(x, 0)$ is the hinge function. As illustrated in Fig. 2(b), although minimizing Eq.(3) enables $t_i^{Neg}$ to be distant from $t_i$ while remaining relatively similar to unpaired images, the broad range of variations makes training convergence difficult. To address this issue, we propose to perform semantic opposite at the relation level instead of the instance level, which is achieved by preserving the geometrical structures among all negative and original text within the batch:
+
+$$
+\mathcal {L} ^ {r e l} = \frac {1}{\tilde {N}} \sum_ {i = 1} ^ {\tilde {N}} \sum_ {j = 1} ^ {\tilde {N}} \left(\left\langle \boldsymbol {t} _ {i}, \boldsymbol {t} _ {j} ^ {N e g} \right\rangle - \left\langle \boldsymbol {t} _ {j}, \boldsymbol {t} _ {i} ^ {N e g} \right\rangle\right) ^ {2}. \tag {4}
+$$
+
+As shown in Fig. 2(c), regularizing the negative-original relation consistency can guide $t_i^{Neg}$ toward a precise location in the feature space.
+
+Image-text Matching Opposite. It aims to model the alignment between the embeddings of negative text and images. As discussed, $t_i^{Neg}$ provides positive supervision to unpaired images while separating from its paired image, which presents opposite matching patterns to the normal contrastive objective. To achieve this, we take inspiration from Sigmoid loss [49] that efficiently supports such multi-positive alignment. Specifically, it guides per cross-modal pair independently by the binary matching target:
+
+$$
+\begin{array}{l} \mathcal {L} ^ {i t m} = \frac {1}{\tilde {N}} \sum_ {i = 1} ^ {\tilde {N}} \sum_ {j = 1} ^ {\tilde {N}} \left(\log \frac {1}{1 + \exp \left(m _ {i j} \left(- \langle \boldsymbol {t} _ {i} , \boldsymbol {v} _ {j} \rangle / \tau\right)\right)} \right. \tag {5} \\ + \log \frac {1}{1 + \exp (- m _ {i j} (- \langle \pmb {t} _ {i} ^ {N e g} , \pmb {v} _ {j} \rangle / \tau))}, \\ \end{array}
+$$
+
+where $m_{ij}$ equals 1 for $i = j$ and $-1$ for $i\neq j$ . In Eq.(5), the first part follows the standard one-to-one matching to retain the original CLIP knowledge, while the second part utilizes the opposite binary target, i.e., $-m_{ij}$ , to bring $t_i^{Neg}$ closer to multiple images.
+
+With the visual encoder frozen, the overall loss for learning the hardest negative semantics is balanced by a scaling factor $\lambda$ and given by:
+
+$$
+\mathcal {L} ^ {H N} = \lambda \left(\mathcal {L} ^ {s e p} + \mathcal {L} ^ {r e l}\right) + \mathcal {L} ^ {i t m}. \tag {6}
+$$
+
+# 4.3. Hardest-Negative Guided Noise Unlearning
+
+The hardest negative semantics serve dual purposes in erasing the learned noisy correspondence: 1) guide CLIP to unlearn the false positive pair $(v_{i},t_{i})$ by matching $v_{i}$ with $t_i^{Neg}$ . 2) While for the well-matched pair $(v_{i},t_{i})$ , $t_i^{Neg}$ assists in inferring the soft alignment among unpaired data to unlearn the false negative pattern. To efficiently fine-tune CLIP, we formalize such twin goals unlearning process into one unified Optimal Transport problem.
+
+Optimal Transport. OT seeks to establish a flexible alignment between images and captions by computing a
+
+
+Figure 3. Overview of the Noisy Correspondence Unlearning process. With the learned negative prompt frozen, we formulate an optimal transport problem guided by the hardest negative and then use the solved transport plan to robustly fine-tune the model $f_{t}$ and $f_{v}$ .
+
+minimal-cost transport plan, where the cost refers to the expense of transporting mass from source to target distribution and is generally set to a distance measure [15]. Let $\mathbf{C} \in \mathbb{R}_{+}^{N \times N}$ denotes the cost matrix for the mini-batch, where $[\mathbf{C}]_{i,j} = 1 - \langle \mathbf{v}_i, \mathbf{t}_j \rangle$ is the cosine distance of $v_i$ and $t_j$ . $\Gamma \in \mathbb{R}_{+}^{N \times N}$ denotes the corresponding transport plan that $[\Gamma]_{i,j}$ represents the alignment probability between $v_i$ and $t_j$ . Formally, the objective of OT is defined as follows:
+
+$$
+\min _ {\Gamma \in \Pi (\pmb {\mu}, \pmb {\nu})} \langle \Gamma , \pmb {C} \rangle - \epsilon H (\Gamma)
+$$
+
+$$
+\mathrm {s . t .} \Pi (\boldsymbol {\mu}, \boldsymbol {\nu}) = \left\{\boldsymbol {\Gamma} \in \mathbb {R} _ {+} ^ {N \times N} \mid \boldsymbol {\Gamma} \mathbb {1} _ {N} = \boldsymbol {\mu}, \boldsymbol {\Gamma} ^ {\top} \mathbb {1} _ {N} = \boldsymbol {\nu} \right\},
+$$
+
+where $\mathbb{1}_N$ denotes a $N$ -dimensional all-one vector, $\mu, \nu \in \mathbb{R}^N$ are probability measures representing the relative importance of each image and caption. Without prior knowledge, $\mu = \frac{1}{N}\mathbb{1}_N$ and $\nu = \frac{1}{N}\mathbb{1}_N$ are considered to be uniformly distributed since each pair is sampled independently. $H(\Gamma)$ is an additional entropy regularizer controlled by the smooth parameter $\epsilon$ , which enables the OT objective to be solved by the rapid Sinkhorn-Knopp algorithm [6].
+
+Boosting OT via Hardest Negatives. To endow the transport plan with dual forgetting purposes, we reformulate Eq.(7) by imposing guidance from the hardest negative information. Specifically, for each image $v_{i}$ , we extend its transport target from $\{t_i\}_{i = 1}^N$ to include its paired negative text $t_i^{Neg}$ . As shown in Fig. 3, the negative text composes a new alignable column for the transport objective, which append the cost matrix $C$ to $\bar{C} \in \mathbb{R}_+^{N\times (N + 1)}$ , i.e.,
+
+$$
+[ \bar {\boldsymbol {C}} ] _ {i, N + 1} = 1 - \langle \pmb {v} _ {i}, \pmb {t} _ {i} ^ {N e g} \rangle , [ \bar {\boldsymbol {C}} ] _ {i, j} = [ \pmb {C} ] _ {i, j}, \forall i, j \in [ 1, N ].
+$$
+
+For the two parts $\mathbb{D}_{FG}$ and $\mathbb{D}_{RT}$ within each batch, the hardest negative should impose different guidance for distinct unlearning goals. To this end, we propose a maskbase constraint to the corresponding transport plan $\bar{\Gamma}$ that regulates the effect of $t_i^{Neg}$ . Specifically, the mask matrix
+
+$M\in \mathbb{R}_{+}^{N\times (N + 1)}$ satisfies that
+
+$$
+[ M ] _ {i, j} = \left\{ \begin{array}{l l} 0, & \text {i f} (v _ {i}, t _ {i}) \in \mathbb {D} _ {F G} \text {a n d} j = i, \\ 0, & \text {i f} (v _ {i}, t _ {i}) \in \mathbb {D} _ {R T} \text {a n d} j = N + 1, \\ 1, & \text {o t h e r w i s e .} \end{array} \right. \tag {8}
+$$
+
+For the toy example illustrated in Fig. 3, if the pair is considered to be mismatched, the transport mass between $v_{i}$ and $t_{i}$ should be constrained to zero. Conversely, for the well-matched pair, $t_{i}^{Neg}$ acts as a lower limit where the transport mass between $v_{i}$ and $t_{j}$ should be higher than it. Following the solver from [15], we model the mask constraint as the Hadamard product form that $\hat{\Gamma} = M \odot \bar{\Gamma}$ , and the optimal alignment is formulated as (detailed Sinkhorn solution is presented in Supplementary B):
+
+$$
+\hat {\Gamma} ^ {*} = \underset {\hat {\Gamma} \in \Pi (\mu , \bar {\nu})} {\arg \min } \left\langle \hat {\Gamma}, \bar {C} \right\rangle - \epsilon H (\hat {\Gamma}), \tag {9}
+$$
+
+where $\bar{\nu} = \frac{1}{N + 1}\mathbb{1}_{N + 1}$ to satisfy the additional column.
+
+The Unlearning Objective. Although $\hat{\Gamma}^*$ provides the more refined alignment, we suggest further incorporating an identity-like matrix $\pmb{I}$ for two merits. First, diagonal elements are set as 1 for true positives to retain the initial alignment. Second, $[I]_{i,N + 1} = 1$ to enhance the unlearning for the possible false positive $(v_{i},t_{i})\in \mathbb{D}_{FG}$ . Thus, the overall alignment balanced by the factor $\gamma$ is defined as:
+
+$$
+\boldsymbol {T} = \gamma \hat {\boldsymbol {\Gamma}} ^ {*} + (1 - \gamma) \boldsymbol {I}. \tag {10}
+$$
+
+To fine-tune CLIP with this soft alignment, we use the KL divergence to optimize the matching distribution. Formally, we denote the batched similarity matrix as $\pmb{P} \in \mathbb{R}^{N \times (N + 1)}$ where $P_{i} = [\langle v_{i}, t_{1} \rangle, \dots, \langle v_{i}, t_{N} \rangle, \langle v_{i}, t_{i}^{Neg} \rangle]^{\top}$ . We obtain $P_{i}^{v2t}$ and $P_{i}^{t2v}$ by applying row-wise and column-wise softmax operation to $P$ , respectively. Correspondingly, let $T_{i}^{v2t}$ and $T_{i}^{t2v}$ be the row-wise and column-wise normalized refined alignment for the $i$ -th sample, respectively. The
+
+OT-guided re-aligning is defined as:
+
+$$
+\mathcal {L} ^ {o t r} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mathrm {K L} \left(\boldsymbol {T} _ {i} ^ {v 2 t} \| \boldsymbol {P} _ {i} ^ {v 2 t}\right) + \frac {1}{N + 1} \sum_ {i = 1} ^ {N + 1} \mathrm {K L} \left(\boldsymbol {T} _ {i} ^ {t 2 v} \| \boldsymbol {P} _ {i} ^ {t 2 v}\right). \tag {11}
+$$
+
+Moreover, we empirically observe that preserving the textual semantic separation term can make the unlearning more stable. Thus, the final unlearning objective is defined as:
+
+$$
+\mathcal {L} ^ {U L} = \mathcal {L} ^ {o t r} + \mathcal {L} ^ {s e p}. \tag {12}
+$$
+
+# 5. Experiment
+
+In this section, we experimentally analyze the effectiveness of NCU in unlearning the NC knowledge from CLIP.
+
+# 5.1. Setup
+
+Datasets. Our experiments are conducted on three vision-language datasets at different scales and noise: Conceptual Captions 3M (CC3M) [39], Conceptual Captions 12M (CC12M) [4], and YFCC15M-R (provided by [14], an LLM-recaptioned subset from the YFCC100M [42]). All datasets are web-crawled and contain an unknown portion of NC pairs, e.g., CC3M is estimated to include at least $3\%$ false positives. We evaluate NCU on ImageNet and 15 common downstream datasets for classification performance and on MSCOCO and Flickr30K for retrieval capability. Details for datasets are shown in Supplementary C.
+
+Unlearning Details. Following CLIP, we consider two architectures for the image encoder, i.e., ViT/B16 and ViT/B32, while the text encoder adopts the transformer architecture. We consider a CLIP pre-trained on dataset $\mathbb{D}$ , e.g., CC3M, CC12M, or YFCC15M-R, as our reference model, then we perform the NC unlearning on $\mathbb{D}$ or its subset to enhance CLIP's robustness. For all experiments, we allocate 2 epochs for learning negative semantics and 8 epochs for noise unlearning. All models are trained with a batch size of 2,048 on 16 NVIDIA V100 GPUs. Detailed training settings are presented in Supplementary D.
+
+Evaluation Protocol. We evaluate NCU's transferability with Zero-Shot (ZS) classification accuracy and Linear Probing (LP) accuracy. For ZS classification, we follow CLIP's [37] prompt templates to compute distances between class text embeddings and image features. For LP, we follow the mainstream setting [8, 37] that trains a linear classifier using L-BFGS on features extracted from the frozen image encoder. Besides, we evaluate the retrieval performance with the Recall at rank K (R@K) metric.
+
+# 5.2. Evaluation on Diverse Downstream Tasks
+
+To verify the generalization of NCU, we compare it with CLIP on three different types of downstream tasks.
+
+Zero-Shot Transfer. We compare the zero-shot performance of CLIP and NCU on 16 popular image classification datasets. We follow the prompt templates suggested in the CLIP paper [37] to form each class name into a natural sentence. As demonstrated in Tab. 1, our NCU approach significantly outperforms the baseline CLIP model on both ImageNet and other downstream datasets. Specifically, across all fine-tuning datasets and all model architectures, NCU gains in the range of $2.8\% \sim 4.1\%$ in top-1 accuracy on ImageNet and $2.5\% \sim 4.0\%$ on average over the other downstream datasets. This reveals that NCU can successfully eliminate the impact of NC on CLIP by robust fine-tuning with the same dataset.
+
+Image-Text Retrieval. We present the zero-shot cross-modal retrieval performance on the testing set of Flickr30K (1K) and MSCOCO (5K) in Tab. 2. Our method considerably outperforms the vanilla CLIP in almost all cases. For instance, when fine-tuning CLIP (ViT-B/32) pre-trained on the CC3M dataset, our NCU method achieves a $7.7\%$ improvement in average recall scores on Flickr30K and $4.8\%$ improvement in average recall scores on MSCOCO. This finding indicates that NCU can remarkably enhance the alignment of images and text in the embedding space.
+
+Linear Probing. Tab. 3 reports the linear probing performance on 4 representative downstream datasets. Our NCU consistently surpasses CLIP in the vast majority of cases, suggesting that the visual embeddings learned by our NCU are more effective and transferable than CLIP.
+
+# 5.3. Compared to Robust Methods
+
+In this section, we compare NCU with other robust-designed techniques against NC on zero-shot ImageNet1K classification task, i.e., gradient ascent (GA), and SoftCLIP [11]. Specifically, we evaluate GA as a standalone method, where $-\mathcal{L}_{CLIP}$ is performed on $\mathbb{D}_{FG}$ for handling FPs and $\mathcal{L}_{CLIP}$ with label smoothing is performed on $\mathbb{D}_{RT}$ for FNs. SoftCLIP is a noise-robust SOTA method that trains CLIP from scratch by additional intra-modal guided alignment, i.e., ROI features. As shown in Tab. 4, although GA is a naive unlearning strategy, it still achieves observable performance gains. Meanwhile, SoftCLIP's self-similarity modeling fails to excavate supervision from false positives, which may explain why it performs worse than GA in some cases, e.g., CC12M with ViT-B/32. By contrast, our NCU achieves solid improvements by forgetting both false positives and false negatives, outperforming SoftCLIP by $1.1\% \sim 2.3\%$ without external guidance.
+
+# 5.4. Ablation Study
+
+To investigate the effectiveness of specific components in our method, we carry out some ablation studies on Ima-
+
+| Dataset | Model | Caltech101 | CIFAR-10 | CIFAR-100 | DTD | Aircraft | SST2 | Flowers102 | Food101 | GTSRB | OxfordPeds | RESISC45 | SUN397 | EuroSAT | StanfordCars | STL10 | Average | ImageNet1K |
| Model Architecture: ViT-B/16 |
| CC3M | CLIP | 52.3 | 55.2 | 24.1 | 10.9 | 1.0 | 50.1 | 11.9 | 11.1 | 6.9 | 12.9 | 19.5 | 25.0 | 13.5 | 0.8 | 81.7 | 25.1 | 16.0 |
| NCU | 59.1 | 54.3 | 28.8 | 12.3 | 1.1 | 50.1 | 14.1 | 14.8 | 7.4 | 16.3 | 22.8 | 32.3 | 21.7 | 1.5 | 86.3 | 28.2↑3.1 | 20.0↑4.0 |
| CC12M | CLIP | 77.0 | 66.5 | 38.3 | 21.2 | 2.5 | 47.7 | 33.4 | 51.9 | 7.3 | 64.2 | 39.0 | 44.7 | 21.2 | 25.5 | 91.4 | 42.1 | 40.6 |
| NCU | 80.9 | 79.3 | 49.1 | 23.2 | 2.7 | 48.0 | 31.7 | 52.7 | 10.1 | 66.5 | 41.9 | 52.6 | 28.6 | 29.0 | 93.2 | 46.0↑3.9 | 43.4↑2.8 |
| Model Architecture: ViT-B/32 |
| CC3M | CLIP | 47.7 | 54.2 | 18.0 | 7.6 | 1.2 | 50.1 | 9.3 | 9.1 | 6.0 | 7.4 | 16.2 | 16.0 | 15.5 | 0.8 | 77.7 | 22.5 | 11.8 |
| NCU | 53.0 | 56.7 | 25.9 | 10.4 | 1.7 | 50.1 | 10.2 | 10.5 | 6.5 | 10.5 | 19.0 | 22.2 | 16.7 | 1.4 | 80.1 | 25.0↑2.5 | 14.6↑2.8 |
| CC12M | CLIP | 76.3 | 68.2 | 35.2 | 16.1 | 2.8 | 50.1 | 29.3 | 37.6 | 6.4 | 54.1 | 30.1 | 39.2 | 22.5 | 14.8 | 90.8 | 38.2 | 33.8 |
| NCU | 80.4 | 68.5 | 41.4 | 19.3 | 2.6 | 52.8 | 28.6 | 43.4 | 7.2 | 62.4 | 35.7 | 48.3 | 31.3 | 18.1 | 92.5 | 42.2↑4.0 | 36.7↑2.9 |
| YFCC15M-R | CLIP | 53.7 | 67.0 | 34.4 | 13.1 | 1.1 | 49.3 | 22.1 | 18.6 | 11.0 | 13.5 | 20.3 | 29.3 | 23.0 | 1.7 | 83.7 | 29.5 | 17.8 |
| NCU | 58.2 | 69.5 | 37.8 | 15.3 | 1.8 | 49.9 | 29.2 | 23.7 | 11.2 | 16.1 | 23.1 | 34.0 | 23.3 | 1.8 | 86.7 | 32.1↑2.6 | 21.9↑4.1 |
+
+Table 1. Zero-shot transfer evaluation of different models.
+
+| Dataset | Architecture | Model | Flickr30K 1K Testing | MSCOCO 5K Testing |
| Image-to-Text | Text-to-Image | Average | Image-to-Text | Text-to-Image | Average | |
| R@1 | R@5 | R@10 | R@1 | R@5 | R@10 | R@1 | R@5 | R@10 | R@1 | R@5 | R@10 | |
| CC3M | ViT-B/16 | CLIP | 27.6 | 54.2 | 65.8 | 19.0 | 40.5 | 51.3 | 43.1 | 12.8 | 30.9 | 42.7 | 9.7 | 25.4 | 35.2 | 26.1 | |
| NCU | 32.1 | 60.7 | 71.9 | 25.2 | 49.5 | 61.0 | 50.1↑7.0 | 15.8 | 36.9 | 48.4 | 12.1 | 29.7 | 40.1 | 30.5↑4.4 | |
| ViT-B/32 | CLIP | 14.0 | 35.2 | 47.7 | 11.5 | 27.9 | 37.8 | 29.0 | 7.0 | 20.1 | 28.9 | 6.0 | 16.7 | 24.0 | 17.1 | |
| NCU | 21.3 | 44.5 | 55.7 | 15.7 | 36.3 | 46.4 | 36.7↑7.7 | 10.7 | 25.7 | 35.4 | 8.1 | 21.3 | 30.2 | 21.9↑4.8 | |
| CC12M | ViT-B/32 | CLIP | 50.3 | 77.2 | 85.9 | 37.9 | 64.8 | 74.2 | 65.1 | 26.8 | 54.0 | 65.9 | 20.0 | 42.4 | 54.2 | 43.9 | |
| NCU | 53.0 | 77.3 | 85.0 | 38.4 | 66.6 | 76.7 | 66.2↑1.1 | 28.2 | 54.7 | 66.7 | 20.0 | 42.8 | 54.3 | 44.5↑0.6 | |
| YFCC15M-R | ViT-B/32 | CLIP | 57.4 | 81.6 | 89.1 | 40.8 | 66.4 | 75.4 | 68.5 | 35.0 | 60.9 | 71.8 | 22.6 | 46.0 | 58.0 | 49.1 | |
| NCU | 58.0 | 83.2 | 89.7 | 42.5 | 69.9 | 78.8 | 70.4↑1.9 | 34.3 | 62.0 | 73.5 | 24.6 | 49.0 | 60.8 | 50.7↑1.6 | |
+
+Table 2. Zero-shot cross-modal retrieval evaluation of different models.
+
+| Dataset | Architecture | Model | SUN397 | OxfordPeds | Food101 | ImageNet |
| CC3M | ViT-B/16 | CLIP | 54.38 | 62.20 | 54.36 | 48.13 |
| NCU | 55.60 | 62.85 | 54.74 | 49.90 |
| ViT-B/32 | CLIP | 46.96 | 52.30 | 46.96 | 40.20 |
| NCU | 48.20 | 52.82 | 46.85 | 41.49 |
| CC12M | ViT-B/16 | CLIP | 70.94 | 82.83 | 78.99 | 66.70 |
| NCU | 71.36 | 84.76 | 79.18 | 66.65 |
| ViT-B/32 | CLIP | 66.05 | 78.41 | 70.12 | 59.19 |
| NCU | 66.63 | 78.63 | 70.76 | 60.34 |
| YFCC15M-R | ViT-B/32 | CLIP | 60.46 | 61.90 | 59.09 | 51.07 |
| NCU | 60.75 | 62.85 | 60.46 | 52.29 |
+
+geNet1K with models unlearned on CC3M. We first ablate the contributions of two key components of NCU, i.e., negative prompt and text relation opposite. Specifically, in the variant $\nu_{1}$ , we replace the learnable prompt tokens by preponding some textual negative prefixes to raw captions, e.g., 'the image has no' or 'this picture lacks'. In the variant $\nu_{2}$ , we use maximal $L_{2}$ distance loss [43] as a substitute for our text relation opposite. Besides, we validate the impact of different NC unlearning by intervening with the refined
+
+Table 3. Linear probing comparison of different models.
+
+| Dataset | Model | Model Architecture | ImageNet1K ZS top-1 |
| CC3M | CLIP | ViT-B/16 | 16.0 |
| Gradient Ascent | 16.7 ↑0.7 |
| SoftCLIP | 18.9 ↑2.9 |
| NCU | 20.0 ↑4.0 |
| CC3M | CLIP | ViT-B/32 | 11.8 |
| Gradient Ascent | 12.1 ↑0.3 |
| SoftCLIP | 13.3 ↑1.5 |
| NCU | 14.6 ↑2.8 |
| CC12M | CLIP | ViT-B/16 | 40.6 |
| Gradient Ascent | 41.6 ↑1.0 |
| SoftCLIP | 42.1 ↑1.5 |
| NCU | 43.4 ↑2.8 |
| CC12M | CLIP | ViT-B/32 | 33.8 |
| Gradient Ascent | 35.1 ↑1.3 |
| SoftCLIP | 34.4 ↑0.6 |
| NCU | 36.7 ↑2.9 |
+
+Table 4. Zero-shot top-1 performance on ImageNet1K.
+
+alignment, i.e., $\mathcal{V}_3$ and $\mathcal{V}_4$ . As shown in Tab. 5, we observe that: 1) Using negative textual prefixes also shows competitive results, demonstrating the generalization of our method. However, we argue that the learnable prompt is preferable, except for performance gains, operating to features makes
+
+| Model | ImageNet1K ZS top-1 |
| ViT-B/16 | ViT-B/32 |
| NCU | 20.0 | 14.6 |
| V1 (w/o Hardest Negative Prompts) | 19.3 ↓0.7 | 14.4 ↓0.2 |
| V2 (w/o Text Relation Opposite) | 18.8 ↓1.2 | 13.9 ↓0.7 |
| V3 (w only False Negatives Unlearning) | 17.7 ↓2.3 | 13.5 ↓1.1 |
| V4 (w only False Positives Unlearning) | 19.2 ↓0.8 | 14.3 ↓0.3 |
+
+Table 5. Ablation studies on zero-shot transfer task (ImageNet1K) of models unlearned on CC3M.
+
+it possible for NCU to extend to modalities beyond text. 2) Simply maximizing the distance between negative and original text embeddings leads to suboptimal performance, which aligns with our analysis in Fig. 2. 3) Both types of NC impair CLIP's performance, among which the false positive causes a more severe impact. While NCU achieves the best performance by forgetting such noisy knowledge.
+
+
+Figure 4. Effect of NCU with varying fine-tuning dataset sizes on zero-shot image classification and cross-modal retrieval.
+
+# 5.5. NC Unlearning with Partial Data
+
+In this section, we conduct an interesting study to verify whether CLIP can improve robustness by only unlearning NC with a portion of the pre-trained data. To this end, given a CLIP pre-trained on CC3M as the reference model, we evaluate NCU using different data portions ranging from 0.5 million to 3 million image-text pairs. Fig. 4 plots the ZS top-1 accuracy on ImageNet1K and the average of recalls on MSCOCO 5K. Remarkably, even when unlearning on less than $20\%$ of the original data (0.5M), NCU achieves significant performance gains while preserving overall knowledge learned in CC3M. With the accessible data increasing, NCU shows consistent improvements on both zero-shot downstream tasks. This phenomenon indicates NCU's flexibility in enhancing the robustness of models with limited data, which is valuable to handling VLMs pre-trained with partially private or proprietary data.
+
+
+(a) NCU
+Figure 5. Similarity scores distribution of positive and negative pairs from CLIP and NCU. Both models are based on ViT/B16 and learning from the CC3M training set.
+
+
+(b) CLIP
+
+# 5.6. Visualization and Analysis
+
+To intuitively show the robust embedding space that is refined by our approach, we plot the distribution of normalized similarity for CLIP and NCU on the validation set of CC3M. In Fig. 5, we illustrate similarity scores for positive pairs, mean of negative pairs, and top $5\%$ maximum of negative pairs. First, we observe that NCU produces a wider distribution of positive similarity scores, capturing more fine-grained matching degrees among positive pairs. Second, NCU improves the feature discrimination, which leads to a more significant separation between positive and negative pairs. Lastly, NCU provides more appropriate measures for hard negatives, which maintains separation from both positive and other negative pairs.
+
+# 6. Limitations and Future Works
+
+Our work still has certain limitations due to the finite computing capability, including 1) This work only uses CLIP to explore the efficacy of NCU. Further research is needed to confirm its applicability in other VLMs, such as BLIP-2 [28], and even larger VLMs like VisionLLM [45] or InternVL [5]. 2) The current experiments are mainly conducted on million-scale data, and we plan to extend it to larger-scale datasets to verify NCU's generalization.
+
+# 7. Conclusion
+
+This work provides a new thinking in robust vision-language learning. Instead of re-training models from scratch, we suggest eliminating the harmful effects of noisy correspondence from pre-trained models. To this end, we propose NCU, a robust fine-tuning framework that efficiently unlearns noisy correspondence in CLIP. Our key concept is to learn the hardest negative information that can provide explicit unlearning direction to resist both FP and FN. We formalize such twin goals unlearning process into one unified OT problem for fast fine-tuning. Extensive experiments are conducted to verify that NCU can endow CLIP with strong robustness against noisy correspondence.
+
+# Acknowledgments
+
+This work was supported in part by the Major Key Project of PCL under Grant PCL2025AS10 and PCL2024A06, and in part by the Shenzhen Science and Technology Program under Grant RCJC20231211085918010.
+
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+ "content": "Noisy Correspondence Learning. Noisy correspondence refers to the alignment error presented in multimodal data. The false positive is a typical NC problem, where irrelevant multimodal pairs are wrongly treated as matched. To alleviate this, several techniques have been developed in various multimodal applications, including cross-modal retrieval [16, 18, 20, 36], video temporal learning [17, 30], multimodal person re-identification [35, 47], question answering [23], and image captioning [10, 24]. In more complex scenarios, e.g., vision-language pre-training [19, 21], models also suffer from false negatives caused by the training paradigm [12], where similar unpaired samples are forced to be distant. Considering the computational burden of large VLMs, this work presents a low-carbon solution to directly improve the robustness of pre-trained VLMs."
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+ "content": "minimal-cost transport plan, where the cost refers to the expense of transporting mass from source to target distribution and is generally set to a distance measure [15]. Let "
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+ "content": " denotes the corresponding transport plan that "
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+ "content": " represents the alignment probability between "
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+ "type": "text",
+ "content": ". Formally, the objective of OT is defined as follows:"
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+ "content": "\\min _ {\\Gamma \\in \\Pi (\\pmb {\\mu}, \\pmb {\\nu})} \\langle \\Gamma , \\pmb {C} \\rangle - \\epsilon H (\\Gamma)",
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+ "content": "\\mathrm {s . t .} \\Pi (\\boldsymbol {\\mu}, \\boldsymbol {\\nu}) = \\left\\{\\boldsymbol {\\Gamma} \\in \\mathbb {R} _ {+} ^ {N \\times N} \\mid \\boldsymbol {\\Gamma} \\mathbb {1} _ {N} = \\boldsymbol {\\mu}, \\boldsymbol {\\Gamma} ^ {\\top} \\mathbb {1} _ {N} = \\boldsymbol {\\nu} \\right\\},",
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+ {
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+ "content": " are probability measures representing the relative importance of each image and caption. Without prior knowledge, "
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+ "type": "text",
+ "content": " are considered to be uniformly distributed since each pair is sampled independently. "
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+ "content": ", which enables the OT objective to be solved by the rapid Sinkhorn-Knopp algorithm [6]."
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+ "content": "Boosting OT via Hardest Negatives. To endow the transport plan with dual forgetting purposes, we reformulate Eq.(7) by imposing guidance from the hardest negative information. Specifically, for each image "
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+ "content": "[ \\bar {\\boldsymbol {C}} ] _ {i, N + 1} = 1 - \\langle \\pmb {v} _ {i}, \\pmb {t} _ {i} ^ {N e g} \\rangle , [ \\bar {\\boldsymbol {C}} ] _ {i, j} = [ \\pmb {C} ] _ {i, j}, \\forall i, j \\in [ 1, N ].",
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+ "type": "text",
+ "content": " within each batch, the hardest negative should impose different guidance for distinct unlearning goals. To this end, we propose a maskbase constraint to the corresponding transport plan "
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+ "content": "[ M ] _ {i, j} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} (v _ {i}, t _ {i}) \\in \\mathbb {D} _ {F G} \\text {a n d} j = i, \\\\ 0, & \\text {i f} (v _ {i}, t _ {i}) \\in \\mathbb {D} _ {R T} \\text {a n d} j = N + 1, \\\\ 1, & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {8}",
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+ "content": "For the toy example illustrated in Fig. 3, if the pair is considered to be mismatched, the transport mass between "
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+ "content": " should be constrained to zero. Conversely, for the well-matched pair, "
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+ "content": " acts as a lower limit where the transport mass between "
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+ "type": "text",
+ "content": " should be higher than it. Following the solver from [15], we model the mask constraint as the Hadamard product form that "
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+ "type": "text",
+ "content": ", and the optimal alignment is formulated as (detailed Sinkhorn solution is presented in Supplementary B):"
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+ "content": "\\hat {\\Gamma} ^ {*} = \\underset {\\hat {\\Gamma} \\in \\Pi (\\mu , \\bar {\\nu})} {\\arg \\min } \\left\\langle \\hat {\\Gamma}, \\bar {C} \\right\\rangle - \\epsilon H (\\hat {\\Gamma}), \\tag {9}",
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+ "content": "where "
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+ "content": "\\bar{\\nu} = \\frac{1}{N + 1}\\mathbb{1}_{N + 1}"
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+ "content": " to satisfy the additional column."
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+ "type": "text",
+ "content": "The Unlearning Objective. Although "
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+ "type": "inline_equation",
+ "content": "\\hat{\\Gamma}^*"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " provides the more refined alignment, we suggest further incorporating an identity-like matrix "
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+ {
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+ "type": "inline_equation",
+ "content": "\\pmb{I}"
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+ {
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+ "type": "text",
+ "content": " for two merits. First, diagonal elements are set as 1 for true positives to retain the initial alignment. Second, "
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+ "type": "inline_equation",
+ "content": "[I]_{i,N + 1} = 1"
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+ "type": "text",
+ "content": " to enhance the unlearning for the possible false positive "
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+ "type": "inline_equation",
+ "content": "(v_{i},t_{i})\\in \\mathbb{D}_{FG}"
+ },
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+ "type": "text",
+ "content": ". Thus, the overall alignment balanced by the factor "
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+ "type": "inline_equation",
+ "content": "\\gamma"
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| CC12M | CLIP | 76.3 | 68.2 | 35.2 | 16.1 | 2.8 | 50.1 | 29.3 | 37.6 | 6.4 | 54.1 | 30.1 | 39.2 | 22.5 | 14.8 | 90.8 | 38.2 | 33.8 |
| NCU | 80.4 | 68.5 | 41.4 | 19.3 | 2.6 | 52.8 | 28.6 | 43.4 | 7.2 | 62.4 | 35.7 | 48.3 | 31.3 | 18.1 | 92.5 | 42.2↑4.0 | 36.7↑2.9 |
| YFCC15M-R | CLIP | 53.7 | 67.0 | 34.4 | 13.1 | 1.1 | 49.3 | 22.1 | 18.6 | 11.0 | 13.5 | 20.3 | 29.3 | 23.0 | 1.7 | 83.7 | 29.5 | 17.8 |
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| NCU | 66.63 | 78.63 | 70.76 | 60.34 |
| YFCC15M-R | ViT-B/32 | CLIP | 60.46 | 61.90 | 59.09 | 51.07 |
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diff --git a/2025/Unleashing High-Quality Image Generation in Diffusion Sampling Using Second-Order Levenberg-Marquardt-Langevin/13cbf79c-7d32-4412-9eee-95252f5be1a0_content_list.json b/2025/Unleashing High-Quality Image Generation in Diffusion Sampling Using Second-Order Levenberg-Marquardt-Langevin/13cbf79c-7d32-4412-9eee-95252f5be1a0_content_list.json
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+ {
+ "type": "text",
+ "text": "Unleashing High-Quality Image Generation in Diffusion Sampling Using Second-Order Levenberg-Marquardt-Langevin",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "Fangyikang Wang $^{1*‡}$ Hubery Yin $^{2*}$ Lei Qian $^{1}$ Yinan Li $^{1}$ Shaobin Zhuang $^{3‡}$ Huminhao Zhu $^{1}$ Yilin Zhang $^{1}$ Yanlong Tang $^{4}$ Chao Zhang $^{1†}$ Hanbin Zhao $^{1}$ Hui Qian $^{1}$ Chen Li $^{2}$ $^{1}$ Zhejiang University $^{2}$ WeChat Vision, Tencent Inc $^{3}$ Shanghai Jiao Tong University $^{4}$ Tencent Lightspeed Studio",
+ "bbox": [
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+ ],
+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "Abstract",
+ "text_level": 1,
+ "bbox": [
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+ 306
+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "The emerging diffusion models (DMs) have demonstrated the remarkable capability of generating images via learning the noised score function of data distribution. Current DM sampling techniques typically rely on first-order Langevin dynamics at each noise level, with efforts concentrated on refining inter-level denoising strategies. While leveraging additional second-order Hessian geometry to enhance the sampling quality of Langevin is a common practice in Markov chain Monte Carlo (MCMC), the naive attempts to utilize Hessian geometry in high-dimensional DMs lead to quadratic-complexity computational costs, rendering them non-scalable. In this work, we introduce a novel Levenberg-Marquardt-Langevin (LML) method that approximates the diffusion Hessian geometry in a training-free manner, drawing inspiration from the celebrated Levenberg-Marquardt optimization algorithm. Our approach introduces two key innovations: (1) A low-rank approximation of the diffusion Hessian, leveraging the DMs' inherent structure and circumventing explicit quadratic-complexity computations; (2) A damping mechanism to stabilize the approximated Hessian. This LML approximated Hessian geometry enables the diffusion sampling to execute more accurate steps and improve the image generation quality. We further conduct a theoretical analysis to substantiate the approximation error bound of low-rank approximation and the convergence property of the damping mechanism. Extensive experiments across multiple pretrained DMs validate that the LML method significantly improves image generation quality, with negligible computational overhead.",
+ "bbox": [
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
+ "bbox": [
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "The emerging diffusion models (DMs) [30, 74, 76, 77], generating samples of data distribution from initial noise, have been proven to be an effective technique for modeling com",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "plex distribution, especially in generating high-quality images [13, 31, 58, 62, 67, 70]. Training DMs can be viewed as using a neural network to match the (Stein) score function of the target distribution corrupted by different levels of noise. The sampling of DMs can be seen as running Langevin dynamics [65] using the learned diffused score and simultaneously slowly decreasing the noise level, which is called annealed Langevin dynamics [76].",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Recently, many sampling methods have been proposed to enhance the quality of generated samples of pretrained DMs. The majority of these efforts focus on refining the denoising scheme, as seen in works such as DDIM [75], DPM-Solvers [51, 52], PNDM [50], and others [7, 85, 91-94]. Some also propose to select more critical denoising timesteps to enhance sampling quality [23, 35, 87, 88]. These efforts are primarily based on the analysis along the denoising path, yet they still perform first-order Langevin using the learned score within a specific noise level.",
+ "bbox": [
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "In the Langevin sampling area, it is common to employ additional second-order Hessian geometry to enhance the sampling quality. The additional second-order information can guide Langevin dynamics to take more accurate steps [12, 54], which is called Newton-Langevin [73]. A natural idea is that we can also leverage the Hessian geometry of DMs within each noise level to enhance the quality of diffusion sampling results. However, it is extremely challenging to calculate the Hessian geometry within the context of high-dimensional DMs [3], cause it requires quadratic-complexity computations. Current methods on diffusion Hessian either require auxiliary networks [15, 84] or maintain memory-intensive states [64], making them inefficient for enhancing DM sampling.",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "In this paper, we introduce a novel method for approximating the diffusion Hessian within a specific noise level. Notably, our approach is the first to approximate the diffusion Hessian and apply it to enhance the sampling quality of pretrained commercial-level DMs. Our method, inspired by the celebrated Levenberg-Marquardt method in optimization [45, 53, 68], is referred to as the Levenberg-Marquardt-Langevin (LML) method. Our approach introduces two key",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "header",
+ "text": "CVF",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
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+ {
+ "type": "page_footnote",
+ "text": "* Equal contribution † Corresponding author",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "page_footnote",
+ "text": "$\\ddagger$ Work done as interns at WeChat Vision",
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+ "page_idx": 0
+ },
+ {
+ "type": "page_number",
+ "text": "10453",
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+ "page_idx": 0
+ },
+ {
+ "type": "image",
+ "img_path": "images/69f6d8ea3f57de3ed9ec093779e29d55712cc5afc08604d1b4f19bf2f6bdaf48.jpg",
+ "image_caption": [
+ "Figure 1. Schematic comparison between our LML method and baselines. While previous works mainly focus on intriguing designs along the annealing path to improve diffusion sampling, they leave operations at specific noise levels to be first-order Langevin. Our approach proposes to leverage the Levenberg-Marquardt approximated Hessian geometry to guide the Langevin update to be more accurate."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "innovations: Initially, we derive a computationally tractable low-rank approximation of the diffusion Hessian by emulating the Gauss-Newton transformation, avoiding explicit quadratic-complexity computations. This approach capitalizes on the inherent structure of DMs to construct a low-rank approximation that captures critical geometric information. Following this, we stabilize the approximated Hessian using the damping mechanism, which addresses its ill-conditioning, and acquire its inverse for geometric guidance. Our method uses this LML-approximated Hessian geometry to enable the Langevin dynamics to take more accurate steps and improve image generation quality.",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "We also conduct comprehensive theoretical analyses for our low-rank approximation and damping mechanism. First, we establish the error bound for the low-rank approximation of the diffusion Hessian. Subsequently, we prove that the damping mechanism preserves an unbiased stationary measure and exhibit exponentially fast convergence in terms of $\\chi^2$ -divergence.",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "Extensive experiments on multiple pretrained DMs, including CIFAR-10, CelebA-HQ, SD-15, SD2-base, SD-XL and PixArt- $\\alpha$ , validate that the LML method significantly improves image generation quality with negligible computational overhead.",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "2. Preliminaries",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "Notation. The Euclidean norm over $\\mathbb{R}^d$ is denoted by $\\| \\cdot \\|$ . Throughout, we simply write $\\int g$ to denote the integral with respect to the Lebesgue measure: $\\int g(x)\\mathrm{d}x$ . When the integral is with respect to a different measure $\\mu$ , we explicitly write $\\int g\\mathrm{d}\\mu$ . The expectation and variance of $g(X)$ when $X\\sim p$ are respectively denoted $\\mathbb{E}_{\\mu}g = \\int g\\mathrm{d}\\mu$ and $\\operatorname{var}_{\\mu}g\\coloneqq \\int (g - \\mathbb{E}_{\\mu}g)^2\\mathrm{d}\\mu$ . When clear from context, we sometimes abuse notation by identifying a measure $\\mu$ with its Lebesgue density. We use $\\pmb{I}_d$ to denote the $d$ -dimensional identity matrix; when clear from context, we sometimes simply write $\\pmb{I}$ . $\\pmb{H}_f$ and $\\pmb{J}_f$ denote the Hessian and Jacobian of $f$ respectively.",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "2.1. Langevin Dynamics and Gradient Descent",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "In statistics, the (Stein) score of a distribution $p(\\pmb{x})$ is defined to be $\\nabla_{\\pmb{x}} \\log p(\\pmb{x})$ . Given an initial value $\\pmb{x}_0 \\sim \\pi(\\pmb{x})$",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "with $\\pi$ being a prior distribution, Langevin dynamics (LD) can produce samples from $p(\\pmb{x})$ using only the score function $\\nabla_{\\pmb{x}}\\log p(\\pmb{x})$ following the SDE,",
+ "bbox": [
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+ ],
+ "page_idx": 1
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} \\boldsymbol {x} _ {t} = \\nabla_ {\\boldsymbol {x}} \\log p (\\boldsymbol {x} _ {t}) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} B _ {t}, \\tag {1}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ {
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+ "text": "where $B_{t}$ is the standard d-dimensional Brownian Motion (BM). The distribution of $\\pmb{x}_t$ equals $p(\\pmb{x})$ when $T \\to \\infty$ , in which case $\\pmb{x}_t$ becomes an exact sample from $p(\\pmb{x})$ under some regularity conditions [86]. Strictly speaking, a Metropolis-Hastings adjustment is needed, but it can often be ignored in practice [9]. There is a deep connection involving the distribution of $\\pmb{x}_t$ in LD to the renowned Gradient Descent method (GD) [56] in optimization. The marginal distribution of a Langevin process $(\\pmb{x}_t)_{t\\geq 0}$ evolves according to a GD, over the Wasserstein probability space, that minimizes the Kullback-Leibler (KL) divergence $D_{\\mathrm{KL}}(\\cdot \\| \\pi)[2,36,81]$ .",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "2.2. Diffusion Models and Annealed Langevin",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "Suppose that we have a d-dimensional random variable $\\pmb{x}(0) \\in \\mathbb{R}^d$ following an unknown target distribution $p_0(\\pmb{x}_0)$ . Diffusion Models (DMs) define a forward process $\\{\\pmb{x}(t)\\}_{t \\in [0,T]}$ with $T > 0$ starting with $\\pmb{x}(0)$ , such that the distribution of $\\pmb{x}(t)$ conditioned on $\\pmb{x}(0)$ satisfies",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\np _ {t | 0} (\\boldsymbol {x} (t) | \\boldsymbol {x} (0)) = \\mathcal {N} (\\boldsymbol {x} (t); \\alpha (t) \\boldsymbol {x} (0), \\sigma^ {2} (t) \\mathbf {I}), \\quad (2)\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "where $\\alpha (\\cdot),\\sigma (\\cdot)\\in \\mathcal{C}([0,T],\\mathbb{R}^{+})$ have bounded derivatives, and we denote them as $\\alpha_{t}$ and $\\sigma_t$ for simplicity. The choice for $\\alpha_{t}$ and $\\sigma_t$ is referred to as the noise schedule of a DM.",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "DMs, both SMLD [76] and DDPM [30], can be seen as learning a network to match the score of the diffused distribution $\\log p_t(\\pmb{x}_t)$ at different noise levels. In practice, DMs usually use $\\varepsilon_{\\theta}(\\pmb{x}(t), t)$ to estimate $-\\sigma(t) \\nabla_{\\pmb{x}(t)} \\log p_t(\\pmb{x}(t), t)$ via optimizing the following denoising score matching objective:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathbb {E} _ {t} \\left\\{\\lambda_ {t} \\mathbb {E} _ {x _ {0}, x _ {t}} \\left[ \\| s _ {\\theta} (x _ {t}, t) - \\nabla_ {x _ {t}} \\log p (x _ {t}, t | x _ {0}, 0) \\| ^ {2} \\right] \\right\\}. \\tag {3}\n$$\n",
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+ {
+ "type": "text",
+ "text": "The sampling process of diffusion models can be seen as annealed Langevin dynamics [76], which executes Langevin updates at each noise level while progressively reducing the noise scale.",
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+ "text": "10454",
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+ {
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+ "img_path": "images/151ec030eaf57ccd66121f643d31c60312cba48ad56a9e973b35850fa2ea9b9d.jpg",
+ "image_caption": [
+ "Figure 2. The relation between optimization algorithms and MCMC sampling algorithms. We initially wanted to develop a diffusion sampler utilizing Hessian geometry, following the path of Newton-Langevin dynamics [73]. However, this approach proved to be highly computationally expensive within the DM context. Drawing inspiration from the Levenberg-Marquardt method used in optimization, our method incorporates low-rank approximation and damping techniques. This enables us to obtain the Hessian geometry in a computationally affordable manner. Subsequently, we use this approximated Hessian geometry to guide the Langevin updates."
+ ],
+ "image_footnote": [],
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+ "type": "text",
+ "text": "2.3. Langevin Guided by Hessian Geometry",
+ "text_level": 1,
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "Newton's method (also called Newton-Raphson) [60] is a famous optimization method that utilizes the second-order Hessian geometry to improve the GD. Developed as an analogy to Newton's method, the Newton-Langevin dynamics [54] utilize Hessian geometry to generate samples that adhere to the SDE",
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} \\boldsymbol {x} _ {t} = \\left[ \\nabla_ {\\boldsymbol {x}} ^ {2} \\log p (\\boldsymbol {x} _ {t}) \\right] ^ {- 1} \\nabla_ {\\boldsymbol {x}} \\log p (\\boldsymbol {x} _ {t}) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} B _ {t} ^ {\\prime}, \\tag {4}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "where the $B_{t}^{\\prime}$ is the BM scaled by the square-rooted Hessian geometry. Calculating the Hessian geometry of high-dimensional distributions poses a significant challenge. Some studies have attempted to alleviate this issue through the Quasi-Newton technique [22, 73]. However, these approaches fail to address the problem in the context of DM-scale dimensional data. For instance, the Stable Diffusionv1.5 model [67] features a latent dimension of 16384, resulting in a Hessian matrix of $16384 \\times 16384$ . Current methods on diffusion Hessian either require auxiliary networks training [15, 84] or maintain memory-intensive states [64]. To the best of our knowledge, there is currently no effective method available to access the diffusion Hessian of advanced commercial-level DMs like SD-XL.",
+ "bbox": [
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "2.4. Levenberg-Marquardt Method",
+ "text_level": 1,
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "In the field of optimization, the Levenberg-Marquardt (LM) method [68] is proposed as a computationally friendly and stabilized analogue to Newton's method. Specifically, it modifies the computation of Hessian geometry in Newton's method in two key aspects:",
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+ "text": "- Low-rank approximated Hessian In the context of least squares problems, the Levenberg-Marquardt method often constructs a low-rank estimation of the Hessian geometry. Specifically, when $f(\\pmb{x}) = \\sum_{i=1}^{m} r_i(\\pmb{x})^2$ , the Levenberg-Marquardt method approximates the Hessian into the following form, which is constructed from the",
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+ "type": "text",
+ "text": "Jacobian $J_{f}(\\pmb {x})$",
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {H} _ {f} (\\boldsymbol {x}) \\approx 2 \\boldsymbol {J} _ {f} (\\boldsymbol {x}) ^ {\\top} \\boldsymbol {J} _ {f} (\\boldsymbol {x}). \\tag {5}\n$$\n",
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+ "text": "This low-rank approximation technique is also referred to as the Gauss-Newton method in some literature [16]. However, it is still unclear how to obtain a Levenberg-Marquardt-type low-rank estimation of the Hessian in the context of diffusion models.",
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+ "text": "- Damping mechanism The Levenberg-Marquardt Method introduces an additional damping identity matrix to the Hessian geometry. That is, it replaces the pure Hessian geometry $\\left[\\boldsymbol{H}_f(\\boldsymbol{x}_k)\\right]^{-1}$ in Newton's method with a combination expressed as $\\left[\\boldsymbol{H}_f(\\boldsymbol{x}_k) + \\lambda \\boldsymbol{I}\\right]^{-1}$ . Consequently, the Levenberg-Marquardt Method with damping is expressed as:",
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+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {x} _ {k + 1} = \\boldsymbol {x} _ {k} - \\eta \\left[ \\boldsymbol {H} _ {f} \\left(\\boldsymbol {x} _ {k}\\right) + \\lambda \\boldsymbol {I} \\right] ^ {- 1} \\nabla_ {\\boldsymbol {x}} f \\left(\\boldsymbol {x} _ {k}\\right). \\tag {6}\n$$\n",
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+ "type": "text",
+ "text": "Empirical evidence suggests that the damping mechanism contributes to numerical stabilization [41], since $\\lambda I$ can resolve the ill-conditioning of the Hessian. While the damping mechanism can be perceived as a trust region approach, it is more intuitive to view $H + \\lambda I$ as a geometrical interpolation between $H$ and $I$ .",
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+ "type": "text",
+ "text": "3. Methodology",
+ "text_level": 1,
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+ "type": "text",
+ "text": "3.1. Low-rank Approximation of Diffusion Hessian",
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+ "text": "Inspired by the low-rank estimation technique of the Hessian in the Levenberg-Marquardt method, we derive a similar low-rank estimation for the diffusion Hessian. Specifically, we follow the intuition of the Levenberg-Marquardt method to approximate the diffusion Hessian by simplifying the second-order partial derivatives. The low-rank approximate Hessian of diffusion models that we obtained is shown below. It is important to note that it includes noise schedule related coefficients, which distinguishes it from the least squares problem case in Eq. 5.",
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+ "type": "page_number",
+ "text": "10455",
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+ {
+ "type": "image",
+ "img_path": "images/7f38192093d022dc878aeb5b08d5e5246c07d8607ecf339ffb8e6444765dbdae.jpg",
+ "image_caption": [
+ "DDIM PNDM DPM-Solver DPM-Solver++ UniPC LML(Ours)",
+ "Figure 3. Visual comparison of images generated by our LML method and other methods, using the pre-trained LDM on CelebAHQ $256\\times 256$ [39] with the same seeds. It shows that our LML method contributes to more vivid and detailed generated images."
+ ],
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+ "text": "Proposition 1. Let $p_t$ be the diffused marginal distribution at time $t$ of the diffusion process, Eq. 2 and $\\varepsilon_\\theta$ is learned via Eq. 3, then the Hessian derivative of its log-density function $\\nabla_{\\boldsymbol{x}_t}^2 \\log p_t(\\boldsymbol{x}_t)$ has a low-rank approximation form of $\\frac{1}{\\sigma(t)^2 \\| \\varepsilon_\\theta \\|^2} \\varepsilon_\\theta \\varepsilon_\\theta^\\top$ .",
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+ "type": "text",
+ "text": "Notice that this approximation form is a scaled outer-product of the score. The detailed derivation can be found in the Supplementary A.2. For here and for the remainder of the paper, we will denote $\\varepsilon_{\\theta}(\\boldsymbol{x}(t), t)$ as $\\varepsilon_{\\theta}$ , provided there is no risk of ambiguity. In section 4.1, we will show that this low-rank approximation possesses an error bound, ensuring that our approximation does not generate excessive errors.",
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+ {
+ "type": "text",
+ "text": "3.2. Damping Mechanism",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "Similar to the scenario in the Levenberg-Marquardt method, we have obtained an accessible approximation of the diffusion Hessian as presented in Proposition 1. However, this form is significantly ill-conditioned, making its inverse impossible to calculate. Specifically, the outer-product Hessian in Proposition 1 has an infinite condition number [32]; hence, its inverse strictly does not exist in mathematical terms. To address this issue, we propose adopting the damping mechanism used in the LML method. We introduce an additional damping identity matrix to the approximate Hes",
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+ "type": "text",
+ "text": "sian as shown in Proposition 1. This damped Hessian geometry is used in place of the full Hessian in the Newton Langevin in Eq. 4, we consequently derive the following damping dynamics:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} \\boldsymbol {x} _ {t} = \\left[ \\nabla_ {\\boldsymbol {x}} ^ {2} \\log p \\left(\\boldsymbol {x} _ {t}\\right) + \\lambda I \\right] ^ {- 1} \\nabla_ {\\boldsymbol {x}} \\log p \\left(\\boldsymbol {x} _ {t}\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} B _ {t} ^ {\\prime}, \\tag {7}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "type": "text",
+ "text": "where the $B_{t}^{\\prime}$ is the BM scaled by the square-rooted LM approximated Hessian geometry. Drawing inspiration from the Levenberg-Marquardt method, we refer to this damping Hessian Langevin in Eq. 7 as the Levenberg-Marquardt-Langevin dynamics (LML dynamics). Similar to the Levenberg-Marquardt method, the damping coefficient $\\lambda$ in Eq. 7 can be interpreted as an interpolation coefficient between the Hessian geometry and Identity geometry. Specifically, as $\\lambda \\rightarrow \\infty$ , Eq. 7 would degenerate to the standard Langevin with normalization on the geometry. We observe that by adding the Levenberg-Marquardt damping identity matrix to the outer-product form of the Hessian in Equation Proposition 1, its inverse can be conveniently computed using the Sherman-Morrison formula [72].",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\boldsymbol {H} _ {L M} ^ {- 1} (\\boldsymbol {x} _ {t}, \\lambda) = \\left[ \\nabla_ {\\boldsymbol {x}} ^ {2} \\log p (\\boldsymbol {x} _ {t}) + \\lambda \\boldsymbol {I} \\right] ^ {- 1} \\\\ \\approx \\left[ \\frac {1}{\\sigma (t) ^ {2} \\| \\varepsilon_ {\\theta} \\| ^ {2}} \\varepsilon_ {\\theta} \\varepsilon_ {\\theta} ^ {\\top} + \\lambda I \\right] ^ {- 1} \\\\ = \\frac {1}{\\sigma (t) ^ {2} \\| \\varepsilon_ {\\theta} \\| ^ {2}} \\left[ \\varepsilon_ {\\theta} \\varepsilon_ {\\theta} ^ {\\top} + \\lambda^ {\\prime} I \\right] ^ {- 1} \\tag {8} \\\\ = \\frac {1}{\\lambda^ {\\prime} \\sigma (t) ^ {2} \\| \\boldsymbol {\\varepsilon} _ {\\theta} \\| ^ {2}} \\left[ \\boldsymbol {I} - \\frac {\\boldsymbol {\\varepsilon} _ {\\theta} \\boldsymbol {\\varepsilon} _ {\\theta} ^ {\\top}}{\\lambda^ {\\prime} + \\| \\boldsymbol {\\varepsilon} _ {\\theta} \\| ^ {2}} \\right], \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "where $\\lambda' = \\sigma(t)^2\\|\\varepsilon_\\theta\\|^2\\lambda$ . We also point out that the coefficients $\\frac{1}{\\lambda'\\sigma(t)^2\\|\\varepsilon_\\theta\\|^2}$ will be absorbed in the discretizing stepsize of the LML dynamics and only affect the norm. The geometry direction essence is in the $\\left[I - \\frac{\\varepsilon_\\theta\\varepsilon_\\theta^\\top}{\\lambda' + \\|\\varepsilon_\\theta\\|^2}\\right]$ part. In the remainder of this paper, we will slightly abuse notation by not distinguishing between $\\lambda$ and $\\lambda'$ . This simplification should not lead to any confusion.",
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+ {
+ "type": "text",
+ "text": "3.3. Annealed Levenberg-Marquardt-Langevin",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "To utilize the LML for diffusion sampling, we perform the discretization of Eq. 7 at each nose level, and gradually decrease the noise level. We called this annealed LML, and point out that its continuous-time form would converge to the following SDE:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} x _ {t} = \\left[ f _ {t} \\boldsymbol {x} _ {t} - g _ {t} ^ {2} \\boldsymbol {H} _ {L M} ^ {- 1} \\nabla_ {x} \\log p _ {t} (\\boldsymbol {x} _ {t}) \\right] \\mathrm {d} t + g _ {t} \\mathrm {d} B _ {t} ^ {\\prime}. \\tag {9}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "Similar to the connection of the reverse SDE and diffusion ODE [77], the LM reverse SDE in Eq. 9 also has an associated ODE, which is a deterministic process that shares the",
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+ "type": "page_number",
+ "text": "10456",
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+ {
+ "type": "text",
+ "text": "Algorithm 1 Levenberg-Marquardt-Langevin (LML) diffusion sampler",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
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+ {
+ "type": "text",
+ "text": "1: Input: pretrained diffusion model noise predictor $\\varepsilon_{\\theta}$ , number of timesteps $N$ , noise schedule $\\{\\alpha_t\\}$ and $\\{\\sigma_t\\}$ , Levenberg-Marquardt damping coefficient $\\lambda > 0$ , EMA coefficient $\\kappa$ .",
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+ {
+ "type": "text",
+ "text": "2: Initiate $\\pmb{x}_{\\mathrm{list}} = []$ , $\\widetilde{\\pmb{H}}_{N + 1}^{-1} = \\pmb{I}$",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "3: Sample $\\pmb{x}_N \\sim \\mathcal{N}(0, \\sigma_{t_N} I)$ .",
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+ "page_idx": 4
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+ {
+ "type": "text",
+ "text": "4: for $i = N, N - 1, \\dots, 1$ do",
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+ "type": "text",
+ "text": "5: $\\varepsilon_{i} = \\varepsilon_{\\theta}(\\pmb{x}_{i},i)$",
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+ "type": "text",
+ "text": "6: if $i\\neq N$ then",
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+ "type": "text",
+ "text": "7: $\\widetilde{\\varepsilon}_i = \\kappa *\\varepsilon_{i + 1} + (1 - \\kappa)*\\varepsilon_i$",
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+ "type": "text",
+ "text": "8: else",
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+ {
+ "type": "text",
+ "text": "9: $\\widetilde{\\varepsilon}_i = \\varepsilon_i$",
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+ {
+ "type": "text",
+ "text": "10: end if",
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+ {
+ "type": "list",
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+ "list_items": [
+ "11: $\\widetilde{H}_i^{-1} = I - \\frac{\\widetilde{\\varepsilon}_i\\widetilde{\\varepsilon}_i^1}{\\lambda + \\| \\widetilde{\\varepsilon}_i\\| ^2}$ {Levenberg-Marquardt approximate Hessian geometry}",
+ "12: $\\varepsilon_{i}^{LM} = \\widetilde{\\pmb{H}}_{i}^{-1}\\varepsilon_{i}$ {Apply the approximate Hessian geometry}",
+ "13: $\\varepsilon_{i}^{LM} = \\frac{\\|\\pmb{\\varepsilon}_{i}\\|}{\\|\\pmb{\\varepsilon}_{i}^{LM}\\|}\\pmb{\\varepsilon}_{i}^{LM}$ {Geometrical normalization}",
+ "14: $\\pmb{x}_{i-1} = \\mathrm{DPM-Solver}(\\pmb{x}_{\\mathrm{list}}, \\pmb{\\varepsilon}_i^{LM}, i)$",
+ "15: $\\mathbf{x}_{\\mathrm{list}} = \\mathbf{x}_{\\mathrm{list}}.$ append $(\\mathbf{x}_{i - 1})$",
+ "16: end for",
+ "17: Output: $x_0$"
+ ],
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "same single-time marginal distribution:",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} x _ {t} = \\left[ f _ {t} \\boldsymbol {x} _ {t} - \\frac {1}{2} g _ {t} ^ {2} \\boldsymbol {H} _ {L M} ^ {- 1} \\nabla_ {\\boldsymbol {x}} \\log p _ {t} (\\boldsymbol {x} _ {t}) \\right] \\mathrm {d} t. \\tag {10}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "The following section will develop a practical LML sampler based on this deterministic LML ODE.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Remark 1. Our LM process can be viewed as the Legendre dual of the classical diffusion process with a transform map of $\\nabla \\log p_t(\\cdot) + \\lambda \\| \\cdot \\|$ . See discussions in Supp. D.3.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "3.4. Levenberg-Marquardt-Langevin Sampler",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "We implement a diffusion sampler based on the LML diffusion ODE in Eq. 10, because it is suggested that deterministic diffusion samplers are far more efficient than the stochastic ones [40]. Our approach is generally consistent with the practices outlined in [76]. The scheme for our LML diffusion sampler is illustrated in Algorithm 1. Primarily, our sampler substitutes the first-order Langevin dynamics with LML at each noise level. At each noise level, we initially compute the LM low-rank approximated and damping Hessian geometry, $\\widetilde{H}_i^{-1}$ , as detailed in step 11 of Algorithm 1. We incorporate the network output from previous steps, as shown in step 7, following studies suggesting that this mixture is closer to the underlying true score due to the manifold's curvature [50]. We then apply this approximate Hessian geometry to our initial gradient, $\\varepsilon_{i}$ , to obtain",
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+ {
+ "type": "image",
+ "img_path": "images/c733b56f89383a5a6b9b8272c48f0994cf3081c14b7eb09a41fce71a38c99c12.jpg",
+ "image_caption": [
+ "Figure 4. Qualitative comparison of our LML method and other methods in text-guided image generation. The evaluation was performed on SD-15 [67], using 10 NFEs and the same seeds."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "the Hessian-guided gradient, $\\varepsilon_{i}^{LM}$ , as detailed in step 12. In terms of the stepsize for our LML sampler, in contrast to some sophisticated ways of choosing the stepsize of second-order methods [25, 43], we follow the approach of [20] to ensure that the Hessian geometry has a unit spectrum, which can be easily implemented through a normalization operation on the Hessian guided gradient $\\varepsilon_{i}^{LM}$ as illustrated in step 13. The rescaling of BM in Eq. 7 can also be absorbed into this normalization operation. Once the Hessian-guided gradient, $\\varepsilon_{i}^{LM}$ , is obtained, we adopt the DPM-Solver as our denoising scheme to calculate the next state, $x_{i-1}$ , as shown in step 14.",
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+ "type": "text",
+ "text": "It is worth noting that our LML does not require additional training, components, or network access. Instead, we only need several additional tensor arithmetic operations.",
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+ {
+ "type": "text",
+ "text": "4. Theoretical Analysis",
+ "text_level": 1,
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+ "type": "text",
+ "text": "In this section, we present rigorous theoretical analyses to substantiate the correctness and efficacy of our LML.",
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+ "type": "text",
+ "text": "4.1. Analysis on Low-rank Approximation",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Here, we establish the error bound of the low-rank approximation of the diffusion Hessian in Proposition 1, thereby ensuring that our approximation does not introduce excess",
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+ {
+ "type": "page_number",
+ "text": "10457",
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+ "page_idx": 4
+ },
+ {
+ "type": "image",
+ "img_path": "images/373093e00ca3dbcafbf1a3e8b63c9efa71cb48c011099442cd6ae2f63df1f9a1.jpg",
+ "image_caption": [
+ "Figure 5. Qualitative comparison of our LML method and other methods in text-guided image generation. The evaluation was performed on SD2-base [67], using 10 NFEs and the same seeds."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "sive errors. Given that we are evaluating the accuracy of a matrix-valued approximation, we choose to use the Hilbert-Schmidt norm [24] as a criterion.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Proposition 2. Assume that the norm of $\\pmb{x}_t$ is bounded by $\\delta_1$ , the approximation error on $\\varepsilon_{\\theta}(\\pmb{x}_t, t)$ is denoted as $\\delta_2$ , $\\delta_3$ denote the bound on the second partial derivative of $\\delta_1$ w.r.t. $\\pmb{x}_t$ , and $\\mathcal{D}_y$ denote the dataset diameter. The approximation error of the LM low-rank Hessian, as referenced in Proposition 1, is at most $(\\delta_1 + \\alpha_t \\delta_2 + \\alpha_t \\mathcal{D}_y) (2 + \\delta_3 + 2 \\frac{\\alpha_t^2}{\\sigma_t^2} \\mathcal{D}_y^2)$ when measured in terms of the Hilbert-Schmidt norm.",
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+ {
+ "type": "text",
+ "text": "Our analysis relies on the analytical form diffusion Fisher [84]. The detailed proof can be found in Supp. A.6.",
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+ {
+ "type": "text",
+ "text": "4.2. Analysis on Damping Mechanism",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "Subsequently, we demonstrate the unbiased, exponentially fast convergence property of the damping mechanism.",
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+ {
+ "type": "text",
+ "text": "4.2.1. Stationary Measure",
+ "text_level": 1,
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "We confirm that the stationary measure of the damping dynamics, as defined in Eq. 7, aligns with the target diffused distribution. This ensures that the damping updates still guide samples towards the correct data distribution.",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "Proposition 3. Under mild regularity conditions, the stationary distribution of the damping dynamics in Eq. 7 exists and is unique, which also coincides with the marginal distribution $p_t(\\boldsymbol{x}_t)$ at every noise level.",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "We achieve this analysis by the Fokker-Planck equation [63]. The detailed proof can be found in Supp. A.7.",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "4.2.2. Ergodic Convergence Rate",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "We also want to determine the speed at which our damping dynamics converge. We demonstrate that our damping dynamics exhibit a satisfyingly fast, exponential convergence rate towards the target distribution.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Proposition 4. Let $\\mu_t$ be the evolving distribution of the damping dynamics in Eq. 7. We have that $\\mu_t$ converges to the stationary distribution at an exponential ergodic convergence rate in terms of $\\chi^2$ -distance at every noise level, under certain regularity conditions.",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "We achieve this analysis by determining the relationship between Eq. 7 and the Mirror-Langevin [12]. The formal version and detailed proof can be found in Supp. A.8.",
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+ },
+ {
+ "type": "text",
+ "text": "Remark 2. Once we establish the exponential ergodic convergence rate in terms of $\\chi^2$ -distance, The exponential convergence results for total variation distance [80], Hellinger distance [28], KL divergence [44] as illustrated in [4, §2.4]. And the exponential convergence results on Wasserstein distance [81] can also be established with a log-Sobolev assumption, as illustrated in [14].",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "5. Experiments",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "In this section, we validate the enhanced sampling quality of our LML method across various pretrained DMs. We evaluate in both pixel-space, latent-space, and text-guided conditional generation scenarios. We select several most commonly-used and advanced sampling methods such as DDIM [77], PNDM [50], DPM-Solver [51], DPM-Solver++ [52] and UniPC [92] as baselines. We will also demonstrate the computational efficiency of our LML method. All experiments are executed using open-source, pretrained DMs, with the datatype set to float32 and the timestep scheme as uniform. More experimental details and results are deferred to Supp. B and C.",
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+ {
+ "type": "text",
+ "text": "5.1. Pixel-Space Image Generation",
+ "text_level": 1,
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+ "type": "text",
+ "text": "We initially compare the unconditional sampling quality of our LML method with baselines on the CIFAR-10 dataset [1]. For each sampler, we generate 50,000 samples for FID evaluation. As illustrated in Table 1 and Figure 6a, our approach improves the sampling performance of the baseline Langevin methods in most NFE scenarios.",
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+ "text": "10458",
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+ "img_path": "images/7c122d4a419e1904fa2ba3d7f59bfa0acfbaf681c39f326a648fd37cbd473540.jpg",
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+ "(a) CIFAR-10"
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+ {
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+ "img_path": "images/168352b810166f4134c7c939f67d54fb35b2743aec8dfd90a3bead57a270eb7c.jpg",
+ "image_caption": [
+ "(b) SD-15 on MS-COCO",
+ "Figure 6. This line chart compares the log-FID scores $(\\downarrow)$ on (a) CIFAR-10, (b) MS-COCO with SD-15 and (c) MS-COCO with SD2-base."
+ ],
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+ {
+ "type": "image",
+ "img_path": "images/b0d78c9bde51e1c261b1358803d2331203418e7259500810dd95d1280baaa92b.jpg",
+ "image_caption": [
+ "(c) SD2-base on MS-COCO"
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+ "type": "table",
+ "img_path": "images/a6c040f674758cc552f61e49aee66aa38749164385da37463bb0ce137149e5d4.jpg",
+ "table_caption": [
+ "Table 1. Comparison of different samplers on FID score( ↓) on CIFAR-10 unconditional generation. Best results are bolded and the second best results are underlined. The FID scores were obtained by generating 50,000 samples, and all samplers were tested using the same seeds on the same checkpoint. It is shown that our LML always achieves the best or second best FID across all different NFEs."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods | FID (↓) on CIFAR-10 generation |
| 5 NFEs | 6 NFEs | 7 NFEs | 8 NFEs | 9 NFEs | 10 NFEs | 12 NFEs | 15 NFEs | 20 NFEs | 30 NFEs | 50 NFEs | 100 NFEs |
| DDIM [75] | 42.17 | 32.09 | 26.21 | 22.38 | 19.64 | 17.45 | 14.27 | 12.67 | 10.60 | 8.58 | 6.96 | 5.72 |
| PNDM [50] | 46.56 | 15.27 | 12.59 | 10.73 | 9.59 | 7.16 | 6.73 | 5.70 | 5.28 | 4.94 | 4.24 | 3.93 |
| DPM-Solver [51] | 33.26 | 23.06 | 17.61 | 14.58 | 12.47 | 11.13 | 9.28 | 4.98 | 4.23 | 3.74 | 3.66 | 3.62 |
| DPM-Solver++ [52] | 30.87 | 20.92 | 16.22 | 13.63 | 11.89 | 10.71 | 10.59 | 10.17 | 9.90 | 6.58 | 5.06 | 4.46 |
| UniPC [92] | 29.81 | 20.64 | 16.10 | 13.59 | 11.84 | 10.70 | 9.02 | 7.51 | 6.03 | 4.66 | 3.82 | 3.58 |
| LML (Ours) | 17.28 | 14.18 | 11.15 | 8.09 | 7.16 | 6.54 | 5.97 | 4.70 | 4.19 | 3.69 | 3.63 | 3.58 |
",
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+ "type": "table",
+ "img_path": "images/6dc59cd0743a9f6e6d3c80aa27fcb6d44ef78cb436cf84e155c6fa775f8282cf.jpg",
+ "table_caption": [
+ "Table 2. Comparison of different samplers on CelebA-HQ unconditional generation. Best results are bolded and the second best results are underlined."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods | Colorful | Face Quality | Aesthetic |
| ColorS(↑) | FS(↑) | DFIQA(↑) | PicS(↑) | EAT(↑) | Laion(↑) |
| DDIM [75] | 34.13 | 4.85 | 0.539 | 19.85 | 4.61 | 5.24 |
| PNDM [50] | 38.29 | 4.89 | 0.553 | 19.70 | 4.28 | 5.11 |
| DPM [51] | 34.85 | 5.06 | 0.566 | 20.00 | 4.51 | 5.29 |
| DPM++ [52] | 35.08 | 5.08 | 0.560 | 19.97 | 4.46 | 5.26 |
| UniPC [92] | 35.95 | 5.09 | 0.568 | 19.97 | 4.47 | 5.26 |
| LML(Ours) | 40.53 | 5.24 | 0.607 | 20.98 | 4.75 | 5.37 |
",
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+ {
+ "type": "text",
+ "text": "5.2. Latent-Space Image Generation",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "We evaluated our LML on the LDM [67] that was trained on CelebA-HQ [39] at a resolution of $256 \\times 256$ . In Table 2, we employed five metrics spanning three aspects to demonstrate the superiority of LML. These aspects include colorfulness [26], face quality (FS [46] and DFIQA [10]), and human-preference-aesthetic scores (PicS [42], EAT [27] and Laion-Aes [71]). Additionally, we present a visual comparison in Figure 3. All these experiments were carried out with a NFE of 10. The results were tested by averaging over 1000 samples and the same seeds.",
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+ "text": "5.3. Text-guided Image Generation",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "5.3.1. Qualitative Comparison",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "Qualitative comparison on SD-15 and SD2-base generation is provided in Figure 4 and 5, clearly indicating that our LML method enhances the quality of image details under",
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+ },
+ {
+ "type": "table",
+ "img_path": "images/9da34a9eee39980553f8cd5e1546ce96e15d8fe70acefc794d0d6eae9224b4f4.jpg",
+ "table_caption": [
+ "Table 3. Comparison of FID score $(\\downarrow)$ for the task of text-guided conditional generation of SD on randomly selected 30,000 MS-COCO prompts. Best results are bolded and the second best results are underlined."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods\\NFEs | FID (↓) on MS-COCO-14 prompts |
| 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 |
| SD-1.5 |
| DDIM [75] | 29.14 | 27.11 | 23.48 | 22.36 | 21.14 | 21.22 | 19.91 | 19.36 |
| PNDM [50] | 35.50 | 34.49 | 29.50 | 27.86 | 24.46 | 22.35 | 19.13 | 17.92 |
| DPM [51] | 22.07 | 20.58 | 19.92 | 19.64 | 19.47 | 19.34 | 19.30 | 17.32 |
| DPM++ [52] | 21.75 | 20.14 | 19.60 | 19.32 | 19.19 | 19.13 | 19.11 | 18.03 |
| UniPC [92] | 21.72 | 20.30 | 19.84 | 19.67 | 19.55 | 19.40 | 19.41 | 19.29 |
| LML (Ours) | 18.68 | 18.13 | 17.61 | 17.50 | 17.58 | 17.60 | 17.55 | 16.98 |
| SD2-base |
| DDIM [75] | 27.34 | 24.25 | 22.47 | 21.48 | 19.73 | 20.43 | 18.73 | 18.19 |
| PNDM [50] | 31.13 | 30.93 | 26.33 | 25.56 | 22.04 | 20.35 | 17.39 | 16.47 |
| DPM [51] | 21.25 | 19.94 | 19.21 | 18.78 | 18.51 | 18.36 | 18.13 | 15.84 |
| DPM++ [52] | 20.94 | 19.51 | 18.77 | 18.43 | 18.21 | 18.06 | 17.86 | 15.99 |
| UniPC [92] | 20.81 | 19.40 | 18.82 | 18.56 | 18.36 | 18.27 | 18.08 | 18.03 |
| LML (Ours) | 17.76 | 16.99 | 16.17 | 16.02 | 16.29 | 15.95 | 16.16 | 15.14 |
",
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+ },
+ {
+ "type": "text",
+ "text": "the same seed and prompt with a NFE of 10.",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "5.3.2. FID on MS-COCO Benchmark",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "Following the approach in [69, 90], we randomly selected 30,000 prompts from the MS-COCO dataset [47] and generated images conditioned on these prompts. We tested our sampler in terms of FID on the SD-1.5 and SD2-base models with resolutions of $512 \\times 512$ and a CFG scale 7.0. Table 3 shows that our LML sampler surpasses the baseline methods on SD models across different NFEs.",
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+ "page_idx": 6
+ },
+ {
+ "type": "page_number",
+ "text": "10459",
+ "bbox": [
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+ },
+ {
+ "type": "table",
+ "img_path": "images/c0ab28b0c476e706debbb62f3f14dd52c4b5b12af50b1592a2650e5e437ccca1.jpg",
+ "table_caption": [
+ "Table 4. Comparison of different samplers in text-guided image generation task on the T2I-BC benchmark [34]. The metrics are Color, Shape, and Texture. Best results are bolded and the second best results are underlined."
+ ],
+ "table_footnote": [],
+ "table_body": "| Metrics | T2I Benchmark on SD-1.5 [67] | T2I Benchmark on SD2-base [67] | T2I Benchmark on SD-XL [59] | T2I Benchmark on PixArt-α [8] |
| Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) |
| DDIM [75] | 0.3864 | 0.3791 | 0.4231 | 0.5111 | 0.4182 | 0.4822 | 0.5670 | 0.4712 | 0.5076 | 0.2933 | 0.3746 | 0.4045 |
| PNDM [50] | 0.3810 | 0.3761 | 0.4331 | 0.5067 | 0.4190 | 0.4863 | 0.5682 | 0.4772 | 0.5085 | 0.4035 | 0.3996 | 0.4225 |
| DPM [51] | 0.3877 | 0.3945 | 0.4294 | 0.5162 | 0.4307 | 0.5002 | 0.5795 | 0.4841 | 0.5194 | 0.3263 | 0.3895 | 0.4349 |
| DPM++ [52] | 0.3881 | 0.3958 | 0.4307 | 0.5202 | 0.4326 | 0.5020 | 0.5798 | 0.4858 | 0.5201 | 0.3136 | 0.3882 | 0.4364 |
| UniPC [92] | 0.3892 | 0.3889 | 0.4306 | 0.5146 | 0.4337 | 0.4995 | 0.5828 | 0.4910 | 0.5234 | 0.3187 | 0.3880 | 0.4266 |
| LML (Ours) | 0.4335 | 0.4252 | 0.4746 | 0.5640 | 0.4792 | 0.5330 | 0.5908 | 0.4938 | 0.5363 | 0.3801 | 0.4265 | 0.4684 |
",
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+ "page_idx": 7
+ },
+ {
+ "type": "image",
+ "img_path": "images/6cb13fbf88ad3a6f2fd8d820490a923a048aa3fc5a89ae44d148827750cf1603.jpg",
+ "image_caption": [
+ "Figure 7. LML integrates seamlessly with ControlNet."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "5.3.3. T2I-CB Benchmark",
+ "text_level": 1,
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "To further validate the enhanced sampling quality of LML in text-to-image generation, we carried out tests on diverse commercial-level DMs (SD-1.5 [67], SD2-base [67], SD-XL [59], and PixArt- $\\alpha$ [8]) using the T2I-CB [34] benchmark. This benchmark is designed for open-world text-to-image generation evaluation. For each model, we evaluated three metrics (color, shape, and texture) to assess the visual quality of the samplers. Each assessment was based on 30,000 images with a NFE of 10. As shown in Table 4, our LML always achieves the best or second best scores on T2I-BC across these models.",
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+ },
+ {
+ "type": "text",
+ "text": "5.3.4. Application on ControlNet",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "Our model can seamlessly integrate with existing diffusion model plugins, such as ControlNet [89]. The results in Fig 7 demonstrate that our method is fully compatible with ControlNet and generates high-quality samples.",
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "5.4. Time-costs Comparison",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "Table 5 presents the average wall-clock time costs for LML across different image generation tasks. These time-cost experiments were conducted on a single NVIDIA RTX 4090 chip and averaged over 200 tests with a batchsize of 1. The results suggest that the additional computational cost incurred by our LML technique is virtually negligible, making LML as time-efficient as DDIM [75].",
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+ },
+ {
+ "type": "table",
+ "img_path": "images/eb7ed311889c2becde4af10e7fda4632d35bdfcc91bda5d1b07a6e89183b49d6.jpg",
+ "table_caption": [
+ "Table 5. Average wall-clock time costs for LML and DDIM."
+ ],
+ "table_footnote": [],
+ "table_body": "| Models | Methods \\NFEs | Time-costs (s) |
| 5 | 10 | 15 | 20 | 30 | 50 | 100 |
| CIFAR-10 | DDIM | 0.13 | 0.20 | 0.27 | 0.34 | 0.52 | 0.81 | 1.49 |
| LML (Ours) | 0.13 | 0.21 | 0.27 | 0.37 | 0.48 | 0.82 | 1.51 |
| CelebA | DDIM | 0.20 | 0.28 | 0.39 | 0.47 | 0.66 | 1.03 | 1.95 |
| LML (Ours) | 0.20 | 0.31 | 0.38 | 0.48 | 0.67 | 1.10 | 2.08 |
| SD-1.5 | DDIM | 0.45 | 0.73 | 1.03 | 1.31 | 1.87 | 3.01 | 5.85 |
| LML (Ours) | 0.45 | 0.74 | 1.04 | 1.32 | 1.89 | 3.03 | 5.89 |
| SD-2base | DDIM | 0.45 | 0.71 | 1.00 | 1.25 | 1.80 | 2.87 | 5.53 |
| LML (Ours) | 0.46 | 0.72 | 0.98 | 1.27 | 1.81 | 2.88 | 5.60 |
| SD-XL | DDIM | 2.32 | 4.25 | 6.23 | 8.12 | 12.06 | 19.82 | 39.48 |
| LML (Ours) | 2.32 | 4.30 | 6.23 | 8.21 | 12.11 | 19.99 | 39.55 |
| PixArt | DDIM | 0.66 | 1.08 | 1.49 | 1.92 | 2.74 | 4.31 | 8.45 |
| LML (Ours) | 0.67 | 1.08 | 1.51 | 1.92 | 2.75 | 4.28 | 8.49 |
",
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+ {
+ "type": "text",
+ "text": "5.5. Hyperparameters",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "Our LML introduces two robust hyperparameters with clear high-level interpretations: the damping coefficient $\\lambda$ and the mixture coefficient $\\kappa$ . The damping coefficient $\\lambda$ determines the degree to which our approximated Hessian is interpolated with the identity matrix. A larger $\\lambda$ value results in the dominance of the identity matrix, leading the LML to degenerate into Langevin. Conversely, a smaller $\\lambda$ value allows more guidance from the Hessian geometry, but a minimal value could lead to ill-conditioning issues. The $\\kappa$ controls the EMA rate of previous information. A small $\\kappa$ would make the LML close to the identity map, but LML contributes to obvious image quality enhancement in practice. More discussions on hyperparameter tuning scheme, setup, and ablation experiments are provided in Supp. B.2.",
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+ {
+ "type": "text",
+ "text": "6. Conclusions",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "In this paper, we propose a training-free method termed Levenberg-Marquardt-Langevin (LML) for improving sampling quality, which uses a low-rank approximated damping Hessian geometry to guide the Langevin update. We provide a theoretical analysis of the approximation error for low-rank approximation, the stationary measure, and the convergence rate for damping dynamics. We conduct extensive experiments to demonstrate that our LML method can contribute to significant improvement in sampling quality, with negligible computational overhead. The code is available at https://github.com/zituitui/LML-diffusion-sampler.",
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+ "type": "page_number",
+ "text": "10460",
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+ {
+ "type": "text",
+ "text": "Acknowledgments",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 8
+ },
+ {
+ "type": "text",
+ "text": "This work was supported in part by the National Natural Science Foundation of China under Grants 62206248 and 62402430, and the Zhejiang Provincial Natural Science Foundation of China under Grant LQN25F020008. Fangyikang Wang would like to extend his gratitude to Pengze Zhang from ByteDance, Binxin Yang, and Xinhang Leng from WeChat Vision for their discussions regarding the experiments. Additionally, he is thankful to Zebang Shen from ETH Zürich and Zhichao Chen from Peking University for their insights on Langevin dynamics.",
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+ {
+ "type": "text",
+ "text": "References",
+ "text_level": 1,
+ "bbox": [
+ 91,
+ 284,
+ 187,
+ 300
+ ],
+ "page_idx": 8
+ },
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+ 0.414
+ ],
+ "angle": 0,
+ "content": "plex distribution, especially in generating high-quality images [13, 31, 58, 62, 67, 70]. Training DMs can be viewed as using a neural network to match the (Stein) score function of the target distribution corrupted by different levels of noise. The sampling of DMs can be seen as running Langevin dynamics [65] using the learned diffused score and simultaneously slowly decreasing the noise level, which is called annealed Langevin dynamics [76]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.415,
+ 0.906,
+ 0.567
+ ],
+ "angle": 0,
+ "content": "Recently, many sampling methods have been proposed to enhance the quality of generated samples of pretrained DMs. The majority of these efforts focus on refining the denoising scheme, as seen in works such as DDIM [75], DPM-Solvers [51, 52], PNDM [50], and others [7, 85, 91-94]. Some also propose to select more critical denoising timesteps to enhance sampling quality [23, 35, 87, 88]. These efforts are primarily based on the analysis along the denoising path, yet they still perform first-order Langevin using the learned score within a specific noise level."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.568,
+ 0.909,
+ 0.78
+ ],
+ "angle": 0,
+ "content": "In the Langevin sampling area, it is common to employ additional second-order Hessian geometry to enhance the sampling quality. The additional second-order information can guide Langevin dynamics to take more accurate steps [12, 54], which is called Newton-Langevin [73]. A natural idea is that we can also leverage the Hessian geometry of DMs within each noise level to enhance the quality of diffusion sampling results. However, it is extremely challenging to calculate the Hessian geometry within the context of high-dimensional DMs [3], cause it requires quadratic-complexity computations. Current methods on diffusion Hessian either require auxiliary networks [15, 84] or maintain memory-intensive states [64], making them inefficient for enhancing DM sampling."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.78,
+ 0.911,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "In this paper, we introduce a novel method for approximating the diffusion Hessian within a specific noise level. Notably, our approach is the first to approximate the diffusion Hessian and apply it to enhance the sampling quality of pretrained commercial-level DMs. Our method, inspired by the celebrated Levenberg-Marquardt method in optimization [45, 53, 68], is referred to as the Levenberg-Marquardt-Langevin (LML) method. Our approach introduces two key"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.109,
+ 0.874,
+ 0.345,
+ 0.888
+ ],
+ "angle": 0,
+ "content": "* Equal contribution † Corresponding author"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.11,
+ 0.888,
+ 0.325,
+ 0.899
+ ],
+ "angle": 0,
+ "content": "\\(\\ddagger\\)Work done as interns at WeChat Vision"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.109,
+ 0.874,
+ 0.345,
+ 0.899
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.945,
+ 0.519,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "10453"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.096,
+ 0.089,
+ 0.9,
+ 0.209
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.211,
+ 0.908,
+ 0.255
+ ],
+ "angle": 0,
+ "content": "Figure 1. Schematic comparison between our LML method and baselines. While previous works mainly focus on intriguing designs along the annealing path to improve diffusion sampling, they leave operations at specific noise levels to be first-order Langevin. Our approach proposes to leverage the Levenberg-Marquardt approximated Hessian geometry to guide the Langevin update to be more accurate."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.264,
+ 0.482,
+ 0.446
+ ],
+ "angle": 0,
+ "content": "innovations: Initially, we derive a computationally tractable low-rank approximation of the diffusion Hessian by emulating the Gauss-Newton transformation, avoiding explicit quadratic-complexity computations. This approach capitalizes on the inherent structure of DMs to construct a low-rank approximation that captures critical geometric information. Following this, we stabilize the approximated Hessian using the damping mechanism, which addresses its ill-conditioning, and acquire its inverse for geometric guidance. Our method uses this LML-approximated Hessian geometry to enable the Langevin dynamics to take more accurate steps and improve image generation quality."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.446,
+ 0.483,
+ 0.551
+ ],
+ "angle": 0,
+ "content": "We also conduct comprehensive theoretical analyses for our low-rank approximation and damping mechanism. First, we establish the error bound for the low-rank approximation of the diffusion Hessian. Subsequently, we prove that the damping mechanism preserves an unbiased stationary measure and exhibit exponentially fast convergence in terms of \\(\\chi^2\\)-divergence."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.552,
+ 0.484,
+ 0.627
+ ],
+ "angle": 0,
+ "content": "Extensive experiments on multiple pretrained DMs, including CIFAR-10, CelebA-HQ, SD-15, SD2-base, SD-XL and PixArt-\\(\\alpha\\), validate that the LML method significantly improves image generation quality with negligible computational overhead."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.631,
+ 0.231,
+ 0.647
+ ],
+ "angle": 0,
+ "content": "2. Preliminaries"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.656,
+ 0.483,
+ 0.839
+ ],
+ "angle": 0,
+ "content": "Notation. The Euclidean norm over \\(\\mathbb{R}^d\\) is denoted by \\(\\| \\cdot \\|\\). Throughout, we simply write \\(\\int g\\) to denote the integral with respect to the Lebesgue measure: \\(\\int g(x)\\mathrm{d}x\\). When the integral is with respect to a different measure \\(\\mu\\), we explicitly write \\(\\int g\\mathrm{d}\\mu\\). The expectation and variance of \\(g(X)\\) when \\(X\\sim p\\) are respectively denoted \\(\\mathbb{E}_{\\mu}g = \\int g\\mathrm{d}\\mu\\) and \\(\\operatorname{var}_{\\mu}g\\coloneqq \\int (g - \\mathbb{E}_{\\mu}g)^2\\mathrm{d}\\mu\\). When clear from context, we sometimes abuse notation by identifying a measure \\(\\mu\\) with its Lebesgue density. We use \\(\\pmb{I}_d\\) to denote the \\(d\\)-dimensional identity matrix; when clear from context, we sometimes simply write \\(\\pmb{I}\\). \\(\\pmb{H}_f\\) and \\(\\pmb{J}_f\\) denote the Hessian and Jacobian of \\(f\\) respectively."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.849,
+ 0.453,
+ 0.866
+ ],
+ "angle": 0,
+ "content": "2.1. Langevin Dynamics and Gradient Descent"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.871,
+ 0.483,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "In statistics, the (Stein) score of a distribution \\( p(\\pmb{x}) \\) is defined to be \\( \\nabla_{\\pmb{x}} \\log p(\\pmb{x}) \\). Given an initial value \\( \\pmb{x}_0 \\sim \\pi(\\pmb{x}) \\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.264,
+ 0.907,
+ 0.311
+ ],
+ "angle": 0,
+ "content": "with \\(\\pi\\) being a prior distribution, Langevin dynamics (LD) can produce samples from \\(p(\\pmb{x})\\) using only the score function \\(\\nabla_{\\pmb{x}}\\log p(\\pmb{x})\\) following the SDE,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.594,
+ 0.32,
+ 0.907,
+ 0.339
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} \\boldsymbol {x} _ {t} = \\nabla_ {\\boldsymbol {x}} \\log p (\\boldsymbol {x} _ {t}) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} B _ {t}, \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.347,
+ 0.907,
+ 0.53
+ ],
+ "angle": 0,
+ "content": "where \\( B_{t} \\) is the standard d-dimensional Brownian Motion (BM). The distribution of \\( \\pmb{x}_t \\) equals \\( p(\\pmb{x}) \\) when \\( T \\to \\infty \\), in which case \\( \\pmb{x}_t \\) becomes an exact sample from \\( p(\\pmb{x}) \\) under some regularity conditions [86]. Strictly speaking, a Metropolis-Hastings adjustment is needed, but it can often be ignored in practice [9]. There is a deep connection involving the distribution of \\( \\pmb{x}_t \\) in LD to the renowned Gradient Descent method (GD) [56] in optimization. The marginal distribution of a Langevin process \\( (\\pmb{x}_t)_{t\\geq 0} \\) evolves according to a GD, over the Wasserstein probability space, that minimizes the Kullback-Leibler (KL) divergence \\( D_{\\mathrm{KL}}(\\cdot \\| \\pi)[2,36,81] \\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.536,
+ 0.869,
+ 0.553
+ ],
+ "angle": 0,
+ "content": "2.2. Diffusion Models and Annealed Langevin"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.558,
+ 0.906,
+ 0.635
+ ],
+ "angle": 0,
+ "content": "Suppose that we have a d-dimensional random variable \\(\\pmb{x}(0) \\in \\mathbb{R}^d\\) following an unknown target distribution \\(p_0(\\pmb{x}_0)\\). Diffusion Models (DMs) define a forward process \\(\\{\\pmb{x}(t)\\}_{t \\in [0,T]}\\) with \\(T > 0\\) starting with \\(\\pmb{x}(0)\\), such that the distribution of \\(\\pmb{x}(t)\\) conditioned on \\(\\pmb{x}(0)\\) satisfies"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.554,
+ 0.643,
+ 0.907,
+ 0.663
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {t | 0} (\\boldsymbol {x} (t) | \\boldsymbol {x} (0)) = \\mathcal {N} (\\boldsymbol {x} (t); \\alpha (t) \\boldsymbol {x} (0), \\sigma^ {2} (t) \\mathbf {I}), \\quad (2)\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.668,
+ 0.906,
+ 0.715
+ ],
+ "angle": 0,
+ "content": "where \\(\\alpha (\\cdot),\\sigma (\\cdot)\\in \\mathcal{C}([0,T],\\mathbb{R}^{+})\\) have bounded derivatives, and we denote them as \\(\\alpha_{t}\\) and \\(\\sigma_t\\) for simplicity. The choice for \\(\\alpha_{t}\\) and \\(\\sigma_t\\) is referred to as the noise schedule of a DM."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.714,
+ 0.906,
+ 0.806
+ ],
+ "angle": 0,
+ "content": "DMs, both SMLD [76] and DDPM [30], can be seen as learning a network to match the score of the diffused distribution \\(\\log p_t(\\pmb{x}_t)\\) at different noise levels. In practice, DMs usually use \\(\\varepsilon_{\\theta}(\\pmb{x}(t), t)\\) to estimate \\(-\\sigma(t) \\nabla_{\\pmb{x}(t)} \\log p_t(\\pmb{x}(t), t)\\) via optimizing the following denoising score matching objective:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.513,
+ 0.814,
+ 0.91,
+ 0.833
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbb {E} _ {t} \\left\\{\\lambda_ {t} \\mathbb {E} _ {x _ {0}, x _ {t}} \\left[ \\| s _ {\\theta} (x _ {t}, t) - \\nabla_ {x _ {t}} \\log p (x _ {t}, t | x _ {0}, 0) \\| ^ {2} \\right] \\right\\}. \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.84,
+ 0.907,
+ 0.9
+ ],
+ "angle": 0,
+ "content": "The sampling process of diffusion models can be seen as annealed Langevin dynamics [76], which executes Langevin updates at each noise level while progressively reducing the noise scale."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.945,
+ 0.52,
+ 0.958
+ ],
+ "angle": 0,
+ "content": "10454"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.097,
+ 0.099,
+ 0.898,
+ 0.229
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
+ 0.24,
+ 0.908,
+ 0.312
+ ],
+ "angle": 0,
+ "content": "Figure 2. The relation between optimization algorithms and MCMC sampling algorithms. We initially wanted to develop a diffusion sampler utilizing Hessian geometry, following the path of Newton-Langevin dynamics [73]. However, this approach proved to be highly computationally expensive within the DM context. Drawing inspiration from the Levenberg-Marquardt method used in optimization, our method incorporates low-rank approximation and damping techniques. This enables us to obtain the Hessian geometry in a computationally affordable manner. Subsequently, we use this approximated Hessian geometry to guide the Langevin updates."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.322,
+ 0.43,
+ 0.339
+ ],
+ "angle": 0,
+ "content": "2.3. Langevin Guided by Hessian Geometry"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.345,
+ 0.484,
+ 0.435
+ ],
+ "angle": 0,
+ "content": "Newton's method (also called Newton-Raphson) [60] is a famous optimization method that utilizes the second-order Hessian geometry to improve the GD. Developed as an analogy to Newton's method, the Newton-Langevin dynamics [54] utilize Hessian geometry to generate samples that adhere to the SDE"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.1,
+ 0.449,
+ 0.483,
+ 0.47
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} \\boldsymbol {x} _ {t} = \\left[ \\nabla_ {\\boldsymbol {x}} ^ {2} \\log p (\\boldsymbol {x} _ {t}) \\right] ^ {- 1} \\nabla_ {\\boldsymbol {x}} \\log p (\\boldsymbol {x} _ {t}) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} B _ {t} ^ {\\prime}, \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.483,
+ 0.484,
+ 0.694
+ ],
+ "angle": 0,
+ "content": "where the \\( B_{t}^{\\prime} \\) is the BM scaled by the square-rooted Hessian geometry. Calculating the Hessian geometry of high-dimensional distributions poses a significant challenge. Some studies have attempted to alleviate this issue through the Quasi-Newton technique [22, 73]. However, these approaches fail to address the problem in the context of DM-scale dimensional data. For instance, the Stable Diffusionv1.5 model [67] features a latent dimension of 16384, resulting in a Hessian matrix of \\( 16384 \\times 16384 \\). Current methods on diffusion Hessian either require auxiliary networks training [15, 84] or maintain memory-intensive states [64]. To the best of our knowledge, there is currently no effective method available to access the diffusion Hessian of advanced commercial-level DMs like SD-XL."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.71,
+ 0.367,
+ 0.725
+ ],
+ "angle": 0,
+ "content": "2.4. Levenberg-Marquardt Method"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.733,
+ 0.484,
+ 0.809
+ ],
+ "angle": 0,
+ "content": "In the field of optimization, the Levenberg-Marquardt (LM) method [68] is proposed as a computationally friendly and stabilized analogue to Newton's method. Specifically, it modifies the computation of Hessian geometry in Newton's method in two key aspects:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.811,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "- Low-rank approximated Hessian In the context of least squares problems, the Levenberg-Marquardt method often constructs a low-rank estimation of the Hessian geometry. Specifically, when \\( f(\\pmb{x}) = \\sum_{i=1}^{m} r_i(\\pmb{x})^2 \\), the Levenberg-Marquardt method approximates the Hessian into the following form, which is constructed from the"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.528,
+ 0.322,
+ 0.646,
+ 0.338
+ ],
+ "angle": 0,
+ "content": "Jacobian \\( J_{f}(\\pmb {x}) \\)"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.626,
+ 0.348,
+ 0.905,
+ 0.366
+ ],
+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {H} _ {f} (\\boldsymbol {x}) \\approx 2 \\boldsymbol {J} _ {f} (\\boldsymbol {x}) ^ {\\top} \\boldsymbol {J} _ {f} (\\boldsymbol {x}). \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.527,
+ 0.377,
+ 0.905,
+ 0.451
+ ],
+ "angle": 0,
+ "content": "This low-rank approximation technique is also referred to as the Gauss-Newton method in some literature [16]. However, it is still unclear how to obtain a Levenberg-Marquardt-type low-rank estimation of the Hessian in the context of diffusion models."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.514,
+ 0.453,
+ 0.907,
+ 0.56
+ ],
+ "angle": 0,
+ "content": "- Damping mechanism The Levenberg-Marquardt Method introduces an additional damping identity matrix to the Hessian geometry. That is, it replaces the pure Hessian geometry \\(\\left[\\boldsymbol{H}_f(\\boldsymbol{x}_k)\\right]^{-1}\\) in Newton's method with a combination expressed as \\(\\left[\\boldsymbol{H}_f(\\boldsymbol{x}_k) + \\lambda \\boldsymbol{I}\\right]^{-1}\\). Consequently, the Levenberg-Marquardt Method with damping is expressed as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.554,
+ 0.57,
+ 0.905,
+ 0.589
+ ],
+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {x} _ {k + 1} = \\boldsymbol {x} _ {k} - \\eta \\left[ \\boldsymbol {H} _ {f} \\left(\\boldsymbol {x} _ {k}\\right) + \\lambda \\boldsymbol {I} \\right] ^ {- 1} \\nabla_ {\\boldsymbol {x}} f \\left(\\boldsymbol {x} _ {k}\\right). \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.526,
+ 0.599,
+ 0.906,
+ 0.69
+ ],
+ "angle": 0,
+ "content": "Empirical evidence suggests that the damping mechanism contributes to numerical stabilization [41], since \\(\\lambda I\\) can resolve the ill-conditioning of the Hessian. While the damping mechanism can be perceived as a trust region approach, it is more intuitive to view \\(H + \\lambda I\\) as a geometrical interpolation between \\(H\\) and \\(I\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
+ 0.703,
+ 0.649,
+ 0.72
+ ],
+ "angle": 0,
+ "content": "3. Methodology"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.728,
+ 0.906,
+ 0.744
+ ],
+ "angle": 0,
+ "content": "3.1. Low-rank Approximation of Diffusion Hessian"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.75,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Inspired by the low-rank estimation technique of the Hessian in the Levenberg-Marquardt method, we derive a similar low-rank estimation for the diffusion Hessian. Specifically, we follow the intuition of the Levenberg-Marquardt method to approximate the diffusion Hessian by simplifying the second-order partial derivatives. The low-rank approximate Hessian of diffusion models that we obtained is shown below. It is important to note that it includes noise schedule related coefficients, which distinguishes it from the least squares problem case in Eq. 5."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.945,
+ 0.519,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "10455"
+ }
+ ],
+ [
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.113,
+ 0.089,
+ 0.478,
+ 0.099
+ ],
+ "angle": 0,
+ "content": "DDIM PNDM DPM-Solver DPM-Solver++ UniPC LML(Ours)"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.097,
+ 0.099,
+ 0.481,
+ 0.446
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.458,
+ 0.483,
+ 0.515
+ ],
+ "angle": 0,
+ "content": "Figure 3. Visual comparison of images generated by our LML method and other methods, using the pre-trained LDM on CelebAHQ \\(256\\times 256\\) [39] with the same seeds. It shows that our LML method contributes to more vivid and detailed generated images."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.528,
+ 0.485,
+ 0.609
+ ],
+ "angle": 0,
+ "content": "Proposition 1. Let \\( p_t \\) be the diffused marginal distribution at time \\( t \\) of the diffusion process, Eq. 2 and \\( \\varepsilon_\\theta \\) is learned via Eq. 3, then the Hessian derivative of its log-density function \\( \\nabla_{\\boldsymbol{x}_t}^2 \\log p_t(\\boldsymbol{x}_t) \\) has a low-rank approximation form of \\( \\frac{1}{\\sigma(t)^2 \\| \\varepsilon_\\theta \\|^2} \\varepsilon_\\theta \\varepsilon_\\theta^\\top \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.614,
+ 0.484,
+ 0.721
+ ],
+ "angle": 0,
+ "content": "Notice that this approximation form is a scaled outer-product of the score. The detailed derivation can be found in the Supplementary A.2. For here and for the remainder of the paper, we will denote \\(\\varepsilon_{\\theta}(\\boldsymbol{x}(t), t)\\) as \\(\\varepsilon_{\\theta}\\), provided there is no risk of ambiguity. In section 4.1, we will show that this low-rank approximation possesses an error bound, ensuring that our approximation does not generate excessive errors."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.728,
+ 0.292,
+ 0.744
+ ],
+ "angle": 0,
+ "content": "3.2. Damping Mechanism"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.75,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Similar to the scenario in the Levenberg-Marquardt method, we have obtained an accessible approximation of the diffusion Hessian as presented in Proposition 1. However, this form is significantly ill-conditioned, making its inverse impossible to calculate. Specifically, the outer-product Hessian in Proposition 1 has an infinite condition number [32]; hence, its inverse strictly does not exist in mathematical terms. To address this issue, we propose adopting the damping mechanism used in the LML method. We introduce an additional damping identity matrix to the approximate Hes"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.906,
+ 0.152
+ ],
+ "angle": 0,
+ "content": "sian as shown in Proposition 1. This damped Hessian geometry is used in place of the full Hessian in the Newton Langevin in Eq. 4, we consequently derive the following damping dynamics:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.513,
+ 0.164,
+ 0.906,
+ 0.198
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} \\boldsymbol {x} _ {t} = \\left[ \\nabla_ {\\boldsymbol {x}} ^ {2} \\log p \\left(\\boldsymbol {x} _ {t}\\right) + \\lambda I \\right] ^ {- 1} \\nabla_ {\\boldsymbol {x}} \\log p \\left(\\boldsymbol {x} _ {t}\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} B _ {t} ^ {\\prime}, \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.199,
+ 0.907,
+ 0.41
+ ],
+ "angle": 0,
+ "content": "where the \\( B_{t}^{\\prime} \\) is the BM scaled by the square-rooted LM approximated Hessian geometry. Drawing inspiration from the Levenberg-Marquardt method, we refer to this damping Hessian Langevin in Eq. 7 as the Levenberg-Marquardt-Langevin dynamics (LML dynamics). Similar to the Levenberg-Marquardt method, the damping coefficient \\( \\lambda \\) in Eq. 7 can be interpreted as an interpolation coefficient between the Hessian geometry and Identity geometry. Specifically, as \\( \\lambda \\rightarrow \\infty \\), Eq. 7 would degenerate to the standard Langevin with normalization on the geometry. We observe that by adding the Levenberg-Marquardt damping identity matrix to the outer-product form of the Hessian in Equation Proposition 1, its inverse can be conveniently computed using the Sherman-Morrison formula [72]."
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ 0.433,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\boldsymbol {H} _ {L M} ^ {- 1} (\\boldsymbol {x} _ {t}, \\lambda) = \\left[ \\nabla_ {\\boldsymbol {x}} ^ {2} \\log p (\\boldsymbol {x} _ {t}) + \\lambda \\boldsymbol {I} \\right] ^ {- 1} \\\\ \\approx \\left[ \\frac {1}{\\sigma (t) ^ {2} \\| \\varepsilon_ {\\theta} \\| ^ {2}} \\varepsilon_ {\\theta} \\varepsilon_ {\\theta} ^ {\\top} + \\lambda I \\right] ^ {- 1} \\\\ = \\frac {1}{\\sigma (t) ^ {2} \\| \\varepsilon_ {\\theta} \\| ^ {2}} \\left[ \\varepsilon_ {\\theta} \\varepsilon_ {\\theta} ^ {\\top} + \\lambda^ {\\prime} I \\right] ^ {- 1} \\tag {8} \\\\ = \\frac {1}{\\lambda^ {\\prime} \\sigma (t) ^ {2} \\| \\boldsymbol {\\varepsilon} _ {\\theta} \\| ^ {2}} \\left[ \\boldsymbol {I} - \\frac {\\boldsymbol {\\varepsilon} _ {\\theta} \\boldsymbol {\\varepsilon} _ {\\theta} ^ {\\top}}{\\lambda^ {\\prime} + \\| \\boldsymbol {\\varepsilon} _ {\\theta} \\| ^ {2}} \\right], \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(\\lambda' = \\sigma(t)^2\\|\\varepsilon_\\theta\\|^2\\lambda\\). We also point out that the coefficients \\(\\frac{1}{\\lambda'\\sigma(t)^2\\|\\varepsilon_\\theta\\|^2}\\) will be absorbed in the discretizing stepsize of the LML dynamics and only affect the norm. The geometry direction essence is in the \\(\\left[I - \\frac{\\varepsilon_\\theta\\varepsilon_\\theta^\\top}{\\lambda' + \\|\\varepsilon_\\theta\\|^2}\\right]\\) part. In the remainder of this paper, we will slightly abuse notation by not distinguishing between \\(\\lambda\\) and \\(\\lambda'\\). This simplification should not lead to any confusion."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3.3. Annealed Levenberg-Marquardt-Langevin"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ "angle": 0,
+ "content": "To utilize the LML for diffusion sampling, we perform the discretization of Eq. 7 at each nose level, and gradually decrease the noise level. We called this annealed LML, and point out that its continuous-time form would converge to the following SDE:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} x _ {t} = \\left[ f _ {t} \\boldsymbol {x} _ {t} - g _ {t} ^ {2} \\boldsymbol {H} _ {L M} ^ {- 1} \\nabla_ {x} \\log p _ {t} (\\boldsymbol {x} _ {t}) \\right] \\mathrm {d} t + g _ {t} \\mathrm {d} B _ {t} ^ {\\prime}. \\tag {9}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Similar to the connection of the reverse SDE and diffusion ODE [77], the LM reverse SDE in Eq. 9 also has an associated ODE, which is a deterministic process that shares the"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "10456"
+ }
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+ [
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "Algorithm 1 Levenberg-Marquardt-Langevin (LML) diffusion sampler"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.126,
+ 0.483,
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+ "angle": 0,
+ "content": "1: Input: pretrained diffusion model noise predictor \\(\\varepsilon_{\\theta}\\), number of timesteps \\(N\\), noise schedule \\(\\{\\alpha_t\\}\\) and \\(\\{\\sigma_t\\}\\), Levenberg-Marquardt damping coefficient \\(\\lambda > 0\\), EMA coefficient \\(\\kappa\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "2: Initiate \\( \\pmb{x}_{\\mathrm{list}} = [] \\), \\( \\widetilde{\\pmb{H}}_{N + 1}^{-1} = \\pmb{I} \\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "3: Sample \\( \\pmb{x}_N \\sim \\mathcal{N}(0, \\sigma_{t_N} I) \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "4: for \\( i = N, N - 1, \\dots, 1 \\) do"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "5: \\(\\varepsilon_{i} = \\varepsilon_{\\theta}(\\pmb{x}_{i},i)\\)"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "6: if \\(i\\neq N\\) then"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "7: \\(\\widetilde{\\varepsilon}_i = \\kappa *\\varepsilon_{i + 1} + (1 - \\kappa)*\\varepsilon_i\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "8: else"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "9: \\(\\widetilde{\\varepsilon}_i = \\varepsilon_i\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "10: end if"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "11: \\(\\widetilde{H}_i^{-1} = I - \\frac{\\widetilde{\\varepsilon}_i\\widetilde{\\varepsilon}_i^1}{\\lambda + \\| \\widetilde{\\varepsilon}_i\\| ^2}\\) {Levenberg-Marquardt approximate Hessian geometry}"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "12: \\(\\varepsilon_{i}^{LM} = \\widetilde{\\pmb{H}}_{i}^{-1}\\varepsilon_{i}\\) {Apply the approximate Hessian geometry}"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "13: \\(\\varepsilon_{i}^{LM} = \\frac{\\|\\pmb{\\varepsilon}_{i}\\|}{\\|\\pmb{\\varepsilon}_{i}^{LM}\\|}\\pmb{\\varepsilon}_{i}^{LM}\\) {Geometrical normalization}"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "14: \\( \\pmb{x}_{i-1} = \\mathrm{DPM-Solver}(\\pmb{x}_{\\mathrm{list}}, \\pmb{\\varepsilon}_i^{LM}, i) \\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "15: \\( \\mathbf{x}_{\\mathrm{list}} = \\mathbf{x}_{\\mathrm{list}}. \\) append \\( (\\mathbf{x}_{i - 1}) \\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "16: end for"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "17: Output: \\( x_0 \\)"
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "same single-time marginal distribution:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} x _ {t} = \\left[ f _ {t} \\boldsymbol {x} _ {t} - \\frac {1}{2} g _ {t} ^ {2} \\boldsymbol {H} _ {L M} ^ {- 1} \\nabla_ {\\boldsymbol {x}} \\log p _ {t} (\\boldsymbol {x} _ {t}) \\right] \\mathrm {d} t. \\tag {10}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.562,
+ 0.483,
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+ ],
+ "angle": 0,
+ "content": "The following section will develop a practical LML sampler based on this deterministic LML ODE."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Remark 1. Our LM process can be viewed as the Legendre dual of the classical diffusion process with a transform map of \\(\\nabla \\log p_t(\\cdot) + \\lambda \\| \\cdot \\|\\). See discussions in Supp. D.3."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.449,
+ 0.668
+ ],
+ "angle": 0,
+ "content": "3.4. Levenberg-Marquardt-Langevin Sampler"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.673,
+ 0.483,
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+ ],
+ "angle": 0,
+ "content": "We implement a diffusion sampler based on the LML diffusion ODE in Eq. 10, because it is suggested that deterministic diffusion samplers are far more efficient than the stochastic ones [40]. Our approach is generally consistent with the practices outlined in [76]. The scheme for our LML diffusion sampler is illustrated in Algorithm 1. Primarily, our sampler substitutes the first-order Langevin dynamics with LML at each noise level. At each noise level, we initially compute the LM low-rank approximated and damping Hessian geometry, \\(\\widetilde{H}_i^{-1}\\), as detailed in step 11 of Algorithm 1. We incorporate the network output from previous steps, as shown in step 7, following studies suggesting that this mixture is closer to the underlying true score due to the manifold's curvature [50]. We then apply this approximate Hessian geometry to our initial gradient, \\(\\varepsilon_{i}\\), to obtain"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ 0.091,
+ 0.914,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.513,
+ 0.466,
+ 0.907,
+ 0.509
+ ],
+ "angle": 0,
+ "content": "Figure 4. Qualitative comparison of our LML method and other methods in text-guided image generation. The evaluation was performed on SD-15 [67], using 10 NFEs and the same seeds."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.524,
+ 0.907,
+ 0.706
+ ],
+ "angle": 0,
+ "content": "the Hessian-guided gradient, \\(\\varepsilon_{i}^{LM}\\), as detailed in step 12. In terms of the stepsize for our LML sampler, in contrast to some sophisticated ways of choosing the stepsize of second-order methods [25, 43], we follow the approach of [20] to ensure that the Hessian geometry has a unit spectrum, which can be easily implemented through a normalization operation on the Hessian guided gradient \\(\\varepsilon_{i}^{LM}\\) as illustrated in step 13. The rescaling of BM in Eq. 7 can also be absorbed into this normalization operation. Once the Hessian-guided gradient, \\(\\varepsilon_{i}^{LM}\\), is obtained, we adopt the DPM-Solver as our denoising scheme to calculate the next state, \\(x_{i-1}\\), as shown in step 14."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.706,
+ 0.906,
+ 0.752
+ ],
+ "angle": 0,
+ "content": "It is worth noting that our LML does not require additional training, components, or network access. Instead, we only need several additional tensor arithmetic operations."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4. Theoretical Analysis"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.792,
+ 0.906,
+ 0.823
+ ],
+ "angle": 0,
+ "content": "In this section, we present rigorous theoretical analyses to substantiate the correctness and efficacy of our LML."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.842,
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+ ],
+ "angle": 0,
+ "content": "4.1. Analysis on Low-rank Approximation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ 0.906,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Here, we establish the error bound of the low-rank approximation of the diffusion Hessian in Proposition 1, thereby ensuring that our approximation does not introduce excess"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
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+ ],
+ "angle": 0,
+ "content": "10457"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.098,
+ 0.09,
+ 0.488,
+ 0.453
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.466,
+ 0.483,
+ 0.508
+ ],
+ "angle": 0,
+ "content": "Figure 5. Qualitative comparison of our LML method and other methods in text-guided image generation. The evaluation was performed on SD2-base [67], using 10 NFEs and the same seeds."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.525,
+ 0.484,
+ 0.571
+ ],
+ "angle": 0,
+ "content": "sive errors. Given that we are evaluating the accuracy of a matrix-valued approximation, we choose to use the Hilbert-Schmidt norm [24] as a criterion."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Proposition 2. Assume that the norm of \\( \\pmb{x}_t \\) is bounded by \\( \\delta_1 \\), the approximation error on \\( \\varepsilon_{\\theta}(\\pmb{x}_t, t) \\) is denoted as \\( \\delta_2 \\), \\( \\delta_3 \\) denote the bound on the second partial derivative of \\( \\delta_1 \\) w.r.t. \\( \\pmb{x}_t \\), and \\( \\mathcal{D}_y \\) denote the dataset diameter. The approximation error of the LM low-rank Hessian, as referenced in Proposition 1, is at most \\( (\\delta_1 + \\alpha_t \\delta_2 + \\alpha_t \\mathcal{D}_y) (2 + \\delta_3 + 2 \\frac{\\alpha_t^2}{\\sigma_t^2} \\mathcal{D}_y^2) \\) when measured in terms of the Hilbert-Schmidt norm."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.737
+ ],
+ "angle": 0,
+ "content": "Our analysis relies on the analytical form diffusion Fisher [84]. The detailed proof can be found in Supp. A.6."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "4.2. Analysis on Damping Mechanism"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.769,
+ 0.483,
+ 0.8
+ ],
+ "angle": 0,
+ "content": "Subsequently, we demonstrate the unbiased, exponentially fast convergence property of the damping mechanism."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.808,
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+ ],
+ "angle": 0,
+ "content": "4.2.1. Stationary Measure"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.827,
+ 0.484,
+ 0.888
+ ],
+ "angle": 0,
+ "content": "We confirm that the stationary measure of the damping dynamics, as defined in Eq. 7, aligns with the target diffused distribution. This ensures that the damping updates still guide samples towards the correct data distribution."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ 0.907,
+ 0.153
+ ],
+ "angle": 0,
+ "content": "Proposition 3. Under mild regularity conditions, the stationary distribution of the damping dynamics in Eq. 7 exists and is unique, which also coincides with the marginal distribution \\( p_t(\\boldsymbol{x}_t) \\) at every noise level."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.165,
+ 0.907,
+ 0.197
+ ],
+ "angle": 0,
+ "content": "We achieve this analysis by the Fokker-Planck equation [63]. The detailed proof can be found in Supp. A.7."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "4.2.2. Ergodic Convergence Rate"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.225,
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+ 0.286
+ ],
+ "angle": 0,
+ "content": "We also want to determine the speed at which our damping dynamics converge. We demonstrate that our damping dynamics exhibit a satisfyingly fast, exponential convergence rate towards the target distribution."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.298,
+ 0.907,
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+ ],
+ "angle": 0,
+ "content": "Proposition 4. Let \\(\\mu_t\\) be the evolving distribution of the damping dynamics in Eq. 7. We have that \\(\\mu_t\\) converges to the stationary distribution at an exponential ergodic convergence rate in terms of \\(\\chi^2\\)-distance at every noise level, under certain regularity conditions."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.387,
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+ 0.433
+ ],
+ "angle": 0,
+ "content": "We achieve this analysis by determining the relationship between Eq. 7 and the Mirror-Langevin [12]. The formal version and detailed proof can be found in Supp. A.8."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Remark 2. Once we establish the exponential ergodic convergence rate in terms of \\(\\chi^2\\)-distance, The exponential convergence results for total variation distance [80], Hellinger distance [28], KL divergence [44] as illustrated in [4, §2.4]. And the exponential convergence results on Wasserstein distance [81] can also be established with a log-Sobolev assumption, as illustrated in [14]."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.645,
+ 0.585
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+ "angle": 0,
+ "content": "5. Experiments"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.594,
+ 0.907,
+ 0.777
+ ],
+ "angle": 0,
+ "content": "In this section, we validate the enhanced sampling quality of our LML method across various pretrained DMs. We evaluate in both pixel-space, latent-space, and text-guided conditional generation scenarios. We select several most commonly-used and advanced sampling methods such as DDIM [77], PNDM [50], DPM-Solver [51], DPM-Solver++ [52] and UniPC [92] as baselines. We will also demonstrate the computational efficiency of our LML method. All experiments are executed using open-source, pretrained DMs, with the datatype set to float32 and the timestep scheme as uniform. More experimental details and results are deferred to Supp. B and C."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.783,
+ 0.804
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+ "angle": 0,
+ "content": "5.1. Pixel-Space Image Generation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.81,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "We initially compare the unconditional sampling quality of our LML method with baselines on the CIFAR-10 dataset [1]. For each sampler, we generate 50,000 samples for FID evaluation. As illustrated in Table 1 and Figure 6a, our approach improves the sampling performance of the baseline Langevin methods in most NFE scenarios."
+ },
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+ "content": "10458"
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+ ],
+ [
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+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(a) CIFAR-10"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.366,
+ 0.09,
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+ "angle": 0,
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+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(b) SD-15 on MS-COCO"
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+ "bbox": [
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+ "angle": 0,
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+ "content": "(c) SD2-base on MS-COCO"
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+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.237,
+ 0.905,
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+ ],
+ "angle": 0,
+ "content": "Figure 6. This line chart compares the log-FID scores \\((\\downarrow)\\) on (a) CIFAR-10, (b) MS-COCO with SD-15 and (c) MS-COCO with SD2-base."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.089,
+ 0.267,
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+ ],
+ "angle": 0,
+ "content": "Table 1. Comparison of different samplers on FID score( ↓) on CIFAR-10 unconditional generation. Best results are bolded and the second best results are underlined. The FID scores were obtained by generating 50,000 samples, and all samplers were tested using the same seeds on the same checkpoint. It is shown that our LML always achieves the best or second best FID across all different NFEs."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ 0.319,
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+ "angle": 0,
+ "content": "| Methods | FID (↓) on CIFAR-10 generation |
| 5 NFEs | 6 NFEs | 7 NFEs | 8 NFEs | 9 NFEs | 10 NFEs | 12 NFEs | 15 NFEs | 20 NFEs | 30 NFEs | 50 NFEs | 100 NFEs |
| DDIM [75] | 42.17 | 32.09 | 26.21 | 22.38 | 19.64 | 17.45 | 14.27 | 12.67 | 10.60 | 8.58 | 6.96 | 5.72 |
| PNDM [50] | 46.56 | 15.27 | 12.59 | 10.73 | 9.59 | 7.16 | 6.73 | 5.70 | 5.28 | 4.94 | 4.24 | 3.93 |
| DPM-Solver [51] | 33.26 | 23.06 | 17.61 | 14.58 | 12.47 | 11.13 | 9.28 | 4.98 | 4.23 | 3.74 | 3.66 | 3.62 |
| DPM-Solver++ [52] | 30.87 | 20.92 | 16.22 | 13.63 | 11.89 | 10.71 | 10.59 | 10.17 | 9.90 | 6.58 | 5.06 | 4.46 |
| UniPC [92] | 29.81 | 20.64 | 16.10 | 13.59 | 11.84 | 10.70 | 9.02 | 7.51 | 6.03 | 4.66 | 3.82 | 3.58 |
| LML (Ours) | 17.28 | 14.18 | 11.15 | 8.09 | 7.16 | 6.54 | 5.97 | 4.70 | 4.19 | 3.69 | 3.63 | 3.58 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Table 2. Comparison of different samplers on CelebA-HQ unconditional generation. Best results are bolded and the second best results are underlined."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ 0.504,
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+ "angle": 0,
+ "content": "| Methods | Colorful | Face Quality | Aesthetic |
| ColorS(↑) | FS(↑) | DFIQA(↑) | PicS(↑) | EAT(↑) | Laion(↑) |
| DDIM [75] | 34.13 | 4.85 | 0.539 | 19.85 | 4.61 | 5.24 |
| PNDM [50] | 38.29 | 4.89 | 0.553 | 19.70 | 4.28 | 5.11 |
| DPM [51] | 34.85 | 5.06 | 0.566 | 20.00 | 4.51 | 5.29 |
| DPM++ [52] | 35.08 | 5.08 | 0.560 | 19.97 | 4.46 | 5.26 |
| UniPC [92] | 35.95 | 5.09 | 0.568 | 19.97 | 4.47 | 5.26 |
| LML(Ours) | 40.53 | 5.24 | 0.607 | 20.98 | 4.75 | 5.37 |
"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.09,
+ 0.626,
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+ "angle": 0,
+ "content": "5.2. Latent-Space Image Generation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.649,
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+ ],
+ "angle": 0,
+ "content": "We evaluated our LML on the LDM [67] that was trained on CelebA-HQ [39] at a resolution of \\(256 \\times 256\\). In Table 2, we employed five metrics spanning three aspects to demonstrate the superiority of LML. These aspects include colorfulness [26], face quality (FS [46] and DFIQA [10]), and human-preference-aesthetic scores (PicS [42], EAT [27] and Laion-Aes [71]). Additionally, we present a visual comparison in Figure 3. All these experiments were carried out with a NFE of 10. The results were tested by averaging over 1000 samples and the same seeds."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.812,
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+ ],
+ "angle": 0,
+ "content": "5.3. Text-guided Image Generation"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
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+ ],
+ "angle": 0,
+ "content": "5.3.1. Qualitative Comparison"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Qualitative comparison on SD-15 and SD2-base generation is provided in Figure 4 and 5, clearly indicating that our LML method enhances the quality of image details under"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.513,
+ 0.45,
+ 0.906,
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+ ],
+ "angle": 0,
+ "content": "Table 3. Comparison of FID score \\((\\downarrow)\\) for the task of text-guided conditional generation of SD on randomly selected 30,000 MS-COCO prompts. Best results are bolded and the second best results are underlined."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "| Methods\\NFEs | FID (↓) on MS-COCO-14 prompts |
| 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 |
| SD-1.5 |
| DDIM [75] | 29.14 | 27.11 | 23.48 | 22.36 | 21.14 | 21.22 | 19.91 | 19.36 |
| PNDM [50] | 35.50 | 34.49 | 29.50 | 27.86 | 24.46 | 22.35 | 19.13 | 17.92 |
| DPM [51] | 22.07 | 20.58 | 19.92 | 19.64 | 19.47 | 19.34 | 19.30 | 17.32 |
| DPM++ [52] | 21.75 | 20.14 | 19.60 | 19.32 | 19.19 | 19.13 | 19.11 | 18.03 |
| UniPC [92] | 21.72 | 20.30 | 19.84 | 19.67 | 19.55 | 19.40 | 19.41 | 19.29 |
| LML (Ours) | 18.68 | 18.13 | 17.61 | 17.50 | 17.58 | 17.60 | 17.55 | 16.98 |
| SD2-base |
| DDIM [75] | 27.34 | 24.25 | 22.47 | 21.48 | 19.73 | 20.43 | 18.73 | 18.19 |
| PNDM [50] | 31.13 | 30.93 | 26.33 | 25.56 | 22.04 | 20.35 | 17.39 | 16.47 |
| DPM [51] | 21.25 | 19.94 | 19.21 | 18.78 | 18.51 | 18.36 | 18.13 | 15.84 |
| DPM++ [52] | 20.94 | 19.51 | 18.77 | 18.43 | 18.21 | 18.06 | 17.86 | 15.99 |
| UniPC [92] | 20.81 | 19.40 | 18.82 | 18.56 | 18.36 | 18.27 | 18.08 | 18.03 |
| LML (Ours) | 17.76 | 16.99 | 16.17 | 16.02 | 16.29 | 15.95 | 16.16 | 15.14 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.739,
+ 0.808,
+ 0.753
+ ],
+ "angle": 0,
+ "content": "the same seed and prompt with a NFE of 10."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.773,
+ 0.777,
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+ ],
+ "angle": 0,
+ "content": "5.3.2. FID on MS-COCO Benchmark"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.795,
+ 0.906,
+ 0.9
+ ],
+ "angle": 0,
+ "content": "Following the approach in [69, 90], we randomly selected 30,000 prompts from the MS-COCO dataset [47] and generated images conditioned on these prompts. We tested our sampler in terms of FID on the SD-1.5 and SD2-base models with resolutions of \\(512 \\times 512\\) and a CFG scale 7.0. Table 3 shows that our LML sampler surpasses the baseline methods on SD models across different NFEs."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "10459"
+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
+ 0.09,
+ 0.908,
+ 0.119
+ ],
+ "angle": 0,
+ "content": "Table 4. Comparison of different samplers in text-guided image generation task on the T2I-BC benchmark [34]. The metrics are Color, Shape, and Texture. Best results are bolded and the second best results are underlined."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.099,
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+ 0.9,
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+ ],
+ "angle": 0,
+ "content": "| Metrics | T2I Benchmark on SD-1.5 [67] | T2I Benchmark on SD2-base [67] | T2I Benchmark on SD-XL [59] | T2I Benchmark on PixArt-α [8] |
| Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) |
| DDIM [75] | 0.3864 | 0.3791 | 0.4231 | 0.5111 | 0.4182 | 0.4822 | 0.5670 | 0.4712 | 0.5076 | 0.2933 | 0.3746 | 0.4045 |
| PNDM [50] | 0.3810 | 0.3761 | 0.4331 | 0.5067 | 0.4190 | 0.4863 | 0.5682 | 0.4772 | 0.5085 | 0.4035 | 0.3996 | 0.4225 |
| DPM [51] | 0.3877 | 0.3945 | 0.4294 | 0.5162 | 0.4307 | 0.5002 | 0.5795 | 0.4841 | 0.5194 | 0.3263 | 0.3895 | 0.4349 |
| DPM++ [52] | 0.3881 | 0.3958 | 0.4307 | 0.5202 | 0.4326 | 0.5020 | 0.5798 | 0.4858 | 0.5201 | 0.3136 | 0.3882 | 0.4364 |
| UniPC [92] | 0.3892 | 0.3889 | 0.4306 | 0.5146 | 0.4337 | 0.4995 | 0.5828 | 0.4910 | 0.5234 | 0.3187 | 0.3880 | 0.4266 |
| LML (Ours) | 0.4335 | 0.4252 | 0.4746 | 0.5640 | 0.4792 | 0.5330 | 0.5908 | 0.4938 | 0.5363 | 0.3801 | 0.4265 | 0.4684 |
"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.093,
+ 0.262,
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+ 0.412
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.125,
+ 0.422,
+ 0.45,
+ 0.436
+ ],
+ "angle": 0,
+ "content": "Figure 7. LML integrates seamlessly with ControlNet."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.468,
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+ ],
+ "angle": 0,
+ "content": "5.3.3. T2I-CB Benchmark"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.489,
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+ ],
+ "angle": 0,
+ "content": "To further validate the enhanced sampling quality of LML in text-to-image generation, we carried out tests on diverse commercial-level DMs (SD-1.5 [67], SD2-base [67], SD-XL [59], and PixArt-\\(\\alpha\\) [8]) using the T2I-CB [34] benchmark. This benchmark is designed for open-world text-to-image generation evaluation. For each model, we evaluated three metrics (color, shape, and texture) to assess the visual quality of the samplers. Each assessment was based on 30,000 images with a NFE of 10. As shown in Table 4, our LML always achieves the best or second best scores on T2I-BC across these models."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.672,
+ 0.325,
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+ ],
+ "angle": 0,
+ "content": "5.3.4. Application on ControlNet"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.754
+ ],
+ "angle": 0,
+ "content": "Our model can seamlessly integrate with existing diffusion model plugins, such as ControlNet [89]. The results in Fig 7 demonstrate that our method is fully compatible with ControlNet and generates high-quality samples."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.771,
+ 0.31,
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+ ],
+ "angle": 0,
+ "content": "5.4. Time-costs Comparison"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Table 5 presents the average wall-clock time costs for LML across different image generation tasks. These time-cost experiments were conducted on a single NVIDIA RTX 4090 chip and averaged over 200 tests with a batchsize of 1. The results suggest that the additional computational cost incurred by our LML technique is virtually negligible, making LML as time-efficient as DDIM [75]."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.53,
+ 0.263,
+ 0.889,
+ 0.276
+ ],
+ "angle": 0,
+ "content": "Table 5. Average wall-clock time costs for LML and DDIM."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "| Models | Methods \\NFEs | Time-costs (s) |
| 5 | 10 | 15 | 20 | 30 | 50 | 100 |
| CIFAR-10 | DDIM | 0.13 | 0.20 | 0.27 | 0.34 | 0.52 | 0.81 | 1.49 |
| LML (Ours) | 0.13 | 0.21 | 0.27 | 0.37 | 0.48 | 0.82 | 1.51 |
| CelebA | DDIM | 0.20 | 0.28 | 0.39 | 0.47 | 0.66 | 1.03 | 1.95 |
| LML (Ours) | 0.20 | 0.31 | 0.38 | 0.48 | 0.67 | 1.10 | 2.08 |
| SD-1.5 | DDIM | 0.45 | 0.73 | 1.03 | 1.31 | 1.87 | 3.01 | 5.85 |
| LML (Ours) | 0.45 | 0.74 | 1.04 | 1.32 | 1.89 | 3.03 | 5.89 |
| SD-2base | DDIM | 0.45 | 0.71 | 1.00 | 1.25 | 1.80 | 2.87 | 5.53 |
| LML (Ours) | 0.46 | 0.72 | 0.98 | 1.27 | 1.81 | 2.88 | 5.60 |
| SD-XL | DDIM | 2.32 | 4.25 | 6.23 | 8.12 | 12.06 | 19.82 | 39.48 |
| LML (Ours) | 2.32 | 4.30 | 6.23 | 8.21 | 12.11 | 19.99 | 39.55 |
| PixArt | DDIM | 0.66 | 1.08 | 1.49 | 1.92 | 2.74 | 4.31 | 8.45 |
| LML (Ours) | 0.67 | 1.08 | 1.51 | 1.92 | 2.75 | 4.28 | 8.49 |
"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.452,
+ 0.688,
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+ ],
+ "angle": 0,
+ "content": "5.5. Hyperparameters"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.474,
+ 0.907,
+ 0.686
+ ],
+ "angle": 0,
+ "content": "Our LML introduces two robust hyperparameters with clear high-level interpretations: the damping coefficient \\(\\lambda\\) and the mixture coefficient \\(\\kappa\\). The damping coefficient \\(\\lambda\\) determines the degree to which our approximated Hessian is interpolated with the identity matrix. A larger \\(\\lambda\\) value results in the dominance of the identity matrix, leading the LML to degenerate into Langevin. Conversely, a smaller \\(\\lambda\\) value allows more guidance from the Hessian geometry, but a minimal value could lead to ill-conditioning issues. The \\(\\kappa\\) controls the EMA rate of previous information. A small \\(\\kappa\\) would make the LML close to the identity map, but LML contributes to obvious image quality enhancement in practice. More discussions on hyperparameter tuning scheme, setup, and ablation experiments are provided in Supp. B.2."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.695,
+ 0.64,
+ 0.71
+ ],
+ "angle": 0,
+ "content": "6. Conclusions"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.72,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "In this paper, we propose a training-free method termed Levenberg-Marquardt-Langevin (LML) for improving sampling quality, which uses a low-rank approximated damping Hessian geometry to guide the Langevin update. We provide a theoretical analysis of the approximation error for low-rank approximation, the stationary measure, and the convergence rate for damping dynamics. We conduct extensive experiments to demonstrate that our LML method can contribute to significant improvement in sampling quality, with negligible computational overhead. The code is available at https://github.com/zituitui/LML-diffusion-sampler."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "10460"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.092,
+ 0.091,
+ 0.251,
+ 0.108
+ ],
+ "angle": 0,
+ "content": "Acknowledgments"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.117,
+ 0.486,
+ 0.269
+ ],
+ "angle": 0,
+ "content": "This work was supported in part by the National Natural Science Foundation of China under Grants 62206248 and 62402430, and the Zhejiang Provincial Natural Science Foundation of China under Grant LQN25F020008. Fangyikang Wang would like to extend his gratitude to Pengze Zhang from ByteDance, Binxin Yang, and Xinhang Leng from WeChat Vision for their discussions regarding the experiments. Additionally, he is thankful to Zebang Shen from ETH Zürich and Zhichao Chen from Peking University for their insights on Langevin dynamics."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.093,
+ 0.285,
+ 0.188,
+ 0.301
+ ],
+ "angle": 0,
+ "content": "References"
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+# Unleashing High-Quality Image Generation in Diffusion Sampling Using Second-Order Levenberg-Marquardt-Langevin
+
+Fangyikang Wang $^{1*‡}$ Hubery Yin $^{2*}$ Lei Qian $^{1}$ Yinan Li $^{1}$ Shaobin Zhuang $^{3‡}$ Huminhao Zhu $^{1}$ Yilin Zhang $^{1}$ Yanlong Tang $^{4}$ Chao Zhang $^{1†}$ Hanbin Zhao $^{1}$ Hui Qian $^{1}$ Chen Li $^{2}$ $^{1}$ Zhejiang University $^{2}$ WeChat Vision, Tencent Inc $^{3}$ Shanghai Jiao Tong University $^{4}$ Tencent Lightspeed Studio
+
+# Abstract
+
+The emerging diffusion models (DMs) have demonstrated the remarkable capability of generating images via learning the noised score function of data distribution. Current DM sampling techniques typically rely on first-order Langevin dynamics at each noise level, with efforts concentrated on refining inter-level denoising strategies. While leveraging additional second-order Hessian geometry to enhance the sampling quality of Langevin is a common practice in Markov chain Monte Carlo (MCMC), the naive attempts to utilize Hessian geometry in high-dimensional DMs lead to quadratic-complexity computational costs, rendering them non-scalable. In this work, we introduce a novel Levenberg-Marquardt-Langevin (LML) method that approximates the diffusion Hessian geometry in a training-free manner, drawing inspiration from the celebrated Levenberg-Marquardt optimization algorithm. Our approach introduces two key innovations: (1) A low-rank approximation of the diffusion Hessian, leveraging the DMs' inherent structure and circumventing explicit quadratic-complexity computations; (2) A damping mechanism to stabilize the approximated Hessian. This LML approximated Hessian geometry enables the diffusion sampling to execute more accurate steps and improve the image generation quality. We further conduct a theoretical analysis to substantiate the approximation error bound of low-rank approximation and the convergence property of the damping mechanism. Extensive experiments across multiple pretrained DMs validate that the LML method significantly improves image generation quality, with negligible computational overhead.
+
+# 1. Introduction
+
+The emerging diffusion models (DMs) [30, 74, 76, 77], generating samples of data distribution from initial noise, have been proven to be an effective technique for modeling com
+
+plex distribution, especially in generating high-quality images [13, 31, 58, 62, 67, 70]. Training DMs can be viewed as using a neural network to match the (Stein) score function of the target distribution corrupted by different levels of noise. The sampling of DMs can be seen as running Langevin dynamics [65] using the learned diffused score and simultaneously slowly decreasing the noise level, which is called annealed Langevin dynamics [76].
+
+Recently, many sampling methods have been proposed to enhance the quality of generated samples of pretrained DMs. The majority of these efforts focus on refining the denoising scheme, as seen in works such as DDIM [75], DPM-Solvers [51, 52], PNDM [50], and others [7, 85, 91-94]. Some also propose to select more critical denoising timesteps to enhance sampling quality [23, 35, 87, 88]. These efforts are primarily based on the analysis along the denoising path, yet they still perform first-order Langevin using the learned score within a specific noise level.
+
+In the Langevin sampling area, it is common to employ additional second-order Hessian geometry to enhance the sampling quality. The additional second-order information can guide Langevin dynamics to take more accurate steps [12, 54], which is called Newton-Langevin [73]. A natural idea is that we can also leverage the Hessian geometry of DMs within each noise level to enhance the quality of diffusion sampling results. However, it is extremely challenging to calculate the Hessian geometry within the context of high-dimensional DMs [3], cause it requires quadratic-complexity computations. Current methods on diffusion Hessian either require auxiliary networks [15, 84] or maintain memory-intensive states [64], making them inefficient for enhancing DM sampling.
+
+In this paper, we introduce a novel method for approximating the diffusion Hessian within a specific noise level. Notably, our approach is the first to approximate the diffusion Hessian and apply it to enhance the sampling quality of pretrained commercial-level DMs. Our method, inspired by the celebrated Levenberg-Marquardt method in optimization [45, 53, 68], is referred to as the Levenberg-Marquardt-Langevin (LML) method. Our approach introduces two key
+
+
+Figure 1. Schematic comparison between our LML method and baselines. While previous works mainly focus on intriguing designs along the annealing path to improve diffusion sampling, they leave operations at specific noise levels to be first-order Langevin. Our approach proposes to leverage the Levenberg-Marquardt approximated Hessian geometry to guide the Langevin update to be more accurate.
+
+innovations: Initially, we derive a computationally tractable low-rank approximation of the diffusion Hessian by emulating the Gauss-Newton transformation, avoiding explicit quadratic-complexity computations. This approach capitalizes on the inherent structure of DMs to construct a low-rank approximation that captures critical geometric information. Following this, we stabilize the approximated Hessian using the damping mechanism, which addresses its ill-conditioning, and acquire its inverse for geometric guidance. Our method uses this LML-approximated Hessian geometry to enable the Langevin dynamics to take more accurate steps and improve image generation quality.
+
+We also conduct comprehensive theoretical analyses for our low-rank approximation and damping mechanism. First, we establish the error bound for the low-rank approximation of the diffusion Hessian. Subsequently, we prove that the damping mechanism preserves an unbiased stationary measure and exhibit exponentially fast convergence in terms of $\chi^2$ -divergence.
+
+Extensive experiments on multiple pretrained DMs, including CIFAR-10, CelebA-HQ, SD-15, SD2-base, SD-XL and PixArt- $\alpha$ , validate that the LML method significantly improves image generation quality with negligible computational overhead.
+
+# 2. Preliminaries
+
+Notation. The Euclidean norm over $\mathbb{R}^d$ is denoted by $\| \cdot \|$ . Throughout, we simply write $\int g$ to denote the integral with respect to the Lebesgue measure: $\int g(x)\mathrm{d}x$ . When the integral is with respect to a different measure $\mu$ , we explicitly write $\int g\mathrm{d}\mu$ . The expectation and variance of $g(X)$ when $X\sim p$ are respectively denoted $\mathbb{E}_{\mu}g = \int g\mathrm{d}\mu$ and $\operatorname{var}_{\mu}g\coloneqq \int (g - \mathbb{E}_{\mu}g)^2\mathrm{d}\mu$ . When clear from context, we sometimes abuse notation by identifying a measure $\mu$ with its Lebesgue density. We use $\pmb{I}_d$ to denote the $d$ -dimensional identity matrix; when clear from context, we sometimes simply write $\pmb{I}$ . $\pmb{H}_f$ and $\pmb{J}_f$ denote the Hessian and Jacobian of $f$ respectively.
+
+# 2.1. Langevin Dynamics and Gradient Descent
+
+In statistics, the (Stein) score of a distribution $p(\pmb{x})$ is defined to be $\nabla_{\pmb{x}} \log p(\pmb{x})$ . Given an initial value $\pmb{x}_0 \sim \pi(\pmb{x})$
+
+with $\pi$ being a prior distribution, Langevin dynamics (LD) can produce samples from $p(\pmb{x})$ using only the score function $\nabla_{\pmb{x}}\log p(\pmb{x})$ following the SDE,
+
+$$
+\mathrm {d} \boldsymbol {x} _ {t} = \nabla_ {\boldsymbol {x}} \log p (\boldsymbol {x} _ {t}) \mathrm {d} t + \sqrt {2} \mathrm {d} B _ {t}, \tag {1}
+$$
+
+where $B_{t}$ is the standard d-dimensional Brownian Motion (BM). The distribution of $\pmb{x}_t$ equals $p(\pmb{x})$ when $T \to \infty$ , in which case $\pmb{x}_t$ becomes an exact sample from $p(\pmb{x})$ under some regularity conditions [86]. Strictly speaking, a Metropolis-Hastings adjustment is needed, but it can often be ignored in practice [9]. There is a deep connection involving the distribution of $\pmb{x}_t$ in LD to the renowned Gradient Descent method (GD) [56] in optimization. The marginal distribution of a Langevin process $(\pmb{x}_t)_{t\geq 0}$ evolves according to a GD, over the Wasserstein probability space, that minimizes the Kullback-Leibler (KL) divergence $D_{\mathrm{KL}}(\cdot \| \pi)[2,36,81]$ .
+
+# 2.2. Diffusion Models and Annealed Langevin
+
+Suppose that we have a d-dimensional random variable $\pmb{x}(0) \in \mathbb{R}^d$ following an unknown target distribution $p_0(\pmb{x}_0)$ . Diffusion Models (DMs) define a forward process $\{\pmb{x}(t)\}_{t \in [0,T]}$ with $T > 0$ starting with $\pmb{x}(0)$ , such that the distribution of $\pmb{x}(t)$ conditioned on $\pmb{x}(0)$ satisfies
+
+$$
+p _ {t | 0} (\boldsymbol {x} (t) | \boldsymbol {x} (0)) = \mathcal {N} (\boldsymbol {x} (t); \alpha (t) \boldsymbol {x} (0), \sigma^ {2} (t) \mathbf {I}), \quad (2)
+$$
+
+where $\alpha (\cdot),\sigma (\cdot)\in \mathcal{C}([0,T],\mathbb{R}^{+})$ have bounded derivatives, and we denote them as $\alpha_{t}$ and $\sigma_t$ for simplicity. The choice for $\alpha_{t}$ and $\sigma_t$ is referred to as the noise schedule of a DM.
+
+DMs, both SMLD [76] and DDPM [30], can be seen as learning a network to match the score of the diffused distribution $\log p_t(\pmb{x}_t)$ at different noise levels. In practice, DMs usually use $\varepsilon_{\theta}(\pmb{x}(t), t)$ to estimate $-\sigma(t) \nabla_{\pmb{x}(t)} \log p_t(\pmb{x}(t), t)$ via optimizing the following denoising score matching objective:
+
+$$
+\mathbb {E} _ {t} \left\{\lambda_ {t} \mathbb {E} _ {x _ {0}, x _ {t}} \left[ \| s _ {\theta} (x _ {t}, t) - \nabla_ {x _ {t}} \log p (x _ {t}, t | x _ {0}, 0) \| ^ {2} \right] \right\}. \tag {3}
+$$
+
+The sampling process of diffusion models can be seen as annealed Langevin dynamics [76], which executes Langevin updates at each noise level while progressively reducing the noise scale.
+
+
+Figure 2. The relation between optimization algorithms and MCMC sampling algorithms. We initially wanted to develop a diffusion sampler utilizing Hessian geometry, following the path of Newton-Langevin dynamics [73]. However, this approach proved to be highly computationally expensive within the DM context. Drawing inspiration from the Levenberg-Marquardt method used in optimization, our method incorporates low-rank approximation and damping techniques. This enables us to obtain the Hessian geometry in a computationally affordable manner. Subsequently, we use this approximated Hessian geometry to guide the Langevin updates.
+
+# 2.3. Langevin Guided by Hessian Geometry
+
+Newton's method (also called Newton-Raphson) [60] is a famous optimization method that utilizes the second-order Hessian geometry to improve the GD. Developed as an analogy to Newton's method, the Newton-Langevin dynamics [54] utilize Hessian geometry to generate samples that adhere to the SDE
+
+$$
+\mathrm {d} \boldsymbol {x} _ {t} = \left[ \nabla_ {\boldsymbol {x}} ^ {2} \log p (\boldsymbol {x} _ {t}) \right] ^ {- 1} \nabla_ {\boldsymbol {x}} \log p (\boldsymbol {x} _ {t}) \mathrm {d} t + \sqrt {2} \mathrm {d} B _ {t} ^ {\prime}, \tag {4}
+$$
+
+where the $B_{t}^{\prime}$ is the BM scaled by the square-rooted Hessian geometry. Calculating the Hessian geometry of high-dimensional distributions poses a significant challenge. Some studies have attempted to alleviate this issue through the Quasi-Newton technique [22, 73]. However, these approaches fail to address the problem in the context of DM-scale dimensional data. For instance, the Stable Diffusionv1.5 model [67] features a latent dimension of 16384, resulting in a Hessian matrix of $16384 \times 16384$ . Current methods on diffusion Hessian either require auxiliary networks training [15, 84] or maintain memory-intensive states [64]. To the best of our knowledge, there is currently no effective method available to access the diffusion Hessian of advanced commercial-level DMs like SD-XL.
+
+# 2.4. Levenberg-Marquardt Method
+
+In the field of optimization, the Levenberg-Marquardt (LM) method [68] is proposed as a computationally friendly and stabilized analogue to Newton's method. Specifically, it modifies the computation of Hessian geometry in Newton's method in two key aspects:
+
+- Low-rank approximated Hessian In the context of least squares problems, the Levenberg-Marquardt method often constructs a low-rank estimation of the Hessian geometry. Specifically, when $f(\pmb{x}) = \sum_{i=1}^{m} r_i(\pmb{x})^2$ , the Levenberg-Marquardt method approximates the Hessian into the following form, which is constructed from the
+
+Jacobian $J_{f}(\pmb {x})$
+
+$$
+\boldsymbol {H} _ {f} (\boldsymbol {x}) \approx 2 \boldsymbol {J} _ {f} (\boldsymbol {x}) ^ {\top} \boldsymbol {J} _ {f} (\boldsymbol {x}). \tag {5}
+$$
+
+This low-rank approximation technique is also referred to as the Gauss-Newton method in some literature [16]. However, it is still unclear how to obtain a Levenberg-Marquardt-type low-rank estimation of the Hessian in the context of diffusion models.
+
+- Damping mechanism The Levenberg-Marquardt Method introduces an additional damping identity matrix to the Hessian geometry. That is, it replaces the pure Hessian geometry $\left[\boldsymbol{H}_f(\boldsymbol{x}_k)\right]^{-1}$ in Newton's method with a combination expressed as $\left[\boldsymbol{H}_f(\boldsymbol{x}_k) + \lambda \boldsymbol{I}\right]^{-1}$ . Consequently, the Levenberg-Marquardt Method with damping is expressed as:
+
+$$
+\boldsymbol {x} _ {k + 1} = \boldsymbol {x} _ {k} - \eta \left[ \boldsymbol {H} _ {f} \left(\boldsymbol {x} _ {k}\right) + \lambda \boldsymbol {I} \right] ^ {- 1} \nabla_ {\boldsymbol {x}} f \left(\boldsymbol {x} _ {k}\right). \tag {6}
+$$
+
+Empirical evidence suggests that the damping mechanism contributes to numerical stabilization [41], since $\lambda I$ can resolve the ill-conditioning of the Hessian. While the damping mechanism can be perceived as a trust region approach, it is more intuitive to view $H + \lambda I$ as a geometrical interpolation between $H$ and $I$ .
+
+# 3. Methodology
+
+# 3.1. Low-rank Approximation of Diffusion Hessian
+
+Inspired by the low-rank estimation technique of the Hessian in the Levenberg-Marquardt method, we derive a similar low-rank estimation for the diffusion Hessian. Specifically, we follow the intuition of the Levenberg-Marquardt method to approximate the diffusion Hessian by simplifying the second-order partial derivatives. The low-rank approximate Hessian of diffusion models that we obtained is shown below. It is important to note that it includes noise schedule related coefficients, which distinguishes it from the least squares problem case in Eq. 5.
+
+
+DDIM PNDM DPM-Solver DPM-Solver++ UniPC LML(Ours)
+Figure 3. Visual comparison of images generated by our LML method and other methods, using the pre-trained LDM on CelebAHQ $256\times 256$ [39] with the same seeds. It shows that our LML method contributes to more vivid and detailed generated images.
+
+Proposition 1. Let $p_t$ be the diffused marginal distribution at time $t$ of the diffusion process, Eq. 2 and $\varepsilon_\theta$ is learned via Eq. 3, then the Hessian derivative of its log-density function $\nabla_{\boldsymbol{x}_t}^2 \log p_t(\boldsymbol{x}_t)$ has a low-rank approximation form of $\frac{1}{\sigma(t)^2 \| \varepsilon_\theta \|^2} \varepsilon_\theta \varepsilon_\theta^\top$ .
+
+Notice that this approximation form is a scaled outer-product of the score. The detailed derivation can be found in the Supplementary A.2. For here and for the remainder of the paper, we will denote $\varepsilon_{\theta}(\boldsymbol{x}(t), t)$ as $\varepsilon_{\theta}$ , provided there is no risk of ambiguity. In section 4.1, we will show that this low-rank approximation possesses an error bound, ensuring that our approximation does not generate excessive errors.
+
+# 3.2. Damping Mechanism
+
+Similar to the scenario in the Levenberg-Marquardt method, we have obtained an accessible approximation of the diffusion Hessian as presented in Proposition 1. However, this form is significantly ill-conditioned, making its inverse impossible to calculate. Specifically, the outer-product Hessian in Proposition 1 has an infinite condition number [32]; hence, its inverse strictly does not exist in mathematical terms. To address this issue, we propose adopting the damping mechanism used in the LML method. We introduce an additional damping identity matrix to the approximate Hes
+
+sian as shown in Proposition 1. This damped Hessian geometry is used in place of the full Hessian in the Newton Langevin in Eq. 4, we consequently derive the following damping dynamics:
+
+$$
+\mathrm {d} \boldsymbol {x} _ {t} = \left[ \nabla_ {\boldsymbol {x}} ^ {2} \log p \left(\boldsymbol {x} _ {t}\right) + \lambda I \right] ^ {- 1} \nabla_ {\boldsymbol {x}} \log p \left(\boldsymbol {x} _ {t}\right) \mathrm {d} t + \sqrt {2} \mathrm {d} B _ {t} ^ {\prime}, \tag {7}
+$$
+
+where the $B_{t}^{\prime}$ is the BM scaled by the square-rooted LM approximated Hessian geometry. Drawing inspiration from the Levenberg-Marquardt method, we refer to this damping Hessian Langevin in Eq. 7 as the Levenberg-Marquardt-Langevin dynamics (LML dynamics). Similar to the Levenberg-Marquardt method, the damping coefficient $\lambda$ in Eq. 7 can be interpreted as an interpolation coefficient between the Hessian geometry and Identity geometry. Specifically, as $\lambda \rightarrow \infty$ , Eq. 7 would degenerate to the standard Langevin with normalization on the geometry. We observe that by adding the Levenberg-Marquardt damping identity matrix to the outer-product form of the Hessian in Equation Proposition 1, its inverse can be conveniently computed using the Sherman-Morrison formula [72].
+
+$$
+\begin{array}{l} \boldsymbol {H} _ {L M} ^ {- 1} (\boldsymbol {x} _ {t}, \lambda) = \left[ \nabla_ {\boldsymbol {x}} ^ {2} \log p (\boldsymbol {x} _ {t}) + \lambda \boldsymbol {I} \right] ^ {- 1} \\ \approx \left[ \frac {1}{\sigma (t) ^ {2} \| \varepsilon_ {\theta} \| ^ {2}} \varepsilon_ {\theta} \varepsilon_ {\theta} ^ {\top} + \lambda I \right] ^ {- 1} \\ = \frac {1}{\sigma (t) ^ {2} \| \varepsilon_ {\theta} \| ^ {2}} \left[ \varepsilon_ {\theta} \varepsilon_ {\theta} ^ {\top} + \lambda^ {\prime} I \right] ^ {- 1} \tag {8} \\ = \frac {1}{\lambda^ {\prime} \sigma (t) ^ {2} \| \boldsymbol {\varepsilon} _ {\theta} \| ^ {2}} \left[ \boldsymbol {I} - \frac {\boldsymbol {\varepsilon} _ {\theta} \boldsymbol {\varepsilon} _ {\theta} ^ {\top}}{\lambda^ {\prime} + \| \boldsymbol {\varepsilon} _ {\theta} \| ^ {2}} \right], \\ \end{array}
+$$
+
+where $\lambda' = \sigma(t)^2\|\varepsilon_\theta\|^2\lambda$ . We also point out that the coefficients $\frac{1}{\lambda'\sigma(t)^2\|\varepsilon_\theta\|^2}$ will be absorbed in the discretizing stepsize of the LML dynamics and only affect the norm. The geometry direction essence is in the $\left[I - \frac{\varepsilon_\theta\varepsilon_\theta^\top}{\lambda' + \|\varepsilon_\theta\|^2}\right]$ part. In the remainder of this paper, we will slightly abuse notation by not distinguishing between $\lambda$ and $\lambda'$ . This simplification should not lead to any confusion.
+
+# 3.3. Annealed Levenberg-Marquardt-Langevin
+
+To utilize the LML for diffusion sampling, we perform the discretization of Eq. 7 at each nose level, and gradually decrease the noise level. We called this annealed LML, and point out that its continuous-time form would converge to the following SDE:
+
+$$
+\mathrm {d} x _ {t} = \left[ f _ {t} \boldsymbol {x} _ {t} - g _ {t} ^ {2} \boldsymbol {H} _ {L M} ^ {- 1} \nabla_ {x} \log p _ {t} (\boldsymbol {x} _ {t}) \right] \mathrm {d} t + g _ {t} \mathrm {d} B _ {t} ^ {\prime}. \tag {9}
+$$
+
+Similar to the connection of the reverse SDE and diffusion ODE [77], the LM reverse SDE in Eq. 9 also has an associated ODE, which is a deterministic process that shares the
+
+# Algorithm 1 Levenberg-Marquardt-Langevin (LML) diffusion sampler
+
+1: Input: pretrained diffusion model noise predictor $\varepsilon_{\theta}$ , number of timesteps $N$ , noise schedule $\{\alpha_t\}$ and $\{\sigma_t\}$ , Levenberg-Marquardt damping coefficient $\lambda > 0$ , EMA coefficient $\kappa$ .
+
+2: Initiate $\pmb{x}_{\mathrm{list}} = []$ , $\widetilde{\pmb{H}}_{N + 1}^{-1} = \pmb{I}$
+
+3: Sample $\pmb{x}_N \sim \mathcal{N}(0, \sigma_{t_N} I)$ .
+
+4: for $i = N, N - 1, \dots, 1$ do
+
+5: $\varepsilon_{i} = \varepsilon_{\theta}(\pmb{x}_{i},i)$
+
+6: if $i\neq N$ then
+
+7: $\widetilde{\varepsilon}_i = \kappa *\varepsilon_{i + 1} + (1 - \kappa)*\varepsilon_i$
+
+8: else
+
+9: $\widetilde{\varepsilon}_i = \varepsilon_i$
+
+10: end if
+
+11: $\widetilde{H}_i^{-1} = I - \frac{\widetilde{\varepsilon}_i\widetilde{\varepsilon}_i^1}{\lambda + \| \widetilde{\varepsilon}_i\| ^2}$ {Levenberg-Marquardt approximate Hessian geometry}
+12: $\varepsilon_{i}^{LM} = \widetilde{\pmb{H}}_{i}^{-1}\varepsilon_{i}$ {Apply the approximate Hessian geometry}
+13: $\varepsilon_{i}^{LM} = \frac{\|\pmb{\varepsilon}_{i}\|}{\|\pmb{\varepsilon}_{i}^{LM}\|}\pmb{\varepsilon}_{i}^{LM}$ {Geometrical normalization}
+14: $\pmb{x}_{i-1} = \mathrm{DPM-Solver}(\pmb{x}_{\mathrm{list}}, \pmb{\varepsilon}_i^{LM}, i)$
+15: $\mathbf{x}_{\mathrm{list}} = \mathbf{x}_{\mathrm{list}}.$ append $(\mathbf{x}_{i - 1})$
+16: end for
+17: Output: $x_0$
+
+same single-time marginal distribution:
+
+$$
+\mathrm {d} x _ {t} = \left[ f _ {t} \boldsymbol {x} _ {t} - \frac {1}{2} g _ {t} ^ {2} \boldsymbol {H} _ {L M} ^ {- 1} \nabla_ {\boldsymbol {x}} \log p _ {t} (\boldsymbol {x} _ {t}) \right] \mathrm {d} t. \tag {10}
+$$
+
+The following section will develop a practical LML sampler based on this deterministic LML ODE.
+
+Remark 1. Our LM process can be viewed as the Legendre dual of the classical diffusion process with a transform map of $\nabla \log p_t(\cdot) + \lambda \| \cdot \|$ . See discussions in Supp. D.3.
+
+# 3.4. Levenberg-Marquardt-Langevin Sampler
+
+We implement a diffusion sampler based on the LML diffusion ODE in Eq. 10, because it is suggested that deterministic diffusion samplers are far more efficient than the stochastic ones [40]. Our approach is generally consistent with the practices outlined in [76]. The scheme for our LML diffusion sampler is illustrated in Algorithm 1. Primarily, our sampler substitutes the first-order Langevin dynamics with LML at each noise level. At each noise level, we initially compute the LM low-rank approximated and damping Hessian geometry, $\widetilde{H}_i^{-1}$ , as detailed in step 11 of Algorithm 1. We incorporate the network output from previous steps, as shown in step 7, following studies suggesting that this mixture is closer to the underlying true score due to the manifold's curvature [50]. We then apply this approximate Hessian geometry to our initial gradient, $\varepsilon_{i}$ , to obtain
+
+
+Figure 4. Qualitative comparison of our LML method and other methods in text-guided image generation. The evaluation was performed on SD-15 [67], using 10 NFEs and the same seeds.
+
+the Hessian-guided gradient, $\varepsilon_{i}^{LM}$ , as detailed in step 12. In terms of the stepsize for our LML sampler, in contrast to some sophisticated ways of choosing the stepsize of second-order methods [25, 43], we follow the approach of [20] to ensure that the Hessian geometry has a unit spectrum, which can be easily implemented through a normalization operation on the Hessian guided gradient $\varepsilon_{i}^{LM}$ as illustrated in step 13. The rescaling of BM in Eq. 7 can also be absorbed into this normalization operation. Once the Hessian-guided gradient, $\varepsilon_{i}^{LM}$ , is obtained, we adopt the DPM-Solver as our denoising scheme to calculate the next state, $x_{i-1}$ , as shown in step 14.
+
+It is worth noting that our LML does not require additional training, components, or network access. Instead, we only need several additional tensor arithmetic operations.
+
+# 4. Theoretical Analysis
+
+In this section, we present rigorous theoretical analyses to substantiate the correctness and efficacy of our LML.
+
+# 4.1. Analysis on Low-rank Approximation
+
+Here, we establish the error bound of the low-rank approximation of the diffusion Hessian in Proposition 1, thereby ensuring that our approximation does not introduce excess
+
+
+Figure 5. Qualitative comparison of our LML method and other methods in text-guided image generation. The evaluation was performed on SD2-base [67], using 10 NFEs and the same seeds.
+
+sive errors. Given that we are evaluating the accuracy of a matrix-valued approximation, we choose to use the Hilbert-Schmidt norm [24] as a criterion.
+
+Proposition 2. Assume that the norm of $\pmb{x}_t$ is bounded by $\delta_1$ , the approximation error on $\varepsilon_{\theta}(\pmb{x}_t, t)$ is denoted as $\delta_2$ , $\delta_3$ denote the bound on the second partial derivative of $\delta_1$ w.r.t. $\pmb{x}_t$ , and $\mathcal{D}_y$ denote the dataset diameter. The approximation error of the LM low-rank Hessian, as referenced in Proposition 1, is at most $(\delta_1 + \alpha_t \delta_2 + \alpha_t \mathcal{D}_y) (2 + \delta_3 + 2 \frac{\alpha_t^2}{\sigma_t^2} \mathcal{D}_y^2)$ when measured in terms of the Hilbert-Schmidt norm.
+
+Our analysis relies on the analytical form diffusion Fisher [84]. The detailed proof can be found in Supp. A.6.
+
+# 4.2. Analysis on Damping Mechanism
+
+Subsequently, we demonstrate the unbiased, exponentially fast convergence property of the damping mechanism.
+
+# 4.2.1. Stationary Measure
+
+We confirm that the stationary measure of the damping dynamics, as defined in Eq. 7, aligns with the target diffused distribution. This ensures that the damping updates still guide samples towards the correct data distribution.
+
+Proposition 3. Under mild regularity conditions, the stationary distribution of the damping dynamics in Eq. 7 exists and is unique, which also coincides with the marginal distribution $p_t(\boldsymbol{x}_t)$ at every noise level.
+
+We achieve this analysis by the Fokker-Planck equation [63]. The detailed proof can be found in Supp. A.7.
+
+# 4.2.2. Ergodic Convergence Rate
+
+We also want to determine the speed at which our damping dynamics converge. We demonstrate that our damping dynamics exhibit a satisfyingly fast, exponential convergence rate towards the target distribution.
+
+Proposition 4. Let $\mu_t$ be the evolving distribution of the damping dynamics in Eq. 7. We have that $\mu_t$ converges to the stationary distribution at an exponential ergodic convergence rate in terms of $\chi^2$ -distance at every noise level, under certain regularity conditions.
+
+We achieve this analysis by determining the relationship between Eq. 7 and the Mirror-Langevin [12]. The formal version and detailed proof can be found in Supp. A.8.
+
+Remark 2. Once we establish the exponential ergodic convergence rate in terms of $\chi^2$ -distance, The exponential convergence results for total variation distance [80], Hellinger distance [28], KL divergence [44] as illustrated in [4, §2.4]. And the exponential convergence results on Wasserstein distance [81] can also be established with a log-Sobolev assumption, as illustrated in [14].
+
+# 5. Experiments
+
+In this section, we validate the enhanced sampling quality of our LML method across various pretrained DMs. We evaluate in both pixel-space, latent-space, and text-guided conditional generation scenarios. We select several most commonly-used and advanced sampling methods such as DDIM [77], PNDM [50], DPM-Solver [51], DPM-Solver++ [52] and UniPC [92] as baselines. We will also demonstrate the computational efficiency of our LML method. All experiments are executed using open-source, pretrained DMs, with the datatype set to float32 and the timestep scheme as uniform. More experimental details and results are deferred to Supp. B and C.
+
+# 5.1. Pixel-Space Image Generation
+
+We initially compare the unconditional sampling quality of our LML method with baselines on the CIFAR-10 dataset [1]. For each sampler, we generate 50,000 samples for FID evaluation. As illustrated in Table 1 and Figure 6a, our approach improves the sampling performance of the baseline Langevin methods in most NFE scenarios.
+
+
+(a) CIFAR-10
+
+
+(b) SD-15 on MS-COCO
+Figure 6. This line chart compares the log-FID scores $(\downarrow)$ on (a) CIFAR-10, (b) MS-COCO with SD-15 and (c) MS-COCO with SD2-base.
+
+
+(c) SD2-base on MS-COCO
+
+Table 1. Comparison of different samplers on FID score( ↓) on CIFAR-10 unconditional generation. Best results are bolded and the second best results are underlined. The FID scores were obtained by generating 50,000 samples, and all samplers were tested using the same seeds on the same checkpoint. It is shown that our LML always achieves the best or second best FID across all different NFEs.
+
+| Methods | FID (↓) on CIFAR-10 generation |
| 5 NFEs | 6 NFEs | 7 NFEs | 8 NFEs | 9 NFEs | 10 NFEs | 12 NFEs | 15 NFEs | 20 NFEs | 30 NFEs | 50 NFEs | 100 NFEs |
| DDIM [75] | 42.17 | 32.09 | 26.21 | 22.38 | 19.64 | 17.45 | 14.27 | 12.67 | 10.60 | 8.58 | 6.96 | 5.72 |
| PNDM [50] | 46.56 | 15.27 | 12.59 | 10.73 | 9.59 | 7.16 | 6.73 | 5.70 | 5.28 | 4.94 | 4.24 | 3.93 |
| DPM-Solver [51] | 33.26 | 23.06 | 17.61 | 14.58 | 12.47 | 11.13 | 9.28 | 4.98 | 4.23 | 3.74 | 3.66 | 3.62 |
| DPM-Solver++ [52] | 30.87 | 20.92 | 16.22 | 13.63 | 11.89 | 10.71 | 10.59 | 10.17 | 9.90 | 6.58 | 5.06 | 4.46 |
| UniPC [92] | 29.81 | 20.64 | 16.10 | 13.59 | 11.84 | 10.70 | 9.02 | 7.51 | 6.03 | 4.66 | 3.82 | 3.58 |
| LML (Ours) | 17.28 | 14.18 | 11.15 | 8.09 | 7.16 | 6.54 | 5.97 | 4.70 | 4.19 | 3.69 | 3.63 | 3.58 |
+
+Table 2. Comparison of different samplers on CelebA-HQ unconditional generation. Best results are bolded and the second best results are underlined.
+
+| Methods | Colorful | Face Quality | Aesthetic |
| ColorS(↑) | FS(↑) | DFIQA(↑) | PicS(↑) | EAT(↑) | Laion(↑) |
| DDIM [75] | 34.13 | 4.85 | 0.539 | 19.85 | 4.61 | 5.24 |
| PNDM [50] | 38.29 | 4.89 | 0.553 | 19.70 | 4.28 | 5.11 |
| DPM [51] | 34.85 | 5.06 | 0.566 | 20.00 | 4.51 | 5.29 |
| DPM++ [52] | 35.08 | 5.08 | 0.560 | 19.97 | 4.46 | 5.26 |
| UniPC [92] | 35.95 | 5.09 | 0.568 | 19.97 | 4.47 | 5.26 |
| LML(Ours) | 40.53 | 5.24 | 0.607 | 20.98 | 4.75 | 5.37 |
+
+# 5.2. Latent-Space Image Generation
+
+We evaluated our LML on the LDM [67] that was trained on CelebA-HQ [39] at a resolution of $256 \times 256$ . In Table 2, we employed five metrics spanning three aspects to demonstrate the superiority of LML. These aspects include colorfulness [26], face quality (FS [46] and DFIQA [10]), and human-preference-aesthetic scores (PicS [42], EAT [27] and Laion-Aes [71]). Additionally, we present a visual comparison in Figure 3. All these experiments were carried out with a NFE of 10. The results were tested by averaging over 1000 samples and the same seeds.
+
+# 5.3. Text-guided Image Generation
+
+# 5.3.1. Qualitative Comparison
+
+Qualitative comparison on SD-15 and SD2-base generation is provided in Figure 4 and 5, clearly indicating that our LML method enhances the quality of image details under
+
+Table 3. Comparison of FID score $(\downarrow)$ for the task of text-guided conditional generation of SD on randomly selected 30,000 MS-COCO prompts. Best results are bolded and the second best results are underlined.
+
+| Methods\NFEs | FID (↓) on MS-COCO-14 prompts |
| 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 |
| SD-1.5 |
| DDIM [75] | 29.14 | 27.11 | 23.48 | 22.36 | 21.14 | 21.22 | 19.91 | 19.36 |
| PNDM [50] | 35.50 | 34.49 | 29.50 | 27.86 | 24.46 | 22.35 | 19.13 | 17.92 |
| DPM [51] | 22.07 | 20.58 | 19.92 | 19.64 | 19.47 | 19.34 | 19.30 | 17.32 |
| DPM++ [52] | 21.75 | 20.14 | 19.60 | 19.32 | 19.19 | 19.13 | 19.11 | 18.03 |
| UniPC [92] | 21.72 | 20.30 | 19.84 | 19.67 | 19.55 | 19.40 | 19.41 | 19.29 |
| LML (Ours) | 18.68 | 18.13 | 17.61 | 17.50 | 17.58 | 17.60 | 17.55 | 16.98 |
| SD2-base |
| DDIM [75] | 27.34 | 24.25 | 22.47 | 21.48 | 19.73 | 20.43 | 18.73 | 18.19 |
| PNDM [50] | 31.13 | 30.93 | 26.33 | 25.56 | 22.04 | 20.35 | 17.39 | 16.47 |
| DPM [51] | 21.25 | 19.94 | 19.21 | 18.78 | 18.51 | 18.36 | 18.13 | 15.84 |
| DPM++ [52] | 20.94 | 19.51 | 18.77 | 18.43 | 18.21 | 18.06 | 17.86 | 15.99 |
| UniPC [92] | 20.81 | 19.40 | 18.82 | 18.56 | 18.36 | 18.27 | 18.08 | 18.03 |
| LML (Ours) | 17.76 | 16.99 | 16.17 | 16.02 | 16.29 | 15.95 | 16.16 | 15.14 |
+
+the same seed and prompt with a NFE of 10.
+
+# 5.3.2. FID on MS-COCO Benchmark
+
+Following the approach in [69, 90], we randomly selected 30,000 prompts from the MS-COCO dataset [47] and generated images conditioned on these prompts. We tested our sampler in terms of FID on the SD-1.5 and SD2-base models with resolutions of $512 \times 512$ and a CFG scale 7.0. Table 3 shows that our LML sampler surpasses the baseline methods on SD models across different NFEs.
+
+Table 4. Comparison of different samplers in text-guided image generation task on the T2I-BC benchmark [34]. The metrics are Color, Shape, and Texture. Best results are bolded and the second best results are underlined.
+
+| Metrics | T2I Benchmark on SD-1.5 [67] | T2I Benchmark on SD2-base [67] | T2I Benchmark on SD-XL [59] | T2I Benchmark on PixArt-α [8] |
| Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) |
| DDIM [75] | 0.3864 | 0.3791 | 0.4231 | 0.5111 | 0.4182 | 0.4822 | 0.5670 | 0.4712 | 0.5076 | 0.2933 | 0.3746 | 0.4045 |
| PNDM [50] | 0.3810 | 0.3761 | 0.4331 | 0.5067 | 0.4190 | 0.4863 | 0.5682 | 0.4772 | 0.5085 | 0.4035 | 0.3996 | 0.4225 |
| DPM [51] | 0.3877 | 0.3945 | 0.4294 | 0.5162 | 0.4307 | 0.5002 | 0.5795 | 0.4841 | 0.5194 | 0.3263 | 0.3895 | 0.4349 |
| DPM++ [52] | 0.3881 | 0.3958 | 0.4307 | 0.5202 | 0.4326 | 0.5020 | 0.5798 | 0.4858 | 0.5201 | 0.3136 | 0.3882 | 0.4364 |
| UniPC [92] | 0.3892 | 0.3889 | 0.4306 | 0.5146 | 0.4337 | 0.4995 | 0.5828 | 0.4910 | 0.5234 | 0.3187 | 0.3880 | 0.4266 |
| LML (Ours) | 0.4335 | 0.4252 | 0.4746 | 0.5640 | 0.4792 | 0.5330 | 0.5908 | 0.4938 | 0.5363 | 0.3801 | 0.4265 | 0.4684 |
+
+
+Figure 7. LML integrates seamlessly with ControlNet.
+
+# 5.3.3. T2I-CB Benchmark
+
+To further validate the enhanced sampling quality of LML in text-to-image generation, we carried out tests on diverse commercial-level DMs (SD-1.5 [67], SD2-base [67], SD-XL [59], and PixArt- $\alpha$ [8]) using the T2I-CB [34] benchmark. This benchmark is designed for open-world text-to-image generation evaluation. For each model, we evaluated three metrics (color, shape, and texture) to assess the visual quality of the samplers. Each assessment was based on 30,000 images with a NFE of 10. As shown in Table 4, our LML always achieves the best or second best scores on T2I-BC across these models.
+
+# 5.3.4. Application on ControlNet
+
+Our model can seamlessly integrate with existing diffusion model plugins, such as ControlNet [89]. The results in Fig 7 demonstrate that our method is fully compatible with ControlNet and generates high-quality samples.
+
+# 5.4. Time-costs Comparison
+
+Table 5 presents the average wall-clock time costs for LML across different image generation tasks. These time-cost experiments were conducted on a single NVIDIA RTX 4090 chip and averaged over 200 tests with a batchsize of 1. The results suggest that the additional computational cost incurred by our LML technique is virtually negligible, making LML as time-efficient as DDIM [75].
+
+Table 5. Average wall-clock time costs for LML and DDIM.
+
+| Models | Methods \NFEs | Time-costs (s) |
| 5 | 10 | 15 | 20 | 30 | 50 | 100 |
| CIFAR-10 | DDIM | 0.13 | 0.20 | 0.27 | 0.34 | 0.52 | 0.81 | 1.49 |
| LML (Ours) | 0.13 | 0.21 | 0.27 | 0.37 | 0.48 | 0.82 | 1.51 |
| CelebA | DDIM | 0.20 | 0.28 | 0.39 | 0.47 | 0.66 | 1.03 | 1.95 |
| LML (Ours) | 0.20 | 0.31 | 0.38 | 0.48 | 0.67 | 1.10 | 2.08 |
| SD-1.5 | DDIM | 0.45 | 0.73 | 1.03 | 1.31 | 1.87 | 3.01 | 5.85 |
| LML (Ours) | 0.45 | 0.74 | 1.04 | 1.32 | 1.89 | 3.03 | 5.89 |
| SD-2base | DDIM | 0.45 | 0.71 | 1.00 | 1.25 | 1.80 | 2.87 | 5.53 |
| LML (Ours) | 0.46 | 0.72 | 0.98 | 1.27 | 1.81 | 2.88 | 5.60 |
| SD-XL | DDIM | 2.32 | 4.25 | 6.23 | 8.12 | 12.06 | 19.82 | 39.48 |
| LML (Ours) | 2.32 | 4.30 | 6.23 | 8.21 | 12.11 | 19.99 | 39.55 |
| PixArt | DDIM | 0.66 | 1.08 | 1.49 | 1.92 | 2.74 | 4.31 | 8.45 |
| LML (Ours) | 0.67 | 1.08 | 1.51 | 1.92 | 2.75 | 4.28 | 8.49 |
+
+# 5.5. Hyperparameters
+
+Our LML introduces two robust hyperparameters with clear high-level interpretations: the damping coefficient $\lambda$ and the mixture coefficient $\kappa$ . The damping coefficient $\lambda$ determines the degree to which our approximated Hessian is interpolated with the identity matrix. A larger $\lambda$ value results in the dominance of the identity matrix, leading the LML to degenerate into Langevin. Conversely, a smaller $\lambda$ value allows more guidance from the Hessian geometry, but a minimal value could lead to ill-conditioning issues. The $\kappa$ controls the EMA rate of previous information. A small $\kappa$ would make the LML close to the identity map, but LML contributes to obvious image quality enhancement in practice. More discussions on hyperparameter tuning scheme, setup, and ablation experiments are provided in Supp. B.2.
+
+# 6. Conclusions
+
+In this paper, we propose a training-free method termed Levenberg-Marquardt-Langevin (LML) for improving sampling quality, which uses a low-rank approximated damping Hessian geometry to guide the Langevin update. We provide a theoretical analysis of the approximation error for low-rank approximation, the stationary measure, and the convergence rate for damping dynamics. We conduct extensive experiments to demonstrate that our LML method can contribute to significant improvement in sampling quality, with negligible computational overhead. The code is available at https://github.com/zituitui/LML-diffusion-sampler.
+
+# Acknowledgments
+
+This work was supported in part by the National Natural Science Foundation of China under Grants 62206248 and 62402430, and the Zhejiang Provincial Natural Science Foundation of China under Grant LQN25F020008. Fangyikang Wang would like to extend his gratitude to Pengze Zhang from ByteDance, Binxin Yang, and Xinhang Leng from WeChat Vision for their discussions regarding the experiments. Additionally, he is thankful to Zebang Shen from ETH Zürich and Zhichao Chen from Peking University for their insights on Langevin dynamics.
+
+# References
+
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+ "content": "The emerging diffusion models (DMs) have demonstrated the remarkable capability of generating images via learning the noised score function of data distribution. Current DM sampling techniques typically rely on first-order Langevin dynamics at each noise level, with efforts concentrated on refining inter-level denoising strategies. While leveraging additional second-order Hessian geometry to enhance the sampling quality of Langevin is a common practice in Markov chain Monte Carlo (MCMC), the naive attempts to utilize Hessian geometry in high-dimensional DMs lead to quadratic-complexity computational costs, rendering them non-scalable. In this work, we introduce a novel Levenberg-Marquardt-Langevin (LML) method that approximates the diffusion Hessian geometry in a training-free manner, drawing inspiration from the celebrated Levenberg-Marquardt optimization algorithm. Our approach introduces two key innovations: (1) A low-rank approximation of the diffusion Hessian, leveraging the DMs' inherent structure and circumventing explicit quadratic-complexity computations; (2) A damping mechanism to stabilize the approximated Hessian. This LML approximated Hessian geometry enables the diffusion sampling to execute more accurate steps and improve the image generation quality. We further conduct a theoretical analysis to substantiate the approximation error bound of low-rank approximation and the convergence property of the damping mechanism. Extensive experiments across multiple pretrained DMs validate that the LML method significantly improves image generation quality, with negligible computational overhead."
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+ "content": "The emerging diffusion models (DMs) [30, 74, 76, 77], generating samples of data distribution from initial noise, have been proven to be an effective technique for modeling com"
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+ "content": "In the Langevin sampling area, it is common to employ additional second-order Hessian geometry to enhance the sampling quality. The additional second-order information can guide Langevin dynamics to take more accurate steps [12, 54], which is called Newton-Langevin [73]. A natural idea is that we can also leverage the Hessian geometry of DMs within each noise level to enhance the quality of diffusion sampling results. However, it is extremely challenging to calculate the Hessian geometry within the context of high-dimensional DMs [3], cause it requires quadratic-complexity computations. Current methods on diffusion Hessian either require auxiliary networks [15, 84] or maintain memory-intensive states [64], making them inefficient for enhancing DM sampling."
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+ "content": ". Current methods on diffusion Hessian either require auxiliary networks training [15, 84] or maintain memory-intensive states [64]. To the best of our knowledge, there is currently no effective method available to access the diffusion Hessian of advanced commercial-level DMs like SD-XL."
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+ "content": "Similar to the scenario in the Levenberg-Marquardt method, we have obtained an accessible approximation of the diffusion Hessian as presented in Proposition 1. However, this form is significantly ill-conditioned, making its inverse impossible to calculate. Specifically, the outer-product Hessian in Proposition 1 has an infinite condition number [32]; hence, its inverse strictly does not exist in mathematical terms. To address this issue, we propose adopting the damping mechanism used in the LML method. We introduce an additional damping identity matrix to the approximate Hes"
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+ "content": "sian as shown in Proposition 1. This damped Hessian geometry is used in place of the full Hessian in the Newton Langevin in Eq. 4, we consequently derive the following damping dynamics:"
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+ "content": " is the BM scaled by the square-rooted LM approximated Hessian geometry. Drawing inspiration from the Levenberg-Marquardt method, we refer to this damping Hessian Langevin in Eq. 7 as the Levenberg-Marquardt-Langevin dynamics (LML dynamics). Similar to the Levenberg-Marquardt method, the damping coefficient "
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+ "content": ", Eq. 7 would degenerate to the standard Langevin with normalization on the geometry. We observe that by adding the Levenberg-Marquardt damping identity matrix to the outer-product form of the Hessian in Equation Proposition 1, its inverse can be conveniently computed using the Sherman-Morrison formula [72]."
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+ "content": "Our analysis relies on the analytical form diffusion Fisher [84]. The detailed proof can be found in Supp. A.6."
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+ "content": "We confirm that the stationary measure of the damping dynamics, as defined in Eq. 7, aligns with the target diffused distribution. This ensures that the damping updates still guide samples towards the correct data distribution."
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| 5 NFEs | 6 NFEs | 7 NFEs | 8 NFEs | 9 NFEs | 10 NFEs | 12 NFEs | 15 NFEs | 20 NFEs | 30 NFEs | 50 NFEs | 100 NFEs |
| DDIM [75] | 42.17 | 32.09 | 26.21 | 22.38 | 19.64 | 17.45 | 14.27 | 12.67 | 10.60 | 8.58 | 6.96 | 5.72 |
| PNDM [50] | 46.56 | 15.27 | 12.59 | 10.73 | 9.59 | 7.16 | 6.73 | 5.70 | 5.28 | 4.94 | 4.24 | 3.93 |
| DPM-Solver [51] | 33.26 | 23.06 | 17.61 | 14.58 | 12.47 | 11.13 | 9.28 | 4.98 | 4.23 | 3.74 | 3.66 | 3.62 |
| DPM-Solver++ [52] | 30.87 | 20.92 | 16.22 | 13.63 | 11.89 | 10.71 | 10.59 | 10.17 | 9.90 | 6.58 | 5.06 | 4.46 |
| UniPC [92] | 29.81 | 20.64 | 16.10 | 13.59 | 11.84 | 10.70 | 9.02 | 7.51 | 6.03 | 4.66 | 3.82 | 3.58 |
| LML (Ours) | 17.28 | 14.18 | 11.15 | 8.09 | 7.16 | 6.54 | 5.97 | 4.70 | 4.19 | 3.69 | 3.63 | 3.58 |
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| DDIM [75] | 34.13 | 4.85 | 0.539 | 19.85 | 4.61 | 5.24 |
| PNDM [50] | 38.29 | 4.89 | 0.553 | 19.70 | 4.28 | 5.11 |
| DPM [51] | 34.85 | 5.06 | 0.566 | 20.00 | 4.51 | 5.29 |
| DPM++ [52] | 35.08 | 5.08 | 0.560 | 19.97 | 4.46 | 5.26 |
| UniPC [92] | 35.95 | 5.09 | 0.568 | 19.97 | 4.47 | 5.26 |
| LML(Ours) | 40.53 | 5.24 | 0.607 | 20.98 | 4.75 | 5.37 |
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| 5 | 6 | 7 | 8 | 9 | 10 | 12 | 15 |
| SD-1.5 |
| DDIM [75] | 29.14 | 27.11 | 23.48 | 22.36 | 21.14 | 21.22 | 19.91 | 19.36 |
| PNDM [50] | 35.50 | 34.49 | 29.50 | 27.86 | 24.46 | 22.35 | 19.13 | 17.92 |
| DPM [51] | 22.07 | 20.58 | 19.92 | 19.64 | 19.47 | 19.34 | 19.30 | 17.32 |
| DPM++ [52] | 21.75 | 20.14 | 19.60 | 19.32 | 19.19 | 19.13 | 19.11 | 18.03 |
| UniPC [92] | 21.72 | 20.30 | 19.84 | 19.67 | 19.55 | 19.40 | 19.41 | 19.29 |
| LML (Ours) | 18.68 | 18.13 | 17.61 | 17.50 | 17.58 | 17.60 | 17.55 | 16.98 |
| SD2-base |
| DDIM [75] | 27.34 | 24.25 | 22.47 | 21.48 | 19.73 | 20.43 | 18.73 | 18.19 |
| PNDM [50] | 31.13 | 30.93 | 26.33 | 25.56 | 22.04 | 20.35 | 17.39 | 16.47 |
| DPM [51] | 21.25 | 19.94 | 19.21 | 18.78 | 18.51 | 18.36 | 18.13 | 15.84 |
| DPM++ [52] | 20.94 | 19.51 | 18.77 | 18.43 | 18.21 | 18.06 | 17.86 | 15.99 |
| UniPC [92] | 20.81 | 19.40 | 18.82 | 18.56 | 18.36 | 18.27 | 18.08 | 18.03 |
| LML (Ours) | 17.76 | 16.99 | 16.17 | 16.02 | 16.29 | 15.95 | 16.16 | 15.14 |
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| Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) | Color(↑) | Shape(↑) | Texture(↑) |
| DDIM [75] | 0.3864 | 0.3791 | 0.4231 | 0.5111 | 0.4182 | 0.4822 | 0.5670 | 0.4712 | 0.5076 | 0.2933 | 0.3746 | 0.4045 |
| PNDM [50] | 0.3810 | 0.3761 | 0.4331 | 0.5067 | 0.4190 | 0.4863 | 0.5682 | 0.4772 | 0.5085 | 0.4035 | 0.3996 | 0.4225 |
| DPM [51] | 0.3877 | 0.3945 | 0.4294 | 0.5162 | 0.4307 | 0.5002 | 0.5795 | 0.4841 | 0.5194 | 0.3263 | 0.3895 | 0.4349 |
| DPM++ [52] | 0.3881 | 0.3958 | 0.4307 | 0.5202 | 0.4326 | 0.5020 | 0.5798 | 0.4858 | 0.5201 | 0.3136 | 0.3882 | 0.4364 |
| UniPC [92] | 0.3892 | 0.3889 | 0.4306 | 0.5146 | 0.4337 | 0.4995 | 0.5828 | 0.4910 | 0.5234 | 0.3187 | 0.3880 | 0.4266 |
| LML (Ours) | 0.4335 | 0.4252 | 0.4746 | 0.5640 | 0.4792 | 0.5330 | 0.5908 | 0.4938 | 0.5363 | 0.3801 | 0.4265 | 0.4684 |
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| 5 | 10 | 15 | 20 | 30 | 50 | 100 |
| CIFAR-10 | DDIM | 0.13 | 0.20 | 0.27 | 0.34 | 0.52 | 0.81 | 1.49 |
| LML (Ours) | 0.13 | 0.21 | 0.27 | 0.37 | 0.48 | 0.82 | 1.51 |
| CelebA | DDIM | 0.20 | 0.28 | 0.39 | 0.47 | 0.66 | 1.03 | 1.95 |
| LML (Ours) | 0.20 | 0.31 | 0.38 | 0.48 | 0.67 | 1.10 | 2.08 |
| SD-1.5 | DDIM | 0.45 | 0.73 | 1.03 | 1.31 | 1.87 | 3.01 | 5.85 |
| LML (Ours) | 0.45 | 0.74 | 1.04 | 1.32 | 1.89 | 3.03 | 5.89 |
| SD-2base | DDIM | 0.45 | 0.71 | 1.00 | 1.25 | 1.80 | 2.87 | 5.53 |
| LML (Ours) | 0.46 | 0.72 | 0.98 | 1.27 | 1.81 | 2.88 | 5.60 |
| SD-XL | DDIM | 2.32 | 4.25 | 6.23 | 8.12 | 12.06 | 19.82 | 39.48 |
| LML (Ours) | 2.32 | 4.30 | 6.23 | 8.21 | 12.11 | 19.99 | 39.55 |
| PixArt | DDIM | 0.66 | 1.08 | 1.49 | 1.92 | 2.74 | 4.31 | 8.45 |
| LML (Ours) | 0.67 | 1.08 | 1.51 | 1.92 | 2.75 | 4.28 | 8.49 |
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+ "content": "This work was supported in part by the National Natural Science Foundation of China under Grants 62206248 and 62402430, and the Zhejiang Provincial Natural Science Foundation of China under Grant LQN25F020008. Fangyikang Wang would like to extend his gratitude to Pengze Zhang from ByteDance, Binxin Yang, and Xinhang Leng from WeChat Vision for their discussions regarding the experiments. Additionally, he is thankful to Zebang Shen from ETH Zürich and Zhichao Chen from Peking University for their insights on Langevin dynamics."
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+ "content": "[92] Wenliang Zhao, Lujia Bai, Yongming Rao, Jie Zhou, and Jiwen Lu. Unipc: A unified predictor-corrector framework for fast sampling of diffusion models. Advances in Neural Information Processing Systems, 36, 2024. 6, 7, 8"
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diff --git a/2025/Unleashing Vecset Diffusion Model for Fast Shape Generation/7b74d35d-3a86-45b7-bf2b-07600548528f_content_list.json b/2025/Unleashing Vecset Diffusion Model for Fast Shape Generation/7b74d35d-3a86-45b7-bf2b-07600548528f_content_list.json
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+[
+ {
+ "type": "text",
+ "text": "Unleashing Vecset Diffusion Model for Fast Shape Generation",
+ "text_level": 1,
+ "bbox": [
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Zeqiang Lai $^{1,2\\star}$ , Yunfei Zhao $^{2,3\\star}$ , Zibo Zhao $^{2,4}$ , Haolin Liu $^{2}$ , Fuyun Wang $^{1}$ , Huiwen Shi $^{2}$ , Xianghui Yang $^{2}$ , Qingxiang Lin $^{2}$ , Jingwei Huang $^{2}$ , Yuhong Liu $^{2}$ , Jie Jiang $^{2}$ , Chunchao Guo $^{2\\dagger}$ , Xiangyu Yue $^{1\\dagger}$ , MMLab, CUHK $^{2}$ , Tencent Hunyuan $^{3}$ , VISG, NJU $^{4}$ , ShanghaiTech https://github.com/Tencent-Hunyuan/FlashVDM",
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+ },
+ {
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+ "img_path": "images/bb398e1404c6b3ea42373863b6e6ef84733f6338cb4eb68a73f55e295a72c3fd.jpg",
+ "image_caption": [
+ "Figure 1. High-resolution 3D shapes generated by Flash Vecset Diffusion Model (FlashVDM) within 1 second."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Abstract",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "3D shape generation has greatly flourished through the development of so-called \"native\" 3D diffusion, particularly through the Vecset Diffusion Model (VDM). While recent advancements have shown promising results in generating high-resolution 3D shapes, VDM still struggles at high-speed generation. Challenges exist because of not only difficulties in accelerating diffusion sampling but also VAE decoding in VDM - areas under-explored in previous works. To address these challenges, we present FlashVDM, a systematic framework for accelerating both VAE and DiT in VDM. For DiT, FlashVDM enables flexible diffusion sampling with as few as 5 inference steps and com",
+ "bbox": [
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "parable quality, which is made possible by stabilizing consistency distillation with our newly introduced Progressive Flow Distillation. For VAE, we introduce a lightning vecset decoder equipped with Adaptive KV Selection, Hierarchical Volume Decoding, and Efficient Network Design. By exploiting the locality of vecset and the sparsity of shape surface in the volume, our decoder drastically lowers FLOPs, minimizing the overall decoding overhead. We apply FlashVDM to Hunyuan3D-2 [58] to obtain Hunyuan3D-2 Turbo. Through systematic evaluation, we show that our model significantly outperforms existing fast 3D generation methods, achieving comparable performance to the state-of-the-art while reducing inference time by over $45 \\times$ for reconstruction and $32 \\times$ for generation.",
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+ {
+ "type": "header",
+ "text": "CVF",
+ "bbox": [
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
+ 238,
+ 0,
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+ "page_idx": 0
+ },
+ {
+ "type": "page_footnote",
+ "text": "$\\star$ Equal contribution. $\\dagger$ Corresponding authors.",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "page_number",
+ "text": "2523",
+ "bbox": [
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+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "3D shape generation has greatly flourished through the development of so-called \"native\" 3D diffusion [46, 56], among which the Vecset Diffusion Model (VDM) [54, 57] receives prominent attention and applications due to its simplicity and scalability. While recent works [18, 56, 58] have demonstrated the capabilities of VDM in generating high-resolution and high-quality 3D shapes, VDM still struggles with high-speed generation, typically requiring over 30 seconds $^{1}$ per shape – far behind the development of image generation counterparts [26, 34, 35, 52]. The notable reasons behind the lags of VDM [54] against previous 2D predecessors [31] lies in not only the lack of research of diffusion distillation [26, 28] for few-step 3D generators, but also the acceleration of Variational Autoencoders (VAE).",
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "Unlike the 2D VAE [6], which utilizes convolution for image compressing and decoding with structured latent, the VAE in VDM takes a fundamentally different approach. Its encoder compresses the point cloud of the mesh surface into a set of latent tokens—typically referred to as a vec-set—through cross-attention (CA), using a set of query tokens [54]. This approach, similar to Q-former [14] and Perceiver [12], offers strong compression capability but also introduces challenges in decoding. To overcome this, VDM employs a symmetric approach, constructing a set of volume queries that evaluate occupancy or Signed Distance Function (SDF) at each grid point using another CA. While the CA decoder design enables VDM to flexibly decode at arbitrary resolutions, the computational cost increases cubically with respect to resolution. For instance, at a typical resolution of 384, the number of query points exceeds 56 million—each requires a CA operation. Even worse, modern VDMs [18, 58] typically use a much larger set of latent tokens for key-value pairs to ensure high-resolution generation, which ends up making the decoding process even slower. As a result, VAE decoding in VDM demands a significant amount of inference time—even longer than diffusion sampling as shown in Fig. 2 (a).",
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+ {
+ "type": "text",
+ "text": "On the other hand, despite the significant advancements in fast image generation through diffusion distillation [26, 28, 34, 35, 52], pushing the speed to real-time, research into native 3D diffusion distillation remains scarce. Most existing distillation methods [26, 34, 52] were originally designed for images, with some adaptations made for video [53, 61]. Many techniques, such as LPIPS loss in Consistency Distillation (CD) [23, 38, 40] and GAN designs [43, 52], are specifically tailored for images. However, the representation of 3D meshes and images differs significantly, making it challenging to adapt these techniques. Additionally, the vastly different latent spaces in VDMs against image DMs [31] could drastically alter the",
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+ "img_path": "images/70b052f9671e26f2e984208a12f2eeca28eb8fc7e572a36d1c21abd0f3a6709a.jpg",
+ "image_caption": [
+ "Figure 2. (a) VDM exhibits different distribution with image DM with much larger percentage in VAE decoding. (b) FlashVDM enables fast shape generation within 1 second on a consumer GPU."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "training dynamics of the distillation, which makes previous strategies unsuitable, potentially leading to instability and unsatisfactory results.",
+ "bbox": [
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+ "page_idx": 1
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+ "type": "text",
+ "text": "To address the aforementioned problems, we present FlashVDM, a framework for transforming pretrained VDM into a high-fidelity and high-speed generator with over $45 \\times$ speedup in VAE decoding and $32 \\times$ speedup overall. Our framework consists of two main components: 1) diffusion acceleration and 2) VAE acceleration.",
+ "bbox": [
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+ "text": "For diffusion acceleration, we carefully analyzed the problems in direct application of CD [40, 43] for VDM and found that the core issue lies in the instability of the target network, which degrades the training and causes unsatisfactory results. As a remedy, we propose Progressive Flow Distillation, a multi-stage distillation method for VDM. It first decouples the CD distillation by warming up with guidance distillation. This prevents the target bias and fluctuations from misleading the student. Then, we carefully ablate the design choices including loss and training strategies in CD, leading to even more stable step distillation. Finally, we introduce adversarial finetuning, leveraging real 3D data as supervision, to help distilled models produce smoother and more accurate results within limited steps. Together, our distilled model could achieve comparable results with only 5 Number of Function Evaluation (NFE).",
+ "bbox": [
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+ "text": "For VAE acceleration, we introduce three techniques, including two training-free methods—Adaptive KV Selection and Hierarchical Volume Decoding—to reduce both the number of number of key-value pairs and the queries. These techniques effectively exploit the locality of VDM point-queries and the sparsity of shape surface in the volume space, resulting in a highly efficient CA with a $97.1\\%$ FLOPs reduction in total. Additionally, we introduce an Efficient Decoder Architecture. By fixing the encoder and fine-tuning only the decoder, our new design further reduces FLOPs by $76.6\\%$ for each query. With these three improvements combined, our final VAE decoder achieves over a",
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+ {
+ "type": "page_footnote",
+ "text": "Measured by the default setting of Hunyuan3D-2 [58].",
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+ {
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+ "text": "2524",
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+ "text": "$45 \\times$ speedup, significantly reducing the decoding time from 22.3s to just 0.49s.",
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "In summary, our contributions are listed as follows:",
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+ "list_items": [
+ "- We introduce FlashVDM, a framework that converts pretrained VDMs into high-speed and -fidelity generators.",
+ "- We present progressive flow distillation for VDM, significantly improving the stability and quality of the distilled model, achieving comparable results with only 5 NFE.",
+ "- We propose a novel algorithm, hierarchical volume decoding with adaptive KV selection and an efficient decoder architecture, obtaining $45 \\times$ speedup in decoding.",
+ "- We apply FlashVDM to Hunyuan3D-2 [58] and obtain Hunyuan3D-2 Turbo, a high-resolution shape generator that matches its teacher's shape quality with over $32 \\times$ speedup, achieving 1 second per shape."
+ ],
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+ "page_idx": 2
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+ "type": "text",
+ "text": "2. Related Works",
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "Diffusion Acceleration. Step distillation [8, 25, 28, 33, 34, 40, 47, 50, 52, 60] is a popular technique for accelerating diffusion models, with early works like Progressive Distillation [28, 33] training student models by halving sampling steps step-by-step. More recent approaches, such as consistency models [39, 40, 43] and score distillation [34, 52], enforce self-consistency or match distributions between student and teacher models. GAN-based approaches [34, 44] further refine score distillation by augmenting loss functions with adversarial objectives. Several works, including UFOGen [48] and LADD [35], combine GANs with pretrained diffusion models as discriminators. Other research focuses on reducing redundancy in sampling processes, such as DPM-Solver [24], SnapFusion [17], and DeepCache [27]. In this work, we introduce progressive flow distillation to address practical issues in 3D foundation models, an area not yet explored in previous research.",
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "VAE Acceleration. The proposed hierarchical volume decoding is generally related to octree decoding [32]. However, we noted that vanilla octree decoding introduces artifacts and holes, whereas our method is nearly lossless. Our adaptive KV selection is broadly related to previous work on token merging [1, 2] in DiT inference, though our approach is specifically designed for VAE acceleration in VDM without the merge operation. To the best of our knowledge, we are the first to explore the efficient design of a VDM decoder. DC-AE [4] is one of the works for image diffusion models [4], but it focuses on achieving a higher compression ratio, which is different from our objective.",
+ "bbox": [
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "Fast 3D Generation. Previous works on fast 3D generation are based on feedforward 3D reconstruction methods [9], which require only a single network evaluation. Benefiting from this property, TripoSR [42] and SF3D [3] can generate a mesh from a single image in under 1 second, but the resulting mesh quality is limited. To address this, multiview images are often used [15, 41], but this re",
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+ "img_path": "images/9235d29df0346ba80407b99e5fabfb29f406da5ea48e70c9cb5d7109aff8fee5.jpg",
+ "image_caption": [
+ "Figure 3. Illustration of four main stages of VDM."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "quires a Multi-View Diffusion (MVD) model [21, 36, 37]. In response, SPAR3D [11] replaces MVD with a small point cloud generator, while Turbo3D [10] distills MVD into a four-step generator. Nevertheless, all these feedforward methods are still limited in mesh quality compared to diffusion-based 3D generators [56, 58].",
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+ "type": "text",
+ "text": "3. Method",
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+ "type": "text",
+ "text": "In this section, we first provide an introduction to VDM pipeline and inference time distribution. Then, we illustrate our approaches for accelerating VAE decoding in Sec. 3.2 and diffusion sampling in Sec. 3.3, respectively.",
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+ "text": "3.1. Preliminary of VDM",
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+ "text": "Pipeline Overview. Here, we provide a brief introduction to the inference pipeline of VDM. We refer interested readers to [5, 54, 56, 58] for more details. As shown in Fig. 3, the inference of VDM consists of four stages: 1) image encoding: an image encoder [29, 30] is used to extract conditional features; 2) diffusion sampling: iteratively calling a denoising transformer to predict shape latent based on conditional features. 3) volume decoding: the predicted shape latent is decoded into volume SDF via several layers of self-attention and a cross-attention. 4) surface extraction: marching cube algorithm [22] is used to extract polygon mesh from the decoded volume.",
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+ {
+ "type": "text",
+ "text": "Inference Time Distribution. The distribution of inference times is shown in Fig. 2(a). We could observe that diffusion sampling (23.9%) and volume decoding (75.8%) account for the majority (99.7%) of the inference time for VDM. However, image encoding and surface extraction remain significant when the total inference time is reduced to less than one second. As a first step, we implement several engineering acceleration techniques, including FP8 attention with SageAttention2 [55], static graph optimization with torch.compile, and etc., which decrease the processing time to 25.09s per shape, as shown in Fig. 5.",
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+ "type": "page_number",
+ "text": "2525",
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+ "type": "image",
+ "img_path": "images/3194c719f6b9e16393f8caa4658b0588a1890f120b3ba1104381c352c471c583.jpg",
+ "image_caption": [
+ "Mesh Internal Missing Point Expand Point Discarded Point",
+ "(a) Sign check"
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+ "img_path": "images/f05a6b63377aee8347fe74560a5f4bc6279563ad177c2c50b6afabe8537fdb69.jpg",
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+ "(b) tSDF without dilate"
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+ {
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+ "(c) tSDF only"
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+ "text": "3.2. Lightning Vecset Decoder",
+ "text_level": 1,
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+ "type": "text",
+ "text": "The majority $(99.9\\%)$ of the computational cost in the original VDM decoder is concentrated in its final cross-attention layer, which is evaluated tens of millions of times. To optimize this layer, we propose three key techniques, each addressing a different aspect: 1) hierarchical volume decoding to reduce the number of queries, 2) adaptive KV selection to minimize the number of keys and values, and 3) an efficient decoder design to reduce computational overhead in each cross-attention operation.",
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+ "text": "Hierarchical Volume Decoding. To decode shape latents into a mesh, the existing VDM decoder relies on dense volume decoding and marching cube algorithms [22], which has cubic complexity with respect to the resolution. It raises challenges for balancing speed and mesh quality. However, unlike image decoders [6] that must predict RGB values for every pixel, the VDM decoder only needs to determine high-resolution SDF values near the shape surface – all voxels far from the surface can be simply classified as inside or outside. Inspired by this characteristic, we propose hierarchical volume decoding that only increases resolution near the surface, thereby reducing the queries by $91.4\\%$ .",
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+ {
+ "type": "text",
+ "text": "Specifically, instead of directly decoding the SDF volume at the target resolution (e.g., 384), we begin by decoding at a smaller resolution (e.g., 75), which provides a coarse SDF volume. Using this coarse volume, we can identify which voxels intersect the shape surface based on the following criterion:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nf (x, y, z) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\exists (i, j, k) \\in N (x, y, z) \\\\ & \\text {s u c h t h a t} f (i, j, k) \\neq f (x, y, z), \\\\ 0 & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {1}\n$$\n",
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+ "type": "text",
+ "text": "where $N(x,y,z)$ represents the set of adjacent voxels to $(x,y,z)$ and $f(x,y,z) = 1$ indicates the voxel intersects with the surface. In short, a voxel does not intersect with the surface only if all its adjacent voxels are either inside or outside. For voxels that do intersect the surface, we subdivide them into higher resolutions and compute the SDF values through cross-attention once more. This process is",
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+ "img_path": "images/f5670f26b80c235733f6b28556743762d342aebedaeda128cfb1d7f5a76781f8.jpg",
+ "image_caption": [
+ "Figure 4. The corner cases in hierarchical volume decoding.",
+ "Figure 5. Step-by-step case study of FlashVDM acceleration techniques and their effects on inference time and IoU."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "type": "text",
+ "text": "repeated until we reach the target resolution. Since the surface shape is highly sparse within the volume, the number of effective queries is significantly reduced.",
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+ "text": "Naively, previous steps could be considered a type of octree decoding [32]. However, we find that it produces artifacts and holes when applied to VDM in practice. To prevent degradation, we need to consider some corner cases. First, when the resolution is low, for very thin meshes, two adjacent voxels may lie on opposite sides of the mesh surface, both having the same sign, as shown in Fig. 4 (a). This causes the missing voxels for resolution increment, leading to holes in the surface. To address this, we use tSDF as supervision during VAE training to help determine whether a voxel is near the mesh surface. Then, during hierarchical decoding, we append all voxels under a certain tSDF threshold (TR). With this strategy, the lowest resolution in hierarchical decoding can be reduced to $w + u * 2$ where $w$ is the minimal mesh width and $u$ is the tSDF TR. Second, failure cases exist even with tSDF augmentation as shown in Fig. 4 (b,c), e.g., uneven distribution of surface between two adjacent voxels and etc. Therefore, we perform a dilation operation after identifying the intersected voxels to prevent unexpected missing points. We leave the choice of tSDF value and more details to the Supplementary Material.",
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+ "text": "Adaptive KV Selection. For each position in volume decoding, a cross-attention operation is performed between",
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+ "img_path": "images/aa18eb3b6607733db8a0550955f4ae831242aa30e11b6729183a33ce20c74599.jpg",
+ "image_caption": [
+ "Figure 6. Histogram of activated token counts with non-zero attention of 70,800 regions from 250 cases."
+ ],
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+ "type": "text",
+ "text": "the queries and key-value pairs (computed from shape latents). Previously, we significantly reduced the number of queries. To further minimize computational overhead, we introduce adaptive KV selection, which reduces the number of key-value pairs. Our method leverages the observation that the correlation between spatial queries and shape latents exhibits strong locality - adjacent spatial points tend to attend to similar latent tokens, with the attention concentrated on a small subset of tokens (denoted as activated tokens). To illustrate, we show two histograms in Figs. 6 and 7. As seen, most regions in 3D volumes attend to at most 1,000 tokens - one-third of the original 3,072, and different regions focus on different set of activated tokens. Moreover, our statistic reveals that the average activated token count for a single query is around only 10, which also indicates strong locality in shape latents.",
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+ "type": "text",
+ "text": "The proposed adaptive KV selection is training-free and able to be combined with hierarchical volume decoding. For simplicity, we first show the algorithm with vanilla volume decoding. In this case, we first divide the entire volume into smaller sub-volumes. Then, within each sub-volume, we uniformly sample a small set of queries to compute their attention scores relative to the keys. To select most correlated key-value pairs, we could simply average the attention score of all queries and select the TopK, or we could merge the TopN of each query to obtain TopM, where N is a small number (e.g., 50) that can include most activated tokens with non-zero attention. The latter one is slightly better but also slightly slower (5%). For other queries within the same sub-volume, we only use the Top-K/M key-value pairs for attention computation. Since the attention scores are estimated using a small set of queries and the number of activated shape latents are much smaller, the overall computation can be reduced by 34%, as shown in Fig. 5.",
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+ "type": "text",
+ "text": "The combination with hierarchical volume decoding needs some extra consideration to ensure performance. The core obstacle lies in the requirement that subvolume should be small to maintain locality. Within hierarchical decoding, the effective queries could be even fewer in a subvolume. Thereafter, naive implementation that process each subvol",
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+ "img_path": "images/c015a98ed22970b1380a646a1a25961819845814998b49a81cea9df413f2310f.jpg",
+ "image_caption": [
+ "Figure 7. Normalized histogram of activated shape tokens with non-zero attention at different regions. Zoom in for a better view. The numbers in the legend indicate the number of activated tokens."
+ ],
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+ {
+ "type": "text",
+ "text": "ume one-by-one would not maximize GPU utilization. As a remedy, we design a packing operation, which precompute the target queries in each volume, pack queries of different subvolume, and process them together. More details on the analysis and the implementation lives in the Supplementary Material.",
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+ "type": "text",
+ "text": "Efficient Decoder Design. Once we have reduced the QKV in CA, further acceleration of the attention operation itself becomes challenging algorithmically. Thereby, our next approach focuses on optimizing the decoder network design. Most existing vectorset decoders [16, 54, 57] share nearly identical architectures, typically consisting of several self-attention (SA) layers and a cross-attention layer, as shown in Fig. 3, with SA layers evaluated only once. Therefore, our goal is to simplify the final CA layer as much as possible, which we believe could be replaced with a simpler one as it only needs to classify the inside/outside status of each position. To this end, we reduce the network width, decrease the MLP expansion ratio, and remove several LayerNorm layers. Through careful ablation studies, we found that these reductions have minimal impact on reconstruction quality while boosting speed by $3.2 \\times$",
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+ "type": "text",
+ "text": "3.3. Progressive Flow Distillation",
+ "text_level": 1,
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+ "text": "Similar to image and video generation [13, 19, 31], we can reduce the sampling steps of VDM through distillation [26, 61]. Initially, we experimented with PCM [43], but we found it hard to yield satisfactory results on VDM. To address this, we propose progressive flow distillation as shown in Fig. 8, systematically identifying and refining key design choices for effective distillation.",
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+ "text": "Consistency Flow Distillation (CFD). Consistency Distillation (CD) [40] is a well-known distillation method for reducing the diffusion sampling steps, though its application to 3D diffusion has yet to be explored. The core of CD is to enforce a consistency property - any point along the ODE trajectory maps to the same target point. To achieve this, CD uses a time difference method, where a starting point $\\mathbf{x}_{t_n}$ is first selected for the target prediction of the",
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+ "img_path": "images/4fc5fa3626e8fa550aa33b3a28878f34af23c3a6ddaba9ec731c2c443640620e.jpg",
+ "image_caption": [
+ "Figure 8. Training pipeline for Progressive Flow Distillation."
+ ],
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+ "type": "text",
+ "text": "student model $\\mathbf{x}_0^{t_n} = \\pmb{f}_{\\pmb{\\theta}}(\\mathbf{x}_{t_n},t_n)$ . For flow-based models, e.g., Hunyuan3D-2 [58], the Euler solver could be employed with a large discretization step $t_n - t_0$ to compute the target $\\mathbf{x}_0^{t_n}$ . For GT target, the teacher model predicts the next point $\\hat{\\mathbf{x}}_{t_{n + 1}}^{\\phi}$ by running one discretization step of an ODE solver, after which the student model predicts the GT target at next timestep $x_0^{t_{n + 1}} = \\pmb {f}_{\\pmb{\\theta}}\\left(\\hat{\\mathbf{x}}_{t_{n + 1}}^{\\phi},t_{n + 1}\\right)$ . The consistency property is enforced by the following loss,",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\left. \\mathcal {L} _ {c f d} (\\boldsymbol {\\theta}) := \\mathbb {E} \\left[ d \\left(\\boldsymbol {f} _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {t _ {n}}, t _ {n}\\right), \\boldsymbol {f} _ {\\boldsymbol {\\theta} ^ {-}} \\left(\\hat {\\mathbf {x}} _ {t _ {n + 1}} ^ {\\phi}, t _ {n + 1}\\right)\\right) \\right], \\right. \\tag {2}\n$$\n",
+ "text_format": "latex",
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+ },
+ {
+ "type": "text",
+ "text": "with a boundary constraint $f(\\mathbf{x}_{\\epsilon}, \\epsilon) = \\mathbf{x}_{\\epsilon}$ , where $d$ is a distance function and $\\theta^{-}$ is a regular copy of student model named as target model.",
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+ "text": "Stabilizing Target Model. In practice, directly applying the distillation method described above does not yield satisfactory results, as shown in Fig. 11 (w/o GD distill). Our analysis reveals that the main challenge lies in the stability of the target model. During training, the student model continually tries to mimic the output of the target model, making it highly sensitive to changes in the target. As a result, we observe significant fluctuations in the predictions throughout the training process. To stabilize the target model, we introduce a progressive training strategy, in which 1) we first perform guidance distillation and initialize the student model as a distilled version. This approach differs from distillation in image models, where guidance distillation can be applied simultaneously with step distillation without issues. We hypothesize that this gap arises from the differences between 2D and 3D models and the more complex optimization landscape in 3D models. 2) Besides, we find that the EMA update of the target model is crucial for stabilizing VDM, which contrasts with a recent study on 2D generation as well [38]. 3) Moreover, we replace commonly used L2 loss with Huber loss as it is less sensitive to outliers, which makes training more stable. 4) Finally, we introduce a multi-stage-multi-phase consistency distil",
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+ "img_path": "images/3f09797d5b58df03f1aaf84074dac25f6171b0cff927d308afab906c6b7f219e.jpg",
+ "image_caption": [
+ "Figure 9. Visual comparison of shape reconstruction methods."
+ ],
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+ {
+ "type": "table",
+ "img_path": "images/63aa0a260ab4e3c341b501a68a2de831c538866298dab84a48c956bc5887b1c3.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": " | V-IoU(↑) | S-IoU(↑) | Time(s↓) |
| 3DShape2VecSet [54] | 87.88% | 84.93% | 16.43 |
| Michelangelo [57] | 84.93% | 76.27% | 16.43 |
| Direct3D [45] | 88.43% | 81.55% | 3.201 |
| Hunyuan3D-2 [58]-1024 | 93.60% | 89.16% | 16.43 |
| \\(\\sqsubseteq\\) with FlashVDM | 91.90% | 88.02% | 0.382 |
| Hunyuan3D-2 [58]-3072 | 96.11% | 93.27% | 22.33 |
| \\(\\sqsubseteq\\) with FlashVDM | 95.55% | 93.10% | 0.491 |
",
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+ "type": "text",
+ "text": "Table 1. Numerical comparisons of shape reconstruction methods.",
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "lation strategy based on PCM [43], in which a single-phase finetuning is performed after five phases pretraining.",
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+ "type": "text",
+ "text": "Aligning Real Data with GAN. With the proposed improvements, our CFD is able to reduce the sampling steps to just 5 while still producing decent results. However, we found that in some cases, the mesh quality is difficult to match the teacher's outputs, which might be attributed to the self-distillation nature of the consistency model. To address this, we seek to further enhance performance by incorporating supervision from ground-truth 3D data through adversarial training [7]. Specifically, we initialize the generator using the model distilled in the previous stage. Inspired by previous works [35, 48], our discriminator operates directly in latent space, eliminating the need for an expensive decoding process, and leverages the intermediate features of the pretrained diffusion model. As shown in Fig. 8, we first extract token sequences from specified attention layers, and then apply independent discriminator heads. Unlike prior works [35, 43, 48, 51] that use noised latents, we did not observe significant improvements with noise, so we opt to use ground-truth latents for simplicity. The discriminator is trained with a hinge adversarial loss [20] as,",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {a d v}} (\\theta , \\gamma) = \\operatorname {R e L U} \\left(1 + \\mathcal {D} _ {\\gamma} \\left(\\mathbf {x} _ {0}\\right)\\right) + \\operatorname {R e L U} \\left(1 - \\mathcal {D} _ {\\gamma} \\left(\\mathbf {x} _ {0} ^ {t _ {n}}\\right)\\right), \\tag {3}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "which distinguishes between ground truth latent $\\mathbf{x}_0$ and latent produced by our generator $\\mathbf{x}_0^{t_n} = f_\\theta (z_{t_n},t_n)$ . Following [43, 51], the final objective is a combination of the adversarial objective and consistency loss $\\mathcal{L} = \\mathcal{L}_{cfd} + \\lambda \\mathcal{L}_{adv}$ where $\\lambda$ is set to 0.1.",
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+ "img_path": "images/dff8c008808ca85f318562860e885153e525712c03cc72b224002a53e9242584.jpg",
+ "image_caption": [
+ "Figure 10. Visual comparison of image-to-3D generation between the proposed FlashVDM and other fast 3D generation methods."
+ ],
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+ "type": "text",
+ "text": "4. Experiments",
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+ "text": "In this section, we apply the proposed FlashVDM to Hunyuan3D-2 [58], which is currently a state-of-the-art open-source VDM. We evaluate our approach in terms of both VAE reconstruction and diffusion generation. We also provide ablation studies of the proposed techniques.",
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+ "text": "4.1. Reconstruction",
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+ "text": "Metrics. We utilize the volume and surface IoU metric to assess the impact of our acceleration techniques on VAE reconstruction performance. The running time is measured at the resolution of 380.",
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+ "type": "text",
+ "text": "Comparison. We compare our method with three competing method, i.e., 3DShape2VecSet [54], Michelan-",
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+ "text": "gelo [57], and Direct3D [45]. We evaluate two resolutions, i.e., 1,024 and 3,072, for our fast version and the base model Hunyuan3D-2 [58]. The numerical comparison is shown in Tab. 1. It demonstrates that our method outperforms all competing methods and preserve the quality of base model with less than $1\\%$ IoU drop while obtaining over $45\\times$ speedup. Fig. 9 shows the visual comparison, which also indicates minimal degradation in quality.",
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+ "type": "text",
+ "text": "4.2. Generation",
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+ "type": "text",
+ "text": "Metrics. To evaluate shape generation performance, we adopt ULIP-I [49] and Uni3D-I [59] to compute the similarity between the generated mesh and input images.",
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+ "type": "text",
+ "text": "Comparison. Three latest fast 3D generation methods, i.e., TripoSR [42], SF3D [3], and SPAR3D [11], and two",
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+ "text": "2529",
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+ "img_path": "images/adcfef0c5e099f1056651d0d1f35f5ae4843c7e7ab6496f3196c2014bd19a9a2.jpg",
+ "image_caption": [
+ "50 Steps VDM"
+ ],
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+ "img_path": "images/a2a2edc8433396df2bbc4d3457634892356fc7a156bb3083bcee213577080c31.jpg",
+ "image_caption": [
+ "5 Steps VDM",
+ "5 Steps FlashVDM",
+ "w/o GD Distill",
+ "w/oEMA",
+ "w/o ADV FT"
+ ],
+ "image_footnote": [],
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+ "text": "",
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "image",
+ "img_path": "images/86ce4aee979b5e99cc59adc591669e643ba7db9b6fcaa7cf8d8e84651f879900.jpg",
+ "image_caption": [
+ "Figure 11. Ablation study of our progressive flow distillation.",
+ "Figure 12. User study of FlashVDM against different methods."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "table",
+ "img_path": "images/d648578fe5abe9bbf4262b24602ede37119fee4edf6d0ce2133d6ae8e2f513c6.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": " | ULIP-I(↑) | Uni3D-I(↑) | Time(s↓) |
| TripoSR [42] | 0.0642 | 0.1425 | 0.958 |
| SF3D [3] | 0.1156 | 0.2676 | 0.212 |
| SPAR3D [11] | 0.1149 | 0.2679 | 1.296 |
| Trellis [46] | 0.1267 | 0.3116 | 7.334 |
| Hunyuan3D-2 [58] | 0.1303 | 0.3151 | 34.85 |
| \\(\\sqsubset\\) with FlashVDM | 0.1260 | 0.3095 | 1.041 |
",
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+ {
+ "type": "table",
+ "img_path": "images/d55cf7cc0bf6a0e686050d4859d20aff818586c448cced277f85ae5fc7007de2.jpg",
+ "table_caption": [
+ "Table 2. Numerical comparisons of shape generation methods."
+ ],
+ "table_footnote": [],
+ "table_body": " | V-IoU(↑) | S-IoU(↑) | Time(s↓) |
| VAE Baseline | 96.11% | 93.27% | 22.33 |
| + Hierarchical Decoding | 96.11% | 93.27% | 2.322 |
| + Efficient Decoder | 96.08% | 93.13% | 0.731 |
| + Adaptive KV Selection | 95.55% | 93.10% | 0.491 |
",
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+ {
+ "type": "text",
+ "text": "Table 3. Step-by-step ablation of our lightning vecset decoder.",
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+ {
+ "type": "text",
+ "text": "state-of-the-art methods Hunyuan3D-2 [58] and Trellis [46] are selected for comparison. The numerical comparison is shown in Tab. 2 and the visual comparison is shown in Fig. 10. It can be observed that our method retain most of capability of the base model, while achieves the best results with a large margin against other fast methods.",
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+ "type": "text",
+ "text": "User Study. We include results of three user studies in Fig. 12. For comparison between FlashVDM and",
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+ "text": "SPAR3D [11], we ask participants to determine which one is better. For comparison between FlashVDM and Hunyuan3D-2 [58], we ask whether the results are comparable. As seen, FlashVDM is preferred over SPAR3D [11] in almost all testcases, and FlashVDM is comparable to its base model Hunyuan3D-2 [58] at 5 steps and the comparable rate increase with more steps.",
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+ "text": "Effectiveness of Lightning Vecset Decoder. The results of step-by-step ablation is shown in Tab. 3, in which we add each component incrementally. It can be observed that hierarchical decoding provides a $10 \\times$ speedup with no degradation in quality. The efficient decoder achieves an extra $3 \\times$ speedup with almost no degradation, while adaptive KV selection results in a $30 \\%$ speedup with minimal degradation.",
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+ "text": "Effectiveness of Progressive Flow Distillation. We present an ablation study to demonstrate the effectiveness of progressive training strategies. The visual comparison is shown in Fig. 11. As seen, the original VDM completely fails at 5 steps, while FlashVDM achieves results comparable to the original 50-step VDM. Additionally, we observe that distillation fails without guidance distillation as a warm-up step, and performance degrades without the use of EMA. Finally, adversarial fine-tuning is shown to help generate smoother and more accurate shapes. More detailed ablation can be found in the Supplementary Material.",
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+ "text": "In this work, we introduce FlashVDM, a general framework for accelerating a pretrained VDM [18, 58]. Our framework encompasses not only a progressive flow distillation method for distilling VDM into a few-step generator, but also several training-free inference techniques and an efficient, lightweight vecset decoder that significantly reduces the FLOPs of decoding. We apply our framework to the state-of-the-art image-to-3D VDM, Hunyuan3D-2 [58], obtaining Hunyuan3D-2 Turbo. Our evaluation demonstrates that FlashVDM excels in both reconstruction and generation, achieving $45 \\times$ and $32 \\times$ speedups, respectively. To the best of our knowledge, FlashVDM is the first work to push large-scale shape generation into the millisecond range, which opens up new possibilities for interactive applications of 3D generative models.",
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "3D shape generation has greatly flourished through the development of so-called \"native\" 3D diffusion [46, 56], among which the Vecset Diffusion Model (VDM) [54, 57] receives prominent attention and applications due to its simplicity and scalability. While recent works [18, 56, 58] have demonstrated the capabilities of VDM in generating high-resolution and high-quality 3D shapes, VDM still struggles with high-speed generation, typically requiring over 30 seconds\\(^{1}\\) per shape – far behind the development of image generation counterparts [26, 34, 35, 52]. The notable reasons behind the lags of VDM [54] against previous 2D predecessors [31] lies in not only the lack of research of diffusion distillation [26, 28] for few-step 3D generators, but also the acceleration of Variational Autoencoders (VAE)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Unlike the 2D VAE [6], which utilizes convolution for image compressing and decoding with structured latent, the VAE in VDM takes a fundamentally different approach. Its encoder compresses the point cloud of the mesh surface into a set of latent tokens—typically referred to as a vec-set—through cross-attention (CA), using a set of query tokens [54]. This approach, similar to Q-former [14] and Perceiver [12], offers strong compression capability but also introduces challenges in decoding. To overcome this, VDM employs a symmetric approach, constructing a set of volume queries that evaluate occupancy or Signed Distance Function (SDF) at each grid point using another CA. While the CA decoder design enables VDM to flexibly decode at arbitrary resolutions, the computational cost increases cubically with respect to resolution. For instance, at a typical resolution of 384, the number of query points exceeds 56 million—each requires a CA operation. Even worse, modern VDMs [18, 58] typically use a much larger set of latent tokens for key-value pairs to ensure high-resolution generation, which ends up making the decoding process even slower. As a result, VAE decoding in VDM demands a significant amount of inference time—even longer than diffusion sampling as shown in Fig. 2 (a)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "On the other hand, despite the significant advancements in fast image generation through diffusion distillation [26, 28, 34, 35, 52], pushing the speed to real-time, research into native 3D diffusion distillation remains scarce. Most existing distillation methods [26, 34, 52] were originally designed for images, with some adaptations made for video [53, 61]. Many techniques, such as LPIPS loss in Consistency Distillation (CD) [23, 38, 40] and GAN designs [43, 52], are specifically tailored for images. However, the representation of 3D meshes and images differs significantly, making it challenging to adapt these techniques. Additionally, the vastly different latent spaces in VDMs against image DMs [31] could drastically alter the"
+ },
+ {
+ "type": "image",
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 2. (a) VDM exhibits different distribution with image DM with much larger percentage in VAE decoding. (b) FlashVDM enables fast shape generation within 1 second on a consumer GPU."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.342,
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+ "angle": 0,
+ "content": "training dynamics of the distillation, which makes previous strategies unsuitable, potentially leading to instability and unsatisfactory results."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To address the aforementioned problems, we present FlashVDM, a framework for transforming pretrained VDM into a high-fidelity and high-speed generator with over \\(45 \\times\\) speedup in VAE decoding and \\(32 \\times\\) speedup overall. Our framework consists of two main components: 1) diffusion acceleration and 2) VAE acceleration."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "For diffusion acceleration, we carefully analyzed the problems in direct application of CD [40, 43] for VDM and found that the core issue lies in the instability of the target network, which degrades the training and causes unsatisfactory results. As a remedy, we propose Progressive Flow Distillation, a multi-stage distillation method for VDM. It first decouples the CD distillation by warming up with guidance distillation. This prevents the target bias and fluctuations from misleading the student. Then, we carefully ablate the design choices including loss and training strategies in CD, leading to even more stable step distillation. Finally, we introduce adversarial finetuning, leveraging real 3D data as supervision, to help distilled models produce smoother and more accurate results within limited steps. Together, our distilled model could achieve comparable results with only 5 Number of Function Evaluation (NFE)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "For VAE acceleration, we introduce three techniques, including two training-free methods—Adaptive KV Selection and Hierarchical Volume Decoding—to reduce both the number of number of key-value pairs and the queries. These techniques effectively exploit the locality of VDM point-queries and the sparsity of shape surface in the volume space, resulting in a highly efficient CA with a \\(97.1\\%\\) FLOPs reduction in total. Additionally, we introduce an Efficient Decoder Architecture. By fixing the encoder and fine-tuning only the decoder, our new design further reduces FLOPs by \\(76.6\\%\\) for each query. With these three improvements combined, our final VAE decoder achieves over a"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "Measured by the default setting of Hunyuan3D-2 [58]."
+ },
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+ "type": "page_number",
+ "bbox": [
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+ "content": "2524"
+ }
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+ [
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "\\(45 \\times\\) speedup, significantly reducing the decoding time from 22.3s to just 0.49s."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In summary, our contributions are listed as follows:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We introduce FlashVDM, a framework that converts pretrained VDMs into high-speed and -fidelity generators."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We present progressive flow distillation for VDM, significantly improving the stability and quality of the distilled model, achieving comparable results with only 5 NFE."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We propose a novel algorithm, hierarchical volume decoding with adaptive KV selection and an efficient decoder architecture, obtaining \\(45 \\times\\) speedup in decoding."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We apply FlashVDM to Hunyuan3D-2 [58] and obtain Hunyuan3D-2 Turbo, a high-resolution shape generator that matches its teacher's shape quality with over \\(32 \\times\\) speedup, achieving 1 second per shape."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ {
+ "type": "title",
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+ "content": "2. Related Works"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Diffusion Acceleration. Step distillation [8, 25, 28, 33, 34, 40, 47, 50, 52, 60] is a popular technique for accelerating diffusion models, with early works like Progressive Distillation [28, 33] training student models by halving sampling steps step-by-step. More recent approaches, such as consistency models [39, 40, 43] and score distillation [34, 52], enforce self-consistency or match distributions between student and teacher models. GAN-based approaches [34, 44] further refine score distillation by augmenting loss functions with adversarial objectives. Several works, including UFOGen [48] and LADD [35], combine GANs with pretrained diffusion models as discriminators. Other research focuses on reducing redundancy in sampling processes, such as DPM-Solver [24], SnapFusion [17], and DeepCache [27]. In this work, we introduce progressive flow distillation to address practical issues in 3D foundation models, an area not yet explored in previous research."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "VAE Acceleration. The proposed hierarchical volume decoding is generally related to octree decoding [32]. However, we noted that vanilla octree decoding introduces artifacts and holes, whereas our method is nearly lossless. Our adaptive KV selection is broadly related to previous work on token merging [1, 2] in DiT inference, though our approach is specifically designed for VAE acceleration in VDM without the merge operation. To the best of our knowledge, we are the first to explore the efficient design of a VDM decoder. DC-AE [4] is one of the works for image diffusion models [4], but it focuses on achieving a higher compression ratio, which is different from our objective."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Fast 3D Generation. Previous works on fast 3D generation are based on feedforward 3D reconstruction methods [9], which require only a single network evaluation. Benefiting from this property, TripoSR [42] and SF3D [3] can generate a mesh from a single image in under 1 second, but the resulting mesh quality is limited. To address this, multiview images are often used [15, 41], but this re"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 3. Illustration of four main stages of VDM."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "quires a Multi-View Diffusion (MVD) model [21, 36, 37]. In response, SPAR3D [11] replaces MVD with a small point cloud generator, while Turbo3D [10] distills MVD into a four-step generator. Nevertheless, all these feedforward methods are still limited in mesh quality compared to diffusion-based 3D generators [56, 58]."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "3. Method"
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+ "angle": 0,
+ "content": "In this section, we first provide an introduction to VDM pipeline and inference time distribution. Then, we illustrate our approaches for accelerating VAE decoding in Sec. 3.2 and diffusion sampling in Sec. 3.3, respectively."
+ },
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+ "angle": 0,
+ "content": "3.1. Preliminary of VDM"
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+ "content": "Pipeline Overview. Here, we provide a brief introduction to the inference pipeline of VDM. We refer interested readers to [5, 54, 56, 58] for more details. As shown in Fig. 3, the inference of VDM consists of four stages: 1) image encoding: an image encoder [29, 30] is used to extract conditional features; 2) diffusion sampling: iteratively calling a denoising transformer to predict shape latent based on conditional features. 3) volume decoding: the predicted shape latent is decoded into volume SDF via several layers of self-attention and a cross-attention. 4) surface extraction: marching cube algorithm [22] is used to extract polygon mesh from the decoded volume."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Inference Time Distribution. The distribution of inference times is shown in Fig. 2(a). We could observe that diffusion sampling (23.9%) and volume decoding (75.8%) account for the majority (99.7%) of the inference time for VDM. However, image encoding and surface extraction remain significant when the total inference time is reduced to less than one second. As a first step, we implement several engineering acceleration techniques, including FP8 attention with SageAttention2 [55], static graph optimization with torch.compile, and etc., which decrease the processing time to 25.09s per shape, as shown in Fig. 5."
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+ "content": "2525"
+ }
+ ],
+ [
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Mesh Internal Missing Point Expand Point Discarded Point"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
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+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "(a) Sign check"
+ },
+ {
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+ "angle": 0,
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+ "angle": 0,
+ "content": "(b) tSDF without dilate"
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+ "content": "(c) tSDF only"
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+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. The corner cases in hierarchical volume decoding."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.2. Lightning Vecset Decoder"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The majority \\((99.9\\%)\\) of the computational cost in the original VDM decoder is concentrated in its final cross-attention layer, which is evaluated tens of millions of times. To optimize this layer, we propose three key techniques, each addressing a different aspect: 1) hierarchical volume decoding to reduce the number of queries, 2) adaptive KV selection to minimize the number of keys and values, and 3) an efficient decoder design to reduce computational overhead in each cross-attention operation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Hierarchical Volume Decoding. To decode shape latents into a mesh, the existing VDM decoder relies on dense volume decoding and marching cube algorithms [22], which has cubic complexity with respect to the resolution. It raises challenges for balancing speed and mesh quality. However, unlike image decoders [6] that must predict RGB values for every pixel, the VDM decoder only needs to determine high-resolution SDF values near the shape surface – all voxels far from the surface can be simply classified as inside or outside. Inspired by this characteristic, we propose hierarchical volume decoding that only increases resolution near the surface, thereby reducing the queries by \\(91.4\\%\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Specifically, instead of directly decoding the SDF volume at the target resolution (e.g., 384), we begin by decoding at a smaller resolution (e.g., 75), which provides a coarse SDF volume. Using this coarse volume, we can identify which voxels intersect the shape surface based on the following criterion:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\nf (x, y, z) = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\exists (i, j, k) \\in N (x, y, z) \\\\ & \\text {s u c h t h a t} f (i, j, k) \\neq f (x, y, z), \\\\ 0 & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {1}\n\\]"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\( N(x,y,z) \\) represents the set of adjacent voxels to \\( (x,y,z) \\) and \\( f(x,y,z) = 1 \\) indicates the voxel intersects with the surface. In short, a voxel does not intersect with the surface only if all its adjacent voxels are either inside or outside. For voxels that do intersect the surface, we subdivide them into higher resolutions and compute the SDF values through cross-attention once more. This process is"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. Step-by-step case study of FlashVDM acceleration techniques and their effects on inference time and IoU."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.503,
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+ ],
+ "angle": 0,
+ "content": "repeated until we reach the target resolution. Since the surface shape is highly sparse within the volume, the number of effective queries is significantly reduced."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Naively, previous steps could be considered a type of octree decoding [32]. However, we find that it produces artifacts and holes when applied to VDM in practice. To prevent degradation, we need to consider some corner cases. First, when the resolution is low, for very thin meshes, two adjacent voxels may lie on opposite sides of the mesh surface, both having the same sign, as shown in Fig. 4 (a). This causes the missing voxels for resolution increment, leading to holes in the surface. To address this, we use tSDF as supervision during VAE training to help determine whether a voxel is near the mesh surface. Then, during hierarchical decoding, we append all voxels under a certain tSDF threshold (TR). With this strategy, the lowest resolution in hierarchical decoding can be reduced to \\( w + u * 2 \\) where \\( w \\) is the minimal mesh width and \\( u \\) is the tSDF TR. Second, failure cases exist even with tSDF augmentation as shown in Fig. 4 (b,c), e.g., uneven distribution of surface between two adjacent voxels and etc. Therefore, we perform a dilation operation after identifying the intersected voxels to prevent unexpected missing points. We leave the choice of tSDF value and more details to the Supplementary Material."
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "Adaptive KV Selection. For each position in volume decoding, a cross-attention operation is performed between"
+ },
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+ }
+ ],
+ [
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 6. Histogram of activated token counts with non-zero attention of 70,800 regions from 250 cases."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "the queries and key-value pairs (computed from shape latents). Previously, we significantly reduced the number of queries. To further minimize computational overhead, we introduce adaptive KV selection, which reduces the number of key-value pairs. Our method leverages the observation that the correlation between spatial queries and shape latents exhibits strong locality - adjacent spatial points tend to attend to similar latent tokens, with the attention concentrated on a small subset of tokens (denoted as activated tokens). To illustrate, we show two histograms in Figs. 6 and 7. As seen, most regions in 3D volumes attend to at most 1,000 tokens - one-third of the original 3,072, and different regions focus on different set of activated tokens. Moreover, our statistic reveals that the average activated token count for a single query is around only 10, which also indicates strong locality in shape latents."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The proposed adaptive KV selection is training-free and able to be combined with hierarchical volume decoding. For simplicity, we first show the algorithm with vanilla volume decoding. In this case, we first divide the entire volume into smaller sub-volumes. Then, within each sub-volume, we uniformly sample a small set of queries to compute their attention scores relative to the keys. To select most correlated key-value pairs, we could simply average the attention score of all queries and select the TopK, or we could merge the TopN of each query to obtain TopM, where N is a small number (e.g., 50) that can include most activated tokens with non-zero attention. The latter one is slightly better but also slightly slower (5%). For other queries within the same sub-volume, we only use the Top-K/M key-value pairs for attention computation. Since the attention scores are estimated using a small set of queries and the number of activated shape latents are much smaller, the overall computation can be reduced by 34%, as shown in Fig. 5."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The combination with hierarchical volume decoding needs some extra consideration to ensure performance. The core obstacle lies in the requirement that subvolume should be small to maintain locality. Within hierarchical decoding, the effective queries could be even fewer in a subvolume. Thereafter, naive implementation that process each subvol"
+ },
+ {
+ "type": "image",
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 7. Normalized histogram of activated shape tokens with non-zero attention at different regions. Zoom in for a better view. The numbers in the legend indicate the number of activated tokens."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "ume one-by-one would not maximize GPU utilization. As a remedy, we design a packing operation, which precompute the target queries in each volume, pack queries of different subvolume, and process them together. More details on the analysis and the implementation lives in the Supplementary Material."
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+ "content": "Efficient Decoder Design. Once we have reduced the QKV in CA, further acceleration of the attention operation itself becomes challenging algorithmically. Thereby, our next approach focuses on optimizing the decoder network design. Most existing vectorset decoders [16, 54, 57] share nearly identical architectures, typically consisting of several self-attention (SA) layers and a cross-attention layer, as shown in Fig. 3, with SA layers evaluated only once. Therefore, our goal is to simplify the final CA layer as much as possible, which we believe could be replaced with a simpler one as it only needs to classify the inside/outside status of each position. To this end, we reduce the network width, decrease the MLP expansion ratio, and remove several LayerNorm layers. Through careful ablation studies, we found that these reductions have minimal impact on reconstruction quality while boosting speed by \\(3.2 \\times\\)"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.3. Progressive Flow Distillation"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Similar to image and video generation [13, 19, 31], we can reduce the sampling steps of VDM through distillation [26, 61]. Initially, we experimented with PCM [43], but we found it hard to yield satisfactory results on VDM. To address this, we propose progressive flow distillation as shown in Fig. 8, systematically identifying and refining key design choices for effective distillation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Consistency Flow Distillation (CFD). Consistency Distillation (CD) [40] is a well-known distillation method for reducing the diffusion sampling steps, though its application to 3D diffusion has yet to be explored. The core of CD is to enforce a consistency property - any point along the ODE trajectory maps to the same target point. To achieve this, CD uses a time difference method, where a starting point \\(\\mathbf{x}_{t_n}\\) is first selected for the target prediction of the"
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+ }
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+ {
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+ "bbox": [
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+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 8. Training pipeline for Progressive Flow Distillation."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "student model \\(\\mathbf{x}_0^{t_n} = \\pmb{f}_{\\pmb{\\theta}}(\\mathbf{x}_{t_n},t_n)\\). For flow-based models, e.g., Hunyuan3D-2 [58], the Euler solver could be employed with a large discretization step \\(t_n - t_0\\) to compute the target \\(\\mathbf{x}_0^{t_n}\\). For GT target, the teacher model predicts the next point \\(\\hat{\\mathbf{x}}_{t_{n + 1}}^{\\phi}\\) by running one discretization step of an ODE solver, after which the student model predicts the GT target at next timestep \\(x_0^{t_{n + 1}} = \\pmb {f}_{\\pmb{\\theta}}\\left(\\hat{\\mathbf{x}}_{t_{n + 1}}^{\\phi},t_{n + 1}\\right)\\). The consistency property is enforced by the following loss,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ 0.469,
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+ "angle": 0,
+ "content": "\\[\n\\left. \\mathcal {L} _ {c f d} (\\boldsymbol {\\theta}) := \\mathbb {E} \\left[ d \\left(\\boldsymbol {f} _ {\\boldsymbol {\\theta}} \\left(\\mathbf {x} _ {t _ {n}}, t _ {n}\\right), \\boldsymbol {f} _ {\\boldsymbol {\\theta} ^ {-}} \\left(\\hat {\\mathbf {x}} _ {t _ {n + 1}} ^ {\\phi}, t _ {n + 1}\\right)\\right) \\right], \\right. \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.508,
+ 0.484,
+ 0.553
+ ],
+ "angle": 0,
+ "content": "with a boundary constraint \\( f(\\mathbf{x}_{\\epsilon}, \\epsilon) = \\mathbf{x}_{\\epsilon} \\), where \\( d \\) is a distance function and \\( \\theta^{-} \\) is a regular copy of student model named as target model."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Stabilizing Target Model. In practice, directly applying the distillation method described above does not yield satisfactory results, as shown in Fig. 11 (w/o GD distill). Our analysis reveals that the main challenge lies in the stability of the target model. During training, the student model continually tries to mimic the output of the target model, making it highly sensitive to changes in the target. As a result, we observe significant fluctuations in the predictions throughout the training process. To stabilize the target model, we introduce a progressive training strategy, in which 1) we first perform guidance distillation and initialize the student model as a distilled version. This approach differs from distillation in image models, where guidance distillation can be applied simultaneously with step distillation without issues. We hypothesize that this gap arises from the differences between 2D and 3D models and the more complex optimization landscape in 3D models. 2) Besides, we find that the EMA update of the target model is crucial for stabilizing VDM, which contrasts with a recent study on 2D generation as well [38]. 3) Moreover, we replace commonly used L2 loss with Huber loss as it is less sensitive to outliers, which makes training more stable. 4) Finally, we introduce a multi-stage-multi-phase consistency distil"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.525,
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+ "angle": 0,
+ "content": "Figure 9. Visual comparison of shape reconstruction methods."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ 0.287,
+ 0.908,
+ 0.404
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+ "angle": 0,
+ "content": " | V-IoU(↑) | S-IoU(↑) | Time(s↓) |
| 3DShape2VecSet [54] | 87.88% | 84.93% | 16.43 |
| Michelangelo [57] | 84.93% | 76.27% | 16.43 |
| Direct3D [45] | 88.43% | 81.55% | 3.201 |
| Hunyuan3D-2 [58]-1024 | 93.60% | 89.16% | 16.43 |
| \\(\\sqsubseteq\\) with FlashVDM | 91.90% | 88.02% | 0.382 |
| Hunyuan3D-2 [58]-3072 | 96.11% | 93.27% | 22.33 |
| \\(\\sqsubseteq\\) with FlashVDM | 95.55% | 93.10% | 0.491 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.514,
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+ ],
+ "angle": 0,
+ "content": "Table 1. Numerical comparisons of shape reconstruction methods."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.453,
+ 0.905,
+ 0.483
+ ],
+ "angle": 0,
+ "content": "lation strategy based on PCM [43], in which a single-phase finetuning is performed after five phases pretraining."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.484,
+ 0.907,
+ 0.786
+ ],
+ "angle": 0,
+ "content": "Aligning Real Data with GAN. With the proposed improvements, our CFD is able to reduce the sampling steps to just 5 while still producing decent results. However, we found that in some cases, the mesh quality is difficult to match the teacher's outputs, which might be attributed to the self-distillation nature of the consistency model. To address this, we seek to further enhance performance by incorporating supervision from ground-truth 3D data through adversarial training [7]. Specifically, we initialize the generator using the model distilled in the previous stage. Inspired by previous works [35, 48], our discriminator operates directly in latent space, eliminating the need for an expensive decoding process, and leverages the intermediate features of the pretrained diffusion model. As shown in Fig. 8, we first extract token sequences from specified attention layers, and then apply independent discriminator heads. Unlike prior works [35, 43, 48, 51] that use noised latents, we did not observe significant improvements with noise, so we opt to use ground-truth latents for simplicity. The discriminator is trained with a hinge adversarial loss [20] as,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.514,
+ 0.794,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {a d v}} (\\theta , \\gamma) = \\operatorname {R e L U} \\left(1 + \\mathcal {D} _ {\\gamma} \\left(\\mathbf {x} _ {0}\\right)\\right) + \\operatorname {R e L U} \\left(1 - \\mathcal {D} _ {\\gamma} \\left(\\mathbf {x} _ {0} ^ {t _ {n}}\\right)\\right), \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.826,
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+ ],
+ "angle": 0,
+ "content": "which distinguishes between ground truth latent \\(\\mathbf{x}_0\\) and latent produced by our generator \\(\\mathbf{x}_0^{t_n} = f_\\theta (z_{t_n},t_n)\\). Following [43, 51], the final objective is a combination of the adversarial objective and consistency loss \\(\\mathcal{L} = \\mathcal{L}_{cfd} + \\lambda \\mathcal{L}_{adv}\\) where \\(\\lambda\\) is set to 0.1."
+ },
+ {
+ "type": "page_number",
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+ "content": "2528"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 10. Visual comparison of image-to-3D generation between the proposed FlashVDM and other fast 3D generation methods."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this section, we apply the proposed FlashVDM to Hunyuan3D-2 [58], which is currently a state-of-the-art open-source VDM. We evaluate our approach in terms of both VAE reconstruction and diffusion generation. We also provide ablation studies of the proposed techniques."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.1. Reconstruction"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Metrics. We utilize the volume and surface IoU metric to assess the impact of our acceleration techniques on VAE reconstruction performance. The running time is measured at the resolution of 380."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Comparison. We compare our method with three competing method, i.e., 3DShape2VecSet [54], Michelan-"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "gelo [57], and Direct3D [45]. We evaluate two resolutions, i.e., 1,024 and 3,072, for our fast version and the base model Hunyuan3D-2 [58]. The numerical comparison is shown in Tab. 1. It demonstrates that our method outperforms all competing methods and preserve the quality of base model with less than \\(1\\%\\) IoU drop while obtaining over \\(45\\times\\) speedup. Fig. 9 shows the visual comparison, which also indicates minimal degradation in quality."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Generation"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Metrics. To evaluate shape generation performance, we adopt ULIP-I [49] and Uni3D-I [59] to compute the similarity between the generated mesh and input images."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Comparison. Three latest fast 3D generation methods, i.e., TripoSR [42], SF3D [3], and SPAR3D [11], and two"
+ },
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+ "type": "page_number",
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+ "angle": 0,
+ "content": "2529"
+ }
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+ [
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "50 Steps VDM"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ 0.181,
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+ ],
+ "angle": 0,
+ "content": "5 Steps VDM"
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+ "bbox": [
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+ "content": null
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+ {
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+ "angle": 0,
+ "content": "5 Steps FlashVDM"
+ },
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+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "w/o GD Distill"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.263,
+ 0.287,
+ 0.313,
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+ "angle": 0,
+ "content": "w/oEMA"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.37,
+ 0.2,
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+ 0.279
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.386,
+ 0.287,
+ 0.45,
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+ "angle": 0,
+ "content": "w/o ADV FT"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.104,
+ 0.325,
+ 0.47,
+ 0.34
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+ "angle": 0,
+ "content": "Figure 11. Ablation study of our progressive flow distillation."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 12. User study of FlashVDM against different methods."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.097,
+ 0.509,
+ 0.478,
+ 0.612
+ ],
+ "angle": 0,
+ "content": " | ULIP-I(↑) | Uni3D-I(↑) | Time(s↓) |
| TripoSR [42] | 0.0642 | 0.1425 | 0.958 |
| SF3D [3] | 0.1156 | 0.2676 | 0.212 |
| SPAR3D [11] | 0.1149 | 0.2679 | 1.296 |
| Trellis [46] | 0.1267 | 0.3116 | 7.334 |
| Hunyuan3D-2 [58] | 0.1303 | 0.3151 | 34.85 |
| \\(\\sqsubset\\) with FlashVDM | 0.1260 | 0.3095 | 1.041 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.101,
+ 0.622,
+ 0.472,
+ 0.637
+ ],
+ "angle": 0,
+ "content": "Table 2. Numerical comparisons of shape generation methods."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.093,
+ 0.652,
+ 0.487,
+ 0.726
+ ],
+ "angle": 0,
+ "content": " | V-IoU(↑) | S-IoU(↑) | Time(s↓) |
| VAE Baseline | 96.11% | 93.27% | 22.33 |
| + Hierarchical Decoding | 96.11% | 93.27% | 2.322 |
| + Efficient Decoder | 96.08% | 93.13% | 0.731 |
| + Adaptive KV Selection | 95.55% | 93.10% | 0.491 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.101,
+ 0.736,
+ 0.472,
+ 0.751
+ ],
+ "angle": 0,
+ "content": "Table 3. Step-by-step ablation of our lightning vecset decoder."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.779,
+ 0.483,
+ 0.869
+ ],
+ "angle": 0,
+ "content": "state-of-the-art methods Hunyuan3D-2 [58] and Trellis [46] are selected for comparison. The numerical comparison is shown in Tab. 2 and the visual comparison is shown in Fig. 10. It can be observed that our method retain most of capability of the base model, while achieves the best results with a large margin against other fast methods."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.871,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "User Study. We include results of three user studies in Fig. 12. For comparison between FlashVDM and"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.198
+ ],
+ "angle": 0,
+ "content": "SPAR3D [11], we ask participants to determine which one is better. For comparison between FlashVDM and Hunyuan3D-2 [58], we ask whether the results are comparable. As seen, FlashVDM is preferred over SPAR3D [11] in almost all testcases, and FlashVDM is comparable to its base model Hunyuan3D-2 [58] at 5 steps and the comparable rate increase with more steps."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.211,
+ 0.667,
+ 0.227
+ ],
+ "angle": 0,
+ "content": "4.3. Ablation Study"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.235,
+ 0.905,
+ 0.341
+ ],
+ "angle": 0,
+ "content": "Effectiveness of Lightning Vecset Decoder. The results of step-by-step ablation is shown in Tab. 3, in which we add each component incrementally. It can be observed that hierarchical decoding provides a \\(10 \\times\\) speedup with no degradation in quality. The efficient decoder achieves an extra \\(3 \\times\\) speedup with almost no degradation, while adaptive KV selection results in a \\(30 \\%\\) speedup with minimal degradation."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.342,
+ 0.907,
+ 0.509
+ ],
+ "angle": 0,
+ "content": "Effectiveness of Progressive Flow Distillation. We present an ablation study to demonstrate the effectiveness of progressive training strategies. The visual comparison is shown in Fig. 11. As seen, the original VDM completely fails at 5 steps, while FlashVDM achieves results comparable to the original 50-step VDM. Additionally, we observe that distillation fails without guidance distillation as a warm-up step, and performance degrades without the use of EMA. Finally, adversarial fine-tuning is shown to help generate smoother and more accurate shapes. More detailed ablation can be found in the Supplementary Material."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.527,
+ 0.633,
+ 0.541
+ ],
+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.553,
+ 0.907,
+ 0.781
+ ],
+ "angle": 0,
+ "content": "In this work, we introduce FlashVDM, a general framework for accelerating a pretrained VDM [18, 58]. Our framework encompasses not only a progressive flow distillation method for distilling VDM into a few-step generator, but also several training-free inference techniques and an efficient, lightweight vecset decoder that significantly reduces the FLOPs of decoding. We apply our framework to the state-of-the-art image-to-3D VDM, Hunyuan3D-2 [58], obtaining Hunyuan3D-2 Turbo. Our evaluation demonstrates that FlashVDM excels in both reconstruction and generation, achieving \\(45 \\times\\) and \\(32 \\times\\) speedups, respectively. To the best of our knowledge, FlashVDM is the first work to push large-scale shape generation into the millisecond range, which opens up new possibilities for interactive applications of 3D generative models."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.799,
+ 0.673,
+ 0.815
+ ],
+ "angle": 0,
+ "content": "Acknowledgement"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.825,
+ 0.905,
+ 0.9
+ ],
+ "angle": 0,
+ "content": "We thank Yixuan Tang for helping create the teasier. Xi-angyu Yue is supported by National Natural Science Foundation of China (No. 62306261) and The Shun Hing Institute of Advanced Engineering (SHIAE) Fund (No. 8115074)."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "2530"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.093,
+ 0.09,
+ 0.188,
+ 0.106
+ ],
+ "angle": 0,
+ "content": "References"
+ },
+ {
+ "type": "ref_text",
+ "bbox": [
+ 0.101,
+ 0.116,
+ 0.482,
+ 0.169
+ ],
+ "angle": 0,
+ "content": "[1] Daniel Bolya and Judy Hoffman. Token merging for fast stable diffusion. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4599-4603, 2023. 3"
+ },
+ {
+ "type": "ref_text",
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+ 0.482,
+ 0.225
+ ],
+ "angle": 0,
+ "content": "[2] Daniel Bolya, Cheng-Yang Fu, Xiaoliang Dai, Peizhao Zhang, Christoph Feichtenhofer, and Judy Hoffman. Token merging: Your vit but faster. arXiv preprint arXiv:2210.09461, 2022.3"
+ },
+ {
+ "type": "ref_text",
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+ 0.282
+ ],
+ "angle": 0,
+ "content": "[3] Mark Boss, Zixuan Huang, Aaryaman Vasishta, and Varun Jampani. Sf3d: Stable fast 3d mesh reconstruction with uv-unwrapping and illumination disentanglement. arXiv preprint arXiv:2408.00653, 2024. 3, 7, 8"
+ },
+ {
+ "type": "ref_text",
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+ 0.482,
+ 0.338
+ ],
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+ "content": "[56] Longwen Zhang, Ziyu Wang, Qixuan Zhang, Qiwei Qiu, Anqi Pang, Haoran Jiang, Wei Yang, Lan Xu, and Jingyi Yu. Clay: A controllable large-scale generative model for creating high-quality 3d assets. ACM Transactions on Graphics (TOG), 43(4):1-20, 2024. 2, 3"
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+ {
+ "type": "ref_text",
+ "bbox": [
+ 0.093,
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+ "content": "[57] Zibo Zhao, Wen Liu, Xin Chen, Xianfang Zeng, Rui Wang, Pei Cheng, Bin Fu, Tao Chen, Gang Yu, and Shenghua Gao. Michelangelo: Conditional 3d shape generation based on shape-image-text aligned latent representation. Advances in Neural Information Processing Systems, 36, 2024. 2, 5, 6, 7"
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+ "type": "ref_text",
+ "bbox": [
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+ "content": "[58] Zibo Zhao, Zeqiang Lai, Qingxiang Lin, Yunfei Zhao, Haolin Liu, Shuhui Yang, Yifei Feng, Mingxin Yang, Sheng Zhang, Xianghui Yang, et al. Hunyuan3d 2.0: Scaling diffusion models for high resolution textured 3d assets generation. arXiv preprint arXiv:2501.12202, 2025. 1, 2, 3, 6, 7, 8"
+ },
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+ "bbox": [
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+ "content": "[59] Junsheng Zhou, Jinsheng Wang, Baorui Ma, Yu-Shen Liu, Tiejun Huang, and Xinlong Wang. Uni3d: Exploring unified 3d representation at scale. arXiv preprint arXiv:2310.06773, 2023. 7"
+ },
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+ "bbox": [
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+ "content": "[60] Mingyuan Zhou, Huangjie Zheng, Zhendong Wang, Mingzhang Yin, and Hai Huang. Score identity distillation: Exponentially fast distillation of pretrained diffusion models for one-step generation. In ICML, 2024. 3"
+ },
+ {
+ "type": "ref_text",
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+ "angle": 0,
+ "content": "[61] Yuanzhi Zhu, Hanshu Yan, Huan Yang, Kai Zhang, and Junnan Li. Accelerating video diffusion models via distribution matching. arXiv preprint arXiv:2412.05899, 2024. 2, 5"
+ },
+ {
+ "type": "list",
+ "bbox": [
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+# Unleashing Vecset Diffusion Model for Fast Shape Generation
+
+Zeqiang Lai $^{1,2\star}$ , Yunfei Zhao $^{2,3\star}$ , Zibo Zhao $^{2,4}$ , Haolin Liu $^{2}$ , Fuyun Wang $^{1}$ , Huiwen Shi $^{2}$ , Xianghui Yang $^{2}$ , Qingxiang Lin $^{2}$ , Jingwei Huang $^{2}$ , Yuhong Liu $^{2}$ , Jie Jiang $^{2}$ , Chunchao Guo $^{2\dagger}$ , Xiangyu Yue $^{1\dagger}$ , MMLab, CUHK $^{2}$ , Tencent Hunyuan $^{3}$ , VISG, NJU $^{4}$ , ShanghaiTech https://github.com/Tencent-Hunyuan/FlashVDM
+
+
+Figure 1. High-resolution 3D shapes generated by Flash Vecset Diffusion Model (FlashVDM) within 1 second.
+
+# Abstract
+
+3D shape generation has greatly flourished through the development of so-called "native" 3D diffusion, particularly through the Vecset Diffusion Model (VDM). While recent advancements have shown promising results in generating high-resolution 3D shapes, VDM still struggles at high-speed generation. Challenges exist because of not only difficulties in accelerating diffusion sampling but also VAE decoding in VDM - areas under-explored in previous works. To address these challenges, we present FlashVDM, a systematic framework for accelerating both VAE and DiT in VDM. For DiT, FlashVDM enables flexible diffusion sampling with as few as 5 inference steps and com
+
+parable quality, which is made possible by stabilizing consistency distillation with our newly introduced Progressive Flow Distillation. For VAE, we introduce a lightning vecset decoder equipped with Adaptive KV Selection, Hierarchical Volume Decoding, and Efficient Network Design. By exploiting the locality of vecset and the sparsity of shape surface in the volume, our decoder drastically lowers FLOPs, minimizing the overall decoding overhead. We apply FlashVDM to Hunyuan3D-2 [58] to obtain Hunyuan3D-2 Turbo. Through systematic evaluation, we show that our model significantly outperforms existing fast 3D generation methods, achieving comparable performance to the state-of-the-art while reducing inference time by over $45 \times$ for reconstruction and $32 \times$ for generation.
+
+# 1. Introduction
+
+3D shape generation has greatly flourished through the development of so-called "native" 3D diffusion [46, 56], among which the Vecset Diffusion Model (VDM) [54, 57] receives prominent attention and applications due to its simplicity and scalability. While recent works [18, 56, 58] have demonstrated the capabilities of VDM in generating high-resolution and high-quality 3D shapes, VDM still struggles with high-speed generation, typically requiring over 30 seconds $^{1}$ per shape – far behind the development of image generation counterparts [26, 34, 35, 52]. The notable reasons behind the lags of VDM [54] against previous 2D predecessors [31] lies in not only the lack of research of diffusion distillation [26, 28] for few-step 3D generators, but also the acceleration of Variational Autoencoders (VAE).
+
+Unlike the 2D VAE [6], which utilizes convolution for image compressing and decoding with structured latent, the VAE in VDM takes a fundamentally different approach. Its encoder compresses the point cloud of the mesh surface into a set of latent tokens—typically referred to as a vec-set—through cross-attention (CA), using a set of query tokens [54]. This approach, similar to Q-former [14] and Perceiver [12], offers strong compression capability but also introduces challenges in decoding. To overcome this, VDM employs a symmetric approach, constructing a set of volume queries that evaluate occupancy or Signed Distance Function (SDF) at each grid point using another CA. While the CA decoder design enables VDM to flexibly decode at arbitrary resolutions, the computational cost increases cubically with respect to resolution. For instance, at a typical resolution of 384, the number of query points exceeds 56 million—each requires a CA operation. Even worse, modern VDMs [18, 58] typically use a much larger set of latent tokens for key-value pairs to ensure high-resolution generation, which ends up making the decoding process even slower. As a result, VAE decoding in VDM demands a significant amount of inference time—even longer than diffusion sampling as shown in Fig. 2 (a).
+
+On the other hand, despite the significant advancements in fast image generation through diffusion distillation [26, 28, 34, 35, 52], pushing the speed to real-time, research into native 3D diffusion distillation remains scarce. Most existing distillation methods [26, 34, 52] were originally designed for images, with some adaptations made for video [53, 61]. Many techniques, such as LPIPS loss in Consistency Distillation (CD) [23, 38, 40] and GAN designs [43, 52], are specifically tailored for images. However, the representation of 3D meshes and images differs significantly, making it challenging to adapt these techniques. Additionally, the vastly different latent spaces in VDMs against image DMs [31] could drastically alter the
+
+
+Figure 2. (a) VDM exhibits different distribution with image DM with much larger percentage in VAE decoding. (b) FlashVDM enables fast shape generation within 1 second on a consumer GPU.
+
+training dynamics of the distillation, which makes previous strategies unsuitable, potentially leading to instability and unsatisfactory results.
+
+To address the aforementioned problems, we present FlashVDM, a framework for transforming pretrained VDM into a high-fidelity and high-speed generator with over $45 \times$ speedup in VAE decoding and $32 \times$ speedup overall. Our framework consists of two main components: 1) diffusion acceleration and 2) VAE acceleration.
+
+For diffusion acceleration, we carefully analyzed the problems in direct application of CD [40, 43] for VDM and found that the core issue lies in the instability of the target network, which degrades the training and causes unsatisfactory results. As a remedy, we propose Progressive Flow Distillation, a multi-stage distillation method for VDM. It first decouples the CD distillation by warming up with guidance distillation. This prevents the target bias and fluctuations from misleading the student. Then, we carefully ablate the design choices including loss and training strategies in CD, leading to even more stable step distillation. Finally, we introduce adversarial finetuning, leveraging real 3D data as supervision, to help distilled models produce smoother and more accurate results within limited steps. Together, our distilled model could achieve comparable results with only 5 Number of Function Evaluation (NFE).
+
+For VAE acceleration, we introduce three techniques, including two training-free methods—Adaptive KV Selection and Hierarchical Volume Decoding—to reduce both the number of number of key-value pairs and the queries. These techniques effectively exploit the locality of VDM point-queries and the sparsity of shape surface in the volume space, resulting in a highly efficient CA with a $97.1\%$ FLOPs reduction in total. Additionally, we introduce an Efficient Decoder Architecture. By fixing the encoder and fine-tuning only the decoder, our new design further reduces FLOPs by $76.6\%$ for each query. With these three improvements combined, our final VAE decoder achieves over a
+
+$45 \times$ speedup, significantly reducing the decoding time from 22.3s to just 0.49s.
+
+In summary, our contributions are listed as follows:
+
+- We introduce FlashVDM, a framework that converts pretrained VDMs into high-speed and -fidelity generators.
+- We present progressive flow distillation for VDM, significantly improving the stability and quality of the distilled model, achieving comparable results with only 5 NFE.
+- We propose a novel algorithm, hierarchical volume decoding with adaptive KV selection and an efficient decoder architecture, obtaining $45 \times$ speedup in decoding.
+- We apply FlashVDM to Hunyuan3D-2 [58] and obtain Hunyuan3D-2 Turbo, a high-resolution shape generator that matches its teacher's shape quality with over $32 \times$ speedup, achieving 1 second per shape.
+
+# 2. Related Works
+
+Diffusion Acceleration. Step distillation [8, 25, 28, 33, 34, 40, 47, 50, 52, 60] is a popular technique for accelerating diffusion models, with early works like Progressive Distillation [28, 33] training student models by halving sampling steps step-by-step. More recent approaches, such as consistency models [39, 40, 43] and score distillation [34, 52], enforce self-consistency or match distributions between student and teacher models. GAN-based approaches [34, 44] further refine score distillation by augmenting loss functions with adversarial objectives. Several works, including UFOGen [48] and LADD [35], combine GANs with pretrained diffusion models as discriminators. Other research focuses on reducing redundancy in sampling processes, such as DPM-Solver [24], SnapFusion [17], and DeepCache [27]. In this work, we introduce progressive flow distillation to address practical issues in 3D foundation models, an area not yet explored in previous research.
+
+VAE Acceleration. The proposed hierarchical volume decoding is generally related to octree decoding [32]. However, we noted that vanilla octree decoding introduces artifacts and holes, whereas our method is nearly lossless. Our adaptive KV selection is broadly related to previous work on token merging [1, 2] in DiT inference, though our approach is specifically designed for VAE acceleration in VDM without the merge operation. To the best of our knowledge, we are the first to explore the efficient design of a VDM decoder. DC-AE [4] is one of the works for image diffusion models [4], but it focuses on achieving a higher compression ratio, which is different from our objective.
+
+Fast 3D Generation. Previous works on fast 3D generation are based on feedforward 3D reconstruction methods [9], which require only a single network evaluation. Benefiting from this property, TripoSR [42] and SF3D [3] can generate a mesh from a single image in under 1 second, but the resulting mesh quality is limited. To address this, multiview images are often used [15, 41], but this re
+
+
+Figure 3. Illustration of four main stages of VDM.
+
+quires a Multi-View Diffusion (MVD) model [21, 36, 37]. In response, SPAR3D [11] replaces MVD with a small point cloud generator, while Turbo3D [10] distills MVD into a four-step generator. Nevertheless, all these feedforward methods are still limited in mesh quality compared to diffusion-based 3D generators [56, 58].
+
+# 3. Method
+
+In this section, we first provide an introduction to VDM pipeline and inference time distribution. Then, we illustrate our approaches for accelerating VAE decoding in Sec. 3.2 and diffusion sampling in Sec. 3.3, respectively.
+
+# 3.1. Preliminary of VDM
+
+Pipeline Overview. Here, we provide a brief introduction to the inference pipeline of VDM. We refer interested readers to [5, 54, 56, 58] for more details. As shown in Fig. 3, the inference of VDM consists of four stages: 1) image encoding: an image encoder [29, 30] is used to extract conditional features; 2) diffusion sampling: iteratively calling a denoising transformer to predict shape latent based on conditional features. 3) volume decoding: the predicted shape latent is decoded into volume SDF via several layers of self-attention and a cross-attention. 4) surface extraction: marching cube algorithm [22] is used to extract polygon mesh from the decoded volume.
+
+Inference Time Distribution. The distribution of inference times is shown in Fig. 2(a). We could observe that diffusion sampling (23.9%) and volume decoding (75.8%) account for the majority (99.7%) of the inference time for VDM. However, image encoding and surface extraction remain significant when the total inference time is reduced to less than one second. As a first step, we implement several engineering acceleration techniques, including FP8 attention with SageAttention2 [55], static graph optimization with torch.compile, and etc., which decrease the processing time to 25.09s per shape, as shown in Fig. 5.
+
+
+Mesh Internal Missing Point Expand Point Discarded Point
+(a) Sign check
+
+
+(b) tSDF without dilate
+
+
+(c) tSDF only
+
+# 3.2. Lightning Vecset Decoder
+
+The majority $(99.9\%)$ of the computational cost in the original VDM decoder is concentrated in its final cross-attention layer, which is evaluated tens of millions of times. To optimize this layer, we propose three key techniques, each addressing a different aspect: 1) hierarchical volume decoding to reduce the number of queries, 2) adaptive KV selection to minimize the number of keys and values, and 3) an efficient decoder design to reduce computational overhead in each cross-attention operation.
+
+Hierarchical Volume Decoding. To decode shape latents into a mesh, the existing VDM decoder relies on dense volume decoding and marching cube algorithms [22], which has cubic complexity with respect to the resolution. It raises challenges for balancing speed and mesh quality. However, unlike image decoders [6] that must predict RGB values for every pixel, the VDM decoder only needs to determine high-resolution SDF values near the shape surface – all voxels far from the surface can be simply classified as inside or outside. Inspired by this characteristic, we propose hierarchical volume decoding that only increases resolution near the surface, thereby reducing the queries by $91.4\%$ .
+
+Specifically, instead of directly decoding the SDF volume at the target resolution (e.g., 384), we begin by decoding at a smaller resolution (e.g., 75), which provides a coarse SDF volume. Using this coarse volume, we can identify which voxels intersect the shape surface based on the following criterion:
+
+$$
+f (x, y, z) = \left\{ \begin{array}{l l} 1 & \text {i f} \exists (i, j, k) \in N (x, y, z) \\ & \text {s u c h t h a t} f (i, j, k) \neq f (x, y, z), \\ 0 & \text {o t h e r w i s e}, \end{array} \right. \tag {1}
+$$
+
+where $N(x,y,z)$ represents the set of adjacent voxels to $(x,y,z)$ and $f(x,y,z) = 1$ indicates the voxel intersects with the surface. In short, a voxel does not intersect with the surface only if all its adjacent voxels are either inside or outside. For voxels that do intersect the surface, we subdivide them into higher resolutions and compute the SDF values through cross-attention once more. This process is
+
+
+Figure 4. The corner cases in hierarchical volume decoding.
+Figure 5. Step-by-step case study of FlashVDM acceleration techniques and their effects on inference time and IoU.
+
+repeated until we reach the target resolution. Since the surface shape is highly sparse within the volume, the number of effective queries is significantly reduced.
+
+Naively, previous steps could be considered a type of octree decoding [32]. However, we find that it produces artifacts and holes when applied to VDM in practice. To prevent degradation, we need to consider some corner cases. First, when the resolution is low, for very thin meshes, two adjacent voxels may lie on opposite sides of the mesh surface, both having the same sign, as shown in Fig. 4 (a). This causes the missing voxels for resolution increment, leading to holes in the surface. To address this, we use tSDF as supervision during VAE training to help determine whether a voxel is near the mesh surface. Then, during hierarchical decoding, we append all voxels under a certain tSDF threshold (TR). With this strategy, the lowest resolution in hierarchical decoding can be reduced to $w + u * 2$ where $w$ is the minimal mesh width and $u$ is the tSDF TR. Second, failure cases exist even with tSDF augmentation as shown in Fig. 4 (b,c), e.g., uneven distribution of surface between two adjacent voxels and etc. Therefore, we perform a dilation operation after identifying the intersected voxels to prevent unexpected missing points. We leave the choice of tSDF value and more details to the Supplementary Material.
+
+Adaptive KV Selection. For each position in volume decoding, a cross-attention operation is performed between
+
+
+Figure 6. Histogram of activated token counts with non-zero attention of 70,800 regions from 250 cases.
+
+the queries and key-value pairs (computed from shape latents). Previously, we significantly reduced the number of queries. To further minimize computational overhead, we introduce adaptive KV selection, which reduces the number of key-value pairs. Our method leverages the observation that the correlation between spatial queries and shape latents exhibits strong locality - adjacent spatial points tend to attend to similar latent tokens, with the attention concentrated on a small subset of tokens (denoted as activated tokens). To illustrate, we show two histograms in Figs. 6 and 7. As seen, most regions in 3D volumes attend to at most 1,000 tokens - one-third of the original 3,072, and different regions focus on different set of activated tokens. Moreover, our statistic reveals that the average activated token count for a single query is around only 10, which also indicates strong locality in shape latents.
+
+The proposed adaptive KV selection is training-free and able to be combined with hierarchical volume decoding. For simplicity, we first show the algorithm with vanilla volume decoding. In this case, we first divide the entire volume into smaller sub-volumes. Then, within each sub-volume, we uniformly sample a small set of queries to compute their attention scores relative to the keys. To select most correlated key-value pairs, we could simply average the attention score of all queries and select the TopK, or we could merge the TopN of each query to obtain TopM, where N is a small number (e.g., 50) that can include most activated tokens with non-zero attention. The latter one is slightly better but also slightly slower (5%). For other queries within the same sub-volume, we only use the Top-K/M key-value pairs for attention computation. Since the attention scores are estimated using a small set of queries and the number of activated shape latents are much smaller, the overall computation can be reduced by 34%, as shown in Fig. 5.
+
+The combination with hierarchical volume decoding needs some extra consideration to ensure performance. The core obstacle lies in the requirement that subvolume should be small to maintain locality. Within hierarchical decoding, the effective queries could be even fewer in a subvolume. Thereafter, naive implementation that process each subvol
+
+
+Figure 7. Normalized histogram of activated shape tokens with non-zero attention at different regions. Zoom in for a better view. The numbers in the legend indicate the number of activated tokens.
+
+ume one-by-one would not maximize GPU utilization. As a remedy, we design a packing operation, which precompute the target queries in each volume, pack queries of different subvolume, and process them together. More details on the analysis and the implementation lives in the Supplementary Material.
+
+Efficient Decoder Design. Once we have reduced the QKV in CA, further acceleration of the attention operation itself becomes challenging algorithmically. Thereby, our next approach focuses on optimizing the decoder network design. Most existing vectorset decoders [16, 54, 57] share nearly identical architectures, typically consisting of several self-attention (SA) layers and a cross-attention layer, as shown in Fig. 3, with SA layers evaluated only once. Therefore, our goal is to simplify the final CA layer as much as possible, which we believe could be replaced with a simpler one as it only needs to classify the inside/outside status of each position. To this end, we reduce the network width, decrease the MLP expansion ratio, and remove several LayerNorm layers. Through careful ablation studies, we found that these reductions have minimal impact on reconstruction quality while boosting speed by $3.2 \times$
+
+# 3.3. Progressive Flow Distillation
+
+Similar to image and video generation [13, 19, 31], we can reduce the sampling steps of VDM through distillation [26, 61]. Initially, we experimented with PCM [43], but we found it hard to yield satisfactory results on VDM. To address this, we propose progressive flow distillation as shown in Fig. 8, systematically identifying and refining key design choices for effective distillation.
+
+Consistency Flow Distillation (CFD). Consistency Distillation (CD) [40] is a well-known distillation method for reducing the diffusion sampling steps, though its application to 3D diffusion has yet to be explored. The core of CD is to enforce a consistency property - any point along the ODE trajectory maps to the same target point. To achieve this, CD uses a time difference method, where a starting point $\mathbf{x}_{t_n}$ is first selected for the target prediction of the
+
+
+Figure 8. Training pipeline for Progressive Flow Distillation.
+
+student model $\mathbf{x}_0^{t_n} = \pmb{f}_{\pmb{\theta}}(\mathbf{x}_{t_n},t_n)$ . For flow-based models, e.g., Hunyuan3D-2 [58], the Euler solver could be employed with a large discretization step $t_n - t_0$ to compute the target $\mathbf{x}_0^{t_n}$ . For GT target, the teacher model predicts the next point $\hat{\mathbf{x}}_{t_{n + 1}}^{\phi}$ by running one discretization step of an ODE solver, after which the student model predicts the GT target at next timestep $x_0^{t_{n + 1}} = \pmb {f}_{\pmb{\theta}}\left(\hat{\mathbf{x}}_{t_{n + 1}}^{\phi},t_{n + 1}\right)$ . The consistency property is enforced by the following loss,
+
+$$
+\left. \mathcal {L} _ {c f d} (\boldsymbol {\theta}) := \mathbb {E} \left[ d \left(\boldsymbol {f} _ {\boldsymbol {\theta}} \left(\mathbf {x} _ {t _ {n}}, t _ {n}\right), \boldsymbol {f} _ {\boldsymbol {\theta} ^ {-}} \left(\hat {\mathbf {x}} _ {t _ {n + 1}} ^ {\phi}, t _ {n + 1}\right)\right) \right], \right. \tag {2}
+$$
+
+with a boundary constraint $f(\mathbf{x}_{\epsilon}, \epsilon) = \mathbf{x}_{\epsilon}$ , where $d$ is a distance function and $\theta^{-}$ is a regular copy of student model named as target model.
+
+Stabilizing Target Model. In practice, directly applying the distillation method described above does not yield satisfactory results, as shown in Fig. 11 (w/o GD distill). Our analysis reveals that the main challenge lies in the stability of the target model. During training, the student model continually tries to mimic the output of the target model, making it highly sensitive to changes in the target. As a result, we observe significant fluctuations in the predictions throughout the training process. To stabilize the target model, we introduce a progressive training strategy, in which 1) we first perform guidance distillation and initialize the student model as a distilled version. This approach differs from distillation in image models, where guidance distillation can be applied simultaneously with step distillation without issues. We hypothesize that this gap arises from the differences between 2D and 3D models and the more complex optimization landscape in 3D models. 2) Besides, we find that the EMA update of the target model is crucial for stabilizing VDM, which contrasts with a recent study on 2D generation as well [38]. 3) Moreover, we replace commonly used L2 loss with Huber loss as it is less sensitive to outliers, which makes training more stable. 4) Finally, we introduce a multi-stage-multi-phase consistency distil
+
+
+Figure 9. Visual comparison of shape reconstruction methods.
+
+ | V-IoU(↑) | S-IoU(↑) | Time(s↓) |
| 3DShape2VecSet [54] | 87.88% | 84.93% | 16.43 |
| Michelangelo [57] | 84.93% | 76.27% | 16.43 |
| Direct3D [45] | 88.43% | 81.55% | 3.201 |
| Hunyuan3D-2 [58]-1024 | 93.60% | 89.16% | 16.43 |
| \(\sqsubseteq\) with FlashVDM | 91.90% | 88.02% | 0.382 |
| Hunyuan3D-2 [58]-3072 | 96.11% | 93.27% | 22.33 |
| \(\sqsubseteq\) with FlashVDM | 95.55% | 93.10% | 0.491 |
+
+Table 1. Numerical comparisons of shape reconstruction methods.
+
+lation strategy based on PCM [43], in which a single-phase finetuning is performed after five phases pretraining.
+
+Aligning Real Data with GAN. With the proposed improvements, our CFD is able to reduce the sampling steps to just 5 while still producing decent results. However, we found that in some cases, the mesh quality is difficult to match the teacher's outputs, which might be attributed to the self-distillation nature of the consistency model. To address this, we seek to further enhance performance by incorporating supervision from ground-truth 3D data through adversarial training [7]. Specifically, we initialize the generator using the model distilled in the previous stage. Inspired by previous works [35, 48], our discriminator operates directly in latent space, eliminating the need for an expensive decoding process, and leverages the intermediate features of the pretrained diffusion model. As shown in Fig. 8, we first extract token sequences from specified attention layers, and then apply independent discriminator heads. Unlike prior works [35, 43, 48, 51] that use noised latents, we did not observe significant improvements with noise, so we opt to use ground-truth latents for simplicity. The discriminator is trained with a hinge adversarial loss [20] as,
+
+$$
+\mathcal {L} _ {\mathrm {a d v}} (\theta , \gamma) = \operatorname {R e L U} \left(1 + \mathcal {D} _ {\gamma} \left(\mathbf {x} _ {0}\right)\right) + \operatorname {R e L U} \left(1 - \mathcal {D} _ {\gamma} \left(\mathbf {x} _ {0} ^ {t _ {n}}\right)\right), \tag {3}
+$$
+
+which distinguishes between ground truth latent $\mathbf{x}_0$ and latent produced by our generator $\mathbf{x}_0^{t_n} = f_\theta (z_{t_n},t_n)$ . Following [43, 51], the final objective is a combination of the adversarial objective and consistency loss $\mathcal{L} = \mathcal{L}_{cfd} + \lambda \mathcal{L}_{adv}$ where $\lambda$ is set to 0.1.
+
+
+Figure 10. Visual comparison of image-to-3D generation between the proposed FlashVDM and other fast 3D generation methods.
+
+# 4. Experiments
+
+In this section, we apply the proposed FlashVDM to Hunyuan3D-2 [58], which is currently a state-of-the-art open-source VDM. We evaluate our approach in terms of both VAE reconstruction and diffusion generation. We also provide ablation studies of the proposed techniques.
+
+# 4.1. Reconstruction
+
+Metrics. We utilize the volume and surface IoU metric to assess the impact of our acceleration techniques on VAE reconstruction performance. The running time is measured at the resolution of 380.
+
+Comparison. We compare our method with three competing method, i.e., 3DShape2VecSet [54], Michelan-
+
+gelo [57], and Direct3D [45]. We evaluate two resolutions, i.e., 1,024 and 3,072, for our fast version and the base model Hunyuan3D-2 [58]. The numerical comparison is shown in Tab. 1. It demonstrates that our method outperforms all competing methods and preserve the quality of base model with less than $1\%$ IoU drop while obtaining over $45\times$ speedup. Fig. 9 shows the visual comparison, which also indicates minimal degradation in quality.
+
+# 4.2. Generation
+
+Metrics. To evaluate shape generation performance, we adopt ULIP-I [49] and Uni3D-I [59] to compute the similarity between the generated mesh and input images.
+
+Comparison. Three latest fast 3D generation methods, i.e., TripoSR [42], SF3D [3], and SPAR3D [11], and two
+
+
+50 Steps VDM
+
+
+5 Steps VDM
+5 Steps FlashVDM
+w/o GD Distill
+w/oEMA
+w/o ADV FT
+
+
+Figure 11. Ablation study of our progressive flow distillation.
+Figure 12. User study of FlashVDM against different methods.
+
+ | ULIP-I(↑) | Uni3D-I(↑) | Time(s↓) |
| TripoSR [42] | 0.0642 | 0.1425 | 0.958 |
| SF3D [3] | 0.1156 | 0.2676 | 0.212 |
| SPAR3D [11] | 0.1149 | 0.2679 | 1.296 |
| Trellis [46] | 0.1267 | 0.3116 | 7.334 |
| Hunyuan3D-2 [58] | 0.1303 | 0.3151 | 34.85 |
| \(\sqsubset\) with FlashVDM | 0.1260 | 0.3095 | 1.041 |
+
+Table 2. Numerical comparisons of shape generation methods.
+
+ | V-IoU(↑) | S-IoU(↑) | Time(s↓) |
| VAE Baseline | 96.11% | 93.27% | 22.33 |
| + Hierarchical Decoding | 96.11% | 93.27% | 2.322 |
| + Efficient Decoder | 96.08% | 93.13% | 0.731 |
| + Adaptive KV Selection | 95.55% | 93.10% | 0.491 |
+
+Table 3. Step-by-step ablation of our lightning vecset decoder.
+
+state-of-the-art methods Hunyuan3D-2 [58] and Trellis [46] are selected for comparison. The numerical comparison is shown in Tab. 2 and the visual comparison is shown in Fig. 10. It can be observed that our method retain most of capability of the base model, while achieves the best results with a large margin against other fast methods.
+
+User Study. We include results of three user studies in Fig. 12. For comparison between FlashVDM and
+
+SPAR3D [11], we ask participants to determine which one is better. For comparison between FlashVDM and Hunyuan3D-2 [58], we ask whether the results are comparable. As seen, FlashVDM is preferred over SPAR3D [11] in almost all testcases, and FlashVDM is comparable to its base model Hunyuan3D-2 [58] at 5 steps and the comparable rate increase with more steps.
+
+# 4.3. Ablation Study
+
+Effectiveness of Lightning Vecset Decoder. The results of step-by-step ablation is shown in Tab. 3, in which we add each component incrementally. It can be observed that hierarchical decoding provides a $10 \times$ speedup with no degradation in quality. The efficient decoder achieves an extra $3 \times$ speedup with almost no degradation, while adaptive KV selection results in a $30 \%$ speedup with minimal degradation.
+
+Effectiveness of Progressive Flow Distillation. We present an ablation study to demonstrate the effectiveness of progressive training strategies. The visual comparison is shown in Fig. 11. As seen, the original VDM completely fails at 5 steps, while FlashVDM achieves results comparable to the original 50-step VDM. Additionally, we observe that distillation fails without guidance distillation as a warm-up step, and performance degrades without the use of EMA. Finally, adversarial fine-tuning is shown to help generate smoother and more accurate shapes. More detailed ablation can be found in the Supplementary Material.
+
+# 5. Conclusion
+
+In this work, we introduce FlashVDM, a general framework for accelerating a pretrained VDM [18, 58]. Our framework encompasses not only a progressive flow distillation method for distilling VDM into a few-step generator, but also several training-free inference techniques and an efficient, lightweight vecset decoder that significantly reduces the FLOPs of decoding. We apply our framework to the state-of-the-art image-to-3D VDM, Hunyuan3D-2 [58], obtaining Hunyuan3D-2 Turbo. Our evaluation demonstrates that FlashVDM excels in both reconstruction and generation, achieving $45 \times$ and $32 \times$ speedups, respectively. To the best of our knowledge, FlashVDM is the first work to push large-scale shape generation into the millisecond range, which opens up new possibilities for interactive applications of 3D generative models.
+
+# Acknowledgement
+
+We thank Yixuan Tang for helping create the teasier. Xi-angyu Yue is supported by National Natural Science Foundation of China (No. 62306261) and The Shun Hing Institute of Advanced Engineering (SHIAE) Fund (No. 8115074).
+
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+ "content": "3D shape generation has greatly flourished through the development of so-called \"native\" 3D diffusion, particularly through the Vecset Diffusion Model (VDM). While recent advancements have shown promising results in generating high-resolution 3D shapes, VDM still struggles at high-speed generation. Challenges exist because of not only difficulties in accelerating diffusion sampling but also VAE decoding in VDM - areas under-explored in previous works. To address these challenges, we present FlashVDM, a systematic framework for accelerating both VAE and DiT in VDM. For DiT, FlashVDM enables flexible diffusion sampling with as few as 5 inference steps and com"
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+ "content": "3D shape generation has greatly flourished through the development of so-called \"native\" 3D diffusion [46, 56], among which the Vecset Diffusion Model (VDM) [54, 57] receives prominent attention and applications due to its simplicity and scalability. While recent works [18, 56, 58] have demonstrated the capabilities of VDM in generating high-resolution and high-quality 3D shapes, VDM still struggles with high-speed generation, typically requiring over 30 seconds"
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| 3DShape2VecSet [54] | 87.88% | 84.93% | 16.43 |
| Michelangelo [57] | 84.93% | 76.27% | 16.43 |
| Direct3D [45] | 88.43% | 81.55% | 3.201 |
| Hunyuan3D-2 [58]-1024 | 93.60% | 89.16% | 16.43 |
| \\(\\sqsubseteq\\) with FlashVDM | 91.90% | 88.02% | 0.382 |
| Hunyuan3D-2 [58]-3072 | 96.11% | 93.27% | 22.33 |
| \\(\\sqsubseteq\\) with FlashVDM | 95.55% | 93.10% | 0.491 |
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| TripoSR [42] | 0.0642 | 0.1425 | 0.958 |
| SF3D [3] | 0.1156 | 0.2676 | 0.212 |
| SPAR3D [11] | 0.1149 | 0.2679 | 1.296 |
| Trellis [46] | 0.1267 | 0.3116 | 7.334 |
| Hunyuan3D-2 [58] | 0.1303 | 0.3151 | 34.85 |
| \\(\\sqsubset\\) with FlashVDM | 0.1260 | 0.3095 | 1.041 |
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| + Hierarchical Decoding | 96.11% | 93.27% | 2.322 |
| + Efficient Decoder | 96.08% | 93.13% | 0.731 |
| + Adaptive KV Selection | 95.55% | 93.10% | 0.491 |
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+ "content": "Effectiveness of Progressive Flow Distillation. We present an ablation study to demonstrate the effectiveness of progressive training strategies. The visual comparison is shown in Fig. 11. As seen, the original VDM completely fails at 5 steps, while FlashVDM achieves results comparable to the original 50-step VDM. Additionally, we observe that distillation fails without guidance distillation as a warm-up step, and performance degrades without the use of EMA. Finally, adversarial fine-tuning is shown to help generate smoother and more accurate shapes. More detailed ablation can be found in the Supplementary Material."
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+ "content": " speedups, respectively. To the best of our knowledge, FlashVDM is the first work to push large-scale shape generation into the millisecond range, which opens up new possibilities for interactive applications of 3D generative models."
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diff --git a/2025/Unleashing the Temporal Potential of Stereo Event Cameras for Continuous-Time 3D Object Detection/32355f2d-a46d-49ce-b53e-d6bb8c2598ef_content_list.json b/2025/Unleashing the Temporal Potential of Stereo Event Cameras for Continuous-Time 3D Object Detection/32355f2d-a46d-49ce-b53e-d6bb8c2598ef_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..6d0945590e5b7632e850b28390d3e5a0f930f2cf
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+ "type": "text",
+ "text": "Unleashing the Temporal Potential of Stereo Event Cameras for Continuous-Time 3D Object Detection",
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+ "text": "Jae-Young Kang*, Hoonhee Cho*, and Kuk-Jin Yoon KAIST",
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+ "type": "text",
+ "text": "{mickeykang,gnsgnsgml,kjyoon}@kaist.ac.kr",
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+ "text": "3D object detection is essential for autonomous systems, enabling precise localization and dimension estimation. While LiDAR and RGB cameras are widely used, their fixed frame rates create perception gaps in high-speed scenarios. Event cameras, with their asynchronous nature and high temporal resolution, offer a solution by capturing motion continuously. The recent approach, which integrates event cameras with conventional sensors for continuous-time detection, struggles in fast-motion scenarios due to its dependency on synchronized sensors. We propose a novel stereo 3D object detection framework that relies solely on event cameras, eliminating the need for conventional 3D sensors. To compensate for the lack of semantic and geometric information in event data, we introduce a dual filter mechanism that extracts both. Additionally, we enhance regression by aligning bounding boxes with object-centric information. Experiments show that our method outperforms prior approaches in dynamic environments, demonstrating the potential of event cameras for robust, continuous-time 3D perception. The code is available at https://github.com/mickeykang16/Ev-Stereo3D.",
+ "bbox": [
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+ "text": "1. Introduction",
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "3D object detection is essential for accurately identifying the position and dimensions of surrounding objects, making it a fundamental task in autonomous systems. Multimodal sensors, such as LiDAR and RGB cameras, play a key role. However, fixed-frame rate sensors have discrete intervals during which data cannot be collected, resulting in inevitable detection delays. This delay in capturing dynamic changes can significantly impact real-time decision-making, emphasizing the importance of high temporal resolution for reliable autonomous driving.",
+ "bbox": [
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+ "page_idx": 0
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+ "type": "text",
+ "text": "Event cameras [27] are asynchronous sensors that continuously stream data over time, allowing them to break the trade-off between bandwidth and delay. Their high tem",
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+ "img_path": "images/3765f6b394ec8e57fc6629148c3577d4a6375893cb413d9e34f264627f22fb61.jpg",
+ "image_caption": [
+ "Figure 1. During blind time, our method enables fast and large motion-aware continuous 3D object detection at arbitrary points in time, including for newly appearing objects."
+ ],
+ "image_footnote": [],
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+ "type": "text",
+ "text": "poral resolution makes them well-suited for capturing fast motion, enabling high-speed perception even in dynamic scenarios. This capability is particularly beneficial for autonomous driving, where rapid response is critical for accident prevention and safe navigation.",
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+ "text": "A recent work, Ev-3DOD [22], integrates an RGB camera, LiDAR, and an event camera to overcome the frame-rate limitations of conventional sensors in 3D object detection. By incorporating event data, it enables perception even during periods when LiDAR and RGB cameras are unavailable. Notably, it introduces continuous-time 3D object detection, allowing inference at arbitrary timestamps before the next synchronized sensor data arrives. Continuous-time 3D object detection enables accurate inference beyond the timeframes when synchronized sensors, such as RGB and LiDAR, provide data. Ev-3DOD [22] defined periods with LiDAR and RGB data as active time and intervals without them as blind time, demonstrating that event cameras can facilitate 3D detection during these blind periods.",
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+ "text": "However, approaches that temporally propagate LiDAR-",
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+ "type": "header",
+ "text": "CVF",
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+ },
+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "type": "page_footnote",
+ "text": "*Equal contribution.",
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+ "type": "page_number",
+ "text": "6869",
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+ "type": "text",
+ "text": "and image-based detection with events are highly dependent on synchronized sensors introducing limitations in dynamic environments. For example, in scenarios like drones with rapid motion during adjacent active times, or high-speed driving causing significant movement during blind periods, fixed frame-rate sensor data does not fully reflect the current 3D geometry. As a result, errors are accumulated over blind time, leading to frequent detection failures.",
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+ "type": "text",
+ "text": "To this end, we propose an event stereo setup that performs precise 3D object detection using only spare and asynchronous event cameras to address the limitations of conventional sensors. As shown in Fig. 1, event stereo can compute 3D information even during blind time, enabling the detection of large-moving and newly appearing objects, which are scenarios that synchronized sensors cannot handle in blind time.",
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+ "type": "text",
+ "text": "One of the challenges when using only event data for 3D object detection is its sparse nature. Event data lacks both semantic and geometric information compared to images and LiDAR, making accurate classification and regression particularly difficult. To overcome this, we propose a dual semantic-geometric filter module that collaboratively filters and enhances both information, fully leveraging stereo event data. The event semantic feature filters the geometric depth feature while the geometric feature simultaneously enhances the semantic information through the estimated disparity. Additionally, following the global detection head, a dense, object-centric semantic event feature is employed to align the local 3D offsets of the bounding boxes, thereby enhancing regression performance. Our proposed method achieves comparable performance in continuous-time 3D object detection without relying on rich fixed frame-rate sensor data. Specifically, through experiments in which the scene undergoes significant changes due to large motion within the same duration, as well as tests involving various intervals for inference, our approach outperforms existing methods. This result can be attributed to the use of asynchronous sensors, which offer distinct advantages in handling dynamic scenarios while fully utilizing both semantic and geometric information of events. The paper highlights the potential and scalability of event cameras to enhance 3D object detection in various environments.",
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+ "type": "text",
+ "text": "2. Related Works",
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+ "text": "Camera-based 3D Object Detection. Cameras offer significant cost advantages over LiDAR, leading many researchers to focus on developing methods for 3D object detection using image-only inputs [15, 39, 43, 56, 59, 61, 64, 84, 87, 88]. However, image-based 3D detection faces challenges due to the lack of direct depth information. To address this, several works [11, 12, 34, 48, 60] propose using stereo and multi-camera systems to compute 3D geometry through multiple views. Despite these advancements, accu",
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+ "type": "text",
+ "text": "rately estimating depth from images remains challenging, causing image-based methods to underperform compared to LiDAR-based approaches.",
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+ "text": "LiDAR-based 3D Object Detection. LiDAR-based 3D object detection can reliably estimate 3D bounding boxes using point clouds captured from LiDAR sensors. Research on representing 3D information from LiDAR has been conducted through various approaches, including point-based methods [25, 38, 80, 82, 95, 98, 104], voxel-based methods [24, 33, 37, 37, 45, 51, 65, 79, 89, 92, 100], and point-voxel fusion networks [36, 66, 81, 94]. To further boost the performance of LiDAR-based 3D detection, multi-modal sensor fusion [9, 40, 41, 49, 50, 58, 83, 90, 99] has emerged, where different sensors, such as cameras and LiDAR, complement each other. Fusion approaches are categorized into early [16, 85, 93], middle [53-55, 57, 62, 74, 76, 96], and late fusion [2, 49, 69]. Multi-modal 3D object detection has garnered significant attention for its ability to improve accuracy and enhance performance compared to unimodal methods. However, there is still room for improvement in terms of safety in autonomous driving. LiDAR and cameras have limited time resolution (i.e., $10 - 20\\mathrm{Hz}$ ) because of their relatively high bandwidths. These limitations are especially noticeable in scenarios like high-speed driving or drone flight. To improve safety, algorithms that can operate at higher speeds are crucial.",
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+ "text": "Event-based Stereo. Event cameras are well-suited for capturing dynamic scenes due to their high temporal resolution, low latency, and ability to operate effectively in challenging lighting conditions. Based on these characteristics, approaches using event cameras in a stereo setup [1, 19-21, 67, 68, 102, 105, 107] have been proposed to better understand the surrounding 3D dynamic scenes. Additionally, research has explored using event cameras in a stereo setup alongside other sensors [3, 10, 17, 18, 63, 103], aiming to leverage the strengths of both event data and conventional sensors to enhance perception capabilities. Building on this research direction, we demonstrate that 3D object detection can be performed using only asynchronous event cameras. Furthermore, we highlight the potential of event cameras for 3D detection in dynamic and rapid motion scenarios.",
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+ "text": "Event-based Object Detection. On the 2D image plane, numerous studies [6, 28, 30, 35, 42, 46, 47, 52, 70, 71, 73, 86, 108] have leveraged the event camera's sensitivity to moving objects for object detection. Various architectures, including graph-based [5, 29, 77], spiking [97], and sparse [72] neural networks, have been explored to achieve streamlined and compelling results tailored to specific objectives. A recent study [22] demonstrated the advantages of high temporal resolution of event cameras in 3D object detection by integrating them with LiDAR and RGB cameras. This study addressed the limitation of synchronized sensors, such as RGB cameras and LiDAR, which operate",
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+ "type": "page_number",
+ "text": "6870",
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+ "type": "image",
+ "img_path": "images/cd3d9831d93a37780aa22c9e084e533b286a969d912f0db3ef125aa433ba9a4e.jpg",
+ "image_caption": [
+ "Figure 2. Overview of the proposed method. Our method is categorized into four components: Geometric Plane-Sweep Volume (Sec. 3.2), Dual Semantic-Geometric Filter (Sec. 3.3), Global 3D Detector (Sec. 3.4), and Object-Centric ROI Alignment (Sec. 3.5)."
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "at fixed frame rates and restrict inference to discrete time intervals. By integrating event cameras, the proposed approach overcomes this constraint, enabling continuous 3D detection even in the absence of synchronized sensor input.",
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+ "type": "text",
+ "text": "Despite these promising results, the approach remains partially dependent on synchronization, as critical information is solely derived from RGB and LiDAR. Consequently, significant errors may occur when rapid motion leads to substantial scene changes during blind time. To address this limitation, we propose the first fully asynchronous system for 3D object detection, utilizing a stereo event camera setup. Thanks to this asynchronous advantage, our method maintains strong performance even when the scene undergoes significant changes during the blind time or when inference is required at a finer continuous-time scale.",
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+ "type": "text",
+ "text": "3. Methods",
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+ "type": "text",
+ "text": "3.1. Preliminaries",
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+ "text": "Event Camera. Traditional frame-based cameras capture images at fixed intervals, whereas event cameras operate asynchronously, recording changes in logarithmic intensity $L(u,v,t)$ only when they exceed a predefined threshold $\\mathcal{C}$ . This can be expressed as:",
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+ "text": "\n$$\nL (u, v, t) - L (u, v, t - \\Delta t) \\geq \\mathbf {p} \\mathcal {C}, \\quad \\mathbf {p} \\in \\{- 1, + 1 \\}, \\tag {1}\n$$\n",
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+ "text": "where $\\Delta t$ represents the time difference, and $\\mathbf{p}$ denotes event polarity, indicating either negative or positive events. The event stream $\\mathcal{E}$ consists of events $e_i$ with spatial coordinates $(u_i, v_i)$ , timestamp $t_i$ , and polarity $p_i$ :",
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+ "text": "\n$$\n\\mathcal {E} = \\left\\{e _ {i} \\right\\} _ {i = 1} ^ {N}, \\quad e _ {i} = \\left(u _ {i}, v _ {i}, t _ {i}, p _ {i}\\right). \\tag {2}\n$$\n",
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+ "text": "Event Representation. We adopt a voxel grid [106] representation, where events are discretized along the time axis into $B$ bins. Given $N$ input events, timestamps are normalized to $[0,B - 1]$ , and the event volume is constructed as:",
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+ "type": "equation",
+ "text": "\n$$\nE (u, v, b) = \\sum_ {i = 1} ^ {N} p _ {i} k _ {\\mathcal {B}} (u - u _ {i}) k _ {\\mathcal {B}} (v - v _ {i}) k _ {\\mathcal {B}} (b - b _ {i} ^ {*}), \\tag {3}\n$$\n",
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+ "type": "text",
+ "text": "where $b_{i}^{*} = (B - 1)(t_{i} - t_{1}) / (t_{N} - t_{1})$ and $k_{\\mathcal{B}}(a)$ is a bilinear sampling kernel. The voxel grid allows efficient feature extraction via 2D convolution across spatial dimensions while conserving temporal information.",
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+ "text": "We use the event stream from the recent interval $\\Delta \\tau$ , denoted as $\\mathcal{E}_{(\\tau - \\Delta \\tau) \\to \\tau} = \\{(u, v, t, p) \\mid \\tau - \\Delta \\tau \\leq t < \\tau\\}$ , to detect 3D boxes at time $\\tau$ . To achieve the continuous-time detection framework, $\\Delta \\tau$ can adapt flexibly to different scenarios. This enables detection at arbitrary time points, making the framework adaptable to various situations. To simplify notation in this section, we represent the voxel grids generated from $\\mathcal{E}_{(\\tau - \\Delta \\tau) \\to \\tau}$ as $E_L$ and $E_R$ for the left and right cameras, respectively.",
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+ "type": "text",
+ "text": "3.2. Geometric Plane-Sweep Volume",
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+ "type": "text",
+ "text": "We illustrate the overall training pipeline in Fig. 2. We modify the PSMNet [7] to design our feature extractor and incorporated an additional feature head to disentangle the roles of semantics-based detection and geometric scene construction. This allows the extractor to separately extract semantic features $F_{L,R}^{sem}$ and geometric features $F_{L,R}^{geo}$ , each with a dimension of $\\mathbb{R}^{H\\times W\\times C}$ . The semantic feature activates well on objects through an auxiliary 2D dense head on the 2D image. The geometric feature activates across the entire scene on the stereo images, concentrating on finding correspondences. First, we generate a geometric plane-sweep volume $\\mathcal{V}_{geo}\\in \\mathbb{R}^{H\\times W\\times D\\times C}$ by concatenating left and corresponding right geometric features at each depth level $D$ as done in previous works [11, 34]. The volume is defined as:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {V} _ {g e o} (u, v, w) = \\left(F _ {L} ^ {g e o} (u, v) | | F _ {R} ^ {g e o} \\left(u - \\frac {f L}{d (w)}, v\\right)\\right), \\quad (4)\n$$\n",
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+ "text": "6871",
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+ "type": "image",
+ "img_path": "images/bfd1545508b42d84e86b91abe9423ec588098664d897954463ea59aaf129b28d.jpg",
+ "image_caption": [
+ "Figure 3. Dual semantic-geometric filter. Semantic and geometric information interact complementarily to enhance both the semantic features and the depth volume."
+ ],
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+ "bbox": [
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+ "type": "text",
+ "text": "where $(u,v)$ are pixel coordinates, $||$ denotes the concatenation, $w = 0,1,\\ldots$ is the candidate depth index, and $d(w) = w\\cdot v_{d} + z_{\\mathrm{min}}$ is the function to calculate the corresponding depth, where $v_{d}$ is the depth interval and $z_{\\mathrm{min}}$ is the minimum depth of the detection area. $f$ and $L$ represent the camera focal length and the baseline of the stereo camera pair, respectively. From the geometric stereo volume $\\nu_{\\mathrm{geo}}$ we apply 3D convolutions to reduce the channel dimension, followed by a softmax operation along the depth dimension, resulting in a depth probability volume $\\mathcal{P}_{\\mathrm{geo}}\\in \\mathbb{R}^{H\\times W\\times D}$ , where $\\mathcal{P}_{\\mathrm{geo}}(u,v,:)$ represents the depth probability for pixel $(u,v)$ across all depth levels.",
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+ "type": "text",
+ "text": "To transform the feature volume from stereo space to a 3D space, the 3D detection area is segmented into uniformly sized voxels, resulting in $\\mathbf{V}_{geo}^{3D}\\in \\mathbb{R}^{X\\times Y\\times Z\\times C}$ . For each voxel, its center coordinates $(x,y,z)$ are projected back into the stereo space using the intrinsic parameters $K$ , resulting in the reprojected pixel coordinates $(u,v)$ and a corresponding depth index $d^{-1}(z) = (z - z_{\\mathrm{min}}) / v_d$ as:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {V} _ {g e o} ^ {3 D} (x, y, z) = \\mathcal {V} _ {g e o} (u, v, d ^ {- 1} (z)). \\qquad (5)\n$$\n",
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+ "type": "text",
+ "text": "3.3. Dual Semantic-Geometric Filter",
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+ "type": "text",
+ "text": "Along with the geometric volume, we leverage the event camera's robustness in detecting objects on the 2D plane by using semantic features to construct a 3D semantic volume $\\mathbf{V}_{sem}^{3D} \\in \\mathbb{R}^{X \\times Y \\times Z \\times C}$ . Creating a 3D volume with only semantic features fails to capture geometric properties. To address this, we propose a dual semantic-geometric filter that combines both semantic and geometric information, as shown in Figure 3.",
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+ "type": "text",
+ "text": "Semantic-guided Depth Refinement. One of the key challenges in 3D detection using stereo cameras is achieving accurate depth inference. Unlike LiDAR, stereo cameras do not provide direct depth measurements from the sensor. To enhance depth accuracy, we utilize semantic information to refine the geometric cost volume. As shown in Fig. 3, we first estimate the initial depth $D_{init}$ by computing the",
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+ "type": "text",
+ "text": "weighted sum over all depth levels using the depth probability volume $\\mathcal{P}_{geo}$ . Additionally, to refine the depth distribution volume by transferring accuracy through the semantic feature, which effectively captures semantic information about the scene, we compute the similarity for each pixel based on the predicted depth as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nS (u, v) = \\left\\langle F _ {L} ^ {s e m} (u, v), F _ {R} ^ {s e m} \\left(u - \\frac {f L}{D _ {i n i t} (u , v)}, v\\right) \\right\\rangle , \\tag {6}\n$$\n",
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+ "type": "text",
+ "text": "where $\\langle \\cdot ,\\cdot \\rangle$ denotes the inner product for similarity. Similar to previous works [8, 75, 78, 91] that handle confidence in stereo matching, we also compute confidence as follows:",
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+ "type": "equation",
+ "text": "\n$$\nC (u, v) = \\sum_ {w} \\mathcal {P} _ {g e o} (u, v, w) \\cdot \\left(d (w) - D ^ {\\text {i n i t}} (u, v)\\right) ^ {2}, \\tag {7}\n$$\n",
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+ "type": "text",
+ "text": "We aim to refine the depth distribution by considering both stereo similarity and confidence. Adapting the refinement process from [91], we generate filtered volume, $\\tilde{\\mathcal{P}}_{geo}$ , by incorporating neighboring probabilities as follows:",
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+ "type": "equation",
+ "text": "\n$$\nW _ {m} (u, v) = S _ {m} (u, v) \\cdot \\text {s i g m o i d} \\left(C _ {m} (u, v)\\right),\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\tilde {\\mathcal {P}} _ {g e o} (u, v, w) = \\sum_ {m = 1} ^ {M} \\mathcal {P} _ {g e o} (u, v, w) \\cdot \\operatorname {s o f t m a x} _ {m} \\left(W _ {m} (u, v)\\right), \\tag {8}\n$$\n",
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+ "type": "text",
+ "text": "where $m = 1,2,3,\\ldots ,M$ are the sampled neighboring pixels and $\\mathrm{softmax}_m$ denotes a softmax across the $m$ dimension. Through this refinement process, depth ambiguity can be resolved, and we estimate the refined depth, $\\tilde{D}$ , from the refined probability.",
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+ "type": "text",
+ "text": "Geometric-filtered Semantic Volume. Although semantic features are well activated for objects, event data is sparse along the spatial dimension, often leading to ambiguity. To compensate for this lack of information, we enhance the left features using the estimated depth and the semantic features from the right camera. As shown in the bottom of Fig. 3, we warp the right semantic features to the left camera using the estimated depth: $\\hat{F}_R^{sem} = \\mathrm{Warp}(F_R^{sem},\\tilde{D})$ . However, directly using these warped features may introduce occlusion issues and fail to fully address potential misalignments between stereo cameras. To handle these challenges, we apply a transformer-based channel attention mechanism to generate enhanced semantic features. We generate the query, key, and value features as follows: $\\mathbf{Q} = W_{Q}(F_{L}^{sem})$ , $\\mathbf{K} = W_{K}(\\hat{F}_{R}^{sem})$ , and $\\mathbf{V} = W_{V}(\\hat{F}_{R}^{sem})$ , where $W_{(\\cdot)}$ represents a $1\\times 1$ convolution. The results of the transformer are computed in this manner:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbb {A} \\left(F _ {L} ^ {\\text {s e m}}, \\hat {F} _ {R} ^ {\\text {s e m}}\\right) = F _ {L} ^ {\\text {s e m}} + W _ {\\mathbb {A}} \\left(\\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {T}}{\\alpha}\\right) \\cdot \\mathbf {V}\\right) \\tag {9}\n$$\n",
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+ "type": "text",
+ "text": "where $\\alpha$ is a learnable parameter. Finally, the geometrically enhanced semantic feature $\\bar{F}_L^{sem}$ is obtained:",
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+ "text": "\n$$\n\\tilde {F} _ {L} ^ {s e m} = F _ {L} ^ {s e m} + \\operatorname {M L P} (\\mathbb {A}) + \\mathbb {A}. \\tag {10}\n$$\n",
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+ "type": "image",
+ "img_path": "images/24f5c7432375e2097ddab118215c2651914d6dbb585a046ac9a5962364eb07bb.jpg",
+ "image_caption": [
+ "Figure 4. Illustration of the object-centric ROI alignment."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Similar to Eq. (5), voxels can be projected onto the image plane to map 2D semantic features to 3D. However, to ensure the transformation is based on geometric information, we apply a depth probability mask as:",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathbf {V} _ {s e m} ^ {3 D} (x, y, z) = \\tilde {F} _ {L} ^ {s e m} (u, v) \\cdot \\tilde {\\mathcal {P}} _ {g e o} (u, v, d ^ {- 1} (z)) \\tag {11}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Fusion of Semantic and Geometric Voxels. We generate two types of voxels in the 3D space: one specialized for geometric information, $\\mathbf{V}_{geo}^{3D}$ , and the other for semantic information, $\\mathbf{V}_{sem}^{3D}$ . To integrate the two voxels into a unified 3D voxel that effectively combines both aspects, we concatenated and then merged them through 3D convolution, resulting in the fused voxel, $\\mathbf{V}^{3D}$ .",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "3.4. Global 3D Detector",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Inspired by recent stereo 3D detection approaches [11, 12, 34], we designed an anchor-based detector. The bird's-eye view (BEV) feature strikes a balance between accuracy and computational efficiency in 3D detection for autonomous driving. The unified 3D voxel features $\\mathbf{V}^{3D} \\in \\mathbb{R}^{X \\times Y \\times Z \\times C}$ are downsampled along the height dimension to produce a BEV feature of size $(X, Z)$ . We utilize fixed-size class anchors, determined based on the training set statistics, and assign a predefined number of anchors with varying sizes and orientations to each BEV feature location $(x, z)$ . Similar to previous works [11, 12, 34], the dense head network performs a regression from the anchor $A = (x_{a}, y_{a}, z_{a}, h_{a}, w_{a}, l_{a}, \\theta_{a})$ to predict the offset $\\Delta P_{G} = (\\delta x, \\delta y, \\delta z, \\delta h, \\delta w, \\delta l, \\delta \\theta)$ . The final prediction is calculated by applying an offset to the anchor to determine the global position using the box decoding function $g_{d}$ ,",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} P _ {G} = g _ {d} (A, \\Delta P _ {G}) = \\left(x _ {a} + \\delta x, y _ {a} + \\delta y, z _ {a} + \\delta z, \\right. \\\\ h _ {a} e ^ {\\delta h}, w _ {a} e ^ {\\delta w}, l _ {a} e ^ {\\delta l}, \\theta_ {a} + \\frac {\\pi}{2} \\tanh (\\delta \\theta)). \\tag {12} \\\\ \\end{array}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "3.5. Object-Centric ROI Alignment",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "The geometric-semantic fused 3D voxels, $\\mathbf{V}^{3D}$ , generated through the semantic-geometric dual filter contain accurate",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "depth and rich semantic information, enabling bounding box prediction in the global scene. However, a single-stage global regression can struggle with ambiguity caused by the motion of objects and the movement of the ego vehicle, especially as motion intensifies, necessitating a method that aligns more accurately with the object. To this end, we propose a method for locally aligning the ROI around the object's bounding box.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "ROI Pooling and Local Regression. As shown in Fig. 4, we use the semantic voxel, $\\mathbf{V}_{sem}^{3D}$ , which focuses on the object and provides rich edge information from event-based semantic data, making it advantageous for ROI alignment. To optimize the computation of alignment, and because most stereo-based detections are prone to error along the $X$ and $Z$ dimensions, we project the voxel features onto the BEV, which corresponds to the transformation of $\\mathbf{B}_{sem}^{2D} \\in \\mathbb{R}^{X \\times Z \\times C'}$ to the BEV of $\\mathbf{V}_{sem}^{3D}$ , rather than using them directly. Since $\\mathbf{B}_{sem}^{2D}$ is splatted based on depth probabilities, it tends to cluster around the high-likelihood hypotheses of the predicted boxes. Therefore, to ensure that not only the exactly overlapping features but also the surrounding information is aggregated during alignment, we use a pooling scheme. Specifically, each bounding box prediction from global 3D detector, $P_{G}$ , is split into an $k \\times k$ voxel grid. The semantic BEV feature, $\\mathbf{B}_{sem}^{2D}$ , is then pooled [23] for each voxel grid. The pooled feature of each bounding box, $\\hat{\\mathbf{B}}_{sem}^{2D} \\in \\mathbb{R}^{k^2 \\times C'}$ , encodes object-centric local information, serving as a cue for precisely aligning the box. Each pooled feature passes through an MLP layer to predict the local alignment offset, $\\Delta P_{L} = (\\delta x', \\delta y', \\delta z', \\delta h', \\delta w', \\delta l', \\delta \\theta')$ . The final fine-grained regression, $\\tilde{P}_{G}$ , is calculated by box decoding function: $\\tilde{P}_{G} = g_{d}(P_{G}, \\Delta P_{L})$",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "3.6. Objective Function",
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+ {
+ "type": "text",
+ "text": "A multi-task loss was applied to train the network, which includes the geometric plane-sweep volume, the dual semantic-geometric branch, the global 3D detector head, and object-centric ROI alignment module as follows:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {i n i t}} + \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {r e f i n e}} + \\mathcal {L} _ {2 D} + \\mathcal {L} _ {\\text {c l s}} + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {g l o b a l}} + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {l o c a l}}. \\tag {13}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "where $\\mathcal{L}_{depth}^{init},\\mathcal{L}_{2D},\\mathcal{L}_{cls}$ are adapted from uni-modal depth loss, 2D detection loss, and classification loss in [34]. For refined depth loss, we utilized smooth $L_{1}$ loss [44] as",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {r e f i n e}} = \\operatorname {s m o o t h} _ {L _ {1}} \\left(D _ {g t} - \\tilde {D}\\right). \\tag {14}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "The regression loss for the global 3D detector and object-centric ROI alignment are as follows:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {r e g} ^ {\\text {g l o b a l}} = \\mathcal {L} _ {r e g} \\left(P _ {G}, G\\right), \\quad \\mathcal {L} _ {r e g} ^ {\\text {l o c a l}} = \\mathcal {L} _ {r e g} \\left(\\tilde {P} _ {G}, G\\right) \\tag {15}\n$$\n",
+ "text_format": "latex",
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+ },
+ {
+ "type": "text",
+ "text": "where $G$ refers to 3D ground-truth bounding box and $\\mathcal{L}_{reg}$ is 3D regression loss adapted from [34].",
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+ {
+ "type": "page_number",
+ "text": "6873",
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+ {
+ "type": "table",
+ "img_path": "images/25480be410309feeea335b8d4aa54536957343a3f175ddf52344df1aa28f002a.jpg",
+ "table_caption": [
+ "Table 1. Comparison on the DSEC-3DOD dataset for vehicle (IoU = 0.7) and pedestrian (IoU = 0.5) detection on 3D and BEV. We follow the evaluation protocol of Ev-3DOD [22] for 100 FPS 3D detection in blind time. Mod. is an abbreviation for moderate, and easy and moderate represent difficulty levels. VEH and PED represent vehicle and pedestrian, respectively."
+ ],
+ "table_footnote": [],
+ "table_body": "| Modality | Methods | VEH AP3D | VEH APBEV | PED AP3D | PED APBEV |
| Easy | Mod. | Easy | Mod. | Easy | Mod. | Easy | Mod. |
| LiDAR | VoxelNeXt [14] | 12.66 | 11.06 | 31.46 | 28.39 | 10.59 | 6.61 | 12.77 | 7.96 |
| HEDNet [101] | 14.31 | 12.96 | 29.94 | 27.85 | 10.16 | 8.29 | 11.90 | 6.89 |
| LiDAR+RGB | Focals Conv [13] | 12.71 | 11.69 | 26.14 | 23.83 | 8.92 | 5.50 | 12.54 | 7.83 |
| LoGoNet [49] | 17.65 | 15.39 | 32.55 | 29.19 | 11.66 | 8.20 | 15.09 | 9.77 |
| LiDAR+RGB+Event | Ev-3DOD [22] | 29.53 | 25.07 | 49.31 | 44.44 | 18.42 | 12.49 | 29.06 | 20.34 |
| RGB-Stereo | DSGN [11] | 16.29 | 13.45 | 31.90 | 27.53 | 4.06 | 2.42 | 6.08 | 3.74 |
| LIGA [34] | 14.26 | 10.98 | 27.25 | 25.11 | 6.02 | 3.58 | 8.73 | 4.89 |
| Event-Stereo | Ours | 23.47 | 19.62 | 40.13 | 33.03 | 19.86 | 12.93 | 22.91 | 14.34 |
",
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+ {
+ "type": "text",
+ "text": "4. Experiments",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "4.1. Dataset",
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+ {
+ "type": "text",
+ "text": "DSEC-3DOD Dataset. The DSEC-3DOD dataset is the real-world event-based 3D detection dataset introduced in the Ev-3DOD [22]. It is based on the DSEC [31], a stereo event dataset for driving scenarios. DSEC-3DOD contains manually created 10 FPS annotations for vehicle and pedestrian classes and provides blind-time annotations at 100 FPS through interpolation and refinement. We used the widely adopted KITTI metric [32] from frame-based stereo methods, which measures performance in both BEV (bird-eyeview) and 3D for each class.",
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+ "type": "text",
+ "text": "4.2. Experiment Setup",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "3D Detection during Blind Time. Consistent with the training and evaluation protocol of existing event-based 3D object detection [22], we train and evaluate using 100 FPS annotations during blind time, when no LiDAR data is available due to the fixed frame rate of LiDAR (i.e., 10 FPS). To achieve this, we sliced the event stream at $\\Delta \\tau = 10$ ms and converted it into a voxel grid.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Motion Scale and Time Slice. The strength of event cameras lies in their ability to provide continuous information over time, even in dynamic motion [4, 26]. Therefore, experiments on dynamic and long-range motion during blind time are crucial to demonstrate the advantages of the asynchronous setup. However, the DSEC-3DOD dataset mostly lacks such scenes, as its average ego velocity is below 10 m/s. To address this, we introduce an experimental setup, motion scale (MS), which scales time axis for large motion experiments that closely resemble the real world. Accumulation and normalization of events over a longer period can approximate events with larger motion over the same time span. Therefore, increasing the motion scale in experiments can depict dynamic environments by skipping consecutive annotations and accumulating events over a longer period. Time slice (TS) refers to the number of divisions applied",
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+ "img_path": "images/f98b4fc3ce2253f531ecaaafc138b4ed46e384c91701d4f85dfae1be6679f368.jpg",
+ "image_caption": [
+ "$t = 0$ $t = 0.3$"
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+ "img_path": "images/6db6b3d498fbb2b967b2704021fb82f8239448719b1c64bb726b911aab11a718.jpg",
+ "image_caption": [
+ "$t = 0.6$ $t = 0.9$"
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+ "img_path": "images/71df26025cd8ed4006030babcebecec7969dad087ed5925da8b680a3bd0fc51c.jpg",
+ "image_caption": [
+ "Figure 5. Comparison of 3D detection during blind time. $t = 0$ and $t = 1$ represent active time, while $t = 0.3$ , 0.6, and 0.9 indicate normalized blind time intervals."
+ ],
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+ {
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+ "img_path": "images/9625636d979184721f832cc0971d86be80b0efe80b5de572c102a28f63c09c1a.jpg",
+ "image_caption": [],
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+ {
+ "type": "text",
+ "text": "to the blind time, where detection performance is evaluated at each time slice instance. Since various event input durations are used, this setup reflects the real-world demand for asynchronous detection. The baseline setup is defined with a motion scale of 1 and a time slice of 10, which corresponds to the 10 FPS fixed-frame rate data provided in the DSEC-3DOD dataset and the blind time annotations sliced into 10 parts (i.e., 100 FPS GT). To ensure compatibility with the original ground truth, experiments were conducted with motion scale values of 2 and 4 and time slice values of 10 and 20. The model is trained using the original 100 FPS GT with a motion scale of 1 and a time slice of 10 and is evaluated across various motion scales and time slices. More details about the experimental settings are provided in the supplementary material.",
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+ {
+ "type": "text",
+ "text": "4.3. Results on 3D Detection during Blind Time",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Table 1 provides the results of 3D detection performed during blind time. Results from previous works [13, 14, 49,",
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+ "type": "page_number",
+ "text": "6874",
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+ "type": "table",
+ "img_path": "images/1d4fd434ec67af0093185b8e327ad56dfc632b4171ccfaeed944d213766828fa.jpg",
+ "table_caption": [
+ "Table 2. Performance evaluation across various motion scales and time slices, presenting results for the easy difficulty level. Each entry corresponds to 3D / BEV detection results. VEH and PED represent vehicle and pedestrian, respectively."
+ ],
+ "table_footnote": [],
+ "table_body": "| Motion Scale | Time Slice | Class | LiDAR | LIDAR+RGB | LiDAR+RGB+Event | RGB Stereo | Event Stereo |
| VoxelNeXt [14] | HEDNet [101] | Focals Conv [13] | LoGoNet [49] | Ev-3DOD [22] | DSGN [11] | LIGA [34] | Ours |
| ×2 | ×10 | VEH | 5.05 / 13.00 | 6.03 / 12.87 | 5.95 / 12.48 | 5.97 / 13.57 | 15.68 / 30.59 | 7.33 / 17.36 | 6.00 / 12.87 | 22.72 / 39.81 |
| PED | 4.07 / 4.89 | 3.40 / 4.05 | 3.16 / 4.79 | 2.24 / 3.72 | 7.88 / 12.19 | 1.87 / 3.04 | 2.27 / 4.00 | 19.04 / 22.71 |
| ×20 | VEH | 4.34 / 11.76 | 5.26 / 11.67 | 5.76 / 11.40 | 5.42 / 12.40 | 15.96 / 31.13 | 7.13 / 16.43 | 5.67 / 12.00 | 23.47 / 40.13 |
| PED | 3.83 / 4.31 | 2.60 / 3.49 | 2.66 / 3.86 | 1.91 / 2.90 | 1.47 / 2.63 | 1.84 / 2.99 | 2.08 / 3.01 | 19.86 / 22.91 |
| ×4 | ×10 | VEH | 2.05 / 5.22 | 2.87 / 4.63 | 2.73 / 4.48 | 1.90 / 5.26 | 6.24 / 11.62 | 3.12 / 7.20 | 2.10 / 4.89 | 20.70 / 37.08 |
| PED | 2.21 / 2.44 | 1.64 / 1.85 | 1.34 / 1.85 | 1.17 / 1.55 | 3.04 / 4.09 | 0.60 / 0.77 | 1.11 / 1.30 | 16.71 / 21.93 |
| ×20 | VEH | 1.71 / 4.55 | 2.27 / 4.29 | 2.73 / 3.94 | 1.90 / 4.66 | 6.36 / 11.70 | 3.09 / 6.52 | 1.54 / 4.17 | 22.72 / 39.81 |
| PED | 2.14 / 2.17 | 1.10 / 1.42 | 1.02 / 1.44 | 0.53 / 1.28 | 0.39 / 0.43 | 0.59 / 0.75 | 0.82 / 1.12 | 19.04 / 22.71 |
",
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+ {
+ "type": "text",
+ "text": "[101] were taken from the supplementary material of Ev-3DOD [22], while we trained and evaluated frame-based stereo methods, DSGN [11] and LIGA [34], from scratch. Methods relying solely on synchronized sensors struggle to handle blind time, resulting in poor performance. On the other hand, both Ev-3DOD and our method utilize event cameras to overcome the limitations of fixed frame rates, enabling effective 3D detection during blind time and achieving high performance. While Ev-3DOD benefits from LiDAR-based depth information, generally outperforming our event-only approach, it is noteworthy that our method achieves superior performance in pedestrian $\\mathrm{AP}_{3D}$ . Pedestrian detection requires fine detail, and our high performance on this class is due to specialized modules that effectively leverage semantic features from event data.",
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+ {
+ "type": "text",
+ "text": "Figure 5 illustrates another advantage of the asynchronous setup. While Ev-3DOD shows a decline in qualitative results as it moves further from active time 0, where LiDAR data is available, our method maintains high performance by computing geometric information from events, allowing it to operate independently of active time.",
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+ "text": "4.4. Diverse Motion Scales and Time Slices",
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+ "text": "Table 2 shows the comparison of ours with different methods across various motion scales and time slices. Methods relying solely on synchronized sensors [11, 13, 14, 34, 49, 101] exhibit a significant performance drop as the motion scale increases during blind time. Our primary comparison method, Ev-3DOD [22], utilizes event data during blind time, allowing it to handle moderate scenarios well, as shown in Table 1. However, as the motion increases, its performance significantly drops. This is because Ev-3DOD relies entirely on LiDAR for 3D geometric information, and when large motion occurs, scene changes make past geometric information less useful for the present. In contrast, our method computes 3D geometric information using asynchronous event data, resulting in more stable performance across different motion scales. Therefore, in scenar",
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+ "Table 3. Ablation study on modules for 3D detection during blind time. DSGF: Dual Semantic-Geometric Filter. SDR: Semantic-Guided Depth Refinement. GSV: Geometric-Filtered Semantic Volume. OCRA: Object-Centric ROI Alignment. The fused voxel source is denoted as G or S, where G represents geometric voxel and S represents semantic voxel."
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+ "table_body": "| DSGF | 3D Voxel Source | OCRA | mAP Easy |
| SDR | GSV | 3D | BEV |
| | G | | 12.92 | 20.78 |
| | G+S | | 14.60 | 24.85 |
| | G | ✓ | 14.56 | 21.73 |
| | G+S | ✓ | 15.95 | 26.12 |
| ✓ | | G+S | | 15.85 | 27.78 |
| ✓ | G+S | | 17.08 | 26.53 |
| ✓ | ✓ | G+S | | 19.12 | 29.64 |
| ✓ | ✓ | G+S | ✓ | 21.66 | 31.52 |
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+ "text": "ios with high-speed driving or significant scene changes due to dynamic motion, our event-based 3D detection proves highly effective during blind time.",
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+ "text": "5. Ablation Study",
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+ "text": "Ablation Study on Modules. As shown in Table 3, we conduct an ablation study on the proposed modules. Starting from a baseline that performs 3D detection using only the geometric plane-sweep volume, we incrementally add the proposed modules to evaluate their impact on performance. We report the easy mAP performance, which is the average value across the two classes, VEH and PED, measured under a motion scale of 1 and a time slice of 10. Compared to the baseline, simply adding semantic information results in sub-optimal performance, yielding only a 1.68 improvement in 3D detection. However, incorporating a dual semantic-geometric filter, which facilitates interaction between semantic and geometric features, leads to a significant performance gain of 6.2 in 3D detection. Additionally, the proposed object-centric ROI alignment consistently improves performance across all settings. When",
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+ "image_caption": [
+ "Figure 6. Comparison of 3D detection during blind time. Ev-3DOD detects new objects only at the active timestamps, $t = 0,1,2$ , using LiDAR and RGB. In contrast, the proposed model can capture the emergence of new objects at arbitrary times."
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+ "Table 4. Performance of RGB fusion. Results of easy difficulty level with a time slice of 10."
+ ],
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+ "table_body": "| Settings | Methods | AP3D | APBEV |
| VEH | PED | VEH | PED |
| Motion ×1 | Ours (E) | 23.47 | 19.86 | 40.13 | 22.91 |
| Ours (E+I) | 25.23 | 21.50 | 46.21 | 29.14 |
| Motion ×2 | Ours (E) | 22.72 | 19.04 | 39.81 | 22.71 |
| Ours (E+I) | 20.14 | 10.50 | 37.93 | 12.76 |
",
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+ "text": "used alongside a dual semantic-geometric filter, it further enhances semantic BEV features, resulting in a more significant performance boost.",
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+ "text": "RGB Fusion. Table 4 presents the results of fusing synchronous RGB information into our method. The stereo RGB features are extracted using a separate feature extractor and concatenated with the event features. This fusion provides improved performance under small motion scales, as the RGB input offers additional semantic guidance. However, under large motion, the performance significantly degrades due to misalignment between the synchronous RGB data and the actual object location. In contrast, our setup that relies solely on event data demonstrates robust performance regardless of scene dynamics.",
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+ "text": "Performance Degradation over Blind Time. Figure 7 shows the performance over time during blind time for our method and other methods [22, 49]. To highlight robustness in challenging scenarios, we use motion scale of 2. $t = 0$ refers to the most recent synchronized sensor input timestamp, while $t = 0.1 \\sim 0.9$ represents the blind interval before the next input. The reason for the performance drop of other methods is that they rely on 3D information from synchronous sensors and struggle as the current scene diverges from recent active time $(t = 0)$ , making it challenging to estimate the present 3D box using past information. Thus, despite using event data, Ev-3DOD struggles to transfer past",
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+ "image_caption": [
+ "Figure 7. Performance comparison with other methods during blind time under the setting of motion scale 2 and time slice 10."
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+ "text": "3D information to the present, causing its performance to resemble LoGoNet as motion increases over time. In contrast, our method asynchronously infers both geometric and semantic information for 3D detection, allowing it to operate independently of active time.",
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+ "text": "6. Conclusion",
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+ "text": "In this paper, we tackle 3D object detection using event stereo in a fully asynchronous setting for the first time. Unlike the previous continuous-time 3D object detection work that utilizes LiDAR, our approach does not rely on LiDAR, leading to lower performance compared to methods that fuse LiDAR and event data. However, by evaluating various motion scales and time slices, we demonstrate that our method is more adaptable and performs robustly in diverse and extreme conditions. Furthermore, we highlight the potential of event-based 3D perception in dynamic environments where event cameras are particularly beneficial, such as drone flights, high-speed driving, and robots. We hope this work inspires further research in this direction.",
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+ "type": "text",
+ "text": "7. Acknowledgments.",
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+ "text": "This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF2022R1A2B5B03002636). This work was also supported by the Technology Innovation Program (1415187329,20024355, Development of autonomous driving connectivity technology based on sensor-infrastructure cooperation) funded By the Ministry of Trade, Industry & Energy(MOTIE, Korea).",
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+ "content": "and image-based detection with events are highly dependent on synchronized sensors introducing limitations in dynamic environments. For example, in scenarios like drones with rapid motion during adjacent active times, or high-speed driving causing significant movement during blind periods, fixed frame-rate sensor data does not fully reflect the current 3D geometry. As a result, errors are accumulated over blind time, leading to frequent detection failures."
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+ "content": "To this end, we propose an event stereo setup that performs precise 3D object detection using only spare and asynchronous event cameras to address the limitations of conventional sensors. As shown in Fig. 1, event stereo can compute 3D information even during blind time, enabling the detection of large-moving and newly appearing objects, which are scenarios that synchronized sensors cannot handle in blind time."
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+ "content": "One of the challenges when using only event data for 3D object detection is its sparse nature. Event data lacks both semantic and geometric information compared to images and LiDAR, making accurate classification and regression particularly difficult. To overcome this, we propose a dual semantic-geometric filter module that collaboratively filters and enhances both information, fully leveraging stereo event data. The event semantic feature filters the geometric depth feature while the geometric feature simultaneously enhances the semantic information through the estimated disparity. Additionally, following the global detection head, a dense, object-centric semantic event feature is employed to align the local 3D offsets of the bounding boxes, thereby enhancing regression performance. Our proposed method achieves comparable performance in continuous-time 3D object detection without relying on rich fixed frame-rate sensor data. Specifically, through experiments in which the scene undergoes significant changes due to large motion within the same duration, as well as tests involving various intervals for inference, our approach outperforms existing methods. This result can be attributed to the use of asynchronous sensors, which offer distinct advantages in handling dynamic scenarios while fully utilizing both semantic and geometric information of events. The paper highlights the potential and scalability of event cameras to enhance 3D object detection in various environments."
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+ "content": "Camera-based 3D Object Detection. Cameras offer significant cost advantages over LiDAR, leading many researchers to focus on developing methods for 3D object detection using image-only inputs [15, 39, 43, 56, 59, 61, 64, 84, 87, 88]. However, image-based 3D detection faces challenges due to the lack of direct depth information. To address this, several works [11, 12, 34, 48, 60] propose using stereo and multi-camera systems to compute 3D geometry through multiple views. Despite these advancements, accu"
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+ "content": "LiDAR-based 3D Object Detection. LiDAR-based 3D object detection can reliably estimate 3D bounding boxes using point clouds captured from LiDAR sensors. Research on representing 3D information from LiDAR has been conducted through various approaches, including point-based methods [25, 38, 80, 82, 95, 98, 104], voxel-based methods [24, 33, 37, 37, 45, 51, 65, 79, 89, 92, 100], and point-voxel fusion networks [36, 66, 81, 94]. To further boost the performance of LiDAR-based 3D detection, multi-modal sensor fusion [9, 40, 41, 49, 50, 58, 83, 90, 99] has emerged, where different sensors, such as cameras and LiDAR, complement each other. Fusion approaches are categorized into early [16, 85, 93], middle [53-55, 57, 62, 74, 76, 96], and late fusion [2, 49, 69]. Multi-modal 3D object detection has garnered significant attention for its ability to improve accuracy and enhance performance compared to unimodal methods. However, there is still room for improvement in terms of safety in autonomous driving. LiDAR and cameras have limited time resolution (i.e., \\(10 - 20\\mathrm{Hz}\\)) because of their relatively high bandwidths. These limitations are especially noticeable in scenarios like high-speed driving or drone flight. To improve safety, algorithms that can operate at higher speeds are crucial."
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+ "content": "Event-based Stereo. Event cameras are well-suited for capturing dynamic scenes due to their high temporal resolution, low latency, and ability to operate effectively in challenging lighting conditions. Based on these characteristics, approaches using event cameras in a stereo setup [1, 19-21, 67, 68, 102, 105, 107] have been proposed to better understand the surrounding 3D dynamic scenes. Additionally, research has explored using event cameras in a stereo setup alongside other sensors [3, 10, 17, 18, 63, 103], aiming to leverage the strengths of both event data and conventional sensors to enhance perception capabilities. Building on this research direction, we demonstrate that 3D object detection can be performed using only asynchronous event cameras. Furthermore, we highlight the potential of event cameras for 3D detection in dynamic and rapid motion scenarios."
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+ "content": "Event-based Object Detection. On the 2D image plane, numerous studies [6, 28, 30, 35, 42, 46, 47, 52, 70, 71, 73, 86, 108] have leveraged the event camera's sensitivity to moving objects for object detection. Various architectures, including graph-based [5, 29, 77], spiking [97], and sparse [72] neural networks, have been explored to achieve streamlined and compelling results tailored to specific objectives. A recent study [22] demonstrated the advantages of high temporal resolution of event cameras in 3D object detection by integrating them with LiDAR and RGB cameras. This study addressed the limitation of synchronized sensors, such as RGB cameras and LiDAR, which operate"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.1,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.303,
+ 0.908,
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+ ],
+ "angle": 0,
+ "content": "Figure 2. Overview of the proposed method. Our method is categorized into four components: Geometric Plane-Sweep Volume (Sec. 3.2), Dual Semantic-Geometric Filter (Sec. 3.3), Global 3D Detector (Sec. 3.4), and Object-Centric ROI Alignment (Sec. 3.5)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.352,
+ 0.483,
+ 0.412
+ ],
+ "angle": 0,
+ "content": "at fixed frame rates and restrict inference to discrete time intervals. By integrating event cameras, the proposed approach overcomes this constraint, enabling continuous 3D detection even in the absence of synchronized sensor input."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.413,
+ 0.484,
+ 0.579
+ ],
+ "angle": 0,
+ "content": "Despite these promising results, the approach remains partially dependent on synchronization, as critical information is solely derived from RGB and LiDAR. Consequently, significant errors may occur when rapid motion leads to substantial scene changes during blind time. To address this limitation, we propose the first fully asynchronous system for 3D object detection, utilizing a stereo event camera setup. Thanks to this asynchronous advantage, our method maintains strong performance even when the scene undergoes significant changes during the blind time or when inference is required at a finer continuous-time scale."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
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+ 0.192,
+ 0.607
+ ],
+ "angle": 0,
+ "content": "3. Methods"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.615,
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+ ],
+ "angle": 0,
+ "content": "3.1. Preliminaries"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.637,
+ 0.484,
+ 0.713
+ ],
+ "angle": 0,
+ "content": "Event Camera. Traditional frame-based cameras capture images at fixed intervals, whereas event cameras operate asynchronously, recording changes in logarithmic intensity \\( L(u,v,t) \\) only when they exceed a predefined threshold \\( \\mathcal{C} \\). This can be expressed as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.101,
+ 0.722,
+ 0.483,
+ 0.739
+ ],
+ "angle": 0,
+ "content": "\\[\nL (u, v, t) - L (u, v, t - \\Delta t) \\geq \\mathbf {p} \\mathcal {C}, \\quad \\mathbf {p} \\in \\{- 1, + 1 \\}, \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.746,
+ 0.484,
+ 0.808
+ ],
+ "angle": 0,
+ "content": "where \\(\\Delta t\\) represents the time difference, and \\(\\mathbf{p}\\) denotes event polarity, indicating either negative or positive events. The event stream \\(\\mathcal{E}\\) consists of events \\(e_i\\) with spatial coordinates \\((u_i, v_i)\\), timestamp \\(t_i\\), and polarity \\(p_i\\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.167,
+ 0.814,
+ 0.483,
+ 0.833
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {E} = \\left\\{e _ {i} \\right\\} _ {i = 1} ^ {N}, \\quad e _ {i} = \\left(u _ {i}, v _ {i}, t _ {i}, p _ {i}\\right). \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.84,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Event Representation. We adopt a voxel grid [106] representation, where events are discretized along the time axis into \\(B\\) bins. Given \\(N\\) input events, timestamps are normalized to \\([0,B - 1]\\), and the event volume is constructed as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.538,
+ 0.369,
+ 0.907,
+ 0.412
+ ],
+ "angle": 0,
+ "content": "\\[\nE (u, v, b) = \\sum_ {i = 1} ^ {N} p _ {i} k _ {\\mathcal {B}} (u - u _ {i}) k _ {\\mathcal {B}} (v - v _ {i}) k _ {\\mathcal {B}} (b - b _ {i} ^ {*}), \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.416,
+ 0.907,
+ 0.476
+ ],
+ "angle": 0,
+ "content": "where \\( b_{i}^{*} = (B - 1)(t_{i} - t_{1}) / (t_{N} - t_{1}) \\) and \\( k_{\\mathcal{B}}(a) \\) is a bilinear sampling kernel. The voxel grid allows efficient feature extraction via 2D convolution across spatial dimensions while conserving temporal information."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.477,
+ 0.909,
+ 0.613
+ ],
+ "angle": 0,
+ "content": "We use the event stream from the recent interval \\(\\Delta \\tau\\), denoted as \\(\\mathcal{E}_{(\\tau - \\Delta \\tau) \\to \\tau} = \\{(u, v, t, p) \\mid \\tau - \\Delta \\tau \\leq t < \\tau\\}\\), to detect 3D boxes at time \\(\\tau\\). To achieve the continuous-time detection framework, \\(\\Delta \\tau\\) can adapt flexibly to different scenarios. This enables detection at arbitrary time points, making the framework adaptable to various situations. To simplify notation in this section, we represent the voxel grids generated from \\(\\mathcal{E}_{(\\tau - \\Delta \\tau) \\to \\tau}\\) as \\(E_L\\) and \\(E_R\\) for the left and right cameras, respectively."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.62,
+ 0.798,
+ 0.636
+ ],
+ "angle": 0,
+ "content": "3.2. Geometric Plane-Sweep Volume"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.642,
+ 0.909,
+ 0.869
+ ],
+ "angle": 0,
+ "content": "We illustrate the overall training pipeline in Fig. 2. We modify the PSMNet [7] to design our feature extractor and incorporated an additional feature head to disentangle the roles of semantics-based detection and geometric scene construction. This allows the extractor to separately extract semantic features \\( F_{L,R}^{sem} \\) and geometric features \\( F_{L,R}^{geo} \\), each with a dimension of \\( \\mathbb{R}^{H\\times W\\times C} \\). The semantic feature activates well on objects through an auxiliary 2D dense head on the 2D image. The geometric feature activates across the entire scene on the stereo images, concentrating on finding correspondences. First, we generate a geometric plane-sweep volume \\( \\mathcal{V}_{geo}\\in \\mathbb{R}^{H\\times W\\times D\\times C} \\) by concatenating left and corresponding right geometric features at each depth level \\( D \\) as done in previous works [11, 34]. The volume is defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.53,
+ 0.872,
+ 0.907,
+ 0.906
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {V} _ {g e o} (u, v, w) = \\left(F _ {L} ^ {g e o} (u, v) | | F _ {R} ^ {g e o} \\left(u - \\frac {f L}{d (w)}, v\\right)\\right), \\quad (4)\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
+ 0.945,
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+ ],
+ "angle": 0,
+ "content": "6871"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.095,
+ 0.089,
+ 0.478,
+ 0.26
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.264,
+ 0.483,
+ 0.307
+ ],
+ "angle": 0,
+ "content": "Figure 3. Dual semantic-geometric filter. Semantic and geometric information interact complementarily to enhance both the semantic features and the depth volume."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.32,
+ 0.484,
+ 0.501
+ ],
+ "angle": 0,
+ "content": "where \\((u,v)\\) are pixel coordinates, \\(||\\) denotes the concatenation, \\(w = 0,1,\\ldots\\) is the candidate depth index, and \\(d(w) = w\\cdot v_{d} + z_{\\mathrm{min}}\\) is the function to calculate the corresponding depth, where \\(v_{d}\\) is the depth interval and \\(z_{\\mathrm{min}}\\) is the minimum depth of the detection area. \\(f\\) and \\(L\\) represent the camera focal length and the baseline of the stereo camera pair, respectively. From the geometric stereo volume \\(\\nu_{\\mathrm{geo}}\\) we apply 3D convolutions to reduce the channel dimension, followed by a softmax operation along the depth dimension, resulting in a depth probability volume \\(\\mathcal{P}_{\\mathrm{geo}}\\in \\mathbb{R}^{H\\times W\\times D}\\), where \\(\\mathcal{P}_{\\mathrm{geo}}(u,v,:)\\) represents the depth probability for pixel \\((u,v)\\) across all depth levels."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.502,
+ 0.484,
+ 0.609
+ ],
+ "angle": 0,
+ "content": "To transform the feature volume from stereo space to a 3D space, the 3D detection area is segmented into uniformly sized voxels, resulting in \\(\\mathbf{V}_{geo}^{3D}\\in \\mathbb{R}^{X\\times Y\\times Z\\times C}\\). For each voxel, its center coordinates \\((x,y,z)\\) are projected back into the stereo space using the intrinsic parameters \\(K\\), resulting in the reprojected pixel coordinates \\((u,v)\\) and a corresponding depth index \\(d^{-1}(z) = (z - z_{\\mathrm{min}}) / v_d\\) as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.166,
+ 0.616,
+ 0.483,
+ 0.637
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {V} _ {g e o} ^ {3 D} (x, y, z) = \\mathcal {V} _ {g e o} (u, v, d ^ {- 1} (z)). \\qquad (5)\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.652,
+ 0.375,
+ 0.668
+ ],
+ "angle": 0,
+ "content": "3.3. Dual Semantic-Geometric Filter"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.675,
+ 0.483,
+ 0.795
+ ],
+ "angle": 0,
+ "content": "Along with the geometric volume, we leverage the event camera's robustness in detecting objects on the 2D plane by using semantic features to construct a 3D semantic volume \\(\\mathbf{V}_{sem}^{3D} \\in \\mathbb{R}^{X \\times Y \\times Z \\times C}\\). Creating a 3D volume with only semantic features fails to capture geometric properties. To address this, we propose a dual semantic-geometric filter that combines both semantic and geometric information, as shown in Figure 3."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.796,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Semantic-guided Depth Refinement. One of the key challenges in 3D detection using stereo cameras is achieving accurate depth inference. Unlike LiDAR, stereo cameras do not provide direct depth measurements from the sensor. To enhance depth accuracy, we utilize semantic information to refine the geometric cost volume. As shown in Fig. 3, we first estimate the initial depth \\( D_{init} \\) by computing the"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.183
+ ],
+ "angle": 0,
+ "content": "weighted sum over all depth levels using the depth probability volume \\(\\mathcal{P}_{geo}\\). Additionally, to refine the depth distribution volume by transferring accuracy through the semantic feature, which effectively captures semantic information about the scene, we compute the similarity for each pixel based on the predicted depth as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.525,
+ 0.187,
+ 0.907,
+ 0.22
+ ],
+ "angle": 0,
+ "content": "\\[\nS (u, v) = \\left\\langle F _ {L} ^ {s e m} (u, v), F _ {R} ^ {s e m} \\left(u - \\frac {f L}{D _ {i n i t} (u , v)}, v\\right) \\right\\rangle , \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.224,
+ 0.905,
+ 0.269
+ ],
+ "angle": 0,
+ "content": "where \\(\\langle \\cdot ,\\cdot \\rangle\\) denotes the inner product for similarity. Similar to previous works [8, 75, 78, 91] that handle confidence in stereo matching, we also compute confidence as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.521,
+ 0.274,
+ 0.907,
+ 0.307
+ ],
+ "angle": 0,
+ "content": "\\[\nC (u, v) = \\sum_ {w} \\mathcal {P} _ {g e o} (u, v, w) \\cdot \\left(d (w) - D ^ {\\text {i n i t}} (u, v)\\right) ^ {2}, \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.311,
+ 0.906,
+ 0.372
+ ],
+ "angle": 0,
+ "content": "We aim to refine the depth distribution by considering both stereo similarity and confidence. Adapting the refinement process from [91], we generate filtered volume, \\(\\tilde{\\mathcal{P}}_{geo}\\), by incorporating neighboring probabilities as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.514,
+ 0.377,
+ 0.815,
+ 0.394
+ ],
+ "angle": 0,
+ "content": "\\[\nW _ {m} (u, v) = S _ {m} (u, v) \\cdot \\text {s i g m o i d} \\left(C _ {m} (u, v)\\right),\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.514,
+ 0.398,
+ 0.907,
+ 0.45
+ ],
+ "angle": 0,
+ "content": "\\[\n\\tilde {\\mathcal {P}} _ {g e o} (u, v, w) = \\sum_ {m = 1} ^ {M} \\mathcal {P} _ {g e o} (u, v, w) \\cdot \\operatorname {s o f t m a x} _ {m} \\left(W _ {m} (u, v)\\right), \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.451,
+ 0.906,
+ 0.527
+ ],
+ "angle": 0,
+ "content": "where \\(m = 1,2,3,\\ldots ,M\\) are the sampled neighboring pixels and \\(\\mathrm{softmax}_m\\) denotes a softmax across the \\(m\\) dimension. Through this refinement process, depth ambiguity can be resolved, and we estimate the refined depth, \\(\\tilde{D}\\), from the refined probability."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.527,
+ 0.907,
+ 0.786
+ ],
+ "angle": 0,
+ "content": "Geometric-filtered Semantic Volume. Although semantic features are well activated for objects, event data is sparse along the spatial dimension, often leading to ambiguity. To compensate for this lack of information, we enhance the left features using the estimated depth and the semantic features from the right camera. As shown in the bottom of Fig. 3, we warp the right semantic features to the left camera using the estimated depth: \\(\\hat{F}_R^{sem} = \\mathrm{Warp}(F_R^{sem},\\tilde{D})\\). However, directly using these warped features may introduce occlusion issues and fail to fully address potential misalignments between stereo cameras. To handle these challenges, we apply a transformer-based channel attention mechanism to generate enhanced semantic features. We generate the query, key, and value features as follows: \\(\\mathbf{Q} = W_{Q}(F_{L}^{sem})\\), \\(\\mathbf{K} = W_{K}(\\hat{F}_{R}^{sem})\\), and \\(\\mathbf{V} = W_{V}(\\hat{F}_{R}^{sem})\\), where \\(W_{(\\cdot)}\\) represents a \\(1\\times 1\\) convolution. The results of the transformer are computed in this manner:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.518,
+ 0.789,
+ 0.905,
+ 0.839
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbb {A} \\left(F _ {L} ^ {\\text {s e m}}, \\hat {F} _ {R} ^ {\\text {s e m}}\\right) = F _ {L} ^ {\\text {s e m}} + W _ {\\mathbb {A}} \\left(\\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {Q K} ^ {T}}{\\alpha}\\right) \\cdot \\mathbf {V}\\right) \\tag {9}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.845,
+ 0.905,
+ 0.876
+ ],
+ "angle": 0,
+ "content": "where \\(\\alpha\\) is a learnable parameter. Finally, the geometrically enhanced semantic feature \\(\\bar{F}_L^{sem}\\) is obtained:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.601,
+ 0.879,
+ 0.905,
+ 0.898
+ ],
+ "angle": 0,
+ "content": "\\[\n\\tilde {F} _ {L} ^ {s e m} = F _ {L} ^ {s e m} + \\operatorname {M L P} (\\mathbb {A}) + \\mathbb {A}. \\tag {10}\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
+ 0.945,
+ 0.516,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "6872"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.107,
+ 0.089,
+ 0.468,
+ 0.25
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.115,
+ 0.256,
+ 0.459,
+ 0.27
+ ],
+ "angle": 0,
+ "content": "Figure 4. Illustration of the object-centric ROI alignment."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.285,
+ 0.484,
+ 0.348
+ ],
+ "angle": 0,
+ "content": "Similar to Eq. (5), voxels can be projected onto the image plane to map 2D semantic features to 3D. However, to ensure the transformation is based on geometric information, we apply a depth probability mask as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.108,
+ 0.357,
+ 0.483,
+ 0.378
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {V} _ {s e m} ^ {3 D} (x, y, z) = \\tilde {F} _ {L} ^ {s e m} (u, v) \\cdot \\tilde {\\mathcal {P}} _ {g e o} (u, v, d ^ {- 1} (z)) \\tag {11}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.388,
+ 0.484,
+ 0.495
+ ],
+ "angle": 0,
+ "content": "Fusion of Semantic and Geometric Voxels. We generate two types of voxels in the 3D space: one specialized for geometric information, \\(\\mathbf{V}_{geo}^{3D}\\), and the other for semantic information, \\(\\mathbf{V}_{sem}^{3D}\\). To integrate the two voxels into a unified 3D voxel that effectively combines both aspects, we concatenated and then merged them through 3D convolution, resulting in the fused voxel, \\(\\mathbf{V}^{3D}\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.506,
+ 0.277,
+ 0.52
+ ],
+ "angle": 0,
+ "content": "3.4. Global 3D Detector"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.527,
+ 0.484,
+ 0.771
+ ],
+ "angle": 0,
+ "content": "Inspired by recent stereo 3D detection approaches [11, 12, 34], we designed an anchor-based detector. The bird's-eye view (BEV) feature strikes a balance between accuracy and computational efficiency in 3D detection for autonomous driving. The unified 3D voxel features \\(\\mathbf{V}^{3D} \\in \\mathbb{R}^{X \\times Y \\times Z \\times C}\\) are downsampled along the height dimension to produce a BEV feature of size \\((X, Z)\\). We utilize fixed-size class anchors, determined based on the training set statistics, and assign a predefined number of anchors with varying sizes and orientations to each BEV feature location \\((x, z)\\). Similar to previous works [11, 12, 34], the dense head network performs a regression from the anchor \\(A = (x_{a}, y_{a}, z_{a}, h_{a}, w_{a}, l_{a}, \\theta_{a})\\) to predict the offset \\(\\Delta P_{G} = (\\delta x, \\delta y, \\delta z, \\delta h, \\delta w, \\delta l, \\delta \\theta)\\). The final prediction is calculated by applying an offset to the anchor to determine the global position using the box decoding function \\(g_{d}\\),"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.1,
+ 0.782,
+ 0.482,
+ 0.827
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} P _ {G} = g _ {d} (A, \\Delta P _ {G}) = \\left(x _ {a} + \\delta x, y _ {a} + \\delta y, z _ {a} + \\delta z, \\right. \\\\ h _ {a} e ^ {\\delta h}, w _ {a} e ^ {\\delta w}, l _ {a} e ^ {\\delta l}, \\theta_ {a} + \\frac {\\pi}{2} \\tanh (\\delta \\theta)). \\tag {12} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.848,
+ 0.367,
+ 0.866
+ ],
+ "angle": 0,
+ "content": "3.5. Object-Centric ROI Alignment"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.87,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "The geometric-semantic fused 3D voxels, \\(\\mathbf{V}^{3D}\\), generated through the semantic-geometric dual filter contain accurate"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.212
+ ],
+ "angle": 0,
+ "content": "depth and rich semantic information, enabling bounding box prediction in the global scene. However, a single-stage global regression can struggle with ambiguity caused by the motion of objects and the movement of the ego vehicle, especially as motion intensifies, necessitating a method that aligns more accurately with the object. To this end, we propose a method for locally aligning the ROI around the object's bounding box."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.213,
+ 0.907,
+ 0.578
+ ],
+ "angle": 0,
+ "content": "ROI Pooling and Local Regression. As shown in Fig. 4, we use the semantic voxel, \\(\\mathbf{V}_{sem}^{3D}\\), which focuses on the object and provides rich edge information from event-based semantic data, making it advantageous for ROI alignment. To optimize the computation of alignment, and because most stereo-based detections are prone to error along the \\(X\\) and \\(Z\\) dimensions, we project the voxel features onto the BEV, which corresponds to the transformation of \\(\\mathbf{B}_{sem}^{2D} \\in \\mathbb{R}^{X \\times Z \\times C'}\\) to the BEV of \\(\\mathbf{V}_{sem}^{3D}\\), rather than using them directly. Since \\(\\mathbf{B}_{sem}^{2D}\\) is splatted based on depth probabilities, it tends to cluster around the high-likelihood hypotheses of the predicted boxes. Therefore, to ensure that not only the exactly overlapping features but also the surrounding information is aggregated during alignment, we use a pooling scheme. Specifically, each bounding box prediction from global 3D detector, \\(P_{G}\\), is split into an \\(k \\times k\\) voxel grid. The semantic BEV feature, \\(\\mathbf{B}_{sem}^{2D}\\), is then pooled [23] for each voxel grid. The pooled feature of each bounding box, \\(\\hat{\\mathbf{B}}_{sem}^{2D} \\in \\mathbb{R}^{k^2 \\times C'}\\), encodes object-centric local information, serving as a cue for precisely aligning the box. Each pooled feature passes through an MLP layer to predict the local alignment offset, \\(\\Delta P_{L} = (\\delta x', \\delta y', \\delta z', \\delta h', \\delta w', \\delta l', \\delta \\theta')\\). The final fine-grained regression, \\(\\tilde{P}_{G}\\), is calculated by box decoding function: \\(\\tilde{P}_{G} = g_{d}(P_{G}, \\Delta P_{L})\\)"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
+ 0.587,
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+ "content": "3.6. Objective Function"
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "A multi-task loss was applied to train the network, which includes the geometric plane-sweep volume, the dual semantic-geometric branch, the global 3D detector head, and object-centric ROI alignment module as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {i n i t}} + \\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {r e f i n e}} + \\mathcal {L} _ {2 D} + \\mathcal {L} _ {\\text {c l s}} + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {g l o b a l}} + \\mathcal {L} _ {\\text {r e g}} ^ {\\text {l o c a l}}. \\tag {13}\n\\]"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(\\mathcal{L}_{depth}^{init},\\mathcal{L}_{2D},\\mathcal{L}_{cls}\\) are adapted from uni-modal depth loss, 2D detection loss, and classification loss in [34]. For refined depth loss, we utilized smooth \\(L_{1}\\) loss [44] as"
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+ "type": "equation",
+ "bbox": [
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+ "content": "\\[\n\\mathcal {L} _ {\\text {d e p t h}} ^ {\\text {r e f i n e}} = \\operatorname {s m o o t h} _ {L _ {1}} \\left(D _ {g t} - \\tilde {D}\\right). \\tag {14}\n\\]"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The regression loss for the global 3D detector and object-centric ROI alignment are as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {r e g} ^ {\\text {g l o b a l}} = \\mathcal {L} _ {r e g} \\left(P _ {G}, G\\right), \\quad \\mathcal {L} _ {r e g} ^ {\\text {l o c a l}} = \\mathcal {L} _ {r e g} \\left(\\tilde {P} _ {G}, G\\right) \\tag {15}\n\\]"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(G\\) refers to 3D ground-truth bounding box and \\(\\mathcal{L}_{reg}\\) is 3D regression loss adapted from [34]."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. Comparison on the DSEC-3DOD dataset for vehicle (IoU = 0.7) and pedestrian (IoU = 0.5) detection on 3D and BEV. We follow the evaluation protocol of Ev-3DOD [22] for 100 FPS 3D detection in blind time. Mod. is an abbreviation for moderate, and easy and moderate represent difficulty levels. VEH and PED represent vehicle and pedestrian, respectively."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "content": "| Modality | Methods | VEH AP3D | VEH APBEV | PED AP3D | PED APBEV |
| Easy | Mod. | Easy | Mod. | Easy | Mod. | Easy | Mod. |
| LiDAR | VoxelNeXt [14] | 12.66 | 11.06 | 31.46 | 28.39 | 10.59 | 6.61 | 12.77 | 7.96 |
| HEDNet [101] | 14.31 | 12.96 | 29.94 | 27.85 | 10.16 | 8.29 | 11.90 | 6.89 |
| LiDAR+RGB | Focals Conv [13] | 12.71 | 11.69 | 26.14 | 23.83 | 8.92 | 5.50 | 12.54 | 7.83 |
| LoGoNet [49] | 17.65 | 15.39 | 32.55 | 29.19 | 11.66 | 8.20 | 15.09 | 9.77 |
| LiDAR+RGB+Event | Ev-3DOD [22] | 29.53 | 25.07 | 49.31 | 44.44 | 18.42 | 12.49 | 29.06 | 20.34 |
| RGB-Stereo | DSGN [11] | 16.29 | 13.45 | 31.90 | 27.53 | 4.06 | 2.42 | 6.08 | 3.74 |
| LIGA [34] | 14.26 | 10.98 | 27.25 | 25.11 | 6.02 | 3.58 | 8.73 | 4.89 |
| Event-Stereo | Ours | 23.47 | 19.62 | 40.13 | 33.03 | 19.86 | 12.93 | 22.91 | 14.34 |
"
+ },
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+ "type": "title",
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+ "content": "4. Experiments"
+ },
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+ "type": "title",
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+ "angle": 0,
+ "content": "4.1. Dataset"
+ },
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+ "content": "DSEC-3DOD Dataset. The DSEC-3DOD dataset is the real-world event-based 3D detection dataset introduced in the Ev-3DOD [22]. It is based on the DSEC [31], a stereo event dataset for driving scenarios. DSEC-3DOD contains manually created 10 FPS annotations for vehicle and pedestrian classes and provides blind-time annotations at 100 FPS through interpolation and refinement. We used the widely adopted KITTI metric [32] from frame-based stereo methods, which measures performance in both BEV (bird-eyeview) and 3D for each class."
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+ "content": "4.2. Experiment Setup"
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+ "content": "3D Detection during Blind Time. Consistent with the training and evaluation protocol of existing event-based 3D object detection [22], we train and evaluate using 100 FPS annotations during blind time, when no LiDAR data is available due to the fixed frame rate of LiDAR (i.e., 10 FPS). To achieve this, we sliced the event stream at \\(\\Delta \\tau = 10\\) ms and converted it into a voxel grid."
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+ "type": "text",
+ "bbox": [
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+ "content": "Motion Scale and Time Slice. The strength of event cameras lies in their ability to provide continuous information over time, even in dynamic motion [4, 26]. Therefore, experiments on dynamic and long-range motion during blind time are crucial to demonstrate the advantages of the asynchronous setup. However, the DSEC-3DOD dataset mostly lacks such scenes, as its average ego velocity is below 10 m/s. To address this, we introduce an experimental setup, motion scale (MS), which scales time axis for large motion experiments that closely resemble the real world. Accumulation and normalization of events over a longer period can approximate events with larger motion over the same time span. Therefore, increasing the motion scale in experiments can depict dynamic environments by skipping consecutive annotations and accumulating events over a longer period. Time slice (TS) refers to the number of divisions applied"
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+ "bbox": [
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+ "content": "\\(t = 0\\) \\(t = 0.3\\)"
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+ "content": "\\(t = 0.6\\) \\(t = 0.9\\)"
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+ {
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 5. Comparison of 3D detection during blind time. \\( t = 0 \\) and \\( t = 1 \\) represent active time, while \\( t = 0.3 \\), 0.6, and 0.9 indicate normalized blind time intervals."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "to the blind time, where detection performance is evaluated at each time slice instance. Since various event input durations are used, this setup reflects the real-world demand for asynchronous detection. The baseline setup is defined with a motion scale of 1 and a time slice of 10, which corresponds to the 10 FPS fixed-frame rate data provided in the DSEC-3DOD dataset and the blind time annotations sliced into 10 parts (i.e., 100 FPS GT). To ensure compatibility with the original ground truth, experiments were conducted with motion scale values of 2 and 4 and time slice values of 10 and 20. The model is trained using the original 100 FPS GT with a motion scale of 1 and a time slice of 10 and is evaluated across various motion scales and time slices. More details about the experimental settings are provided in the supplementary material."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.3. Results on 3D Detection during Blind Time"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1 provides the results of 3D detection performed during blind time. Results from previous works [13, 14, 49,"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Performance evaluation across various motion scales and time slices, presenting results for the easy difficulty level. Each entry corresponds to 3D / BEV detection results. VEH and PED represent vehicle and pedestrian, respectively."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Motion Scale | Time Slice | Class | LiDAR | LIDAR+RGB | LiDAR+RGB+Event | RGB Stereo | Event Stereo |
| VoxelNeXt [14] | HEDNet [101] | Focals Conv [13] | LoGoNet [49] | Ev-3DOD [22] | DSGN [11] | LIGA [34] | Ours |
| ×2 | ×10 | VEH | 5.05 / 13.00 | 6.03 / 12.87 | 5.95 / 12.48 | 5.97 / 13.57 | 15.68 / 30.59 | 7.33 / 17.36 | 6.00 / 12.87 | 22.72 / 39.81 |
| PED | 4.07 / 4.89 | 3.40 / 4.05 | 3.16 / 4.79 | 2.24 / 3.72 | 7.88 / 12.19 | 1.87 / 3.04 | 2.27 / 4.00 | 19.04 / 22.71 |
| ×20 | VEH | 4.34 / 11.76 | 5.26 / 11.67 | 5.76 / 11.40 | 5.42 / 12.40 | 15.96 / 31.13 | 7.13 / 16.43 | 5.67 / 12.00 | 23.47 / 40.13 |
| PED | 3.83 / 4.31 | 2.60 / 3.49 | 2.66 / 3.86 | 1.91 / 2.90 | 1.47 / 2.63 | 1.84 / 2.99 | 2.08 / 3.01 | 19.86 / 22.91 |
| ×4 | ×10 | VEH | 2.05 / 5.22 | 2.87 / 4.63 | 2.73 / 4.48 | 1.90 / 5.26 | 6.24 / 11.62 | 3.12 / 7.20 | 2.10 / 4.89 | 20.70 / 37.08 |
| PED | 2.21 / 2.44 | 1.64 / 1.85 | 1.34 / 1.85 | 1.17 / 1.55 | 3.04 / 4.09 | 0.60 / 0.77 | 1.11 / 1.30 | 16.71 / 21.93 |
| ×20 | VEH | 1.71 / 4.55 | 2.27 / 4.29 | 2.73 / 3.94 | 1.90 / 4.66 | 6.36 / 11.70 | 3.09 / 6.52 | 1.54 / 4.17 | 22.72 / 39.81 |
| PED | 2.14 / 2.17 | 1.10 / 1.42 | 1.02 / 1.44 | 0.53 / 1.28 | 0.39 / 0.43 | 0.59 / 0.75 | 0.82 / 1.12 | 19.04 / 22.71 |
"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "[101] were taken from the supplementary material of Ev-3DOD [22], while we trained and evaluated frame-based stereo methods, DSGN [11] and LIGA [34], from scratch. Methods relying solely on synchronized sensors struggle to handle blind time, resulting in poor performance. On the other hand, both Ev-3DOD and our method utilize event cameras to overcome the limitations of fixed frame rates, enabling effective 3D detection during blind time and achieving high performance. While Ev-3DOD benefits from LiDAR-based depth information, generally outperforming our event-only approach, it is noteworthy that our method achieves superior performance in pedestrian \\(\\mathrm{AP}_{3D}\\). Pedestrian detection requires fine detail, and our high performance on this class is due to specialized modules that effectively leverage semantic features from event data."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5 illustrates another advantage of the asynchronous setup. While Ev-3DOD shows a decline in qualitative results as it moves further from active time 0, where LiDAR data is available, our method maintains high performance by computing geometric information from events, allowing it to operate independently of active time."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Diverse Motion Scales and Time Slices"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2 shows the comparison of ours with different methods across various motion scales and time slices. Methods relying solely on synchronized sensors [11, 13, 14, 34, 49, 101] exhibit a significant performance drop as the motion scale increases during blind time. Our primary comparison method, Ev-3DOD [22], utilizes event data during blind time, allowing it to handle moderate scenarios well, as shown in Table 1. However, as the motion increases, its performance significantly drops. This is because Ev-3DOD relies entirely on LiDAR for 3D geometric information, and when large motion occurs, scene changes make past geometric information less useful for the present. In contrast, our method computes 3D geometric information using asynchronous event data, resulting in more stable performance across different motion scales. Therefore, in scenar"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Table 3. Ablation study on modules for 3D detection during blind time. DSGF: Dual Semantic-Geometric Filter. SDR: Semantic-Guided Depth Refinement. GSV: Geometric-Filtered Semantic Volume. OCRA: Object-Centric ROI Alignment. The fused voxel source is denoted as G or S, where G represents geometric voxel and S represents semantic voxel."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| DSGF | 3D Voxel Source | OCRA | mAP Easy |
| SDR | GSV | 3D | BEV |
| | G | | 12.92 | 20.78 |
| | G+S | | 14.60 | 24.85 |
| | G | ✓ | 14.56 | 21.73 |
| | G+S | ✓ | 15.95 | 26.12 |
| ✓ | | G+S | | 15.85 | 27.78 |
| ✓ | G+S | | 17.08 | 26.53 |
| ✓ | ✓ | G+S | | 19.12 | 29.64 |
| ✓ | ✓ | G+S | ✓ | 21.66 | 31.52 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "ios with high-speed driving or significant scene changes due to dynamic motion, our event-based 3D detection proves highly effective during blind time."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Ablation Study"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Ablation Study on Modules. As shown in Table 3, we conduct an ablation study on the proposed modules. Starting from a baseline that performs 3D detection using only the geometric plane-sweep volume, we incrementally add the proposed modules to evaluate their impact on performance. We report the easy mAP performance, which is the average value across the two classes, VEH and PED, measured under a motion scale of 1 and a time slice of 10. Compared to the baseline, simply adding semantic information results in sub-optimal performance, yielding only a 1.68 improvement in 3D detection. However, incorporating a dual semantic-geometric filter, which facilitates interaction between semantic and geometric features, leads to a significant performance gain of 6.2 in 3D detection. Additionally, the proposed object-centric ROI alignment consistently improves performance across all settings. When"
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+ ],
+ [
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 6. Comparison of 3D detection during blind time. Ev-3DOD detects new objects only at the active timestamps, \\( t = 0,1,2 \\), using LiDAR and RGB. In contrast, the proposed model can capture the emergence of new objects at arbitrary times."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Performance of RGB fusion. Results of easy difficulty level with a time slice of 10."
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "| Settings | Methods | AP3D | APBEV |
| VEH | PED | VEH | PED |
| Motion ×1 | Ours (E) | 23.47 | 19.86 | 40.13 | 22.91 |
| Ours (E+I) | 25.23 | 21.50 | 46.21 | 29.14 |
| Motion ×2 | Ours (E) | 22.72 | 19.04 | 39.81 | 22.71 |
| Ours (E+I) | 20.14 | 10.50 | 37.93 | 12.76 |
"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "used alongside a dual semantic-geometric filter, it further enhances semantic BEV features, resulting in a more significant performance boost."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "RGB Fusion. Table 4 presents the results of fusing synchronous RGB information into our method. The stereo RGB features are extracted using a separate feature extractor and concatenated with the event features. This fusion provides improved performance under small motion scales, as the RGB input offers additional semantic guidance. However, under large motion, the performance significantly degrades due to misalignment between the synchronous RGB data and the actual object location. In contrast, our setup that relies solely on event data demonstrates robust performance regardless of scene dynamics."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Performance Degradation over Blind Time. Figure 7 shows the performance over time during blind time for our method and other methods [22, 49]. To highlight robustness in challenging scenarios, we use motion scale of 2. \\( t = 0 \\) refers to the most recent synchronized sensor input timestamp, while \\( t = 0.1 \\sim 0.9 \\) represents the blind interval before the next input. The reason for the performance drop of other methods is that they rely on 3D information from synchronous sensors and struggle as the current scene diverges from recent active time \\( (t = 0) \\), making it challenging to estimate the present 3D box using past information. Thus, despite using event data, Ev-3DOD struggles to transfer past"
+ },
+ {
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+ "bbox": [
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 7. Performance comparison with other methods during blind time under the setting of motion scale 2 and time slice 10."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "3D information to the present, causing its performance to resemble LoGoNet as motion increases over time. In contrast, our method asynchronously infers both geometric and semantic information for 3D detection, allowing it to operate independently of active time."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "6. Conclusion"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this paper, we tackle 3D object detection using event stereo in a fully asynchronous setting for the first time. Unlike the previous continuous-time 3D object detection work that utilizes LiDAR, our approach does not rely on LiDAR, leading to lower performance compared to methods that fuse LiDAR and event data. However, by evaluating various motion scales and time slices, we demonstrate that our method is more adaptable and performs robustly in diverse and extreme conditions. Furthermore, we highlight the potential of event-based 3D perception in dynamic environments where event cameras are particularly beneficial, such as drone flights, high-speed driving, and robots. We hope this work inspires further research in this direction."
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+ "content": "7. Acknowledgments."
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+ "content": "This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF2022R1A2B5B03002636). This work was also supported by the Technology Innovation Program (1415187329,20024355, Development of autonomous driving connectivity technology based on sensor-infrastructure cooperation) funded By the Ministry of Trade, Industry & Energy(MOTIE, Korea)."
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+ },
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+ },
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+ "type": "ref_text",
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+# Unleashing the Temporal Potential of Stereo Event Cameras for Continuous-Time 3D Object Detection
+
+Jae-Young Kang*, Hoonhee Cho*, and Kuk-Jin Yoon KAIST
+
+{mickeykang,gnsgnsgml,kjyoon}@kaist.ac.kr
+
+# Abstract
+
+3D object detection is essential for autonomous systems, enabling precise localization and dimension estimation. While LiDAR and RGB cameras are widely used, their fixed frame rates create perception gaps in high-speed scenarios. Event cameras, with their asynchronous nature and high temporal resolution, offer a solution by capturing motion continuously. The recent approach, which integrates event cameras with conventional sensors for continuous-time detection, struggles in fast-motion scenarios due to its dependency on synchronized sensors. We propose a novel stereo 3D object detection framework that relies solely on event cameras, eliminating the need for conventional 3D sensors. To compensate for the lack of semantic and geometric information in event data, we introduce a dual filter mechanism that extracts both. Additionally, we enhance regression by aligning bounding boxes with object-centric information. Experiments show that our method outperforms prior approaches in dynamic environments, demonstrating the potential of event cameras for robust, continuous-time 3D perception. The code is available at https://github.com/mickeykang16/Ev-Stereo3D.
+
+# 1. Introduction
+
+3D object detection is essential for accurately identifying the position and dimensions of surrounding objects, making it a fundamental task in autonomous systems. Multimodal sensors, such as LiDAR and RGB cameras, play a key role. However, fixed-frame rate sensors have discrete intervals during which data cannot be collected, resulting in inevitable detection delays. This delay in capturing dynamic changes can significantly impact real-time decision-making, emphasizing the importance of high temporal resolution for reliable autonomous driving.
+
+Event cameras [27] are asynchronous sensors that continuously stream data over time, allowing them to break the trade-off between bandwidth and delay. Their high tem
+
+
+Figure 1. During blind time, our method enables fast and large motion-aware continuous 3D object detection at arbitrary points in time, including for newly appearing objects.
+
+poral resolution makes them well-suited for capturing fast motion, enabling high-speed perception even in dynamic scenarios. This capability is particularly beneficial for autonomous driving, where rapid response is critical for accident prevention and safe navigation.
+
+A recent work, Ev-3DOD [22], integrates an RGB camera, LiDAR, and an event camera to overcome the frame-rate limitations of conventional sensors in 3D object detection. By incorporating event data, it enables perception even during periods when LiDAR and RGB cameras are unavailable. Notably, it introduces continuous-time 3D object detection, allowing inference at arbitrary timestamps before the next synchronized sensor data arrives. Continuous-time 3D object detection enables accurate inference beyond the timeframes when synchronized sensors, such as RGB and LiDAR, provide data. Ev-3DOD [22] defined periods with LiDAR and RGB data as active time and intervals without them as blind time, demonstrating that event cameras can facilitate 3D detection during these blind periods.
+
+However, approaches that temporally propagate LiDAR-
+
+and image-based detection with events are highly dependent on synchronized sensors introducing limitations in dynamic environments. For example, in scenarios like drones with rapid motion during adjacent active times, or high-speed driving causing significant movement during blind periods, fixed frame-rate sensor data does not fully reflect the current 3D geometry. As a result, errors are accumulated over blind time, leading to frequent detection failures.
+
+To this end, we propose an event stereo setup that performs precise 3D object detection using only spare and asynchronous event cameras to address the limitations of conventional sensors. As shown in Fig. 1, event stereo can compute 3D information even during blind time, enabling the detection of large-moving and newly appearing objects, which are scenarios that synchronized sensors cannot handle in blind time.
+
+One of the challenges when using only event data for 3D object detection is its sparse nature. Event data lacks both semantic and geometric information compared to images and LiDAR, making accurate classification and regression particularly difficult. To overcome this, we propose a dual semantic-geometric filter module that collaboratively filters and enhances both information, fully leveraging stereo event data. The event semantic feature filters the geometric depth feature while the geometric feature simultaneously enhances the semantic information through the estimated disparity. Additionally, following the global detection head, a dense, object-centric semantic event feature is employed to align the local 3D offsets of the bounding boxes, thereby enhancing regression performance. Our proposed method achieves comparable performance in continuous-time 3D object detection without relying on rich fixed frame-rate sensor data. Specifically, through experiments in which the scene undergoes significant changes due to large motion within the same duration, as well as tests involving various intervals for inference, our approach outperforms existing methods. This result can be attributed to the use of asynchronous sensors, which offer distinct advantages in handling dynamic scenarios while fully utilizing both semantic and geometric information of events. The paper highlights the potential and scalability of event cameras to enhance 3D object detection in various environments.
+
+# 2. Related Works
+
+Camera-based 3D Object Detection. Cameras offer significant cost advantages over LiDAR, leading many researchers to focus on developing methods for 3D object detection using image-only inputs [15, 39, 43, 56, 59, 61, 64, 84, 87, 88]. However, image-based 3D detection faces challenges due to the lack of direct depth information. To address this, several works [11, 12, 34, 48, 60] propose using stereo and multi-camera systems to compute 3D geometry through multiple views. Despite these advancements, accu
+
+rately estimating depth from images remains challenging, causing image-based methods to underperform compared to LiDAR-based approaches.
+
+LiDAR-based 3D Object Detection. LiDAR-based 3D object detection can reliably estimate 3D bounding boxes using point clouds captured from LiDAR sensors. Research on representing 3D information from LiDAR has been conducted through various approaches, including point-based methods [25, 38, 80, 82, 95, 98, 104], voxel-based methods [24, 33, 37, 37, 45, 51, 65, 79, 89, 92, 100], and point-voxel fusion networks [36, 66, 81, 94]. To further boost the performance of LiDAR-based 3D detection, multi-modal sensor fusion [9, 40, 41, 49, 50, 58, 83, 90, 99] has emerged, where different sensors, such as cameras and LiDAR, complement each other. Fusion approaches are categorized into early [16, 85, 93], middle [53-55, 57, 62, 74, 76, 96], and late fusion [2, 49, 69]. Multi-modal 3D object detection has garnered significant attention for its ability to improve accuracy and enhance performance compared to unimodal methods. However, there is still room for improvement in terms of safety in autonomous driving. LiDAR and cameras have limited time resolution (i.e., $10 - 20\mathrm{Hz}$ ) because of their relatively high bandwidths. These limitations are especially noticeable in scenarios like high-speed driving or drone flight. To improve safety, algorithms that can operate at higher speeds are crucial.
+
+Event-based Stereo. Event cameras are well-suited for capturing dynamic scenes due to their high temporal resolution, low latency, and ability to operate effectively in challenging lighting conditions. Based on these characteristics, approaches using event cameras in a stereo setup [1, 19-21, 67, 68, 102, 105, 107] have been proposed to better understand the surrounding 3D dynamic scenes. Additionally, research has explored using event cameras in a stereo setup alongside other sensors [3, 10, 17, 18, 63, 103], aiming to leverage the strengths of both event data and conventional sensors to enhance perception capabilities. Building on this research direction, we demonstrate that 3D object detection can be performed using only asynchronous event cameras. Furthermore, we highlight the potential of event cameras for 3D detection in dynamic and rapid motion scenarios.
+
+Event-based Object Detection. On the 2D image plane, numerous studies [6, 28, 30, 35, 42, 46, 47, 52, 70, 71, 73, 86, 108] have leveraged the event camera's sensitivity to moving objects for object detection. Various architectures, including graph-based [5, 29, 77], spiking [97], and sparse [72] neural networks, have been explored to achieve streamlined and compelling results tailored to specific objectives. A recent study [22] demonstrated the advantages of high temporal resolution of event cameras in 3D object detection by integrating them with LiDAR and RGB cameras. This study addressed the limitation of synchronized sensors, such as RGB cameras and LiDAR, which operate
+
+
+Figure 2. Overview of the proposed method. Our method is categorized into four components: Geometric Plane-Sweep Volume (Sec. 3.2), Dual Semantic-Geometric Filter (Sec. 3.3), Global 3D Detector (Sec. 3.4), and Object-Centric ROI Alignment (Sec. 3.5).
+
+at fixed frame rates and restrict inference to discrete time intervals. By integrating event cameras, the proposed approach overcomes this constraint, enabling continuous 3D detection even in the absence of synchronized sensor input.
+
+Despite these promising results, the approach remains partially dependent on synchronization, as critical information is solely derived from RGB and LiDAR. Consequently, significant errors may occur when rapid motion leads to substantial scene changes during blind time. To address this limitation, we propose the first fully asynchronous system for 3D object detection, utilizing a stereo event camera setup. Thanks to this asynchronous advantage, our method maintains strong performance even when the scene undergoes significant changes during the blind time or when inference is required at a finer continuous-time scale.
+
+# 3. Methods
+
+# 3.1. Preliminaries
+
+Event Camera. Traditional frame-based cameras capture images at fixed intervals, whereas event cameras operate asynchronously, recording changes in logarithmic intensity $L(u,v,t)$ only when they exceed a predefined threshold $\mathcal{C}$ . This can be expressed as:
+
+$$
+L (u, v, t) - L (u, v, t - \Delta t) \geq \mathbf {p} \mathcal {C}, \quad \mathbf {p} \in \{- 1, + 1 \}, \tag {1}
+$$
+
+where $\Delta t$ represents the time difference, and $\mathbf{p}$ denotes event polarity, indicating either negative or positive events. The event stream $\mathcal{E}$ consists of events $e_i$ with spatial coordinates $(u_i, v_i)$ , timestamp $t_i$ , and polarity $p_i$ :
+
+$$
+\mathcal {E} = \left\{e _ {i} \right\} _ {i = 1} ^ {N}, \quad e _ {i} = \left(u _ {i}, v _ {i}, t _ {i}, p _ {i}\right). \tag {2}
+$$
+
+Event Representation. We adopt a voxel grid [106] representation, where events are discretized along the time axis into $B$ bins. Given $N$ input events, timestamps are normalized to $[0,B - 1]$ , and the event volume is constructed as:
+
+$$
+E (u, v, b) = \sum_ {i = 1} ^ {N} p _ {i} k _ {\mathcal {B}} (u - u _ {i}) k _ {\mathcal {B}} (v - v _ {i}) k _ {\mathcal {B}} (b - b _ {i} ^ {*}), \tag {3}
+$$
+
+where $b_{i}^{*} = (B - 1)(t_{i} - t_{1}) / (t_{N} - t_{1})$ and $k_{\mathcal{B}}(a)$ is a bilinear sampling kernel. The voxel grid allows efficient feature extraction via 2D convolution across spatial dimensions while conserving temporal information.
+
+We use the event stream from the recent interval $\Delta \tau$ , denoted as $\mathcal{E}_{(\tau - \Delta \tau) \to \tau} = \{(u, v, t, p) \mid \tau - \Delta \tau \leq t < \tau\}$ , to detect 3D boxes at time $\tau$ . To achieve the continuous-time detection framework, $\Delta \tau$ can adapt flexibly to different scenarios. This enables detection at arbitrary time points, making the framework adaptable to various situations. To simplify notation in this section, we represent the voxel grids generated from $\mathcal{E}_{(\tau - \Delta \tau) \to \tau}$ as $E_L$ and $E_R$ for the left and right cameras, respectively.
+
+# 3.2. Geometric Plane-Sweep Volume
+
+We illustrate the overall training pipeline in Fig. 2. We modify the PSMNet [7] to design our feature extractor and incorporated an additional feature head to disentangle the roles of semantics-based detection and geometric scene construction. This allows the extractor to separately extract semantic features $F_{L,R}^{sem}$ and geometric features $F_{L,R}^{geo}$ , each with a dimension of $\mathbb{R}^{H\times W\times C}$ . The semantic feature activates well on objects through an auxiliary 2D dense head on the 2D image. The geometric feature activates across the entire scene on the stereo images, concentrating on finding correspondences. First, we generate a geometric plane-sweep volume $\mathcal{V}_{geo}\in \mathbb{R}^{H\times W\times D\times C}$ by concatenating left and corresponding right geometric features at each depth level $D$ as done in previous works [11, 34]. The volume is defined as:
+
+$$
+\mathcal {V} _ {g e o} (u, v, w) = \left(F _ {L} ^ {g e o} (u, v) | | F _ {R} ^ {g e o} \left(u - \frac {f L}{d (w)}, v\right)\right), \quad (4)
+$$
+
+
+Figure 3. Dual semantic-geometric filter. Semantic and geometric information interact complementarily to enhance both the semantic features and the depth volume.
+
+where $(u,v)$ are pixel coordinates, $||$ denotes the concatenation, $w = 0,1,\ldots$ is the candidate depth index, and $d(w) = w\cdot v_{d} + z_{\mathrm{min}}$ is the function to calculate the corresponding depth, where $v_{d}$ is the depth interval and $z_{\mathrm{min}}$ is the minimum depth of the detection area. $f$ and $L$ represent the camera focal length and the baseline of the stereo camera pair, respectively. From the geometric stereo volume $\nu_{\mathrm{geo}}$ we apply 3D convolutions to reduce the channel dimension, followed by a softmax operation along the depth dimension, resulting in a depth probability volume $\mathcal{P}_{\mathrm{geo}}\in \mathbb{R}^{H\times W\times D}$ , where $\mathcal{P}_{\mathrm{geo}}(u,v,:)$ represents the depth probability for pixel $(u,v)$ across all depth levels.
+
+To transform the feature volume from stereo space to a 3D space, the 3D detection area is segmented into uniformly sized voxels, resulting in $\mathbf{V}_{geo}^{3D}\in \mathbb{R}^{X\times Y\times Z\times C}$ . For each voxel, its center coordinates $(x,y,z)$ are projected back into the stereo space using the intrinsic parameters $K$ , resulting in the reprojected pixel coordinates $(u,v)$ and a corresponding depth index $d^{-1}(z) = (z - z_{\mathrm{min}}) / v_d$ as:
+
+$$
+\mathbf {V} _ {g e o} ^ {3 D} (x, y, z) = \mathcal {V} _ {g e o} (u, v, d ^ {- 1} (z)). \qquad (5)
+$$
+
+# 3.3. Dual Semantic-Geometric Filter
+
+Along with the geometric volume, we leverage the event camera's robustness in detecting objects on the 2D plane by using semantic features to construct a 3D semantic volume $\mathbf{V}_{sem}^{3D} \in \mathbb{R}^{X \times Y \times Z \times C}$ . Creating a 3D volume with only semantic features fails to capture geometric properties. To address this, we propose a dual semantic-geometric filter that combines both semantic and geometric information, as shown in Figure 3.
+
+Semantic-guided Depth Refinement. One of the key challenges in 3D detection using stereo cameras is achieving accurate depth inference. Unlike LiDAR, stereo cameras do not provide direct depth measurements from the sensor. To enhance depth accuracy, we utilize semantic information to refine the geometric cost volume. As shown in Fig. 3, we first estimate the initial depth $D_{init}$ by computing the
+
+weighted sum over all depth levels using the depth probability volume $\mathcal{P}_{geo}$ . Additionally, to refine the depth distribution volume by transferring accuracy through the semantic feature, which effectively captures semantic information about the scene, we compute the similarity for each pixel based on the predicted depth as:
+
+$$
+S (u, v) = \left\langle F _ {L} ^ {s e m} (u, v), F _ {R} ^ {s e m} \left(u - \frac {f L}{D _ {i n i t} (u , v)}, v\right) \right\rangle , \tag {6}
+$$
+
+where $\langle \cdot ,\cdot \rangle$ denotes the inner product for similarity. Similar to previous works [8, 75, 78, 91] that handle confidence in stereo matching, we also compute confidence as follows:
+
+$$
+C (u, v) = \sum_ {w} \mathcal {P} _ {g e o} (u, v, w) \cdot \left(d (w) - D ^ {\text {i n i t}} (u, v)\right) ^ {2}, \tag {7}
+$$
+
+We aim to refine the depth distribution by considering both stereo similarity and confidence. Adapting the refinement process from [91], we generate filtered volume, $\tilde{\mathcal{P}}_{geo}$ , by incorporating neighboring probabilities as follows:
+
+$$
+W _ {m} (u, v) = S _ {m} (u, v) \cdot \text {s i g m o i d} \left(C _ {m} (u, v)\right),
+$$
+
+$$
+\tilde {\mathcal {P}} _ {g e o} (u, v, w) = \sum_ {m = 1} ^ {M} \mathcal {P} _ {g e o} (u, v, w) \cdot \operatorname {s o f t m a x} _ {m} \left(W _ {m} (u, v)\right), \tag {8}
+$$
+
+where $m = 1,2,3,\ldots ,M$ are the sampled neighboring pixels and $\mathrm{softmax}_m$ denotes a softmax across the $m$ dimension. Through this refinement process, depth ambiguity can be resolved, and we estimate the refined depth, $\tilde{D}$ , from the refined probability.
+
+Geometric-filtered Semantic Volume. Although semantic features are well activated for objects, event data is sparse along the spatial dimension, often leading to ambiguity. To compensate for this lack of information, we enhance the left features using the estimated depth and the semantic features from the right camera. As shown in the bottom of Fig. 3, we warp the right semantic features to the left camera using the estimated depth: $\hat{F}_R^{sem} = \mathrm{Warp}(F_R^{sem},\tilde{D})$ . However, directly using these warped features may introduce occlusion issues and fail to fully address potential misalignments between stereo cameras. To handle these challenges, we apply a transformer-based channel attention mechanism to generate enhanced semantic features. We generate the query, key, and value features as follows: $\mathbf{Q} = W_{Q}(F_{L}^{sem})$ , $\mathbf{K} = W_{K}(\hat{F}_{R}^{sem})$ , and $\mathbf{V} = W_{V}(\hat{F}_{R}^{sem})$ , where $W_{(\cdot)}$ represents a $1\times 1$ convolution. The results of the transformer are computed in this manner:
+
+$$
+\mathbb {A} \left(F _ {L} ^ {\text {s e m}}, \hat {F} _ {R} ^ {\text {s e m}}\right) = F _ {L} ^ {\text {s e m}} + W _ {\mathbb {A}} \left(\operatorname {s o f t m a x} \left(\frac {\mathbf {Q K} ^ {T}}{\alpha}\right) \cdot \mathbf {V}\right) \tag {9}
+$$
+
+where $\alpha$ is a learnable parameter. Finally, the geometrically enhanced semantic feature $\bar{F}_L^{sem}$ is obtained:
+
+$$
+\tilde {F} _ {L} ^ {s e m} = F _ {L} ^ {s e m} + \operatorname {M L P} (\mathbb {A}) + \mathbb {A}. \tag {10}
+$$
+
+
+Figure 4. Illustration of the object-centric ROI alignment.
+
+Similar to Eq. (5), voxels can be projected onto the image plane to map 2D semantic features to 3D. However, to ensure the transformation is based on geometric information, we apply a depth probability mask as:
+
+$$
+\mathbf {V} _ {s e m} ^ {3 D} (x, y, z) = \tilde {F} _ {L} ^ {s e m} (u, v) \cdot \tilde {\mathcal {P}} _ {g e o} (u, v, d ^ {- 1} (z)) \tag {11}
+$$
+
+Fusion of Semantic and Geometric Voxels. We generate two types of voxels in the 3D space: one specialized for geometric information, $\mathbf{V}_{geo}^{3D}$ , and the other for semantic information, $\mathbf{V}_{sem}^{3D}$ . To integrate the two voxels into a unified 3D voxel that effectively combines both aspects, we concatenated and then merged them through 3D convolution, resulting in the fused voxel, $\mathbf{V}^{3D}$ .
+
+# 3.4. Global 3D Detector
+
+Inspired by recent stereo 3D detection approaches [11, 12, 34], we designed an anchor-based detector. The bird's-eye view (BEV) feature strikes a balance between accuracy and computational efficiency in 3D detection for autonomous driving. The unified 3D voxel features $\mathbf{V}^{3D} \in \mathbb{R}^{X \times Y \times Z \times C}$ are downsampled along the height dimension to produce a BEV feature of size $(X, Z)$ . We utilize fixed-size class anchors, determined based on the training set statistics, and assign a predefined number of anchors with varying sizes and orientations to each BEV feature location $(x, z)$ . Similar to previous works [11, 12, 34], the dense head network performs a regression from the anchor $A = (x_{a}, y_{a}, z_{a}, h_{a}, w_{a}, l_{a}, \theta_{a})$ to predict the offset $\Delta P_{G} = (\delta x, \delta y, \delta z, \delta h, \delta w, \delta l, \delta \theta)$ . The final prediction is calculated by applying an offset to the anchor to determine the global position using the box decoding function $g_{d}$ ,
+
+$$
+\begin{array}{l} P _ {G} = g _ {d} (A, \Delta P _ {G}) = \left(x _ {a} + \delta x, y _ {a} + \delta y, z _ {a} + \delta z, \right. \\ h _ {a} e ^ {\delta h}, w _ {a} e ^ {\delta w}, l _ {a} e ^ {\delta l}, \theta_ {a} + \frac {\pi}{2} \tanh (\delta \theta)). \tag {12} \\ \end{array}
+$$
+
+# 3.5. Object-Centric ROI Alignment
+
+The geometric-semantic fused 3D voxels, $\mathbf{V}^{3D}$ , generated through the semantic-geometric dual filter contain accurate
+
+depth and rich semantic information, enabling bounding box prediction in the global scene. However, a single-stage global regression can struggle with ambiguity caused by the motion of objects and the movement of the ego vehicle, especially as motion intensifies, necessitating a method that aligns more accurately with the object. To this end, we propose a method for locally aligning the ROI around the object's bounding box.
+
+ROI Pooling and Local Regression. As shown in Fig. 4, we use the semantic voxel, $\mathbf{V}_{sem}^{3D}$ , which focuses on the object and provides rich edge information from event-based semantic data, making it advantageous for ROI alignment. To optimize the computation of alignment, and because most stereo-based detections are prone to error along the $X$ and $Z$ dimensions, we project the voxel features onto the BEV, which corresponds to the transformation of $\mathbf{B}_{sem}^{2D} \in \mathbb{R}^{X \times Z \times C'}$ to the BEV of $\mathbf{V}_{sem}^{3D}$ , rather than using them directly. Since $\mathbf{B}_{sem}^{2D}$ is splatted based on depth probabilities, it tends to cluster around the high-likelihood hypotheses of the predicted boxes. Therefore, to ensure that not only the exactly overlapping features but also the surrounding information is aggregated during alignment, we use a pooling scheme. Specifically, each bounding box prediction from global 3D detector, $P_{G}$ , is split into an $k \times k$ voxel grid. The semantic BEV feature, $\mathbf{B}_{sem}^{2D}$ , is then pooled [23] for each voxel grid. The pooled feature of each bounding box, $\hat{\mathbf{B}}_{sem}^{2D} \in \mathbb{R}^{k^2 \times C'}$ , encodes object-centric local information, serving as a cue for precisely aligning the box. Each pooled feature passes through an MLP layer to predict the local alignment offset, $\Delta P_{L} = (\delta x', \delta y', \delta z', \delta h', \delta w', \delta l', \delta \theta')$ . The final fine-grained regression, $\tilde{P}_{G}$ , is calculated by box decoding function: $\tilde{P}_{G} = g_{d}(P_{G}, \Delta P_{L})$
+
+# 3.6. Objective Function
+
+A multi-task loss was applied to train the network, which includes the geometric plane-sweep volume, the dual semantic-geometric branch, the global 3D detector head, and object-centric ROI alignment module as follows:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {d e p t h}} ^ {\text {i n i t}} + \mathcal {L} _ {\text {d e p t h}} ^ {\text {r e f i n e}} + \mathcal {L} _ {2 D} + \mathcal {L} _ {\text {c l s}} + \mathcal {L} _ {\text {r e g}} ^ {\text {g l o b a l}} + \mathcal {L} _ {\text {r e g}} ^ {\text {l o c a l}}. \tag {13}
+$$
+
+where $\mathcal{L}_{depth}^{init},\mathcal{L}_{2D},\mathcal{L}_{cls}$ are adapted from uni-modal depth loss, 2D detection loss, and classification loss in [34]. For refined depth loss, we utilized smooth $L_{1}$ loss [44] as
+
+$$
+\mathcal {L} _ {\text {d e p t h}} ^ {\text {r e f i n e}} = \operatorname {s m o o t h} _ {L _ {1}} \left(D _ {g t} - \tilde {D}\right). \tag {14}
+$$
+
+The regression loss for the global 3D detector and object-centric ROI alignment are as follows:
+
+$$
+\mathcal {L} _ {r e g} ^ {\text {g l o b a l}} = \mathcal {L} _ {r e g} \left(P _ {G}, G\right), \quad \mathcal {L} _ {r e g} ^ {\text {l o c a l}} = \mathcal {L} _ {r e g} \left(\tilde {P} _ {G}, G\right) \tag {15}
+$$
+
+where $G$ refers to 3D ground-truth bounding box and $\mathcal{L}_{reg}$ is 3D regression loss adapted from [34].
+
+Table 1. Comparison on the DSEC-3DOD dataset for vehicle (IoU = 0.7) and pedestrian (IoU = 0.5) detection on 3D and BEV. We follow the evaluation protocol of Ev-3DOD [22] for 100 FPS 3D detection in blind time. Mod. is an abbreviation for moderate, and easy and moderate represent difficulty levels. VEH and PED represent vehicle and pedestrian, respectively.
+
+| Modality | Methods | VEH AP3D | VEH APBEV | PED AP3D | PED APBEV |
| Easy | Mod. | Easy | Mod. | Easy | Mod. | Easy | Mod. |
| LiDAR | VoxelNeXt [14] | 12.66 | 11.06 | 31.46 | 28.39 | 10.59 | 6.61 | 12.77 | 7.96 |
| HEDNet [101] | 14.31 | 12.96 | 29.94 | 27.85 | 10.16 | 8.29 | 11.90 | 6.89 |
| LiDAR+RGB | Focals Conv [13] | 12.71 | 11.69 | 26.14 | 23.83 | 8.92 | 5.50 | 12.54 | 7.83 |
| LoGoNet [49] | 17.65 | 15.39 | 32.55 | 29.19 | 11.66 | 8.20 | 15.09 | 9.77 |
| LiDAR+RGB+Event | Ev-3DOD [22] | 29.53 | 25.07 | 49.31 | 44.44 | 18.42 | 12.49 | 29.06 | 20.34 |
| RGB-Stereo | DSGN [11] | 16.29 | 13.45 | 31.90 | 27.53 | 4.06 | 2.42 | 6.08 | 3.74 |
| LIGA [34] | 14.26 | 10.98 | 27.25 | 25.11 | 6.02 | 3.58 | 8.73 | 4.89 |
| Event-Stereo | Ours | 23.47 | 19.62 | 40.13 | 33.03 | 19.86 | 12.93 | 22.91 | 14.34 |
+
+# 4. Experiments
+
+# 4.1. Dataset
+
+DSEC-3DOD Dataset. The DSEC-3DOD dataset is the real-world event-based 3D detection dataset introduced in the Ev-3DOD [22]. It is based on the DSEC [31], a stereo event dataset for driving scenarios. DSEC-3DOD contains manually created 10 FPS annotations for vehicle and pedestrian classes and provides blind-time annotations at 100 FPS through interpolation and refinement. We used the widely adopted KITTI metric [32] from frame-based stereo methods, which measures performance in both BEV (bird-eyeview) and 3D for each class.
+
+# 4.2. Experiment Setup
+
+3D Detection during Blind Time. Consistent with the training and evaluation protocol of existing event-based 3D object detection [22], we train and evaluate using 100 FPS annotations during blind time, when no LiDAR data is available due to the fixed frame rate of LiDAR (i.e., 10 FPS). To achieve this, we sliced the event stream at $\Delta \tau = 10$ ms and converted it into a voxel grid.
+
+Motion Scale and Time Slice. The strength of event cameras lies in their ability to provide continuous information over time, even in dynamic motion [4, 26]. Therefore, experiments on dynamic and long-range motion during blind time are crucial to demonstrate the advantages of the asynchronous setup. However, the DSEC-3DOD dataset mostly lacks such scenes, as its average ego velocity is below 10 m/s. To address this, we introduce an experimental setup, motion scale (MS), which scales time axis for large motion experiments that closely resemble the real world. Accumulation and normalization of events over a longer period can approximate events with larger motion over the same time span. Therefore, increasing the motion scale in experiments can depict dynamic environments by skipping consecutive annotations and accumulating events over a longer period. Time slice (TS) refers to the number of divisions applied
+
+
+$t = 0$ $t = 0.3$
+
+
+$t = 0.6$ $t = 0.9$
+
+
+
+
+
+
+Figure 5. Comparison of 3D detection during blind time. $t = 0$ and $t = 1$ represent active time, while $t = 0.3$ , 0.6, and 0.9 indicate normalized blind time intervals.
+
+
+
+
+
+
+
+
+
+
+
+
+
+to the blind time, where detection performance is evaluated at each time slice instance. Since various event input durations are used, this setup reflects the real-world demand for asynchronous detection. The baseline setup is defined with a motion scale of 1 and a time slice of 10, which corresponds to the 10 FPS fixed-frame rate data provided in the DSEC-3DOD dataset and the blind time annotations sliced into 10 parts (i.e., 100 FPS GT). To ensure compatibility with the original ground truth, experiments were conducted with motion scale values of 2 and 4 and time slice values of 10 and 20. The model is trained using the original 100 FPS GT with a motion scale of 1 and a time slice of 10 and is evaluated across various motion scales and time slices. More details about the experimental settings are provided in the supplementary material.
+
+# 4.3. Results on 3D Detection during Blind Time
+
+Table 1 provides the results of 3D detection performed during blind time. Results from previous works [13, 14, 49,
+
+Table 2. Performance evaluation across various motion scales and time slices, presenting results for the easy difficulty level. Each entry corresponds to 3D / BEV detection results. VEH and PED represent vehicle and pedestrian, respectively.
+
+| Motion Scale | Time Slice | Class | LiDAR | LIDAR+RGB | LiDAR+RGB+Event | RGB Stereo | Event Stereo |
| VoxelNeXt [14] | HEDNet [101] | Focals Conv [13] | LoGoNet [49] | Ev-3DOD [22] | DSGN [11] | LIGA [34] | Ours |
| ×2 | ×10 | VEH | 5.05 / 13.00 | 6.03 / 12.87 | 5.95 / 12.48 | 5.97 / 13.57 | 15.68 / 30.59 | 7.33 / 17.36 | 6.00 / 12.87 | 22.72 / 39.81 |
| PED | 4.07 / 4.89 | 3.40 / 4.05 | 3.16 / 4.79 | 2.24 / 3.72 | 7.88 / 12.19 | 1.87 / 3.04 | 2.27 / 4.00 | 19.04 / 22.71 |
| ×20 | VEH | 4.34 / 11.76 | 5.26 / 11.67 | 5.76 / 11.40 | 5.42 / 12.40 | 15.96 / 31.13 | 7.13 / 16.43 | 5.67 / 12.00 | 23.47 / 40.13 |
| PED | 3.83 / 4.31 | 2.60 / 3.49 | 2.66 / 3.86 | 1.91 / 2.90 | 1.47 / 2.63 | 1.84 / 2.99 | 2.08 / 3.01 | 19.86 / 22.91 |
| ×4 | ×10 | VEH | 2.05 / 5.22 | 2.87 / 4.63 | 2.73 / 4.48 | 1.90 / 5.26 | 6.24 / 11.62 | 3.12 / 7.20 | 2.10 / 4.89 | 20.70 / 37.08 |
| PED | 2.21 / 2.44 | 1.64 / 1.85 | 1.34 / 1.85 | 1.17 / 1.55 | 3.04 / 4.09 | 0.60 / 0.77 | 1.11 / 1.30 | 16.71 / 21.93 |
| ×20 | VEH | 1.71 / 4.55 | 2.27 / 4.29 | 2.73 / 3.94 | 1.90 / 4.66 | 6.36 / 11.70 | 3.09 / 6.52 | 1.54 / 4.17 | 22.72 / 39.81 |
| PED | 2.14 / 2.17 | 1.10 / 1.42 | 1.02 / 1.44 | 0.53 / 1.28 | 0.39 / 0.43 | 0.59 / 0.75 | 0.82 / 1.12 | 19.04 / 22.71 |
+
+[101] were taken from the supplementary material of Ev-3DOD [22], while we trained and evaluated frame-based stereo methods, DSGN [11] and LIGA [34], from scratch. Methods relying solely on synchronized sensors struggle to handle blind time, resulting in poor performance. On the other hand, both Ev-3DOD and our method utilize event cameras to overcome the limitations of fixed frame rates, enabling effective 3D detection during blind time and achieving high performance. While Ev-3DOD benefits from LiDAR-based depth information, generally outperforming our event-only approach, it is noteworthy that our method achieves superior performance in pedestrian $\mathrm{AP}_{3D}$ . Pedestrian detection requires fine detail, and our high performance on this class is due to specialized modules that effectively leverage semantic features from event data.
+
+Figure 5 illustrates another advantage of the asynchronous setup. While Ev-3DOD shows a decline in qualitative results as it moves further from active time 0, where LiDAR data is available, our method maintains high performance by computing geometric information from events, allowing it to operate independently of active time.
+
+# 4.4. Diverse Motion Scales and Time Slices
+
+Table 2 shows the comparison of ours with different methods across various motion scales and time slices. Methods relying solely on synchronized sensors [11, 13, 14, 34, 49, 101] exhibit a significant performance drop as the motion scale increases during blind time. Our primary comparison method, Ev-3DOD [22], utilizes event data during blind time, allowing it to handle moderate scenarios well, as shown in Table 1. However, as the motion increases, its performance significantly drops. This is because Ev-3DOD relies entirely on LiDAR for 3D geometric information, and when large motion occurs, scene changes make past geometric information less useful for the present. In contrast, our method computes 3D geometric information using asynchronous event data, resulting in more stable performance across different motion scales. Therefore, in scenar
+
+Table 3. Ablation study on modules for 3D detection during blind time. DSGF: Dual Semantic-Geometric Filter. SDR: Semantic-Guided Depth Refinement. GSV: Geometric-Filtered Semantic Volume. OCRA: Object-Centric ROI Alignment. The fused voxel source is denoted as G or S, where G represents geometric voxel and S represents semantic voxel.
+
+| DSGF | 3D Voxel Source | OCRA | mAP Easy |
| SDR | GSV | 3D | BEV |
| | G | | 12.92 | 20.78 |
| | G+S | | 14.60 | 24.85 |
| | G | ✓ | 14.56 | 21.73 |
| | G+S | ✓ | 15.95 | 26.12 |
| ✓ | | G+S | | 15.85 | 27.78 |
| ✓ | G+S | | 17.08 | 26.53 |
| ✓ | ✓ | G+S | | 19.12 | 29.64 |
| ✓ | ✓ | G+S | ✓ | 21.66 | 31.52 |
+
+ios with high-speed driving or significant scene changes due to dynamic motion, our event-based 3D detection proves highly effective during blind time.
+
+# 5. Ablation Study
+
+Ablation Study on Modules. As shown in Table 3, we conduct an ablation study on the proposed modules. Starting from a baseline that performs 3D detection using only the geometric plane-sweep volume, we incrementally add the proposed modules to evaluate their impact on performance. We report the easy mAP performance, which is the average value across the two classes, VEH and PED, measured under a motion scale of 1 and a time slice of 10. Compared to the baseline, simply adding semantic information results in sub-optimal performance, yielding only a 1.68 improvement in 3D detection. However, incorporating a dual semantic-geometric filter, which facilitates interaction between semantic and geometric features, leads to a significant performance gain of 6.2 in 3D detection. Additionally, the proposed object-centric ROI alignment consistently improves performance across all settings. When
+
+
+Figure 6. Comparison of 3D detection during blind time. Ev-3DOD detects new objects only at the active timestamps, $t = 0,1,2$ , using LiDAR and RGB. In contrast, the proposed model can capture the emergence of new objects at arbitrary times.
+
+Table 4. Performance of RGB fusion. Results of easy difficulty level with a time slice of 10.
+
+| Settings | Methods | AP3D | APBEV |
| VEH | PED | VEH | PED |
| Motion ×1 | Ours (E) | 23.47 | 19.86 | 40.13 | 22.91 |
| Ours (E+I) | 25.23 | 21.50 | 46.21 | 29.14 |
| Motion ×2 | Ours (E) | 22.72 | 19.04 | 39.81 | 22.71 |
| Ours (E+I) | 20.14 | 10.50 | 37.93 | 12.76 |
+
+used alongside a dual semantic-geometric filter, it further enhances semantic BEV features, resulting in a more significant performance boost.
+
+RGB Fusion. Table 4 presents the results of fusing synchronous RGB information into our method. The stereo RGB features are extracted using a separate feature extractor and concatenated with the event features. This fusion provides improved performance under small motion scales, as the RGB input offers additional semantic guidance. However, under large motion, the performance significantly degrades due to misalignment between the synchronous RGB data and the actual object location. In contrast, our setup that relies solely on event data demonstrates robust performance regardless of scene dynamics.
+
+Performance Degradation over Blind Time. Figure 7 shows the performance over time during blind time for our method and other methods [22, 49]. To highlight robustness in challenging scenarios, we use motion scale of 2. $t = 0$ refers to the most recent synchronized sensor input timestamp, while $t = 0.1 \sim 0.9$ represents the blind interval before the next input. The reason for the performance drop of other methods is that they rely on 3D information from synchronous sensors and struggle as the current scene diverges from recent active time $(t = 0)$ , making it challenging to estimate the present 3D box using past information. Thus, despite using event data, Ev-3DOD struggles to transfer past
+
+
+Figure 7. Performance comparison with other methods during blind time under the setting of motion scale 2 and time slice 10.
+
+3D information to the present, causing its performance to resemble LoGoNet as motion increases over time. In contrast, our method asynchronously infers both geometric and semantic information for 3D detection, allowing it to operate independently of active time.
+
+# 6. Conclusion
+
+In this paper, we tackle 3D object detection using event stereo in a fully asynchronous setting for the first time. Unlike the previous continuous-time 3D object detection work that utilizes LiDAR, our approach does not rely on LiDAR, leading to lower performance compared to methods that fuse LiDAR and event data. However, by evaluating various motion scales and time slices, we demonstrate that our method is more adaptable and performs robustly in diverse and extreme conditions. Furthermore, we highlight the potential of event-based 3D perception in dynamic environments where event cameras are particularly beneficial, such as drone flights, high-speed driving, and robots. We hope this work inspires further research in this direction.
+
+# 7. Acknowledgments.
+
+This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (NRF2022R1A2B5B03002636). This work was also supported by the Technology Innovation Program (1415187329,20024355, Development of autonomous driving connectivity technology based on sensor-infrastructure cooperation) funded By the Ministry of Trade, Industry & Energy(MOTIE, Korea).
+
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| Easy | Mod. | Easy | Mod. | Easy | Mod. | Easy | Mod. |
| LiDAR | VoxelNeXt [14] | 12.66 | 11.06 | 31.46 | 28.39 | 10.59 | 6.61 | 12.77 | 7.96 |
| HEDNet [101] | 14.31 | 12.96 | 29.94 | 27.85 | 10.16 | 8.29 | 11.90 | 6.89 |
| LiDAR+RGB | Focals Conv [13] | 12.71 | 11.69 | 26.14 | 23.83 | 8.92 | 5.50 | 12.54 | 7.83 |
| LoGoNet [49] | 17.65 | 15.39 | 32.55 | 29.19 | 11.66 | 8.20 | 15.09 | 9.77 |
| LiDAR+RGB+Event | Ev-3DOD [22] | 29.53 | 25.07 | 49.31 | 44.44 | 18.42 | 12.49 | 29.06 | 20.34 |
| RGB-Stereo | DSGN [11] | 16.29 | 13.45 | 31.90 | 27.53 | 4.06 | 2.42 | 6.08 | 3.74 |
| LIGA [34] | 14.26 | 10.98 | 27.25 | 25.11 | 6.02 | 3.58 | 8.73 | 4.89 |
| Event-Stereo | Ours | 23.47 | 19.62 | 40.13 | 33.03 | 19.86 | 12.93 | 22.91 | 14.34 |
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| VoxelNeXt [14] | HEDNet [101] | Focals Conv [13] | LoGoNet [49] | Ev-3DOD [22] | DSGN [11] | LIGA [34] | Ours |
| ×2 | ×10 | VEH | 5.05 / 13.00 | 6.03 / 12.87 | 5.95 / 12.48 | 5.97 / 13.57 | 15.68 / 30.59 | 7.33 / 17.36 | 6.00 / 12.87 | 22.72 / 39.81 |
| PED | 4.07 / 4.89 | 3.40 / 4.05 | 3.16 / 4.79 | 2.24 / 3.72 | 7.88 / 12.19 | 1.87 / 3.04 | 2.27 / 4.00 | 19.04 / 22.71 |
| ×20 | VEH | 4.34 / 11.76 | 5.26 / 11.67 | 5.76 / 11.40 | 5.42 / 12.40 | 15.96 / 31.13 | 7.13 / 16.43 | 5.67 / 12.00 | 23.47 / 40.13 |
| PED | 3.83 / 4.31 | 2.60 / 3.49 | 2.66 / 3.86 | 1.91 / 2.90 | 1.47 / 2.63 | 1.84 / 2.99 | 2.08 / 3.01 | 19.86 / 22.91 |
| ×4 | ×10 | VEH | 2.05 / 5.22 | 2.87 / 4.63 | 2.73 / 4.48 | 1.90 / 5.26 | 6.24 / 11.62 | 3.12 / 7.20 | 2.10 / 4.89 | 20.70 / 37.08 |
| PED | 2.21 / 2.44 | 1.64 / 1.85 | 1.34 / 1.85 | 1.17 / 1.55 | 3.04 / 4.09 | 0.60 / 0.77 | 1.11 / 1.30 | 16.71 / 21.93 |
| ×20 | VEH | 1.71 / 4.55 | 2.27 / 4.29 | 2.73 / 3.94 | 1.90 / 4.66 | 6.36 / 11.70 | 3.09 / 6.52 | 1.54 / 4.17 | 22.72 / 39.81 |
| PED | 2.14 / 2.17 | 1.10 / 1.42 | 1.02 / 1.44 | 0.53 / 1.28 | 0.39 / 0.43 | 0.59 / 0.75 | 0.82 / 1.12 | 19.04 / 22.71 |
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| | G | | 12.92 | 20.78 |
| | G+S | | 14.60 | 24.85 |
| | G | ✓ | 14.56 | 21.73 |
| | G+S | ✓ | 15.95 | 26.12 |
| ✓ | | G+S | | 15.85 | 27.78 |
| ✓ | G+S | | 17.08 | 26.53 |
| ✓ | ✓ | G+S | | 19.12 | 29.64 |
| ✓ | ✓ | G+S | ✓ | 21.66 | 31.52 |
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| Motion ×1 | Ours (E) | 23.47 | 19.86 | 40.13 | 22.91 |
| Ours (E+I) | 25.23 | 21.50 | 46.21 | 29.14 |
| Motion ×2 | Ours (E) | 22.72 | 19.04 | 39.81 | 22.71 |
| Ours (E+I) | 20.14 | 10.50 | 37.93 | 12.76 |
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diff --git a/2025/Unlocking Constraints_ Source-Free Occlusion-Aware Seamless Segmentation/918ec0ce-e376-4559-8192-30fc256f6bbd_content_list.json b/2025/Unlocking Constraints_ Source-Free Occlusion-Aware Seamless Segmentation/918ec0ce-e376-4559-8192-30fc256f6bbd_content_list.json
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+ "text": "Unlocking Constraints: Source-Free Occlusion-Aware Seamless Segmentation",
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+ "text": "Yihong Cao $^{1,2,*}$ Jiaming Zhang $^{3,4,*}$ Xu Zheng $^{5,6}$ Hao Shi $^{7}$ Kunyu Peng $^{3}$ Hang Liu $^{1}$ Kailun Yang $^{1,\\dagger}$ Hui Zhang $^{1,\\dagger}$ $^{1}$ Hunan University $^{2}$ Hunan Normal University $^{3}$ Karlsruhe Institute of Technology $^{4}$ ETH Zürich HKUST(GZ) $^{6}$ INSAIT, Sofia University \"St. Kliment Ohridski\" $^{7}$ Zhejiang University",
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+ "img_path": "images/6c0974c00964d04066d20884bf4d14158ad0704ff13694f858871e2352b2f6b7.jpg",
+ "image_caption": [
+ "Figure 1. UNLOCK framework $(a)$ solves the Source-Free Occlusion-Aware Seamless Segmentation (SFOASS), enabling segmentation with $360^{\\circ}$ viewpoint coverage and occlusion-aware reasoning while adapting without requiring source data and target labels, and $(b)$ outperforms existing SFDA methods on the Real-to-Real scenario [7] across all five segmentation metrics (i.e., mAPQ for amodal panoptic, mPQ for panoptic, mIoU for semantic, mAAP for amodal instance, and mAP for instance)."
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+ "text": "Abstract",
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+ {
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+ "text": "Panoramic image processing is essential for omnicontext perception, yet faces constraints like distortions, perspective occlusions, and limited annotations. Previous unsupervised domain adaptation methods transfer knowledge from labeled pinhole data to unlabeled panoramic images, but they require access to source pinhole data. To address these, we introduce a more practical task, i.e., Source-Free Occlusion-Aware Seamless Segmentation (SFOASS), and propose its first solution, called UNconstrained Learning Omni-Context Knowledge (UNLOCK). Specifically, UNLOCK includes two key modules: Omni Pseudo-Labeling Learning and Amodal-Driven Context Learning. While adapting without relying on source data or target labels, this framework enhances models to achieve segmentation with $360^{\\circ}$ viewpoint coverage and occlusion-aware reasoning. Furthermore, we benchmark the proposed SFOASS task through both real-to-real and synthetic-to-real adaptation settings. Experimental results show that our source-free method achieves performance comparable to source-dependent methods, yielding state-of-the-art",
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+ "text": "scores of 10.9 in mAAP and 11.6 in mAP, along with an absolute improvement of +4.3 in mAPQ over the source-only method. All data and code will be made publicly available at https://github.com/yihong-97/UNLOCK.",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Scene understanding is a foundational task in computer vision, essential for various downstream applications like autonomous driving [44, 77], virtual reality [11, 58], and robotics [3, 60]. Despite significant advances in the field, current methods still face challenges in achieving both comprehensive and human-like perceptions of surrounding environments, limiting their ability to fully understand scenes. Multiple critical research questions remain unsolved.",
+ "bbox": [
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+ {
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+ "text": "1) How to efficiently expand to $360^{\\circ}$ field of view? Traditional scene understanding methods [9, 21, 70] tailored for pinhole imagery, are limited by a narrow Field of View (FoV). In contrast, panoramic vision offers $360^{\\circ}$ view in a single shot, which has the potential to facilitate more comprehensive scene understanding [1, 19]. However, directly applying traditional methods to panoramic data often results in unreliable performance due to challenges such as",
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+ {
+ "type": "header",
+ "text": "CVF",
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+ "page_idx": 0
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+ {
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
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+ {
+ "type": "page_footnote",
+ "text": "* Equal contribution. † Corresponding authors (e-mail: kailun.yang@hnu.edu.cn, zhanghuihby@126.com).",
+ "bbox": [
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+ "page_idx": 0
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+ "type": "page_number",
+ "text": "8961",
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "distortions [92]. For effective panoramic understanding, it is essential to learn omni-context knowledge when transferring from the pinhole domain to the panoramic domain. This knowledge transfer is crucial for accurate feature interpretation and wide-FoV representation, ultimately enabling seamless $360^{\\circ}$ scene understanding [84, 85].",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "2) How can amodal prediction be improved to extend the depth of view? Amodal perception [34, 53], the ability to predict an occluded object's complete shape, is key to robust scene understanding [83] and mirrors human-like perception. Extending the depth of view (vertical to field of view) means that models can achieve seamless perception, which refers to pixel-level segmentation of the background and occlusion-aware instance-level segmentation of the foreground. Beyond the previous amodal segmentation methods [16, 98], how to improve occlusion-aware reasoning like OASS [7] in both directions (depth and field of view) simultaneously remains challenging.",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "3) How can models adapt to panoramic domains without source data? Apart from the field and depth of view, the scarcity of labeled data presents a significant limitation in panoramic vision. To address the lack of labeled data, Unsupervised Domain Adaptation (UDA) leverages labeled data from the source domain while training on unlabeled data from the target domain [7, 24, 25, 28, 32, 65]. However, UDA methods still rely on access to source domain, which can often be challenging or even impossible due to privacy concerns or commercial restrictions on source datasets, such as in autonomous driving [40, 95, 96]. This restriction leads us to source-free learning, i.e. how to adapt models to panoramic domains without source data. However, it remains under-explored in amodal panoramic vision.",
+ "bbox": [
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+ "page_idx": 1
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+ "text": "In this work, to address the aforementioned challenges in scene understanding, we extend the OASS [7] task and introduce a more practical task, i.e., Source-Free Occlusion-Aware Seamless Segmentation (SFOASS). To tackle this task, we propose its first solution, called UNconstrained Learning Omni-Context Knowledge (UNLOCK). As shown in Fig. 1a, UNLOCK improves panoramic seamless segmentation performance under adaptation constraints without requiring source data and target labels. Specifically, to effectively capture the domain-invariant knowledge from the source domain, a method called Omni PseudoLabeling Learning (OPLL) is proposed. Besides, to learn intra-domain knowledge and integrate the domain-invariant knowledge, we put forward the Amodal-Driven Context Learning (ADCL) strategy. Together, OPLL and ADCL adapt the source model trained on pinhole data to target panoramic images while enhancing panoramic perception and occlusion-aware reasoning. With OPLL as the key and ADCL performing the unlocking action, they work in synergy to unlock the constraints in SFOASS, thereby enabling seamless perception of the model towards panoramic data.",
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+ "text": "Aside from Real-to-Real source-free adaptation on the KITTI360-APS $\\rightarrow$ BlendPASS benchmark [7], we pioneer Synthetic-to-Real adaptation in OASS and SFOASS and introduce AmodalSynthDrive $\\rightarrow$ BlendPASS to investigate the potential of adapting synthetic panoramic images to the real panoramic image domain. Extensive experiments are conducted on both SFOASS benchmarks. Without access to the original source data (neither images nor labels), our UNLOCK framework can obtain on-par performance as compared to UDA-based methods that require all source data. Surprisingly, as shown in Fig. 1b, results on the Real-to-Real scenario [7] show an absolute improvement of $+4.3$ in mAPQ, reaching 26.4, compared to the source-only method, and outperforms UDA methods using $12K$ images in instance-level segmentation, with state-of-the-art scores of 10.9 in mAAP and 11.6 in mAP, respectively.",
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+ "text": "In this work, we propose contributions as follows:",
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+ "- We introduce the Source-Free Occlusion-Aware Seamless Segmentation (SFOASS) task and its first solution, UNconstrained Learning Omni-Context Knowledge (UNLOCK). The UNLOCK framework enables models to achieve segmentation with $360^{\\circ}$ viewpoint coverage and occlusion-aware reasoning while adapting without the need for source data and target labels.",
+ "- To fully exploit the knowledge from source and target domains, Omni Pseudo-Labeling Learning (OPLL) and Amodal-Driven Context Learning (ADCL) strategies are introduced in UNLOCK to achieve occlusion-aware seamless segmentation for panoramic images.",
+ "- Extensive experiments conducted on two SFOASS scenarios, Real-to-Real and Synthetic-to-Real, demonstrate the effectiveness of the UNLOCK framework, highlighting its ability to achieve competitive performance."
+ ],
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+ "text": "2. Related Work",
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+ "text": "Seamless segmentation. Seamless segmentation, as introduced by [7], aims to achieve amodal-level segmentation for large-FoV images, enabling unified, occlusion-aware scene understanding. Wide-FoV segmentation on fisheye [12, 56, 59, 78, 80] and panoramic images [22, 35, 75, 76, 97] facilitates comprehensive $360^{\\circ}$ scene comprehension [74]. Panoramic panoptic segmentation enhances scene understanding by providing instance-level insights [17, 30, 47, 52]. Amodal segmentation extends this concept by predicting both visible and occluded object regions [4, 10, 15, 23, 38, 41, 61, 63]. Li et al. [34] pioneered amodal instance segmentation, introducing occlusion-aware segmentation through iterative regression. Subsequent datasets adapted for amodal segmentation [98] and occlusion classification [53] have driven further advances. Shape and contour priors [8, 18, 36, 37, 69] have further refined segmentation accuracy. In addition to instance segmentation, amodal panoptic segmentation has been explored [5, 26, 98]. Mo",
+ "bbox": [
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+ "type": "page_number",
+ "text": "8962",
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "han et al. [48, 49] combined semantic and amodal segmentation for amodal panoptic segmentation. Recent methods, including pix2gestalt [51], AISDiff [64], and Xu et al. [72], leverage diffusion model priors for amodal segmentation. Although seamless segmentation [7] unifies aforementioned segmentation paradigms to form occlusion-aware scene understanding for panoramic vision, our work emphasizes source-free seamless segmentation, aiming for high accuracy even with restricted access to labeled source data.",
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+ "page_idx": 2
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+ "text": "Source-free domain adaptation. Existing works dealing with domain gaps on semantic segmentation tasks mostly focus on UDA where labeled source domain data is required [20, 62, 68, 71, 84, 84, 85, 91, 93, 94, 99]. Source-Free Domain Adaptation (SFDA) [6, 14, 33, 40, 43, 54, 67, 79, 81] is a more practical approach compared with UDA, as it removes the need for access to source data during the adaptation process. As sub-directions of scene segmentation, domain adaptation of panoptic segmentation is challenging as it must distinguish and integrate semantic and instance information across domains, as highlighted in existing works [27, 45, 46, 55, 87]. To overcome the limitations of the FoV, domain adaptation in panoramic segmentation facilitates comprehensive scene understanding across a full $360^{\\circ}$ perception, while effectively harnessing the rich knowledge from label-dense pinhole domains. Researchers have explored both UDA [31, 84, 85, 88-90, 94] and SFDA [95, 96] settings for panoramic segmentation. Jaus et al. [29, 30] illustrate the need for panoramic panoptic segmentation in autonomous driving. Zheng et al. [95, 96] for the first time, explored SFDA in panoramic semantic segmentation. However, the SFDA challenge remains unexplored for OASS [7]. In this work, we introduce the novel SFOASS task and benchmark it across two scenarios. We also proposed the first solution UNLOCK, a novel method designed to unlock constraints posed by SFOASS.",
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+ "text": "3.UNLOCK Framework",
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+ "text": "3.1. Overview",
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+ "text": "OASS. In the OASS [7], the objective is to use a labeled source pinhole domain $\\mathcal{D}^{pin} = \\{x_i^{pin}, y_i^{pin}\\}_{i=1}^{N^{pin}}$ and an unlabeled target panoramic domain $\\mathcal{D}^{pan} = \\{x_i^{pan}\\}_{i=1}^{N^{pan}}$ to obtain an OASS model $F$ that performs well in $\\mathcal{D}^{pan}$ . Both domains share the same $C$ categories, which can be further divided into $C^{stu}$ Stuff classes and $C^{thi}$ Thing classes. Ultimately, the $F$ should be able to output five segmentation results with the input panoramic image at once: semantic, instance, amodal instance, panoptic, and amodal panoptic maps. Typically, $F$ is designed to contain a shared encoder and three detection branches: semantic, instance, and amodal instance branches, each outputting corresponding predictions $p_i^{sem}, p_i^{ins}, p_i^{ains}$ , denoted as",
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+ {
+ "type": "equation",
+ "text": "\n$$\np _ {i} ^ {\\text {s e m}}, p _ {i} ^ {\\text {i n s}}, p _ {i} ^ {\\text {a i n s}} = F (x _ {i}), \\tag {1}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "where $p_i^{sem} \\in \\mathbb{R}^{H \\times W \\times C}$ represents the semantic prediction of the input image $x_i \\in \\mathbb{R}^{H \\times W \\times 3}$ . $p_i^{ins}$ and $p_i^{ains}$ represent the instance and amodal instance predictions, respectively, with each including class $\\in \\mathbb{R}^{C^{thi}}$ , score $\\in [0,1]$ , and mask $\\in \\mathbb{R}^{H \\times W}$ predictions for jth object. During adaptation, the label $y_i$ of $x_i$ consists of three components: semantic $y_i^{sem}$ , instance $y_i^{ins}$ , and amodal instance $y_i^{ains}$ labels, used for supervised learning in their respective branches. In the inference phase, the predictions from all three branches are fused to produce five segmentation maps of OASS.",
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+ "type": "text",
+ "text": "SFOASS. Considering privacy and storage limitations, this work introduces a more practical task, i.e., SFOASS. In the adaptation phase, the source pinhole domain $\\mathcal{D}^{pin}$ is locked and inaccessible. Given a source model $F^{pin}$ well-trained from $\\mathcal{D}^{pin}$ , and $\\mathcal{D}^{pan}$ , the goal of SFOASS is to adapt the source model $F^{pin}$ with only unlabeled panoramic data $\\{x_{i}^{pan}\\}_{i=1}^{N^{pan}}$ , obtaining a target model $F^{pan}$ that performs well in the target panoramic domain. (For ease of expression, the superscript \"pan\" for target panoramic domain will be omitted henceforth.)",
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+ "type": "text",
+ "text": "How can models adapt to panoramic domains without source data, while expanding the field and depth of view? To answer this, we propose a novel method called UNconstrained Learning Omni-Context Knowledge (UNLOCK). It can further enhance the performance of panoramic seamless prediction while improving occlusion-aware reasoning. Specifically, as shown in Fig. 2, in response to the challenge that existing self-training methods are ineffective for the SFOASS task, we designed an Omni Pseudo-Labeling Learning (OPLL) approach. This approach leverages all predictions to generate omni soft labels. These generated labels serve as the \"key\" to the proposed UNLOCK. Furthermore, we propose a brand-new Amodal-Driven Contextual Learning (ADCL) strategy, which effectively resolves the conflict between the real object shapes and contextual knowledge for the occluded object. Ultimately, the ADCL holds the \"key\" and performs the \"unlocking\" action, completing the source-free adaptation to the panoramic domain.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "3.2. Omni Pseudo-Labeling Learning",
+ "text_level": 1,
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+ "type": "text",
+ "text": "In the SFOASS, only unlabeled target panoramic images $\\{x_i\\}_{i=1}^N$ are accessible. Common solutions [2, 6, 33] typically involve generating pseudo-labels of target images for training. Pseudo-label generation usually entails filtering model predictions based on pre-defined thresholds. However, we found that directly using the filtered pseudo-labels for self-training in the SFOASS led to performance degradation for instance and amodal instance branches compared to the source model. The OASS task consists of a pixel-wise semantic branch and two object-wise instance-level branches (instance and amodal instance) based on region proposals. For the instance-level branches, each object is",
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+ "type": "page_number",
+ "text": "8963",
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+ "type": "image",
+ "img_path": "images/0218ab54492e4ff5cc9d7736b9b8469d71af61d1b9d7c1e80ad29eebaebd3ecc.jpg",
+ "image_caption": [
+ "Figure 2. Illustration of the proposed UNLOCK. To address the challenge of the inaccessible source domain and target labels in SFOASS, we propose Omni Pseudo-labeling Learning (OPLL) and Amodal-Driven Contextual Learning (ADCL) modules. OPLL serves as the key, and ADCL, holding the key, unlocks the constraints of SFOASS, enabling effective adaptation of the target model to the panoramic domain."
+ ],
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+ {
+ "type": "text",
+ "text": "assigned a binary mask for binary cross-entropy loss. However, inaccurate pseudo-labels can hinder learning. When object parts are mistakenly labeled as background, even if the model correctly detects the objects, the pseudo-labels may force it to incorrectly classify them as absent.",
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+ "img_path": "images/3d83033db808790bd11b0a401b9b363b5f5c3bd0809b79b86452f5d2541eba3e.jpg",
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+ "Image"
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+ "img_path": "images/c5dbe7ee59c5335565ddd6943148081612148bf4718276e6a019b64d00e819a8.jpg",
+ "image_caption": [
+ "Semantic Predictions"
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+ "Instance Predictions"
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+ "image_caption": [
+ "(a) Incorrect predictions (cyclists in red) of the Stuff class.",
+ "All Predictions",
+ "(b) Omni pseudo-label generation with CS thresholds.",
+ "Figure 3. Solution to the challenge of predictions from the source model in OPLL, illustrated with the amodal instance branch."
+ ],
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+ "img_path": "images/a7e46ec189d835e44898b9ed8ab91a3eed1c60147ce1c14e66073f6371e3446f.jpg",
+ "image_caption": [
+ "Certain Pseudo-Labels"
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+ "img_path": "images/0eff033091cdff9e471cec4b84712380f7d45069c55736f25dccd08215ea099a.jpg",
+ "image_caption": [
+ "Uncertainty Region"
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+ "type": "text",
+ "text": "To address this, we developed the OPLL method, which introduces generating omni pseudo-labels using Classwise Self-tuning (CS) thresholds and applying uncertainty-guided instance loss. Since the two instance-level branches perform the same operations, we will introduce one branch as an example below. Specifically, we first utilized the semantic branch's predictions to impose additional constraints on the predictions of both instance-level branches. As shown in Fig. 3a, we observed that the instance-level branch, constrained by local information, may misclassify the statue in the shop window as a cyclist of Thing class. In contrast, the semantic branch, aided by global information, can usually understand the scenes correctly. For each",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "panoramic image $x_{i}$ , we obtain the Thing mask $m^{th i}$ by the semantic prediction, then use it to revise the object mask of instance-level predictions $p_{i}^{il}$ , $il \\in \\{ins, ains\\}$ :",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\nm ^ {t h i} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\operatorname {a r g m a x} p ^ {s e m} \\in C ^ {t h i} \\\\ 0, & \\text {e l s e} \\end{array} , \\right. \\tag {2}\n$$\n",
+ "text_format": "latex",
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+ "page_idx": 3
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\tilde {p} _ {i} ^ {i l} = p _ {i} ^ {i l} \\cap m ^ {t h i}. \\tag {3}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "Then, considering the inconsistent number of objects and the significant imbalance in the source model's capabilities across different Thing classes (as shown in SourceOnly of Table 2), we propose a simple and effective CS threshold method for the predictions of the SFOASS task. For each branch, the CS thresholds $\\tau = \\{\\tau_c\\}_{c=1}^{C^{thi}}$ is determined by:",
+ "bbox": [
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\tau_ {c} = \\operatorname {a r g m a x} _ {\\tau \\in \\left\\{\\tau^ {f i x}, \\tau^ {p e r} \\right\\}} N _ {c} ^ {\\tau}, c \\in C ^ {t h i}, \\tag {4}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "where $N_{c}^{\\tau^{fix}}$ represents the number of objects of class $c$ whose score exceeds $\\tau^{fix}$ across all predictions $\\{\\hat{p}_i\\}_{i=1}^N$ , and $N_{c}^{\\tau^{per}}$ denotes the number of objects of class $c$ in the top $\\tau^{per}$ percentage when the score of all predictions $\\{\\hat{p}_i\\}_{i=1}^N$ are sorted in descending order. For the semantic branch, the score is replaced with the maximum predicted probability of $p_i^{sem}$ . This approach generates high-quality pseudo-labels while effectively addressing the issue of low confidence scores for certain classes, caused by the source model $F^{pin}$ inconsistent performance across classes.",
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+ {
+ "type": "text",
+ "text": "Then, we filter out high-quality predictions based on CS thresholds $\\pmb{\\tau}$ as certain pseudo-labels $\\hat{y}_i^{cer}$ :",
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+ "page_idx": 3
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\hat {y} _ {i} ^ {c e r} = \\left\\{\\hat {p} _ {i} ^ {(j)} \\mid \\hat {p} _ {i} ^ {(j)} > \\tau \\right\\}, \\tag {5}\n$$\n",
+ "text_format": "latex",
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "where $\\hat{p}_i^{(j)}$ represent the prediction of $j$ th object in predictions $p_i$ for input image $x_i$ . To fully utilize the predictions,",
+ "bbox": [
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+ "page_idx": 3
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+ {
+ "type": "page_number",
+ "text": "8964",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "image",
+ "img_path": "images/19a91f47de60fbefa8ef65a658130b22db85fc9a9b00df87843ecb832c65d84b.jpg",
+ "image_caption": [
+ "Figure 4. Comparison of object extraction methods: Amodal instance extraction mixes information from other objects, while instance-based extraction may yield incomplete shapes. Our method avoids these issues and preserves spatial awareness."
+ ],
+ "image_footnote": [],
+ "bbox": [
+ 112,
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "we treat the remaining masks of the other predictions as uncertainty region $\\hat{y}_i^{uncer}$ for the current image:",
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\hat {y} _ {i} ^ {\\text {u n c e r}} = \\left(1 - \\mathbf {1} _ {\\left\\{\\sum_ {j} \\hat {y} _ {i} ^ {\\text {c e r}} > 0 \\right\\}}\\right) \\cap \\left(\\mathbf {1} _ {\\left\\{\\sum_ {j} \\left(\\hat {p} _ {i} ^ {(j)} \\mid \\hat {p} _ {i} ^ {(j)} < \\boldsymbol {\\tau}\\right) > 0 \\right\\}}\\right), \\tag {6}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "where $\\mathbf{1}_{\\{\\cdot\\}}$ is indicator function. The left-hand side of $\\cap$ in Eq. 6 ensures that the object region of $\\hat{y}_i^{cer}$ is not misassigned as the uncertain region. They form the omni pseudo-labels $\\hat{y}_i = \\{\\hat{p}_i^{(1)}, \\hat{p}_i^{(2)}, \\dots, \\hat{y}_i^{uncer}\\}$ of the training panoramic image $x_i$ . We believe that all predictions from both instance-level branches of the source model can provide effective knowledge. For the semantic branch, the $j$ is replaced with the pixel spatial location. Finally, for each training panoramic image $x_i$ , we obtain three types of omni pseudo-labels $\\hat{y}_i^{sem}, \\hat{y}_i^{ins}, \\hat{y}_i^{ains}$ for training. During the adaptation process of the target model $F^{pan}$ , following [7], the cross-entropy loss is used for the semantic branch. For the instance-level branches, we introduce a novel uncertain-guided Binary Cross Entropy (BCE) loss $\\mathcal{L}_{ur}$ , specifically tailored for the SFOASS task.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {u r} = \\left(1 - \\hat {y} _ {i} ^ {u n c e r}\\right) \\odot \\mathrm {B C E} \\left(F ^ {p a n} \\left(x _ {i}\\right), \\hat {y} _ {i} ^ {c e r}\\right). \\tag {7}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "This approach effectively mitigates prediction errors of the target panoramic data arising from the source pinhole model, allowing the target model to focus on high-quality object samples during the adaptation process.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "3.3. Amodal-Driven Contextual Learning",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Through OPLL, we leverage the source model to generate omni pseudo-labels of the unlabeled panoramic data, obtaining the \"key\" for adapting the model to the target domain. It primarily extracts domain-invariant knowledge from the pinhole-tolerant source model. We further introduce the ADCL strategy to learn intra-domain knowledge while integrating domain-invariant knowledge. It holds the \"key\" to complete the \"unlocking\" action, and achieves the adaptation to the panoramic images in a source-free manner.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Mixing is an effective strategy often used in UDA methods [2, 50, 82]. The typical approach involves randomly extracting objects from other data and pasting them into the current training image to form new mixed training samples. However, this approach is not suitable for the OASS model",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "with an amodal instance branch, and it can confuse semantic context and hinder model learning. Specifically, since the two instance branches in the OASS model are independent, their predictions are not correlated, leaving us with the option of relying on one of the predictions. As shown by the car in Fig. 4, the amodal instance prediction captures the complete shape of the car. However, this prediction only provides the full mask for the object, meaning that the occluded areas in the mask may inadvertently include parts of other objects. If these masks are directly used for mixing, incorrect contextual information can be introduced. On the other hand, relying on instance predictions focuses only on non-occluded regions, making it difficult for the model to learn the full shape of objects. This dual challenge complicates the learning process in SFOASS tasks.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "First, we use OPLL with stricter thresholds $\\tau^{\\prime fix}$ and $\\tau^{\\prime per}$ to build a buffer pool $\\mathcal{B}$ of $K$ high-quality object samples, relying solely on predictions from the amodal instance branch to accurately capture object shapes.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {B} = \\left\\{o ^ {(1)}, o ^ {(2)}, \\dots , o ^ {(K)} \\right\\}, \\tag {8}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "where $o^{(k)}\\in \\{\\hat{y}_i^{ains\\to cer}|\\big(\\tau^{\\prime^{fix}},\\tau^{\\prime^{per}}\\big)\\}_{i = 1}^{N^{pan}}$",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "The $o^{(k)}$ represents the filtered certain object obtained through OPLL from the panoramic data. Additionally, for each $o^{(k)} = \\{o_{ful}^{(k)}, o_{ovp}^{(k)}\\}$ , we include not only the mask $o_{ful}$ of the predicted full region but also record the overlapping region $o_{ovp}$ between the object and other objects in the same image, regardless of whether they are occluded. This process results in an amodal-driven object pool $\\mathcal{B}$ .",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Furthermore, we introduce a novel spatial-aware mixing strategy based on the amodal-driven object pool, enriching the diversity of unlabeled panoramic images by generating amodal-driven mixed samples while respecting panoramic layouts. This spatially consistent mixing ensures semantic coherence, aligning distortions in the panoramic layout even after object insertion. During the adaptation phase, we randomly select $R$ object samples $\\mathcal{O} = \\{o^{(r)}\\}_{r=1}^{R}$ from $\\mathcal{B}$ and integrate them into the current training image $x_{i}$ :",
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\tilde {x} _ {i} = \\left(1 - o _ {f u l} ^ {(r)}\\right) \\odot x _ {i} + o _ {f u l} ^ {(r)} \\odot x _ {r}, \\tag {9}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "where $x_{r}$ represents the image corresponding to the paste object $o^{(r)}$ . For ambiguous regions of $o^{(r)}$ (i.e., potentially occluded areas), we assign zero pixels during the mixing process while keeping the complete mask as the label according to the $o_{ovp}^{(r)}$ .",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\tilde {x} _ {i} = \\left(1 - o _ {o v p} ^ {(r)}\\right) \\odot \\tilde {x} _ {i}. \\tag {10}\n$$\n",
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+ "type": "text",
+ "text": "For the three pseudo-labels $\\tilde{y}_i^{sem},\\tilde{y}_i^{ins},\\tilde{y}_i^{ains}$ of the mixed image $\\tilde{x}_i$ , we only use $\\{o_{ful}^{(r)}\\}_{r = 1}^{R}$ to modify them accordingly. This strategy preserves the full shape of objects while",
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+ {
+ "type": "page_number",
+ "text": "8965",
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+ {
+ "type": "table",
+ "img_path": "images/a28fe75a389f9e5feb87db2448b822e254d76ef683f0c6261cb153367c30566e.jpg",
+ "table_caption": [],
+ "table_footnote": [
+ "Table 1. Scene Segmentation results on the K2B benchmark. Metrics are reported as: mAPQ for Amodal Panoptic Segmentation (APS), mPQ for Panoptic Segmentation (PS), and mIoU for Semantic Segmentation (SS). Per-class results are reported as APQ, PQ, and IoU. $\\uparrow$ represents the improvement over the baseline of the Source-only method. $x^{pin}$ and $x^{pan}$ represent the images, and $y^{pin}$ and $y^{pan}$ represent the labels, from the pinhole source and panoramic target domains, respectively."
+ ],
+ "table_body": "| Task | Constraint | Method | Metric | road | sidew. | buid. | wall | fence | pole | tlnight | Insign | lager | fermin | sky | Pedes | cylulus | car | Ink | outch | van | whlte |
| APS | (ypan) | DATR [93] | 20.3 | 51.8 | 09.2 | 59.9 | 11.9 | 12.0 | 02.0 | 00.0 | 03.9 | 64.6 | 14.1 | 70.4 | 11.1 | 00.0 | 39.3 | 00.0 | 03.2 | 10.1 | 01.3 |
| Trans4PASS [85] | 22.9 | 53.9 | 14.1 | 69.4 | 19.2 | 11.8 | 03.8 | 00.0 | 05.2 | 67.6 | 16.0 | 77.4 | 15.3 | 04.2 | 41.1 | 06.6 | 00.0 | 00.0 | 07.4 |
| EDAPS [55] | 23.1 | 54.9 | 17.0 | 66.9 | 18.8 | 14.5 | 05.8 | 04.0 | 04.6 | 68.2 | 16.0 | 72.8 | 19.0 | 00.0 | 36.7 | 05.8 | 04.4 | 00.0 | 07.2 |
| UnmaskFormer [7] | 26.6 | 61.8 | 24.7 | 66.8 | 20.8 | 15.8 | 05.3 | 04.3 | 03.3 | 69.0 | 18.4 | 79.4 | 20.5 | 03.1 | 44.6 | 12.8 | 11.3 | 00.0 | 16.6 |
| (xpan,ypan) | Source-only | 22.1 | 57.1 | 14.2 | 73.6 | 15.5 | 07.6 | 00.7 | 00.0 | 10.4 | 58.3 | 12.4 | 83.1 | 15.2 | 00.0 | 40.3 | 03.8 | 00.0 | 00.0 | 06.1 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 24.5 | 60.3 | 16.8 | 71.7 | 14.1 | 07.7 | 00.0 | 00.0 | 08.4 | 55.6 | 13.6 | 81.3 | 21.5 | 03.2 | 46.3 | 19.4 | 02.2 | 00.0 | 19.4 |
| UNLOCK (Ours) | 26.4 (↑4.3) | 62.7 | 14.4 | 74.8 | 20.2 | 11.2 | 00.8 | 00.0 | 08.0 | 62.9 | 18.3 | 84.0 | 21.9 | 03.6 | 45.8 | 19.4 | 00.0 | 03.1 | 24.4 |
| PS | (ypan) | DATR [93] | 19.6 | 50.4 | 09.1 | 59.9 | 11.9 | 12.0 | 02.0 | 00.0 | 03.9 | 64.6 | 14.1 | 70.5 | 12.2 | 00.0 | 38.1 | 00.0 | 03.4 | 00.0 | 01.3 |
| Trans4PASS [85] | 22.7 | 53.9 | 14.1 | 69.4 | 19.2 | 11.8 | 03.8 | 00.0 | 05.2 | 67.6 | 16.0 | 77.4 | 14.6 | 04.1 | 38.2 | 06.9 | 00.0 | 00.0 | 07.2 |
| UniDAPS [86] | 22.7 | 66.0 | 09.5 | 66.3 | 17.4 | 14.3 | 04.8 | 00.0 | 06.1 | 67.2 | 16.1 | 72.7 | 08.3 | 00.0 | 27.3 | 14.8 | 09.2 | 00.0 | 08.9 |
| EDAPS [55] | 23.1 | 55.0 | 17.1 | 66.8 | 18.7 | 14.5 | 05.8 | 04.0 | 04.7 | 68.2 | 16.0 | 72.8 | 19.6 | 00.0 | 37.8 | 01.8 | 04.4 | 00.0 | 07.9 |
| UnmaskFormer [7] | 26.2 | 61.7 | 24.7 | 66.8 | 20.8 | 15.8 | 05.2 | 04.3 | 03.3 | 69.0 | 18.4 | 79.4 | 20.9 | 03.5 | 43.0 | 11.3 | 07.6 | 00.0 | 16.0 |
| (xpan,ypan) | Source-only | 22.3 | 57.8 | 14.2 | 73.8 | 15.5 | 07.6 | 00.7 | 00.0 | 10.4 | 58.3 | 12.4 | 83.2 | 14.9 | 00.0 | 39.1 | 06.0 | 00.0 | 00.0 | 07.7 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 23.7 | 61.3 | 16.8 | 72.2 | 14.1 | 07.6 | 00.0 | 00.0 | 08.4 | 55.9 | 13.6 | 81.3 | 18.4 | 00.0 | 40.6 | 16.4 | 02.4 | 00.0 | 17.6 |
| UNLOCK (Ours) | 25.1 (↑2.8) | 60.4 | 14.4 | 75.7 | 20.2 | 11.2 | 00.7 | 00.0 | 08.0 | 63.6 | 18.3 | 84.0 | 16.9 | 00.0 | 40.0 | 18.5 | 00.0 | 00.0 | 19.4 |
| SS | (ypan) | DATR [93] | 34.9 | 71.9 | 27.2 | 70.6 | 22.8 | 36.0 | 23.9 | 00.0 | 04.5 | 77.1 | 37.1 | 80.1 | 51.2 | 02.2 | 70.2 | 08.9 | 06.0 | 11.0 | 27.8 |
| Trans4PASS [85] | 40.7 | 72.8 | 33.8 | 78.4 | 33.5 | 37.1 | 26.6 | 05.3 | 55.4 | 77.4 | 37.9 | 84.7 | 57.5 | 04.5 | 76.6 | 19.0 | 17.0 | 12.7 | 51.7 |
| UniDAPS [86] | 38.5 | 72.3 | 29.2 | 75.8 | 33.9 | 38.9 | 25.9 | 11.4 | 07.5 | 77.6 | 37.4 | 81.4 | 47.6 | 03.0 | 75.6 | 21.3 | 03.4 | 01.3 | 48.9 |
| EDAPS [55] | 40.2 | 74.4 | 35.9 | 77.0 | 36.5 | 40.4 | 28.0 | 16.1 | 05.1 | 78.1 | 39.5 | 82.3 | 55.5 | 03.3 | 74.4 | 06.7 | 14.1 | 05.2 | 50.9 |
| UnmaskFormer [7] | 43.7 | 76.5 | 37.8 | 77.1 | 34.7 | 44.1 | 28.3 | 17.8 | 02.8 | 78.7 | 41.7 | 85.0 | 57.3 | 06.0 | 80.6 | 23.5 | 21.7 | 18.8 | 53.6 |
| (xpan,ypan) | Source-only | 38.7 | 73.0 | 29.1 | 82.0 | 31.2 | 31.4 | 18.0 | 00.0 | 16.0 | 74.1 | 33.7 | 88.7 | 50.2 | 04.0 | 80.4 | 18.0 | 11.0 | 04.6 | 50.2 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 39.4 | 74.6 | 32.2 | 81.2 | 30.7 | 31.9 | 18.1 | 00.0 | 15.6 | 72.6 | 38.3 | 89.2 | 50.6 | 04.6 | 80.5 | 20.4 | 11.6 | 05.3 | 51.0 |
| UNLOCK (Ours) | 41.6 (↑2.9) | 74.7 | 32.1 | 83.7 | 34.7 | 40.8 | 18.5 | 00.0 | 18.9 | 76.1 | 39.9 | 89.5 | 53.7 | 05.8 | 82.2 | 26.1 | 00.8 | 14.0 | 57.8 |
",
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+ "text": "avoiding confusion about the semantic content of other objects. The zero-pixel ambiguous regions act as a masked strategy to enhance the model's ability to reconstruct occluded areas and infer the complete shape of occluded objects. This improves the model's ability to learn contextual knowledge from the target panoramic domain, improving its understanding of both individual objects and their relationships within the scene.",
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+ "text": "4. Experiments",
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+ "text": "4.1. Datasets",
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+ "text": "In this paper, we extend the Real-to-Real adaptation on the KITTI360-APS $\\rightarrow$ BlendPASS (K2B for short)) benchmark [7] to SFOASS. Moreover, we pioneer Synthetic-to-Real adaptation in both OASS and SFOASS, introducing AmodalSynthDrive $\\rightarrow$ BlendPASS benchmark (A2B for short) to conduct seamless segmentation research from synthetic to real scenarios.",
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+ "text": "Source pinhole domain: (1) KITTI360-APS [48]: It extends KITTI360 [39] and includes additional annotations for inmodal and amodal instances. A total of 12,320 annotated images $(1408\\times 376$ pixels) are captured using pinhole cameras across 9 cities. It covers 11 Stuff classes and 7 Thing classes. (2) AmodalSynthDrive [57]: The first synthetic dataset applicable to the OASS task, generated using CARLA [13]. It provides images and annotations from four surround-view cameras with a pinhole perspective, with 10,500 training images $(1920\\times 1080$ pixels) for each viewpoint. It covers 11 Stuff classes and 7 Thing classes.",
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+ "text": "Target panoramic domain: The BlendPASS dataset [7] consists of 2,000 unlabeled training panoramic images and",
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+ "text": "100 labeled test panoramic images $(2048 \\times 400$ pixels), captured in real driving scenes across 40 cities on multiple continents. It covers 11 Stuff and 8 Thing classes.",
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+ "text": "Domain gap analysis: Fig. 5 shows the feature distributions of car and pedestrians between the target domain and two source domains, where there is a large domain gap between different datasets, especially for the A2B.",
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+ "img_path": "images/a9d0f4611b911c4023de34c5ad2337039ca9613e29180307dd04c702abb53a5a.jpg",
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+ "Figure 5. Example images from the datasets [7, 48, 57] and the class distribution visualized via t-SNE [66]."
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+ "text": "4.2. Experiment Setups",
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+ "text": "Following [7], we use the proposed architecture as the backbone of our UNLOCK and the reproduced 360SFUDA++ [95]. In the A2B benchmark, we reproduce existing methods [55, 85, 86, 93, 95] and train the pinhole source model following the framework in [7]. In the K2B benchmark, we directly use the Source-only model from [7] as the pinhole source model. The AdamW optimizer [42] is employed, with a learning rate set to $1 \\times 10^{-7}$ , and a weight decay of 0.01, followed by polynomial decay. The batch size is set to 4, with crop sizes of $376 \\times 376$ for K2B and $400 \\times 400$ for A2B, and both are trained for $10k$ iterations. In UNLOCK, $\\tau^{fix}$ and $\\tau^{per}$ for amodal instance predictions are set to 0.3 and 0.5; for instance predictions to 0.5 and 0.3; and for semantic predictions, to 0.5 and 0.8. For ADCL, they are set to 0.95 and 0.1, with the sample object count $R$",
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+ "table_body": "| Task | Method | Metric | Preds. | Cyclings | Car | Musk | Opt. | Van | WhWhite |
| AIS | B | DATR [93] | 08.7 | 13.1 | 00.0 | 30.6 | 06.9 | 04.7 | 01.7 | 03.8 |
| Trans4PASS [85] | 09.9 | 16.0 | 00.2 | 31.7 | 08.3 | 06.0 | 00.4 | 06.4 |
| EDAPS [55] | 10.7 | 15.8 | 00.1 | 30.0 | 09.0 | 12.2 | 00.4 | 07.4 |
| UnmaskFormer [7] | 10.5 | 16.1 | 00.1 | 34.1 | 12.3 | 02.2 | 00.6 | 08.2 |
| B | Source-only | 10.2 | 15.2 | 00.0 | 33.4 | 12.6 | 03.3 | 00.4 | 06.8 |
| 360SFUDA++ [95] | 10.3 | 15.2 | 00.0 | 33.4 | 13.1 | 03.3 | 00.4 | 06.8 |
| UNLOCK (Ours) | 10.9 (↑0.7) | 17.1 | 00.0 | 34.9 | 14.6 | 01.7 | 00.2 | 07.9 |
| IS | B | DATR [93] | 08.7 | 14.2 | 00.0 | 31.2 | 07.6 | 03.7 | 00.4 | 03.6 |
| Trans4PASS [85] | 10.0 | 16.5 | 00.0 | 32.2 | 10.2 | 05.3 | 00.2 | 05.6 |
| UniDAPS [86] | 03.4 | 02.3 | 00.0 | 11.3 | 06.2 | 02.8 | 00.0 | 01.5 |
| EDAPS [55] | 10.3 | 16.6 | 00.0 | 30.8 | 06.5 | 11.4 | 00.4 | 06.2 |
| UnmaskFormer [7] | 11.1 | 17.6 | 00.0 | 35.2 | 14.2 | 02.9 | 00.8 | 07.1 |
| B | Source-only | 10.5 | 15.8 | 00.0 | 33.9 | 13.5 | 03.6 | 00.2 | 06.8 |
| 360SFUDA++ [95] | 10.5 | 15.7 | 00.0 | 33.9 | 13.3 | 03.6 | 00.2 | 06.8 |
| UNLOCK (Ours) | 11.6 (↑1.1) | 17.7 | 00.0 | 36.1 | 16.3 | 03.4 | 00.1 | 07.4 |
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+ "table_body": "| Task | Method | Metric | Person | ride | car | huck | bus | monor. | bicycle |
| AIS | Δ | DATR [93] | 08.1 | 14.1 | 00.4 | 23.5 | 09.6 | 04.3 | 04.7 | 00.0 |
| Trans4PASS [85] | 09.2 | 13.0 | 00.2 | 24.7 | 13.0 | 07.6 | 05.7 | 00.0 |
| EDAPS [55] | 09.5 | 16.7 | 00.2 | 25.2 | 11.6 | 06.6 | 06.1 | 00.0 |
| UnmaskFormer [7] | 10.2 | 16.6 | 00.1 | 26.5 | 12.8 | 08.6 | 06.4 | 00.0 |
| Δ | Source-only | 09.7 | 16.0 | 00.0 | 24.9 | 11.9 | 09.1 | 05.6 | 00.0 |
| 360SFUDA++ [95] | 09.6 | 16.2 | 00.0 | 25.3 | 11.7 | 08.9 | 05.2 | 00.0 |
| UNLOCK (Ours) | 10.0 (↑0.3) | 17.3 | 00.0 | 28.9 | 09.2 | 08.3 | 06.4 | 00.0 |
| IS | Δ | DATR [93] | 08.0 | 14.9 | 00.4 | 25.3 | 09.2 | 01.0 | 04.9 | 00.0 |
| Trans4PASS [85] | 09.0 | 15.0 | 00.1 | 27.2 | 11.8 | 04.1 | 05.0 | 00.0 |
| UniDAPS [86] | 00.3 | 00.8 | 00.0 | 00.8 | 00.1 | 00.0 | 00.5 | 00.0 |
| EDAPS [55] | 09.5 | 16.4 | 00.1 | 28.2 | 10.7 | 05.3 | 05.8 | 00.0 |
| UnmaskFormer [7] | 09.6 | 17.0 | 00.1 | 28.4 | 11.9 | 03.8 | 05.9 | 00.0 |
| Δ | Source-only | 09.3 | 17.4 | 00.0 | 26.9 | 11.6 | 04.4 | 04.9 | 00.0 |
| 360SFUDA++ [95] | 09.4 | 17.5 | 00.0 | 27.1 | 11.1 | 05.4 | 04.8 | 00.0 |
| UNLOCK (Ours) | 09.7 (↑0.4) | 17.7 | 00.0 | 29.3 | 09.0 | 05.9 | 06.1 | 00.0 |
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+ "text": "Table 2. Instance-level Segmentation results on the K2B (left) and A2B (right) benchmark. Metrics are reported as: mAAP for Amodal Instance Segmentation (AIS) and mAAP for Instance Segmentation (IS). Per-class results are reported as AAP and AP.",
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+ "image_caption": [
+ "Figure 6. Visualization results. From top to bottom are (a) Image, (b) GT, (c) Source-only, and (d) 360SFUDA++ [95], and (e) UNLOCK."
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+ "text": "set to 10. The analysis of these thresholds is provided in the supplementary material. Our experiments are conducted on a single NVIDIA GTX 3090 GPU using PyTorch.",
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+ "text": "4.3. Results of SFOASS",
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+ "text": "K2B. As shown by the Real-to-Real adaptation results in Table 1 and the left side of Table 2, UNLOCK sets a new benchmark for SFOASS, delivering outstanding performance and effectively addressing the unique challenges of limited FoV, occlusion, and constrained data. Compared to the baseline Source-only, UNLOCK outperforms in key metrics for scene understanding including mAPQ, mPQ, and mIoU, with improvements of $+4.3$ , $+2.8$ , and $+2.9$ , respectively. Even compared to UnmaskFormer [7], which has access to both source domain and target images, UNLOCK achieves comparable results in mAPQ. Notably, in instance-level segmentation, UNLOCK surpasses all existing UDA methods[7, 55, 85, 93]—even without access to source domain data containing $12K$ images-label pairs, reaching the highest mAAP of 10.9 and mAP of 11.6, showcasing its robustness and adaptability. As shown in Fig. 6, UNLOCK successfully and precisely segments numerous Thing objects with better shape coherence.",
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+ "text": "A2B. The results from another Synthetic-to-Real adaptation scenario, shown in Table 3 and the right side of Table 2,",
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+ "text": "further demonstrate UNLOCK's exceptional performance. Compared to 360SFUDA++ [95], which is specifically designed for panoramic data, our method significantly outperforms across all SFOASS metrics. This success is driven by the OPLL pseudo-label generation strategy, which is tailored specifically for SFOASS. The instance-level segmentation results highlight a clear advantage for our method, reflecting its enhanced accuracy in segmenting individual object instances within complex scenes.",
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+ "text": "4.4. Ablation Study",
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+ "text": "We conduct a series of ablation studies on the K2B scenario to evaluate the effectiveness of our method.",
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+ "text": "Effectiveness of OPLL. An ablation study was conducted to validate the effectiveness of the OPLL. Table 4 presents the comparison of three different approaches for self-training. Using the final predicted labels from the source model as pseudo-labels or directly using all predictions from the three branches fails to adapt the instance-level branches to the panoramic domain, as evidenced by both mAAP and mAP scores, which are even worse than the no-adaptation Source-only model. With the OPLL designed by us, the knowledge of the source model can be effectively adapted to the target domain by using omni pseudo-labels. Compared with Source-only, OPLL achieves a significant",
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+ "table_footnote": [],
+ "table_body": "| Task | Constraint | Method | Metric | road | sidew | build | wall | fence | pole | lights | sign | vestor | terrain | fly | person | rider | car | track | bus | motor | bicycle |
| APS | (ypan) | DATR [93] | 19.4 | 36.1 | 00.0 | 72.4 | 00.0 | 01.3 | 02.4 | 00.0 | 07.1 | 64.8 | 00.0 | 88.9 | 08.3 | 02.7 | 31.6 | 18.4 | 00.0 | 14.8 | 00.0 |
| TransPASS [85] | 21.5 | 38.7 | 00.0 | 71.9 | 00.0 | 10.0 | 03.8 | 00.0 | 07.4 | 65.3 | 00.0 | 89.2 | 11.1 | 03.7 | 35.3 | 25.4 | 07.6 | 15.9 | 00.9 |
| EDAPS [55] | 21.7 | 45.5 | 00.0 | 74.9 | 00.0 | 08.5 | 04.1 | 00.0 | 06.0 | 63.7 | 00.0 | 89.5 | 12.1 | 02.8 | 35.9 | 20.7 | 09.7 | 17.0 | 00.0 |
| UnmaskFormer [7] | 22.9 | 44.1 | 00.6 | 67.5 | 00.0 | 09.6 | 04.3 | 00.0 | 05.0 | 67.0 | 00.0 | 90.2 | 16.6 | 00.0 | 38.7 | 29.2 | 17.1 | 22.2 | 00.0 |
| (xpan,ypan) | Source-only | 18.9 | 47.1 | 01.9 | 68.5 | 00.0 | 00.9 | 00.5 | 00.0 | 01.6 | 43.0 | 00.0 | 84.7 | 09.5 | 00.0 | 36.3 | 21.5 | 07.5 | 16.7 | 00.0 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 19.4 | 46.6 | 01.9 | 68.1 | 00.0 | 01.0 | 00.5 | 00.0 | 01.7 | 48.2 | 00.0 | 86.1 | 18.8 | 00.0 | 38.5 | 18.1 | 06.4 | 14.1 | 00.0 |
| UNLOCK (Ours) | 21.4 (↑2.5) | 50.8 | 04.7 | 73.5 | 00.0 | 04.8 | 00.6 | 00.0 | 03.9 | 49.8 | 00.0 | 86.2 | 17.5 | 01.2 | 41.4 | 20.2 | 09.3 | 20.9 | 00.0 |
| PS | (ypan) | DATR [93] | 19.5 | 35.7 | 00.0 | 71.5 | 00.0 | 01.3 | 01.8 | 00.0 | 07.1 | 64.8 | 00.0 | 88.9 | 08.3 | 05.0 | 32.2 | 15.8 | 02.4 | 15.5 | 00.0 |
| TransPASS [85] | 20.9 | 38.1 | 00.0 | 71.9 | 00.0 | 10.0 | 03.8 | 00.0 | 07.4 | 65.3 | 00.0 | 89.2 | 09.6 | 00.0 | 36.5 | 25.0 | 03.3 | 15.9 | 00.0 |
| UniDAPS [86] | 18.2 | 53.1 | 00.0 | 72.4 | 01.8 | 07.8 | 05.5 | 00.0 | 07.7 | 67.8 | 00.0 | 88.7 | 07.0 | 00.0 | 07.7 | 01.6 | 00.0 | 07.0 | 00.0 |
| EDAPS [55] | 21.9 | 46.7 | 00.0 | 75.1 | 00.0 | 08.5 | 04.1 | 00.0 | 06.1 | 63.6 | 00.0 | 89.5 | 11.8 | 02.5 | 36.9 | 23.4 | 08.9 | 16.5 | 00.0 |
| UnmaskFormer [7] | 20.7 | 42.9 | 00.6 | 67.0 | 00.0 | 09.6 | 03.6 | 00.0 | 05.0 | 66.9 | 00.0 | 90.2 | 16.6 | 00.0 | 37.3 | 25.9 | 07.5 | 00.0 | 00.0 |
| (xpan,ypan) | Source-only | 19.0 | 48.8 | 01.9 | 68.6 | 00.0 | 00.9 | 00.5 | 00.0 | 01.6 | 42.8 | 00.0 | 84.7 | 12.7 | 00.0 | 36.2 | 20.3 | 06.4 | 16.8 | 00.0 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 19.3 | 46.5 | 01.9 | 69.9 | 00.0 | 01.0 | 00.5 | 00.0 | 01.7 | 47.9 | 00.0 | 86.0 | 15.6 | 00.0 | 36.5 | 18.9 | 06.5 | 15.2 | 00.0 |
| UNLOCK (Ours) | 20.4 (↑1.4) | 50.5 | 04.2 | 74.0 | 00.0 | 04.8 | 00.6 | 00.0 | 03.9 | 49.2 | 00.0 | 86.3 | 14.3 | 00.0 | 38.1 | 18.8 | 05.7 | 16.8 | 00.0 |
| SS | (ypan) | DATR [93] | 31.5 | 59.5 | 06.3 | 77.7 | 00.2 | 09.2 | 22.9 | 02.4 | 10.3 | 76.6 | 00.0 | 93.4 | 37.7 | 01.9 | 68.8 | 20.8 | 01.5 | 54.1 | 24.2 |
| TransPASS [85] | 34.3 | 58.9 | 07.6 | 77.3 | 00.2 | 28.7 | 26.7 | 05.2 | 11.1 | 76.1 | 00.0 | 93.6 | 35.8 | 01.8 | 73.6 | 28.3 | 06.8 | 55.2 | 30.1 |
| UniDAPS [86] | 36.0 | 61.5 | 07.5 | 76.6 | 00.8 | 30.4 | 27.7 | 10.2 | 11.1 | 77.4 | 00.0 | 93.6 | 47.3 | 02.1 | 49.4 | 25.9 | 33.0 | 62.3 | 30.6 |
| EDAPS [55] | 36.2 | 62.2 | 10.8 | 81.1 | 00.5 | 28.7 | 22.9 | 10.6 | 10.5 | 75.5 | 00.1 | 93.3 | 42.7 | 02.3 | 72.1 | 33.6 | 18.8 | 58.6 | 26.7 |
| UnmaskFormer [7] | 36.1 | 60.6 | 13.3 | 74.2 | 00.9 | 32.7 | 21.6 | 14.2 | 06.9 | 76.7 | 00.0 | 93.9 | 45.2 | 01.2 | 73.3 | 34.1 | 22.0 | 56.9 | 22.7 |
| (xpan,ypan) | Source-only | 31.0 | 67.1 | 21.5 | 76.9 | 03.2 | 17.0 | 17.7 | 02.7 | 06.3 | 64.7 | 00.0 | 90.7 | 40.0 | 01.8 | 69.2 | 19.5 | 04.6 | 47.4 | 08.5 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 31.2 | 64.8 | 21.3 | 77.7 | 03.4 | 16.2 | 18.9 | 02.7 | 06.0 | 66.6 | 00.0 | 91.7 | 41.9 | 02.0 | 67.9 | 19.1 | 04.6 | 49.1 | 07.9 |
| UNLOCK (Ours) | 34.3 (↑3.3) | 69.1 | 25.2 | 81.5 | 00.1 | 25.1 | 20.0 | 03.7 | 10.5 | 68.0 | 00.0 | 91.6 | 45.9 | 01.6 | 71.4 | 24.0 | 07.2 | 50.8 | 21.4 |
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+ "img_path": "images/c1d708024ceba9d17ae088adbe7e7ca12317afea63ca720dec805f61fe7fa379.jpg",
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+ "Table 3. Scene Segmentation results on the A2B benchmark. Metrics are reported as: mAPQ for Amodal Panoptic Segmentation (APS), mPQ for Panoptic Segmentation (PS), and mIoU for Semantic Segmentation (SS). Per-class results are reported as APQ, PQ, and IoU."
+ ],
+ "table_footnote": [],
+ "table_body": " | mAPQ | mPQ | mIoU | mAAP | mAP |
| Source-only | 22.13 | 22.30 | 38.65 | 10.22 | 10.54 |
| Pseudo-Labels | 21.90 | 22.07 | 39.12 | 10.09 | 10.37 |
| All Predictions | 22.38 | 22.31 | 38.90 | 10.15 | 10.50 |
| OPLL (Ours) | 24.71 | 24.00 | 39.03 | 10.52 | 10.52 |
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+ "table_caption": [
+ "Table 4. Ablation analysis for OPLL."
+ ],
+ "table_footnote": [],
+ "table_body": "| Backbone | mAPQ | mPQ | mIoU | mAAP | mAP |
| Source-only | 22.1 | 22.3 | 38.7 | 10.2 | 10.5 |
| Trans4PASS [85] | 26.1 | 25.3 | 40.0 | 10.9 | 11.3 |
| EDAPS [55] | 26.3 | 25.1 | 40.5 | 10.7 | 11.4 |
| UnmaskFormer [7] | 26.4 | 25.1 | 41.6 | 10.9 | 11.6 |
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+ "img_path": "images/bc1b454fef81e47fc30f07bf7a41acac80a9bfc477fee2d92f13d7d5fa92f4aa.jpg",
+ "table_caption": [
+ "Table 5. Ablation analysis for backbones."
+ ],
+ "table_footnote": [],
+ "table_body": "| OPLL | ADCL | mAPQ | mPQ | mIoU | mAAP | mAP |
| | 22.13 | 22.30 | 38.65 | 10.22 | 10.54 |
| ✓ | | 24.71 | 24.00 | 39.03 | 10.52 | 10.52 |
| ✓ | 25.84 | 24.55 | 40.31 | 10.93 | 11.47 |
| ✓ | ✓ | 26.41 | 25.07 | 41.64 | 10.91 | 11.58 |
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+ "table_caption": [
+ "Table 6. Ablation analysis for components."
+ ],
+ "table_footnote": [],
+ "table_body": " | mAPQ | mPO | mLOU | mAAP | mAP |
| Source-only | 22.13 | 22.30 | 38.65 | 10.22 | 10.54 |
| Instance | 25.03 | 24.23 | 38.93 | 10.33 | 10.55 |
| Amodal Instance | 25.71 | 24.50 | 39.06 | 10.77 | 11.22 |
| AoMix [7] | 25.32 | 24.67 | 38.04 | 10.62 | 11.26 |
| ADCL-Random | 24.81 | 23.90 | 38.92 | 10.69 | 11.19 |
| ADCL-Zero (Ours) | 25.84 | 24.55 | 40.31 | 10.93 | 11.47 |
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+ "table_caption": [
+ "Table 7. Ablation analysis for ADCL."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | mIoU |
| SFDA [40] | 42.70 |
| DATC [73] | 43.06 |
| 360SFUDA [96] | 50.12 |
| 360SFUDA++[95] | 52.99 |
| UNLOCK (Ours) | 54.55 |
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+ {
+ "type": "text",
+ "text": "Table 8. SS results on the C2D benchmark.",
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+ {
+ "type": "text",
+ "text": "improvement of 2.58 in mAPQ.",
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+ {
+ "type": "text",
+ "text": "Effectiveness of ADCL. Another ablation study was conducted to validate the effectiveness of the ADCL. Table 7 presents a comparison of different object mixing strategies. Due to incomplete object shapes, instance-based mixing yields limited improvement in mAPQ and mAAP. Directly using amodal instances causes confusion in contextual information. Unlike AoMix [7], which zeros out full amodal object regions of the input image, our method in UNLOCK sets only the overlapping regions to zero (ADCL-Zero), effectively preserving contextual cues. Replacing overlaps with random values (ADCL-Random) yields inferior results, while ADCL-Zero achieves the best mAPQ of 25.84. Component Ablation. As shown in Table 6, by combining OPLL and ADCL, our UNLOCK method achieves the best overall performance, outperforming the Source-only trained on the source pinhole domain with $+4.28$ gains in mAPQ. It shows that our methods can successfully adapt to the target panoramic domain under source-free constraints.",
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+ "text": "Backbone Ablation. As shown in Table 5, we evaluated the performance of UNLOCK across different backbones to verify the effectiveness of the UNLOCK strategy itself. The",
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+ "type": "text",
+ "text": "results indicate that UNLOCK maintains consistent performance across diverse backbone architectures, confirming its backbone-agnostic nature as an SFDA framework.",
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+ "type": "text",
+ "text": "4.5. Results of Panoramic Semantic Segmentation",
+ "text_level": 1,
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+ "type": "text",
+ "text": "To investigate the generalization capability of UNLOCK, we extend UNLOCK to the Semantic Segmentation (SS) task and evaluate it on the Cityscapes-to-DensePASS (C2D) benchmark. As shown in Table 8, UNLOCK achieves a significant improvement of $+1.56$ in mIoU over 360SFUDA++ [95]. Under the pinhole-to-panoramic C2D adaptation scenario, our UNLOCK achieves the new state-of-the-art result of 54.55 in mIoU.",
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+ "text": "5. Conclusion",
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+ "text": "In this paper, we address key constraints in comprehensive scene understanding, to achieve seamless segmentation with $360^{\\circ}$ viewpoint coverage and occlusion-aware reasoning, while adapting without relying on source data and target labels. To this end, we introduce a new task, Source-Free Occlusion-Aware Seamless Segmentation (SFOASS), and propose its first solution UNLOCK. We further applied two SFOASS benchmarks for evaluation: Real-to-Real and Synthetic-to-Real. Extensive experimental results demonstrate the effectiveness of the proposed method.",
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+ "text": "8968",
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+ "type": "text",
+ "text": "Acknowledgment",
+ "text_level": 1,
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+ "text": "This work was supported in part by the National Natural Science Foundation of China (No. 62473139, 62027810), the Major Research Plan of the National Natural Science Foundation of China (No. 92148204), the Top Ten Technical Research Projects of Hunan Province (No. 2024GK1010), the Key Program of Natural Science Foundation of Hunan Province, China (No. 2025JJ30024), the National Key Research and Development Program of China (No. 2024YFB4708900), the Hunan Provincial Research and Development Project (No. 2025QK3019), in part by the Open Research Project of the State Key Laboratory of Industrial Control Technology, China (No. ICT2025B20), and the Science and Technology Project of State Grid Corporation of China (SGCC) Co., LTD (No. 5700-202423229A-1-1-ZN).",
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+ "[86] Jingyi Zhang, Jiaxing Huang, and Shijian Lu. Hierarchical mask calibration for unified domain adaptive panoptic segmentation. In CVPR, 2023. 6, 7, 8",
+ "[87] Jingyi Zhang, Jiaxing Huang, Xiaoqin Zhang, and Shijian Lu. UniDAformer: Unified domain adaptive panoptic segmentation transformer via hierarchical mask calibration. In CVPR, 2023. 3",
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+ "[89] Weiming Zhang, Yexin Liu, Xu Zheng, and Lin Wang. GoodSAM: Bridging domain and capacity gaps via segment anything model for distortion-aware panoramic semantic segmentation. In CVPR, 2024.",
+ "[90] Weiming Zhang, Yexin Liu, Xu Zheng, and Lin Wang. GoodSAM++: Bridging domain and capacity gaps via segment anything model for panoramic semantic segmentation. arXiv preprint arXiv:2408.09115, 2024. 3",
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+ "[92] Junwei Zheng, Ruiping Liu, Yufan Chen, Kunyu Peng, Chengzhi Wu, Kailun Yang, Jiaming Zhang, and Rainer Stiefelhagen. Open panoramic segmentation. In ECCV, 2024. 2",
+ "[93] Xu Zheng, Tianbo Pan, Yunhao Luo, and Lin Wang. Look at the neighbor: Distortion-aware unsupervised domain adaptation for panoramic semantic segmentation. In ICCV, 2023. 3, 6, 7, 8",
+ "[94] Xu Zheng, Jinjing Zhu, Yexin Liu, Zidong Cao, Chong Fu, and Lin Wang. Both style and distortion matter: Dualpath unsupervised domain adaptation for panoramic semantic segmentation. In CVPR, 2023. 3",
+ "[95] Xu Zheng, Pengyuan Zhou, Athanasios V. Vasilakos, and Lin Wang. 360SFUDA++. Towards source-free UDA for panoramic segmentation by learning reliable category prototypes. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2024. 2, 3, 6, 7, 8",
+ "[96] Xu Zheng, Pengyuan Zhou, Athanasios V. Vasilakos, and Lin Wang. Semantics distortion and style matter: Towards source-free UDA for panoramic segmentation. In CVPR, 2024. 2, 3, 8",
+ "[97] Zishuo Zheng, Chunyu Lin, Lang Nie, Kang Liao, Zhijie Shen, and Yao Zhao. Complementary bi-directional feature compression for indoor $360^{\\circ}$ semantic segmentation with self-distillation. In WACV, 2023. 2",
+ "[98] Yan Zhu, Yuandong Tian, Dimitris Metaxas, and Piotr Dóllár. Semantic amodal segmentation. In CVPR, 2017. 2",
+ "[99] Yang Zou, Zhiding Yu, B. V. K. Vijaya Kumar, and Jinsong Wang. Unsupervised domain adaptation for semantic segmentation via class-balanced self-training. In ECCV, 2018. 3"
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diff --git a/2025/Unlocking Constraints_ Source-Free Occlusion-Aware Seamless Segmentation/918ec0ce-e376-4559-8192-30fc256f6bbd_model.json b/2025/Unlocking Constraints_ Source-Free Occlusion-Aware Seamless Segmentation/918ec0ce-e376-4559-8192-30fc256f6bbd_model.json
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+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
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+ "type": "title",
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+ "content": "Unlocking Constraints: Source-Free Occlusion-Aware Seamless Segmentation"
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+ "content": "Yihong Cao\\(^{1,2,*}\\) Jiaming Zhang\\(^{3,4,*}\\) Xu Zheng\\(^{5,6}\\) Hao Shi\\(^{7}\\) Kunyu Peng\\(^{3}\\) Hang Liu\\(^{1}\\) Kailun Yang\\(^{1,\\dagger}\\) Hui Zhang\\(^{1,\\dagger}\\) \n\\(^{1}\\)Hunan University \\(^{2}\\)Hunan Normal University \\(^{3}\\)Karlsruhe Institute of Technology \\(^{4}\\)ETH Zürich HKUST(GZ) \\(^{6}\\)INSAIT, Sofia University \"St. Kliment Ohridski\" \\(^{7}\\)Zhejiang University"
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+ "content": "Figure 1. UNLOCK framework \\((a)\\) solves the Source-Free Occlusion-Aware Seamless Segmentation (SFOASS), enabling segmentation with \\(360^{\\circ}\\) viewpoint coverage and occlusion-aware reasoning while adapting without requiring source data and target labels, and \\((b)\\) outperforms existing SFDA methods on the Real-to-Real scenario [7] across all five segmentation metrics (i.e., mAPQ for amodal panoptic, mPQ for panoptic, mIoU for semantic, mAAP for amodal instance, and mAP for instance)."
+ },
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+ "type": "title",
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+ "content": "Abstract"
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+ "content": "Panoramic image processing is essential for omnicontext perception, yet faces constraints like distortions, perspective occlusions, and limited annotations. Previous unsupervised domain adaptation methods transfer knowledge from labeled pinhole data to unlabeled panoramic images, but they require access to source pinhole data. To address these, we introduce a more practical task, i.e., Source-Free Occlusion-Aware Seamless Segmentation (SFOASS), and propose its first solution, called UNconstrained Learning Omni-Context Knowledge (UNLOCK). Specifically, UNLOCK includes two key modules: Omni Pseudo-Labeling Learning and Amodal-Driven Context Learning. While adapting without relying on source data or target labels, this framework enhances models to achieve segmentation with \\(360^{\\circ}\\) viewpoint coverage and occlusion-aware reasoning. Furthermore, we benchmark the proposed SFOASS task through both real-to-real and synthetic-to-real adaptation settings. Experimental results show that our source-free method achieves performance comparable to source-dependent methods, yielding state-of-the-art"
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+ "content": "scores of 10.9 in mAAP and 11.6 in mAP, along with an absolute improvement of +4.3 in mAPQ over the source-only method. All data and code will be made publicly available at https://github.com/yihong-97/UNLOCK."
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+ "content": "1. Introduction"
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+ "content": "Scene understanding is a foundational task in computer vision, essential for various downstream applications like autonomous driving [44, 77], virtual reality [11, 58], and robotics [3, 60]. Despite significant advances in the field, current methods still face challenges in achieving both comprehensive and human-like perceptions of surrounding environments, limiting their ability to fully understand scenes. Multiple critical research questions remain unsolved."
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+ "content": "1) How to efficiently expand to \\(360^{\\circ}\\) field of view? Traditional scene understanding methods [9, 21, 70] tailored for pinhole imagery, are limited by a narrow Field of View (FoV). In contrast, panoramic vision offers \\(360^{\\circ}\\) view in a single shot, which has the potential to facilitate more comprehensive scene understanding [1, 19]. However, directly applying traditional methods to panoramic data often results in unreliable performance due to challenges such as"
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+ "content": "* Equal contribution. † Corresponding authors (e-mail: kailun.yang@hnu.edu.cn, zhanghuihby@126.com)."
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+ "content": "distortions [92]. For effective panoramic understanding, it is essential to learn omni-context knowledge when transferring from the pinhole domain to the panoramic domain. This knowledge transfer is crucial for accurate feature interpretation and wide-FoV representation, ultimately enabling seamless \\(360^{\\circ}\\) scene understanding [84, 85]."
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+ "content": "2) How can amodal prediction be improved to extend the depth of view? Amodal perception [34, 53], the ability to predict an occluded object's complete shape, is key to robust scene understanding [83] and mirrors human-like perception. Extending the depth of view (vertical to field of view) means that models can achieve seamless perception, which refers to pixel-level segmentation of the background and occlusion-aware instance-level segmentation of the foreground. Beyond the previous amodal segmentation methods [16, 98], how to improve occlusion-aware reasoning like OASS [7] in both directions (depth and field of view) simultaneously remains challenging."
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+ "content": "3) How can models adapt to panoramic domains without source data? Apart from the field and depth of view, the scarcity of labeled data presents a significant limitation in panoramic vision. To address the lack of labeled data, Unsupervised Domain Adaptation (UDA) leverages labeled data from the source domain while training on unlabeled data from the target domain [7, 24, 25, 28, 32, 65]. However, UDA methods still rely on access to source domain, which can often be challenging or even impossible due to privacy concerns or commercial restrictions on source datasets, such as in autonomous driving [40, 95, 96]. This restriction leads us to source-free learning, i.e. how to adapt models to panoramic domains without source data. However, it remains under-explored in amodal panoramic vision."
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+ "type": "text",
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+ "content": "In this work, to address the aforementioned challenges in scene understanding, we extend the OASS [7] task and introduce a more practical task, i.e., Source-Free Occlusion-Aware Seamless Segmentation (SFOASS). To tackle this task, we propose its first solution, called UNconstrained Learning Omni-Context Knowledge (UNLOCK). As shown in Fig. 1a, UNLOCK improves panoramic seamless segmentation performance under adaptation constraints without requiring source data and target labels. Specifically, to effectively capture the domain-invariant knowledge from the source domain, a method called Omni PseudoLabeling Learning (OPLL) is proposed. Besides, to learn intra-domain knowledge and integrate the domain-invariant knowledge, we put forward the Amodal-Driven Context Learning (ADCL) strategy. Together, OPLL and ADCL adapt the source model trained on pinhole data to target panoramic images while enhancing panoramic perception and occlusion-aware reasoning. With OPLL as the key and ADCL performing the unlocking action, they work in synergy to unlock the constraints in SFOASS, thereby enabling seamless perception of the model towards panoramic data."
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+ "content": "Aside from Real-to-Real source-free adaptation on the KITTI360-APS \\(\\rightarrow\\) BlendPASS benchmark [7], we pioneer Synthetic-to-Real adaptation in OASS and SFOASS and introduce AmodalSynthDrive \\(\\rightarrow\\) BlendPASS to investigate the potential of adapting synthetic panoramic images to the real panoramic image domain. Extensive experiments are conducted on both SFOASS benchmarks. Without access to the original source data (neither images nor labels), our UNLOCK framework can obtain on-par performance as compared to UDA-based methods that require all source data. Surprisingly, as shown in Fig. 1b, results on the Real-to-Real scenario [7] show an absolute improvement of \\(+4.3\\) in mAPQ, reaching 26.4, compared to the source-only method, and outperforms UDA methods using \\(12K\\) images in instance-level segmentation, with state-of-the-art scores of 10.9 in mAAP and 11.6 in mAP, respectively."
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+ "type": "text",
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+ "content": "In this work, we propose contributions as follows:"
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+ "content": "- We introduce the Source-Free Occlusion-Aware Seamless Segmentation (SFOASS) task and its first solution, UNconstrained Learning Omni-Context Knowledge (UNLOCK). The UNLOCK framework enables models to achieve segmentation with \\(360^{\\circ}\\) viewpoint coverage and occlusion-aware reasoning while adapting without the need for source data and target labels."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- To fully exploit the knowledge from source and target domains, Omni Pseudo-Labeling Learning (OPLL) and Amodal-Driven Context Learning (ADCL) strategies are introduced in UNLOCK to achieve occlusion-aware seamless segmentation for panoramic images."
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+ "content": "- Extensive experiments conducted on two SFOASS scenarios, Real-to-Real and Synthetic-to-Real, demonstrate the effectiveness of the UNLOCK framework, highlighting its ability to achieve competitive performance."
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+ "content": "2. Related Work"
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+ "content": "Seamless segmentation. Seamless segmentation, as introduced by [7], aims to achieve amodal-level segmentation for large-FoV images, enabling unified, occlusion-aware scene understanding. Wide-FoV segmentation on fisheye [12, 56, 59, 78, 80] and panoramic images [22, 35, 75, 76, 97] facilitates comprehensive \\(360^{\\circ}\\) scene comprehension [74]. Panoramic panoptic segmentation enhances scene understanding by providing instance-level insights [17, 30, 47, 52]. Amodal segmentation extends this concept by predicting both visible and occluded object regions [4, 10, 15, 23, 38, 41, 61, 63]. Li et al. [34] pioneered amodal instance segmentation, introducing occlusion-aware segmentation through iterative regression. Subsequent datasets adapted for amodal segmentation [98] and occlusion classification [53] have driven further advances. Shape and contour priors [8, 18, 36, 37, 69] have further refined segmentation accuracy. In addition to instance segmentation, amodal panoptic segmentation has been explored [5, 26, 98]. Mo"
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+ "content": "han et al. [48, 49] combined semantic and amodal segmentation for amodal panoptic segmentation. Recent methods, including pix2gestalt [51], AISDiff [64], and Xu et al. [72], leverage diffusion model priors for amodal segmentation. Although seamless segmentation [7] unifies aforementioned segmentation paradigms to form occlusion-aware scene understanding for panoramic vision, our work emphasizes source-free seamless segmentation, aiming for high accuracy even with restricted access to labeled source data."
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+ "content": "Source-free domain adaptation. Existing works dealing with domain gaps on semantic segmentation tasks mostly focus on UDA where labeled source domain data is required [20, 62, 68, 71, 84, 84, 85, 91, 93, 94, 99]. Source-Free Domain Adaptation (SFDA) [6, 14, 33, 40, 43, 54, 67, 79, 81] is a more practical approach compared with UDA, as it removes the need for access to source data during the adaptation process. As sub-directions of scene segmentation, domain adaptation of panoptic segmentation is challenging as it must distinguish and integrate semantic and instance information across domains, as highlighted in existing works [27, 45, 46, 55, 87]. To overcome the limitations of the FoV, domain adaptation in panoramic segmentation facilitates comprehensive scene understanding across a full \\(360^{\\circ}\\) perception, while effectively harnessing the rich knowledge from label-dense pinhole domains. Researchers have explored both UDA [31, 84, 85, 88-90, 94] and SFDA [95, 96] settings for panoramic segmentation. Jaus et al. [29, 30] illustrate the need for panoramic panoptic segmentation in autonomous driving. Zheng et al. [95, 96] for the first time, explored SFDA in panoramic semantic segmentation. However, the SFDA challenge remains unexplored for OASS [7]. In this work, we introduce the novel SFOASS task and benchmark it across two scenarios. We also proposed the first solution UNLOCK, a novel method designed to unlock constraints posed by SFOASS."
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+ "content": "3.1. Overview"
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+ "content": "OASS. In the OASS [7], the objective is to use a labeled source pinhole domain \\(\\mathcal{D}^{pin} = \\{x_i^{pin}, y_i^{pin}\\}_{i=1}^{N^{pin}}\\) and an unlabeled target panoramic domain \\(\\mathcal{D}^{pan} = \\{x_i^{pan}\\}_{i=1}^{N^{pan}}\\) to obtain an OASS model \\(F\\) that performs well in \\(\\mathcal{D}^{pan}\\). Both domains share the same \\(C\\) categories, which can be further divided into \\(C^{stu}\\) Stuff classes and \\(C^{thi}\\) Thing classes. Ultimately, the \\(F\\) should be able to output five segmentation results with the input panoramic image at once: semantic, instance, amodal instance, panoptic, and amodal panoptic maps. Typically, \\(F\\) is designed to contain a shared encoder and three detection branches: semantic, instance, and amodal instance branches, each outputting corresponding predictions \\(p_i^{sem}, p_i^{ins}, p_i^{ains}\\), denoted as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.195,
+ 0.885,
+ 0.483,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {i} ^ {\\text {s e m}}, p _ {i} ^ {\\text {i n s}}, p _ {i} ^ {\\text {a i n s}} = F (x _ {i}), \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.091,
+ 0.905,
+ 0.244
+ ],
+ "angle": 0,
+ "content": "where \\( p_i^{sem} \\in \\mathbb{R}^{H \\times W \\times C} \\) represents the semantic prediction of the input image \\( x_i \\in \\mathbb{R}^{H \\times W \\times 3} \\). \\( p_i^{ins} \\) and \\( p_i^{ains} \\) represent the instance and amodal instance predictions, respectively, with each including class \\( \\in \\mathbb{R}^{C^{thi}} \\), score \\( \\in [0,1] \\), and mask \\( \\in \\mathbb{R}^{H \\times W} \\) predictions for jth object. During adaptation, the label \\( y_i \\) of \\( x_i \\) consists of three components: semantic \\( y_i^{sem} \\), instance \\( y_i^{ins} \\), and amodal instance \\( y_i^{ains} \\) labels, used for supervised learning in their respective branches. In the inference phase, the predictions from all three branches are fused to produce five segmentation maps of OASS."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.245,
+ 0.907,
+ 0.395
+ ],
+ "angle": 0,
+ "content": "SFOASS. Considering privacy and storage limitations, this work introduces a more practical task, i.e., SFOASS. In the adaptation phase, the source pinhole domain \\( \\mathcal{D}^{pin} \\) is locked and inaccessible. Given a source model \\( F^{pin} \\) well-trained from \\( \\mathcal{D}^{pin} \\), and \\( \\mathcal{D}^{pan} \\), the goal of SFOASS is to adapt the source model \\( F^{pin} \\) with only unlabeled panoramic data \\( \\{x_{i}^{pan}\\}_{i=1}^{N^{pan}} \\), obtaining a target model \\( F^{pan} \\) that performs well in the target panoramic domain. (For ease of expression, the superscript \"pan\" for target panoramic domain will be omitted henceforth.)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.398,
+ 0.907,
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+ ],
+ "angle": 0,
+ "content": "How can models adapt to panoramic domains without source data, while expanding the field and depth of view? To answer this, we propose a novel method called UNconstrained Learning Omni-Context Knowledge (UNLOCK). It can further enhance the performance of panoramic seamless prediction while improving occlusion-aware reasoning. Specifically, as shown in Fig. 2, in response to the challenge that existing self-training methods are ineffective for the SFOASS task, we designed an Omni Pseudo-Labeling Learning (OPLL) approach. This approach leverages all predictions to generate omni soft labels. These generated labels serve as the \"key\" to the proposed UNLOCK. Furthermore, we propose a brand-new Amodal-Driven Contextual Learning (ADCL) strategy, which effectively resolves the conflict between the real object shapes and contextual knowledge for the occluded object. Ultimately, the ADCL holds the \"key\" and performs the \"unlocking\" action, completing the source-free adaptation to the panoramic domain."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.697,
+ 0.805,
+ 0.714
+ ],
+ "angle": 0,
+ "content": "3.2. Omni Pseudo-Labeling Learning"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.72,
+ 0.907,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "In the SFOASS, only unlabeled target panoramic images \\(\\{x_i\\}_{i=1}^N\\) are accessible. Common solutions [2, 6, 33] typically involve generating pseudo-labels of target images for training. Pseudo-label generation usually entails filtering model predictions based on pre-defined thresholds. However, we found that directly using the filtered pseudo-labels for self-training in the SFOASS led to performance degradation for instance and amodal instance branches compared to the source model. The OASS task consists of a pixel-wise semantic branch and two object-wise instance-level branches (instance and amodal instance) based on region proposals. For the instance-level branches, each object is"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
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+ "angle": 0,
+ "content": "8963"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.097,
+ 0.09,
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+ 0.335
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.344,
+ 0.908,
+ 0.388
+ ],
+ "angle": 0,
+ "content": "Figure 2. Illustration of the proposed UNLOCK. To address the challenge of the inaccessible source domain and target labels in SFOASS, we propose Omni Pseudo-labeling Learning (OPLL) and Amodal-Driven Contextual Learning (ADCL) modules. OPLL serves as the key, and ADCL, holding the key, unlocks the constraints of SFOASS, enabling effective adaptation of the target model to the panoramic domain."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.402,
+ 0.484,
+ 0.477
+ ],
+ "angle": 0,
+ "content": "assigned a binary mask for binary cross-entropy loss. However, inaccurate pseudo-labels can hinder learning. When object parts are mistakenly labeled as background, even if the model correctly detects the objects, the pseudo-labels may force it to incorrectly classify them as absent."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.123,
+ 0.483,
+ 0.231,
+ 0.545
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.165,
+ 0.546,
+ 0.189,
+ 0.554
+ ],
+ "angle": 0,
+ "content": "Image"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ 0.483,
+ 0.341,
+ 0.544
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ 0.545,
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+ ],
+ "angle": 0,
+ "content": "Semantic Predictions"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.346,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ 0.545,
+ 0.439,
+ 0.554
+ ],
+ "angle": 0,
+ "content": "Instance Predictions"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.134,
+ 0.558,
+ 0.441,
+ 0.571
+ ],
+ "angle": 0,
+ "content": "(a) Incorrect predictions (cyclists in red) of the Stuff class."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.123,
+ 0.576,
+ 0.231,
+ 0.638
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.148,
+ 0.639,
+ 0.206,
+ 0.647
+ ],
+ "angle": 0,
+ "content": "All Predictions"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.235,
+ 0.576,
+ 0.342,
+ 0.638
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.245,
+ 0.639,
+ 0.333,
+ 0.647
+ ],
+ "angle": 0,
+ "content": "Certain Pseudo-Labels"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.346,
+ 0.576,
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+ 0.638
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.363,
+ 0.639,
+ 0.438,
+ 0.648
+ ],
+ "angle": 0,
+ "content": "Uncertainty Region"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.144,
+ 0.651,
+ 0.43,
+ 0.663
+ ],
+ "angle": 0,
+ "content": "(b) Omni pseudo-label generation with CS thresholds."
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.671,
+ 0.483,
+ 0.698
+ ],
+ "angle": 0,
+ "content": "Figure 3. Solution to the challenge of predictions from the source model in OPLL, illustrated with the amodal instance branch."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.705,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "To address this, we developed the OPLL method, which introduces generating omni pseudo-labels using Classwise Self-tuning (CS) thresholds and applying uncertainty-guided instance loss. Since the two instance-level branches perform the same operations, we will introduce one branch as an example below. Specifically, we first utilized the semantic branch's predictions to impose additional constraints on the predictions of both instance-level branches. As shown in Fig. 3a, we observed that the instance-level branch, constrained by local information, may misclassify the statue in the shop window as a cyclist of Thing class. In contrast, the semantic branch, aided by global information, can usually understand the scenes correctly. For each"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.401,
+ 0.907,
+ 0.448
+ ],
+ "angle": 0,
+ "content": "panoramic image \\( x_{i} \\), we obtain the Thing mask \\( m^{th i} \\) by the semantic prediction, then use it to revise the object mask of instance-level predictions \\( p_{i}^{il} \\), \\( il \\in \\{ins, ains\\} \\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.573,
+ 0.454,
+ 0.906,
+ 0.488
+ ],
+ "angle": 0,
+ "content": "\\[\nm ^ {t h i} = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\operatorname {a r g m a x} p ^ {s e m} \\in C ^ {t h i} \\\\ 0, & \\text {e l s e} \\end{array} , \\right. \\tag {2}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.651,
+ 0.5,
+ 0.905,
+ 0.518
+ ],
+ "angle": 0,
+ "content": "\\[\n\\tilde {p} _ {i} ^ {i l} = p _ {i} ^ {i l} \\cap m ^ {t h i}. \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.522,
+ 0.907,
+ 0.616
+ ],
+ "angle": 0,
+ "content": "Then, considering the inconsistent number of objects and the significant imbalance in the source model's capabilities across different Thing classes (as shown in SourceOnly of Table 2), we propose a simple and effective CS threshold method for the predictions of the SFOASS task. For each branch, the CS thresholds \\(\\tau = \\{\\tau_c\\}_{c=1}^{C^{thi}}\\) is determined by:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.574,
+ 0.622,
+ 0.905,
+ 0.642
+ ],
+ "angle": 0,
+ "content": "\\[\n\\tau_ {c} = \\operatorname {a r g m a x} _ {\\tau \\in \\left\\{\\tau^ {f i x}, \\tau^ {p e r} \\right\\}} N _ {c} ^ {\\tau}, c \\in C ^ {t h i}, \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.65,
+ 0.907,
+ 0.802
+ ],
+ "angle": 0,
+ "content": "where \\( N_{c}^{\\tau^{fix}} \\) represents the number of objects of class \\( c \\) whose score exceeds \\( \\tau^{fix} \\) across all predictions \\( \\{\\hat{p}_i\\}_{i=1}^N \\), and \\( N_{c}^{\\tau^{per}} \\) denotes the number of objects of class \\( c \\) in the top \\( \\tau^{per} \\) percentage when the score of all predictions \\( \\{\\hat{p}_i\\}_{i=1}^N \\) are sorted in descending order. For the semantic branch, the score is replaced with the maximum predicted probability of \\( p_i^{sem} \\). This approach generates high-quality pseudo-labels while effectively addressing the issue of low confidence scores for certain classes, caused by the source model \\( F^{pin} \\) inconsistent performance across classes."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.802,
+ 0.905,
+ 0.833
+ ],
+ "angle": 0,
+ "content": "Then, we filter out high-quality predictions based on CS thresholds \\(\\pmb{\\tau}\\) as certain pseudo-labels \\(\\hat{y}_i^{cer}\\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.627,
+ 0.845,
+ 0.905,
+ 0.865
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {y} _ {i} ^ {c e r} = \\left\\{\\hat {p} _ {i} ^ {(j)} \\mid \\hat {p} _ {i} ^ {(j)} > \\tau \\right\\}, \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.869,
+ 0.905,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "where \\(\\hat{p}_i^{(j)}\\) represent the prediction of \\(j\\)th object in predictions \\(p_i\\) for input image \\(x_i\\). To fully utilize the predictions,"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
+ 0.945,
+ 0.516,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "8964"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.113,
+ 0.09,
+ 0.462,
+ 0.171
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.177,
+ 0.486,
+ 0.234
+ ],
+ "angle": 0,
+ "content": "Figure 4. Comparison of object extraction methods: Amodal instance extraction mixes information from other objects, while instance-based extraction may yield incomplete shapes. Our method avoids these issues and preserves spatial awareness."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.258,
+ 0.483,
+ 0.29
+ ],
+ "angle": 0,
+ "content": "we treat the remaining masks of the other predictions as uncertainty region \\(\\hat{y}_i^{uncer}\\) for the current image:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.097,
+ 0.297,
+ 0.484,
+ 0.334
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {y} _ {i} ^ {\\text {u n c e r}} = \\left(1 - \\mathbf {1} _ {\\left\\{\\sum_ {j} \\hat {y} _ {i} ^ {\\text {c e r}} > 0 \\right\\}}\\right) \\cap \\left(\\mathbf {1} _ {\\left\\{\\sum_ {j} \\left(\\hat {p} _ {i} ^ {(j)} \\mid \\hat {p} _ {i} ^ {(j)} < \\boldsymbol {\\tau}\\right) > 0 \\right\\}}\\right), \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.334,
+ 0.485,
+ 0.564
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbf{1}_{\\{\\cdot\\}}\\) is indicator function. The left-hand side of \\(\\cap\\) in Eq. 6 ensures that the object region of \\(\\hat{y}_i^{cer}\\) is not misassigned as the uncertain region. They form the omni pseudo-labels \\(\\hat{y}_i = \\{\\hat{p}_i^{(1)}, \\hat{p}_i^{(2)}, \\dots, \\hat{y}_i^{uncer}\\}\\) of the training panoramic image \\(x_i\\). We believe that all predictions from both instance-level branches of the source model can provide effective knowledge. For the semantic branch, the \\(j\\) is replaced with the pixel spatial location. Finally, for each training panoramic image \\(x_i\\), we obtain three types of omni pseudo-labels \\(\\hat{y}_i^{sem}, \\hat{y}_i^{ins}, \\hat{y}_i^{ains}\\) for training. During the adaptation process of the target model \\(F^{pan}\\), following [7], the cross-entropy loss is used for the semantic branch. For the instance-level branches, we introduce a novel uncertain-guided Binary Cross Entropy (BCE) loss \\(\\mathcal{L}_{ur}\\), specifically tailored for the SFOASS task."
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.135,
+ 0.572,
+ 0.483,
+ 0.591
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {u r} = \\left(1 - \\hat {y} _ {i} ^ {u n c e r}\\right) \\odot \\mathrm {B C E} \\left(F ^ {p a n} \\left(x _ {i}\\right), \\hat {y} _ {i} ^ {c e r}\\right). \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.599,
+ 0.484,
+ 0.661
+ ],
+ "angle": 0,
+ "content": "This approach effectively mitigates prediction errors of the target panoramic data arising from the source pinhole model, allowing the target model to focus on high-quality object samples during the adaptation process."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.668,
+ 0.414,
+ 0.685
+ ],
+ "angle": 0,
+ "content": "3.3. Amodal-Driven Contextual Learning"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.689,
+ 0.483,
+ 0.825
+ ],
+ "angle": 0,
+ "content": "Through OPLL, we leverage the source model to generate omni pseudo-labels of the unlabeled panoramic data, obtaining the \"key\" for adapting the model to the target domain. It primarily extracts domain-invariant knowledge from the pinhole-tolerant source model. We further introduce the ADCL strategy to learn intra-domain knowledge while integrating domain-invariant knowledge. It holds the \"key\" to complete the \"unlocking\" action, and achieves the adaptation to the panoramic images in a source-free manner."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.826,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Mixing is an effective strategy often used in UDA methods [2, 50, 82]. The typical approach involves randomly extracting objects from other data and pasting them into the current training image to form new mixed training samples. However, this approach is not suitable for the OASS model"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.318
+ ],
+ "angle": 0,
+ "content": "with an amodal instance branch, and it can confuse semantic context and hinder model learning. Specifically, since the two instance branches in the OASS model are independent, their predictions are not correlated, leaving us with the option of relying on one of the predictions. As shown by the car in Fig. 4, the amodal instance prediction captures the complete shape of the car. However, this prediction only provides the full mask for the object, meaning that the occluded areas in the mask may inadvertently include parts of other objects. If these masks are directly used for mixing, incorrect contextual information can be introduced. On the other hand, relying on instance predictions focuses only on non-occluded regions, making it difficult for the model to learn the full shape of objects. This dual challenge complicates the learning process in SFOASS tasks."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.318,
+ 0.905,
+ 0.381
+ ],
+ "angle": 0,
+ "content": "First, we use OPLL with stricter thresholds \\(\\tau^{\\prime fix}\\) and \\(\\tau^{\\prime per}\\) to build a buffer pool \\(\\mathcal{B}\\) of \\(K\\) high-quality object samples, relying solely on predictions from the amodal instance branch to accurately capture object shapes."
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.532,
+ 0.391,
+ 0.905,
+ 0.418
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {B} = \\left\\{o ^ {(1)}, o ^ {(2)}, \\dots , o ^ {(K)} \\right\\}, \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.562,
+ 0.412,
+ 0.868,
+ 0.433
+ ],
+ "angle": 0,
+ "content": "where \\(o^{(k)}\\in \\{\\hat{y}_i^{ains\\to cer}|\\big(\\tau^{\\prime^{fix}},\\tau^{\\prime^{per}}\\big)\\}_{i = 1}^{N^{pan}}\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.446,
+ 0.906,
+ 0.554
+ ],
+ "angle": 0,
+ "content": "The \\( o^{(k)} \\) represents the filtered certain object obtained through OPLL from the panoramic data. Additionally, for each \\( o^{(k)} = \\{o_{ful}^{(k)}, o_{ovp}^{(k)}\\} \\), we include not only the mask \\( o_{ful} \\) of the predicted full region but also record the overlapping region \\( o_{ovp} \\) between the object and other objects in the same image, regardless of whether they are occluded. This process results in an amodal-driven object pool \\( \\mathcal{B} \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.555,
+ 0.906,
+ 0.691
+ ],
+ "angle": 0,
+ "content": "Furthermore, we introduce a novel spatial-aware mixing strategy based on the amodal-driven object pool, enriching the diversity of unlabeled panoramic images by generating amodal-driven mixed samples while respecting panoramic layouts. This spatially consistent mixing ensures semantic coherence, aligning distortions in the panoramic layout even after object insertion. During the adaptation phase, we randomly select \\( R \\) object samples \\( \\mathcal{O} = \\{o^{(r)}\\}_{r=1}^{R} \\) from \\( \\mathcal{B} \\) and integrate them into the current training image \\( x_{i} \\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.599,
+ 0.701,
+ 0.905,
+ 0.726
+ ],
+ "angle": 0,
+ "content": "\\[\n\\tilde {x} _ {i} = \\left(1 - o _ {f u l} ^ {(r)}\\right) \\odot x _ {i} + o _ {f u l} ^ {(r)} \\odot x _ {r}, \\tag {9}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.733,
+ 0.906,
+ 0.812
+ ],
+ "angle": 0,
+ "content": "where \\( x_{r} \\) represents the image corresponding to the paste object \\( o^{(r)} \\). For ambiguous regions of \\( o^{(r)} \\) (i.e., potentially occluded areas), we assign zero pixels during the mixing process while keeping the complete mask as the label according to the \\( o_{ovp}^{(r)} \\)."
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.634,
+ 0.822,
+ 0.905,
+ 0.842
+ ],
+ "angle": 0,
+ "content": "\\[\n\\tilde {x} _ {i} = \\left(1 - o _ {o v p} ^ {(r)}\\right) \\odot \\tilde {x} _ {i}. \\tag {10}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.853,
+ 0.906,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "For the three pseudo-labels \\(\\tilde{y}_i^{sem},\\tilde{y}_i^{ins},\\tilde{y}_i^{ains}\\) of the mixed image \\(\\tilde{x}_i\\) , we only use \\(\\{o_{ful}^{(r)}\\}_{r = 1}^{R}\\) to modify them accordingly. This strategy preserves the full shape of objects while"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "8965"
+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
+ 0.095,
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+ "angle": 0,
+ "content": "| Task | Constraint | Method | Metric | road | sidew. | buid. | wall | fence | pole | tlnight | Insign | lager | fermin | sky | Pedes | cylulus | car | Ink | outch | van | whlte |
| APS | (ypan) | DATR [93] | 20.3 | 51.8 | 09.2 | 59.9 | 11.9 | 12.0 | 02.0 | 00.0 | 03.9 | 64.6 | 14.1 | 70.4 | 11.1 | 00.0 | 39.3 | 00.0 | 03.2 | 10.1 | 01.3 |
| Trans4PASS [85] | 22.9 | 53.9 | 14.1 | 69.4 | 19.2 | 11.8 | 03.8 | 00.0 | 05.2 | 67.6 | 16.0 | 77.4 | 15.3 | 04.2 | 41.1 | 06.6 | 00.0 | 00.0 | 07.4 |
| EDAPS [55] | 23.1 | 54.9 | 17.0 | 66.9 | 18.8 | 14.5 | 05.8 | 04.0 | 04.6 | 68.2 | 16.0 | 72.8 | 19.0 | 00.0 | 36.7 | 05.8 | 04.4 | 00.0 | 07.2 |
| UnmaskFormer [7] | 26.6 | 61.8 | 24.7 | 66.8 | 20.8 | 15.8 | 05.3 | 04.3 | 03.3 | 69.0 | 18.4 | 79.4 | 20.5 | 03.1 | 44.6 | 12.8 | 11.3 | 00.0 | 16.6 |
| (xpan,ypan) | Source-only | 22.1 | 57.1 | 14.2 | 73.6 | 15.5 | 07.6 | 00.7 | 00.0 | 10.4 | 58.3 | 12.4 | 83.1 | 15.2 | 00.0 | 40.3 | 03.8 | 00.0 | 00.0 | 06.1 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 24.5 | 60.3 | 16.8 | 71.7 | 14.1 | 07.7 | 00.0 | 00.0 | 08.4 | 55.6 | 13.6 | 81.3 | 21.5 | 03.2 | 46.3 | 19.4 | 02.2 | 00.0 | 19.4 |
| UNLOCK (Ours) | 26.4 (↑4.3) | 62.7 | 14.4 | 74.8 | 20.2 | 11.2 | 00.8 | 00.0 | 08.0 | 62.9 | 18.3 | 84.0 | 21.9 | 03.6 | 45.8 | 19.4 | 00.0 | 03.1 | 24.4 |
| PS | (ypan) | DATR [93] | 19.6 | 50.4 | 09.1 | 59.9 | 11.9 | 12.0 | 02.0 | 00.0 | 03.9 | 64.6 | 14.1 | 70.5 | 12.2 | 00.0 | 38.1 | 00.0 | 03.4 | 00.0 | 01.3 |
| Trans4PASS [85] | 22.7 | 53.9 | 14.1 | 69.4 | 19.2 | 11.8 | 03.8 | 00.0 | 05.2 | 67.6 | 16.0 | 77.4 | 14.6 | 04.1 | 38.2 | 06.9 | 00.0 | 00.0 | 07.2 |
| UniDAPS [86] | 22.7 | 66.0 | 09.5 | 66.3 | 17.4 | 14.3 | 04.8 | 00.0 | 06.1 | 67.2 | 16.1 | 72.7 | 08.3 | 00.0 | 27.3 | 14.8 | 09.2 | 00.0 | 08.9 |
| EDAPS [55] | 23.1 | 55.0 | 17.1 | 66.8 | 18.7 | 14.5 | 05.8 | 04.0 | 04.7 | 68.2 | 16.0 | 72.8 | 19.6 | 00.0 | 37.8 | 01.8 | 04.4 | 00.0 | 07.9 |
| UnmaskFormer [7] | 26.2 | 61.7 | 24.7 | 66.8 | 20.8 | 15.8 | 05.2 | 04.3 | 03.3 | 69.0 | 18.4 | 79.4 | 20.9 | 03.5 | 43.0 | 11.3 | 07.6 | 00.0 | 16.0 |
| (xpan,ypan) | Source-only | 22.3 | 57.8 | 14.2 | 73.8 | 15.5 | 07.6 | 00.7 | 00.0 | 10.4 | 58.3 | 12.4 | 83.2 | 14.9 | 00.0 | 39.1 | 06.0 | 00.0 | 00.0 | 07.7 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 23.7 | 61.3 | 16.8 | 72.2 | 14.1 | 07.6 | 00.0 | 00.0 | 08.4 | 55.9 | 13.6 | 81.3 | 18.4 | 00.0 | 40.6 | 16.4 | 02.4 | 00.0 | 17.6 |
| UNLOCK (Ours) | 25.1 (↑2.8) | 60.4 | 14.4 | 75.7 | 20.2 | 11.2 | 00.7 | 00.0 | 08.0 | 63.6 | 18.3 | 84.0 | 16.9 | 00.0 | 40.0 | 18.5 | 00.0 | 00.0 | 19.4 |
| SS | (ypan) | DATR [93] | 34.9 | 71.9 | 27.2 | 70.6 | 22.8 | 36.0 | 23.9 | 00.0 | 04.5 | 77.1 | 37.1 | 80.1 | 51.2 | 02.2 | 70.2 | 08.9 | 06.0 | 11.0 | 27.8 |
| Trans4PASS [85] | 40.7 | 72.8 | 33.8 | 78.4 | 33.5 | 37.1 | 26.6 | 05.3 | 55.4 | 77.4 | 37.9 | 84.7 | 57.5 | 04.5 | 76.6 | 19.0 | 17.0 | 12.7 | 51.7 |
| UniDAPS [86] | 38.5 | 72.3 | 29.2 | 75.8 | 33.9 | 38.9 | 25.9 | 11.4 | 07.5 | 77.6 | 37.4 | 81.4 | 47.6 | 03.0 | 75.6 | 21.3 | 03.4 | 01.3 | 48.9 |
| EDAPS [55] | 40.2 | 74.4 | 35.9 | 77.0 | 36.5 | 40.4 | 28.0 | 16.1 | 05.1 | 78.1 | 39.5 | 82.3 | 55.5 | 03.3 | 74.4 | 06.7 | 14.1 | 05.2 | 50.9 |
| UnmaskFormer [7] | 43.7 | 76.5 | 37.8 | 77.1 | 34.7 | 44.1 | 28.3 | 17.8 | 02.8 | 78.7 | 41.7 | 85.0 | 57.3 | 06.0 | 80.6 | 23.5 | 21.7 | 18.8 | 53.6 |
| (xpan,ypan) | Source-only | 38.7 | 73.0 | 29.1 | 82.0 | 31.2 | 31.4 | 18.0 | 00.0 | 16.0 | 74.1 | 33.7 | 88.7 | 50.2 | 04.0 | 80.4 | 18.0 | 11.0 | 04.6 | 50.2 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 39.4 | 74.6 | 32.2 | 81.2 | 30.7 | 31.9 | 18.1 | 00.0 | 15.6 | 72.6 | 38.3 | 89.2 | 50.6 | 04.6 | 80.5 | 20.4 | 11.6 | 05.3 | 51.0 |
| UNLOCK (Ours) | 41.6 (↑2.9) | 74.7 | 32.1 | 83.7 | 34.7 | 40.8 | 18.5 | 00.0 | 18.9 | 76.1 | 39.9 | 89.5 | 53.7 | 05.8 | 82.2 | 26.1 | 00.8 | 14.0 | 57.8 |
"
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+ {
+ "type": "table_footnote",
+ "bbox": [
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+ "content": "Table 1. Scene Segmentation results on the K2B benchmark. Metrics are reported as: mAPQ for Amodal Panoptic Segmentation (APS), mPQ for Panoptic Segmentation (PS), and mIoU for Semantic Segmentation (SS). Per-class results are reported as APQ, PQ, and IoU. \\(\\uparrow\\) represents the improvement over the baseline of the Source-only method. \\(x^{pin}\\) and \\(x^{pan}\\) represent the images, and \\(y^{pin}\\) and \\(y^{pan}\\) represent the labels, from the pinhole source and panoramic target domains, respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "avoiding confusion about the semantic content of other objects. The zero-pixel ambiguous regions act as a masked strategy to enhance the model's ability to reconstruct occluded areas and infer the complete shape of occluded objects. This improves the model's ability to learn contextual knowledge from the target panoramic domain, improving its understanding of both individual objects and their relationships within the scene."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.1. Datasets"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this paper, we extend the Real-to-Real adaptation on the KITTI360-APS \\(\\rightarrow\\) BlendPASS (K2B for short)) benchmark [7] to SFOASS. Moreover, we pioneer Synthetic-to-Real adaptation in both OASS and SFOASS, introducing AmodalSynthDrive \\(\\rightarrow\\) BlendPASS benchmark (A2B for short) to conduct seamless segmentation research from synthetic to real scenarios."
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+ "type": "text",
+ "bbox": [
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+ "content": "Source pinhole domain: (1) KITTI360-APS [48]: It extends KITTI360 [39] and includes additional annotations for inmodal and amodal instances. A total of 12,320 annotated images \\((1408\\times 376\\) pixels) are captured using pinhole cameras across 9 cities. It covers 11 Stuff classes and 7 Thing classes. (2) AmodalSynthDrive [57]: The first synthetic dataset applicable to the OASS task, generated using CARLA [13]. It provides images and annotations from four surround-view cameras with a pinhole perspective, with 10,500 training images \\((1920\\times 1080\\) pixels) for each viewpoint. It covers 11 Stuff classes and 7 Thing classes."
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+ "type": "text",
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+ "angle": 0,
+ "content": "Target panoramic domain: The BlendPASS dataset [7] consists of 2,000 unlabeled training panoramic images and"
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+ "angle": 0,
+ "content": "100 labeled test panoramic images \\((2048 \\times 400\\) pixels), captured in real driving scenes across 40 cities on multiple continents. It covers 11 Stuff and 8 Thing classes."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Domain gap analysis: Fig. 5 shows the feature distributions of car and pedestrians between the target domain and two source domains, where there is a large domain gap between different datasets, especially for the A2B."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "content": null
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+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. Example images from the datasets [7, 48, 57] and the class distribution visualized via t-SNE [66]."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Experiment Setups"
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+ "type": "text",
+ "bbox": [
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+ "content": "Following [7], we use the proposed architecture as the backbone of our UNLOCK and the reproduced 360SFUDA++ [95]. In the A2B benchmark, we reproduce existing methods [55, 85, 86, 93, 95] and train the pinhole source model following the framework in [7]. In the K2B benchmark, we directly use the Source-only model from [7] as the pinhole source model. The AdamW optimizer [42] is employed, with a learning rate set to \\(1 \\times 10^{-7}\\), and a weight decay of 0.01, followed by polynomial decay. The batch size is set to 4, with crop sizes of \\(376 \\times 376\\) for K2B and \\(400 \\times 400\\) for A2B, and both are trained for \\(10k\\) iterations. In UNLOCK, \\(\\tau^{fix}\\) and \\(\\tau^{per}\\) for amodal instance predictions are set to 0.3 and 0.5; for instance predictions to 0.5 and 0.3; and for semantic predictions, to 0.5 and 0.8. For ADCL, they are set to 0.95 and 0.1, with the sample object count \\(R\\)"
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+ "angle": 0,
+ "content": "| Task | Method | Metric | Preds. | Cyclings | Car | Musk | Opt. | Van | WhWhite |
| AIS | B | DATR [93] | 08.7 | 13.1 | 00.0 | 30.6 | 06.9 | 04.7 | 01.7 | 03.8 |
| Trans4PASS [85] | 09.9 | 16.0 | 00.2 | 31.7 | 08.3 | 06.0 | 00.4 | 06.4 |
| EDAPS [55] | 10.7 | 15.8 | 00.1 | 30.0 | 09.0 | 12.2 | 00.4 | 07.4 |
| UnmaskFormer [7] | 10.5 | 16.1 | 00.1 | 34.1 | 12.3 | 02.2 | 00.6 | 08.2 |
| B | Source-only | 10.2 | 15.2 | 00.0 | 33.4 | 12.6 | 03.3 | 00.4 | 06.8 |
| 360SFUDA++ [95] | 10.3 | 15.2 | 00.0 | 33.4 | 13.1 | 03.3 | 00.4 | 06.8 |
| UNLOCK (Ours) | 10.9 (↑0.7) | 17.1 | 00.0 | 34.9 | 14.6 | 01.7 | 00.2 | 07.9 |
| IS | B | DATR [93] | 08.7 | 14.2 | 00.0 | 31.2 | 07.6 | 03.7 | 00.4 | 03.6 |
| Trans4PASS [85] | 10.0 | 16.5 | 00.0 | 32.2 | 10.2 | 05.3 | 00.2 | 05.6 |
| UniDAPS [86] | 03.4 | 02.3 | 00.0 | 11.3 | 06.2 | 02.8 | 00.0 | 01.5 |
| EDAPS [55] | 10.3 | 16.6 | 00.0 | 30.8 | 06.5 | 11.4 | 00.4 | 06.2 |
| UnmaskFormer [7] | 11.1 | 17.6 | 00.0 | 35.2 | 14.2 | 02.9 | 00.8 | 07.1 |
| B | Source-only | 10.5 | 15.8 | 00.0 | 33.9 | 13.5 | 03.6 | 00.2 | 06.8 |
| 360SFUDA++ [95] | 10.5 | 15.7 | 00.0 | 33.9 | 13.3 | 03.6 | 00.2 | 06.8 |
| UNLOCK (Ours) | 11.6 (↑1.1) | 17.7 | 00.0 | 36.1 | 16.3 | 03.4 | 00.1 | 07.4 |
"
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Task | Method | Metric | Person | ride | car | huck | bus | monor. | bicycle |
| AIS | Δ | DATR [93] | 08.1 | 14.1 | 00.4 | 23.5 | 09.6 | 04.3 | 04.7 | 00.0 |
| Trans4PASS [85] | 09.2 | 13.0 | 00.2 | 24.7 | 13.0 | 07.6 | 05.7 | 00.0 |
| EDAPS [55] | 09.5 | 16.7 | 00.2 | 25.2 | 11.6 | 06.6 | 06.1 | 00.0 |
| UnmaskFormer [7] | 10.2 | 16.6 | 00.1 | 26.5 | 12.8 | 08.6 | 06.4 | 00.0 |
| Δ | Source-only | 09.7 | 16.0 | 00.0 | 24.9 | 11.9 | 09.1 | 05.6 | 00.0 |
| 360SFUDA++ [95] | 09.6 | 16.2 | 00.0 | 25.3 | 11.7 | 08.9 | 05.2 | 00.0 |
| UNLOCK (Ours) | 10.0 (↑0.3) | 17.3 | 00.0 | 28.9 | 09.2 | 08.3 | 06.4 | 00.0 |
| IS | Δ | DATR [93] | 08.0 | 14.9 | 00.4 | 25.3 | 09.2 | 01.0 | 04.9 | 00.0 |
| Trans4PASS [85] | 09.0 | 15.0 | 00.1 | 27.2 | 11.8 | 04.1 | 05.0 | 00.0 |
| UniDAPS [86] | 00.3 | 00.8 | 00.0 | 00.8 | 00.1 | 00.0 | 00.5 | 00.0 |
| EDAPS [55] | 09.5 | 16.4 | 00.1 | 28.2 | 10.7 | 05.3 | 05.8 | 00.0 |
| UnmaskFormer [7] | 09.6 | 17.0 | 00.1 | 28.4 | 11.9 | 03.8 | 05.9 | 00.0 |
| Δ | Source-only | 09.3 | 17.4 | 00.0 | 26.9 | 11.6 | 04.4 | 04.9 | 00.0 |
| 360SFUDA++ [95] | 09.4 | 17.5 | 00.0 | 27.1 | 11.1 | 05.4 | 04.8 | 00.0 |
| UNLOCK (Ours) | 09.7 (↑0.4) | 17.7 | 00.0 | 29.3 | 09.0 | 05.9 | 06.1 | 00.0 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Instance-level Segmentation results on the K2B (left) and A2B (right) benchmark. Metrics are reported as: mAAP for Amodal Instance Segmentation (AIS) and mAAP for Instance Segmentation (IS). Per-class results are reported as AAP and AP."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 6. Visualization results. From top to bottom are (a) Image, (b) GT, (c) Source-only, and (d) 360SFUDA++ [95], and (e) UNLOCK."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "set to 10. The analysis of these thresholds is provided in the supplementary material. Our experiments are conducted on a single NVIDIA GTX 3090 GPU using PyTorch."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.3. Results of SFOASS"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "K2B. As shown by the Real-to-Real adaptation results in Table 1 and the left side of Table 2, UNLOCK sets a new benchmark for SFOASS, delivering outstanding performance and effectively addressing the unique challenges of limited FoV, occlusion, and constrained data. Compared to the baseline Source-only, UNLOCK outperforms in key metrics for scene understanding including mAPQ, mPQ, and mIoU, with improvements of \\(+4.3\\), \\(+2.8\\), and \\(+2.9\\), respectively. Even compared to UnmaskFormer [7], which has access to both source domain and target images, UNLOCK achieves comparable results in mAPQ. Notably, in instance-level segmentation, UNLOCK surpasses all existing UDA methods[7, 55, 85, 93]—even without access to source domain data containing \\(12K\\) images-label pairs, reaching the highest mAAP of 10.9 and mAP of 11.6, showcasing its robustness and adaptability. As shown in Fig. 6, UNLOCK successfully and precisely segments numerous Thing objects with better shape coherence."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "A2B. The results from another Synthetic-to-Real adaptation scenario, shown in Table 3 and the right side of Table 2,"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "further demonstrate UNLOCK's exceptional performance. Compared to 360SFUDA++ [95], which is specifically designed for panoramic data, our method significantly outperforms across all SFOASS metrics. This success is driven by the OPLL pseudo-label generation strategy, which is tailored specifically for SFOASS. The instance-level segmentation results highlight a clear advantage for our method, reflecting its enhanced accuracy in segmenting individual object instances within complex scenes."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Ablation Study"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We conduct a series of ablation studies on the K2B scenario to evaluate the effectiveness of our method."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Effectiveness of OPLL. An ablation study was conducted to validate the effectiveness of the OPLL. Table 4 presents the comparison of three different approaches for self-training. Using the final predicted labels from the source model as pseudo-labels or directly using all predictions from the three branches fails to adapt the instance-level branches to the panoramic domain, as evidenced by both mAAP and mAP scores, which are even worse than the no-adaptation Source-only model. With the OPLL designed by us, the knowledge of the source model can be effectively adapted to the target domain by using omni pseudo-labels. Compared with Source-only, OPLL achieves a significant"
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+ [
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Task | Constraint | Method | Metric | road | sidew | build | wall | fence | pole | lights | sign | vestor | terrain | fly | person | rider | car | track | bus | motor | bicycle |
| APS | (ypan) | DATR [93] | 19.4 | 36.1 | 00.0 | 72.4 | 00.0 | 01.3 | 02.4 | 00.0 | 07.1 | 64.8 | 00.0 | 88.9 | 08.3 | 02.7 | 31.6 | 18.4 | 00.0 | 14.8 | 00.0 |
| TransPASS [85] | 21.5 | 38.7 | 00.0 | 71.9 | 00.0 | 10.0 | 03.8 | 00.0 | 07.4 | 65.3 | 00.0 | 89.2 | 11.1 | 03.7 | 35.3 | 25.4 | 07.6 | 15.9 | 00.9 |
| EDAPS [55] | 21.7 | 45.5 | 00.0 | 74.9 | 00.0 | 08.5 | 04.1 | 00.0 | 06.0 | 63.7 | 00.0 | 89.5 | 12.1 | 02.8 | 35.9 | 20.7 | 09.7 | 17.0 | 00.0 |
| UnmaskFormer [7] | 22.9 | 44.1 | 00.6 | 67.5 | 00.0 | 09.6 | 04.3 | 00.0 | 05.0 | 67.0 | 00.0 | 90.2 | 16.6 | 00.0 | 38.7 | 29.2 | 17.1 | 22.2 | 00.0 |
| (xpan,ypan) | Source-only | 18.9 | 47.1 | 01.9 | 68.5 | 00.0 | 00.9 | 00.5 | 00.0 | 01.6 | 43.0 | 00.0 | 84.7 | 09.5 | 00.0 | 36.3 | 21.5 | 07.5 | 16.7 | 00.0 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 19.4 | 46.6 | 01.9 | 68.1 | 00.0 | 01.0 | 00.5 | 00.0 | 01.7 | 48.2 | 00.0 | 86.1 | 18.8 | 00.0 | 38.5 | 18.1 | 06.4 | 14.1 | 00.0 |
| UNLOCK (Ours) | 21.4 (↑2.5) | 50.8 | 04.7 | 73.5 | 00.0 | 04.8 | 00.6 | 00.0 | 03.9 | 49.8 | 00.0 | 86.2 | 17.5 | 01.2 | 41.4 | 20.2 | 09.3 | 20.9 | 00.0 |
| PS | (ypan) | DATR [93] | 19.5 | 35.7 | 00.0 | 71.5 | 00.0 | 01.3 | 01.8 | 00.0 | 07.1 | 64.8 | 00.0 | 88.9 | 08.3 | 05.0 | 32.2 | 15.8 | 02.4 | 15.5 | 00.0 |
| TransPASS [85] | 20.9 | 38.1 | 00.0 | 71.9 | 00.0 | 10.0 | 03.8 | 00.0 | 07.4 | 65.3 | 00.0 | 89.2 | 09.6 | 00.0 | 36.5 | 25.0 | 03.3 | 15.9 | 00.0 |
| UniDAPS [86] | 18.2 | 53.1 | 00.0 | 72.4 | 01.8 | 07.8 | 05.5 | 00.0 | 07.7 | 67.8 | 00.0 | 88.7 | 07.0 | 00.0 | 07.7 | 01.6 | 00.0 | 07.0 | 00.0 |
| EDAPS [55] | 21.9 | 46.7 | 00.0 | 75.1 | 00.0 | 08.5 | 04.1 | 00.0 | 06.1 | 63.6 | 00.0 | 89.5 | 11.8 | 02.5 | 36.9 | 23.4 | 08.9 | 16.5 | 00.0 |
| UnmaskFormer [7] | 20.7 | 42.9 | 00.6 | 67.0 | 00.0 | 09.6 | 03.6 | 00.0 | 05.0 | 66.9 | 00.0 | 90.2 | 16.6 | 00.0 | 37.3 | 25.9 | 07.5 | 00.0 | 00.0 |
| (xpan,ypan) | Source-only | 19.0 | 48.8 | 01.9 | 68.6 | 00.0 | 00.9 | 00.5 | 00.0 | 01.6 | 42.8 | 00.0 | 84.7 | 12.7 | 00.0 | 36.2 | 20.3 | 06.4 | 16.8 | 00.0 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 19.3 | 46.5 | 01.9 | 69.9 | 00.0 | 01.0 | 00.5 | 00.0 | 01.7 | 47.9 | 00.0 | 86.0 | 15.6 | 00.0 | 36.5 | 18.9 | 06.5 | 15.2 | 00.0 |
| UNLOCK (Ours) | 20.4 (↑1.4) | 50.5 | 04.2 | 74.0 | 00.0 | 04.8 | 00.6 | 00.0 | 03.9 | 49.2 | 00.0 | 86.3 | 14.3 | 00.0 | 38.1 | 18.8 | 05.7 | 16.8 | 00.0 |
| SS | (ypan) | DATR [93] | 31.5 | 59.5 | 06.3 | 77.7 | 00.2 | 09.2 | 22.9 | 02.4 | 10.3 | 76.6 | 00.0 | 93.4 | 37.7 | 01.9 | 68.8 | 20.8 | 01.5 | 54.1 | 24.2 |
| TransPASS [85] | 34.3 | 58.9 | 07.6 | 77.3 | 00.2 | 28.7 | 26.7 | 05.2 | 11.1 | 76.1 | 00.0 | 93.6 | 35.8 | 01.8 | 73.6 | 28.3 | 06.8 | 55.2 | 30.1 |
| UniDAPS [86] | 36.0 | 61.5 | 07.5 | 76.6 | 00.8 | 30.4 | 27.7 | 10.2 | 11.1 | 77.4 | 00.0 | 93.6 | 47.3 | 02.1 | 49.4 | 25.9 | 33.0 | 62.3 | 30.6 |
| EDAPS [55] | 36.2 | 62.2 | 10.8 | 81.1 | 00.5 | 28.7 | 22.9 | 10.6 | 10.5 | 75.5 | 00.1 | 93.3 | 42.7 | 02.3 | 72.1 | 33.6 | 18.8 | 58.6 | 26.7 |
| UnmaskFormer [7] | 36.1 | 60.6 | 13.3 | 74.2 | 00.9 | 32.7 | 21.6 | 14.2 | 06.9 | 76.7 | 00.0 | 93.9 | 45.2 | 01.2 | 73.3 | 34.1 | 22.0 | 56.9 | 22.7 |
| (xpan,ypan) | Source-only | 31.0 | 67.1 | 21.5 | 76.9 | 03.2 | 17.0 | 17.7 | 02.7 | 06.3 | 64.7 | 00.0 | 90.7 | 40.0 | 01.8 | 69.2 | 19.5 | 04.6 | 47.4 | 08.5 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 31.2 | 64.8 | 21.3 | 77.7 | 03.4 | 16.2 | 18.9 | 02.7 | 06.0 | 66.6 | 00.0 | 91.7 | 41.9 | 02.0 | 67.9 | 19.1 | 04.6 | 49.1 | 07.9 |
| UNLOCK (Ours) | 34.3 (↑3.3) | 69.1 | 25.2 | 81.5 | 00.1 | 25.1 | 20.0 | 03.7 | 10.5 | 68.0 | 00.0 | 91.6 | 45.9 | 01.6 | 71.4 | 24.0 | 07.2 | 50.8 | 21.4 |
"
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+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Scene Segmentation results on the A2B benchmark. Metrics are reported as: mAPQ for Amodal Panoptic Segmentation (APS), mPQ for Panoptic Segmentation (PS), and mIoU for Semantic Segmentation (SS). Per-class results are reported as APQ, PQ, and IoU."
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": " | mAPQ | mPQ | mIoU | mAAP | mAP |
| Source-only | 22.13 | 22.30 | 38.65 | 10.22 | 10.54 |
| Pseudo-Labels | 21.90 | 22.07 | 39.12 | 10.09 | 10.37 |
| All Predictions | 22.38 | 22.31 | 38.90 | 10.15 | 10.50 |
| OPLL (Ours) | 24.71 | 24.00 | 39.03 | 10.52 | 10.52 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Ablation analysis for OPLL."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Backbone | mAPQ | mPQ | mIoU | mAAP | mAP |
| Source-only | 22.1 | 22.3 | 38.7 | 10.2 | 10.5 |
| Trans4PASS [85] | 26.1 | 25.3 | 40.0 | 10.9 | 11.3 |
| EDAPS [55] | 26.3 | 25.1 | 40.5 | 10.7 | 11.4 |
| UnmaskFormer [7] | 26.4 | 25.1 | 41.6 | 10.9 | 11.6 |
"
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+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 5. Ablation analysis for backbones."
+ },
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| OPLL | ADCL | mAPQ | mPQ | mIoU | mAAP | mAP |
| | 22.13 | 22.30 | 38.65 | 10.22 | 10.54 |
| ✓ | | 24.71 | 24.00 | 39.03 | 10.52 | 10.52 |
| ✓ | 25.84 | 24.55 | 40.31 | 10.93 | 11.47 |
| ✓ | ✓ | 26.41 | 25.07 | 41.64 | 10.91 | 11.58 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Table 6. Ablation analysis for components."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": " | mAPQ | mPO | mLOU | mAAP | mAP |
| Source-only | 22.13 | 22.30 | 38.65 | 10.22 | 10.54 |
| Instance | 25.03 | 24.23 | 38.93 | 10.33 | 10.55 |
| Amodal Instance | 25.71 | 24.50 | 39.06 | 10.77 | 11.22 |
| AoMix [7] | 25.32 | 24.67 | 38.04 | 10.62 | 11.26 |
| ADCL-Random | 24.81 | 23.90 | 38.92 | 10.69 | 11.19 |
| ADCL-Zero (Ours) | 25.84 | 24.55 | 40.31 | 10.93 | 11.47 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Table 7. Ablation analysis for ADCL."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "| Method | mIoU |
| SFDA [40] | 42.70 |
| DATC [73] | 43.06 |
| 360SFUDA [96] | 50.12 |
| 360SFUDA++[95] | 52.99 |
| UNLOCK (Ours) | 54.55 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.342,
+ 0.527,
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+ 0.553
+ ],
+ "angle": 0,
+ "content": "Table 8. SS results on the C2D benchmark."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "improvement of 2.58 in mAPQ."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
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+ ],
+ "angle": 0,
+ "content": "Effectiveness of ADCL. Another ablation study was conducted to validate the effectiveness of the ADCL. Table 7 presents a comparison of different object mixing strategies. Due to incomplete object shapes, instance-based mixing yields limited improvement in mAPQ and mAAP. Directly using amodal instances causes confusion in contextual information. Unlike AoMix [7], which zeros out full amodal object regions of the input image, our method in UNLOCK sets only the overlapping regions to zero (ADCL-Zero), effectively preserving contextual cues. Replacing overlaps with random values (ADCL-Random) yields inferior results, while ADCL-Zero achieves the best mAPQ of 25.84. Component Ablation. As shown in Table 6, by combining OPLL and ADCL, our UNLOCK method achieves the best overall performance, outperforming the Source-only trained on the source pinhole domain with \\(+4.28\\) gains in mAPQ. It shows that our methods can successfully adapt to the target panoramic domain under source-free constraints."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.901
+ ],
+ "angle": 0,
+ "content": "Backbone Ablation. As shown in Table 5, we evaluated the performance of UNLOCK across different backbones to verify the effectiveness of the UNLOCK strategy itself. The"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "results indicate that UNLOCK maintains consistent performance across diverse backbone architectures, confirming its backbone-agnostic nature as an SFDA framework."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.54,
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+ ],
+ "angle": 0,
+ "content": "4.5. Results of Panoramic Semantic Segmentation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.568,
+ 0.907,
+ 0.688
+ ],
+ "angle": 0,
+ "content": "To investigate the generalization capability of UNLOCK, we extend UNLOCK to the Semantic Segmentation (SS) task and evaluate it on the Cityscapes-to-DensePASS (C2D) benchmark. As shown in Table 8, UNLOCK achieves a significant improvement of \\(+1.56\\) in mIoU over 360SFUDA++ [95]. Under the pinhole-to-panoramic C2D adaptation scenario, our UNLOCK achieves the new state-of-the-art result of 54.55 in mIoU."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.75,
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+ "angle": 0,
+ "content": "In this paper, we address key constraints in comprehensive scene understanding, to achieve seamless segmentation with \\(360^{\\circ}\\) viewpoint coverage and occlusion-aware reasoning, while adapting without relying on source data and target labels. To this end, we introduce a new task, Source-Free Occlusion-Aware Seamless Segmentation (SFOASS), and propose its first solution UNLOCK. We further applied two SFOASS benchmarks for evaluation: Real-to-Real and Synthetic-to-Real. Extensive experimental results demonstrate the effectiveness of the proposed method."
+ },
+ {
+ "type": "page_number",
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+ "content": "8968"
+ }
+ ],
+ [
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "Acknowledgment"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This work was supported in part by the National Natural Science Foundation of China (No. 62473139, 62027810), the Major Research Plan of the National Natural Science Foundation of China (No. 92148204), the Top Ten Technical Research Projects of Hunan Province (No. 2024GK1010), the Key Program of Natural Science Foundation of Hunan Province, China (No. 2025JJ30024), the National Key Research and Development Program of China (No. 2024YFB4708900), the Hunan Provincial Research and Development Project (No. 2025QK3019), in part by the Open Research Project of the State Key Laboratory of Industrial Control Technology, China (No. ICT2025B20), and the Science and Technology Project of State Grid Corporation of China (SGCC) Co., LTD (No. 5700-202423229A-1-1-ZN)."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "References"
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+# Unlocking Constraints: Source-Free Occlusion-Aware Seamless Segmentation
+
+Yihong Cao $^{1,2,*}$ Jiaming Zhang $^{3,4,*}$ Xu Zheng $^{5,6}$ Hao Shi $^{7}$ Kunyu Peng $^{3}$ Hang Liu $^{1}$ Kailun Yang $^{1,\dagger}$ Hui Zhang $^{1,\dagger}$ $^{1}$ Hunan University $^{2}$ Hunan Normal University $^{3}$ Karlsruhe Institute of Technology $^{4}$ ETH Zürich HKUST(GZ) $^{6}$ INSAIT, Sofia University "St. Kliment Ohridski" $^{7}$ Zhejiang University
+
+
+Figure 1. UNLOCK framework $(a)$ solves the Source-Free Occlusion-Aware Seamless Segmentation (SFOASS), enabling segmentation with $360^{\circ}$ viewpoint coverage and occlusion-aware reasoning while adapting without requiring source data and target labels, and $(b)$ outperforms existing SFDA methods on the Real-to-Real scenario [7] across all five segmentation metrics (i.e., mAPQ for amodal panoptic, mPQ for panoptic, mIoU for semantic, mAAP for amodal instance, and mAP for instance).
+
+
+
+# Abstract
+
+Panoramic image processing is essential for omnicontext perception, yet faces constraints like distortions, perspective occlusions, and limited annotations. Previous unsupervised domain adaptation methods transfer knowledge from labeled pinhole data to unlabeled panoramic images, but they require access to source pinhole data. To address these, we introduce a more practical task, i.e., Source-Free Occlusion-Aware Seamless Segmentation (SFOASS), and propose its first solution, called UNconstrained Learning Omni-Context Knowledge (UNLOCK). Specifically, UNLOCK includes two key modules: Omni Pseudo-Labeling Learning and Amodal-Driven Context Learning. While adapting without relying on source data or target labels, this framework enhances models to achieve segmentation with $360^{\circ}$ viewpoint coverage and occlusion-aware reasoning. Furthermore, we benchmark the proposed SFOASS task through both real-to-real and synthetic-to-real adaptation settings. Experimental results show that our source-free method achieves performance comparable to source-dependent methods, yielding state-of-the-art
+
+scores of 10.9 in mAAP and 11.6 in mAP, along with an absolute improvement of +4.3 in mAPQ over the source-only method. All data and code will be made publicly available at https://github.com/yihong-97/UNLOCK.
+
+# 1. Introduction
+
+Scene understanding is a foundational task in computer vision, essential for various downstream applications like autonomous driving [44, 77], virtual reality [11, 58], and robotics [3, 60]. Despite significant advances in the field, current methods still face challenges in achieving both comprehensive and human-like perceptions of surrounding environments, limiting their ability to fully understand scenes. Multiple critical research questions remain unsolved.
+
+1) How to efficiently expand to $360^{\circ}$ field of view? Traditional scene understanding methods [9, 21, 70] tailored for pinhole imagery, are limited by a narrow Field of View (FoV). In contrast, panoramic vision offers $360^{\circ}$ view in a single shot, which has the potential to facilitate more comprehensive scene understanding [1, 19]. However, directly applying traditional methods to panoramic data often results in unreliable performance due to challenges such as
+
+distortions [92]. For effective panoramic understanding, it is essential to learn omni-context knowledge when transferring from the pinhole domain to the panoramic domain. This knowledge transfer is crucial for accurate feature interpretation and wide-FoV representation, ultimately enabling seamless $360^{\circ}$ scene understanding [84, 85].
+
+2) How can amodal prediction be improved to extend the depth of view? Amodal perception [34, 53], the ability to predict an occluded object's complete shape, is key to robust scene understanding [83] and mirrors human-like perception. Extending the depth of view (vertical to field of view) means that models can achieve seamless perception, which refers to pixel-level segmentation of the background and occlusion-aware instance-level segmentation of the foreground. Beyond the previous amodal segmentation methods [16, 98], how to improve occlusion-aware reasoning like OASS [7] in both directions (depth and field of view) simultaneously remains challenging.
+
+3) How can models adapt to panoramic domains without source data? Apart from the field and depth of view, the scarcity of labeled data presents a significant limitation in panoramic vision. To address the lack of labeled data, Unsupervised Domain Adaptation (UDA) leverages labeled data from the source domain while training on unlabeled data from the target domain [7, 24, 25, 28, 32, 65]. However, UDA methods still rely on access to source domain, which can often be challenging or even impossible due to privacy concerns or commercial restrictions on source datasets, such as in autonomous driving [40, 95, 96]. This restriction leads us to source-free learning, i.e. how to adapt models to panoramic domains without source data. However, it remains under-explored in amodal panoramic vision.
+
+In this work, to address the aforementioned challenges in scene understanding, we extend the OASS [7] task and introduce a more practical task, i.e., Source-Free Occlusion-Aware Seamless Segmentation (SFOASS). To tackle this task, we propose its first solution, called UNconstrained Learning Omni-Context Knowledge (UNLOCK). As shown in Fig. 1a, UNLOCK improves panoramic seamless segmentation performance under adaptation constraints without requiring source data and target labels. Specifically, to effectively capture the domain-invariant knowledge from the source domain, a method called Omni PseudoLabeling Learning (OPLL) is proposed. Besides, to learn intra-domain knowledge and integrate the domain-invariant knowledge, we put forward the Amodal-Driven Context Learning (ADCL) strategy. Together, OPLL and ADCL adapt the source model trained on pinhole data to target panoramic images while enhancing panoramic perception and occlusion-aware reasoning. With OPLL as the key and ADCL performing the unlocking action, they work in synergy to unlock the constraints in SFOASS, thereby enabling seamless perception of the model towards panoramic data.
+
+Aside from Real-to-Real source-free adaptation on the KITTI360-APS $\rightarrow$ BlendPASS benchmark [7], we pioneer Synthetic-to-Real adaptation in OASS and SFOASS and introduce AmodalSynthDrive $\rightarrow$ BlendPASS to investigate the potential of adapting synthetic panoramic images to the real panoramic image domain. Extensive experiments are conducted on both SFOASS benchmarks. Without access to the original source data (neither images nor labels), our UNLOCK framework can obtain on-par performance as compared to UDA-based methods that require all source data. Surprisingly, as shown in Fig. 1b, results on the Real-to-Real scenario [7] show an absolute improvement of $+4.3$ in mAPQ, reaching 26.4, compared to the source-only method, and outperforms UDA methods using $12K$ images in instance-level segmentation, with state-of-the-art scores of 10.9 in mAAP and 11.6 in mAP, respectively.
+
+In this work, we propose contributions as follows:
+
+- We introduce the Source-Free Occlusion-Aware Seamless Segmentation (SFOASS) task and its first solution, UNconstrained Learning Omni-Context Knowledge (UNLOCK). The UNLOCK framework enables models to achieve segmentation with $360^{\circ}$ viewpoint coverage and occlusion-aware reasoning while adapting without the need for source data and target labels.
+- To fully exploit the knowledge from source and target domains, Omni Pseudo-Labeling Learning (OPLL) and Amodal-Driven Context Learning (ADCL) strategies are introduced in UNLOCK to achieve occlusion-aware seamless segmentation for panoramic images.
+- Extensive experiments conducted on two SFOASS scenarios, Real-to-Real and Synthetic-to-Real, demonstrate the effectiveness of the UNLOCK framework, highlighting its ability to achieve competitive performance.
+
+# 2. Related Work
+
+Seamless segmentation. Seamless segmentation, as introduced by [7], aims to achieve amodal-level segmentation for large-FoV images, enabling unified, occlusion-aware scene understanding. Wide-FoV segmentation on fisheye [12, 56, 59, 78, 80] and panoramic images [22, 35, 75, 76, 97] facilitates comprehensive $360^{\circ}$ scene comprehension [74]. Panoramic panoptic segmentation enhances scene understanding by providing instance-level insights [17, 30, 47, 52]. Amodal segmentation extends this concept by predicting both visible and occluded object regions [4, 10, 15, 23, 38, 41, 61, 63]. Li et al. [34] pioneered amodal instance segmentation, introducing occlusion-aware segmentation through iterative regression. Subsequent datasets adapted for amodal segmentation [98] and occlusion classification [53] have driven further advances. Shape and contour priors [8, 18, 36, 37, 69] have further refined segmentation accuracy. In addition to instance segmentation, amodal panoptic segmentation has been explored [5, 26, 98]. Mo
+
+han et al. [48, 49] combined semantic and amodal segmentation for amodal panoptic segmentation. Recent methods, including pix2gestalt [51], AISDiff [64], and Xu et al. [72], leverage diffusion model priors for amodal segmentation. Although seamless segmentation [7] unifies aforementioned segmentation paradigms to form occlusion-aware scene understanding for panoramic vision, our work emphasizes source-free seamless segmentation, aiming for high accuracy even with restricted access to labeled source data.
+
+Source-free domain adaptation. Existing works dealing with domain gaps on semantic segmentation tasks mostly focus on UDA where labeled source domain data is required [20, 62, 68, 71, 84, 84, 85, 91, 93, 94, 99]. Source-Free Domain Adaptation (SFDA) [6, 14, 33, 40, 43, 54, 67, 79, 81] is a more practical approach compared with UDA, as it removes the need for access to source data during the adaptation process. As sub-directions of scene segmentation, domain adaptation of panoptic segmentation is challenging as it must distinguish and integrate semantic and instance information across domains, as highlighted in existing works [27, 45, 46, 55, 87]. To overcome the limitations of the FoV, domain adaptation in panoramic segmentation facilitates comprehensive scene understanding across a full $360^{\circ}$ perception, while effectively harnessing the rich knowledge from label-dense pinhole domains. Researchers have explored both UDA [31, 84, 85, 88-90, 94] and SFDA [95, 96] settings for panoramic segmentation. Jaus et al. [29, 30] illustrate the need for panoramic panoptic segmentation in autonomous driving. Zheng et al. [95, 96] for the first time, explored SFDA in panoramic semantic segmentation. However, the SFDA challenge remains unexplored for OASS [7]. In this work, we introduce the novel SFOASS task and benchmark it across two scenarios. We also proposed the first solution UNLOCK, a novel method designed to unlock constraints posed by SFOASS.
+
+# 3.UNLOCK Framework
+
+# 3.1. Overview
+
+OASS. In the OASS [7], the objective is to use a labeled source pinhole domain $\mathcal{D}^{pin} = \{x_i^{pin}, y_i^{pin}\}_{i=1}^{N^{pin}}$ and an unlabeled target panoramic domain $\mathcal{D}^{pan} = \{x_i^{pan}\}_{i=1}^{N^{pan}}$ to obtain an OASS model $F$ that performs well in $\mathcal{D}^{pan}$ . Both domains share the same $C$ categories, which can be further divided into $C^{stu}$ Stuff classes and $C^{thi}$ Thing classes. Ultimately, the $F$ should be able to output five segmentation results with the input panoramic image at once: semantic, instance, amodal instance, panoptic, and amodal panoptic maps. Typically, $F$ is designed to contain a shared encoder and three detection branches: semantic, instance, and amodal instance branches, each outputting corresponding predictions $p_i^{sem}, p_i^{ins}, p_i^{ains}$ , denoted as
+
+$$
+p _ {i} ^ {\text {s e m}}, p _ {i} ^ {\text {i n s}}, p _ {i} ^ {\text {a i n s}} = F (x _ {i}), \tag {1}
+$$
+
+where $p_i^{sem} \in \mathbb{R}^{H \times W \times C}$ represents the semantic prediction of the input image $x_i \in \mathbb{R}^{H \times W \times 3}$ . $p_i^{ins}$ and $p_i^{ains}$ represent the instance and amodal instance predictions, respectively, with each including class $\in \mathbb{R}^{C^{thi}}$ , score $\in [0,1]$ , and mask $\in \mathbb{R}^{H \times W}$ predictions for jth object. During adaptation, the label $y_i$ of $x_i$ consists of three components: semantic $y_i^{sem}$ , instance $y_i^{ins}$ , and amodal instance $y_i^{ains}$ labels, used for supervised learning in their respective branches. In the inference phase, the predictions from all three branches are fused to produce five segmentation maps of OASS.
+
+SFOASS. Considering privacy and storage limitations, this work introduces a more practical task, i.e., SFOASS. In the adaptation phase, the source pinhole domain $\mathcal{D}^{pin}$ is locked and inaccessible. Given a source model $F^{pin}$ well-trained from $\mathcal{D}^{pin}$ , and $\mathcal{D}^{pan}$ , the goal of SFOASS is to adapt the source model $F^{pin}$ with only unlabeled panoramic data $\{x_{i}^{pan}\}_{i=1}^{N^{pan}}$ , obtaining a target model $F^{pan}$ that performs well in the target panoramic domain. (For ease of expression, the superscript "pan" for target panoramic domain will be omitted henceforth.)
+
+How can models adapt to panoramic domains without source data, while expanding the field and depth of view? To answer this, we propose a novel method called UNconstrained Learning Omni-Context Knowledge (UNLOCK). It can further enhance the performance of panoramic seamless prediction while improving occlusion-aware reasoning. Specifically, as shown in Fig. 2, in response to the challenge that existing self-training methods are ineffective for the SFOASS task, we designed an Omni Pseudo-Labeling Learning (OPLL) approach. This approach leverages all predictions to generate omni soft labels. These generated labels serve as the "key" to the proposed UNLOCK. Furthermore, we propose a brand-new Amodal-Driven Contextual Learning (ADCL) strategy, which effectively resolves the conflict between the real object shapes and contextual knowledge for the occluded object. Ultimately, the ADCL holds the "key" and performs the "unlocking" action, completing the source-free adaptation to the panoramic domain.
+
+# 3.2. Omni Pseudo-Labeling Learning
+
+In the SFOASS, only unlabeled target panoramic images $\{x_i\}_{i=1}^N$ are accessible. Common solutions [2, 6, 33] typically involve generating pseudo-labels of target images for training. Pseudo-label generation usually entails filtering model predictions based on pre-defined thresholds. However, we found that directly using the filtered pseudo-labels for self-training in the SFOASS led to performance degradation for instance and amodal instance branches compared to the source model. The OASS task consists of a pixel-wise semantic branch and two object-wise instance-level branches (instance and amodal instance) based on region proposals. For the instance-level branches, each object is
+
+
+Figure 2. Illustration of the proposed UNLOCK. To address the challenge of the inaccessible source domain and target labels in SFOASS, we propose Omni Pseudo-labeling Learning (OPLL) and Amodal-Driven Contextual Learning (ADCL) modules. OPLL serves as the key, and ADCL, holding the key, unlocks the constraints of SFOASS, enabling effective adaptation of the target model to the panoramic domain.
+
+assigned a binary mask for binary cross-entropy loss. However, inaccurate pseudo-labels can hinder learning. When object parts are mistakenly labeled as background, even if the model correctly detects the objects, the pseudo-labels may force it to incorrectly classify them as absent.
+
+
+Image
+
+
+Semantic Predictions
+
+
+Instance Predictions
+
+
+(a) Incorrect predictions (cyclists in red) of the Stuff class.
+All Predictions
+(b) Omni pseudo-label generation with CS thresholds.
+Figure 3. Solution to the challenge of predictions from the source model in OPLL, illustrated with the amodal instance branch.
+
+
+Certain Pseudo-Labels
+
+
+Uncertainty Region
+
+To address this, we developed the OPLL method, which introduces generating omni pseudo-labels using Classwise Self-tuning (CS) thresholds and applying uncertainty-guided instance loss. Since the two instance-level branches perform the same operations, we will introduce one branch as an example below. Specifically, we first utilized the semantic branch's predictions to impose additional constraints on the predictions of both instance-level branches. As shown in Fig. 3a, we observed that the instance-level branch, constrained by local information, may misclassify the statue in the shop window as a cyclist of Thing class. In contrast, the semantic branch, aided by global information, can usually understand the scenes correctly. For each
+
+panoramic image $x_{i}$ , we obtain the Thing mask $m^{th i}$ by the semantic prediction, then use it to revise the object mask of instance-level predictions $p_{i}^{il}$ , $il \in \{ins, ains\}$ :
+
+$$
+m ^ {t h i} = \left\{ \begin{array}{l l} 1, & \text {i f} \operatorname {a r g m a x} p ^ {s e m} \in C ^ {t h i} \\ 0, & \text {e l s e} \end{array} , \right. \tag {2}
+$$
+
+$$
+\tilde {p} _ {i} ^ {i l} = p _ {i} ^ {i l} \cap m ^ {t h i}. \tag {3}
+$$
+
+Then, considering the inconsistent number of objects and the significant imbalance in the source model's capabilities across different Thing classes (as shown in SourceOnly of Table 2), we propose a simple and effective CS threshold method for the predictions of the SFOASS task. For each branch, the CS thresholds $\tau = \{\tau_c\}_{c=1}^{C^{thi}}$ is determined by:
+
+$$
+\tau_ {c} = \operatorname {a r g m a x} _ {\tau \in \left\{\tau^ {f i x}, \tau^ {p e r} \right\}} N _ {c} ^ {\tau}, c \in C ^ {t h i}, \tag {4}
+$$
+
+where $N_{c}^{\tau^{fix}}$ represents the number of objects of class $c$ whose score exceeds $\tau^{fix}$ across all predictions $\{\hat{p}_i\}_{i=1}^N$ , and $N_{c}^{\tau^{per}}$ denotes the number of objects of class $c$ in the top $\tau^{per}$ percentage when the score of all predictions $\{\hat{p}_i\}_{i=1}^N$ are sorted in descending order. For the semantic branch, the score is replaced with the maximum predicted probability of $p_i^{sem}$ . This approach generates high-quality pseudo-labels while effectively addressing the issue of low confidence scores for certain classes, caused by the source model $F^{pin}$ inconsistent performance across classes.
+
+Then, we filter out high-quality predictions based on CS thresholds $\pmb{\tau}$ as certain pseudo-labels $\hat{y}_i^{cer}$ :
+
+$$
+\hat {y} _ {i} ^ {c e r} = \left\{\hat {p} _ {i} ^ {(j)} \mid \hat {p} _ {i} ^ {(j)} > \tau \right\}, \tag {5}
+$$
+
+where $\hat{p}_i^{(j)}$ represent the prediction of $j$ th object in predictions $p_i$ for input image $x_i$ . To fully utilize the predictions,
+
+
+Figure 4. Comparison of object extraction methods: Amodal instance extraction mixes information from other objects, while instance-based extraction may yield incomplete shapes. Our method avoids these issues and preserves spatial awareness.
+
+we treat the remaining masks of the other predictions as uncertainty region $\hat{y}_i^{uncer}$ for the current image:
+
+$$
+\hat {y} _ {i} ^ {\text {u n c e r}} = \left(1 - \mathbf {1} _ {\left\{\sum_ {j} \hat {y} _ {i} ^ {\text {c e r}} > 0 \right\}}\right) \cap \left(\mathbf {1} _ {\left\{\sum_ {j} \left(\hat {p} _ {i} ^ {(j)} \mid \hat {p} _ {i} ^ {(j)} < \boldsymbol {\tau}\right) > 0 \right\}}\right), \tag {6}
+$$
+
+where $\mathbf{1}_{\{\cdot\}}$ is indicator function. The left-hand side of $\cap$ in Eq. 6 ensures that the object region of $\hat{y}_i^{cer}$ is not misassigned as the uncertain region. They form the omni pseudo-labels $\hat{y}_i = \{\hat{p}_i^{(1)}, \hat{p}_i^{(2)}, \dots, \hat{y}_i^{uncer}\}$ of the training panoramic image $x_i$ . We believe that all predictions from both instance-level branches of the source model can provide effective knowledge. For the semantic branch, the $j$ is replaced with the pixel spatial location. Finally, for each training panoramic image $x_i$ , we obtain three types of omni pseudo-labels $\hat{y}_i^{sem}, \hat{y}_i^{ins}, \hat{y}_i^{ains}$ for training. During the adaptation process of the target model $F^{pan}$ , following [7], the cross-entropy loss is used for the semantic branch. For the instance-level branches, we introduce a novel uncertain-guided Binary Cross Entropy (BCE) loss $\mathcal{L}_{ur}$ , specifically tailored for the SFOASS task.
+
+$$
+\mathcal {L} _ {u r} = \left(1 - \hat {y} _ {i} ^ {u n c e r}\right) \odot \mathrm {B C E} \left(F ^ {p a n} \left(x _ {i}\right), \hat {y} _ {i} ^ {c e r}\right). \tag {7}
+$$
+
+This approach effectively mitigates prediction errors of the target panoramic data arising from the source pinhole model, allowing the target model to focus on high-quality object samples during the adaptation process.
+
+# 3.3. Amodal-Driven Contextual Learning
+
+Through OPLL, we leverage the source model to generate omni pseudo-labels of the unlabeled panoramic data, obtaining the "key" for adapting the model to the target domain. It primarily extracts domain-invariant knowledge from the pinhole-tolerant source model. We further introduce the ADCL strategy to learn intra-domain knowledge while integrating domain-invariant knowledge. It holds the "key" to complete the "unlocking" action, and achieves the adaptation to the panoramic images in a source-free manner.
+
+Mixing is an effective strategy often used in UDA methods [2, 50, 82]. The typical approach involves randomly extracting objects from other data and pasting them into the current training image to form new mixed training samples. However, this approach is not suitable for the OASS model
+
+with an amodal instance branch, and it can confuse semantic context and hinder model learning. Specifically, since the two instance branches in the OASS model are independent, their predictions are not correlated, leaving us with the option of relying on one of the predictions. As shown by the car in Fig. 4, the amodal instance prediction captures the complete shape of the car. However, this prediction only provides the full mask for the object, meaning that the occluded areas in the mask may inadvertently include parts of other objects. If these masks are directly used for mixing, incorrect contextual information can be introduced. On the other hand, relying on instance predictions focuses only on non-occluded regions, making it difficult for the model to learn the full shape of objects. This dual challenge complicates the learning process in SFOASS tasks.
+
+First, we use OPLL with stricter thresholds $\tau^{\prime fix}$ and $\tau^{\prime per}$ to build a buffer pool $\mathcal{B}$ of $K$ high-quality object samples, relying solely on predictions from the amodal instance branch to accurately capture object shapes.
+
+$$
+\mathcal {B} = \left\{o ^ {(1)}, o ^ {(2)}, \dots , o ^ {(K)} \right\}, \tag {8}
+$$
+
+where $o^{(k)}\in \{\hat{y}_i^{ains\to cer}|\big(\tau^{\prime^{fix}},\tau^{\prime^{per}}\big)\}_{i = 1}^{N^{pan}}$
+
+The $o^{(k)}$ represents the filtered certain object obtained through OPLL from the panoramic data. Additionally, for each $o^{(k)} = \{o_{ful}^{(k)}, o_{ovp}^{(k)}\}$ , we include not only the mask $o_{ful}$ of the predicted full region but also record the overlapping region $o_{ovp}$ between the object and other objects in the same image, regardless of whether they are occluded. This process results in an amodal-driven object pool $\mathcal{B}$ .
+
+Furthermore, we introduce a novel spatial-aware mixing strategy based on the amodal-driven object pool, enriching the diversity of unlabeled panoramic images by generating amodal-driven mixed samples while respecting panoramic layouts. This spatially consistent mixing ensures semantic coherence, aligning distortions in the panoramic layout even after object insertion. During the adaptation phase, we randomly select $R$ object samples $\mathcal{O} = \{o^{(r)}\}_{r=1}^{R}$ from $\mathcal{B}$ and integrate them into the current training image $x_{i}$ :
+
+$$
+\tilde {x} _ {i} = \left(1 - o _ {f u l} ^ {(r)}\right) \odot x _ {i} + o _ {f u l} ^ {(r)} \odot x _ {r}, \tag {9}
+$$
+
+where $x_{r}$ represents the image corresponding to the paste object $o^{(r)}$ . For ambiguous regions of $o^{(r)}$ (i.e., potentially occluded areas), we assign zero pixels during the mixing process while keeping the complete mask as the label according to the $o_{ovp}^{(r)}$ .
+
+$$
+\tilde {x} _ {i} = \left(1 - o _ {o v p} ^ {(r)}\right) \odot \tilde {x} _ {i}. \tag {10}
+$$
+
+For the three pseudo-labels $\tilde{y}_i^{sem},\tilde{y}_i^{ins},\tilde{y}_i^{ains}$ of the mixed image $\tilde{x}_i$ , we only use $\{o_{ful}^{(r)}\}_{r = 1}^{R}$ to modify them accordingly. This strategy preserves the full shape of objects while
+
+| Task | Constraint | Method | Metric | road | sidew. | buid. | wall | fence | pole | tlnight | Insign | lager | fermin | sky | Pedes | cylulus | car | Ink | outch | van | whlte |
| APS | (ypan) | DATR [93] | 20.3 | 51.8 | 09.2 | 59.9 | 11.9 | 12.0 | 02.0 | 00.0 | 03.9 | 64.6 | 14.1 | 70.4 | 11.1 | 00.0 | 39.3 | 00.0 | 03.2 | 10.1 | 01.3 |
| Trans4PASS [85] | 22.9 | 53.9 | 14.1 | 69.4 | 19.2 | 11.8 | 03.8 | 00.0 | 05.2 | 67.6 | 16.0 | 77.4 | 15.3 | 04.2 | 41.1 | 06.6 | 00.0 | 00.0 | 07.4 |
| EDAPS [55] | 23.1 | 54.9 | 17.0 | 66.9 | 18.8 | 14.5 | 05.8 | 04.0 | 04.6 | 68.2 | 16.0 | 72.8 | 19.0 | 00.0 | 36.7 | 05.8 | 04.4 | 00.0 | 07.2 |
| UnmaskFormer [7] | 26.6 | 61.8 | 24.7 | 66.8 | 20.8 | 15.8 | 05.3 | 04.3 | 03.3 | 69.0 | 18.4 | 79.4 | 20.5 | 03.1 | 44.6 | 12.8 | 11.3 | 00.0 | 16.6 |
| (xpan,ypan) | Source-only | 22.1 | 57.1 | 14.2 | 73.6 | 15.5 | 07.6 | 00.7 | 00.0 | 10.4 | 58.3 | 12.4 | 83.1 | 15.2 | 00.0 | 40.3 | 03.8 | 00.0 | 00.0 | 06.1 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 24.5 | 60.3 | 16.8 | 71.7 | 14.1 | 07.7 | 00.0 | 00.0 | 08.4 | 55.6 | 13.6 | 81.3 | 21.5 | 03.2 | 46.3 | 19.4 | 02.2 | 00.0 | 19.4 |
| UNLOCK (Ours) | 26.4 (↑4.3) | 62.7 | 14.4 | 74.8 | 20.2 | 11.2 | 00.8 | 00.0 | 08.0 | 62.9 | 18.3 | 84.0 | 21.9 | 03.6 | 45.8 | 19.4 | 00.0 | 03.1 | 24.4 |
| PS | (ypan) | DATR [93] | 19.6 | 50.4 | 09.1 | 59.9 | 11.9 | 12.0 | 02.0 | 00.0 | 03.9 | 64.6 | 14.1 | 70.5 | 12.2 | 00.0 | 38.1 | 00.0 | 03.4 | 00.0 | 01.3 |
| Trans4PASS [85] | 22.7 | 53.9 | 14.1 | 69.4 | 19.2 | 11.8 | 03.8 | 00.0 | 05.2 | 67.6 | 16.0 | 77.4 | 14.6 | 04.1 | 38.2 | 06.9 | 00.0 | 00.0 | 07.2 |
| UniDAPS [86] | 22.7 | 66.0 | 09.5 | 66.3 | 17.4 | 14.3 | 04.8 | 00.0 | 06.1 | 67.2 | 16.1 | 72.7 | 08.3 | 00.0 | 27.3 | 14.8 | 09.2 | 00.0 | 08.9 |
| EDAPS [55] | 23.1 | 55.0 | 17.1 | 66.8 | 18.7 | 14.5 | 05.8 | 04.0 | 04.7 | 68.2 | 16.0 | 72.8 | 19.6 | 00.0 | 37.8 | 01.8 | 04.4 | 00.0 | 07.9 |
| UnmaskFormer [7] | 26.2 | 61.7 | 24.7 | 66.8 | 20.8 | 15.8 | 05.2 | 04.3 | 03.3 | 69.0 | 18.4 | 79.4 | 20.9 | 03.5 | 43.0 | 11.3 | 07.6 | 00.0 | 16.0 |
| (xpan,ypan) | Source-only | 22.3 | 57.8 | 14.2 | 73.8 | 15.5 | 07.6 | 00.7 | 00.0 | 10.4 | 58.3 | 12.4 | 83.2 | 14.9 | 00.0 | 39.1 | 06.0 | 00.0 | 00.0 | 07.7 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 23.7 | 61.3 | 16.8 | 72.2 | 14.1 | 07.6 | 00.0 | 00.0 | 08.4 | 55.9 | 13.6 | 81.3 | 18.4 | 00.0 | 40.6 | 16.4 | 02.4 | 00.0 | 17.6 |
| UNLOCK (Ours) | 25.1 (↑2.8) | 60.4 | 14.4 | 75.7 | 20.2 | 11.2 | 00.7 | 00.0 | 08.0 | 63.6 | 18.3 | 84.0 | 16.9 | 00.0 | 40.0 | 18.5 | 00.0 | 00.0 | 19.4 |
| SS | (ypan) | DATR [93] | 34.9 | 71.9 | 27.2 | 70.6 | 22.8 | 36.0 | 23.9 | 00.0 | 04.5 | 77.1 | 37.1 | 80.1 | 51.2 | 02.2 | 70.2 | 08.9 | 06.0 | 11.0 | 27.8 |
| Trans4PASS [85] | 40.7 | 72.8 | 33.8 | 78.4 | 33.5 | 37.1 | 26.6 | 05.3 | 55.4 | 77.4 | 37.9 | 84.7 | 57.5 | 04.5 | 76.6 | 19.0 | 17.0 | 12.7 | 51.7 |
| UniDAPS [86] | 38.5 | 72.3 | 29.2 | 75.8 | 33.9 | 38.9 | 25.9 | 11.4 | 07.5 | 77.6 | 37.4 | 81.4 | 47.6 | 03.0 | 75.6 | 21.3 | 03.4 | 01.3 | 48.9 |
| EDAPS [55] | 40.2 | 74.4 | 35.9 | 77.0 | 36.5 | 40.4 | 28.0 | 16.1 | 05.1 | 78.1 | 39.5 | 82.3 | 55.5 | 03.3 | 74.4 | 06.7 | 14.1 | 05.2 | 50.9 |
| UnmaskFormer [7] | 43.7 | 76.5 | 37.8 | 77.1 | 34.7 | 44.1 | 28.3 | 17.8 | 02.8 | 78.7 | 41.7 | 85.0 | 57.3 | 06.0 | 80.6 | 23.5 | 21.7 | 18.8 | 53.6 |
| (xpan,ypan) | Source-only | 38.7 | 73.0 | 29.1 | 82.0 | 31.2 | 31.4 | 18.0 | 00.0 | 16.0 | 74.1 | 33.7 | 88.7 | 50.2 | 04.0 | 80.4 | 18.0 | 11.0 | 04.6 | 50.2 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 39.4 | 74.6 | 32.2 | 81.2 | 30.7 | 31.9 | 18.1 | 00.0 | 15.6 | 72.6 | 38.3 | 89.2 | 50.6 | 04.6 | 80.5 | 20.4 | 11.6 | 05.3 | 51.0 |
| UNLOCK (Ours) | 41.6 (↑2.9) | 74.7 | 32.1 | 83.7 | 34.7 | 40.8 | 18.5 | 00.0 | 18.9 | 76.1 | 39.9 | 89.5 | 53.7 | 05.8 | 82.2 | 26.1 | 00.8 | 14.0 | 57.8 |
+
+Table 1. Scene Segmentation results on the K2B benchmark. Metrics are reported as: mAPQ for Amodal Panoptic Segmentation (APS), mPQ for Panoptic Segmentation (PS), and mIoU for Semantic Segmentation (SS). Per-class results are reported as APQ, PQ, and IoU. $\uparrow$ represents the improvement over the baseline of the Source-only method. $x^{pin}$ and $x^{pan}$ represent the images, and $y^{pin}$ and $y^{pan}$ represent the labels, from the pinhole source and panoramic target domains, respectively.
+
+avoiding confusion about the semantic content of other objects. The zero-pixel ambiguous regions act as a masked strategy to enhance the model's ability to reconstruct occluded areas and infer the complete shape of occluded objects. This improves the model's ability to learn contextual knowledge from the target panoramic domain, improving its understanding of both individual objects and their relationships within the scene.
+
+# 4. Experiments
+
+# 4.1. Datasets
+
+In this paper, we extend the Real-to-Real adaptation on the KITTI360-APS $\rightarrow$ BlendPASS (K2B for short)) benchmark [7] to SFOASS. Moreover, we pioneer Synthetic-to-Real adaptation in both OASS and SFOASS, introducing AmodalSynthDrive $\rightarrow$ BlendPASS benchmark (A2B for short) to conduct seamless segmentation research from synthetic to real scenarios.
+
+Source pinhole domain: (1) KITTI360-APS [48]: It extends KITTI360 [39] and includes additional annotations for inmodal and amodal instances. A total of 12,320 annotated images $(1408\times 376$ pixels) are captured using pinhole cameras across 9 cities. It covers 11 Stuff classes and 7 Thing classes. (2) AmodalSynthDrive [57]: The first synthetic dataset applicable to the OASS task, generated using CARLA [13]. It provides images and annotations from four surround-view cameras with a pinhole perspective, with 10,500 training images $(1920\times 1080$ pixels) for each viewpoint. It covers 11 Stuff classes and 7 Thing classes.
+
+Target panoramic domain: The BlendPASS dataset [7] consists of 2,000 unlabeled training panoramic images and
+
+100 labeled test panoramic images $(2048 \times 400$ pixels), captured in real driving scenes across 40 cities on multiple continents. It covers 11 Stuff and 8 Thing classes.
+
+Domain gap analysis: Fig. 5 shows the feature distributions of car and pedestrians between the target domain and two source domains, where there is a large domain gap between different datasets, especially for the A2B.
+
+
+Figure 5. Example images from the datasets [7, 48, 57] and the class distribution visualized via t-SNE [66].
+
+# 4.2. Experiment Setups
+
+Following [7], we use the proposed architecture as the backbone of our UNLOCK and the reproduced 360SFUDA++ [95]. In the A2B benchmark, we reproduce existing methods [55, 85, 86, 93, 95] and train the pinhole source model following the framework in [7]. In the K2B benchmark, we directly use the Source-only model from [7] as the pinhole source model. The AdamW optimizer [42] is employed, with a learning rate set to $1 \times 10^{-7}$ , and a weight decay of 0.01, followed by polynomial decay. The batch size is set to 4, with crop sizes of $376 \times 376$ for K2B and $400 \times 400$ for A2B, and both are trained for $10k$ iterations. In UNLOCK, $\tau^{fix}$ and $\tau^{per}$ for amodal instance predictions are set to 0.3 and 0.5; for instance predictions to 0.5 and 0.3; and for semantic predictions, to 0.5 and 0.8. For ADCL, they are set to 0.95 and 0.1, with the sample object count $R$
+
+| Task | Method | Metric | Preds. | Cyclings | Car | Musk | Opt. | Van | WhWhite |
| AIS | B | DATR [93] | 08.7 | 13.1 | 00.0 | 30.6 | 06.9 | 04.7 | 01.7 | 03.8 |
| Trans4PASS [85] | 09.9 | 16.0 | 00.2 | 31.7 | 08.3 | 06.0 | 00.4 | 06.4 |
| EDAPS [55] | 10.7 | 15.8 | 00.1 | 30.0 | 09.0 | 12.2 | 00.4 | 07.4 |
| UnmaskFormer [7] | 10.5 | 16.1 | 00.1 | 34.1 | 12.3 | 02.2 | 00.6 | 08.2 |
| B | Source-only | 10.2 | 15.2 | 00.0 | 33.4 | 12.6 | 03.3 | 00.4 | 06.8 |
| 360SFUDA++ [95] | 10.3 | 15.2 | 00.0 | 33.4 | 13.1 | 03.3 | 00.4 | 06.8 |
| UNLOCK (Ours) | 10.9 (↑0.7) | 17.1 | 00.0 | 34.9 | 14.6 | 01.7 | 00.2 | 07.9 |
| IS | B | DATR [93] | 08.7 | 14.2 | 00.0 | 31.2 | 07.6 | 03.7 | 00.4 | 03.6 |
| Trans4PASS [85] | 10.0 | 16.5 | 00.0 | 32.2 | 10.2 | 05.3 | 00.2 | 05.6 |
| UniDAPS [86] | 03.4 | 02.3 | 00.0 | 11.3 | 06.2 | 02.8 | 00.0 | 01.5 |
| EDAPS [55] | 10.3 | 16.6 | 00.0 | 30.8 | 06.5 | 11.4 | 00.4 | 06.2 |
| UnmaskFormer [7] | 11.1 | 17.6 | 00.0 | 35.2 | 14.2 | 02.9 | 00.8 | 07.1 |
| B | Source-only | 10.5 | 15.8 | 00.0 | 33.9 | 13.5 | 03.6 | 00.2 | 06.8 |
| 360SFUDA++ [95] | 10.5 | 15.7 | 00.0 | 33.9 | 13.3 | 03.6 | 00.2 | 06.8 |
| UNLOCK (Ours) | 11.6 (↑1.1) | 17.7 | 00.0 | 36.1 | 16.3 | 03.4 | 00.1 | 07.4 |
+
+| Task | Method | Metric | Person | ride | car | huck | bus | monor. | bicycle |
| AIS | Δ | DATR [93] | 08.1 | 14.1 | 00.4 | 23.5 | 09.6 | 04.3 | 04.7 | 00.0 |
| Trans4PASS [85] | 09.2 | 13.0 | 00.2 | 24.7 | 13.0 | 07.6 | 05.7 | 00.0 |
| EDAPS [55] | 09.5 | 16.7 | 00.2 | 25.2 | 11.6 | 06.6 | 06.1 | 00.0 |
| UnmaskFormer [7] | 10.2 | 16.6 | 00.1 | 26.5 | 12.8 | 08.6 | 06.4 | 00.0 |
| Δ | Source-only | 09.7 | 16.0 | 00.0 | 24.9 | 11.9 | 09.1 | 05.6 | 00.0 |
| 360SFUDA++ [95] | 09.6 | 16.2 | 00.0 | 25.3 | 11.7 | 08.9 | 05.2 | 00.0 |
| UNLOCK (Ours) | 10.0 (↑0.3) | 17.3 | 00.0 | 28.9 | 09.2 | 08.3 | 06.4 | 00.0 |
| IS | Δ | DATR [93] | 08.0 | 14.9 | 00.4 | 25.3 | 09.2 | 01.0 | 04.9 | 00.0 |
| Trans4PASS [85] | 09.0 | 15.0 | 00.1 | 27.2 | 11.8 | 04.1 | 05.0 | 00.0 |
| UniDAPS [86] | 00.3 | 00.8 | 00.0 | 00.8 | 00.1 | 00.0 | 00.5 | 00.0 |
| EDAPS [55] | 09.5 | 16.4 | 00.1 | 28.2 | 10.7 | 05.3 | 05.8 | 00.0 |
| UnmaskFormer [7] | 09.6 | 17.0 | 00.1 | 28.4 | 11.9 | 03.8 | 05.9 | 00.0 |
| Δ | Source-only | 09.3 | 17.4 | 00.0 | 26.9 | 11.6 | 04.4 | 04.9 | 00.0 |
| 360SFUDA++ [95] | 09.4 | 17.5 | 00.0 | 27.1 | 11.1 | 05.4 | 04.8 | 00.0 |
| UNLOCK (Ours) | 09.7 (↑0.4) | 17.7 | 00.0 | 29.3 | 09.0 | 05.9 | 06.1 | 00.0 |
+
+Table 2. Instance-level Segmentation results on the K2B (left) and A2B (right) benchmark. Metrics are reported as: mAAP for Amodal Instance Segmentation (AIS) and mAAP for Instance Segmentation (IS). Per-class results are reported as AAP and AP.
+
+
+Figure 6. Visualization results. From top to bottom are (a) Image, (b) GT, (c) Source-only, and (d) 360SFUDA++ [95], and (e) UNLOCK.
+
+
+
+
+
+set to 10. The analysis of these thresholds is provided in the supplementary material. Our experiments are conducted on a single NVIDIA GTX 3090 GPU using PyTorch.
+
+# 4.3. Results of SFOASS
+
+K2B. As shown by the Real-to-Real adaptation results in Table 1 and the left side of Table 2, UNLOCK sets a new benchmark for SFOASS, delivering outstanding performance and effectively addressing the unique challenges of limited FoV, occlusion, and constrained data. Compared to the baseline Source-only, UNLOCK outperforms in key metrics for scene understanding including mAPQ, mPQ, and mIoU, with improvements of $+4.3$ , $+2.8$ , and $+2.9$ , respectively. Even compared to UnmaskFormer [7], which has access to both source domain and target images, UNLOCK achieves comparable results in mAPQ. Notably, in instance-level segmentation, UNLOCK surpasses all existing UDA methods[7, 55, 85, 93]—even without access to source domain data containing $12K$ images-label pairs, reaching the highest mAAP of 10.9 and mAP of 11.6, showcasing its robustness and adaptability. As shown in Fig. 6, UNLOCK successfully and precisely segments numerous Thing objects with better shape coherence.
+
+A2B. The results from another Synthetic-to-Real adaptation scenario, shown in Table 3 and the right side of Table 2,
+
+further demonstrate UNLOCK's exceptional performance. Compared to 360SFUDA++ [95], which is specifically designed for panoramic data, our method significantly outperforms across all SFOASS metrics. This success is driven by the OPLL pseudo-label generation strategy, which is tailored specifically for SFOASS. The instance-level segmentation results highlight a clear advantage for our method, reflecting its enhanced accuracy in segmenting individual object instances within complex scenes.
+
+# 4.4. Ablation Study
+
+We conduct a series of ablation studies on the K2B scenario to evaluate the effectiveness of our method.
+
+Effectiveness of OPLL. An ablation study was conducted to validate the effectiveness of the OPLL. Table 4 presents the comparison of three different approaches for self-training. Using the final predicted labels from the source model as pseudo-labels or directly using all predictions from the three branches fails to adapt the instance-level branches to the panoramic domain, as evidenced by both mAAP and mAP scores, which are even worse than the no-adaptation Source-only model. With the OPLL designed by us, the knowledge of the source model can be effectively adapted to the target domain by using omni pseudo-labels. Compared with Source-only, OPLL achieves a significant
+
+| Task | Constraint | Method | Metric | road | sidew | build | wall | fence | pole | lights | sign | vestor | terrain | fly | person | rider | car | track | bus | motor | bicycle |
| APS | (ypan) | DATR [93] | 19.4 | 36.1 | 00.0 | 72.4 | 00.0 | 01.3 | 02.4 | 00.0 | 07.1 | 64.8 | 00.0 | 88.9 | 08.3 | 02.7 | 31.6 | 18.4 | 00.0 | 14.8 | 00.0 |
| TransPASS [85] | 21.5 | 38.7 | 00.0 | 71.9 | 00.0 | 10.0 | 03.8 | 00.0 | 07.4 | 65.3 | 00.0 | 89.2 | 11.1 | 03.7 | 35.3 | 25.4 | 07.6 | 15.9 | 00.9 |
| EDAPS [55] | 21.7 | 45.5 | 00.0 | 74.9 | 00.0 | 08.5 | 04.1 | 00.0 | 06.0 | 63.7 | 00.0 | 89.5 | 12.1 | 02.8 | 35.9 | 20.7 | 09.7 | 17.0 | 00.0 |
| UnmaskFormer [7] | 22.9 | 44.1 | 00.6 | 67.5 | 00.0 | 09.6 | 04.3 | 00.0 | 05.0 | 67.0 | 00.0 | 90.2 | 16.6 | 00.0 | 38.7 | 29.2 | 17.1 | 22.2 | 00.0 |
| (xpan,ypan) | Source-only | 18.9 | 47.1 | 01.9 | 68.5 | 00.0 | 00.9 | 00.5 | 00.0 | 01.6 | 43.0 | 00.0 | 84.7 | 09.5 | 00.0 | 36.3 | 21.5 | 07.5 | 16.7 | 00.0 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 19.4 | 46.6 | 01.9 | 68.1 | 00.0 | 01.0 | 00.5 | 00.0 | 01.7 | 48.2 | 00.0 | 86.1 | 18.8 | 00.0 | 38.5 | 18.1 | 06.4 | 14.1 | 00.0 |
| UNLOCK (Ours) | 21.4 (↑2.5) | 50.8 | 04.7 | 73.5 | 00.0 | 04.8 | 00.6 | 00.0 | 03.9 | 49.8 | 00.0 | 86.2 | 17.5 | 01.2 | 41.4 | 20.2 | 09.3 | 20.9 | 00.0 |
| PS | (ypan) | DATR [93] | 19.5 | 35.7 | 00.0 | 71.5 | 00.0 | 01.3 | 01.8 | 00.0 | 07.1 | 64.8 | 00.0 | 88.9 | 08.3 | 05.0 | 32.2 | 15.8 | 02.4 | 15.5 | 00.0 |
| TransPASS [85] | 20.9 | 38.1 | 00.0 | 71.9 | 00.0 | 10.0 | 03.8 | 00.0 | 07.4 | 65.3 | 00.0 | 89.2 | 09.6 | 00.0 | 36.5 | 25.0 | 03.3 | 15.9 | 00.0 |
| UniDAPS [86] | 18.2 | 53.1 | 00.0 | 72.4 | 01.8 | 07.8 | 05.5 | 00.0 | 07.7 | 67.8 | 00.0 | 88.7 | 07.0 | 00.0 | 07.7 | 01.6 | 00.0 | 07.0 | 00.0 |
| EDAPS [55] | 21.9 | 46.7 | 00.0 | 75.1 | 00.0 | 08.5 | 04.1 | 00.0 | 06.1 | 63.6 | 00.0 | 89.5 | 11.8 | 02.5 | 36.9 | 23.4 | 08.9 | 16.5 | 00.0 |
| UnmaskFormer [7] | 20.7 | 42.9 | 00.6 | 67.0 | 00.0 | 09.6 | 03.6 | 00.0 | 05.0 | 66.9 | 00.0 | 90.2 | 16.6 | 00.0 | 37.3 | 25.9 | 07.5 | 00.0 | 00.0 |
| (xpan,ypan) | Source-only | 19.0 | 48.8 | 01.9 | 68.6 | 00.0 | 00.9 | 00.5 | 00.0 | 01.6 | 42.8 | 00.0 | 84.7 | 12.7 | 00.0 | 36.2 | 20.3 | 06.4 | 16.8 | 00.0 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 19.3 | 46.5 | 01.9 | 69.9 | 00.0 | 01.0 | 00.5 | 00.0 | 01.7 | 47.9 | 00.0 | 86.0 | 15.6 | 00.0 | 36.5 | 18.9 | 06.5 | 15.2 | 00.0 |
| UNLOCK (Ours) | 20.4 (↑1.4) | 50.5 | 04.2 | 74.0 | 00.0 | 04.8 | 00.6 | 00.0 | 03.9 | 49.2 | 00.0 | 86.3 | 14.3 | 00.0 | 38.1 | 18.8 | 05.7 | 16.8 | 00.0 |
| SS | (ypan) | DATR [93] | 31.5 | 59.5 | 06.3 | 77.7 | 00.2 | 09.2 | 22.9 | 02.4 | 10.3 | 76.6 | 00.0 | 93.4 | 37.7 | 01.9 | 68.8 | 20.8 | 01.5 | 54.1 | 24.2 |
| TransPASS [85] | 34.3 | 58.9 | 07.6 | 77.3 | 00.2 | 28.7 | 26.7 | 05.2 | 11.1 | 76.1 | 00.0 | 93.6 | 35.8 | 01.8 | 73.6 | 28.3 | 06.8 | 55.2 | 30.1 |
| UniDAPS [86] | 36.0 | 61.5 | 07.5 | 76.6 | 00.8 | 30.4 | 27.7 | 10.2 | 11.1 | 77.4 | 00.0 | 93.6 | 47.3 | 02.1 | 49.4 | 25.9 | 33.0 | 62.3 | 30.6 |
| EDAPS [55] | 36.2 | 62.2 | 10.8 | 81.1 | 00.5 | 28.7 | 22.9 | 10.6 | 10.5 | 75.5 | 00.1 | 93.3 | 42.7 | 02.3 | 72.1 | 33.6 | 18.8 | 58.6 | 26.7 |
| UnmaskFormer [7] | 36.1 | 60.6 | 13.3 | 74.2 | 00.9 | 32.7 | 21.6 | 14.2 | 06.9 | 76.7 | 00.0 | 93.9 | 45.2 | 01.2 | 73.3 | 34.1 | 22.0 | 56.9 | 22.7 |
| (xpan,ypan) | Source-only | 31.0 | 67.1 | 21.5 | 76.9 | 03.2 | 17.0 | 17.7 | 02.7 | 06.3 | 64.7 | 00.0 | 90.7 | 40.0 | 01.8 | 69.2 | 19.5 | 04.6 | 47.4 | 08.5 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 31.2 | 64.8 | 21.3 | 77.7 | 03.4 | 16.2 | 18.9 | 02.7 | 06.0 | 66.6 | 00.0 | 91.7 | 41.9 | 02.0 | 67.9 | 19.1 | 04.6 | 49.1 | 07.9 |
| UNLOCK (Ours) | 34.3 (↑3.3) | 69.1 | 25.2 | 81.5 | 00.1 | 25.1 | 20.0 | 03.7 | 10.5 | 68.0 | 00.0 | 91.6 | 45.9 | 01.6 | 71.4 | 24.0 | 07.2 | 50.8 | 21.4 |
+
+Table 3. Scene Segmentation results on the A2B benchmark. Metrics are reported as: mAPQ for Amodal Panoptic Segmentation (APS), mPQ for Panoptic Segmentation (PS), and mIoU for Semantic Segmentation (SS). Per-class results are reported as APQ, PQ, and IoU.
+
+ | mAPQ | mPQ | mIoU | mAAP | mAP |
| Source-only | 22.13 | 22.30 | 38.65 | 10.22 | 10.54 |
| Pseudo-Labels | 21.90 | 22.07 | 39.12 | 10.09 | 10.37 |
| All Predictions | 22.38 | 22.31 | 38.90 | 10.15 | 10.50 |
| OPLL (Ours) | 24.71 | 24.00 | 39.03 | 10.52 | 10.52 |
+
+Table 4. Ablation analysis for OPLL.
+
+| Backbone | mAPQ | mPQ | mIoU | mAAP | mAP |
| Source-only | 22.1 | 22.3 | 38.7 | 10.2 | 10.5 |
| Trans4PASS [85] | 26.1 | 25.3 | 40.0 | 10.9 | 11.3 |
| EDAPS [55] | 26.3 | 25.1 | 40.5 | 10.7 | 11.4 |
| UnmaskFormer [7] | 26.4 | 25.1 | 41.6 | 10.9 | 11.6 |
+
+Table 5. Ablation analysis for backbones.
+
+| OPLL | ADCL | mAPQ | mPQ | mIoU | mAAP | mAP |
| | 22.13 | 22.30 | 38.65 | 10.22 | 10.54 |
| ✓ | | 24.71 | 24.00 | 39.03 | 10.52 | 10.52 |
| ✓ | 25.84 | 24.55 | 40.31 | 10.93 | 11.47 |
| ✓ | ✓ | 26.41 | 25.07 | 41.64 | 10.91 | 11.58 |
+
+Table 6. Ablation analysis for components.
+
+ | mAPQ | mPO | mLOU | mAAP | mAP |
| Source-only | 22.13 | 22.30 | 38.65 | 10.22 | 10.54 |
| Instance | 25.03 | 24.23 | 38.93 | 10.33 | 10.55 |
| Amodal Instance | 25.71 | 24.50 | 39.06 | 10.77 | 11.22 |
| AoMix [7] | 25.32 | 24.67 | 38.04 | 10.62 | 11.26 |
| ADCL-Random | 24.81 | 23.90 | 38.92 | 10.69 | 11.19 |
| ADCL-Zero (Ours) | 25.84 | 24.55 | 40.31 | 10.93 | 11.47 |
+
+Table 7. Ablation analysis for ADCL.
+
+| Method | mIoU |
| SFDA [40] | 42.70 |
| DATC [73] | 43.06 |
| 360SFUDA [96] | 50.12 |
| 360SFUDA++[95] | 52.99 |
| UNLOCK (Ours) | 54.55 |
+
+Table 8. SS results on the C2D benchmark.
+
+improvement of 2.58 in mAPQ.
+
+Effectiveness of ADCL. Another ablation study was conducted to validate the effectiveness of the ADCL. Table 7 presents a comparison of different object mixing strategies. Due to incomplete object shapes, instance-based mixing yields limited improvement in mAPQ and mAAP. Directly using amodal instances causes confusion in contextual information. Unlike AoMix [7], which zeros out full amodal object regions of the input image, our method in UNLOCK sets only the overlapping regions to zero (ADCL-Zero), effectively preserving contextual cues. Replacing overlaps with random values (ADCL-Random) yields inferior results, while ADCL-Zero achieves the best mAPQ of 25.84. Component Ablation. As shown in Table 6, by combining OPLL and ADCL, our UNLOCK method achieves the best overall performance, outperforming the Source-only trained on the source pinhole domain with $+4.28$ gains in mAPQ. It shows that our methods can successfully adapt to the target panoramic domain under source-free constraints.
+
+Backbone Ablation. As shown in Table 5, we evaluated the performance of UNLOCK across different backbones to verify the effectiveness of the UNLOCK strategy itself. The
+
+results indicate that UNLOCK maintains consistent performance across diverse backbone architectures, confirming its backbone-agnostic nature as an SFDA framework.
+
+# 4.5. Results of Panoramic Semantic Segmentation
+
+To investigate the generalization capability of UNLOCK, we extend UNLOCK to the Semantic Segmentation (SS) task and evaluate it on the Cityscapes-to-DensePASS (C2D) benchmark. As shown in Table 8, UNLOCK achieves a significant improvement of $+1.56$ in mIoU over 360SFUDA++ [95]. Under the pinhole-to-panoramic C2D adaptation scenario, our UNLOCK achieves the new state-of-the-art result of 54.55 in mIoU.
+
+# 5. Conclusion
+
+In this paper, we address key constraints in comprehensive scene understanding, to achieve seamless segmentation with $360^{\circ}$ viewpoint coverage and occlusion-aware reasoning, while adapting without relying on source data and target labels. To this end, we introduce a new task, Source-Free Occlusion-Aware Seamless Segmentation (SFOASS), and propose its first solution UNLOCK. We further applied two SFOASS benchmarks for evaluation: Real-to-Real and Synthetic-to-Real. Extensive experimental results demonstrate the effectiveness of the proposed method.
+
+# Acknowledgment
+
+This work was supported in part by the National Natural Science Foundation of China (No. 62473139, 62027810), the Major Research Plan of the National Natural Science Foundation of China (No. 92148204), the Top Ten Technical Research Projects of Hunan Province (No. 2024GK1010), the Key Program of Natural Science Foundation of Hunan Province, China (No. 2025JJ30024), the National Key Research and Development Program of China (No. 2024YFB4708900), the Hunan Provincial Research and Development Project (No. 2025QK3019), in part by the Open Research Project of the State Key Laboratory of Industrial Control Technology, China (No. ICT2025B20), and the Science and Technology Project of State Grid Corporation of China (SGCC) Co., LTD (No. 5700-202423229A-1-1-ZN).
+
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+ "content": "* Equal contribution. † Corresponding authors (e-mail: kailun.yang@hnu.edu.cn, zhanghuihby@126.com)."
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| APS | (ypan) | DATR [93] | 20.3 | 51.8 | 09.2 | 59.9 | 11.9 | 12.0 | 02.0 | 00.0 | 03.9 | 64.6 | 14.1 | 70.4 | 11.1 | 00.0 | 39.3 | 00.0 | 03.2 | 10.1 | 01.3 |
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| EDAPS [55] | 23.1 | 54.9 | 17.0 | 66.9 | 18.8 | 14.5 | 05.8 | 04.0 | 04.6 | 68.2 | 16.0 | 72.8 | 19.0 | 00.0 | 36.7 | 05.8 | 04.4 | 00.0 | 07.2 |
| UnmaskFormer [7] | 26.6 | 61.8 | 24.7 | 66.8 | 20.8 | 15.8 | 05.3 | 04.3 | 03.3 | 69.0 | 18.4 | 79.4 | 20.5 | 03.1 | 44.6 | 12.8 | 11.3 | 00.0 | 16.6 |
| (xpan,ypan) | Source-only | 22.1 | 57.1 | 14.2 | 73.6 | 15.5 | 07.6 | 00.7 | 00.0 | 10.4 | 58.3 | 12.4 | 83.1 | 15.2 | 00.0 | 40.3 | 03.8 | 00.0 | 00.0 | 06.1 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 24.5 | 60.3 | 16.8 | 71.7 | 14.1 | 07.7 | 00.0 | 00.0 | 08.4 | 55.6 | 13.6 | 81.3 | 21.5 | 03.2 | 46.3 | 19.4 | 02.2 | 00.0 | 19.4 |
| UNLOCK (Ours) | 26.4 (↑4.3) | 62.7 | 14.4 | 74.8 | 20.2 | 11.2 | 00.8 | 00.0 | 08.0 | 62.9 | 18.3 | 84.0 | 21.9 | 03.6 | 45.8 | 19.4 | 00.0 | 03.1 | 24.4 |
| PS | (ypan) | DATR [93] | 19.6 | 50.4 | 09.1 | 59.9 | 11.9 | 12.0 | 02.0 | 00.0 | 03.9 | 64.6 | 14.1 | 70.5 | 12.2 | 00.0 | 38.1 | 00.0 | 03.4 | 00.0 | 01.3 |
| Trans4PASS [85] | 22.7 | 53.9 | 14.1 | 69.4 | 19.2 | 11.8 | 03.8 | 00.0 | 05.2 | 67.6 | 16.0 | 77.4 | 14.6 | 04.1 | 38.2 | 06.9 | 00.0 | 00.0 | 07.2 |
| UniDAPS [86] | 22.7 | 66.0 | 09.5 | 66.3 | 17.4 | 14.3 | 04.8 | 00.0 | 06.1 | 67.2 | 16.1 | 72.7 | 08.3 | 00.0 | 27.3 | 14.8 | 09.2 | 00.0 | 08.9 |
| EDAPS [55] | 23.1 | 55.0 | 17.1 | 66.8 | 18.7 | 14.5 | 05.8 | 04.0 | 04.7 | 68.2 | 16.0 | 72.8 | 19.6 | 00.0 | 37.8 | 01.8 | 04.4 | 00.0 | 07.9 |
| UnmaskFormer [7] | 26.2 | 61.7 | 24.7 | 66.8 | 20.8 | 15.8 | 05.2 | 04.3 | 03.3 | 69.0 | 18.4 | 79.4 | 20.9 | 03.5 | 43.0 | 11.3 | 07.6 | 00.0 | 16.0 |
| (xpan,ypan) | Source-only | 22.3 | 57.8 | 14.2 | 73.8 | 15.5 | 07.6 | 00.7 | 00.0 | 10.4 | 58.3 | 12.4 | 83.2 | 14.9 | 00.0 | 39.1 | 06.0 | 00.0 | 00.0 | 07.7 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 23.7 | 61.3 | 16.8 | 72.2 | 14.1 | 07.6 | 00.0 | 00.0 | 08.4 | 55.9 | 13.6 | 81.3 | 18.4 | 00.0 | 40.6 | 16.4 | 02.4 | 00.0 | 17.6 |
| UNLOCK (Ours) | 25.1 (↑2.8) | 60.4 | 14.4 | 75.7 | 20.2 | 11.2 | 00.7 | 00.0 | 08.0 | 63.6 | 18.3 | 84.0 | 16.9 | 00.0 | 40.0 | 18.5 | 00.0 | 00.0 | 19.4 |
| SS | (ypan) | DATR [93] | 34.9 | 71.9 | 27.2 | 70.6 | 22.8 | 36.0 | 23.9 | 00.0 | 04.5 | 77.1 | 37.1 | 80.1 | 51.2 | 02.2 | 70.2 | 08.9 | 06.0 | 11.0 | 27.8 |
| Trans4PASS [85] | 40.7 | 72.8 | 33.8 | 78.4 | 33.5 | 37.1 | 26.6 | 05.3 | 55.4 | 77.4 | 37.9 | 84.7 | 57.5 | 04.5 | 76.6 | 19.0 | 17.0 | 12.7 | 51.7 |
| UniDAPS [86] | 38.5 | 72.3 | 29.2 | 75.8 | 33.9 | 38.9 | 25.9 | 11.4 | 07.5 | 77.6 | 37.4 | 81.4 | 47.6 | 03.0 | 75.6 | 21.3 | 03.4 | 01.3 | 48.9 |
| EDAPS [55] | 40.2 | 74.4 | 35.9 | 77.0 | 36.5 | 40.4 | 28.0 | 16.1 | 05.1 | 78.1 | 39.5 | 82.3 | 55.5 | 03.3 | 74.4 | 06.7 | 14.1 | 05.2 | 50.9 |
| UnmaskFormer [7] | 43.7 | 76.5 | 37.8 | 77.1 | 34.7 | 44.1 | 28.3 | 17.8 | 02.8 | 78.7 | 41.7 | 85.0 | 57.3 | 06.0 | 80.6 | 23.5 | 21.7 | 18.8 | 53.6 |
| (xpan,ypan) | Source-only | 38.7 | 73.0 | 29.1 | 82.0 | 31.2 | 31.4 | 18.0 | 00.0 | 16.0 | 74.1 | 33.7 | 88.7 | 50.2 | 04.0 | 80.4 | 18.0 | 11.0 | 04.6 | 50.2 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 39.4 | 74.6 | 32.2 | 81.2 | 30.7 | 31.9 | 18.1 | 00.0 | 15.6 | 72.6 | 38.3 | 89.2 | 50.6 | 04.6 | 80.5 | 20.4 | 11.6 | 05.3 | 51.0 |
| UNLOCK (Ours) | 41.6 (↑2.9) | 74.7 | 32.1 | 83.7 | 34.7 | 40.8 | 18.5 | 00.0 | 18.9 | 76.1 | 39.9 | 89.5 | 53.7 | 05.8 | 82.2 | 26.1 | 00.8 | 14.0 | 57.8 |
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| AIS | B | DATR [93] | 08.7 | 13.1 | 00.0 | 30.6 | 06.9 | 04.7 | 01.7 | 03.8 |
| Trans4PASS [85] | 09.9 | 16.0 | 00.2 | 31.7 | 08.3 | 06.0 | 00.4 | 06.4 |
| EDAPS [55] | 10.7 | 15.8 | 00.1 | 30.0 | 09.0 | 12.2 | 00.4 | 07.4 |
| UnmaskFormer [7] | 10.5 | 16.1 | 00.1 | 34.1 | 12.3 | 02.2 | 00.6 | 08.2 |
| B | Source-only | 10.2 | 15.2 | 00.0 | 33.4 | 12.6 | 03.3 | 00.4 | 06.8 |
| 360SFUDA++ [95] | 10.3 | 15.2 | 00.0 | 33.4 | 13.1 | 03.3 | 00.4 | 06.8 |
| UNLOCK (Ours) | 10.9 (↑0.7) | 17.1 | 00.0 | 34.9 | 14.6 | 01.7 | 00.2 | 07.9 |
| IS | B | DATR [93] | 08.7 | 14.2 | 00.0 | 31.2 | 07.6 | 03.7 | 00.4 | 03.6 |
| Trans4PASS [85] | 10.0 | 16.5 | 00.0 | 32.2 | 10.2 | 05.3 | 00.2 | 05.6 |
| UniDAPS [86] | 03.4 | 02.3 | 00.0 | 11.3 | 06.2 | 02.8 | 00.0 | 01.5 |
| EDAPS [55] | 10.3 | 16.6 | 00.0 | 30.8 | 06.5 | 11.4 | 00.4 | 06.2 |
| UnmaskFormer [7] | 11.1 | 17.6 | 00.0 | 35.2 | 14.2 | 02.9 | 00.8 | 07.1 |
| B | Source-only | 10.5 | 15.8 | 00.0 | 33.9 | 13.5 | 03.6 | 00.2 | 06.8 |
| 360SFUDA++ [95] | 10.5 | 15.7 | 00.0 | 33.9 | 13.3 | 03.6 | 00.2 | 06.8 |
| UNLOCK (Ours) | 11.6 (↑1.1) | 17.7 | 00.0 | 36.1 | 16.3 | 03.4 | 00.1 | 07.4 |
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| AIS | Δ | DATR [93] | 08.1 | 14.1 | 00.4 | 23.5 | 09.6 | 04.3 | 04.7 | 00.0 |
| Trans4PASS [85] | 09.2 | 13.0 | 00.2 | 24.7 | 13.0 | 07.6 | 05.7 | 00.0 |
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| IS | Δ | DATR [93] | 08.0 | 14.9 | 00.4 | 25.3 | 09.2 | 01.0 | 04.9 | 00.0 |
| Trans4PASS [85] | 09.0 | 15.0 | 00.1 | 27.2 | 11.8 | 04.1 | 05.0 | 00.0 |
| UniDAPS [86] | 00.3 | 00.8 | 00.0 | 00.8 | 00.1 | 00.0 | 00.5 | 00.0 |
| EDAPS [55] | 09.5 | 16.4 | 00.1 | 28.2 | 10.7 | 05.3 | 05.8 | 00.0 |
| UnmaskFormer [7] | 09.6 | 17.0 | 00.1 | 28.4 | 11.9 | 03.8 | 05.9 | 00.0 |
| Δ | Source-only | 09.3 | 17.4 | 00.0 | 26.9 | 11.6 | 04.4 | 04.9 | 00.0 |
| 360SFUDA++ [95] | 09.4 | 17.5 | 00.0 | 27.1 | 11.1 | 05.4 | 04.8 | 00.0 |
| UNLOCK (Ours) | 09.7 (↑0.4) | 17.7 | 00.0 | 29.3 | 09.0 | 05.9 | 06.1 | 00.0 |
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| APS | (ypan) | DATR [93] | 19.4 | 36.1 | 00.0 | 72.4 | 00.0 | 01.3 | 02.4 | 00.0 | 07.1 | 64.8 | 00.0 | 88.9 | 08.3 | 02.7 | 31.6 | 18.4 | 00.0 | 14.8 | 00.0 |
| TransPASS [85] | 21.5 | 38.7 | 00.0 | 71.9 | 00.0 | 10.0 | 03.8 | 00.0 | 07.4 | 65.3 | 00.0 | 89.2 | 11.1 | 03.7 | 35.3 | 25.4 | 07.6 | 15.9 | 00.9 |
| EDAPS [55] | 21.7 | 45.5 | 00.0 | 74.9 | 00.0 | 08.5 | 04.1 | 00.0 | 06.0 | 63.7 | 00.0 | 89.5 | 12.1 | 02.8 | 35.9 | 20.7 | 09.7 | 17.0 | 00.0 |
| UnmaskFormer [7] | 22.9 | 44.1 | 00.6 | 67.5 | 00.0 | 09.6 | 04.3 | 00.0 | 05.0 | 67.0 | 00.0 | 90.2 | 16.6 | 00.0 | 38.7 | 29.2 | 17.1 | 22.2 | 00.0 |
| (xpan,ypan) | Source-only | 18.9 | 47.1 | 01.9 | 68.5 | 00.0 | 00.9 | 00.5 | 00.0 | 01.6 | 43.0 | 00.0 | 84.7 | 09.5 | 00.0 | 36.3 | 21.5 | 07.5 | 16.7 | 00.0 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 19.4 | 46.6 | 01.9 | 68.1 | 00.0 | 01.0 | 00.5 | 00.0 | 01.7 | 48.2 | 00.0 | 86.1 | 18.8 | 00.0 | 38.5 | 18.1 | 06.4 | 14.1 | 00.0 |
| UNLOCK (Ours) | 21.4 (↑2.5) | 50.8 | 04.7 | 73.5 | 00.0 | 04.8 | 00.6 | 00.0 | 03.9 | 49.8 | 00.0 | 86.2 | 17.5 | 01.2 | 41.4 | 20.2 | 09.3 | 20.9 | 00.0 |
| PS | (ypan) | DATR [93] | 19.5 | 35.7 | 00.0 | 71.5 | 00.0 | 01.3 | 01.8 | 00.0 | 07.1 | 64.8 | 00.0 | 88.9 | 08.3 | 05.0 | 32.2 | 15.8 | 02.4 | 15.5 | 00.0 |
| TransPASS [85] | 20.9 | 38.1 | 00.0 | 71.9 | 00.0 | 10.0 | 03.8 | 00.0 | 07.4 | 65.3 | 00.0 | 89.2 | 09.6 | 00.0 | 36.5 | 25.0 | 03.3 | 15.9 | 00.0 |
| UniDAPS [86] | 18.2 | 53.1 | 00.0 | 72.4 | 01.8 | 07.8 | 05.5 | 00.0 | 07.7 | 67.8 | 00.0 | 88.7 | 07.0 | 00.0 | 07.7 | 01.6 | 00.0 | 07.0 | 00.0 |
| EDAPS [55] | 21.9 | 46.7 | 00.0 | 75.1 | 00.0 | 08.5 | 04.1 | 00.0 | 06.1 | 63.6 | 00.0 | 89.5 | 11.8 | 02.5 | 36.9 | 23.4 | 08.9 | 16.5 | 00.0 |
| UnmaskFormer [7] | 20.7 | 42.9 | 00.6 | 67.0 | 00.0 | 09.6 | 03.6 | 00.0 | 05.0 | 66.9 | 00.0 | 90.2 | 16.6 | 00.0 | 37.3 | 25.9 | 07.5 | 00.0 | 00.0 |
| (xpan,ypan) | Source-only | 19.0 | 48.8 | 01.9 | 68.6 | 00.0 | 00.9 | 00.5 | 00.0 | 01.6 | 42.8 | 00.0 | 84.7 | 12.7 | 00.0 | 36.2 | 20.3 | 06.4 | 16.8 | 00.0 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 19.3 | 46.5 | 01.9 | 69.9 | 00.0 | 01.0 | 00.5 | 00.0 | 01.7 | 47.9 | 00.0 | 86.0 | 15.6 | 00.0 | 36.5 | 18.9 | 06.5 | 15.2 | 00.0 |
| UNLOCK (Ours) | 20.4 (↑1.4) | 50.5 | 04.2 | 74.0 | 00.0 | 04.8 | 00.6 | 00.0 | 03.9 | 49.2 | 00.0 | 86.3 | 14.3 | 00.0 | 38.1 | 18.8 | 05.7 | 16.8 | 00.0 |
| SS | (ypan) | DATR [93] | 31.5 | 59.5 | 06.3 | 77.7 | 00.2 | 09.2 | 22.9 | 02.4 | 10.3 | 76.6 | 00.0 | 93.4 | 37.7 | 01.9 | 68.8 | 20.8 | 01.5 | 54.1 | 24.2 |
| TransPASS [85] | 34.3 | 58.9 | 07.6 | 77.3 | 00.2 | 28.7 | 26.7 | 05.2 | 11.1 | 76.1 | 00.0 | 93.6 | 35.8 | 01.8 | 73.6 | 28.3 | 06.8 | 55.2 | 30.1 |
| UniDAPS [86] | 36.0 | 61.5 | 07.5 | 76.6 | 00.8 | 30.4 | 27.7 | 10.2 | 11.1 | 77.4 | 00.0 | 93.6 | 47.3 | 02.1 | 49.4 | 25.9 | 33.0 | 62.3 | 30.6 |
| EDAPS [55] | 36.2 | 62.2 | 10.8 | 81.1 | 00.5 | 28.7 | 22.9 | 10.6 | 10.5 | 75.5 | 00.1 | 93.3 | 42.7 | 02.3 | 72.1 | 33.6 | 18.8 | 58.6 | 26.7 |
| UnmaskFormer [7] | 36.1 | 60.6 | 13.3 | 74.2 | 00.9 | 32.7 | 21.6 | 14.2 | 06.9 | 76.7 | 00.0 | 93.9 | 45.2 | 01.2 | 73.3 | 34.1 | 22.0 | 56.9 | 22.7 |
| (xpan,ypan) | Source-only | 31.0 | 67.1 | 21.5 | 76.9 | 03.2 | 17.0 | 17.7 | 02.7 | 06.3 | 64.7 | 00.0 | 90.7 | 40.0 | 01.8 | 69.2 | 19.5 | 04.6 | 47.4 | 08.5 |
| (xpin,ypin,ypan) | 360SFUDA++ [95] | 31.2 | 64.8 | 21.3 | 77.7 | 03.4 | 16.2 | 18.9 | 02.7 | 06.0 | 66.6 | 00.0 | 91.7 | 41.9 | 02.0 | 67.9 | 19.1 | 04.6 | 49.1 | 07.9 |
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| ✓ | 25.84 | 24.55 | 40.31 | 10.93 | 11.47 |
| ✓ | ✓ | 26.41 | 25.07 | 41.64 | 10.91 | 11.58 |
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| Amodal Instance | 25.71 | 24.50 | 39.06 | 10.77 | 11.22 |
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| 360SFUDA++[95] | 52.99 |
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diff --git a/2025/Unlocking the Potential of Diffusion Priors in Blind Face Restoration/29e022b8-6392-48f4-9ca2-0f6888716bc8_content_list.json b/2025/Unlocking the Potential of Diffusion Priors in Blind Face Restoration/29e022b8-6392-48f4-9ca2-0f6888716bc8_content_list.json
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+ "type": "text",
+ "text": "Unlocking the Potential of Diffusion Priors in Blind Face Restoration",
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+ "text": "Yunqi Miao $^{1}$ Zhiyu Qu $^{3}$ Mingqi Gao $^{2}$ Changrui Chen $^{1}$",
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+ "text": "Jifei Song $^{3}$ Jungong Han $^{2}$ Jiankang Deng $^{4}$",
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+ "page_idx": 0
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+ "text": "$^{1}$ University of Warwick $^{2}$ University of Sheffield $^{3}$ University of Surrey $^{4}$ Imperial College London",
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+ "text": "{yunqimiao709, im.mingqi, jungonghan77, jiankangdeng}@gmail.com, changrui.chen@warwick.ac.uk, z.qu@surrey.ac.uk",
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+ "text": "Although diffusion prior is rising as a powerful solution for blind face restoration (BFR), the inherent gap between the vanilla diffusion model and BFR settings hinders its seamless adaptation. The gap mainly stems from the discrepancy between 1) high-quality (HQ) and low-quality (LQ) images and 2) synthesized and real-world images. The vanilla diffusion model is trained on images with no or less degradations, whereas BFR handles moderately to severely degraded images. Additionally, LQ images used for training are synthesized by a naive degradation model with limited degradation patterns, which fails to simulate complex and unknown degradations in real-world scenarios. In this work, we use a unified network FLIPNET that switches between two modes to resolve specific gaps. In restoration mode, the model gradually integrates BFR-oriented features and face embeddings from LQ images to achieve authentic and faithful face restoration. In degradation mode, the model synthesizes real-world like degraded images based on the knowledge learned from real-world degradation datasets. Extensive evaluations on benchmark datasets show that our model 1) outperforms previous diffusion prior based BFR methods in terms of authenticity and fidelity, and 2) outperforms the naive degradation model in modeling the real-world degradations.",
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+ "text": "1. Introduction",
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+ "text": "Blind face restoration (BFR) aims to recover high-quality (HQ) facial images from various degradations. The ill-posed nature of this task stems from the complexity and uncertainty of degradations in real-world scenarios. Versatile facial priors have been used to help BFR, such as facial landmarks [4], referential HQ images or features [31, 35], and the pretrained StyleGAN [33, 40]. The success of diffusion models (DMs) [7, 28] in generation tasks has recently excited the restoration field, as their ability to generate HQ content from noise aligns perfectly with the restoration objective [21, 22, 36, 38]. Despite its powerful generative ability, the inherent gap between the vanilla diffusion process",
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+ "(d) WaveFace(w/o SwinIR)",
+ "Figure 1. Restoration results of WIDER [39]. Pre-processing module (i.e., SwinIR) based methods (i.e., DiffBIR) fail to render fine-grained details. Methods with condition-concatenated inputs (i.e., WaveFace) unable to handle unknown and complex degradation in real-world scenarios, leading to over-smoothed results."
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+ "(e) Ours(w/SwinIR)"
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+ {
+ "type": "text",
+ "text": "and the BFR setting hinders its seamless adaptation. The gap arises mainly from the distribution mismatch between: 1) HQ images and low-quality (LQ) images and 2) synthesized images and real-world images.",
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+ "type": "text",
+ "text": "The vanilla DMs are trained on natural images with minor or no degradation, making them unfit the BFR task, which primarily targets moderately to severely degraded face images. To bridge the gap, previous attempts [21, 23] brutally remove the severe degradations via a pre-processing module [20], followed by a DM to render facial details. However, the pre-processing module also removes discriminative details such as wrinkle and freckle (Fig. 1(b)), thus compromising the fidelity of restoration (Fig. 1(c)). Some approaches [22] bypass the pre-processing module by concatenating the degraded images, acting as the condition, to HQ inputs. Although the first gap is mitigated by gradually introducing LQ features throughout denoising, they fail to deliver adequate results on real-world data (Fig. 1(d)) as the degradation model used for training set synthesizing fails to simulate real-world",
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+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
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+ "type": "text",
+ "text": "degradations. A pioneering work [34] applies the naive degradation model repeatedly to HQ images to create LQ counterparts. Although effective, this work generates less diverse data due to its reliance on limited degradation patterns, which is incompatible with \"blind\" face restoration.",
+ "bbox": [
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+ "text": "To address these problems, this work uses only a large-scale Text-to-Image (T2I) model with few trainable parameters, eliminating the reliance on pre-processing modules in both training and inference. Our goal is to steer the pretrained T2I model towards authentic and faithful face restoration while preserving its strong image prior by properly integrating contributive features from LQ images. Despite offering valuable cues such as color and structure for faithful face restoration, LQ images also carry the degradation that affects authenticity. To strike a balance, we propose BoostHub to selectively integrate BFR-oriented features from LQ inputs while discarding irrelevant ones. Meanwhile, we identify the misalignment between face embeddings used in personalized T2I generation [24, 25] and those needed for BFR, which inspires us to explore BFR-oriented face embeddings. Apart from face restoration, we unlock the potential of diffusion prior in modeling real-world degradations. Being trained with HQ and degraded image pairs collected from real-world scenarios, the T2I model learns the distribution of real-world degradations, which is used to synthesize degraded images.",
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+ "text": "In this work, we unify the above solutions into a single model, i.e., FLIPNET, which takes HQ and LQ image pairs as input. By simply flipping the inputs, the model switches between restoration mode and degradation mode, achieving authentic and faithful face restoration and real-world degradation synthesis, respectively. The contributions of this work can be summarized as follows:",
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+ "- A two-pronged solution, i.e., FLIPNET, is proposed to bridge two inherent gaps that hinder the seamless adaptation of diffusion prior in BFR by simply switching between restoration mode and degradation mode.",
+ "- When switching to restoration mode, FLIPNET achieves authentic and faithful face restoration by integrating BFR-oriented features and face embeddings from LQ images.",
+ "- When switching to degradation mode, FLIPNET learns from degraded images in real-world scenarios and, in turn, synthesizes such images with acquired knowledge.",
+ "- Comprehensive experiments demonstrate the superiority of FLIPNET in integrating diffusion prior to BFR."
+ ],
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+ "text": "2. Related works",
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+ "type": "text",
+ "text": "Blind face restoration (BFR). BFR works are generally based on three priors: 1) Geometric priors, including facial landmarks [4, 6] and facial parsing maps [3, 43], are used to provide explicit facial structure information. They often yield inferior restoration results due to the imprecise prediction on degraded images. 2) Reference priors based meth",
+ "bbox": [
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+ "type": "text",
+ "text": "ods either leverage high-quality (HQ) reference images to provide identity information [32] or construct a dictionary that restores HQ facial features [31, 35]. But the restoration performance is restricted by the authenticity of reference images and the size of the codebook. 3) Generative priors encapsulated in StyleGAN2 [14] are used to provide rich facial details for restoration. GFP-GAN [33] and GPEN [40] restore degraded faces by learning the mapping from LQ input to the latent space where GAN prior network can reproduce the desired HQ face images.",
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+ "text": "Diffusion prior in BFR. Inspired by the ability of diffusion models (DMs) [28, 30] in emerging HQ content from noise, diffusion prior has become a favorable solution for BFR. However, DMs are typically trained on images with less or no degradation while BFR deals with moderately to severely degraded images, which makes its seamless adaptation challenging. Therefore, some works break BFR down to two stages: degradation removal and details generation. DR2 [36] employs the diffusion prior at first stage to obtain degradation-invariant images, where HQ counterparts are obtained by the follow-up face restoration model. DiffBIR [21] and PMRF [23] first coarsely remove severe degradations with a pretrained pre-processing module [20]. Given the obtained intermediate results, DiffBIR renders realistic facial details via a follow-up T2I model. Whilst PMRF takes such images as the initial state of the distribution transportation, where a rectified flow model is optimized to model the path to HQ counterparts. Instead of adopting such a two-stage scheme, PGDiff [38] uses a pretrained BFR model [34] to provide instructive semantics. Throughout the denoising process, the model is trained to minimize the discrepancy between intermediate outputs and target properties. WaveFace [22] uses diffusion prior to restore the low-frequency component exclusively, where low-frequency subbands of LQ images are concatenated to noise and serve as condition for generation. Although exciting restoration results have been achieved, the pre-processing module will also smooth out facial details, thereby compromising the fidelity. Additionally, the reliance on other face restoration models imposes limitations on the potential of the proposed model. How to effectively unleash the potential T2I model in BFR task has NOT been fully exploited.",
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+ "text": "Real-world degradation modeling. Apart from the gap between HQ and LQ images, diffusion prior BFR methods general deliver inferior performance on real-world images as the degradation model used to synthesize training set fail to simulate that in real-world scenarios. Classical degradation model [18] includes four types of degradations: blur, noise, resize, and JPEG compression. The simple combination fails to handle real-world cases where images typically spread several times over different digital devices. Thus, Real-ESRGAN [34] proposes a \"high-order\" degradation model, where classical degradations with different hyper",
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+ "text": "13472",
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+ "text": "parameters are applied repeatedly on HQ images to synthesize the degraded counterparts. While this may serve as a stopgap, the synthesis remains constrained by the limited degradation patterns. How to effectively simulate complex and blind degradations remains a formidable challenge.",
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+ "type": "text",
+ "text": "In this work, we address above challenges with a unified model that is solely based on a large-scale T2I model with few trainable parameters. The model provides a two-pronged solution to both authentic and faithful face restoration and real-world degradation modeling.",
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+ "type": "text",
+ "text": "3. Preliminary",
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+ "text": "Stable Diffusion is a large-scale text-to-image (T2I) latent diffusion model, which performs both diffusion and denoising processes in latent space. Specifically, an autoencoder [16] converts an image $x$ to a latent $z$ with encoder $\\mathcal{E}$ and reconstructs it with decoder $\\mathcal{D}$ , i.e., $\\hat{x} = \\mathcal{D}(\\mathcal{E}(x))$ . In diffusion process, Gaussian noise $\\epsilon \\sim \\mathcal{N}(0, 1)$ is applied to the starting latent $z_0$ to achieve noisy latent $z_t$ :",
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+ "type": "equation",
+ "text": "\n$$\nz _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} z _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}\n$$\n",
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+ "text": "where $\\{\\bar{\\alpha}_t\\}_{t = 1}^T$ is a pre-defined noise variance schedule over timestep $t$ . For denoising, a network $\\epsilon_{\\theta}$ is optimized to predict the noise $\\epsilon$ at a particular timestep $t$ conditioned on $c$ , such as text prompt, which follows the objective:",
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+ "text": "\n$$\n\\mathcal {L} _ {l d m} = \\mathbb {E} _ {z, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(z _ {t}, t, c\\right) \\| _ {2} ^ {2} \\right]. \\tag {2}\n$$\n",
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+ "text": "Given the noise predicted at timestep $t$ , the denoised latent $\\hat{z}_0$ can be predicted by:",
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+ "text": "\n$$\n\\hat {z} _ {0} = \\frac {1}{\\sqrt {\\bar {\\alpha} _ {t}}} \\left(z _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon_ {\\theta} \\left(z _ {t}, t, c\\right)\\right). \\tag {3}\n$$\n",
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+ "type": "text",
+ "text": "The denoised image can be further obtained by $\\hat{x}_0 = \\mathcal{D}(\\hat{z}_0)$ .",
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+ "text": "Low-Rank Adaptation (LoRA) is widely used for the efficient adaptation of large language models or text-to-image models to downstream tasks [10]. Concretely, two low-rank matrices $B \\in \\mathbb{R}^{n \\times r}$ and $A \\in \\mathbb{R}^{r \\times m}$ are introduced to update the base model weights $W_0 \\in \\mathbb{R}^{n \\times m}$ with $\\triangle W = BA$ , where $r \\ll \\min(n, m)$ refers to the intrinsic rank of $\\triangle W$ . The updated weight matrix $W = W_0 + \\triangle W$ is used for inference. By updating $A$ and $B$ exclusively during training, the base model gradually adapts to the specific domains. Meanwhile, since $W_0$ is frozen throughout the optimization, the generative ability of base model is well preserved. For efficiency, LoRA is typically applied only to attention layers for model fine-tuning.",
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+ "type": "text",
+ "text": "4. Methodology",
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+ "text": "This work aims to handle inherent gaps between the vanilla diffusion prior and blind face restoration (BFR) setting,",
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+ "text": "which stem from the distribution mismatch between 1) high-quality (HQ) and low-quality (LQ) images, and 2) synthesized and real-world images. Unlike previous attempts addressing the first gap with pre-processing modules [21, 23] or guidance from other face restoration methods [38], our model, namely FLIPNET, is simply built upon a T2I model with few trainable parameters. The framework is illustrated in Fig. 2, which takes pairs of HQ and LQ images as input. By simply flipping the input, the model switches between restoration mode (Sec. 4.1) and degradation mode (Sec. 4.2) to achieve authentic and faithful face restoration and synthesizing real-world degraded images, respectively. Note that, to preserve the strong image prior of the large-scale T2I model, we fine-tune only the LoRA weights [10] plugged to all attention layers.",
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+ "text": "4.1. Restoration mode",
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+ "text": "In restoration mode, the denoising network takes HQ images $\\mathbf{x}$ as input and LQ images $\\mathbf{y}$ as condition. Unlike previous works concatenating LQ images [22] or pre-processed results [21, 23] to HQ images, our model is conditioned on diffused LQ images. Specifically, the diffusion process (Eq. (1)) is applied to both HQ and LQ images, where noise $(\\epsilon_{x},\\epsilon_{y})$ and timestep $(t_x,t_y)$ are sampled separately. The noisy pairs $(\\pmb {x}_{t_x},\\pmb {y}_{t_y})$ are concatenated along the batch axis and fed to the denoising network, which is optimized to simultaneously denoise both inputs, enabling the restoration of HQ images from LQ counterparts under varying noise levels. However, LQ images act as a double-edged sword, which improves the restoration fidelity by providing structural information while compromising the authenticity. To strike a balance, BoostHub is proposed to selectively integrate BFR-oriented features, and meanwhile, discard irrelevant ones. Additionally, we identify the misalignment between face embeddings widely-used for personalized generation [24, 25] and those required by BFR, which inspires us to explore BFR-oriented face embeddings.",
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+ "text": "BoostHub. Following the pioneering T2I model [28], our denoising network $\\epsilon_{\\theta}$ is implemented as UNet, with its blocks comprising ResNet layers, self-attention layers, and cross-attention layers. Inspired by a joint module used in conditioned generation [19], we use BoostHub to enhance noisy HQ features with BFR-oriented features from LQ conditions. As shown in Fig. 2, BoostHub is placed in parallel to self-attention layers to involve LQ features without interrupting the spatial relationships within HQ images.",
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+ "type": "text",
+ "text": "As illustrated in Fig. 2, given the noisy HQ and LQ features $(F_x,F_y)$ , BoostHub projects them to query, key and value via projection matrices $W_{Q_x}$ , $W_{K_y}$ and $W_{V_y}$ and then integrate them with attention mechanism:",
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+ "text": "\n$$\n\\begin{array}{l} F _ {r o} = W _ {O} \\cdot \\operatorname {A t t n} \\left(Q _ {x}, K _ {y}, V _ {y}\\right) \\\\ = W _ {O} \\cdot \\operatorname {S o f t m a x} \\left(Q _ {x} K _ {y} ^ {T} / \\sqrt {d}\\right) V _ {y}, \\tag {4} \\\\ \\end{array}\n$$\n",
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+ "text": "13473",
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+ {
+ "type": "image",
+ "img_path": "images/97552068e9e8e07120fbcc78d30d4a926c2e6889de1244f9babf7505b1b93f89.jpg",
+ "image_caption": [
+ "Figure 2. FLIPNET pipeline. FLIPNET takes noisy high-quality (HQ) and low-quality (LQ) image pairs as input. It can switch between restoration mode and degradation mode. Taking restoration mode as an example, HQ images are used as input while LQ images are condition, where a BoostHub is placed in parallel to each self-attention layer to selectively integrate the BFR-oriented LQ features for denoising. Additionally, LoRA weights are plugged to all self-attention and cross-attention layers to adapt the base model to face domain. By simply flipping the image-condition order, it switches to degradation mode to synthesize degraded data with real-world degradations."
+ ],
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+ "type": "text",
+ "text": "where $Q_{x} = W_{Q_{x}}F_{x}$ , $K_{y} = W_{K_{y}}F_{y}$ , and $V_{y} = W_{V_{y}}F_{y}$ . Following prior arts [8], $W_{Q_x}$ , $W_{K_y}$ and $W_{V_y}$ are initialized by corresponding self-attention weight of the base model and the output projection matrices $W_{O}$ are initialized by all-zero matrix to avoid harmful effects that additional modules might introduce. The BFR-oriented features $F_{ro}$ are then combined with self-attention output $F_{sa_{x}}$ as:",
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+ "type": "equation",
+ "text": "\n$$\nF _ {j o i n t} = F _ {s a _ {x}} + \\phi \\cdot F _ {r o} = \\text {S e l f - A t t n} (F _ {x}) + \\phi \\cdot F _ {r o}, \\tag {5}\n$$\n",
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+ "type": "text",
+ "text": "where the enhance weight $\\phi$ is set to control how much LQ features will be involved. Subsequently, the joint features $F_{joint}$ are integrated with text prompts as well as BFR-oriented face embeddings via cross-attention.",
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+ "text": "BFR-oriented face embeddings. In personalized generation works [24, 25], face embeddings, acting as an additional condition, are integrated via cross-attention layers to control the identity. However, prior arts generally leverage ID embeddings from a face recognition network [5]. Yet, such embeddings are trained to distinguish different persons instead of preserving fine-grained facial details, making them ineffective in providing instructive guidance for restoration. To this end, this work aims to explore BFR-oriented face embeddings, which should 1) well represent the appearance of the given person, and 2) be positioned in the common latent space of both HQ and LQ inputs so that they will not be biased when integrating with joint features from BoostHub in cross-attention layers. Inspired by the",
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+ "type": "text",
+ "text": "training scheme used in DAEFR [31], we propose to obtain such embeddings from an autoencoder [16] trained for face reconstruction. Instead of the discrete codebook, we adopt continuous latent features which can provide fine-grained details. A two-stage learning scheme is adopted.",
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+ "a) Reconstruction stage. First, HQ/LQ autoencoders are trained to reconstruct input face images. HQ/LQ images $\\boldsymbol{x} / \\boldsymbol{y} \\in \\mathbb{R}^{H \\times W \\times 3}$ are projected to latent space $\\boldsymbol{z}_{x / y} \\in \\mathbb{R}^{h \\times w \\times d}$ via encoder and then projected back to images $\\hat{\\boldsymbol{x}} / \\hat{\\boldsymbol{y}}$ by decoder. To achieve faithful reconstruction, the objective consists of L1 loss $\\mathcal{L}_1$ , perceptual loss $\\mathcal{L}_p$ , and adversarial loss $\\mathcal{L}_{adv}$ , i.e., $\\mathcal{L}_{ae} = \\mathcal{L}_1 + \\lambda_{ap} \\cdot \\mathcal{L}_p + \\lambda_{adv} \\cdot \\mathcal{L}_{adv}$ , where $\\lambda_{ap}$ and $\\lambda_{adv}$ are set as 0.5 and 0.8, respectively.",
+ "b) Association stage. Similar to CLIP [26], we fine-tune the autoencoders via the cross-entropy loss to map HQ/LQ features into a common latent space. HQ and LQ latents are first flattened to $\\{z_{x / y}^{i}\\in \\mathbb{R}^{d}\\}_{i = 1}^{N},N = h\\times w$ . The similarity matrix between $z_{x}$ and $z_{y}$ can be computed as $\\mathcal{M}\\in \\mathbb{R}^{N\\times N}$ . We adopt the cross-entropy loss $(\\mathcal{L}_{ce}^{H}$ and $\\mathcal{L}_{ce}^{L})$ to maximize the similarity between corresponding patches via maximizing scores in the diagonal:"
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c e}} ^ {H (L)} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {N} y _ {i, j} \\log \\left(z _ {x (y)} ^ {i, j}\\right), \\tag {6}\n$$\n",
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+ "type": "text",
+ "text": "where $y_{i,j}$ represents ground-truth labels. The objective of the association stage is $\\mathcal{L}_{\\text{asso}} = \\mathcal{L}_{ae} + (\\mathcal{L}_{ce}^{H} + \\mathcal{L}_{ce}^{L}) / 2$",
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+ "type": "page_number",
+ "text": "13474",
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+ "type": "text",
+ "text": "Once trained, the LQ encoder is used to extract face embeddings $\\mathbf{z}_y \\in \\mathbb{R}^{N \\times d}$ , which are then passed through a lightweight adapter $\\tau(\\cdot)$ to align with the dimensionality of text tokens before integrating with the T2I model, i.e., $c_{\\mathrm{id}} = \\tau(\\mathbf{z}_y)$ . The adapter consists of several linear layers with Layer Normalization [41].",
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+ "type": "text",
+ "text": "Objectives. In restoration mode, the model learns how to denoise the noisy $(\\pmb{x}_{t_x},\\pmb{y}_{t_y})$ jointly following the objective:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {l d m} = \\mathbb {E} _ {\\boldsymbol {x}, \\boldsymbol {y}, \\epsilon , t _ {x}, t _ {y}} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t _ {x}}, \\boldsymbol {y} _ {t _ {y}}, t _ {x}, t _ {y}, c\\right) \\| ^ {2} \\right], \\tag {7}\n$$\n",
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+ "type": "text",
+ "text": "where $\\epsilon = (\\epsilon_{x},\\epsilon_{y})$ and $c = (c_{\\mathrm{text}},c_{\\mathrm{id}})$ . Beyond latent-level constraints, image-level constraints are applied to the denoised predictions $\\hat{x}_0$ at each timestep obtained by Eq. (3), which include MSE loss $\\mathcal{L}_{mse}$ and perceptual loss $\\mathcal{L}_p$ :",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {m s e} = \\| \\pmb {x} - \\hat {\\pmb {x}} _ {0} \\| _ {2} ^ {2}, \\quad \\mathcal {L} _ {p} = \\| \\phi (\\pmb {x}) - \\phi (\\hat {\\pmb {x}} _ {0}) \\| _ {2} ^ {2}, \\qquad (8)\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "where $\\phi (\\cdot)$ represents VGG19 [29] backbone. The overall training objective is $\\mathcal{L}_{rm} = \\mathcal{L}_{ldm} + \\lambda_{mse}\\cdot \\mathcal{L}_{mse} + \\lambda_p\\cdot \\mathcal{L}_p$ $\\lambda_{mse}$ and $\\lambda_{p}$ are set as 1 and 0.01 throughout the training.",
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+ "type": "text",
+ "text": "4.2. Degradation mode",
+ "text_level": 1,
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+ "text": "By simply flipping the input, i.e., LQ images $\\mathbf{y}$ serving as input while HQ images $\\mathbf{x}$ as condition, our FLIPNET switches to degradation mode. To learn the real-world degradations, our model needs to be trained with paired HQ and LQ images collected from real-world scenarios. In the absence of such face datasets, we gather multiple low-level vision datasets captured in real-world scenarios to construct the training dataset for degradation mode, including Dense-Haze [2] for image dehazing, LOL [37] for low light enhancement, SIDD [1] for image denoising, and RealBlur [27] for image deblurring. To construct the training set, full set of Dense-Haze and LOL are included and 1000 pairs are randomly selected from SIDD and RealBlurJ, obtaining a real-world dataset with around 2500 pairs. To keep the model's ability in synthesizing the classical degradations Eq. (9), 4000 face images are randomly selected from FFHQ to synthesize LQ counterparts on-the-fly during training. The training process is the same with restoration mode, except for the condition and the objective.",
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+ "type": "text",
+ "text": "Cross-attention conditions. Being trained on both face and non-face datasets, we do NOT leverage BFR-oriented face embeddings in this mode. In other words, text prompts are the only condition for cross-attention layers, which are generated by BLIP [17] following previous works [8].",
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+ "type": "text",
+ "text": "Objectives. Only diffusion loss $\\mathcal{L}_{ldm}$ is used, i.e., $\\mathcal{L}_{dm} = \\mathcal{L}_{ldm}$ , as imposing image-level constraints on degraded images will introduce unforeseen noise to predictions.",
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+ "type": "text",
+ "text": "Once trained, the model can be used to synthesize degraded counterparts of HQ face images with the acquired knowledge. The generated images carry diverse and complex degradations, with the intensity of degradation remaining entirely unknown, which are more suitable for",
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+ "text": "\"BLIND\" face restoration. The visualization and distribution of degraded images synthesized by a prior art [34] and our method are illustrated in Fig. 5. As observed, FLIPNET could well model real-world degradations, evidenced by its diverse distribution across multiple real-world face datasets. The synthesized degraded images can be subsequently used to train our FLIPNET under restoration mode.",
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+ "type": "text",
+ "text": "5. Experiments",
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+ "type": "text",
+ "text": "5.1. Datasets and Settings",
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+ "text": "Training Dataset. FFHQ [13], containing 70k high-quality (HQ) face images, is used as the training set. Following previous works [33, 36], images are resized to $512 \\times 512$ before synthesis. Two degradation models are adopted to synthesize low-quality (LQ) counterparts:",
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+ "type": "text",
+ "text": "1) On-the-fly degradation. Considering its efficiency, Real-ESRGAN [34] is used to synthesize degraded images online following the formula:",
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+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {y} = \\left\\{\\left[ (\\boldsymbol {x} \\otimes \\boldsymbol {k} _ {\\sigma}) \\downarrow_ {s} + \\boldsymbol {n} _ {\\delta} \\right] _ {\\mathrm {J P E G} _ {q}} \\right\\} \\uparrow_ {s}, \\tag {9}\n$$\n",
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+ "text": "where a HQ image $\\pmb{x}$ is firstly blurred by a Gaussian kernel $k_{\\sigma}$ , followed by a downsampling of scale $s$ . Afterward, Gaussian noise $n_{\\delta}$ and JPEG compression with quality factor $q$ are applied to the image, which is then upsampled back to the original size to obtain its LQ counterpart $\\pmb{y}$ . The hyper-parameters $\\sigma$ , $s$ , $\\delta$ , and $q$ are uniformly sampled from [0.1, 15], [0.8, 32], [0, 20], and [30, 95] respectively. On top of this, the process is performed for the second time, where random degradations are applied in shuffled order.",
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+ "text": "2) Off-shelf degradation. In light of its diversity and authenticity, our FLIPNET is switched to degradation mode to synthesize degraded images offline. For each HQ face image, we generate five images with diverse and unknown degradations, serving as LQ counterparts.",
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+ "text": "For each iteration, degraded images generated by on-the-fly and off-shelf schemes are selected by a probability of 0.5 to construct a training batch.",
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+ "text": "Testing Dataset. We evaluate FLIPNET on a synthetic dataset: CelebA-Test and three real-world datasets: LFW [11], WebPhoto [33] and WIDER [44]. CelebA-Test contains 3000 HQ images from CelebA-HQ [12]. Akin to the training set, LQ counterparts in test set are synthesized by both on-the-fly and off-shelf degradation scheme at equal probability. In terms of three real-world datasets, LFW contains 1711 mildly degraded face images in the wild, which comprises the first image for each person in LFW [11]. WebPhoto includes 407 images crawled from the internet, some of which are old photos with severe degradation. WIDER consists of 970 images with severe degradations from the WIDER dataset [39].",
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+ "text": "Evaluation Metrics. For evaluation, we adopt two pixelwise metrics (PSNR and SSIM), a reference perceptual met",
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+ "img_path": "images/56af356dc332be8106a41bb4fb60d04409a9b3e6cc0ffbc03c8eb1a34da98dab.jpg",
+ "image_caption": [
+ "LQ",
+ "Figure 3. Visualization of the effectiveness of enhance weight $\\phi$ on CelebA-Test. $\\phi$ strikes a balance between fidelity and authenticity by determining the amount of LQ features involved. PSNR(↑) / Deg.(↓) are reported."
+ ],
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+ "(17.80dB / 64.45)",
+ "$\\phi = 0$"
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+ "$\\phi = 1$"
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+ "$\\phi = 2$"
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+ "img_path": "images/fdbf021be96c1c2b933fe6b9c13baaed40187440706e32d7aa79afa57ac1acf4.jpg",
+ "image_caption": [
+ "HQ"
+ ],
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+ "text": "ric (LPIPS [42]), and a non-reference perceptual metric (FID [9]). To measure the consistency of identity, the angle between ID embeddings extracted by ArcFace (\"Deg.\") [5] is used. All metrics are used for the evaluation of synthetic dataset while only FID is used for real-world datasets due to the lack of ground-truth HQ images.",
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+ "text": "Implementation Details. We adopt Stable Diffusion 2.1-base1 as the base T2I model and plug LoRA modules to all self-attention and cross-attention layers. We train LoRA for 90k iterations (batch size=16), with the intrinsic rank set to 64. The text prompts are generated by BLIP [17] for all datasets. We use AdamW [15] optimizer with the learning rate 5e-5. The training process is conducted on $512 \\times 512$ resolution with 8 NVIDIA V100 GPUs.",
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+ "text": "For restoration mode, autoencoders are initialized by the pretrained weight [28]. We trained model for $200\\mathrm{k}$ at reconstruction stage and $80\\mathrm{k}$ at association stage (batch size $= 32$ ). For non-face datasets, the model takes no embeddings other than text prompts as condition. During training, we use a probability of 0.5 to drop text prompt and 0.3 to drop face embeddings to enhance the robustness. For inference, we use words such as \"low quality\", \"blurry\", and \"poorly rendered hands\" as the negative prompt for restoration mode while use null text prompt for degradation mode. The classifier-free guidance (CFG) scale is set as 1.5.",
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+ "text": "5.2. Ablation Studies",
+ "text_level": 1,
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+ "text": "5.2.1. Restoration mode",
+ "text_level": 1,
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+ "text": "BoostHub enhance weight. According to Eq. (5), the enhance weight $\\phi$ determines the amount of BFR-oriented features integrated from LQ inputs. When less LQ features are involved, the ability of the T2I model in generating high-quality contents is fully exploited while features that facilitate face restoration, such as color and structure, are ignored, thereby affecting the authenticity. Conversely, an over-injection of such features will compromise the restoration quality. Restoration results with different en",
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+ {
+ "type": "text",
+ "text": "hance weights as illustrated in Fig. 3.",
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+ "text": "As observed, without guidance from LQ images $(\\phi = 0)$ , the restoration strictly relies on text prompt and face embeddings. Despite its high quality, the restoration deviates significantly from the original identity. In contrast, LQ features dominate the generation when $\\phi = 2$ , leading to the poor quality with fine-grained facial details being smoothed out. When we set $\\phi = 1$ , the model could strike a good balance between fidelity and authenticity.",
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+ "text": "BFR-oriented face embeddings. We identify the misalignment between the widely-used face embeddings from a face recognition model [5] and those required by blind face restoration (BFR). To make a comparison, we visualize the restoration results, conditioned on ArcFace embeddings and our BFR-oriented face embeddings in Fig. 4(a) and Fig. 4(c), as well as corresponding attention maps. As observed, the face recognition model, trained to distinguish different persons, exclusively focuses on features at discriminative regions, such as eyes. As a result, the restoration fails to render fine-grained details at cheeks or hairs.",
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+ "text": "Beyond presenting facial details, the alignment between HQ and LQ face embeddings is important for our model as face embeddings are supposed to integrated with joint features (Eq. (5)) via cross-attention, which include both HQ features from self-attention layers and BFR-oriented LQ features from BoostHub. The alignment is achieved by \"Association stage\". To demonstrate its effectiveness, we use face embeddings from the autoencoder trained only with reconstruction stage to perform the restoration. The result is shown in Fig. 4(b). Due to the absence of \"Association stage\", face embeddings are biased on BFR-oriented LQ features while neglecting HQ ones, leading to compromised the restoration quality. On the contrary, when BFR-oriented face embeddings integrating with the aligned HQ and LQ features, our model is able to deliver faithful results with face details such as wrinkle well preserved (Fig. 4(c)).",
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+ "text": "5.2.2. Degradation mode",
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+ "text": "Synthesized images and distribution. We visualize the degraded images generated by Real-ESRGAN [34] and our",
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+ "text": "1Stable Diffusion v2.1: https://github.com/Stability-AI/stablediffusion",
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+ "text": "13476",
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+ "(a) Arc (23.05dB / 48.47)"
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+ {
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+ "image_caption": [
+ "(b) $\\mathrm{BO}_{w / o}\\mathrm{Asso}$ (22.89 dB /46.02)",
+ "Figure 4. Restoration results (Right) of the model conditioning on face embeddings extracted from ArcFace (Arc), our BFR-oriented ones trained without $(\\mathrm{BO}_{w / o A s s o})$ and with (BO) \"Association stage\" on CelebA-Test. Corresponding attention maps (Left) of embeddings are also shown. PSNR(↑) / Deg.(↓) are reported. The lighter the color, the higher the attention scores."
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+ "(c) BO (23.39dB / 43.81)"
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+ "image_caption": [
+ "Synthesized LQ vs Real LQ"
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+ {
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+ "img_path": "images/fa73a8909256f4c0114ecb9bd9721e89ef780067ef83103897d67cc168d02634.jpg",
+ "image_caption": [
+ "Figure 5. Distribution of degraded images synthesized by Real-ESRGAN [34] and our FLIPNET compared to three real-world datasets: LFW, WebPhoto and WIDER. Synthesized images of Real-ESRGAN and Ours are shown below."
+ ],
+ "image_footnote": [],
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+ {
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+ "text": "FLIPNET in Fig. 5. To evaluate how well they fit real-world degradations, the feature distribution of degraded images synthesized by both methods and three real-world datasets: LFW [11], WIDER [44] and WebPhoto [33] is also illustrated. Our model is capable of synthesizing degraded images that are widely distributed across different real-world datasets whereas Real-ESRGAN generates data gathering in a limited region. This can be proved by examples shown below. Images degraded by our model present diverse degradations while that by Real-ESRGAN demonstrate limited degradation patterns.",
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+ "text": "5.3. Comparisons with State-of-the-Art Methods",
+ "text_level": 1,
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+ {
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+ "text": "Evaluations are performed on synthetic and real-world datasets. Unlike previous BFR methods, our training data are synthesized by dual degradation schemes (on-the-fly",
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+ {
+ "type": "table",
+ "img_path": "images/434d3258eaa161ed3751c6bb6a4cfb71a44c0d138c40bdc66b572e3a5a77299f.jpg",
+ "table_caption": [
+ "Table 1. Quantitative comparison on CelebA-Test. “RF++” and “ $\\mathcal{F}$ ” refer to “RestoreFormer++” and our FLIPNET. “+O”: on-the-fly synthesized images. “+O/F”: both on-the-fly and off-shelf synthesized images. “Deg.” refers to the angle between identity embeddings of restored images and HQ counterparts. The best and the second best results are indicated."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods | PSNR↑ | SSIM↑ | LPIPS↓ | FID↓ | Deg.↓ |
| GPEN | 23.65/22.86 | 0.61/0.60 | 0.42/0.43 | 18.67/20.20 | 47.24/51.33 |
| GFP-GAN | 23.85/22.70 | 0.61/0.61 | 0.40/0.40 | 17.38/18.52 | 44.96/47.99 |
| RF++ | 24.03/23.15 | 0.63/0.62 | 0.38/0.40 | 14.98/15.15 | 44.00/45.86 |
| DAEFR | 22.70/21.96 | 0.62/0.61 | 0.38/0.39 | 14.43/15.65 | 48.44/49.85 |
| DR2 | 22.27/21.83 | 0.63/0.61 | 0.44/0.44 | 31.59/34.49 | 59.24/61.29 |
| PGDiff | 22.87/22.08 | 0.63/0.62 | 0.42/0.42 | 19.48/21.35 | 59.43/60.38 |
| DiffBIR | 24.37/23.39 | 0.62/0.60 | 0.42/0.43 | 20.78/22.54 | 46.58/47.00 |
| WaveFace | 24.16/23.05 | 0.62/0.62 | 0.42/0.43 | 21.44/23.48 | 43.80/46.50 |
| PMRF | 24.70/23.40 | 0.63/0.62 | 0.42/0.42 | 13.48/15.36 | 44.75/45.76 |
| F+O/+O/F | 24.44/23.39 | 0.64/0.63 | 0.42/0.42 | 13.82/15.06 | 43.29/43.81 |
",
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+ "img_path": "images/c6de41ac8ea468ecc841506c3973dce2acd28fc0c425f2784a32003469dd084c.jpg",
+ "table_caption": [
+ "Table 2. Quantitative comparisons on real-world datasets in terms of $\\mathbf{{FID}}\\left( \\downarrow \\right)$ . \"RF+\" and \"F\" refer to \"Restore-Former++\" and our FLIPNET. \" $+ \\mathrm{O}$ \" : on-the-fly synthesized images. \" $+ \\mathrm{O}/\\mathrm{F}$ \" : both on-the-fly and off-shelf synthesized images. The best and the second best results are indicated."
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods | LFW | WebPhoto | WIDER |
| Input | 124.974 | 170.112 | 199.961 |
| GPEN [40] | 50.792 | 80.572 | 46.340 |
| GFP-GAN [33] | 49.560 | 87.584 | 39.499 |
| RF++ [35] | 50.439 | 75.059 | 49.395 |
| DAEFR [31] | 47.310 | 75.453 | 35.344 |
| DR2 [36] | 45.298 | 112.344 | 45.348 |
| PGDiff [38] | 44.630 | 89.754 | 36.807 |
| DiffBIR [21] | 44.383 | 91.777 | 35.343 |
| WaveFace [22] | 43.175 | 81.525 | 36.913 |
| PMRF [23] | 50.275 | 81.064 | 40.685 |
| F+O/+OF | 43.10/42.98 | 83.34/81.37 | 33.09/31.81 |
",
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+ {
+ "type": "text",
+ "text": "and off-shelf). To make a fair comparison, we also synthesize another group with only on-the-fly degradation scheme. The quantitative results are indicated by “+O/F” and “+O” in Tab. 1 and Tab. 2.",
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+ "text": "Synthetic dataset. Quantitative comparisons on CelebA-Test [12] are illustrated in Tab. 1. Methods tend to yield inferior performance on the test set synthesized by dual degradation schemes, as the degradation better aligns with real-world scenarios, in other words, are more challenging.",
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+ {
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+ "img_path": "images/b63f31da805e46208af697920743ee98e29774f3e519660225a099271c588cc5.jpg",
+ "image_caption": [
+ "Figure 6. Qualitative comparison with state-of-the-art BFR methods on CelebA-Test. Our method achieves authentic and faithful restoration with fine-grained facial details being well preserved. (Zoom in for best view)."
+ ],
+ "image_footnote": [],
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+ },
+ {
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+ "img_path": "images/1b569e96a76b7cb56cc34e4d6a802c684e916c98f76a0899504f03936a66a191.jpg",
+ "image_caption": [
+ "Figure 7. Qualitative comparison with state-of-the-art BFR methods on real-world datasets, including LFW (first row), WebPhoto (second row), and WIDER (third row). (Zoom in for best view)."
+ ],
+ "image_footnote": [],
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+ {
+ "type": "text",
+ "text": "For visualization, we present qualitative comparisons with SOTA methods with increasing degradations in Fig. 6. GFPGAN [33] and RestoreFormer++ [35] struggle with obvious artifacts especially when images are corrupted by mild or severe degradation. They also fail to preserve the identity as the restoration is based on, and also, limited by the StyleGAN prior [33] or the pre-constructed dictionary [35]. As inherent gaps between the vanilla diffusion models and the BFR setting have not been properly handled, previous diffusion prior based methods generally yield unsatisfactory results. DR2 [36] and PGDiff [38] tend to deliver either faithful or authentic results, as the restoration starts from a preliminary result from another face restoration model, making their method suboptimal. DiffBIR [21] and PMRF [23], based on a pre-processing module, typically suffer from rendering vivid facial details or avoiding unexpected artifacts. In comparison, our model delivers authentic and faithful results.",
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+ },
+ {
+ "type": "text",
+ "text": "Real-world datasets. We show the quantitative comparison on real-world datasets in Tab. 2. FLIPNET outperforms SOTA methods on LFW [11] and WIDER [44]. Qualitative comparisons (Fig. 7) show that previous diffusion prior based methods yield over-smoothed faces and fail to preserve discriminative facial details. For severely-degraded images (Row 3), most methods are plagued by artifacts caused by unknown and complex real-world degradation. In contrast, our approach delivers faithful and authentic restoration results with rich facial details such as mustache.",
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+ {
+ "type": "text",
+ "text": "6. Conclusion",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "We propose FLIPNET to bridge the inherent gap between vanilla diffusion model and BFR settings. The model provides a two-pronged solution, enabling authentic and faithful face restoration and real-world degradations modeling by simply switching between restoration mode and degradation mode.",
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+ {
+ "type": "text",
+ "text": "References",
+ "text_level": 1,
+ "bbox": [
+ 91,
+ 90,
+ 187,
+ 104
+ ],
+ "page_idx": 8
+ },
+ {
+ "type": "list",
+ "sub_type": "ref_text",
+ "list_items": [
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+ "content": "Figure 1. Restoration results of WIDER [39]. Pre-processing module (i.e., SwinIR) based methods (i.e., DiffBIR) fail to render fine-grained details. Methods with condition-concatenated inputs (i.e., WaveFace) unable to handle unknown and complex degradation in real-world scenarios, leading to over-smoothed results."
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+ "content": "degradations. A pioneering work [34] applies the naive degradation model repeatedly to HQ images to create LQ counterparts. Although effective, this work generates less diverse data due to its reliance on limited degradation patterns, which is incompatible with \"blind\" face restoration."
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+ "content": "To address these problems, this work uses only a large-scale Text-to-Image (T2I) model with few trainable parameters, eliminating the reliance on pre-processing modules in both training and inference. Our goal is to steer the pretrained T2I model towards authentic and faithful face restoration while preserving its strong image prior by properly integrating contributive features from LQ images. Despite offering valuable cues such as color and structure for faithful face restoration, LQ images also carry the degradation that affects authenticity. To strike a balance, we propose BoostHub to selectively integrate BFR-oriented features from LQ inputs while discarding irrelevant ones. Meanwhile, we identify the misalignment between face embeddings used in personalized T2I generation [24, 25] and those needed for BFR, which inspires us to explore BFR-oriented face embeddings. Apart from face restoration, we unlock the potential of diffusion prior in modeling real-world degradations. Being trained with HQ and degraded image pairs collected from real-world scenarios, the T2I model learns the distribution of real-world degradations, which is used to synthesize degraded images."
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+ "content": "Diffusion prior in BFR. Inspired by the ability of diffusion models (DMs) [28, 30] in emerging HQ content from noise, diffusion prior has become a favorable solution for BFR. However, DMs are typically trained on images with less or no degradation while BFR deals with moderately to severely degraded images, which makes its seamless adaptation challenging. Therefore, some works break BFR down to two stages: degradation removal and details generation. DR2 [36] employs the diffusion prior at first stage to obtain degradation-invariant images, where HQ counterparts are obtained by the follow-up face restoration model. DiffBIR [21] and PMRF [23] first coarsely remove severe degradations with a pretrained pre-processing module [20]. Given the obtained intermediate results, DiffBIR renders realistic facial details via a follow-up T2I model. Whilst PMRF takes such images as the initial state of the distribution transportation, where a rectified flow model is optimized to model the path to HQ counterparts. Instead of adopting such a two-stage scheme, PGDiff [38] uses a pretrained BFR model [34] to provide instructive semantics. Throughout the denoising process, the model is trained to minimize the discrepancy between intermediate outputs and target properties. WaveFace [22] uses diffusion prior to restore the low-frequency component exclusively, where low-frequency subbands of LQ images are concatenated to noise and serve as condition for generation. Although exciting restoration results have been achieved, the pre-processing module will also smooth out facial details, thereby compromising the fidelity. Additionally, the reliance on other face restoration models imposes limitations on the potential of the proposed model. How to effectively unleash the potential T2I model in BFR task has NOT been fully exploited."
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+ "content": "Real-world degradation modeling. Apart from the gap between HQ and LQ images, diffusion prior BFR methods general deliver inferior performance on real-world images as the degradation model used to synthesize training set fail to simulate that in real-world scenarios. Classical degradation model [18] includes four types of degradations: blur, noise, resize, and JPEG compression. The simple combination fails to handle real-world cases where images typically spread several times over different digital devices. Thus, Real-ESRGAN [34] proposes a \"high-order\" degradation model, where classical degradations with different hyper"
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+ "angle": 0,
+ "content": "In this work, we address above challenges with a unified model that is solely based on a large-scale T2I model with few trainable parameters. The model provides a two-pronged solution to both authentic and faithful face restoration and real-world degradation modeling."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.257,
+ 0.218,
+ 0.274
+ ],
+ "angle": 0,
+ "content": "3. Preliminary"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.282,
+ 0.483,
+ 0.388
+ ],
+ "angle": 0,
+ "content": "Stable Diffusion is a large-scale text-to-image (T2I) latent diffusion model, which performs both diffusion and denoising processes in latent space. Specifically, an autoencoder [16] converts an image \\( x \\) to a latent \\( z \\) with encoder \\( \\mathcal{E} \\) and reconstructs it with decoder \\( \\mathcal{D} \\), i.e., \\( \\hat{x} = \\mathcal{D}(\\mathcal{E}(x)) \\). In diffusion process, Gaussian noise \\( \\epsilon \\sim \\mathcal{N}(0, 1) \\) is applied to the starting latent \\( z_0 \\) to achieve noisy latent \\( z_t \\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.2,
+ 0.4,
+ 0.482,
+ 0.417
+ ],
+ "angle": 0,
+ "content": "\\[\nz _ {t} = \\sqrt {\\bar {\\alpha} _ {t}} z _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon , \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.428,
+ 0.483,
+ 0.492
+ ],
+ "angle": 0,
+ "content": "where \\(\\{\\bar{\\alpha}_t\\}_{t = 1}^T\\) is a pre-defined noise variance schedule over timestep \\(t\\). For denoising, a network \\(\\epsilon_{\\theta}\\) is optimized to predict the noise \\(\\epsilon\\) at a particular timestep \\(t\\) conditioned on \\(c\\), such as text prompt, which follows the objective:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.144,
+ 0.5,
+ 0.483,
+ 0.526
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {l d m} = \\mathbb {E} _ {z, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(z _ {t}, t, c\\right) \\| _ {2} ^ {2} \\right]. \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.536,
+ 0.483,
+ 0.567
+ ],
+ "angle": 0,
+ "content": "Given the noise predicted at timestep \\(t\\), the denoised latent \\(\\hat{z}_0\\) can be predicted by:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.157,
+ 0.577,
+ 0.483,
+ 0.609
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {z} _ {0} = \\frac {1}{\\sqrt {\\bar {\\alpha} _ {t}}} \\left(z _ {t} - \\sqrt {1 - \\bar {\\alpha} _ {t}} \\epsilon_ {\\theta} \\left(z _ {t}, t, c\\right)\\right). \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.62,
+ 0.483,
+ 0.636
+ ],
+ "angle": 0,
+ "content": "The denoised image can be further obtained by \\(\\hat{x}_0 = \\mathcal{D}(\\hat{z}_0)\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.636,
+ 0.483,
+ 0.832
+ ],
+ "angle": 0,
+ "content": "Low-Rank Adaptation (LoRA) is widely used for the efficient adaptation of large language models or text-to-image models to downstream tasks [10]. Concretely, two low-rank matrices \\( B \\in \\mathbb{R}^{n \\times r} \\) and \\( A \\in \\mathbb{R}^{r \\times m} \\) are introduced to update the base model weights \\( W_0 \\in \\mathbb{R}^{n \\times m} \\) with \\( \\triangle W = BA \\), where \\( r \\ll \\min(n, m) \\) refers to the intrinsic rank of \\( \\triangle W \\). The updated weight matrix \\( W = W_0 + \\triangle W \\) is used for inference. By updating \\( A \\) and \\( B \\) exclusively during training, the base model gradually adapts to the specific domains. Meanwhile, since \\( W_0 \\) is frozen throughout the optimization, the generative ability of base model is well preserved. For efficiency, LoRA is typically applied only to attention layers for model fine-tuning."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4. Methodology"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "This work aims to handle inherent gaps between the vanilla diffusion prior and blind face restoration (BFR) setting,"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
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+ ],
+ "angle": 0,
+ "content": "which stem from the distribution mismatch between 1) high-quality (HQ) and low-quality (LQ) images, and 2) synthesized and real-world images. Unlike previous attempts addressing the first gap with pre-processing modules [21, 23] or guidance from other face restoration methods [38], our model, namely FLIPNET, is simply built upon a T2I model with few trainable parameters. The framework is illustrated in Fig. 2, which takes pairs of HQ and LQ images as input. By simply flipping the input, the model switches between restoration mode (Sec. 4.1) and degradation mode (Sec. 4.2) to achieve authentic and faithful face restoration and synthesizing real-world degraded images, respectively. Note that, to preserve the strong image prior of the large-scale T2I model, we fine-tune only the LoRA weights [10] plugged to all attention layers."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.1. Restoration mode"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.352,
+ 0.907,
+ 0.655
+ ],
+ "angle": 0,
+ "content": "In restoration mode, the denoising network takes HQ images \\( \\mathbf{x} \\) as input and LQ images \\( \\mathbf{y} \\) as condition. Unlike previous works concatenating LQ images [22] or pre-processed results [21, 23] to HQ images, our model is conditioned on diffused LQ images. Specifically, the diffusion process (Eq. (1)) is applied to both HQ and LQ images, where noise \\( (\\epsilon_{x},\\epsilon_{y}) \\) and timestep \\( (t_x,t_y) \\) are sampled separately. The noisy pairs \\( (\\pmb {x}_{t_x},\\pmb {y}_{t_y}) \\) are concatenated along the batch axis and fed to the denoising network, which is optimized to simultaneously denoise both inputs, enabling the restoration of HQ images from LQ counterparts under varying noise levels. However, LQ images act as a double-edged sword, which improves the restoration fidelity by providing structural information while compromising the authenticity. To strike a balance, BoostHub is proposed to selectively integrate BFR-oriented features, and meanwhile, discard irrelevant ones. Additionally, we identify the misalignment between face embeddings widely-used for personalized generation [24, 25] and those required by BFR, which inspires us to explore BFR-oriented face embeddings."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.655,
+ 0.906,
+ 0.791
+ ],
+ "angle": 0,
+ "content": "BoostHub. Following the pioneering T2I model [28], our denoising network \\(\\epsilon_{\\theta}\\) is implemented as UNet, with its blocks comprising ResNet layers, self-attention layers, and cross-attention layers. Inspired by a joint module used in conditioned generation [19], we use BoostHub to enhance noisy HQ features with BFR-oriented features from LQ conditions. As shown in Fig. 2, BoostHub is placed in parallel to self-attention layers to involve LQ features without interrupting the spatial relationships within HQ images."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.792,
+ 0.905,
+ 0.852
+ ],
+ "angle": 0,
+ "content": "As illustrated in Fig. 2, given the noisy HQ and LQ features \\((F_x,F_y)\\), BoostHub projects them to query, key and value via projection matrices \\(W_{Q_x}\\), \\(W_{K_y}\\) and \\(W_{V_y}\\) and then integrate them with attention mechanism:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.582,
+ 0.865,
+ 0.905,
+ 0.905
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} F _ {r o} = W _ {O} \\cdot \\operatorname {A t t n} \\left(Q _ {x}, K _ {y}, V _ {y}\\right) \\\\ = W _ {O} \\cdot \\operatorname {S o f t m a x} \\left(Q _ {x} K _ {y} ^ {T} / \\sqrt {d}\\right) V _ {y}, \\tag {4} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.48,
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+ "angle": 0,
+ "content": "13473"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.091,
+ 0.086,
+ 0.907,
+ 0.401
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
+ 0.41,
+ 0.907,
+ 0.482
+ ],
+ "angle": 0,
+ "content": "Figure 2. FLIPNET pipeline. FLIPNET takes noisy high-quality (HQ) and low-quality (LQ) image pairs as input. It can switch between restoration mode and degradation mode. Taking restoration mode as an example, HQ images are used as input while LQ images are condition, where a BoostHub is placed in parallel to each self-attention layer to selectively integrate the BFR-oriented LQ features for denoising. Additionally, LoRA weights are plugged to all self-attention and cross-attention layers to adapt the base model to face domain. By simply flipping the image-condition order, it switches to degradation mode to synthesize degraded data with real-world degradations."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.491,
+ 0.482,
+ 0.599
+ ],
+ "angle": 0,
+ "content": "where \\( Q_{x} = W_{Q_{x}}F_{x} \\), \\( K_{y} = W_{K_{y}}F_{y} \\), and \\( V_{y} = W_{V_{y}}F_{y} \\). Following prior arts [8], \\( W_{Q_x} \\), \\( W_{K_y} \\) and \\( W_{V_y} \\) are initialized by corresponding self-attention weight of the base model and the output projection matrices \\( W_{O} \\) are initialized by all-zero matrix to avoid harmful effects that additional modules might introduce. The BFR-oriented features \\( F_{ro} \\) are then combined with self-attention output \\( F_{sa_{x}} \\) as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.103,
+ 0.606,
+ 0.483,
+ 0.623
+ ],
+ "angle": 0,
+ "content": "\\[\nF _ {j o i n t} = F _ {s a _ {x}} + \\phi \\cdot F _ {r o} = \\text {S e l f - A t t n} (F _ {x}) + \\phi \\cdot F _ {r o}, \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.629,
+ 0.483,
+ 0.689
+ ],
+ "angle": 0,
+ "content": "where the enhance weight \\(\\phi\\) is set to control how much LQ features will be involved. Subsequently, the joint features \\(F_{joint}\\) are integrated with text prompts as well as BFR-oriented face embeddings via cross-attention."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.689,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "BFR-oriented face embeddings. In personalized generation works [24, 25], face embeddings, acting as an additional condition, are integrated via cross-attention layers to control the identity. However, prior arts generally leverage ID embeddings from a face recognition network [5]. Yet, such embeddings are trained to distinguish different persons instead of preserving fine-grained facial details, making them ineffective in providing instructive guidance for restoration. To this end, this work aims to explore BFR-oriented face embeddings, which should 1) well represent the appearance of the given person, and 2) be positioned in the common latent space of both HQ and LQ inputs so that they will not be biased when integrating with joint features from BoostHub in cross-attention layers. Inspired by the"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.492,
+ 0.907,
+ 0.568
+ ],
+ "angle": 0,
+ "content": "training scheme used in DAEFR [31], we propose to obtain such embeddings from an autoencoder [16] trained for face reconstruction. Instead of the discrete codebook, we adopt continuous latent features which can provide fine-grained details. A two-stage learning scheme is adopted."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.567,
+ 0.906,
+ 0.689
+ ],
+ "angle": 0,
+ "content": "a) Reconstruction stage. First, HQ/LQ autoencoders are trained to reconstruct input face images. HQ/LQ images \\( \\boldsymbol{x} / \\boldsymbol{y} \\in \\mathbb{R}^{H \\times W \\times 3} \\) are projected to latent space \\( \\boldsymbol{z}_{x / y} \\in \\mathbb{R}^{h \\times w \\times d} \\) via encoder and then projected back to images \\( \\hat{\\boldsymbol{x}} / \\hat{\\boldsymbol{y}} \\) by decoder. To achieve faithful reconstruction, the objective consists of L1 loss \\( \\mathcal{L}_1 \\), perceptual loss \\( \\mathcal{L}_p \\), and adversarial loss \\( \\mathcal{L}_{adv} \\), i.e., \\( \\mathcal{L}_{ae} = \\mathcal{L}_1 + \\lambda_{ap} \\cdot \\mathcal{L}_p + \\lambda_{adv} \\cdot \\mathcal{L}_{adv} \\), where \\( \\lambda_{ap} \\) and \\( \\lambda_{adv} \\) are set as 0.5 and 0.8, respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.689,
+ 0.906,
+ 0.811
+ ],
+ "angle": 0,
+ "content": "b) Association stage. Similar to CLIP [26], we fine-tune the autoencoders via the cross-entropy loss to map HQ/LQ features into a common latent space. HQ and LQ latents are first flattened to \\(\\{z_{x / y}^{i}\\in \\mathbb{R}^{d}\\}_{i = 1}^{N},N = h\\times w\\). The similarity matrix between \\(z_{x}\\) and \\(z_{y}\\) can be computed as \\(\\mathcal{M}\\in \\mathbb{R}^{N\\times N}\\). We adopt the cross-entropy loss \\((\\mathcal{L}_{ce}^{H}\\) and \\(\\mathcal{L}_{ce}^{L})\\) to maximize the similarity between corresponding patches via maximizing scores in the diagonal:"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.512,
+ 0.567,
+ 0.906,
+ 0.811
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.583,
+ 0.82,
+ 0.907,
+ 0.862
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {c e}} ^ {H (L)} = - \\frac {1}{N} \\sum_ {i = 1} ^ {N} \\sum_ {j = 1} ^ {N} y _ {i, j} \\log \\left(z _ {x (y)} ^ {i, j}\\right), \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.871,
+ 0.907,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "where \\(y_{i,j}\\) represents ground-truth labels. The objective of the association stage is \\(\\mathcal{L}_{\\text{asso}} = \\mathcal{L}_{ae} + (\\mathcal{L}_{ce}^{H} + \\mathcal{L}_{ce}^{L}) / 2\\)"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.945,
+ 0.52,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "13474"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.482,
+ 0.182
+ ],
+ "angle": 0,
+ "content": "Once trained, the LQ encoder is used to extract face embeddings \\( \\mathbf{z}_y \\in \\mathbb{R}^{N \\times d} \\), which are then passed through a lightweight adapter \\( \\tau(\\cdot) \\) to align with the dimensionality of text tokens before integrating with the T2I model, i.e., \\( c_{\\mathrm{id}} = \\tau(\\mathbf{z}_y) \\). The adapter consists of several linear layers with Layer Normalization [41]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.182,
+ 0.483,
+ 0.214
+ ],
+ "angle": 0,
+ "content": "Objectives. In restoration mode, the model learns how to denoise the noisy \\((\\pmb{x}_{t_x},\\pmb{y}_{t_y})\\) jointly following the objective:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.107,
+ 0.22,
+ 0.483,
+ 0.247
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {l d m} = \\mathbb {E} _ {\\boldsymbol {x}, \\boldsymbol {y}, \\epsilon , t _ {x}, t _ {y}} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t _ {x}}, \\boldsymbol {y} _ {t _ {y}}, t _ {x}, t _ {y}, c\\right) \\| ^ {2} \\right], \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.252,
+ 0.483,
+ 0.314
+ ],
+ "angle": 0,
+ "content": "where \\(\\epsilon = (\\epsilon_{x},\\epsilon_{y})\\) and \\(c = (c_{\\mathrm{text}},c_{\\mathrm{id}})\\). Beyond latent-level constraints, image-level constraints are applied to the denoised predictions \\(\\hat{x}_0\\) at each timestep obtained by Eq. (3), which include MSE loss \\(\\mathcal{L}_{mse}\\) and perceptual loss \\(\\mathcal{L}_p\\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.117,
+ 0.318,
+ 0.483,
+ 0.339
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {m s e} = \\| \\pmb {x} - \\hat {\\pmb {x}} _ {0} \\| _ {2} ^ {2}, \\quad \\mathcal {L} _ {p} = \\| \\phi (\\pmb {x}) - \\phi (\\hat {\\pmb {x}} _ {0}) \\| _ {2} ^ {2}, \\qquad (8)\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.343,
+ 0.483,
+ 0.39
+ ],
+ "angle": 0,
+ "content": "where \\(\\phi (\\cdot)\\) represents VGG19 [29] backbone. The overall training objective is \\(\\mathcal{L}_{rm} = \\mathcal{L}_{ldm} + \\lambda_{mse}\\cdot \\mathcal{L}_{mse} + \\lambda_p\\cdot \\mathcal{L}_p\\) \\(\\lambda_{mse}\\) and \\(\\lambda_{p}\\) are set as 1 and 0.01 throughout the training."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.396,
+ 0.271,
+ 0.412
+ ],
+ "angle": 0,
+ "content": "4.2. Degradation mode"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.418,
+ 0.483,
+ 0.705
+ ],
+ "angle": 0,
+ "content": "By simply flipping the input, i.e., LQ images \\( \\mathbf{y} \\) serving as input while HQ images \\( \\mathbf{x} \\) as condition, our FLIPNET switches to degradation mode. To learn the real-world degradations, our model needs to be trained with paired HQ and LQ images collected from real-world scenarios. In the absence of such face datasets, we gather multiple low-level vision datasets captured in real-world scenarios to construct the training dataset for degradation mode, including Dense-Haze [2] for image dehazing, LOL [37] for low light enhancement, SIDD [1] for image denoising, and RealBlur [27] for image deblurring. To construct the training set, full set of Dense-Haze and LOL are included and 1000 pairs are randomly selected from SIDD and RealBlurJ, obtaining a real-world dataset with around 2500 pairs. To keep the model's ability in synthesizing the classical degradations Eq. (9), 4000 face images are randomly selected from FFHQ to synthesize LQ counterparts on-the-fly during training. The training process is the same with restoration mode, except for the condition and the objective."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.705,
+ 0.483,
+ 0.781
+ ],
+ "angle": 0,
+ "content": "Cross-attention conditions. Being trained on both face and non-face datasets, we do NOT leverage BFR-oriented face embeddings in this mode. In other words, text prompts are the only condition for cross-attention layers, which are generated by BLIP [17] following previous works [8]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.781,
+ 0.483,
+ 0.826
+ ],
+ "angle": 0,
+ "content": "Objectives. Only diffusion loss \\(\\mathcal{L}_{ldm}\\) is used, i.e., \\(\\mathcal{L}_{dm} = \\mathcal{L}_{ldm}\\), as imposing image-level constraints on degraded images will introduce unforeseen noise to predictions."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.826,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Once trained, the model can be used to synthesize degraded counterparts of HQ face images with the acquired knowledge. The generated images carry diverse and complex degradations, with the intensity of degradation remaining entirely unknown, which are more suitable for"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.198
+ ],
+ "angle": 0,
+ "content": "\"BLIND\" face restoration. The visualization and distribution of degraded images synthesized by a prior art [34] and our method are illustrated in Fig. 5. As observed, FLIPNET could well model real-world degradations, evidenced by its diverse distribution across multiple real-world face datasets. The synthesized degraded images can be subsequently used to train our FLIPNET under restoration mode."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.207,
+ 0.646,
+ 0.224
+ ],
+ "angle": 0,
+ "content": "5. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.232,
+ 0.715,
+ 0.248
+ ],
+ "angle": 0,
+ "content": "5.1. Datasets and Settings"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.253,
+ 0.905,
+ 0.329
+ ],
+ "angle": 0,
+ "content": "Training Dataset. FFHQ [13], containing 70k high-quality (HQ) face images, is used as the training set. Following previous works [33, 36], images are resized to \\(512 \\times 512\\) before synthesis. Two degradation models are adopted to synthesize low-quality (LQ) counterparts:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.33,
+ 0.905,
+ 0.374
+ ],
+ "angle": 0,
+ "content": "1) On-the-fly degradation. Considering its efficiency, Real-ESRGAN [34] is used to synthesize degraded images online following the formula:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.587,
+ 0.384,
+ 0.905,
+ 0.41
+ ],
+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {y} = \\left\\{\\left[ (\\boldsymbol {x} \\otimes \\boldsymbol {k} _ {\\sigma}) \\downarrow_ {s} + \\boldsymbol {n} _ {\\delta} \\right] _ {\\mathrm {J P E G} _ {q}} \\right\\} \\uparrow_ {s}, \\tag {9}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.418,
+ 0.906,
+ 0.553
+ ],
+ "angle": 0,
+ "content": "where a HQ image \\(\\pmb{x}\\) is firstly blurred by a Gaussian kernel \\(k_{\\sigma}\\), followed by a downsampling of scale \\(s\\). Afterward, Gaussian noise \\(n_{\\delta}\\) and JPEG compression with quality factor \\(q\\) are applied to the image, which is then upsampled back to the original size to obtain its LQ counterpart \\(\\pmb{y}\\). The hyper-parameters \\(\\sigma\\), \\(s\\), \\(\\delta\\), and \\(q\\) are uniformly sampled from [0.1, 15], [0.8, 32], [0, 20], and [30, 95] respectively. On top of this, the process is performed for the second time, where random degradations are applied in shuffled order."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.554,
+ 0.905,
+ 0.629
+ ],
+ "angle": 0,
+ "content": "2) Off-shelf degradation. In light of its diversity and authenticity, our FLIPNET is switched to degradation mode to synthesize degraded images offline. For each HQ face image, we generate five images with diverse and unknown degradations, serving as LQ counterparts."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.63,
+ 0.905,
+ 0.674
+ ],
+ "angle": 0,
+ "content": "For each iteration, degraded images generated by on-the-fly and off-shelf schemes are selected by a probability of 0.5 to construct a training batch."
+ },
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+ "type": "text",
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+ "content": "Testing Dataset. We evaluate FLIPNET on a synthetic dataset: CelebA-Test and three real-world datasets: LFW [11], WebPhoto [33] and WIDER [44]. CelebA-Test contains 3000 HQ images from CelebA-HQ [12]. Akin to the training set, LQ counterparts in test set are synthesized by both on-the-fly and off-shelf degradation scheme at equal probability. In terms of three real-world datasets, LFW contains 1711 mildly degraded face images in the wild, which comprises the first image for each person in LFW [11]. WebPhoto includes 407 images crawled from the internet, some of which are old photos with severe degradation. WIDER consists of 970 images with severe degradations from the WIDER dataset [39]."
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+ "content": "Evaluation Metrics. For evaluation, we adopt two pixelwise metrics (PSNR and SSIM), a reference perceptual met"
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+ "content": "(17.80dB / 64.45)"
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+ "type": "image_caption",
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+ "content": "LQ"
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+ "angle": 0,
+ "content": "\\(\\phi = 0\\)"
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+ "content": "\\(\\phi = 1\\)"
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+ "content": "\\(\\phi = 2\\)"
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+ "angle": 0,
+ "content": "HQ"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 3. Visualization of the effectiveness of enhance weight \\(\\phi\\) on CelebA-Test. \\(\\phi\\) strikes a balance between fidelity and authenticity by determining the amount of LQ features involved. PSNR(↑) / Deg.(↓) are reported."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "ric (LPIPS [42]), and a non-reference perceptual metric (FID [9]). To measure the consistency of identity, the angle between ID embeddings extracted by ArcFace (\"Deg.\") [5] is used. All metrics are used for the evaluation of synthetic dataset while only FID is used for real-world datasets due to the lack of ground-truth HQ images."
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+ "content": "Implementation Details. We adopt Stable Diffusion 2.1-base1 as the base T2I model and plug LoRA modules to all self-attention and cross-attention layers. We train LoRA for 90k iterations (batch size=16), with the intrinsic rank set to 64. The text prompts are generated by BLIP [17] for all datasets. We use AdamW [15] optimizer with the learning rate 5e-5. The training process is conducted on \\(512 \\times 512\\) resolution with 8 NVIDIA V100 GPUs."
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+ "content": "For restoration mode, autoencoders are initialized by the pretrained weight [28]. We trained model for \\(200\\mathrm{k}\\) at reconstruction stage and \\(80\\mathrm{k}\\) at association stage (batch size \\(= 32\\)). For non-face datasets, the model takes no embeddings other than text prompts as condition. During training, we use a probability of 0.5 to drop text prompt and 0.3 to drop face embeddings to enhance the robustness. For inference, we use words such as \"low quality\", \"blurry\", and \"poorly rendered hands\" as the negative prompt for restoration mode while use null text prompt for degradation mode. The classifier-free guidance (CFG) scale is set as 1.5."
+ },
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+ "content": "5.2. Ablation Studies"
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+ "content": "5.2.1. Restoration mode"
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+ "bbox": [
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+ "angle": 0,
+ "content": "BoostHub enhance weight. According to Eq. (5), the enhance weight \\(\\phi\\) determines the amount of BFR-oriented features integrated from LQ inputs. When less LQ features are involved, the ability of the T2I model in generating high-quality contents is fully exploited while features that facilitate face restoration, such as color and structure, are ignored, thereby affecting the authenticity. Conversely, an over-injection of such features will compromise the restoration quality. Restoration results with different en"
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+ "content": "hance weights as illustrated in Fig. 3."
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "As observed, without guidance from LQ images \\((\\phi = 0)\\), the restoration strictly relies on text prompt and face embeddings. Despite its high quality, the restoration deviates significantly from the original identity. In contrast, LQ features dominate the generation when \\(\\phi = 2\\), leading to the poor quality with fine-grained facial details being smoothed out. When we set \\(\\phi = 1\\), the model could strike a good balance between fidelity and authenticity."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "BFR-oriented face embeddings. We identify the misalignment between the widely-used face embeddings from a face recognition model [5] and those required by blind face restoration (BFR). To make a comparison, we visualize the restoration results, conditioned on ArcFace embeddings and our BFR-oriented face embeddings in Fig. 4(a) and Fig. 4(c), as well as corresponding attention maps. As observed, the face recognition model, trained to distinguish different persons, exclusively focuses on features at discriminative regions, such as eyes. As a result, the restoration fails to render fine-grained details at cheeks or hairs."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Beyond presenting facial details, the alignment between HQ and LQ face embeddings is important for our model as face embeddings are supposed to integrated with joint features (Eq. (5)) via cross-attention, which include both HQ features from self-attention layers and BFR-oriented LQ features from BoostHub. The alignment is achieved by \"Association stage\". To demonstrate its effectiveness, we use face embeddings from the autoencoder trained only with reconstruction stage to perform the restoration. The result is shown in Fig. 4(b). Due to the absence of \"Association stage\", face embeddings are biased on BFR-oriented LQ features while neglecting HQ ones, leading to compromised the restoration quality. On the contrary, when BFR-oriented face embeddings integrating with the aligned HQ and LQ features, our model is able to deliver faithful results with face details such as wrinkle well preserved (Fig. 4(c))."
+ },
+ {
+ "type": "title",
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+ "content": "5.2.2. Degradation mode"
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+ "angle": 0,
+ "content": "Synthesized images and distribution. We visualize the degraded images generated by Real-ESRGAN [34] and our"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "1Stable Diffusion v2.1: https://github.com/Stability-AI/stablediffusion"
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+ "content": "13476"
+ }
+ ],
+ [
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+ {
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+ "content": "(a) Arc (23.05dB / 48.47)"
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+ "content": "(b) \\(\\mathrm{BO}_{w / o}\\mathrm{Asso}\\) (22.89 dB /46.02)"
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+ "content": "(c) BO (23.39dB / 43.81)"
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+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. Restoration results (Right) of the model conditioning on face embeddings extracted from ArcFace (Arc), our BFR-oriented ones trained without \\((\\mathrm{BO}_{w / o A s s o})\\) and with (BO) \"Association stage\" on CelebA-Test. Corresponding attention maps (Left) of embeddings are also shown. PSNR(↑) / Deg.(↓) are reported. The lighter the color, the higher the attention scores."
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Synthesized LQ vs Real LQ"
+ },
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+ {
+ "type": "image",
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. Distribution of degraded images synthesized by Real-ESRGAN [34] and our FLIPNET compared to three real-world datasets: LFW, WebPhoto and WIDER. Synthesized images of Real-ESRGAN and Ours are shown below."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "FLIPNET in Fig. 5. To evaluate how well they fit real-world degradations, the feature distribution of degraded images synthesized by both methods and three real-world datasets: LFW [11], WIDER [44] and WebPhoto [33] is also illustrated. Our model is capable of synthesizing degraded images that are widely distributed across different real-world datasets whereas Real-ESRGAN generates data gathering in a limited region. This can be proved by examples shown below. Images degraded by our model present diverse degradations while that by Real-ESRGAN demonstrate limited degradation patterns."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5.3. Comparisons with State-of-the-Art Methods"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Evaluations are performed on synthetic and real-world datasets. Unlike previous BFR methods, our training data are synthesized by dual degradation schemes (on-the-fly"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "Table 1. Quantitative comparison on CelebA-Test. “RF++” and “\\(\\mathcal{F}\\)” refer to “RestoreFormer++” and our FLIPNET. “+O”: on-the-fly synthesized images. “+O/F”: both on-the-fly and off-shelf synthesized images. “Deg.” refers to the angle between identity embeddings of restored images and HQ counterparts. The best and the second best results are indicated."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ 0.498
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+ "angle": 0,
+ "content": "| Methods | PSNR↑ | SSIM↑ | LPIPS↓ | FID↓ | Deg.↓ |
| GPEN | 23.65/22.86 | 0.61/0.60 | 0.42/0.43 | 18.67/20.20 | 47.24/51.33 |
| GFP-GAN | 23.85/22.70 | 0.61/0.61 | 0.40/0.40 | 17.38/18.52 | 44.96/47.99 |
| RF++ | 24.03/23.15 | 0.63/0.62 | 0.38/0.40 | 14.98/15.15 | 44.00/45.86 |
| DAEFR | 22.70/21.96 | 0.62/0.61 | 0.38/0.39 | 14.43/15.65 | 48.44/49.85 |
| DR2 | 22.27/21.83 | 0.63/0.61 | 0.44/0.44 | 31.59/34.49 | 59.24/61.29 |
| PGDiff | 22.87/22.08 | 0.63/0.62 | 0.42/0.42 | 19.48/21.35 | 59.43/60.38 |
| DiffBIR | 24.37/23.39 | 0.62/0.60 | 0.42/0.43 | 20.78/22.54 | 46.58/47.00 |
| WaveFace | 24.16/23.05 | 0.62/0.62 | 0.42/0.43 | 21.44/23.48 | 43.80/46.50 |
| PMRF | 24.70/23.40 | 0.63/0.62 | 0.42/0.42 | 13.48/15.36 | 44.75/45.76 |
| F+O/+O/F | 24.44/23.39 | 0.64/0.63 | 0.42/0.42 | 13.82/15.06 | 43.29/43.81 |
"
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+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "Table 2. Quantitative comparisons on real-world datasets in terms of \\( \\mathbf{{FID}}\\left( \\downarrow \\right) \\) . \"RF+\" and \"F\" refer to \"Restore-Former++\" and our FLIPNET. \" \\( + \\mathrm{O} \\) \" : on-the-fly synthesized images. \" \\( + \\mathrm{O}/\\mathrm{F} \\) \" : both on-the-fly and off-shelf synthesized images. The best and the second best results are indicated."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Methods | LFW | WebPhoto | WIDER |
| Input | 124.974 | 170.112 | 199.961 |
| GPEN [40] | 50.792 | 80.572 | 46.340 |
| GFP-GAN [33] | 49.560 | 87.584 | 39.499 |
| RF++ [35] | 50.439 | 75.059 | 49.395 |
| DAEFR [31] | 47.310 | 75.453 | 35.344 |
| DR2 [36] | 45.298 | 112.344 | 45.348 |
| PGDiff [38] | 44.630 | 89.754 | 36.807 |
| DiffBIR [21] | 44.383 | 91.777 | 35.343 |
| WaveFace [22] | 43.175 | 81.525 | 36.913 |
| PMRF [23] | 50.275 | 81.064 | 40.685 |
| F+O/+OF | 43.10/42.98 | 83.34/81.37 | 33.09/31.81 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.765,
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+ 0.824
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+ "angle": 0,
+ "content": "and off-shelf). To make a fair comparison, we also synthesize another group with only on-the-fly degradation scheme. The quantitative results are indicated by “+O/F” and “+O” in Tab. 1 and Tab. 2."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.826,
+ 0.905,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Synthetic dataset. Quantitative comparisons on CelebA-Test [12] are illustrated in Tab. 1. Methods tend to yield inferior performance on the test set synthesized by dual degradation schemes, as the degradation better aligns with real-world scenarios, in other words, are more challenging."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.325,
+ 0.907,
+ 0.354
+ ],
+ "angle": 0,
+ "content": "Figure 6. Qualitative comparison with state-of-the-art BFR methods on CelebA-Test. Our method achieves authentic and faithful restoration with fine-grained facial details being well preserved. (Zoom in for best view)."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.093,
+ 0.355,
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+ 0.586
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Figure 7. Qualitative comparison with state-of-the-art BFR methods on real-world datasets, including LFW (first row), WebPhoto (second row), and WIDER (third row). (Zoom in for best view)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.627,
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+ 0.899
+ ],
+ "angle": 0,
+ "content": "For visualization, we present qualitative comparisons with SOTA methods with increasing degradations in Fig. 6. GFPGAN [33] and RestoreFormer++ [35] struggle with obvious artifacts especially when images are corrupted by mild or severe degradation. They also fail to preserve the identity as the restoration is based on, and also, limited by the StyleGAN prior [33] or the pre-constructed dictionary [35]. As inherent gaps between the vanilla diffusion models and the BFR setting have not been properly handled, previous diffusion prior based methods generally yield unsatisfactory results. DR2 [36] and PGDiff [38] tend to deliver either faithful or authentic results, as the restoration starts from a preliminary result from another face restoration model, making their method suboptimal. DiffBIR [21] and PMRF [23], based on a pre-processing module, typically suffer from rendering vivid facial details or avoiding unexpected artifacts. In comparison, our model delivers authentic and faithful results."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.627,
+ 0.909,
+ 0.779
+ ],
+ "angle": 0,
+ "content": "Real-world datasets. We show the quantitative comparison on real-world datasets in Tab. 2. FLIPNET outperforms SOTA methods on LFW [11] and WIDER [44]. Qualitative comparisons (Fig. 7) show that previous diffusion prior based methods yield over-smoothed faces and fail to preserve discriminative facial details. For severely-degraded images (Row 3), most methods are plagued by artifacts caused by unknown and complex real-world degradation. In contrast, our approach delivers faithful and authentic restoration results with rich facial details such as mustache."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.634,
+ 0.801
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+ "angle": 0,
+ "content": "6. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.81,
+ 0.909,
+ 0.9
+ ],
+ "angle": 0,
+ "content": "We propose FLIPNET to bridge the inherent gap between vanilla diffusion model and BFR settings. The model provides a two-pronged solution, enabling authentic and faithful face restoration and real-world degradations modeling by simply switching between restoration mode and degradation mode."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "13478"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "References"
+ },
+ {
+ "type": "ref_text",
+ "bbox": [
+ 0.101,
+ 0.115,
+ 0.483,
+ 0.157
+ ],
+ "angle": 0,
+ "content": "[1] Abdelrahman Abdelhamed, Stephen Lin, and Michael S Brown. A high-quality denoising dataset for smartphone cameras. In CVPR, pages 1692-1700, 2018. 5"
+ },
+ {
+ "type": "ref_text",
+ "bbox": [
+ 0.101,
+ 0.159,
+ 0.483,
+ 0.212
+ ],
+ "angle": 0,
+ "content": "[2] Codruta O Ancuti, Cosmin Ancuti, Mateu Sbert, and Radu Timofte. Dense-haze: A benchmark for image dehazing with dense-haze and haze-free images. In ICIP, pages 1014-1018, 2019. 5"
+ },
+ {
+ "type": "ref_text",
+ "bbox": [
+ 0.102,
+ 0.215,
+ 0.483,
+ 0.271
+ ],
+ "angle": 0,
+ "content": "[3] Chaofeng Chen, Xiaoming Li, Lingbo Yang, Xianhui Lin, Lei Zhang, and Kwan-Yee K Wong. Progressive semantic-aware style transformation for blind face restoration. In CVPR, 2021. 2"
+ },
+ {
+ "type": "ref_text",
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+# Unlocking the Potential of Diffusion Priors in Blind Face Restoration
+
+Yunqi Miao $^{1}$ Zhiyu Qu $^{3}$ Mingqi Gao $^{2}$ Changrui Chen $^{1}$
+
+Jifei Song $^{3}$ Jungong Han $^{2}$ Jiankang Deng $^{4}$
+
+$^{1}$ University of Warwick $^{2}$ University of Sheffield $^{3}$ University of Surrey $^{4}$ Imperial College London
+
+{yunqimiao709, im.mingqi, jungonghan77, jiankangdeng}@gmail.com, changrui.chen@warwick.ac.uk, z.qu@surrey.ac.uk
+
+# Abstract
+
+Although diffusion prior is rising as a powerful solution for blind face restoration (BFR), the inherent gap between the vanilla diffusion model and BFR settings hinders its seamless adaptation. The gap mainly stems from the discrepancy between 1) high-quality (HQ) and low-quality (LQ) images and 2) synthesized and real-world images. The vanilla diffusion model is trained on images with no or less degradations, whereas BFR handles moderately to severely degraded images. Additionally, LQ images used for training are synthesized by a naive degradation model with limited degradation patterns, which fails to simulate complex and unknown degradations in real-world scenarios. In this work, we use a unified network FLIPNET that switches between two modes to resolve specific gaps. In restoration mode, the model gradually integrates BFR-oriented features and face embeddings from LQ images to achieve authentic and faithful face restoration. In degradation mode, the model synthesizes real-world like degraded images based on the knowledge learned from real-world degradation datasets. Extensive evaluations on benchmark datasets show that our model 1) outperforms previous diffusion prior based BFR methods in terms of authenticity and fidelity, and 2) outperforms the naive degradation model in modeling the real-world degradations.
+
+# 1. Introduction
+
+Blind face restoration (BFR) aims to recover high-quality (HQ) facial images from various degradations. The ill-posed nature of this task stems from the complexity and uncertainty of degradations in real-world scenarios. Versatile facial priors have been used to help BFR, such as facial landmarks [4], referential HQ images or features [31, 35], and the pretrained StyleGAN [33, 40]. The success of diffusion models (DMs) [7, 28] in generation tasks has recently excited the restoration field, as their ability to generate HQ content from noise aligns perfectly with the restoration objective [21, 22, 36, 38]. Despite its powerful generative ability, the inherent gap between the vanilla diffusion process
+
+
+(a) LQ
+
+
+(b) SwinIR
+
+
+(c) DiffBIR
+
+
+(d) WaveFace(w/o SwinIR)
+Figure 1. Restoration results of WIDER [39]. Pre-processing module (i.e., SwinIR) based methods (i.e., DiffBIR) fail to render fine-grained details. Methods with condition-concatenated inputs (i.e., WaveFace) unable to handle unknown and complex degradation in real-world scenarios, leading to over-smoothed results.
+
+
+(e) Ours(w/SwinIR)
+
+
+(f) Ours
+
+and the BFR setting hinders its seamless adaptation. The gap arises mainly from the distribution mismatch between: 1) HQ images and low-quality (LQ) images and 2) synthesized images and real-world images.
+
+The vanilla DMs are trained on natural images with minor or no degradation, making them unfit the BFR task, which primarily targets moderately to severely degraded face images. To bridge the gap, previous attempts [21, 23] brutally remove the severe degradations via a pre-processing module [20], followed by a DM to render facial details. However, the pre-processing module also removes discriminative details such as wrinkle and freckle (Fig. 1(b)), thus compromising the fidelity of restoration (Fig. 1(c)). Some approaches [22] bypass the pre-processing module by concatenating the degraded images, acting as the condition, to HQ inputs. Although the first gap is mitigated by gradually introducing LQ features throughout denoising, they fail to deliver adequate results on real-world data (Fig. 1(d)) as the degradation model used for training set synthesizing fails to simulate real-world
+
+degradations. A pioneering work [34] applies the naive degradation model repeatedly to HQ images to create LQ counterparts. Although effective, this work generates less diverse data due to its reliance on limited degradation patterns, which is incompatible with "blind" face restoration.
+
+To address these problems, this work uses only a large-scale Text-to-Image (T2I) model with few trainable parameters, eliminating the reliance on pre-processing modules in both training and inference. Our goal is to steer the pretrained T2I model towards authentic and faithful face restoration while preserving its strong image prior by properly integrating contributive features from LQ images. Despite offering valuable cues such as color and structure for faithful face restoration, LQ images also carry the degradation that affects authenticity. To strike a balance, we propose BoostHub to selectively integrate BFR-oriented features from LQ inputs while discarding irrelevant ones. Meanwhile, we identify the misalignment between face embeddings used in personalized T2I generation [24, 25] and those needed for BFR, which inspires us to explore BFR-oriented face embeddings. Apart from face restoration, we unlock the potential of diffusion prior in modeling real-world degradations. Being trained with HQ and degraded image pairs collected from real-world scenarios, the T2I model learns the distribution of real-world degradations, which is used to synthesize degraded images.
+
+In this work, we unify the above solutions into a single model, i.e., FLIPNET, which takes HQ and LQ image pairs as input. By simply flipping the inputs, the model switches between restoration mode and degradation mode, achieving authentic and faithful face restoration and real-world degradation synthesis, respectively. The contributions of this work can be summarized as follows:
+
+- A two-pronged solution, i.e., FLIPNET, is proposed to bridge two inherent gaps that hinder the seamless adaptation of diffusion prior in BFR by simply switching between restoration mode and degradation mode.
+- When switching to restoration mode, FLIPNET achieves authentic and faithful face restoration by integrating BFR-oriented features and face embeddings from LQ images.
+- When switching to degradation mode, FLIPNET learns from degraded images in real-world scenarios and, in turn, synthesizes such images with acquired knowledge.
+- Comprehensive experiments demonstrate the superiority of FLIPNET in integrating diffusion prior to BFR.
+
+# 2. Related works
+
+Blind face restoration (BFR). BFR works are generally based on three priors: 1) Geometric priors, including facial landmarks [4, 6] and facial parsing maps [3, 43], are used to provide explicit facial structure information. They often yield inferior restoration results due to the imprecise prediction on degraded images. 2) Reference priors based meth
+
+ods either leverage high-quality (HQ) reference images to provide identity information [32] or construct a dictionary that restores HQ facial features [31, 35]. But the restoration performance is restricted by the authenticity of reference images and the size of the codebook. 3) Generative priors encapsulated in StyleGAN2 [14] are used to provide rich facial details for restoration. GFP-GAN [33] and GPEN [40] restore degraded faces by learning the mapping from LQ input to the latent space where GAN prior network can reproduce the desired HQ face images.
+
+Diffusion prior in BFR. Inspired by the ability of diffusion models (DMs) [28, 30] in emerging HQ content from noise, diffusion prior has become a favorable solution for BFR. However, DMs are typically trained on images with less or no degradation while BFR deals with moderately to severely degraded images, which makes its seamless adaptation challenging. Therefore, some works break BFR down to two stages: degradation removal and details generation. DR2 [36] employs the diffusion prior at first stage to obtain degradation-invariant images, where HQ counterparts are obtained by the follow-up face restoration model. DiffBIR [21] and PMRF [23] first coarsely remove severe degradations with a pretrained pre-processing module [20]. Given the obtained intermediate results, DiffBIR renders realistic facial details via a follow-up T2I model. Whilst PMRF takes such images as the initial state of the distribution transportation, where a rectified flow model is optimized to model the path to HQ counterparts. Instead of adopting such a two-stage scheme, PGDiff [38] uses a pretrained BFR model [34] to provide instructive semantics. Throughout the denoising process, the model is trained to minimize the discrepancy between intermediate outputs and target properties. WaveFace [22] uses diffusion prior to restore the low-frequency component exclusively, where low-frequency subbands of LQ images are concatenated to noise and serve as condition for generation. Although exciting restoration results have been achieved, the pre-processing module will also smooth out facial details, thereby compromising the fidelity. Additionally, the reliance on other face restoration models imposes limitations on the potential of the proposed model. How to effectively unleash the potential T2I model in BFR task has NOT been fully exploited.
+
+Real-world degradation modeling. Apart from the gap between HQ and LQ images, diffusion prior BFR methods general deliver inferior performance on real-world images as the degradation model used to synthesize training set fail to simulate that in real-world scenarios. Classical degradation model [18] includes four types of degradations: blur, noise, resize, and JPEG compression. The simple combination fails to handle real-world cases where images typically spread several times over different digital devices. Thus, Real-ESRGAN [34] proposes a "high-order" degradation model, where classical degradations with different hyper
+
+parameters are applied repeatedly on HQ images to synthesize the degraded counterparts. While this may serve as a stopgap, the synthesis remains constrained by the limited degradation patterns. How to effectively simulate complex and blind degradations remains a formidable challenge.
+
+In this work, we address above challenges with a unified model that is solely based on a large-scale T2I model with few trainable parameters. The model provides a two-pronged solution to both authentic and faithful face restoration and real-world degradation modeling.
+
+# 3. Preliminary
+
+Stable Diffusion is a large-scale text-to-image (T2I) latent diffusion model, which performs both diffusion and denoising processes in latent space. Specifically, an autoencoder [16] converts an image $x$ to a latent $z$ with encoder $\mathcal{E}$ and reconstructs it with decoder $\mathcal{D}$ , i.e., $\hat{x} = \mathcal{D}(\mathcal{E}(x))$ . In diffusion process, Gaussian noise $\epsilon \sim \mathcal{N}(0, 1)$ is applied to the starting latent $z_0$ to achieve noisy latent $z_t$ :
+
+$$
+z _ {t} = \sqrt {\bar {\alpha} _ {t}} z _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon , \tag {1}
+$$
+
+where $\{\bar{\alpha}_t\}_{t = 1}^T$ is a pre-defined noise variance schedule over timestep $t$ . For denoising, a network $\epsilon_{\theta}$ is optimized to predict the noise $\epsilon$ at a particular timestep $t$ conditioned on $c$ , such as text prompt, which follows the objective:
+
+$$
+\mathcal {L} _ {l d m} = \mathbb {E} _ {z, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, c\right) \| _ {2} ^ {2} \right]. \tag {2}
+$$
+
+Given the noise predicted at timestep $t$ , the denoised latent $\hat{z}_0$ can be predicted by:
+
+$$
+\hat {z} _ {0} = \frac {1}{\sqrt {\bar {\alpha} _ {t}}} \left(z _ {t} - \sqrt {1 - \bar {\alpha} _ {t}} \epsilon_ {\theta} \left(z _ {t}, t, c\right)\right). \tag {3}
+$$
+
+The denoised image can be further obtained by $\hat{x}_0 = \mathcal{D}(\hat{z}_0)$ .
+
+Low-Rank Adaptation (LoRA) is widely used for the efficient adaptation of large language models or text-to-image models to downstream tasks [10]. Concretely, two low-rank matrices $B \in \mathbb{R}^{n \times r}$ and $A \in \mathbb{R}^{r \times m}$ are introduced to update the base model weights $W_0 \in \mathbb{R}^{n \times m}$ with $\triangle W = BA$ , where $r \ll \min(n, m)$ refers to the intrinsic rank of $\triangle W$ . The updated weight matrix $W = W_0 + \triangle W$ is used for inference. By updating $A$ and $B$ exclusively during training, the base model gradually adapts to the specific domains. Meanwhile, since $W_0$ is frozen throughout the optimization, the generative ability of base model is well preserved. For efficiency, LoRA is typically applied only to attention layers for model fine-tuning.
+
+# 4. Methodology
+
+This work aims to handle inherent gaps between the vanilla diffusion prior and blind face restoration (BFR) setting,
+
+which stem from the distribution mismatch between 1) high-quality (HQ) and low-quality (LQ) images, and 2) synthesized and real-world images. Unlike previous attempts addressing the first gap with pre-processing modules [21, 23] or guidance from other face restoration methods [38], our model, namely FLIPNET, is simply built upon a T2I model with few trainable parameters. The framework is illustrated in Fig. 2, which takes pairs of HQ and LQ images as input. By simply flipping the input, the model switches between restoration mode (Sec. 4.1) and degradation mode (Sec. 4.2) to achieve authentic and faithful face restoration and synthesizing real-world degraded images, respectively. Note that, to preserve the strong image prior of the large-scale T2I model, we fine-tune only the LoRA weights [10] plugged to all attention layers.
+
+# 4.1. Restoration mode
+
+In restoration mode, the denoising network takes HQ images $\mathbf{x}$ as input and LQ images $\mathbf{y}$ as condition. Unlike previous works concatenating LQ images [22] or pre-processed results [21, 23] to HQ images, our model is conditioned on diffused LQ images. Specifically, the diffusion process (Eq. (1)) is applied to both HQ and LQ images, where noise $(\epsilon_{x},\epsilon_{y})$ and timestep $(t_x,t_y)$ are sampled separately. The noisy pairs $(\pmb {x}_{t_x},\pmb {y}_{t_y})$ are concatenated along the batch axis and fed to the denoising network, which is optimized to simultaneously denoise both inputs, enabling the restoration of HQ images from LQ counterparts under varying noise levels. However, LQ images act as a double-edged sword, which improves the restoration fidelity by providing structural information while compromising the authenticity. To strike a balance, BoostHub is proposed to selectively integrate BFR-oriented features, and meanwhile, discard irrelevant ones. Additionally, we identify the misalignment between face embeddings widely-used for personalized generation [24, 25] and those required by BFR, which inspires us to explore BFR-oriented face embeddings.
+
+BoostHub. Following the pioneering T2I model [28], our denoising network $\epsilon_{\theta}$ is implemented as UNet, with its blocks comprising ResNet layers, self-attention layers, and cross-attention layers. Inspired by a joint module used in conditioned generation [19], we use BoostHub to enhance noisy HQ features with BFR-oriented features from LQ conditions. As shown in Fig. 2, BoostHub is placed in parallel to self-attention layers to involve LQ features without interrupting the spatial relationships within HQ images.
+
+As illustrated in Fig. 2, given the noisy HQ and LQ features $(F_x,F_y)$ , BoostHub projects them to query, key and value via projection matrices $W_{Q_x}$ , $W_{K_y}$ and $W_{V_y}$ and then integrate them with attention mechanism:
+
+$$
+\begin{array}{l} F _ {r o} = W _ {O} \cdot \operatorname {A t t n} \left(Q _ {x}, K _ {y}, V _ {y}\right) \\ = W _ {O} \cdot \operatorname {S o f t m a x} \left(Q _ {x} K _ {y} ^ {T} / \sqrt {d}\right) V _ {y}, \tag {4} \\ \end{array}
+$$
+
+
+Figure 2. FLIPNET pipeline. FLIPNET takes noisy high-quality (HQ) and low-quality (LQ) image pairs as input. It can switch between restoration mode and degradation mode. Taking restoration mode as an example, HQ images are used as input while LQ images are condition, where a BoostHub is placed in parallel to each self-attention layer to selectively integrate the BFR-oriented LQ features for denoising. Additionally, LoRA weights are plugged to all self-attention and cross-attention layers to adapt the base model to face domain. By simply flipping the image-condition order, it switches to degradation mode to synthesize degraded data with real-world degradations.
+
+where $Q_{x} = W_{Q_{x}}F_{x}$ , $K_{y} = W_{K_{y}}F_{y}$ , and $V_{y} = W_{V_{y}}F_{y}$ . Following prior arts [8], $W_{Q_x}$ , $W_{K_y}$ and $W_{V_y}$ are initialized by corresponding self-attention weight of the base model and the output projection matrices $W_{O}$ are initialized by all-zero matrix to avoid harmful effects that additional modules might introduce. The BFR-oriented features $F_{ro}$ are then combined with self-attention output $F_{sa_{x}}$ as:
+
+$$
+F _ {j o i n t} = F _ {s a _ {x}} + \phi \cdot F _ {r o} = \text {S e l f - A t t n} (F _ {x}) + \phi \cdot F _ {r o}, \tag {5}
+$$
+
+where the enhance weight $\phi$ is set to control how much LQ features will be involved. Subsequently, the joint features $F_{joint}$ are integrated with text prompts as well as BFR-oriented face embeddings via cross-attention.
+
+BFR-oriented face embeddings. In personalized generation works [24, 25], face embeddings, acting as an additional condition, are integrated via cross-attention layers to control the identity. However, prior arts generally leverage ID embeddings from a face recognition network [5]. Yet, such embeddings are trained to distinguish different persons instead of preserving fine-grained facial details, making them ineffective in providing instructive guidance for restoration. To this end, this work aims to explore BFR-oriented face embeddings, which should 1) well represent the appearance of the given person, and 2) be positioned in the common latent space of both HQ and LQ inputs so that they will not be biased when integrating with joint features from BoostHub in cross-attention layers. Inspired by the
+
+training scheme used in DAEFR [31], we propose to obtain such embeddings from an autoencoder [16] trained for face reconstruction. Instead of the discrete codebook, we adopt continuous latent features which can provide fine-grained details. A two-stage learning scheme is adopted.
+
+a) Reconstruction stage. First, HQ/LQ autoencoders are trained to reconstruct input face images. HQ/LQ images $\boldsymbol{x} / \boldsymbol{y} \in \mathbb{R}^{H \times W \times 3}$ are projected to latent space $\boldsymbol{z}_{x / y} \in \mathbb{R}^{h \times w \times d}$ via encoder and then projected back to images $\hat{\boldsymbol{x}} / \hat{\boldsymbol{y}}$ by decoder. To achieve faithful reconstruction, the objective consists of L1 loss $\mathcal{L}_1$ , perceptual loss $\mathcal{L}_p$ , and adversarial loss $\mathcal{L}_{adv}$ , i.e., $\mathcal{L}_{ae} = \mathcal{L}_1 + \lambda_{ap} \cdot \mathcal{L}_p + \lambda_{adv} \cdot \mathcal{L}_{adv}$ , where $\lambda_{ap}$ and $\lambda_{adv}$ are set as 0.5 and 0.8, respectively.
+b) Association stage. Similar to CLIP [26], we fine-tune the autoencoders via the cross-entropy loss to map HQ/LQ features into a common latent space. HQ and LQ latents are first flattened to $\{z_{x / y}^{i}\in \mathbb{R}^{d}\}_{i = 1}^{N},N = h\times w$ . The similarity matrix between $z_{x}$ and $z_{y}$ can be computed as $\mathcal{M}\in \mathbb{R}^{N\times N}$ . We adopt the cross-entropy loss $(\mathcal{L}_{ce}^{H}$ and $\mathcal{L}_{ce}^{L})$ to maximize the similarity between corresponding patches via maximizing scores in the diagonal:
+
+$$
+\mathcal {L} _ {\mathrm {c e}} ^ {H (L)} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {N} y _ {i, j} \log \left(z _ {x (y)} ^ {i, j}\right), \tag {6}
+$$
+
+where $y_{i,j}$ represents ground-truth labels. The objective of the association stage is $\mathcal{L}_{\text{asso}} = \mathcal{L}_{ae} + (\mathcal{L}_{ce}^{H} + \mathcal{L}_{ce}^{L}) / 2$
+
+Once trained, the LQ encoder is used to extract face embeddings $\mathbf{z}_y \in \mathbb{R}^{N \times d}$ , which are then passed through a lightweight adapter $\tau(\cdot)$ to align with the dimensionality of text tokens before integrating with the T2I model, i.e., $c_{\mathrm{id}} = \tau(\mathbf{z}_y)$ . The adapter consists of several linear layers with Layer Normalization [41].
+
+Objectives. In restoration mode, the model learns how to denoise the noisy $(\pmb{x}_{t_x},\pmb{y}_{t_y})$ jointly following the objective:
+
+$$
+\mathcal {L} _ {l d m} = \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y}, \epsilon , t _ {x}, t _ {y}} \left[ \| \epsilon - \epsilon_ {\theta} \left(\boldsymbol {x} _ {t _ {x}}, \boldsymbol {y} _ {t _ {y}}, t _ {x}, t _ {y}, c\right) \| ^ {2} \right], \tag {7}
+$$
+
+where $\epsilon = (\epsilon_{x},\epsilon_{y})$ and $c = (c_{\mathrm{text}},c_{\mathrm{id}})$ . Beyond latent-level constraints, image-level constraints are applied to the denoised predictions $\hat{x}_0$ at each timestep obtained by Eq. (3), which include MSE loss $\mathcal{L}_{mse}$ and perceptual loss $\mathcal{L}_p$ :
+
+$$
+\mathcal {L} _ {m s e} = \| \pmb {x} - \hat {\pmb {x}} _ {0} \| _ {2} ^ {2}, \quad \mathcal {L} _ {p} = \| \phi (\pmb {x}) - \phi (\hat {\pmb {x}} _ {0}) \| _ {2} ^ {2}, \qquad (8)
+$$
+
+where $\phi (\cdot)$ represents VGG19 [29] backbone. The overall training objective is $\mathcal{L}_{rm} = \mathcal{L}_{ldm} + \lambda_{mse}\cdot \mathcal{L}_{mse} + \lambda_p\cdot \mathcal{L}_p$ $\lambda_{mse}$ and $\lambda_{p}$ are set as 1 and 0.01 throughout the training.
+
+# 4.2. Degradation mode
+
+By simply flipping the input, i.e., LQ images $\mathbf{y}$ serving as input while HQ images $\mathbf{x}$ as condition, our FLIPNET switches to degradation mode. To learn the real-world degradations, our model needs to be trained with paired HQ and LQ images collected from real-world scenarios. In the absence of such face datasets, we gather multiple low-level vision datasets captured in real-world scenarios to construct the training dataset for degradation mode, including Dense-Haze [2] for image dehazing, LOL [37] for low light enhancement, SIDD [1] for image denoising, and RealBlur [27] for image deblurring. To construct the training set, full set of Dense-Haze and LOL are included and 1000 pairs are randomly selected from SIDD and RealBlurJ, obtaining a real-world dataset with around 2500 pairs. To keep the model's ability in synthesizing the classical degradations Eq. (9), 4000 face images are randomly selected from FFHQ to synthesize LQ counterparts on-the-fly during training. The training process is the same with restoration mode, except for the condition and the objective.
+
+Cross-attention conditions. Being trained on both face and non-face datasets, we do NOT leverage BFR-oriented face embeddings in this mode. In other words, text prompts are the only condition for cross-attention layers, which are generated by BLIP [17] following previous works [8].
+
+Objectives. Only diffusion loss $\mathcal{L}_{ldm}$ is used, i.e., $\mathcal{L}_{dm} = \mathcal{L}_{ldm}$ , as imposing image-level constraints on degraded images will introduce unforeseen noise to predictions.
+
+Once trained, the model can be used to synthesize degraded counterparts of HQ face images with the acquired knowledge. The generated images carry diverse and complex degradations, with the intensity of degradation remaining entirely unknown, which are more suitable for
+
+"BLIND" face restoration. The visualization and distribution of degraded images synthesized by a prior art [34] and our method are illustrated in Fig. 5. As observed, FLIPNET could well model real-world degradations, evidenced by its diverse distribution across multiple real-world face datasets. The synthesized degraded images can be subsequently used to train our FLIPNET under restoration mode.
+
+# 5. Experiments
+
+# 5.1. Datasets and Settings
+
+Training Dataset. FFHQ [13], containing 70k high-quality (HQ) face images, is used as the training set. Following previous works [33, 36], images are resized to $512 \times 512$ before synthesis. Two degradation models are adopted to synthesize low-quality (LQ) counterparts:
+
+1) On-the-fly degradation. Considering its efficiency, Real-ESRGAN [34] is used to synthesize degraded images online following the formula:
+
+$$
+\boldsymbol {y} = \left\{\left[ (\boldsymbol {x} \otimes \boldsymbol {k} _ {\sigma}) \downarrow_ {s} + \boldsymbol {n} _ {\delta} \right] _ {\mathrm {J P E G} _ {q}} \right\} \uparrow_ {s}, \tag {9}
+$$
+
+where a HQ image $\pmb{x}$ is firstly blurred by a Gaussian kernel $k_{\sigma}$ , followed by a downsampling of scale $s$ . Afterward, Gaussian noise $n_{\delta}$ and JPEG compression with quality factor $q$ are applied to the image, which is then upsampled back to the original size to obtain its LQ counterpart $\pmb{y}$ . The hyper-parameters $\sigma$ , $s$ , $\delta$ , and $q$ are uniformly sampled from [0.1, 15], [0.8, 32], [0, 20], and [30, 95] respectively. On top of this, the process is performed for the second time, where random degradations are applied in shuffled order.
+
+2) Off-shelf degradation. In light of its diversity and authenticity, our FLIPNET is switched to degradation mode to synthesize degraded images offline. For each HQ face image, we generate five images with diverse and unknown degradations, serving as LQ counterparts.
+
+For each iteration, degraded images generated by on-the-fly and off-shelf schemes are selected by a probability of 0.5 to construct a training batch.
+
+Testing Dataset. We evaluate FLIPNET on a synthetic dataset: CelebA-Test and three real-world datasets: LFW [11], WebPhoto [33] and WIDER [44]. CelebA-Test contains 3000 HQ images from CelebA-HQ [12]. Akin to the training set, LQ counterparts in test set are synthesized by both on-the-fly and off-shelf degradation scheme at equal probability. In terms of three real-world datasets, LFW contains 1711 mildly degraded face images in the wild, which comprises the first image for each person in LFW [11]. WebPhoto includes 407 images crawled from the internet, some of which are old photos with severe degradation. WIDER consists of 970 images with severe degradations from the WIDER dataset [39].
+
+Evaluation Metrics. For evaluation, we adopt two pixelwise metrics (PSNR and SSIM), a reference perceptual met
+
+
+LQ
+Figure 3. Visualization of the effectiveness of enhance weight $\phi$ on CelebA-Test. $\phi$ strikes a balance between fidelity and authenticity by determining the amount of LQ features involved. PSNR(↑) / Deg.(↓) are reported.
+
+
+(17.80dB / 64.45)
+$\phi = 0$
+
+
+$\phi = 1$
+
+
+$\phi = 2$
+
+
+HQ
+
+ric (LPIPS [42]), and a non-reference perceptual metric (FID [9]). To measure the consistency of identity, the angle between ID embeddings extracted by ArcFace ("Deg.") [5] is used. All metrics are used for the evaluation of synthetic dataset while only FID is used for real-world datasets due to the lack of ground-truth HQ images.
+
+Implementation Details. We adopt Stable Diffusion 2.1-base1 as the base T2I model and plug LoRA modules to all self-attention and cross-attention layers. We train LoRA for 90k iterations (batch size=16), with the intrinsic rank set to 64. The text prompts are generated by BLIP [17] for all datasets. We use AdamW [15] optimizer with the learning rate 5e-5. The training process is conducted on $512 \times 512$ resolution with 8 NVIDIA V100 GPUs.
+
+For restoration mode, autoencoders are initialized by the pretrained weight [28]. We trained model for $200\mathrm{k}$ at reconstruction stage and $80\mathrm{k}$ at association stage (batch size $= 32$ ). For non-face datasets, the model takes no embeddings other than text prompts as condition. During training, we use a probability of 0.5 to drop text prompt and 0.3 to drop face embeddings to enhance the robustness. For inference, we use words such as "low quality", "blurry", and "poorly rendered hands" as the negative prompt for restoration mode while use null text prompt for degradation mode. The classifier-free guidance (CFG) scale is set as 1.5.
+
+# 5.2. Ablation Studies
+
+# 5.2.1. Restoration mode
+
+BoostHub enhance weight. According to Eq. (5), the enhance weight $\phi$ determines the amount of BFR-oriented features integrated from LQ inputs. When less LQ features are involved, the ability of the T2I model in generating high-quality contents is fully exploited while features that facilitate face restoration, such as color and structure, are ignored, thereby affecting the authenticity. Conversely, an over-injection of such features will compromise the restoration quality. Restoration results with different en
+
+hance weights as illustrated in Fig. 3.
+
+As observed, without guidance from LQ images $(\phi = 0)$ , the restoration strictly relies on text prompt and face embeddings. Despite its high quality, the restoration deviates significantly from the original identity. In contrast, LQ features dominate the generation when $\phi = 2$ , leading to the poor quality with fine-grained facial details being smoothed out. When we set $\phi = 1$ , the model could strike a good balance between fidelity and authenticity.
+
+BFR-oriented face embeddings. We identify the misalignment between the widely-used face embeddings from a face recognition model [5] and those required by blind face restoration (BFR). To make a comparison, we visualize the restoration results, conditioned on ArcFace embeddings and our BFR-oriented face embeddings in Fig. 4(a) and Fig. 4(c), as well as corresponding attention maps. As observed, the face recognition model, trained to distinguish different persons, exclusively focuses on features at discriminative regions, such as eyes. As a result, the restoration fails to render fine-grained details at cheeks or hairs.
+
+Beyond presenting facial details, the alignment between HQ and LQ face embeddings is important for our model as face embeddings are supposed to integrated with joint features (Eq. (5)) via cross-attention, which include both HQ features from self-attention layers and BFR-oriented LQ features from BoostHub. The alignment is achieved by "Association stage". To demonstrate its effectiveness, we use face embeddings from the autoencoder trained only with reconstruction stage to perform the restoration. The result is shown in Fig. 4(b). Due to the absence of "Association stage", face embeddings are biased on BFR-oriented LQ features while neglecting HQ ones, leading to compromised the restoration quality. On the contrary, when BFR-oriented face embeddings integrating with the aligned HQ and LQ features, our model is able to deliver faithful results with face details such as wrinkle well preserved (Fig. 4(c)).
+
+# 5.2.2. Degradation mode
+
+Synthesized images and distribution. We visualize the degraded images generated by Real-ESRGAN [34] and our
+
+
+(a) Arc (23.05dB / 48.47)
+
+
+(b) $\mathrm{BO}_{w / o}\mathrm{Asso}$ (22.89 dB /46.02)
+Figure 4. Restoration results (Right) of the model conditioning on face embeddings extracted from ArcFace (Arc), our BFR-oriented ones trained without $(\mathrm{BO}_{w / o A s s o})$ and with (BO) "Association stage" on CelebA-Test. Corresponding attention maps (Left) of embeddings are also shown. PSNR(↑) / Deg.(↓) are reported. The lighter the color, the higher the attention scores.
+
+
+(c) BO (23.39dB / 43.81)
+
+
+Synthesized LQ vs Real LQ
+
+
+
+
+Figure 5. Distribution of degraded images synthesized by Real-ESRGAN [34] and our FLIPNET compared to three real-world datasets: LFW, WebPhoto and WIDER. Synthesized images of Real-ESRGAN and Ours are shown below.
+
+FLIPNET in Fig. 5. To evaluate how well they fit real-world degradations, the feature distribution of degraded images synthesized by both methods and three real-world datasets: LFW [11], WIDER [44] and WebPhoto [33] is also illustrated. Our model is capable of synthesizing degraded images that are widely distributed across different real-world datasets whereas Real-ESRGAN generates data gathering in a limited region. This can be proved by examples shown below. Images degraded by our model present diverse degradations while that by Real-ESRGAN demonstrate limited degradation patterns.
+
+# 5.3. Comparisons with State-of-the-Art Methods
+
+Evaluations are performed on synthetic and real-world datasets. Unlike previous BFR methods, our training data are synthesized by dual degradation schemes (on-the-fly
+
+Table 1. Quantitative comparison on CelebA-Test. “RF++” and “ $\mathcal{F}$ ” refer to “RestoreFormer++” and our FLIPNET. “+O”: on-the-fly synthesized images. “+O/F”: both on-the-fly and off-shelf synthesized images. “Deg.” refers to the angle between identity embeddings of restored images and HQ counterparts. The best and the second best results are indicated.
+
+| Methods | PSNR↑ | SSIM↑ | LPIPS↓ | FID↓ | Deg.↓ |
| GPEN | 23.65/22.86 | 0.61/0.60 | 0.42/0.43 | 18.67/20.20 | 47.24/51.33 |
| GFP-GAN | 23.85/22.70 | 0.61/0.61 | 0.40/0.40 | 17.38/18.52 | 44.96/47.99 |
| RF++ | 24.03/23.15 | 0.63/0.62 | 0.38/0.40 | 14.98/15.15 | 44.00/45.86 |
| DAEFR | 22.70/21.96 | 0.62/0.61 | 0.38/0.39 | 14.43/15.65 | 48.44/49.85 |
| DR2 | 22.27/21.83 | 0.63/0.61 | 0.44/0.44 | 31.59/34.49 | 59.24/61.29 |
| PGDiff | 22.87/22.08 | 0.63/0.62 | 0.42/0.42 | 19.48/21.35 | 59.43/60.38 |
| DiffBIR | 24.37/23.39 | 0.62/0.60 | 0.42/0.43 | 20.78/22.54 | 46.58/47.00 |
| WaveFace | 24.16/23.05 | 0.62/0.62 | 0.42/0.43 | 21.44/23.48 | 43.80/46.50 |
| PMRF | 24.70/23.40 | 0.63/0.62 | 0.42/0.42 | 13.48/15.36 | 44.75/45.76 |
| F+O/+O/F | 24.44/23.39 | 0.64/0.63 | 0.42/0.42 | 13.82/15.06 | 43.29/43.81 |
+
+Table 2. Quantitative comparisons on real-world datasets in terms of $\mathbf{{FID}}\left( \downarrow \right)$ . "RF+" and "F" refer to "Restore-Former++" and our FLIPNET. " $+ \mathrm{O}$ " : on-the-fly synthesized images. " $+ \mathrm{O}/\mathrm{F}$ " : both on-the-fly and off-shelf synthesized images. The best and the second best results are indicated.
+
+| Methods | LFW | WebPhoto | WIDER |
| Input | 124.974 | 170.112 | 199.961 |
| GPEN [40] | 50.792 | 80.572 | 46.340 |
| GFP-GAN [33] | 49.560 | 87.584 | 39.499 |
| RF++ [35] | 50.439 | 75.059 | 49.395 |
| DAEFR [31] | 47.310 | 75.453 | 35.344 |
| DR2 [36] | 45.298 | 112.344 | 45.348 |
| PGDiff [38] | 44.630 | 89.754 | 36.807 |
| DiffBIR [21] | 44.383 | 91.777 | 35.343 |
| WaveFace [22] | 43.175 | 81.525 | 36.913 |
| PMRF [23] | 50.275 | 81.064 | 40.685 |
| F+O/+OF | 43.10/42.98 | 83.34/81.37 | 33.09/31.81 |
+
+and off-shelf). To make a fair comparison, we also synthesize another group with only on-the-fly degradation scheme. The quantitative results are indicated by “+O/F” and “+O” in Tab. 1 and Tab. 2.
+
+Synthetic dataset. Quantitative comparisons on CelebA-Test [12] are illustrated in Tab. 1. Methods tend to yield inferior performance on the test set synthesized by dual degradation schemes, as the degradation better aligns with real-world scenarios, in other words, are more challenging.
+
+
+Figure 6. Qualitative comparison with state-of-the-art BFR methods on CelebA-Test. Our method achieves authentic and faithful restoration with fine-grained facial details being well preserved. (Zoom in for best view).
+
+
+Figure 7. Qualitative comparison with state-of-the-art BFR methods on real-world datasets, including LFW (first row), WebPhoto (second row), and WIDER (third row). (Zoom in for best view).
+
+For visualization, we present qualitative comparisons with SOTA methods with increasing degradations in Fig. 6. GFPGAN [33] and RestoreFormer++ [35] struggle with obvious artifacts especially when images are corrupted by mild or severe degradation. They also fail to preserve the identity as the restoration is based on, and also, limited by the StyleGAN prior [33] or the pre-constructed dictionary [35]. As inherent gaps between the vanilla diffusion models and the BFR setting have not been properly handled, previous diffusion prior based methods generally yield unsatisfactory results. DR2 [36] and PGDiff [38] tend to deliver either faithful or authentic results, as the restoration starts from a preliminary result from another face restoration model, making their method suboptimal. DiffBIR [21] and PMRF [23], based on a pre-processing module, typically suffer from rendering vivid facial details or avoiding unexpected artifacts. In comparison, our model delivers authentic and faithful results.
+
+Real-world datasets. We show the quantitative comparison on real-world datasets in Tab. 2. FLIPNET outperforms SOTA methods on LFW [11] and WIDER [44]. Qualitative comparisons (Fig. 7) show that previous diffusion prior based methods yield over-smoothed faces and fail to preserve discriminative facial details. For severely-degraded images (Row 3), most methods are plagued by artifacts caused by unknown and complex real-world degradation. In contrast, our approach delivers faithful and authentic restoration results with rich facial details such as mustache.
+
+# 6. Conclusion
+
+We propose FLIPNET to bridge the inherent gap between vanilla diffusion model and BFR settings. The model provides a two-pronged solution, enabling authentic and faithful face restoration and real-world degradations modeling by simply switching between restoration mode and degradation mode.
+
+# References
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\ No newline at end of file
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+ "html": "| Methods | PSNR↑ | SSIM↑ | LPIPS↓ | FID↓ | Deg.↓ |
| GPEN | 23.65/22.86 | 0.61/0.60 | 0.42/0.43 | 18.67/20.20 | 47.24/51.33 |
| GFP-GAN | 23.85/22.70 | 0.61/0.61 | 0.40/0.40 | 17.38/18.52 | 44.96/47.99 |
| RF++ | 24.03/23.15 | 0.63/0.62 | 0.38/0.40 | 14.98/15.15 | 44.00/45.86 |
| DAEFR | 22.70/21.96 | 0.62/0.61 | 0.38/0.39 | 14.43/15.65 | 48.44/49.85 |
| DR2 | 22.27/21.83 | 0.63/0.61 | 0.44/0.44 | 31.59/34.49 | 59.24/61.29 |
| PGDiff | 22.87/22.08 | 0.63/0.62 | 0.42/0.42 | 19.48/21.35 | 59.43/60.38 |
| DiffBIR | 24.37/23.39 | 0.62/0.60 | 0.42/0.43 | 20.78/22.54 | 46.58/47.00 |
| WaveFace | 24.16/23.05 | 0.62/0.62 | 0.42/0.43 | 21.44/23.48 | 43.80/46.50 |
| PMRF | 24.70/23.40 | 0.63/0.62 | 0.42/0.42 | 13.48/15.36 | 44.75/45.76 |
| F+O/+O/F | 24.44/23.39 | 0.64/0.63 | 0.42/0.42 | 13.82/15.06 | 43.29/43.81 |
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| Input | 124.974 | 170.112 | 199.961 |
| GPEN [40] | 50.792 | 80.572 | 46.340 |
| GFP-GAN [33] | 49.560 | 87.584 | 39.499 |
| RF++ [35] | 50.439 | 75.059 | 49.395 |
| DAEFR [31] | 47.310 | 75.453 | 35.344 |
| DR2 [36] | 45.298 | 112.344 | 45.348 |
| PGDiff [38] | 44.630 | 89.754 | 36.807 |
| DiffBIR [21] | 44.383 | 91.777 | 35.343 |
| WaveFace [22] | 43.175 | 81.525 | 36.913 |
| PMRF [23] | 50.275 | 81.064 | 40.685 |
| F+O/+OF | 43.10/42.98 | 83.34/81.37 | 33.09/31.81 |
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+ "content": "Real-world datasets. We show the quantitative comparison on real-world datasets in Tab. 2. FLIPNET outperforms SOTA methods on LFW [11] and WIDER [44]. Qualitative comparisons (Fig. 7) show that previous diffusion prior based methods yield over-smoothed faces and fail to preserve discriminative facial details. For severely-degraded images (Row 3), most methods are plagued by artifacts caused by unknown and complex real-world degradation. In contrast, our approach delivers faithful and authentic restoration results with rich facial details such as mustache."
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+ "type": "text",
+ "text": "Unraveling the Effects of Synthetic Data on End-to-End Autonomous Driving",
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+ "text": "Junhao Ge $^{1*}$ Zuhong Liu $^{1,5*}$ Longteng Fan $^{1*}$ Yifan Jiang $^{1*}$",
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+ "text": "$^{1}$ {cancaries, albert.liu, michaelfan, fiona.jiang, sjq2022, sihengc} $@$ sjtu.edu.cn",
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+ "Side Left",
+ "Figure 1. SceneCrafter is a high-fidelity simulator capable of generating realistic synthetic driving data and providing an effective closed-loop evaluation for end-to-end autonomous driving models. Given real-world datasets, SceneCrafter can reconstruct dynamic driving scenes and incorporate interactive traffic flows to generate novel, realistic, and consistent scenarios."
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+ "text": "End-to-end (E2E) autonomous driving (AD) models require diverse, high-quality data to perform well across various driving scenarios. However, collecting large-scale real-world data is expensive and time-consuming, making high-fidelity synthetic data essential for enhancing data diversity and model robustness. Existing driving simulators have significant limitations for synthetic data generation: game-engine-based simulators struggle to produce realistic sensor data, while NeRF-based and diffusion-based methods face efficiency challenges. Additionally, recent simulators designed for closed-loop evaluation provide limited interaction with other vehicles, failing to simulate complex real-world traffic dynamics. To address these issues, we introduce SceneCrafter, a realistic, interactive, and efficient AD simulator based on 3D Gaussian Splatting (3DGS). SceneCrafter not only efficiently generates realistic driving logs across diverse traffic scenarios but also enables robust closed-loop evaluation of end-to-end models. Experimental results demonstrate that SceneCrafter serves as both a",
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+ },
+ {
+ "type": "text",
+ "text": "reliable evaluation platform and a efficient data generator that significantly improves end-to-end model generalization. Our code will be released at https://github.com/cancaries/SceneCrafter.",
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+ "type": "text",
+ "text": "1. Introduction",
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+ {
+ "type": "text",
+ "text": "Recently, autonomous driving (AD) has gradually progressed from modular paradigms [7, 16, 22, 42] to end-to-end models [5, 6, 9, 10, 19-21, 36, 37, 51], which learn from sensor data and ego status to plan future motion. Most end-to-end models are fundamentally data-driven[52], where scenario diversity and vehicle trajectory distributions plays a decisive role in model effectiveness. However, gathering extensive, high quality and wide coverage real data for driving scenarios is not only time-consuming but also costly.",
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+ "text": "Given these constraints, generating high-fidelity, diverse synthetic data is essential for complementing real-world datasets, improving the robustness of end-to-end models. Nonetheless, current closed-loop simulators struggle to balance realism, efficiency, and interaction modeling, limiting",
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+ "page_idx": 0
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+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "table_caption": [],
+ "table_footnote": [
+ "Table 1. Comparison of existing and proposed simulation platforms for autonomous driving. ST Consistency represents Spatial-Temporal Consistency. DataGen For E2E represents Data Generation for end-to-end models."
+ ],
+ "table_body": "| Name | Real Time | ST Consistency | Real Images | Interactive Traffic Flow | DataGen For E2E |
| CARLA[12] | ✓ | ✓ | ✗ | ✓ | ✓ |
| SUMO[32] | ✓ | ✓ | ✗ | ✓ | ✗ |
| MetaDrive[24] | ✓ | ✓ | ✗ | ✓ | ✓ |
| NeuroNCAP[30] | ✗ | ✓ | ✓ | ✗ | ✗ |
| UniSim[48] | ✗ | ✓ | ✓ | ✗ | ✗ |
| DriveArena[47] | ✗ | ✗ | ✓ | ✓ | ✓ |
| HugSim[53] | ✓ | ✓ | ✓ | ✗ | ✗ |
| Ours | ✓ | ✓ | ✓ | ✓ | ✓ |
",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "high-quality synthetic data generation. Game engine-based approaches [12, 17, 24, 29, 32, 43] provide extensive customization for scene editing; however, the sim-to-real gap in sensor realism limits their transferability. In contrast, diffusion-based methods [4, 31, 44, 47] enhance image realism but are constrained by high computational and time costs, as well as spatial-temporal inconsistencies in generated images. [53] utilizes Gaussian Splatting for real-time image rendering but lacks reasonable interaction modeling for foreground objects. These limitations hinder current simulators from effectively generating synthetic data or fully evaluating end-to-end models.",
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+ "text": "To address these challenges, we present SceneCrafter, a unified simulation framework designed for high-quality synthetic data generation as well as closed-loop evaluation for end-to-end models. Fig. 2 shows the overview of SceneCrafter. It consists of two key components: Scene Controller and Scene Renderer. Scene Controller initializes the simulation with real-world road map data and generates diverse, interactive traffic flows. Scene Renderer then integrates these foreground traffic agents into the reconstructed background, producing high-fidelity images that capture the evolving traffic scenario. Compared with existing methods, SceneCrafter improves realism, interactivity and efficiency to better bridge the gap between simulation and real-world driving. Tab. 1 shows the comparison between our method and existing driving simulators.",
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "To achieve realistic simulation, we enhance ego agent dynamics, vehicle appearance and vehicle placement in images through several innovations. To capture real agents movement, our Scene Controller integrates an adaptive kinematic model trained on real-world IMU sensor data, ensuring realistic vehicle displacement and dynamics. Additionally, our Scene Renderer incorporates global illumination estimation to generate directional shadow Gaussian models, enhancing sensor image realism in dynamic scenes. To improve spatial modeling accuracy, we introduce an optimization-based ground height estimation algorithm that correct z-axis map offsets based on LiDAR points, ensuring precise vehicle positioning and rendering consistency.",
+ "bbox": [
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+ "type": "text",
+ "text": "Unlike existing closed-loop simulators [53] that focus",
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+ "page_idx": 1
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+ "type": "text",
+ "text": "on agent-to-ego interactions, SceneCrafter models bidirectional interactions between the ego vehicle and surrounding agents in Scene Controller. By dynamically updating agent behaviors through heuristic vehicle placement and actor models, it generates diverse and reasonable driving patterns to improve end-to-end model generalization.",
+ "bbox": [
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+ "text": "Beides, SceneCrafter leverages 3D Gaussian Splatting (3DGS) to model dynamic driving scenes. It achieves significantly higher efficiency and lower computational costs compared to NeRF-based [30, 48], or diffusion-based [4, 31, 44, 47] approaches, allowing the potential for large-scale synthetic data generation and evaluation.",
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+ "text": "Our experiments demonstrate that the synthetic data generated by SceneCrafter closely matches real-world sensor images and vehicle dynamics from the perspective of end-to-end models. We also assess the interactivity and efficiency of our method. Furthermore, we show that augmenting real-world datasets with our synthetic data enhances model generalization in interactive, closed-loop driving environments, achieving $18\\%$ higher Route Completion rate. In summary, our main contributions are as follows:",
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+ "type": "list",
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+ "list_items": [
+ "- Efficient and Reliable Synthetic Data Generation. SceneCrafter achieves superior efficiency and realism based on 3D Gaussian Splitting (3DGS). This approach ensures efficient and reliable synthetic data production.",
+ "- Interactive Closed-Loop Simulation Platform. SceneCrafter provides an interactive simulation environment with precise control over agent vehicles which allows comprehensive assessment of model robustness across diverse traffic interactions.",
+ "- Enhanced End-to-End Models Generalization. With SceneCrafter, we examine the influence of synthetic data on the training of the models. Our insights contribute to enhancing both model performance and generalization."
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+ "text": "End-to-End Model. Recent attention in AD has shifted from modular paradigms [7, 16, 22, 42] to end-to-end solutions [5, 6, 9, 10, 19–21, 36, 37, 51]. These models integrate perception [26], prediction [18], and planning [34] into a single framework, addressing issues such as information loss, error accumulation, and feature misalignment between modules [20]. Vision-based end-to-end models [19–21, 51] trained on real-world datasets attempt to extract more valuable information to enhance model performance. UniAD [20] integrates information from preceding modules to achieve significant improvements in planning performance. VAD [21] leverages the potential of vectorized scene representation, simplifying the input data and makes the model more efficient and scalable. GenAD [51] enhances the multi-modality of ego vehicle trajectories using a generative approach, enabling more flexible motion planning. [52] identifies scaling laws in imitation learning",
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+ "img_path": "images/2f0792977a20a5d68880af2ce3d23fd044440029d19d0dbcda97fcf1f254f87f.jpg",
+ "image_caption": [
+ "Figure 2. Overview of SceneCrafter framework. Simulation is initialized with world config, map topology and camera config. Scene Controller updates interactive traffic flow, based on which Scene Renderer generates realistic driving scenes. End-to-End Driving Model plans future ego trajectory depending on simulation modes including synthetic data generation and closed-loop evaluation."
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+ "text": "based end-to-end autonomous driving models, demonstrating a power-law relationship between model performance and real training data volume. However, collecting large-scale real-world datasets is costly and time-consuming, highlighting the need for efficient methods to generate high-quality, diverse simulated data. Our work contributes to this direction by providing an approach to generating diverse, high-fidelity simulated data.",
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+ "type": "text",
+ "text": "Synthetic Data for Autonomous Driving. Data augmentation is a widely used technique for enhancing model performance across various autonomous driving tasks. Prior works [8, 28, 40, 50] have primarily focused on generating synthetic data to improve 3D perception. [40] enhances 3D object detection by inserting 3D assets into a NeRF-reconstructed background using simple car replacement heuristics, while [28] investigates the real-to-simulated domain gap by evaluating object detection and online mapping performance across different settings. However, limited research has explored the role of synthetic data in vision-based planning. [15] improves semantic segmentation and driving performance of end-to-end models in the CARLA simulator by generating data conditioned on semantic maps. To the best of our knowledge, this is the first study to investigate the impact of synthetic data on imitation learning-based end-to-end models trained on real-world driving data and evaluated in a photorealistic closed-loop environment.",
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+ "text": "End-to-End Model Evaluation. Most open-loop evaluations of end-to-end models compare the model's plan against GT records, such as L2 distance to GT trajectories or collision rates [2, 3, 38]. However, this approach increasingly proves inadequate for assessing planning quality. Studies have identified distribution biases related to ego status [27, 49], leading models to learn shortcuts that fit training data but fail to generalize. In unseen scenarios, these models may struggle with adaptable planning or accurate trajectory prediction [1]. To overcome open-loop limitations, many simulators [12, 17, 24, 29, 32, 43] provide",
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+ "text": "robust closed-loop evaluation environments, though the sim-to-real gap hinders real-world transferability [25, 35]. Recent NeRF-based [30, 48] and diffusion-based [4, 31, 39, 41, 46, 47] methods generate realistic sensor data for closed-loop evaluation but suffer from high computational and time costs for large-scale testing. HugSim [53] reconstructs scenes using 3DGS but lacks reasonable and ego-to-agent interaction. In contrast, our work ensures realistic, interactive and efficient simulation.",
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+ "text": "3. SceneCrafter Framework",
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+ "text": "SceneCrafter offers a unified simulation framework supporting both synthetic data generation and closed-loop evaluation for end-to-end autonomous driving models. It consists of two components: Scene Controller and Scene Renderer. Scene Controller manages agents in the environment by dynamically updating their states and behaviors at each simulation step. Scene Renderer generates new driving scenes based on updates from Scene Controller and Driving Planner $\\pi$ , ensuring realistic and interactive environments.",
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+ "text": "3.1. Scene Controller",
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+ "text": "Scene Controller dynamically updates the states and current behavior of ego based on their past states, ego vehicle's states, planned routes and map topology. It leverages control factors for different behavior modes, ensuring smooth and natural interactions in complex driving environments.",
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+ "text": "Heuristic Agent Spawn. The entire scene is initialized based on a configurable world setup $W$ , including vehicle max spawn number, behavior modes and types. Scene Controller leverages HD maps derived directly from real-world datasets. By utilizing labeled information within HD maps [38], we build a map topological representation $\\mathcal{M}$ , which enables both precise navigation and localization.",
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+ "text": "With map topology, we can spawn $N$ agent vehicles by following two types of approaches: route-based and trigger-",
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+ "Ego Vehicle",
+ "Blocking Agent Other Agent",
+ "(a) Original"
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+ "(c) Left Turn",
+ "Figure 3. (a) illustrates the original scenario, where no vehicles are present except ego vehicle, which simply maintains a constant speed. In contrast, (b), (c), and (d) demonstrate how ego vehicle's behavior is altered due to the influence of the blocking agent, while ego vehicle impacts the surrounding agents. Example video is given in supplementary material."
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+ "(b) Following",
+ "(d)Right Turn"
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+ "text": "based. Agents are initialized with states $(s_j)_{j=1:N}^0$ and behaviors $(b_j)_{j=1:N}^0$ .",
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+ "- Route-based. Spawn points with a higher likelihood of interaction with ego vehicle are prioritized as initialization conditions for agents. Then, we generate diverse global trajectories for agent vehicles, ensuring that the routes closely resemble real-world driving patterns.",
+ "- Trigger-based. By selecting specific points along ego vehicle's trajectory as trigger points, we identify potential spawn points with map topology where agents could interact with ego vehicle. Once ego vehicle reaches a trigger point, the corresponding agent vehicles are activated to execute their trajectories. This approach can facilitate customized safety-critical test scenarios."
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+ "type": "text",
+ "text": "Appendix A explain these approaches in detail.",
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+ "text": "Bi-interactive Agent Control. For status and behavior control, we adopt an approach inspired by CARLA [12], incorporating control factors such as speed limits and safe following distances derived from the original scenario. Agents determine driving behaviors $b_{j}^{t}$ based on their interaction with other agents at each time, which establishes a bidirectional interactive relation between ego and agent vehicles. Fig. 3 shows some common interaction scenes. Beyond regular driving scenarios, we also introduce dangerous behavior modes for agent vehicles, which can trigger actions such as lane changes, aggressive overtakes, emergency stops, or disregarding safe distances when interacting with ego vehicle, providing potential for long-tail scenario evaluation.",
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+ "text": "Adaptive Kinematic Model. We propose an Adaptive Kinematic Model (AKM) to refine vehicle control signals, addressing the discrepancy between simulated and real ego dynamics during simulation, which can significantly impact planning [27]. Given front length $l_{f}$ and rear length $l_{r}$ , AKM updates vehicle states using Eq. (1).",
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+ "type": "equation",
+ "text": "\n$$\n\\beta_ {t} = \\arctan \\left(\\frac {l _ {r}}{l _ {f} + l _ {r}} \\tan (\\delta_ {t})\\right), \\quad v _ {t + 1} = v _ {t} + a _ {t} \\Delta t,\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\varphi_ {t + 1} = \\varphi_ {t} + \\frac {v _ {t}}{l _ {f}} \\sin (\\beta_ {t}) \\Delta t, \\quad v _ {u} = (1 - \\boldsymbol {u} _ {\\mathbf {1}}) v _ {t} + \\boldsymbol {u} _ {\\mathbf {1}} v _ {t + 1},\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} x _ {t + 1} = x _ {t} + v _ {u} \\cos (\\varphi_ {t} + \\boldsymbol {u} _ {\\boldsymbol {2}} \\cdot \\beta_ {t}) \\Delta t, \\\\ y _ {t + 1} = y _ {t} + v _ {u} \\sin \\left(\\varphi_ {t} + \\boldsymbol {u} _ {\\boldsymbol {2}} \\cdot \\beta_ {t}\\right) \\Delta t. \\tag {1} \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "where $\\beta_{t}$ is the slip angle, $v_{t}$ is the vehicle velocity, $\\varphi_{t}$ is the yaw angle, $\\delta$ is the steering angle and $x_{t}, y_{t}$ represent the vehicle position. Compared with standard bicycle model, it incorporates two learnable parameters, $u_{1}$ and $u_{2}$ , estimated from real-world IMU sensor data. These parameters help prevent unrealistic displacements by adjusting velocity and orientation dynamically. By ensuring smoother and more natural vehicle movement, this approach enhances the realism and continuity of the simulation environment.",
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+ "text": "3.2. Scene Renderer",
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+ "text": "Scene Renderer generates high-fidelity driving scenes that reflect dynamic traffic flows with spatial-temporal consistency. It builds a Model Library using Gaussian Splatting for editable background and dynamic foreground models. We also propose ground height estimation and directional shadow rendering to enhance rendering realism. Figure 1 demonstrates example images from Scene Renderer.",
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+ "text": "Gaussian-Splatting-Based Model Library. Model library consists of two components: background model and foreground model, both are built based on Gaussian Splatting. For background, we train models by Street Gaussians [39] with only static elements retained to provide a stable background free from motion artifacts and allow for clean integration of dynamic foreground models. For foreground, due to the limited available angles of vehicles in the original scenario, we construct our virtual vehicle assets with BlenderNeRF [33] and 3DRealCar [13] to build foreground model libraries through training with 3DGS. The explicit nature of Gaussian Splatting allows direct editing of the scene using models from the library. Detailed construction steps are provided in Appendix B.",
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+ "type": "text",
+ "text": "Ground Height Estimation. To prevent artifacts from sinking into or floating above the ground in environments with large elevation variations, we propose learning a global ground model defined as $\\hat{z} = f(x,y)$ . Inspired by [11], we extract ground LiDAR points from each frame using RANSAC [14] and fit a ground model for the entire scene, implemented as a three-layer MLP, to predict the z-axis offset during object placement. The loss is designed as follows to penalize less those LiDAR points above the ground:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\text {h e i g h t}} (\\hat {z}, z) = \\left\\{ \\begin{array}{l l} (\\hat {z} - z) ^ {2} & \\hat {z} > z \\\\ \\operatorname {H u b e r} (\\hat {z}, z) & \\hat {z} \\leq z \\end{array} \\right. \\tag {2}\n$$\n",
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+ "text": "Directional Shadow Rendering. To enhance the realism of foreground vehicles appearance in the scene, we generate",
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+ "text": "vehicle shadow 3DGS models in multiple directions based on the Gaussian models from the foreground library. For each scene, we pre-estimate the global illumination based on the images from the original dataset as following:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n1 = \\frac {\\left[ G _ {x} \\left(p ^ {*}\\right) , G _ {y} \\left(p ^ {*}\\right) , - 1 \\right] ^ {\\top}}{\\sqrt {G _ {x} ^ {2} \\left(p ^ {*}\\right) + G _ {y} ^ {2} \\left(p ^ {*}\\right) + 1}} \\tag {3}\n$$\n",
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+ "type": "text",
+ "text": "where $p^* = \\arg \\max_p \\| \\nabla I(p) \\|_2$ is the point with maximum gradient magnitude, $\\nabla I(p) = [G_x, G_y]^\\top$ denotes the Sobel gradient after Gaussian blur. During simulation, the global illumination and the current heading angle decide shadow model selection, which is combined with the original model for rendering. A visual comparison of foreground objects with shadow rendering and ground model placement is provided in Fig. 11 in the supplementary.",
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+ "text": "Composition Rendering. Scene Renderer determines ego vehicle's viewpoint by camera configuration. Based on the agent vehicle poses provided by Scene Controller, foreground models are integrated into the background model. Ego vehicle's pose is then used to compute the camera's extrinsic parameters for rendering driving images. Utilizing composite Gaussian model with definite, precise control on spatial positions of foreground objects and overall appearance, our rendered images maintain spatial-temporal consistency. This ensures both the reliability of the generated data and the full controllability required for closed-loop evaluation. Detailed demonstration for spatial-temporal consistency can be found in Appendix F.",
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+ "type": "text",
+ "text": "3.3. Simulation Modes",
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+ "text": "SceneCrafter offers two simulation modes: synthetic data generation for realistic training and closed-loop simulation for interactive model evaluation. Algorithm 1 outlines the simulation process for each mode.",
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+ "text": "Synthetic Data Generation. To generate training datasets for end-to-end models, this mode employs an expert planner $\\pi_{exp}$ to control the ego vehicle while dynamically updating surrounding agents. Ego vehicle follows its original trajectory from the real dataset while adjusting its pace based on different driving scenarios to maintain consistent rendering quality. At each simulation step, our Scene Controller dynamically updates the status $s_j^t$ and behavior $b_j^t$ of surrounding agents. The policy $\\pi_{exp}$ generates control signals using privileged information $(s_{ego}^t,(s_j)^t_{j = 1:N},\\mathcal{M})$ to ensure safe and natural driving behavior. The kinematic model $KM$ then applies these control signals to refine ego vehicle's position and status for the Scene Renderer to generate new sensor observations. This cycle continues until either ego vehicle times out or reaches the target point.",
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+ "text": "Closed-Loop Simulation. To evaluate end-to-end models in realistic interactive environments, the closed-loop mode replaces the expert planner with a learned policy $\\pi_{AD}$ .",
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+ "text": "Compared with data generation mode, the policy takes sensor inputs, control command and ego status as input to provide future action. The control command $c$ is generated from the original ego trajectory plan from real world data.",
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+ "code_caption": [
+ "Algorithm 1: SceneCrafter Workflow"
+ ],
+ "code_body": "Input : World Setup W, Number of Agents N, Simulation Mode M ∈ {SYN, CL}, Driving Planner π, Kinematic Model KM Initialize: Map Topology M, Ego Initial State $s_{ego}^0$ , Agents Initial States $(s_j)_{j=1:N}^0$ , Agents Initial Behaviors $(b_j)_{j=1:N}^0$ , Sensor Images $(I_k)_{j=1:C}^0$ Output : Driving Simulation Log $\\tilde{\\mathcal{D}}$ $\\{(s_j)_{j=1:N}^{1:T_{max}}, (I_k)_{j=1:C}^{1:T_{max}}, s_{ego}^{1:T_{max}}, \\mathcal{M}\\}$ while t < Tmax do for j ← 1 to N do $s_j^{t+1}, b_j^{t+1} \\gets \\text{SceneController}(s_{ego}^t, (s_j)^t_{j=1:N}, b_j^t, \\mathcal{M})$ if M = SYN then $a_{ego}^{t+1} \\gets \\pi_{\\text{exp}}(s_{ego}^t, (s_j + 1)^t_{j=1:N}, \\mathcal{M}); // \\text{Synthetic data generation}$ else $a_{ego}^{t+1} \\gets \\pi_{\\text{AD}}(s_{ego}^t, (I_k)^t_{k=1:C}, c); // \\text{Closed-loop evaluation}$ $s_{ego}^{t+1} \\gets \\text{KM}(a_{ego}^{t+1}, s_{ego}^t); (I_k)^{t+1}_{k=1:C} \\gets \\text{SceneRenderer}(s_{ego}^{t+1}, (s_j)^{t+1}_{j=1:N}) t \\gets t + 1$",
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+ "type": "text",
+ "text": "4. Experiment",
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+ "text": "In Section 4.1, we explain our simulation setups for Scene Controller and Scene Renderer. In Section 4.2, we share quantitative results that assess how well simulated data can replace real data, focusing on realism from the perspective of end-to-end autonomous driving models. Note that we do not compare our simulator with existing photorealistic simulators because they are unable to generate synthetic driving logs that include both sensor inputs and ego dynamics. Detailed justification are provided in Appendix E. Section 4.3 evaluates interactivity, while Section 4.4 assesses closed-loop performance, highlighting improvements in generalization and robustness. Additional runtime efficiency comparisons are provided in Appendix C.",
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+ "text": "4.1. Simulation Settings",
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+ "text": "Dataset. Our simulator is based on Waymo Open Dataset [38], which is split according to its official con",
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+ "type": "text",
+ "text": "Figuration into 797 training scenes and 200 validation scenes. These scenes and their corresponding data samples are denoted as $(S_{train},\\mathcal{D}_{train})$ for the training set and $(S_{val},\\mathcal{D}_{val})$ for the validation set. For data generation, we select 60 representative scenes from the training set, covering both suburban and urban environments. These scenes include a variety of road types including straight roads and intersections, and span different weather conditions. The indices of these selected scenes are denoted as $S_{recon}\\subset S_{train}$ , while the rest indices are denoted as $S_{recon}^{c}$ . In addition, for closed-loop evaluation, we reconstruct 30 scenes from $S_{val}$ to assess the generalization capability of end-to-end models.",
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+ "text": "Scene Controller and Scene Renderer Setups. For Scene Controller, the updating frequency of vehicles' status in the scene is set to $10\\mathrm{Hz}$ to ensure more precise control. The rendering frequency of Scene Renderer is set to $2\\mathrm{Hz}$ following the input frequency of end-to-end models [20, 21, 51] previously trained on nuScenes [2].",
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+ "type": "text",
+ "text": "End-to-End Models and Evaluation Metrics. We select VAD [21] and its enhanced version, GenAD [51], as our end-to-end models due to their efficiency and effectiveness. Both methods share the same auxiliary tasks: 3D Object Detection (3DOD), Motion Prediction and Online Map Segmentation (MapSeg). For open-loop evaluation, we assess planning performance using the L2 displacement error and collision rate, following the standard end-to-end benchmark [21, 51]. In closed-loop evaluation, we adopt key metrics from Carla [12], including route completion (RC), vehicle collision rate (VCR), and layout collision rate (LCR). Detailed formulas are provided in Appendix G.",
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+ "text": "4.2. Simulation Realism Evaluation",
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+ "text": "To assess the reliability of SceneCrafter, we examine the real-simulation gap between real data and generated data from the perspective of end-to-end models in an open-loop manner to show that SceneCrafter can achieve real kinematic controls and high rendering quality for synthetic data.",
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+ "text": "4.2.1. Data Augmentation with Synthetic Data",
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+ "text": "To demonstrate the complementary benefits of our synthetic data, we train VAD with a mix of real-world and simulated data in an incremental learning setup. This enables us to assess whether the model surpasses one trained solely on real data, validating the fidelity of our synthetic data. Specifically, we construct two real-world training sets: $\\mathcal{D}_{recon}^{c}$ and driving logs from 200 sampled scenes in $S_{recon}^{c}$ , forming a smaller-scale real training set $D_{200}$ . We generate one driving log per scene from $S_{recon}$ to create the synthetic training set $\\tilde{\\mathcal{D}}_{train}$ with around 2,000 samples. End-to-end models are evaluated on all samples $D_{val}$ from $S_{val}$ .",
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+ "text": "Tab. 2 presents the quantitative results. The inclusion of synthetic data significantly improves planning performance",
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+ "table_body": "| Setting | Volume | Planning L2 (m) ↓ | CR ↓ |
| Real | Sim | 1s | 2s | 3s | Avg | 1s | 2s | 3s | Avg |
| D200 | 8k | - | 0.61 | 1.31 | 2.24 | 1.39 | 0.34 | 0.36 | 0.86 | 0.52 |
| D200 + Dtr | 8k | 2k | 0.48 | 1.09 | 1.99 | 1.18 | 0.28 | 0.32 | 0.75 | 0.45 |
| Dreccon | 28k | - | 0.43 | 1.02 | 1.82 | 1.09 | 0.21 | 0.27 | 0.47 | 0.32 |
| Dreccon + Dtr | 28k | 2k | 0.38 | 0.94 | 1.79 | 1.04 | 0.08 | 0.14 | 0.53 | 0.25 |
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+ "text": "Table 2. Performance comparison of data augmentation with synthetic samples $\\hat{\\mathcal{D}}_{tr}$ using different real data amounts $\\mathcal{D}_{200}$ and $\\mathcal{D}_{\\text{recon}}^c$ . The inclusion of synthetic data improves planning performance on both settings.",
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+ "text": "when the real training set is small, demonstrating its potential to supplement real-world data. However, its impact is relatively marginal when the original training set is large. We attribute this to the fact that the Waymo validation set primarily consists of normal driving scenarios, such as cruising straightly in a scenario with fewer interaction with other agents, which are already well covered by large-scale real-world training data. This limitation of real-world open-loop evaluation benchmarks is also discussed in [27].",
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+ "text": "4.2.2. Inference with E2E Models as Proxy Evaluators",
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+ "text": "Unlike most related works that primarily focus on image quality comparison for realism validation, we approach the problem by using VAD trained on real-world samples $\\mathcal{D}_{recon}^{c}$ from scenes $S_{recon}^{c}$ as a zero-shot proxy evaluator. This model is assumed to exhibit certain perception ability and reasonable coherence with the real world ground truth trajectory after large-scale training. We then evaluate the model on both real data $\\mathcal{D}_{recon}$ and synthetic data $\\tilde{\\mathcal{D}}_{recon}$ generated from scenes $S_{recon}$ , comparing their performance on all autonomous driving tasks and assessing the output trajectory of end-to-end models with the generated trajectory annotations by the simulator. This comparison aims to investigate the realism of the generated data from both the sensor input and vehicle kinematics perspectives. Specifically, we consider the following settings:",
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+ "- Real Data: This setting uses real-world driving logs from the scenes $S_{\\text{recon}}$ in the Waymo dataset. It includes actual sensor images and ego IMU data as inputs for VAD, along with annotated labels for other agents.",
+ "- VirVehicle Rep.: This setting uses real ego IMU data and annotated agents' labels from scenes $S_{recon}$ , but replaces the real sensor images with rendered images generated by Scene Renderer. The images are generated using the original camera configurations, with real dynamic foreground objects replaced by assets from the virtual vehicle library [33], without adding shadows.",
+ "- 3DRealCar Rep.: This setting mirrors VirVehicle Rep. but replaces real foreground objects with 3DRealCar[13] assets and adding directional shadow during rendering.",
+ "- Sim Data w/ BM: This setting generates synthetic data with traffic flow controlled by Scene Controller, using a vanilla Bicycle Model as the kinematic model. The num"
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+ "table_body": "| Setting | Volume | Rendering Config | Prediction (Car) | 3DOD↑ | MapSeg↑ |
| Car Lib | Shadow | EPA ↑ | ADE ↓ | FDE ↓ | Car AP | AP 0.5 | AP 1.0 | AP 1.5 |
| Real Data | 2k | - | - | 0.30 | 0.71 | 0.96 | 44.1 | 0.245 | 0.482 | 0.644 |
| VirVehicle Rep. | 2k | Virtual | × | 0.25 | 0.26 | 1.02 | 38.4 | 0.227 | 0.476 | 0.633 |
| 3DRealCar Rep. | 2k | 3DRealCar | ✓ | 0.25 | 0.77 | 1.01 | 39.6 | 0.212 | 0.467 | 0.622 |
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+ "Table 3. Perception and prediction performance comparison with VAD trained on $\\mathcal{D}_{recon}^{c}$ over real and synthetic data. Car Lib represents the foreground object source, and Shadow denotes whether shadow rendering is applied. 3DRealCar Rep. achieves a higher detection score compared with VirVehicle Rep., demonstrating the enhanced realism of our foreground rendering."
+ ],
+ "table_footnote": [],
+ "table_body": "| Setting | Volume | Planning L2 (m)↓ | Prediction (Car) | MapSeg↑ |
| 1s | 2s | 3s | EPA ↑ | ADE ↓ | FDE ↓ | AP 0.5 | AP 1.0 | AP 1.5 |
| Real Data | 2k | 0.39 | 0.94 | 1.72 | 0.30 | 0.71 | 0.96 | 0.245 | 0.482 | 0.644 |
| Sim Data w/ BM | 2k | 0.47 | 1.24 | 2.43 | 0.27 | 0.80 | 1.10 | 0.170 | 0.435 | 0.574 |
| Sim Data w/ AKM (Ours) | 2k | 0.38 | 1.04 | 2.06 | 0.28 | 0.77 | 0.92 | 0.185 | 0.453 | 0.590 |
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+ "text": "Table 4. Inference results on Waymo reconstructed scenes with VAD trained on ${\\mathcal{D}}_{\\text{recon }}^{c}$ . Our Adaptive Kinematic Model (AKM) produces ego trajectories closer to planning results than the Bicycle Model (BM), leading to improved prediction and perception performance.",
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+ "image_caption": [
+ "Figure 4. (a) and (b) show that ego trajectories generated by AKM are smoother and more realistic than those by BM. (c) and (d) illustrate that end-to-end planning result deviates more from the simulated GT trajectory with AKM than with BM, which indicates AKM aligns better with real world dynamics. The color bar indicates vehicle velocity norms."
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+ "text": "ber of agents is set to match the average number of dynamic foreground objects in the original scenes.",
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+ "text": "- Sim Data w/ AKM: This setting generates synthetic data similar to Sim Data w/ BM, but uses AKM as the kinematic model instead of the vanilla Bicycle Model.",
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+ "text": "Tab. 3 presents the realism assessment of images generated by Scene Renderer. Notably, replacing all foreground objects with reconstructed 3D assets and rendered background model results in only a minor decline in perception performance (3DOD and MapSeg), demonstrating the high fidelity of our rendered images. This performance gap is primarily due to an increase in false positive bounding boxes, which is less critical than false negatives. Additionally, foreground objects from 3DRealCar, which include added shadows, achieve higher detection scores compared to virtual vehicles, further validating their realism.",
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+ "text": "Regarding the kinematic model, Tab. 4 shows that the ego trajectory generated by the Adaptive Kinematic Model (AKM) aligns more closely with planning results than that generated by the simpler Bicycle Model. Fig. 4 further illustrates the differences in turning trajectory annotations compared to real trajectories. The ego trajectory produced",
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+ "text": "by the Bicycle Model often results in unnatural vehicle orientations, whereas AKM corrects this issue through its learnable parameters, leading to more realistic ego motions.",
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+ "text": "4.3. Interactivity Evaluation",
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+ "text": "To assess our interactivity, we compare statistics including bidirectional interactions and ego speed alteration in scenes from $S_{recon}$ on our synthetic data and real data. Interaction Rate measures the proportion of scenes containing either ego-to-agent or agent-to-ego interactions across all scenes. Ego Speed Alteration quantifies how often the ego vehicle's speed tendency shifts (from acceleration to deceleration or vice versa) within the next $t = 6$ time steps due to interactions with other vehicles.",
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+ "text": "As shown in Fig. 5, our synthetic data exhibits a higher interaction rate compared to the original Waymo dataset. Furthermore, the Ego Speed Alteration metric reveals a longer-tail distribution than real data, indicating greater diversity in ego vehicle speed variations influenced by surrounding agents. This variability helps prevent models from learning flawed patterns, such as consistently accelerating or decelerating that are more prevalent in real-world data. These findings highlight the enhanced diversity and interactivity of our simulation, reinforcing its value as a complementary resource to real-world datasets. Detailed definitions of the Ego Speed Alteration and Interaction Rate metrics are provided in Appendix D.",
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+ "image_caption": [
+ "Figure 5. Our synthetic data shows a higher Interaction Rate and a longer-tail distribution of Ego Speed Alteration, reflecting greater interactivity and diversity in generated traffic flow."
+ ],
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+ "text": "4.4. Closed-Loop Evaluation",
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+ "text": "With SceneCrafter generating realistic sensor data, it also enables interactive closed-loop evaluation, providing a",
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+ "Figure 6. Qualitative comparison from front camera view of the original end-to-end models and those fine-tuned with our synthetic data. The Red car represents ego vehicle controlled by $\\pi_{AD}$ . The red and green arrows respectively indicate the locations where the collision occurs or is avoided. Fine-tuned models offer more reasonable driving behaviors in complex scenarios while models solely trained on real"
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+ "text": "data, showcasing enhanced generalization.",
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+ "page_idx": 7
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+ {
+ "type": "text",
+ "text": "more comprehensive assessment of end-to-end model performance in real driving scenarios. To see how our data contributes to the enhancement of models, we generate three random trajectories per scene with more involved agents than in Sec. 4.2 to construct a synthetic dataset for finetuning VAD and GenAD which are initially trained on $\\mathcal{D}_{train}$ . We initialize each scene with three different seeds and the ego vehicle at two starting positions.",
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+ "text": "Generalizable Capacity. Tab. 5 shows the results of original and fine-tuned models evaluated on unseen scenes from $S_{val}$ . We see that for both VAD and GenAD, the fine-tuned versions achieve a much higher route completion with a lower collision rate with dynamic agents and static map elements. This improvement in closed-loop evaluation further proves the feasibility to improve AD models' generalization ability by simulated data.",
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+ "text": "Qualitative Results. Fig. 6 shows qualitative comparison between original and fine-tuned end-to-end models. The fine-tuned models demonstrate improved performance in various complex driving scenarios, including intersection handling, highway car-following, and lane merging, highlighting their enhanced generalization capabilities.",
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+ "text": "5. Conclusion",
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+ "text": "Summary. In this paper, we introduce SceneCrafter, a unified simulator designed for training and testing vision-based end-to-end autonomous driving models. By leveraging 3DGS, SceneCrafter efficiently generates spatial-",
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+ "table_footnote": [],
+ "table_body": "| Model | Volume | All Test Scenes | Turn Scenes |
| Real | Sim | RC↑ | VC↓ | LCR↓ | RC↑ | VC↓ | LCR↓ |
| VAD | 32k | - | 42.01 | 7.55 | 7.48 | 25.71 | 7.90 | 9.84 |
| 32k | 6k | 53.03 | 3.43 | 6.08 | 34.72 | 3.78 | 8.08 |
| GenAD | 32k | - | 44.87 | 7.62 | 8.50 | 28.47 | 7.23 | 9.25 |
| 32k | 6k | 49.65 | 5.45 | 5.76 | 34.02 | 5.63 | 8.14 |
",
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+ "text": "Table 5. Closed-loop evaluation performance comparison. Metrics include: RC (Route Completion), VC (Vehicle Collision Rate), and LCR (Layout Collision Rate). Models fine-tuned with synthetic data exhibit improved performance in closed-loop evaluation compared to models trained on real data alone.",
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+ "type": "text",
+ "text": "temporally consistent images, which is crucial for both data generation and closed-loop evaluation. To enhance realism, SceneCrafter integrates an adaptive kinematic model and high-fidelity foreground rendering. Additionally, it creates an interactive and responsive environment using heuristic vehicle placement and actor models, enabling real-world-level interactions. Experimental results demonstrate the high fidelity of our framework and highlight its potential to improve the generalization capability of autonomous driving models in real-world scenarios.",
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+ "text": "Limitation and future work. Current types of traffic participants are limited. Future work will focus on increasing the agent diversity, such as cyclist and pedestrian, to further enrich traffic scenarios and make the interaction more challenging. Besides, We aim to enhance this by incorporating lightweight local diffusion models to address unseen scenarios, thereby expanding the rendering range and improving overall rendering quality.",
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+ "text": "References",
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+ },
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+ "end-to-end autonomous driving in nuscenes. arXiv preprint arXiv:2305.10430, 2023. 3",
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+ "[53] Hongyu Zhou, Longzhong Lin, Jiabao Wang, Yichong Lu, Dongfeng Bai, Bingbing Liu, Yue Wang, Andreas Geiger, and Yiyi Liao. Hugsim: A real-time, photo-realistic and closed-loop simulator for autonomous driving. arXiv preprint arXiv:2412.01718, 2024. 2, 3"
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+ "content": "| Name | Real Time | ST Consistency | Real Images | Interactive Traffic Flow | DataGen For E2E |
| CARLA[12] | ✓ | ✓ | ✗ | ✓ | ✓ |
| SUMO[32] | ✓ | ✓ | ✗ | ✓ | ✗ |
| MetaDrive[24] | ✓ | ✓ | ✗ | ✓ | ✓ |
| NeuroNCAP[30] | ✗ | ✓ | ✓ | ✗ | ✗ |
| UniSim[48] | ✗ | ✓ | ✓ | ✗ | ✗ |
| DriveArena[47] | ✗ | ✗ | ✓ | ✓ | ✓ |
| HugSim[53] | ✓ | ✓ | ✓ | ✗ | ✗ |
| Ours | ✓ | ✓ | ✓ | ✓ | ✓ |
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+ "content": "high-quality synthetic data generation. Game engine-based approaches [12, 17, 24, 29, 32, 43] provide extensive customization for scene editing; however, the sim-to-real gap in sensor realism limits their transferability. In contrast, diffusion-based methods [4, 31, 44, 47] enhance image realism but are constrained by high computational and time costs, as well as spatial-temporal inconsistencies in generated images. [53] utilizes Gaussian Splatting for real-time image rendering but lacks reasonable interaction modeling for foreground objects. These limitations hinder current simulators from effectively generating synthetic data or fully evaluating end-to-end models."
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+ "content": "To address these challenges, we present SceneCrafter, a unified simulation framework designed for high-quality synthetic data generation as well as closed-loop evaluation for end-to-end models. Fig. 2 shows the overview of SceneCrafter. It consists of two key components: Scene Controller and Scene Renderer. Scene Controller initializes the simulation with real-world road map data and generates diverse, interactive traffic flows. Scene Renderer then integrates these foreground traffic agents into the reconstructed background, producing high-fidelity images that capture the evolving traffic scenario. Compared with existing methods, SceneCrafter improves realism, interactivity and efficiency to better bridge the gap between simulation and real-world driving. Tab. 1 shows the comparison between our method and existing driving simulators."
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+ "content": "- Enhanced End-to-End Models Generalization. With SceneCrafter, we examine the influence of synthetic data on the training of the models. Our insights contribute to enhancing both model performance and generalization."
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+ "content": "Figure 2. Overview of SceneCrafter framework. Simulation is initialized with world config, map topology and camera config. Scene Controller updates interactive traffic flow, based on which Scene Renderer generates realistic driving scenes. End-to-End Driving Model plans future ego trajectory depending on simulation modes including synthetic data generation and closed-loop evaluation."
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+ "content": "based end-to-end autonomous driving models, demonstrating a power-law relationship between model performance and real training data volume. However, collecting large-scale real-world datasets is costly and time-consuming, highlighting the need for efficient methods to generate high-quality, diverse simulated data. Our work contributes to this direction by providing an approach to generating diverse, high-fidelity simulated data."
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+ "content": "Synthetic Data for Autonomous Driving. Data augmentation is a widely used technique for enhancing model performance across various autonomous driving tasks. Prior works [8, 28, 40, 50] have primarily focused on generating synthetic data to improve 3D perception. [40] enhances 3D object detection by inserting 3D assets into a NeRF-reconstructed background using simple car replacement heuristics, while [28] investigates the real-to-simulated domain gap by evaluating object detection and online mapping performance across different settings. However, limited research has explored the role of synthetic data in vision-based planning. [15] improves semantic segmentation and driving performance of end-to-end models in the CARLA simulator by generating data conditioned on semantic maps. To the best of our knowledge, this is the first study to investigate the impact of synthetic data on imitation learning-based end-to-end models trained on real-world driving data and evaluated in a photorealistic closed-loop environment."
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+ "angle": 0,
+ "content": "End-to-End Model Evaluation. Most open-loop evaluations of end-to-end models compare the model's plan against GT records, such as L2 distance to GT trajectories or collision rates [2, 3, 38]. However, this approach increasingly proves inadequate for assessing planning quality. Studies have identified distribution biases related to ego status [27, 49], leading models to learn shortcuts that fit training data but fail to generalize. In unseen scenarios, these models may struggle with adaptable planning or accurate trajectory prediction [1]. To overcome open-loop limitations, many simulators [12, 17, 24, 29, 32, 43] provide"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "robust closed-loop evaluation environments, though the sim-to-real gap hinders real-world transferability [25, 35]. Recent NeRF-based [30, 48] and diffusion-based [4, 31, 39, 41, 46, 47] methods generate realistic sensor data for closed-loop evaluation but suffer from high computational and time costs for large-scale testing. HugSim [53] reconstructs scenes using 3DGS but lacks reasonable and ego-to-agent interaction. In contrast, our work ensures realistic, interactive and efficient simulation."
+ },
+ {
+ "type": "title",
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+ "content": "3. SceneCrafter Framework"
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+ "type": "text",
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+ "content": "SceneCrafter offers a unified simulation framework supporting both synthetic data generation and closed-loop evaluation for end-to-end autonomous driving models. It consists of two components: Scene Controller and Scene Renderer. Scene Controller manages agents in the environment by dynamically updating their states and behaviors at each simulation step. Scene Renderer generates new driving scenes based on updates from Scene Controller and Driving Planner \\(\\pi\\), ensuring realistic and interactive environments."
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+ "content": "3.1. Scene Controller"
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+ "content": "Scene Controller dynamically updates the states and current behavior of ego based on their past states, ego vehicle's states, planned routes and map topology. It leverages control factors for different behavior modes, ensuring smooth and natural interactions in complex driving environments."
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+ "content": "Heuristic Agent Spawn. The entire scene is initialized based on a configurable world setup \\( W \\), including vehicle max spawn number, behavior modes and types. Scene Controller leverages HD maps derived directly from real-world datasets. By utilizing labeled information within HD maps [38], we build a map topological representation \\( \\mathcal{M} \\), which enables both precise navigation and localization."
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+ "content": "With map topology, we can spawn \\(N\\) agent vehicles by following two types of approaches: route-based and trigger-"
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+ {
+ "type": "image_caption",
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+ "content": "Ego Vehicle"
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+ "content": "Blocking Agent Other Agent"
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+ "type": "image_caption",
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+ "content": "(a) Original"
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+ "content": "(b) Following"
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+ "content": "(c) Left Turn"
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+ "content": "(d)Right Turn"
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+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 3. (a) illustrates the original scenario, where no vehicles are present except ego vehicle, which simply maintains a constant speed. In contrast, (b), (c), and (d) demonstrate how ego vehicle's behavior is altered due to the influence of the blocking agent, while ego vehicle impacts the surrounding agents. Example video is given in supplementary material."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "based. Agents are initialized with states \\((s_j)_{j=1:N}^0\\) and behaviors \\((b_j)_{j=1:N}^0\\)."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "- Route-based. Spawn points with a higher likelihood of interaction with ego vehicle are prioritized as initialization conditions for agents. Then, we generate diverse global trajectories for agent vehicles, ensuring that the routes closely resemble real-world driving patterns."
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+ "type": "text",
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+ "content": "- Trigger-based. By selecting specific points along ego vehicle's trajectory as trigger points, we identify potential spawn points with map topology where agents could interact with ego vehicle. Once ego vehicle reaches a trigger point, the corresponding agent vehicles are activated to execute their trajectories. This approach can facilitate customized safety-critical test scenarios."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "content": "Appendix A explain these approaches in detail."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "Bi-interactive Agent Control. For status and behavior control, we adopt an approach inspired by CARLA [12], incorporating control factors such as speed limits and safe following distances derived from the original scenario. Agents determine driving behaviors \\( b_{j}^{t} \\) based on their interaction with other agents at each time, which establishes a bidirectional interactive relation between ego and agent vehicles. Fig. 3 shows some common interaction scenes. Beyond regular driving scenarios, we also introduce dangerous behavior modes for agent vehicles, which can trigger actions such as lane changes, aggressive overtakes, emergency stops, or disregarding safe distances when interacting with ego vehicle, providing potential for long-tail scenario evaluation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Adaptive Kinematic Model. We propose an Adaptive Kinematic Model (AKM) to refine vehicle control signals, addressing the discrepancy between simulated and real ego dynamics during simulation, which can significantly impact planning [27]. Given front length \\( l_{f} \\) and rear length \\( l_{r} \\), AKM updates vehicle states using Eq. (1)."
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\beta_ {t} = \\arctan \\left(\\frac {l _ {r}}{l _ {f} + l _ {r}} \\tan (\\delta_ {t})\\right), \\quad v _ {t + 1} = v _ {t} + a _ {t} \\Delta t,\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\varphi_ {t + 1} = \\varphi_ {t} + \\frac {v _ {t}}{l _ {f}} \\sin (\\beta_ {t}) \\Delta t, \\quad v _ {u} = (1 - \\boldsymbol {u} _ {\\mathbf {1}}) v _ {t} + \\boldsymbol {u} _ {\\mathbf {1}} v _ {t + 1},\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} x _ {t + 1} = x _ {t} + v _ {u} \\cos (\\varphi_ {t} + \\boldsymbol {u} _ {\\boldsymbol {2}} \\cdot \\beta_ {t}) \\Delta t, \\\\ y _ {t + 1} = y _ {t} + v _ {u} \\sin \\left(\\varphi_ {t} + \\boldsymbol {u} _ {\\boldsymbol {2}} \\cdot \\beta_ {t}\\right) \\Delta t. \\tag {1} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(\\beta_{t}\\) is the slip angle, \\(v_{t}\\) is the vehicle velocity, \\(\\varphi_{t}\\) is the yaw angle, \\(\\delta\\) is the steering angle and \\(x_{t}, y_{t}\\) represent the vehicle position. Compared with standard bicycle model, it incorporates two learnable parameters, \\(u_{1}\\) and \\(u_{2}\\), estimated from real-world IMU sensor data. These parameters help prevent unrealistic displacements by adjusting velocity and orientation dynamically. By ensuring smoother and more natural vehicle movement, this approach enhances the realism and continuity of the simulation environment."
+ },
+ {
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+ "bbox": [
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+ "content": "3.2. Scene Renderer"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Scene Renderer generates high-fidelity driving scenes that reflect dynamic traffic flows with spatial-temporal consistency. It builds a Model Library using Gaussian Splatting for editable background and dynamic foreground models. We also propose ground height estimation and directional shadow rendering to enhance rendering realism. Figure 1 demonstrates example images from Scene Renderer."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Gaussian-Splatting-Based Model Library. Model library consists of two components: background model and foreground model, both are built based on Gaussian Splatting. For background, we train models by Street Gaussians [39] with only static elements retained to provide a stable background free from motion artifacts and allow for clean integration of dynamic foreground models. For foreground, due to the limited available angles of vehicles in the original scenario, we construct our virtual vehicle assets with BlenderNeRF [33] and 3DRealCar [13] to build foreground model libraries through training with 3DGS. The explicit nature of Gaussian Splatting allows direct editing of the scene using models from the library. Detailed construction steps are provided in Appendix B."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Ground Height Estimation. To prevent artifacts from sinking into or floating above the ground in environments with large elevation variations, we propose learning a global ground model defined as \\(\\hat{z} = f(x,y)\\). Inspired by [11], we extract ground LiDAR points from each frame using RANSAC [14] and fit a ground model for the entire scene, implemented as a three-layer MLP, to predict the z-axis offset during object placement. The loss is designed as follows to penalize less those LiDAR points above the ground:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {h e i g h t}} (\\hat {z}, z) = \\left\\{ \\begin{array}{l l} (\\hat {z} - z) ^ {2} & \\hat {z} > z \\\\ \\operatorname {H u b e r} (\\hat {z}, z) & \\hat {z} \\leq z \\end{array} \\right. \\tag {2}\n\\]"
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "Directional Shadow Rendering. To enhance the realism of foreground vehicles appearance in the scene, we generate"
+ },
+ {
+ "type": "page_number",
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+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "vehicle shadow 3DGS models in multiple directions based on the Gaussian models from the foreground library. For each scene, we pre-estimate the global illumination based on the images from the original dataset as following:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n1 = \\frac {\\left[ G _ {x} \\left(p ^ {*}\\right) , G _ {y} \\left(p ^ {*}\\right) , - 1 \\right] ^ {\\top}}{\\sqrt {G _ {x} ^ {2} \\left(p ^ {*}\\right) + G _ {y} ^ {2} \\left(p ^ {*}\\right) + 1}} \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(p^* = \\arg \\max_p \\| \\nabla I(p) \\|_2\\) is the point with maximum gradient magnitude, \\(\\nabla I(p) = [G_x, G_y]^\\top\\) denotes the Sobel gradient after Gaussian blur. During simulation, the global illumination and the current heading angle decide shadow model selection, which is combined with the original model for rendering. A visual comparison of foreground objects with shadow rendering and ground model placement is provided in Fig. 11 in the supplementary."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Composition Rendering. Scene Renderer determines ego vehicle's viewpoint by camera configuration. Based on the agent vehicle poses provided by Scene Controller, foreground models are integrated into the background model. Ego vehicle's pose is then used to compute the camera's extrinsic parameters for rendering driving images. Utilizing composite Gaussian model with definite, precise control on spatial positions of foreground objects and overall appearance, our rendered images maintain spatial-temporal consistency. This ensures both the reliability of the generated data and the full controllability required for closed-loop evaluation. Detailed demonstration for spatial-temporal consistency can be found in Appendix F."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.3. Simulation Modes"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "SceneCrafter offers two simulation modes: synthetic data generation for realistic training and closed-loop simulation for interactive model evaluation. Algorithm 1 outlines the simulation process for each mode."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "Synthetic Data Generation. To generate training datasets for end-to-end models, this mode employs an expert planner \\(\\pi_{exp}\\) to control the ego vehicle while dynamically updating surrounding agents. Ego vehicle follows its original trajectory from the real dataset while adjusting its pace based on different driving scenarios to maintain consistent rendering quality. At each simulation step, our Scene Controller dynamically updates the status \\(s_j^t\\) and behavior \\(b_j^t\\) of surrounding agents. The policy \\(\\pi_{exp}\\) generates control signals using privileged information \\((s_{ego}^t,(s_j)^t_{j = 1:N},\\mathcal{M})\\) to ensure safe and natural driving behavior. The kinematic model \\(KM\\) then applies these control signals to refine ego vehicle's position and status for the Scene Renderer to generate new sensor observations. This cycle continues until either ego vehicle times out or reaches the target point."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Closed-Loop Simulation. To evaluate end-to-end models in realistic interactive environments, the closed-loop mode replaces the expert planner with a learned policy \\(\\pi_{AD}\\)."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Compared with data generation mode, the policy takes sensor inputs, control command and ego status as input to provide future action. The control command \\( c \\) is generated from the original ego trajectory plan from real world data."
+ },
+ {
+ "type": "code_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Algorithm 1: SceneCrafter Workflow"
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+ "type": "algorithm",
+ "bbox": [
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+ "angle": 0,
+ "content": "Input : World Setup W, Number of Agents N, Simulation Mode M ∈ {SYN, CL}, Driving Planner π, Kinematic Model KM Initialize: Map Topology M, Ego Initial State \\( s_{ego}^0 \\), Agents Initial States \\( (s_j)_{j=1:N}^0 \\), Agents Initial Behaviors \\( (b_j)_{j=1:N}^0 \\), Sensor Images \\( (I_k)_{j=1:C}^0 \\) Output : Driving Simulation Log \\( \\tilde{\\mathcal{D}} \\) \\( \\{(s_j)_{j=1:N}^{1:T_{max}}, (I_k)_{j=1:C}^{1:T_{max}}, s_{ego}^{1:T_{max}}, \\mathcal{M}\\} \\) while t < Tmax do for j ← 1 to N do \\( s_j^{t+1}, b_j^{t+1} \\gets \\text{SceneController}(s_{ego}^t, (s_j)^t_{j=1:N}, b_j^t, \\mathcal{M}) \\) if M = SYN then \\( a_{ego}^{t+1} \\gets \\pi_{\\text{exp}}(s_{ego}^t, (s_j + 1)^t_{j=1:N}, \\mathcal{M}); // \\text{Synthetic data generation} \\) else \\( a_{ego}^{t+1} \\gets \\pi_{\\text{AD}}(s_{ego}^t, (I_k)^t_{k=1:C}, c); // \\text{Closed-loop evaluation} \\) \\( s_{ego}^{t+1} \\gets \\text{KM}(a_{ego}^{t+1}, s_{ego}^t); (I_k)^{t+1}_{k=1:C} \\gets \\text{SceneRenderer}(s_{ego}^{t+1}, (s_j)^{t+1}_{j=1:N}) t \\gets t + 1 \\)"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4. Experiment"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In Section 4.1, we explain our simulation setups for Scene Controller and Scene Renderer. In Section 4.2, we share quantitative results that assess how well simulated data can replace real data, focusing on realism from the perspective of end-to-end autonomous driving models. Note that we do not compare our simulator with existing photorealistic simulators because they are unable to generate synthetic driving logs that include both sensor inputs and ego dynamics. Detailed justification are provided in Appendix E. Section 4.3 evaluates interactivity, while Section 4.4 assesses closed-loop performance, highlighting improvements in generalization and robustness. Additional runtime efficiency comparisons are provided in Appendix C."
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+ {
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+ "angle": 0,
+ "content": "4.1. Simulation Settings"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Dataset. Our simulator is based on Waymo Open Dataset [38], which is split according to its official con"
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+ [
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figuration into 797 training scenes and 200 validation scenes. These scenes and their corresponding data samples are denoted as \\((S_{train},\\mathcal{D}_{train})\\) for the training set and \\((S_{val},\\mathcal{D}_{val})\\) for the validation set. For data generation, we select 60 representative scenes from the training set, covering both suburban and urban environments. These scenes include a variety of road types including straight roads and intersections, and span different weather conditions. The indices of these selected scenes are denoted as \\(S_{recon}\\subset S_{train}\\), while the rest indices are denoted as \\(S_{recon}^{c}\\). In addition, for closed-loop evaluation, we reconstruct 30 scenes from \\(S_{val}\\) to assess the generalization capability of end-to-end models."
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+ "bbox": [
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+ "angle": 0,
+ "content": "Scene Controller and Scene Renderer Setups. For Scene Controller, the updating frequency of vehicles' status in the scene is set to \\(10\\mathrm{Hz}\\) to ensure more precise control. The rendering frequency of Scene Renderer is set to \\(2\\mathrm{Hz}\\) following the input frequency of end-to-end models [20, 21, 51] previously trained on nuScenes [2]."
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+ "bbox": [
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+ "content": "End-to-End Models and Evaluation Metrics. We select VAD [21] and its enhanced version, GenAD [51], as our end-to-end models due to their efficiency and effectiveness. Both methods share the same auxiliary tasks: 3D Object Detection (3DOD), Motion Prediction and Online Map Segmentation (MapSeg). For open-loop evaluation, we assess planning performance using the L2 displacement error and collision rate, following the standard end-to-end benchmark [21, 51]. In closed-loop evaluation, we adopt key metrics from Carla [12], including route completion (RC), vehicle collision rate (VCR), and layout collision rate (LCR). Detailed formulas are provided in Appendix G."
+ },
+ {
+ "type": "title",
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+ "content": "4.2. Simulation Realism Evaluation"
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+ "bbox": [
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+ "angle": 0,
+ "content": "To assess the reliability of SceneCrafter, we examine the real-simulation gap between real data and generated data from the perspective of end-to-end models in an open-loop manner to show that SceneCrafter can achieve real kinematic controls and high rendering quality for synthetic data."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "4.2.1. Data Augmentation with Synthetic Data"
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+ "content": "To demonstrate the complementary benefits of our synthetic data, we train VAD with a mix of real-world and simulated data in an incremental learning setup. This enables us to assess whether the model surpasses one trained solely on real data, validating the fidelity of our synthetic data. Specifically, we construct two real-world training sets: \\(\\mathcal{D}_{recon}^{c}\\) and driving logs from 200 sampled scenes in \\(S_{recon}^{c}\\), forming a smaller-scale real training set \\(D_{200}\\). We generate one driving log per scene from \\(S_{recon}\\) to create the synthetic training set \\(\\tilde{\\mathcal{D}}_{train}\\) with around 2,000 samples. End-to-end models are evaluated on all samples \\(D_{val}\\) from \\(S_{val}\\)."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Tab. 2 presents the quantitative results. The inclusion of synthetic data significantly improves planning performance"
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+ "content": "| Setting | Volume | Planning L2 (m) ↓ | CR ↓ |
| Real | Sim | 1s | 2s | 3s | Avg | 1s | 2s | 3s | Avg |
| D200 | 8k | - | 0.61 | 1.31 | 2.24 | 1.39 | 0.34 | 0.36 | 0.86 | 0.52 |
| D200 + Dtr | 8k | 2k | 0.48 | 1.09 | 1.99 | 1.18 | 0.28 | 0.32 | 0.75 | 0.45 |
| Dreccon | 28k | - | 0.43 | 1.02 | 1.82 | 1.09 | 0.21 | 0.27 | 0.47 | 0.32 |
| Dreccon + Dtr | 28k | 2k | 0.38 | 0.94 | 1.79 | 1.04 | 0.08 | 0.14 | 0.53 | 0.25 |
"
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+ "type": "table_caption",
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+ "content": "Table 2. Performance comparison of data augmentation with synthetic samples \\(\\hat{\\mathcal{D}}_{tr}\\) using different real data amounts \\(\\mathcal{D}_{200}\\) and \\(\\mathcal{D}_{\\text{recon}}^c\\). The inclusion of synthetic data improves planning performance on both settings."
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "when the real training set is small, demonstrating its potential to supplement real-world data. However, its impact is relatively marginal when the original training set is large. We attribute this to the fact that the Waymo validation set primarily consists of normal driving scenarios, such as cruising straightly in a scenario with fewer interaction with other agents, which are already well covered by large-scale real-world training data. This limitation of real-world open-loop evaluation benchmarks is also discussed in [27]."
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+ "content": "4.2.2. Inference with E2E Models as Proxy Evaluators"
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+ "content": "Unlike most related works that primarily focus on image quality comparison for realism validation, we approach the problem by using VAD trained on real-world samples \\(\\mathcal{D}_{recon}^{c}\\) from scenes \\(S_{recon}^{c}\\) as a zero-shot proxy evaluator. This model is assumed to exhibit certain perception ability and reasonable coherence with the real world ground truth trajectory after large-scale training. We then evaluate the model on both real data \\(\\mathcal{D}_{recon}\\) and synthetic data \\(\\tilde{\\mathcal{D}}_{recon}\\) generated from scenes \\(S_{recon}\\), comparing their performance on all autonomous driving tasks and assessing the output trajectory of end-to-end models with the generated trajectory annotations by the simulator. This comparison aims to investigate the realism of the generated data from both the sensor input and vehicle kinematics perspectives. Specifically, we consider the following settings:"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- Real Data: This setting uses real-world driving logs from the scenes \\(S_{\\text{recon}}\\) in the Waymo dataset. It includes actual sensor images and ego IMU data as inputs for VAD, along with annotated labels for other agents."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- VirVehicle Rep.: This setting uses real ego IMU data and annotated agents' labels from scenes \\( S_{recon} \\), but replaces the real sensor images with rendered images generated by Scene Renderer. The images are generated using the original camera configurations, with real dynamic foreground objects replaced by assets from the virtual vehicle library [33], without adding shadows."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- 3DRealCar Rep.: This setting mirrors VirVehicle Rep. but replaces real foreground objects with 3DRealCar[13] assets and adding directional shadow during rendering."
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+ "bbox": [
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+ "angle": 0,
+ "content": "- Sim Data w/ BM: This setting generates synthetic data with traffic flow controlled by Scene Controller, using a vanilla Bicycle Model as the kinematic model. The num"
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+ "bbox": [
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+ "angle": 0,
+ "content": "| Setting | Volume | Rendering Config | Prediction (Car) | 3DOD↑ | MapSeg↑ |
| Car Lib | Shadow | EPA ↑ | ADE ↓ | FDE ↓ | Car AP | AP 0.5 | AP 1.0 | AP 1.5 |
| Real Data | 2k | - | - | 0.30 | 0.71 | 0.96 | 44.1 | 0.245 | 0.482 | 0.644 |
| VirVehicle Rep. | 2k | Virtual | × | 0.25 | 0.26 | 1.02 | 38.4 | 0.227 | 0.476 | 0.633 |
| 3DRealCar Rep. | 2k | 3DRealCar | ✓ | 0.25 | 0.77 | 1.01 | 39.6 | 0.212 | 0.467 | 0.622 |
"
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+ "bbox": [
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+ "content": "Table 3. Perception and prediction performance comparison with VAD trained on \\( \\mathcal{D}_{recon}^{c} \\) over real and synthetic data. Car Lib represents the foreground object source, and Shadow denotes whether shadow rendering is applied. 3DRealCar Rep. achieves a higher detection score compared with VirVehicle Rep., demonstrating the enhanced realism of our foreground rendering."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Setting | Volume | Planning L2 (m)↓ | Prediction (Car) | MapSeg↑ |
| 1s | 2s | 3s | EPA ↑ | ADE ↓ | FDE ↓ | AP 0.5 | AP 1.0 | AP 1.5 |
| Real Data | 2k | 0.39 | 0.94 | 1.72 | 0.30 | 0.71 | 0.96 | 0.245 | 0.482 | 0.644 |
| Sim Data w/ BM | 2k | 0.47 | 1.24 | 2.43 | 0.27 | 0.80 | 1.10 | 0.170 | 0.435 | 0.574 |
| Sim Data w/ AKM (Ours) | 2k | 0.38 | 1.04 | 2.06 | 0.28 | 0.77 | 0.92 | 0.185 | 0.453 | 0.590 |
"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Inference results on Waymo reconstructed scenes with VAD trained on \\( {\\mathcal{D}}_{\\text{recon }}^{c} \\) . Our Adaptive Kinematic Model (AKM) produces ego trajectories closer to planning results than the Bicycle Model (BM), leading to improved prediction and perception performance."
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+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
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+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. (a) and (b) show that ego trajectories generated by AKM are smoother and more realistic than those by BM. (c) and (d) illustrate that end-to-end planning result deviates more from the simulated GT trajectory with AKM than with BM, which indicates AKM aligns better with real world dynamics. The color bar indicates vehicle velocity norms."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.104,
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+ "angle": 0,
+ "content": "ber of agents is set to match the average number of dynamic foreground objects in the original scenes."
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "- Sim Data w/ AKM: This setting generates synthetic data similar to Sim Data w/ BM, but uses AKM as the kinematic model instead of the vanilla Bicycle Model."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
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+ 0.809
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+ "angle": 0,
+ "content": "Tab. 3 presents the realism assessment of images generated by Scene Renderer. Notably, replacing all foreground objects with reconstructed 3D assets and rendered background model results in only a minor decline in perception performance (3DOD and MapSeg), demonstrating the high fidelity of our rendered images. This performance gap is primarily due to an increase in false positive bounding boxes, which is less critical than false negatives. Additionally, foreground objects from 3DRealCar, which include added shadows, achieve higher detection scores compared to virtual vehicles, further validating their realism."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Regarding the kinematic model, Tab. 4 shows that the ego trajectory generated by the Adaptive Kinematic Model (AKM) aligns more closely with planning results than that generated by the simpler Bicycle Model. Fig. 4 further illustrates the differences in turning trajectory annotations compared to real trajectories. The ego trajectory produced"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.32,
+ 0.907,
+ 0.366
+ ],
+ "angle": 0,
+ "content": "by the Bicycle Model often results in unnatural vehicle orientations, whereas AKM corrects this issue through its learnable parameters, leading to more realistic ego motions."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.3. Interactivity Evaluation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.395,
+ 0.907,
+ 0.529
+ ],
+ "angle": 0,
+ "content": "To assess our interactivity, we compare statistics including bidirectional interactions and ego speed alteration in scenes from \\( S_{recon} \\) on our synthetic data and real data. Interaction Rate measures the proportion of scenes containing either ego-to-agent or agent-to-ego interactions across all scenes. Ego Speed Alteration quantifies how often the ego vehicle's speed tendency shifts (from acceleration to deceleration or vice versa) within the next \\( t = 6 \\) time steps due to interactions with other vehicles."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.531,
+ 0.909,
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+ "angle": 0,
+ "content": "As shown in Fig. 5, our synthetic data exhibits a higher interaction rate compared to the original Waymo dataset. Furthermore, the Ego Speed Alteration metric reveals a longer-tail distribution than real data, indicating greater diversity in ego vehicle speed variations influenced by surrounding agents. This variability helps prevent models from learning flawed patterns, such as consistently accelerating or decelerating that are more prevalent in real-world data. These findings highlight the enhanced diversity and interactivity of our simulation, reinforcing its value as a complementary resource to real-world datasets. Detailed definitions of the Ego Speed Alteration and Interaction Rate metrics are provided in Appendix D."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. Our synthetic data shows a higher Interaction Rate and a longer-tail distribution of Ego Speed Alteration, reflecting greater interactivity and diversity in generated traffic flow."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Closed-Loop Evaluation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "With SceneCrafter generating realistic sensor data, it also enables interactive closed-loop evaluation, providing a"
+ },
+ {
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+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Figure 6. Qualitative comparison from front camera view of the original end-to-end models and those fine-tuned with our synthetic data. The Red car represents ego vehicle controlled by \\(\\pi_{AD}\\). The red and green arrows respectively indicate the locations where the collision occurs or is avoided. Fine-tuned models offer more reasonable driving behaviors in complex scenarios while models solely trained on real"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.459,
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+ "angle": 0,
+ "content": "data, showcasing enhanced generalization."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.474,
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+ 0.594
+ ],
+ "angle": 0,
+ "content": "more comprehensive assessment of end-to-end model performance in real driving scenarios. To see how our data contributes to the enhancement of models, we generate three random trajectories per scene with more involved agents than in Sec. 4.2 to construct a synthetic dataset for finetuning VAD and GenAD which are initially trained on \\(\\mathcal{D}_{train}\\). We initialize each scene with three different seeds and the ego vehicle at two starting positions."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.483,
+ 0.715
+ ],
+ "angle": 0,
+ "content": "Generalizable Capacity. Tab. 5 shows the results of original and fine-tuned models evaluated on unseen scenes from \\( S_{val} \\). We see that for both VAD and GenAD, the fine-tuned versions achieve a much higher route completion with a lower collision rate with dynamic agents and static map elements. This improvement in closed-loop evaluation further proves the feasibility to improve AD models' generalization ability by simulated data."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Qualitative Results. Fig. 6 shows qualitative comparison between original and fine-tuned end-to-end models. The fine-tuned models demonstrate improved performance in various complex driving scenarios, including intersection handling, highway car-following, and lane merging, highlighting their enhanced generalization capabilities."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Summary. In this paper, we introduce SceneCrafter, a unified simulator designed for training and testing vision-based end-to-end autonomous driving models. By leveraging 3DGS, SceneCrafter efficiently generates spatial-"
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.515,
+ 0.465,
+ 0.91,
+ 0.565
+ ],
+ "angle": 0,
+ "content": "| Model | Volume | All Test Scenes | Turn Scenes |
| Real | Sim | RC↑ | VC↓ | LCR↓ | RC↑ | VC↓ | LCR↓ |
| VAD | 32k | - | 42.01 | 7.55 | 7.48 | 25.71 | 7.90 | 9.84 |
| 32k | 6k | 53.03 | 3.43 | 6.08 | 34.72 | 3.78 | 8.08 |
| GenAD | 32k | - | 44.87 | 7.62 | 8.50 | 28.47 | 7.23 | 9.25 |
| 32k | 6k | 49.65 | 5.45 | 5.76 | 34.02 | 5.63 | 8.14 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "Table 5. Closed-loop evaluation performance comparison. Metrics include: RC (Route Completion), VC (Vehicle Collision Rate), and LCR (Layout Collision Rate). Models fine-tuned with synthetic data exhibit improved performance in closed-loop evaluation compared to models trained on real data alone."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.638,
+ 0.907,
+ 0.788
+ ],
+ "angle": 0,
+ "content": "temporally consistent images, which is crucial for both data generation and closed-loop evaluation. To enhance realism, SceneCrafter integrates an adaptive kinematic model and high-fidelity foreground rendering. Additionally, it creates an interactive and responsive environment using heuristic vehicle placement and actor models, enabling real-world-level interactions. Experimental results demonstrate the high fidelity of our framework and highlight its potential to improve the generalization capability of autonomous driving models in real-world scenarios."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.789,
+ 0.909,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Limitation and future work. Current types of traffic participants are limited. Future work will focus on increasing the agent diversity, such as cyclist and pedestrian, to further enrich traffic scenarios and make the interaction more challenging. Besides, We aim to enhance this by incorporating lightweight local diffusion models to address unseen scenarios, thereby expanding the rendering range and improving overall rendering quality."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "References"
+ },
+ {
+ "type": "ref_text",
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+ 0.483,
+ 0.241
+ ],
+ "angle": 0,
+ "content": "[1] Mohammadhossein Bahari, Saeed Saadatnejad, Ahmad Rahimi, Mohammad Shaverdikondori, Amir Hossein Shahidzadeh, Seyed-Mohsen Moosavi-Dezfooli, and Alexandre Alahi. Vehicle trajectory prediction works, but not everywhere. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17123-17133, 2022. 3"
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+# Unraveling the Effects of Synthetic Data on End-to-End Autonomous Driving
+
+Junhao Ge $^{1*}$ Zuhong Liu $^{1,5*}$ Longteng Fan $^{1*}$ Yifan Jiang $^{1*}$
+
+Jiaqi Su1 Yiming Li2 Zhejun Zhang3 Siheng Chen1,4
+
+$^{1}$ Shanghai Jiao Tong University $^{2}$ New York University $^{3}$ ETH Zurich
+
+$^{4}$ Shanghai Artificial Intelligence Laboratory $^{5}$ SJTU Paris Elite Institute of Technology
+
+$^{1}$ {cancaries, albert.liu, michaelfan, fiona.jiang, sjq2022, sihengc} $@$ sjtu.edu.cn
+
+2{yimingli}@nyu.edu 3{zhejun.zhang} $@$ vision.ee.ethz.ch
+
+
+Side Left
+Figure 1. SceneCrafter is a high-fidelity simulator capable of generating realistic synthetic driving data and providing an effective closed-loop evaluation for end-to-end autonomous driving models. Given real-world datasets, SceneCrafter can reconstruct dynamic driving scenes and incorporate interactive traffic flows to generate novel, realistic, and consistent scenarios.
+
+# Abstract
+
+End-to-end (E2E) autonomous driving (AD) models require diverse, high-quality data to perform well across various driving scenarios. However, collecting large-scale real-world data is expensive and time-consuming, making high-fidelity synthetic data essential for enhancing data diversity and model robustness. Existing driving simulators have significant limitations for synthetic data generation: game-engine-based simulators struggle to produce realistic sensor data, while NeRF-based and diffusion-based methods face efficiency challenges. Additionally, recent simulators designed for closed-loop evaluation provide limited interaction with other vehicles, failing to simulate complex real-world traffic dynamics. To address these issues, we introduce SceneCrafter, a realistic, interactive, and efficient AD simulator based on 3D Gaussian Splatting (3DGS). SceneCrafter not only efficiently generates realistic driving logs across diverse traffic scenarios but also enables robust closed-loop evaluation of end-to-end models. Experimental results demonstrate that SceneCrafter serves as both a
+
+reliable evaluation platform and a efficient data generator that significantly improves end-to-end model generalization. Our code will be released at https://github.com/cancaries/SceneCrafter.
+
+# 1. Introduction
+
+Recently, autonomous driving (AD) has gradually progressed from modular paradigms [7, 16, 22, 42] to end-to-end models [5, 6, 9, 10, 19-21, 36, 37, 51], which learn from sensor data and ego status to plan future motion. Most end-to-end models are fundamentally data-driven[52], where scenario diversity and vehicle trajectory distributions plays a decisive role in model effectiveness. However, gathering extensive, high quality and wide coverage real data for driving scenarios is not only time-consuming but also costly.
+
+Given these constraints, generating high-fidelity, diverse synthetic data is essential for complementing real-world datasets, improving the robustness of end-to-end models. Nonetheless, current closed-loop simulators struggle to balance realism, efficiency, and interaction modeling, limiting
+
+| Name | Real Time | ST Consistency | Real Images | Interactive Traffic Flow | DataGen For E2E |
| CARLA[12] | ✓ | ✓ | ✗ | ✓ | ✓ |
| SUMO[32] | ✓ | ✓ | ✗ | ✓ | ✗ |
| MetaDrive[24] | ✓ | ✓ | ✗ | ✓ | ✓ |
| NeuroNCAP[30] | ✗ | ✓ | ✓ | ✗ | ✗ |
| UniSim[48] | ✗ | ✓ | ✓ | ✗ | ✗ |
| DriveArena[47] | ✗ | ✗ | ✓ | ✓ | ✓ |
| HugSim[53] | ✓ | ✓ | ✓ | ✗ | ✗ |
| Ours | ✓ | ✓ | ✓ | ✓ | ✓ |
+
+Table 1. Comparison of existing and proposed simulation platforms for autonomous driving. ST Consistency represents Spatial-Temporal Consistency. DataGen For E2E represents Data Generation for end-to-end models.
+
+high-quality synthetic data generation. Game engine-based approaches [12, 17, 24, 29, 32, 43] provide extensive customization for scene editing; however, the sim-to-real gap in sensor realism limits their transferability. In contrast, diffusion-based methods [4, 31, 44, 47] enhance image realism but are constrained by high computational and time costs, as well as spatial-temporal inconsistencies in generated images. [53] utilizes Gaussian Splatting for real-time image rendering but lacks reasonable interaction modeling for foreground objects. These limitations hinder current simulators from effectively generating synthetic data or fully evaluating end-to-end models.
+
+To address these challenges, we present SceneCrafter, a unified simulation framework designed for high-quality synthetic data generation as well as closed-loop evaluation for end-to-end models. Fig. 2 shows the overview of SceneCrafter. It consists of two key components: Scene Controller and Scene Renderer. Scene Controller initializes the simulation with real-world road map data and generates diverse, interactive traffic flows. Scene Renderer then integrates these foreground traffic agents into the reconstructed background, producing high-fidelity images that capture the evolving traffic scenario. Compared with existing methods, SceneCrafter improves realism, interactivity and efficiency to better bridge the gap between simulation and real-world driving. Tab. 1 shows the comparison between our method and existing driving simulators.
+
+To achieve realistic simulation, we enhance ego agent dynamics, vehicle appearance and vehicle placement in images through several innovations. To capture real agents movement, our Scene Controller integrates an adaptive kinematic model trained on real-world IMU sensor data, ensuring realistic vehicle displacement and dynamics. Additionally, our Scene Renderer incorporates global illumination estimation to generate directional shadow Gaussian models, enhancing sensor image realism in dynamic scenes. To improve spatial modeling accuracy, we introduce an optimization-based ground height estimation algorithm that correct z-axis map offsets based on LiDAR points, ensuring precise vehicle positioning and rendering consistency.
+
+Unlike existing closed-loop simulators [53] that focus
+
+on agent-to-ego interactions, SceneCrafter models bidirectional interactions between the ego vehicle and surrounding agents in Scene Controller. By dynamically updating agent behaviors through heuristic vehicle placement and actor models, it generates diverse and reasonable driving patterns to improve end-to-end model generalization.
+
+Beides, SceneCrafter leverages 3D Gaussian Splatting (3DGS) to model dynamic driving scenes. It achieves significantly higher efficiency and lower computational costs compared to NeRF-based [30, 48], or diffusion-based [4, 31, 44, 47] approaches, allowing the potential for large-scale synthetic data generation and evaluation.
+
+Our experiments demonstrate that the synthetic data generated by SceneCrafter closely matches real-world sensor images and vehicle dynamics from the perspective of end-to-end models. We also assess the interactivity and efficiency of our method. Furthermore, we show that augmenting real-world datasets with our synthetic data enhances model generalization in interactive, closed-loop driving environments, achieving $18\%$ higher Route Completion rate. In summary, our main contributions are as follows:
+
+- Efficient and Reliable Synthetic Data Generation. SceneCrafter achieves superior efficiency and realism based on 3D Gaussian Splitting (3DGS). This approach ensures efficient and reliable synthetic data production.
+- Interactive Closed-Loop Simulation Platform. SceneCrafter provides an interactive simulation environment with precise control over agent vehicles which allows comprehensive assessment of model robustness across diverse traffic interactions.
+- Enhanced End-to-End Models Generalization. With SceneCrafter, we examine the influence of synthetic data on the training of the models. Our insights contribute to enhancing both model performance and generalization.
+
+# 2. Related Work
+
+End-to-End Model. Recent attention in AD has shifted from modular paradigms [7, 16, 22, 42] to end-to-end solutions [5, 6, 9, 10, 19–21, 36, 37, 51]. These models integrate perception [26], prediction [18], and planning [34] into a single framework, addressing issues such as information loss, error accumulation, and feature misalignment between modules [20]. Vision-based end-to-end models [19–21, 51] trained on real-world datasets attempt to extract more valuable information to enhance model performance. UniAD [20] integrates information from preceding modules to achieve significant improvements in planning performance. VAD [21] leverages the potential of vectorized scene representation, simplifying the input data and makes the model more efficient and scalable. GenAD [51] enhances the multi-modality of ego vehicle trajectories using a generative approach, enabling more flexible motion planning. [52] identifies scaling laws in imitation learning
+
+
+Figure 2. Overview of SceneCrafter framework. Simulation is initialized with world config, map topology and camera config. Scene Controller updates interactive traffic flow, based on which Scene Renderer generates realistic driving scenes. End-to-End Driving Model plans future ego trajectory depending on simulation modes including synthetic data generation and closed-loop evaluation.
+
+based end-to-end autonomous driving models, demonstrating a power-law relationship between model performance and real training data volume. However, collecting large-scale real-world datasets is costly and time-consuming, highlighting the need for efficient methods to generate high-quality, diverse simulated data. Our work contributes to this direction by providing an approach to generating diverse, high-fidelity simulated data.
+
+Synthetic Data for Autonomous Driving. Data augmentation is a widely used technique for enhancing model performance across various autonomous driving tasks. Prior works [8, 28, 40, 50] have primarily focused on generating synthetic data to improve 3D perception. [40] enhances 3D object detection by inserting 3D assets into a NeRF-reconstructed background using simple car replacement heuristics, while [28] investigates the real-to-simulated domain gap by evaluating object detection and online mapping performance across different settings. However, limited research has explored the role of synthetic data in vision-based planning. [15] improves semantic segmentation and driving performance of end-to-end models in the CARLA simulator by generating data conditioned on semantic maps. To the best of our knowledge, this is the first study to investigate the impact of synthetic data on imitation learning-based end-to-end models trained on real-world driving data and evaluated in a photorealistic closed-loop environment.
+
+End-to-End Model Evaluation. Most open-loop evaluations of end-to-end models compare the model's plan against GT records, such as L2 distance to GT trajectories or collision rates [2, 3, 38]. However, this approach increasingly proves inadequate for assessing planning quality. Studies have identified distribution biases related to ego status [27, 49], leading models to learn shortcuts that fit training data but fail to generalize. In unseen scenarios, these models may struggle with adaptable planning or accurate trajectory prediction [1]. To overcome open-loop limitations, many simulators [12, 17, 24, 29, 32, 43] provide
+
+robust closed-loop evaluation environments, though the sim-to-real gap hinders real-world transferability [25, 35]. Recent NeRF-based [30, 48] and diffusion-based [4, 31, 39, 41, 46, 47] methods generate realistic sensor data for closed-loop evaluation but suffer from high computational and time costs for large-scale testing. HugSim [53] reconstructs scenes using 3DGS but lacks reasonable and ego-to-agent interaction. In contrast, our work ensures realistic, interactive and efficient simulation.
+
+# 3. SceneCrafter Framework
+
+SceneCrafter offers a unified simulation framework supporting both synthetic data generation and closed-loop evaluation for end-to-end autonomous driving models. It consists of two components: Scene Controller and Scene Renderer. Scene Controller manages agents in the environment by dynamically updating their states and behaviors at each simulation step. Scene Renderer generates new driving scenes based on updates from Scene Controller and Driving Planner $\pi$ , ensuring realistic and interactive environments.
+
+# 3.1. Scene Controller
+
+Scene Controller dynamically updates the states and current behavior of ego based on their past states, ego vehicle's states, planned routes and map topology. It leverages control factors for different behavior modes, ensuring smooth and natural interactions in complex driving environments.
+
+Heuristic Agent Spawn. The entire scene is initialized based on a configurable world setup $W$ , including vehicle max spawn number, behavior modes and types. Scene Controller leverages HD maps derived directly from real-world datasets. By utilizing labeled information within HD maps [38], we build a map topological representation $\mathcal{M}$ , which enables both precise navigation and localization.
+
+With map topology, we can spawn $N$ agent vehicles by following two types of approaches: route-based and trigger-
+
+
+Ego Vehicle
+Blocking Agent Other Agent
+(a) Original
+
+
+
+
+(c) Left Turn
+Figure 3. (a) illustrates the original scenario, where no vehicles are present except ego vehicle, which simply maintains a constant speed. In contrast, (b), (c), and (d) demonstrate how ego vehicle's behavior is altered due to the influence of the blocking agent, while ego vehicle impacts the surrounding agents. Example video is given in supplementary material.
+
+
+(b) Following
+(d)Right Turn
+
+based. Agents are initialized with states $(s_j)_{j=1:N}^0$ and behaviors $(b_j)_{j=1:N}^0$ .
+
+- Route-based. Spawn points with a higher likelihood of interaction with ego vehicle are prioritized as initialization conditions for agents. Then, we generate diverse global trajectories for agent vehicles, ensuring that the routes closely resemble real-world driving patterns.
+- Trigger-based. By selecting specific points along ego vehicle's trajectory as trigger points, we identify potential spawn points with map topology where agents could interact with ego vehicle. Once ego vehicle reaches a trigger point, the corresponding agent vehicles are activated to execute their trajectories. This approach can facilitate customized safety-critical test scenarios.
+
+Appendix A explain these approaches in detail.
+
+Bi-interactive Agent Control. For status and behavior control, we adopt an approach inspired by CARLA [12], incorporating control factors such as speed limits and safe following distances derived from the original scenario. Agents determine driving behaviors $b_{j}^{t}$ based on their interaction with other agents at each time, which establishes a bidirectional interactive relation between ego and agent vehicles. Fig. 3 shows some common interaction scenes. Beyond regular driving scenarios, we also introduce dangerous behavior modes for agent vehicles, which can trigger actions such as lane changes, aggressive overtakes, emergency stops, or disregarding safe distances when interacting with ego vehicle, providing potential for long-tail scenario evaluation.
+
+Adaptive Kinematic Model. We propose an Adaptive Kinematic Model (AKM) to refine vehicle control signals, addressing the discrepancy between simulated and real ego dynamics during simulation, which can significantly impact planning [27]. Given front length $l_{f}$ and rear length $l_{r}$ , AKM updates vehicle states using Eq. (1).
+
+$$
+\beta_ {t} = \arctan \left(\frac {l _ {r}}{l _ {f} + l _ {r}} \tan (\delta_ {t})\right), \quad v _ {t + 1} = v _ {t} + a _ {t} \Delta t,
+$$
+
+$$
+\varphi_ {t + 1} = \varphi_ {t} + \frac {v _ {t}}{l _ {f}} \sin (\beta_ {t}) \Delta t, \quad v _ {u} = (1 - \boldsymbol {u} _ {\mathbf {1}}) v _ {t} + \boldsymbol {u} _ {\mathbf {1}} v _ {t + 1},
+$$
+
+$$
+\begin{array}{l} x _ {t + 1} = x _ {t} + v _ {u} \cos (\varphi_ {t} + \boldsymbol {u} _ {\boldsymbol {2}} \cdot \beta_ {t}) \Delta t, \\ y _ {t + 1} = y _ {t} + v _ {u} \sin \left(\varphi_ {t} + \boldsymbol {u} _ {\boldsymbol {2}} \cdot \beta_ {t}\right) \Delta t. \tag {1} \\ \end{array}
+$$
+
+where $\beta_{t}$ is the slip angle, $v_{t}$ is the vehicle velocity, $\varphi_{t}$ is the yaw angle, $\delta$ is the steering angle and $x_{t}, y_{t}$ represent the vehicle position. Compared with standard bicycle model, it incorporates two learnable parameters, $u_{1}$ and $u_{2}$ , estimated from real-world IMU sensor data. These parameters help prevent unrealistic displacements by adjusting velocity and orientation dynamically. By ensuring smoother and more natural vehicle movement, this approach enhances the realism and continuity of the simulation environment.
+
+# 3.2. Scene Renderer
+
+Scene Renderer generates high-fidelity driving scenes that reflect dynamic traffic flows with spatial-temporal consistency. It builds a Model Library using Gaussian Splatting for editable background and dynamic foreground models. We also propose ground height estimation and directional shadow rendering to enhance rendering realism. Figure 1 demonstrates example images from Scene Renderer.
+
+Gaussian-Splatting-Based Model Library. Model library consists of two components: background model and foreground model, both are built based on Gaussian Splatting. For background, we train models by Street Gaussians [39] with only static elements retained to provide a stable background free from motion artifacts and allow for clean integration of dynamic foreground models. For foreground, due to the limited available angles of vehicles in the original scenario, we construct our virtual vehicle assets with BlenderNeRF [33] and 3DRealCar [13] to build foreground model libraries through training with 3DGS. The explicit nature of Gaussian Splatting allows direct editing of the scene using models from the library. Detailed construction steps are provided in Appendix B.
+
+Ground Height Estimation. To prevent artifacts from sinking into or floating above the ground in environments with large elevation variations, we propose learning a global ground model defined as $\hat{z} = f(x,y)$ . Inspired by [11], we extract ground LiDAR points from each frame using RANSAC [14] and fit a ground model for the entire scene, implemented as a three-layer MLP, to predict the z-axis offset during object placement. The loss is designed as follows to penalize less those LiDAR points above the ground:
+
+$$
+\mathcal {L} _ {\text {h e i g h t}} (\hat {z}, z) = \left\{ \begin{array}{l l} (\hat {z} - z) ^ {2} & \hat {z} > z \\ \operatorname {H u b e r} (\hat {z}, z) & \hat {z} \leq z \end{array} \right. \tag {2}
+$$
+
+Directional Shadow Rendering. To enhance the realism of foreground vehicles appearance in the scene, we generate
+
+vehicle shadow 3DGS models in multiple directions based on the Gaussian models from the foreground library. For each scene, we pre-estimate the global illumination based on the images from the original dataset as following:
+
+$$
+1 = \frac {\left[ G _ {x} \left(p ^ {*}\right) , G _ {y} \left(p ^ {*}\right) , - 1 \right] ^ {\top}}{\sqrt {G _ {x} ^ {2} \left(p ^ {*}\right) + G _ {y} ^ {2} \left(p ^ {*}\right) + 1}} \tag {3}
+$$
+
+where $p^* = \arg \max_p \| \nabla I(p) \|_2$ is the point with maximum gradient magnitude, $\nabla I(p) = [G_x, G_y]^\top$ denotes the Sobel gradient after Gaussian blur. During simulation, the global illumination and the current heading angle decide shadow model selection, which is combined with the original model for rendering. A visual comparison of foreground objects with shadow rendering and ground model placement is provided in Fig. 11 in the supplementary.
+
+Composition Rendering. Scene Renderer determines ego vehicle's viewpoint by camera configuration. Based on the agent vehicle poses provided by Scene Controller, foreground models are integrated into the background model. Ego vehicle's pose is then used to compute the camera's extrinsic parameters for rendering driving images. Utilizing composite Gaussian model with definite, precise control on spatial positions of foreground objects and overall appearance, our rendered images maintain spatial-temporal consistency. This ensures both the reliability of the generated data and the full controllability required for closed-loop evaluation. Detailed demonstration for spatial-temporal consistency can be found in Appendix F.
+
+# 3.3. Simulation Modes
+
+SceneCrafter offers two simulation modes: synthetic data generation for realistic training and closed-loop simulation for interactive model evaluation. Algorithm 1 outlines the simulation process for each mode.
+
+Synthetic Data Generation. To generate training datasets for end-to-end models, this mode employs an expert planner $\pi_{exp}$ to control the ego vehicle while dynamically updating surrounding agents. Ego vehicle follows its original trajectory from the real dataset while adjusting its pace based on different driving scenarios to maintain consistent rendering quality. At each simulation step, our Scene Controller dynamically updates the status $s_j^t$ and behavior $b_j^t$ of surrounding agents. The policy $\pi_{exp}$ generates control signals using privileged information $(s_{ego}^t,(s_j)^t_{j = 1:N},\mathcal{M})$ to ensure safe and natural driving behavior. The kinematic model $KM$ then applies these control signals to refine ego vehicle's position and status for the Scene Renderer to generate new sensor observations. This cycle continues until either ego vehicle times out or reaches the target point.
+
+Closed-Loop Simulation. To evaluate end-to-end models in realistic interactive environments, the closed-loop mode replaces the expert planner with a learned policy $\pi_{AD}$ .
+
+Compared with data generation mode, the policy takes sensor inputs, control command and ego status as input to provide future action. The control command $c$ is generated from the original ego trajectory plan from real world data.
+
+Algorithm 1: SceneCrafter Workflow
+Input : World Setup W, Number of Agents N, Simulation Mode M ∈ {SYN, CL}, Driving Planner π, Kinematic Model KM Initialize: Map Topology M, Ego Initial State $s_{ego}^0$ , Agents Initial States $(s_j)_{j=1:N}^0$ , Agents Initial Behaviors $(b_j)_{j=1:N}^0$ , Sensor Images $(I_k)_{j=1:C}^0$ Output : Driving Simulation Log $\tilde{\mathcal{D}}$ $\{(s_j)_{j=1:N}^{1:T_{max}}, (I_k)_{j=1:C}^{1:T_{max}}, s_{ego}^{1:T_{max}}, \mathcal{M}\}$ while t < Tmax do for j ← 1 to N do $s_j^{t+1}, b_j^{t+1} \gets \text{SceneController}(s_{ego}^t, (s_j)^t_{j=1:N}, b_j^t, \mathcal{M})$ if M = SYN then $a_{ego}^{t+1} \gets \pi_{\text{exp}}(s_{ego}^t, (s_j + 1)^t_{j=1:N}, \mathcal{M}); // \text{Synthetic data generation}$ else $a_{ego}^{t+1} \gets \pi_{\text{AD}}(s_{ego}^t, (I_k)^t_{k=1:C}, c); // \text{Closed-loop evaluation}$ $s_{ego}^{t+1} \gets \text{KM}(a_{ego}^{t+1}, s_{ego}^t); (I_k)^{t+1}_{k=1:C} \gets \text{SceneRenderer}(s_{ego}^{t+1}, (s_j)^{t+1}_{j=1:N}) t \gets t + 1$
+
+# 4. Experiment
+
+In Section 4.1, we explain our simulation setups for Scene Controller and Scene Renderer. In Section 4.2, we share quantitative results that assess how well simulated data can replace real data, focusing on realism from the perspective of end-to-end autonomous driving models. Note that we do not compare our simulator with existing photorealistic simulators because they are unable to generate synthetic driving logs that include both sensor inputs and ego dynamics. Detailed justification are provided in Appendix E. Section 4.3 evaluates interactivity, while Section 4.4 assesses closed-loop performance, highlighting improvements in generalization and robustness. Additional runtime efficiency comparisons are provided in Appendix C.
+
+# 4.1. Simulation Settings
+
+Dataset. Our simulator is based on Waymo Open Dataset [38], which is split according to its official con
+
+Figuration into 797 training scenes and 200 validation scenes. These scenes and their corresponding data samples are denoted as $(S_{train},\mathcal{D}_{train})$ for the training set and $(S_{val},\mathcal{D}_{val})$ for the validation set. For data generation, we select 60 representative scenes from the training set, covering both suburban and urban environments. These scenes include a variety of road types including straight roads and intersections, and span different weather conditions. The indices of these selected scenes are denoted as $S_{recon}\subset S_{train}$ , while the rest indices are denoted as $S_{recon}^{c}$ . In addition, for closed-loop evaluation, we reconstruct 30 scenes from $S_{val}$ to assess the generalization capability of end-to-end models.
+
+Scene Controller and Scene Renderer Setups. For Scene Controller, the updating frequency of vehicles' status in the scene is set to $10\mathrm{Hz}$ to ensure more precise control. The rendering frequency of Scene Renderer is set to $2\mathrm{Hz}$ following the input frequency of end-to-end models [20, 21, 51] previously trained on nuScenes [2].
+
+End-to-End Models and Evaluation Metrics. We select VAD [21] and its enhanced version, GenAD [51], as our end-to-end models due to their efficiency and effectiveness. Both methods share the same auxiliary tasks: 3D Object Detection (3DOD), Motion Prediction and Online Map Segmentation (MapSeg). For open-loop evaluation, we assess planning performance using the L2 displacement error and collision rate, following the standard end-to-end benchmark [21, 51]. In closed-loop evaluation, we adopt key metrics from Carla [12], including route completion (RC), vehicle collision rate (VCR), and layout collision rate (LCR). Detailed formulas are provided in Appendix G.
+
+# 4.2. Simulation Realism Evaluation
+
+To assess the reliability of SceneCrafter, we examine the real-simulation gap between real data and generated data from the perspective of end-to-end models in an open-loop manner to show that SceneCrafter can achieve real kinematic controls and high rendering quality for synthetic data.
+
+# 4.2.1. Data Augmentation with Synthetic Data
+
+To demonstrate the complementary benefits of our synthetic data, we train VAD with a mix of real-world and simulated data in an incremental learning setup. This enables us to assess whether the model surpasses one trained solely on real data, validating the fidelity of our synthetic data. Specifically, we construct two real-world training sets: $\mathcal{D}_{recon}^{c}$ and driving logs from 200 sampled scenes in $S_{recon}^{c}$ , forming a smaller-scale real training set $D_{200}$ . We generate one driving log per scene from $S_{recon}$ to create the synthetic training set $\tilde{\mathcal{D}}_{train}$ with around 2,000 samples. End-to-end models are evaluated on all samples $D_{val}$ from $S_{val}$ .
+
+Tab. 2 presents the quantitative results. The inclusion of synthetic data significantly improves planning performance
+
+| Setting | Volume | Planning L2 (m) ↓ | CR ↓ |
| Real | Sim | 1s | 2s | 3s | Avg | 1s | 2s | 3s | Avg |
| D200 | 8k | - | 0.61 | 1.31 | 2.24 | 1.39 | 0.34 | 0.36 | 0.86 | 0.52 |
| D200 + Dtr | 8k | 2k | 0.48 | 1.09 | 1.99 | 1.18 | 0.28 | 0.32 | 0.75 | 0.45 |
| Dreccon | 28k | - | 0.43 | 1.02 | 1.82 | 1.09 | 0.21 | 0.27 | 0.47 | 0.32 |
| Dreccon + Dtr | 28k | 2k | 0.38 | 0.94 | 1.79 | 1.04 | 0.08 | 0.14 | 0.53 | 0.25 |
+
+Table 2. Performance comparison of data augmentation with synthetic samples $\hat{\mathcal{D}}_{tr}$ using different real data amounts $\mathcal{D}_{200}$ and $\mathcal{D}_{\text{recon}}^c$ . The inclusion of synthetic data improves planning performance on both settings.
+
+when the real training set is small, demonstrating its potential to supplement real-world data. However, its impact is relatively marginal when the original training set is large. We attribute this to the fact that the Waymo validation set primarily consists of normal driving scenarios, such as cruising straightly in a scenario with fewer interaction with other agents, which are already well covered by large-scale real-world training data. This limitation of real-world open-loop evaluation benchmarks is also discussed in [27].
+
+# 4.2.2. Inference with E2E Models as Proxy Evaluators
+
+Unlike most related works that primarily focus on image quality comparison for realism validation, we approach the problem by using VAD trained on real-world samples $\mathcal{D}_{recon}^{c}$ from scenes $S_{recon}^{c}$ as a zero-shot proxy evaluator. This model is assumed to exhibit certain perception ability and reasonable coherence with the real world ground truth trajectory after large-scale training. We then evaluate the model on both real data $\mathcal{D}_{recon}$ and synthetic data $\tilde{\mathcal{D}}_{recon}$ generated from scenes $S_{recon}$ , comparing their performance on all autonomous driving tasks and assessing the output trajectory of end-to-end models with the generated trajectory annotations by the simulator. This comparison aims to investigate the realism of the generated data from both the sensor input and vehicle kinematics perspectives. Specifically, we consider the following settings:
+
+- Real Data: This setting uses real-world driving logs from the scenes $S_{\text{recon}}$ in the Waymo dataset. It includes actual sensor images and ego IMU data as inputs for VAD, along with annotated labels for other agents.
+- VirVehicle Rep.: This setting uses real ego IMU data and annotated agents' labels from scenes $S_{recon}$ , but replaces the real sensor images with rendered images generated by Scene Renderer. The images are generated using the original camera configurations, with real dynamic foreground objects replaced by assets from the virtual vehicle library [33], without adding shadows.
+- 3DRealCar Rep.: This setting mirrors VirVehicle Rep. but replaces real foreground objects with 3DRealCar[13] assets and adding directional shadow during rendering.
+- Sim Data w/ BM: This setting generates synthetic data with traffic flow controlled by Scene Controller, using a vanilla Bicycle Model as the kinematic model. The num
+
+| Setting | Volume | Rendering Config | Prediction (Car) | 3DOD↑ | MapSeg↑ |
| Car Lib | Shadow | EPA ↑ | ADE ↓ | FDE ↓ | Car AP | AP 0.5 | AP 1.0 | AP 1.5 |
| Real Data | 2k | - | - | 0.30 | 0.71 | 0.96 | 44.1 | 0.245 | 0.482 | 0.644 |
| VirVehicle Rep. | 2k | Virtual | × | 0.25 | 0.26 | 1.02 | 38.4 | 0.227 | 0.476 | 0.633 |
| 3DRealCar Rep. | 2k | 3DRealCar | ✓ | 0.25 | 0.77 | 1.01 | 39.6 | 0.212 | 0.467 | 0.622 |
+
+Table 3. Perception and prediction performance comparison with VAD trained on $\mathcal{D}_{recon}^{c}$ over real and synthetic data. Car Lib represents the foreground object source, and Shadow denotes whether shadow rendering is applied. 3DRealCar Rep. achieves a higher detection score compared with VirVehicle Rep., demonstrating the enhanced realism of our foreground rendering.
+
+| Setting | Volume | Planning L2 (m)↓ | Prediction (Car) | MapSeg↑ |
| 1s | 2s | 3s | EPA ↑ | ADE ↓ | FDE ↓ | AP 0.5 | AP 1.0 | AP 1.5 |
| Real Data | 2k | 0.39 | 0.94 | 1.72 | 0.30 | 0.71 | 0.96 | 0.245 | 0.482 | 0.644 |
| Sim Data w/ BM | 2k | 0.47 | 1.24 | 2.43 | 0.27 | 0.80 | 1.10 | 0.170 | 0.435 | 0.574 |
| Sim Data w/ AKM (Ours) | 2k | 0.38 | 1.04 | 2.06 | 0.28 | 0.77 | 0.92 | 0.185 | 0.453 | 0.590 |
+
+Table 4. Inference results on Waymo reconstructed scenes with VAD trained on ${\mathcal{D}}_{\text{recon }}^{c}$ . Our Adaptive Kinematic Model (AKM) produces ego trajectories closer to planning results than the Bicycle Model (BM), leading to improved prediction and perception performance.
+
+
+
+
+Figure 4. (a) and (b) show that ego trajectories generated by AKM are smoother and more realistic than those by BM. (c) and (d) illustrate that end-to-end planning result deviates more from the simulated GT trajectory with AKM than with BM, which indicates AKM aligns better with real world dynamics. The color bar indicates vehicle velocity norms.
+
+
+
+
+
+ber of agents is set to match the average number of dynamic foreground objects in the original scenes.
+
+- Sim Data w/ AKM: This setting generates synthetic data similar to Sim Data w/ BM, but uses AKM as the kinematic model instead of the vanilla Bicycle Model.
+
+Tab. 3 presents the realism assessment of images generated by Scene Renderer. Notably, replacing all foreground objects with reconstructed 3D assets and rendered background model results in only a minor decline in perception performance (3DOD and MapSeg), demonstrating the high fidelity of our rendered images. This performance gap is primarily due to an increase in false positive bounding boxes, which is less critical than false negatives. Additionally, foreground objects from 3DRealCar, which include added shadows, achieve higher detection scores compared to virtual vehicles, further validating their realism.
+
+Regarding the kinematic model, Tab. 4 shows that the ego trajectory generated by the Adaptive Kinematic Model (AKM) aligns more closely with planning results than that generated by the simpler Bicycle Model. Fig. 4 further illustrates the differences in turning trajectory annotations compared to real trajectories. The ego trajectory produced
+
+by the Bicycle Model often results in unnatural vehicle orientations, whereas AKM corrects this issue through its learnable parameters, leading to more realistic ego motions.
+
+# 4.3. Interactivity Evaluation
+
+To assess our interactivity, we compare statistics including bidirectional interactions and ego speed alteration in scenes from $S_{recon}$ on our synthetic data and real data. Interaction Rate measures the proportion of scenes containing either ego-to-agent or agent-to-ego interactions across all scenes. Ego Speed Alteration quantifies how often the ego vehicle's speed tendency shifts (from acceleration to deceleration or vice versa) within the next $t = 6$ time steps due to interactions with other vehicles.
+
+As shown in Fig. 5, our synthetic data exhibits a higher interaction rate compared to the original Waymo dataset. Furthermore, the Ego Speed Alteration metric reveals a longer-tail distribution than real data, indicating greater diversity in ego vehicle speed variations influenced by surrounding agents. This variability helps prevent models from learning flawed patterns, such as consistently accelerating or decelerating that are more prevalent in real-world data. These findings highlight the enhanced diversity and interactivity of our simulation, reinforcing its value as a complementary resource to real-world datasets. Detailed definitions of the Ego Speed Alteration and Interaction Rate metrics are provided in Appendix D.
+
+
+Figure 5. Our synthetic data shows a higher Interaction Rate and a longer-tail distribution of Ego Speed Alteration, reflecting greater interactivity and diversity in generated traffic flow.
+
+# 4.4. Closed-Loop Evaluation
+
+With SceneCrafter generating realistic sensor data, it also enables interactive closed-loop evaluation, providing a
+
+
+Figure 6. Qualitative comparison from front camera view of the original end-to-end models and those fine-tuned with our synthetic data. The Red car represents ego vehicle controlled by $\pi_{AD}$ . The red and green arrows respectively indicate the locations where the collision occurs or is avoided. Fine-tuned models offer more reasonable driving behaviors in complex scenarios while models solely trained on real
+
+data, showcasing enhanced generalization.
+
+more comprehensive assessment of end-to-end model performance in real driving scenarios. To see how our data contributes to the enhancement of models, we generate three random trajectories per scene with more involved agents than in Sec. 4.2 to construct a synthetic dataset for finetuning VAD and GenAD which are initially trained on $\mathcal{D}_{train}$ . We initialize each scene with three different seeds and the ego vehicle at two starting positions.
+
+Generalizable Capacity. Tab. 5 shows the results of original and fine-tuned models evaluated on unseen scenes from $S_{val}$ . We see that for both VAD and GenAD, the fine-tuned versions achieve a much higher route completion with a lower collision rate with dynamic agents and static map elements. This improvement in closed-loop evaluation further proves the feasibility to improve AD models' generalization ability by simulated data.
+
+Qualitative Results. Fig. 6 shows qualitative comparison between original and fine-tuned end-to-end models. The fine-tuned models demonstrate improved performance in various complex driving scenarios, including intersection handling, highway car-following, and lane merging, highlighting their enhanced generalization capabilities.
+
+# 5. Conclusion
+
+Summary. In this paper, we introduce SceneCrafter, a unified simulator designed for training and testing vision-based end-to-end autonomous driving models. By leveraging 3DGS, SceneCrafter efficiently generates spatial-
+
+| Model | Volume | All Test Scenes | Turn Scenes |
| Real | Sim | RC↑ | VC↓ | LCR↓ | RC↑ | VC↓ | LCR↓ |
| VAD | 32k | - | 42.01 | 7.55 | 7.48 | 25.71 | 7.90 | 9.84 |
| 32k | 6k | 53.03 | 3.43 | 6.08 | 34.72 | 3.78 | 8.08 |
| GenAD | 32k | - | 44.87 | 7.62 | 8.50 | 28.47 | 7.23 | 9.25 |
| 32k | 6k | 49.65 | 5.45 | 5.76 | 34.02 | 5.63 | 8.14 |
+
+Table 5. Closed-loop evaluation performance comparison. Metrics include: RC (Route Completion), VC (Vehicle Collision Rate), and LCR (Layout Collision Rate). Models fine-tuned with synthetic data exhibit improved performance in closed-loop evaluation compared to models trained on real data alone.
+
+temporally consistent images, which is crucial for both data generation and closed-loop evaluation. To enhance realism, SceneCrafter integrates an adaptive kinematic model and high-fidelity foreground rendering. Additionally, it creates an interactive and responsive environment using heuristic vehicle placement and actor models, enabling real-world-level interactions. Experimental results demonstrate the high fidelity of our framework and highlight its potential to improve the generalization capability of autonomous driving models in real-world scenarios.
+
+Limitation and future work. Current types of traffic participants are limited. Future work will focus on increasing the agent diversity, such as cyclist and pedestrian, to further enrich traffic scenarios and make the interaction more challenging. Besides, We aim to enhance this by incorporating lightweight local diffusion models to address unseen scenarios, thereby expanding the rendering range and improving overall rendering quality.
+
+# References
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+ "html": "| Name | Real Time | ST Consistency | Real Images | Interactive Traffic Flow | DataGen For E2E |
| CARLA[12] | ✓ | ✓ | ✗ | ✓ | ✓ |
| SUMO[32] | ✓ | ✓ | ✗ | ✓ | ✗ |
| MetaDrive[24] | ✓ | ✓ | ✗ | ✓ | ✓ |
| NeuroNCAP[30] | ✗ | ✓ | ✓ | ✗ | ✗ |
| UniSim[48] | ✗ | ✓ | ✓ | ✗ | ✗ |
| DriveArena[47] | ✗ | ✗ | ✓ | ✓ | ✓ |
| HugSim[53] | ✓ | ✓ | ✓ | ✗ | ✗ |
| Ours | ✓ | ✓ | ✓ | ✓ | ✓ |
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+ "content": " to control the ego vehicle while dynamically updating surrounding agents. Ego vehicle follows its original trajectory from the real dataset while adjusting its pace based on different driving scenarios to maintain consistent rendering quality. At each simulation step, our Scene Controller dynamically updates the status "
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+ "content": " then applies these control signals to refine ego vehicle's position and status for the Scene Renderer to generate new sensor observations. This cycle continues until either ego vehicle times out or reaches the target point."
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+ "type": "text",
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+ "content": " is generated from the original ego trajectory plan from real world data."
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+ "content": "Input : World Setup W, Number of Agents N, Simulation Mode M ∈ {SYN, CL}, Driving Planner π, Kinematic Model KM Initialize: Map Topology M, Ego Initial State "
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+ "content": "(b_j)_{j=1:N}^0"
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+ "content": " Output : Driving Simulation Log "
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+ "content": "\\tilde{\\mathcal{D}}"
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+ "content": "\\{(s_j)_{j=1:N}^{1:T_{max}}, (I_k)_{j=1:C}^{1:T_{max}}, s_{ego}^{1:T_{max}}, \\mathcal{M}\\}"
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+ "content": "s_j^{t+1}, b_j^{t+1} \\gets \\text{SceneController}(s_{ego}^t, (s_j)^t_{j=1:N}, b_j^t, \\mathcal{M})"
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+ "content": " if M = SYN then "
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+ "type": "inline_equation",
+ "content": "a_{ego}^{t+1} \\gets \\pi_{\\text{exp}}(s_{ego}^t, (s_j + 1)^t_{j=1:N}, \\mathcal{M}); // \\text{Synthetic data generation}"
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+ "type": "text",
+ "content": " else "
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+ "type": "inline_equation",
+ "content": "a_{ego}^{t+1} \\gets \\pi_{\\text{AD}}(s_{ego}^t, (I_k)^t_{k=1:C}, c); // \\text{Closed-loop evaluation}"
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+ "content": "s_{ego}^{t+1} \\gets \\text{KM}(a_{ego}^{t+1}, s_{ego}^t); (I_k)^{t+1}_{k=1:C} \\gets \\text{SceneRenderer}(s_{ego}^{t+1}, (s_j)^{t+1}_{j=1:N}) t \\gets t + 1"
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+ "content": "4. Experiment"
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+ "content": "In Section 4.1, we explain our simulation setups for Scene Controller and Scene Renderer. In Section 4.2, we share quantitative results that assess how well simulated data can replace real data, focusing on realism from the perspective of end-to-end autonomous driving models. Note that we do not compare our simulator with existing photorealistic simulators because they are unable to generate synthetic driving logs that include both sensor inputs and ego dynamics. Detailed justification are provided in Appendix E. Section 4.3 evaluates interactivity, while Section 4.4 assesses closed-loop performance, highlighting improvements in generalization and robustness. Additional runtime efficiency comparisons are provided in Appendix C."
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+ "content": "Dataset. Our simulator is based on Waymo Open Dataset [38], which is split according to its official con"
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+ "content": "Figuration into 797 training scenes and 200 validation scenes. These scenes and their corresponding data samples are denoted as "
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+ "content": " for the validation set. For data generation, we select 60 representative scenes from the training set, covering both suburban and urban environments. These scenes include a variety of road types including straight roads and intersections, and span different weather conditions. The indices of these selected scenes are denoted as "
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+ "content": " following the input frequency of end-to-end models [20, 21, 51] previously trained on nuScenes [2]."
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+ "content": "End-to-End Models and Evaluation Metrics. We select VAD [21] and its enhanced version, GenAD [51], as our end-to-end models due to their efficiency and effectiveness. Both methods share the same auxiliary tasks: 3D Object Detection (3DOD), Motion Prediction and Online Map Segmentation (MapSeg). For open-loop evaluation, we assess planning performance using the L2 displacement error and collision rate, following the standard end-to-end benchmark [21, 51]. In closed-loop evaluation, we adopt key metrics from Carla [12], including route completion (RC), vehicle collision rate (VCR), and layout collision rate (LCR). Detailed formulas are provided in Appendix G."
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+ "content": "Tab. 2 presents the quantitative results. The inclusion of synthetic data significantly improves planning performance"
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+ "html": "| Setting | Volume | Planning L2 (m) ↓ | CR ↓ |
| Real | Sim | 1s | 2s | 3s | Avg | 1s | 2s | 3s | Avg |
| D200 | 8k | - | 0.61 | 1.31 | 2.24 | 1.39 | 0.34 | 0.36 | 0.86 | 0.52 |
| D200 + Dtr | 8k | 2k | 0.48 | 1.09 | 1.99 | 1.18 | 0.28 | 0.32 | 0.75 | 0.45 |
| Dreccon | 28k | - | 0.43 | 1.02 | 1.82 | 1.09 | 0.21 | 0.27 | 0.47 | 0.32 |
| Dreccon + Dtr | 28k | 2k | 0.38 | 0.94 | 1.79 | 1.04 | 0.08 | 0.14 | 0.53 | 0.25 |
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+ "content": " using different real data amounts "
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+ "content": " and "
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+ "type": "text",
+ "content": ". The inclusion of synthetic data improves planning performance on both settings."
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+ "content": "when the real training set is small, demonstrating its potential to supplement real-world data. However, its impact is relatively marginal when the original training set is large. We attribute this to the fact that the Waymo validation set primarily consists of normal driving scenarios, such as cruising straightly in a scenario with fewer interaction with other agents, which are already well covered by large-scale real-world training data. This limitation of real-world open-loop evaluation benchmarks is also discussed in [27]."
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+ "type": "text",
+ "content": " as a zero-shot proxy evaluator. This model is assumed to exhibit certain perception ability and reasonable coherence with the real world ground truth trajectory after large-scale training. We then evaluate the model on both real data "
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+ "content": " and synthetic data "
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+ "content": " generated from scenes "
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+ "type": "text",
+ "content": ", comparing their performance on all autonomous driving tasks and assessing the output trajectory of end-to-end models with the generated trajectory annotations by the simulator. This comparison aims to investigate the realism of the generated data from both the sensor input and vehicle kinematics perspectives. Specifically, we consider the following settings:"
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+ "content": "- Real Data: This setting uses real-world driving logs from the scenes "
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| Sim Data w/ BM | 2k | 0.47 | 1.24 | 2.43 | 0.27 | 0.80 | 1.10 | 0.170 | 0.435 | 0.574 |
| Sim Data w/ AKM (Ours) | 2k | 0.38 | 1.04 | 2.06 | 0.28 | 0.77 | 0.92 | 0.185 | 0.453 | 0.590 |
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| Real | Sim | RC↑ | VC↓ | LCR↓ | RC↑ | VC↓ | LCR↓ |
| VAD | 32k | - | 42.01 | 7.55 | 7.48 | 25.71 | 7.90 | 9.84 |
| 32k | 6k | 53.03 | 3.43 | 6.08 | 34.72 | 3.78 | 8.08 |
| GenAD | 32k | - | 44.87 | 7.62 | 8.50 | 28.47 | 7.23 | 9.25 |
| 32k | 6k | 49.65 | 5.45 | 5.76 | 34.02 | 5.63 | 8.14 |
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+ {
+ "type": "text",
+ "text": "Unraveling the Smoothness Properties of Diffusion Models: A Gaussian Mixture Perspective",
+ "text_level": 1,
+ "bbox": [
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+ "text": "Yingyu Liang $^{1,3,\\dagger}$ Zhizhou Sha $^{2}$ Zhenmei Shi $^{3}$ Zhao Song $^{4,*}$ Mingda Wan $^{5}$ Yufa Zhou $^{6}$ $^{1}$ The University of Hong Kong, $^{2}$ University of Texas at Austin, $^{3}$ University of Wisconsin-Madison \n $^{4}$ University of California, Berkeley, $^{5}$ Independent Researcher, $^{6}$ University of Pennsylvania",
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+ "text": "*magic.linuxkde@gmail.com, †yliang@cs.wisc.edu,yingyul@hku.hk",
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+ "text": "Abstract",
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+ "type": "text",
+ "text": "Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking. In this paper, we bridge this gap by providing a detailed examination of these smoothness properties for the case where the target data distribution is a mixture of Gaussians, which serves as a universal approximator for smooth densities such as image data. We prove that if the target distribution is a $k$ -mixture of Gaussians, the density of the entire diffusion process will also be a $k$ -mixture of Gaussians. We then derive tight upper bounds on the Lipschitz constant and second momentum that are independent of the number of mixture components $k$ . Finally, we apply our analysis to various diffusion solvers, both SDE and ODE based, to establish concrete error guarantees in terms of the total variation distance and KL divergence between the target and learned distributions. Furthermore, our preliminary experiments support our theoretical analysis. Our results provide deeper theoretical insights into the dynamics of the diffusion process under common data distributions.",
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+ "text": "1. Introduction",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "Diffusion models, a prominent generative modeling framework, have rapid progress and garnered significant attention in recent years, due to their potential powerful ability to generate high-quality samples across various domains and diverse applications. Score-based generative diffusion models [30, 63] can generate high-quality image samples comparable to GANs, which require adversarial optimization. Based on the U-Net [50], stable diffusion [49], a conditional multi-modality generation model, can successfully generate business-used images. Based on the Transformer (DiT) [45], OpenAI released a video diffusion model, SORA [44], with a surprising performance.",
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+ "text": "However, despite these technological strides, a critical gap persists in the theoretical understanding of diffusion processes, especially concerning the Lipschitz continuity and second momentum properties of these models. Many existing studies ([10, 13, 14, 21, 35] and many more) make simplifying assumptions about these key smoothness properties but lack rigorous formulation or comprehensive analysis. This paper aims to bridge this theoretical gap by providing a detailed examination of the Lipschitz and second momentum characteristics. To make the data distribution analyzable, we consider the mixture of Gaussian data distribution (see illustration in Figure 1), which is a universal approximation (Fact 1.1) for any smooth density, such as complex image and video data distributions.",
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+ "text": "Fact 1.1. A Gaussian mixture model is a universal approximator of densities, in the sense that any smooth density can be approximated with any specific nonzero amount of error by a Gaussian mixture model with enough components [52].",
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+ "text": "Furthermore, we prove that if the target data distribution is a $k$ -mixture of Gaussian, the density of the whole diffusion process will be a $k$ -mixture of Gaussian (Proposition 3.2). Thus, our focus is studying a mixture of Gaussian target data distribution in the diffusion process, where we can gain a concrete Lipschitz constant and second momentum (Lemma 3.5 and Lemma 3.6). Moreover, we explore the implications of these properties through the lens of various solvers, both Stochastic Differential Equation (SDE) and Ordinary Differential Equation (ODE) based, providing a deeper insight into the dynamic behavior of diffusion processes and concrete guarantees in Table 1. Moreover, our preliminary experiments support our theoretical analysis.",
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+ "text": "- As the Gaussian mixture model is a universal approximator of densities (Fact 1.1), we assume the target/image data distribution as a $k$ -mixture of Gaussian. Then, we show that the density of the whole diffusion process is a $k$ -mixture of Gaussian (Proposition 3.2).",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "Figure 1. An illustration of discrete diffusion process for 8 mixture of Gaussian as shown in Eq. (2). The left figure represents the target 2-dimensional data distribution $p_0$ . The right figure represents the standard normal distribution $p_T = \\mathcal{N}(0, I_{2\\times 2})$ , where $T = 3$ . This experimental setup is also used in [13]."
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+ "- We analyze the Lipschitz and second momentum of $k$ -mixture of Gaussian data distribution and provide a tight upper bound, which is independent of $k$ , (Lemma 3.5 and Lemma 3.6), even when $k$ goes to infinity (see more discussion in Section 3.1).",
+ "- After applying our analysis to DDPM, which is the SDE version of reverse process, we prove the dynamic of the diffusion process satisfies some concrete total variation bound (Theorem 5.4) and concrete KL divergence bound (Theorem 5.5 and Theorem 5.6) under choosing some total discretization steps. See a summary in Table 1.",
+ "- After applying our analysis to DPOM and DPUM, which is the ODE version of the reverse process, we prove the dynamic of the diffusion process satisfies some concrete total variation bound (Theorem 5.7 and Theorem 5.8) under choosing some total discretization steps."
+ ],
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+ "text": "Studies of the mixture of Gaussian under diffusion.",
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+ "text": "There is a rich line of work that studies a mixture of Gaussian data distribution under the diffusion process, sharing a similar popular setting. However, none focuses on the Lipschitz smoothness and second momentum property as ours. We provide a short summary here for convenience. [71] analyses the effect of diffusion guidance and provides theoretical insights on the instillation of task-specific information into the score function and conditional generation, e.g., text-to-image, by studying the mixture of Gaussian data distribution as a case study. [27] propose a new SDE-solver for diffusion models under a mixture of Gaussian data. [26, 53] learn mixtures of Gaussian data using the DDPM objective and gives bound for sample complexity by assuming all covariance matrices are identity but does not use Lipschitz, while our work does not need identity assumptions. [16] mainly focuses on solving $k$ -mixture of Gaussian in diffusion model by leveraging the property of the mixture of Gaussian and polynomial approximation methods and gives bound for sample complexity by assuming the covariance matrices have bounded condition number and that the mean vectors and covariance matrices lie in a bounded ball.",
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+ "text": "Diffusion models and score-based models. [30] introduced the concept of denoising diffusion probabilistic models (DDPM), which learn to reverse a gradual noising process to generate samples and have been applied to many area [68-70]. Then, [63] used Stochastic Differential Equations (SDE) to build the diffusion model and explored the equivalence between score-based generative models (SGMs) and diffusion models, generalizing the diffusion model to continuous time. There is a line of works [58] studying the connection between diffusion models and nonequilibrium thermodynamics, providing a theoretical foundation for these models. Another line of work has focused on improving the efficiency and quality of diffusion models [42]. Particularly, [59] leverages score matching to train diffusion models more efficiently; [43] improved architectures and training techniques for diffusion models. Diffusion models have been applied to various domains beyond image generation, achieving impressive results, e.g., text-to-image synthesis [12], audio synthesis [33], image superresolution [51], and so on.",
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+ "text": "Mixture of Gaussian. Mixtures of Gaussian are among the most fundamental and widely used statistical models [1, 3-6, 8, 9, 19, 20, 22-25, 37, 41, 55, 56, 66, 72] and studied in neural networks learning [39, 47, 54, 57]. Recently, they have also been widely studied in diffusion models [16, 26, 27, 53, 71] (see detailed discussion in Section 1).",
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+ "text": "Lipschitz and second momentum in score estimation. There is a line of work using bounded Lipschitz and second momentum as their key smoothness assumptions for the whole diffusion process without giving any concrete formulation [7, 10, 11, 13-15, 32, 34, 35, 40, 74], while our work gives a \"close-form\" formulation of Lipschitz and second momentum. [73] primarily identifies the existence of Lipschitz singularities without deriving tight bounds for arbitrary data distributions. In contrast, our analysis provides explicit bounds for the Lipschitz constant in terms of the pa",
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+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Type | Error guarantee | Steps for Φ(ε02) error | Reference |
| DDPM [13] | TV(p0, q)2 | Θ(d/ε02) | Theorem 5.4 |
| DDPM [10] | KL(p0, q) | Θ(d/ε02) | Theorem 5.5 |
| DDPM [10] | KL(p0, q) | Θ(d2/ε02) | Theorem 5.6 |
| DPOM [14] | TV(p0, q)2 | Θ(d/ε02) | Theorem 5.7 |
| DPUM [14] | TV(p0, q)2 | Θ(√d/ε0) | Theorem 5.8 |
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+ "text": "Table 1. A summary of our applications using our Lipschitz and second momentum bound, when we assume $\\sigma_{\\min (pt)}$ as a constant (defined in Definition 3.3). The third column means the number of discretization points required to guarantee a small total variation/KL divergence distance between the target data distribution $p_0$ and the learned distribution $\\widehat{q}$",
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+ "text": "rameters of the underlying mixture model. It connects these Lipschitz properties to concrete error guarantees for various solvers. There is another rich line of work studying how to train the diffusion models to have a better theoretical guarantee [11, 14-16, 26-28, 31, 36, 40, 48, 53, 59-62, 64, 65].",
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+ "text": "In this section, we discuss the notations used, several key definitions for $k$ mixtures of Gaussian distributions, and lemmas concerning the Lipschitz continuity and second momentum of these mixtures. We begin by presenting the notations that are used throughout the paper.",
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+ "text": "Notations. For two vectors $x \\in \\mathbb{R}^n$ and $y \\in \\mathbb{R}^n$ , we use $\\langle x, y \\rangle$ to denote the inner product between $x, y$ , i.e., $\\langle x, y \\rangle = \\sum_{i=1}^{n} x_i y_i$ . We use $\\operatorname{Pr}[]$ to denote the probability, we use $\\mathbb{E}[]$ to denote the expectation. We use $e_i$ to denote a vector where only $i$ -th coordinate is 1, and other entries are 0. For each $a, b \\in \\mathbb{R}^n$ , we use $a \\circ b \\in \\mathbb{R}^n$ to denote the vector where $i$ -th entry is $(a \\circ b)_i = a_i b_i$ for all $i \\in [n]$ , and this is the Hardamard product. We use $\\mathbf{1}_n$ to denote a length- $n$ vector where all the entries are ones. We use $x_{i,j}$ to denote the $j$ -th coordinate of $x_i \\in \\mathbb{R}^n$ . We use $\\|x\\|_p$ to denote the $\\ell_p$ norm of a vector $x \\in \\mathbb{R}^n$ , i.e. $\\|x\\|_1 := \\sum_{i=1}^{n} |x_i|$ , $\\|x\\|_2 := (\\sum_{i=1}^{n} x_i^2)^{1/2}$ , and $\\|x\\|_\\infty := \\max_{i \\in [n]} |x_i|$ . For $k > n$ , for any matrix $A \\in \\mathbb{R}^{k \\times n}$ , we use $\\|A\\|$ to denote the spectral norm of $A$ , i.e. $\\|A\\| := \\sup_{x \\in \\mathbb{R}^n} \\|Ax\\|_2 / \\|x\\|_2$ . We use $\\sigma_{\\min}(A), \\sigma_{\\max}(A)$ to denote the minimum/maximum singular value of matrix $A$ . For a square matrix $A$ , we use $\\mathrm{tr}[A]$ to denote the trace of $A$ , i.e., $\\mathrm{tr}[A] = \\sum_{i=1}^{n} A_{i,i}$ . We use $\\det(A)$ to denote the determinant of matrix $A$ . We use $f * g$ to denote the convolution of 2 functions $f, g$ . In addition to $O(\\cdot)$ notation, for two functions $f, g$ , we use the shorthand $f \\lesssim g$ (resp. $\\gtrsim$ ) to indicate that $f \\leq Cg$ (resp. $\\geq$ ) for an absolute constant $C$ .",
+ "bbox": [
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+ "type": "text",
+ "text": "$k$ mixtures of Gaussian. Now, we are ready to introduce $k$ mixtures of Gaussian. Formally, we can have the following definition of the pdf for $k$ mixtures of Gaussian.",
+ "bbox": [
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+ "type": "text",
+ "text": "Definition 3.1 ( $k$ mixtures of Gaussian pdf). Let $x \\in \\mathbb{R}^d$ , $i \\in [k]$ , $t \\geq 0 \\in \\mathbb{R}$ . For a fixed timestamp $t$ , (1) let $\\alpha_i(t) \\in$",
+ "bbox": [
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+ "type": "text",
+ "text": "(0,1) be the weight for the $i$ -th Gaussian component at time $t$ and $\\sum_{i=1}^{k} \\alpha_i(t) = 1$ ; (2) let $\\mu_i(t) \\in \\mathbb{R}^d$ and $\\Sigma_i(t) \\in \\mathbb{R}^{d \\times d}$ be the mean vector and covariance matrix for the $i$ -th Gaussian component at time $t$ . Then, we define",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} p _ {t} (x) := \\sum_ {i = 1} ^ {k} \\frac {\\alpha_ {i} (t)}{(2 \\pi) ^ {d / 2} \\det (\\Sigma_ {i} (t)) ^ {1 / 2}} \\\\ \\cdot \\exp (- \\frac {1}{2} (x - \\mu_ {i} (t)) ^ {\\top} \\Sigma_ {i} (t) ^ {- 1} (x - \\mu_ {i} (t))). \\\\ \\end{array}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "type": "text",
+ "text": "Then, the following lemma shows that the linear combination between $k$ mixtures of Gaussian and a single standard Gaussian is still a $k$ mixtures of Gaussian. The proof is in Appendix H.",
+ "bbox": [
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+ "type": "text",
+ "text": "Proposition 3.2 (Informal version of Proposition H.1). Let $a, b \\in \\mathbb{R}$ . Let $\\mathcal{D}$ be a $k$ -mixture of Gaussian distribution, and let $p$ be its pdf defined in Definition 3.1, i.e.,",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} p (x) := \\sum_ {i = 1} ^ {k} \\frac {\\alpha_ {i}}{(2 \\pi) ^ {d / 2} \\det (\\Sigma_ {i}) ^ {1 / 2}} \\\\ \\cdot \\exp \\left(- \\frac {1}{2} (x - \\mu_ {i}) ^ {\\top} \\Sigma_ {i} ^ {- 1} (x - \\mu_ {i})\\right) \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "Let $x \\in \\mathbb{R}^d$ sample from $\\mathcal{D}$ . Let $z \\in \\mathbb{R}^d$ and $z \\sim \\mathcal{N}(0, I)$ which is independent from $x$ . Then, we have a new random variable $y = ax + bz$ which is also a $k$ -mixture of Gaussian distribution $\\widetilde{\\mathcal{D}}$ , whose pdf is",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\widetilde {p} (x) := \\sum_ {i = 1} ^ {k} \\frac {\\alpha_ {i}}{(2 \\pi) ^ {d / 2} \\det (\\widetilde {\\Sigma} _ {i}) ^ {1 / 2}} \\\\ \\cdot \\exp (- \\frac {1}{2} (x - \\widetilde {\\mu} _ {i}) ^ {\\top} \\widetilde {\\Sigma} _ {i} ^ {- 1} (x - \\widetilde {\\mu} _ {i})), \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "where $\\widetilde{\\mu}_i = a\\mu_i,\\widetilde{\\Sigma}_i = a^2\\Sigma_i + b^2 I.$",
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+ "type": "text",
+ "text": "The Gaussian mixture model is a universal approximator of densities (Fact 1.1). Then, it is natural to assume that the target/image $(p_0)$ data distribution as the $k$ mixtures of Gaussian. Proposition 3.2 tells us that if the target data distribution is $k$ mixtures of Gaussian, then by Eq. (2), the pdf",
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+ {
+ "type": "page_number",
+ "text": "11438",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "of the whole diffusion process is $k$ mixtures of Gaussian, i.e., the $p_t$ for any $t \\in [0, T]$ . See details in Section 4.",
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+ "type": "text",
+ "text": "Main properties. Thus, we only need to analyze the property, i.e., Lipschitz constant and second momentum, of $k$ mixtures of Gaussian, to have a clear guarantee for the whole diffusion process. In the following two lemmas, we will give concrete bounds of the Lipschitz constant and second momentum of $k$ mixtures of Gaussian. Both proofs can be found in Appendix H.",
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+ "type": "text",
+ "text": "First, we define the following conditions of the $k$ mixtures of Gaussian.",
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+ "type": "text",
+ "text": "Definition 3.3. The first two definitions here are related to the beginning time density $p_0$ in Eq. (9). The last two definitions are related to the all time density $p_t$ in Eq. (10), where $t \\in [0, T]$ .",
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+ "type": "list",
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+ "list_items": [
+ "- Let $\\sigma_{\\min(p_0)} =: \\min_{i \\in [k]} \\{\\sigma_{\\min}(\\Sigma_i)\\}$ and $\\sigma_{\\max(p_0)} =: \\max_{i \\in [k]} \\{\\sigma_{\\max}(\\Sigma_i)\\}$ .",
+ "- Let $\\mu_{\\max(p_0)} =: \\max_{i \\in [k]} \\{ \\| \\mu_i \\|_2^2 \\}$ and $\\operatorname*{det}_{\\min(p_0)} =: \\min_{i \\in [k]} \\{ \\operatorname*{det}(\\Sigma_i) \\}$ .",
+ "- Let $\\sigma_{\\min(p_t)} := \\min_{i \\in [k]} \\{ \\sigma_{\\min}(a_t^2 \\Sigma_i + b_t^2 I) \\}$ , $\\sigma_{\\max(p_t)} := \\max_{i \\in [k]} \\{ \\sigma_{\\max}(a_t^2 \\Sigma_i + b_t^2 I) \\}$ .",
+ "- Let $\\operatorname*{det}_{\\min (p_t)}\\coloneqq \\min_{i\\in [k]}\\{\\operatorname *{det}(a_t^2\\Sigma_i + b_t^2 I)\\} .$"
+ ],
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "Definition 3.3 denotes $\\sigma_{\\min(p_0)}$ , $\\sigma_{\\max(p_0)}$ , $\\sigma_{\\min(p_t)}$ , $\\sigma_{\\max(p_t)}$ as the minimum/maximum singular value between the covariance matrices of $k$ -components at the original distribution $p_0$ and $p_t$ . $\\mu_{\\max(p_0)}$ is the maximum $\\ell_2^2$ -norm between mean vectors of the $k$ -components at $p_0$ . $\\operatorname{det}_{\\min(p_0)}$ is the minimum determinant between the covariance matrices of $k$ -components at $p_0$ .",
+ "bbox": [
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+ "type": "text",
+ "text": "Condition 3.4. All conditions here are related to the all time density $p_t$ in Eq. (10), where $t \\in [0, T]$ . Let $x \\in \\mathbb{R}^d$ and $a_t, b_t$ be defined by Definition 4.1. We only consider the $x$ satisfying the following conditions:",
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+ "type": "list",
+ "sub_type": "text",
+ "list_items": [
+ "- Let $\\beta \\leq \\| x - a_t\\mu_i\\| _2\\leq R$ , where $R\\geq 1$ and $\\beta \\in (0,0.1)$ for each $i\\in [k]$",
+ "- Let $p_t(x)$ be defined as Eq. (10) and $p_t(x) \\geq \\gamma$ , where $\\gamma \\in (0, 0.1)$ ."
+ ],
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "In Condition 3.4, $\\beta, R$ are the lower/upper bound of the $\\ell_2$ distance between the input data $x$ and all $k$ scaled mean vectors $a_t\\mu_i$ at timestep $t$ . Let $\\gamma$ be the lower bound of $p_t(x)$ , the pdf at time $t$ and $\\operatorname*{det}_{\\min(p_t)}$ be the minimum determinant at $p_t$ . We assume $\\beta$ and $\\gamma$ are lower bounded/constant, implying that each Gaussian component in the mixture is well-conditioned. This is a standard assumption in diffusion theory and is consistent with other theoretical findings [16, 17, 26, 38, 53, 71]. Clearly, we have $\\sigma_{\\max(p_t)} \\geq \\sigma_{\\max(p_0)}$ .",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Lemma 3.5 (Lipschitz, informal version of Lemma H.3). Assume Condition 3.4 holds. The Lipschitz constant for the",
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+ {
+ "type": "text",
+ "text": "score function $\\frac{\\mathrm{d}\\log(p_t(x))}{\\mathrm{d}x}$ is given by:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} L = \\frac {1}{\\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)} ^ {2}} \\cdot \\exp \\left(- \\frac {\\beta^ {2}}{2 \\sigma_ {\\operatorname* {m a x} \\left(p _ {t}\\right)}}\\right) \\\\ \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\operatorname* {d e t} _ {\\min \\left(p _ {t}\\right)}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\operatorname* {d e t} _ {\\min \\left(p _ {t}\\right)} ^ {1 / 2}}\\right). \\\\ \\end{array}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "In Lemma 3.5, we can clearly see that roughly $L = O(1 / \\mathrm{poly}(\\sigma_{\\min(p_t)}))$ , which means the Lipschitz is only conditioned on the smallest singular value of all Gaussian components but independent of $k$ . The bounded region required in Condition 3.4 applies to where most of the probability mass lies, which is a common assumption in diffusion literature (e.g., [16, 26, 73]). Outside this region, the score function indeed may not be Lipschitz, but this affects regions with negligible probability mass, similar to observations in [73]. We provide an additional empirical study in Section 6 to support our analysis.",
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+ },
+ {
+ "type": "text",
+ "text": "Lemma 3.6 (Second momentum, informal version of Lemma H.2). Let $x_0 \\sim p_0$ , where $p_0$ is defined by Eq. (9). Then, we have",
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} m _ {2} ^ {2} := \\underset {x _ {0} \\sim p _ {0}} {\\mathbb {E}} [ \\| x _ {0} \\| _ {2} ^ {2} ] = \\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ]) \\\\ \\leq \\max _ {i \\in [ k ]} \\left\\{\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} \\left[ \\Sigma_ {i} \\right] \\right\\}. \\\\ \\end{array}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "The proof idea of Lemma 3.5 and Lemma 3.6 is that we first consider the case when $k = 1$ in Appendix D and then we extend to 2 mixtures of Gaussian setting in Appendix E. Finally, we can generalize to $k$ setting in Appendix F and summarize it in Appendix H. In Lemma 3.6, we can see that $m_2^2 = O(1)$ roughly, which is independent of $k$ as well. Later, we will apply our Lemma 3.5 and Lemma 3.6 in Section 5 to get concrete bound for each diffusion process, e.g., DDPM, DPOM and DPUM.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "3.1. Practical insights",
+ "text_level": 1,
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+ "type": "text",
+ "text": "We believe our results in Lemma 3.5 is non-trivial. First, the Lipschitz bound depends inversely exponential on the dimension $d$ . If $d$ grows larger, the Lipschitz constant $L$ becomes much smaller. Second, in practice, the $k$ will be super large for complicated data distribution, e.g., millions of Gaussian components for an image distribution. Many studies need to overcome the large $k$ hardness in learning Gaussian mixture models [5, 8, 47, 57], while our Lipschitz upper-bound is independent with $k$ . These theoretical insights can help practitioners make more informed decisions about model architecture, optimization strategies, and computational resources needed for different applications.",
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+ "type": "page_number",
+ "text": "11439",
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+ {
+ "type": "text",
+ "text": "4. Score Based Model and Diffusion Model",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "In Section 4.1, we first briefly introduce DDPM [30], a stochastic differential equations (SDE) version of the reverse diffusion process, and score-based generative models (SGMs) [63], a generalization of DDPM. In Section 4.2, we introduce multiple solvers for the reverse process.",
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+ "type": "text",
+ "text": "4.1. Background on score based diffusion model",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "First, we denote the input data as $x \\in \\mathbb{R}^d$ and the target original data distribution as $p_0(x)$ . Assuming that the noisy latent state of score-based generative models (SGMs) at time $t$ is a stochastic process $x_{t}$ for $0 \\leq t \\leq T$ , we have the forward SDE is defined by:",
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} x _ {t} = f \\left(x _ {t}, t\\right) \\mathrm {d} t + g (t) \\mathrm {d} w _ {t}, \\quad x _ {0} \\sim p _ {0}, \\quad 0 \\leq t \\leq T \\tag {1}\n$$\n",
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+ "bbox": [
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+ "type": "text",
+ "text": "where $w_{t}\\in \\mathbb{R}^{d}$ is the standard Brownian motion, $f(\\cdot ,t):$ $\\mathbb{R}^d\\to \\mathbb{R}^d$ which is called drift coefficient, and $g(t):\\mathbb{R}\\rightarrow$ $\\mathbb{R}$ which is called diffusion coefficient. We use $p_t(x)$ to denote the marginal probability density function of $x_{t}$ . The pdf at last time step $p_T$ is the prior distribution which often defined as standard Gaussian $p_T(x) = \\mathcal{N}(0,I)$",
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+ "type": "text",
+ "text": "The continuous forward SDE Eq. (1) also has the discrete Markov chain form as",
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\nx _ {t} = a _ {t} x _ {0} + b _ {t} z, \\quad x _ {0} \\sim p _ {0} \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "where $x_0 \\sim p_0(x)$ and $z \\sim \\mathcal{N}(0, I)$ , and $a_t, b_t \\in \\mathbb{R}$ are functions of time. Additionally, we assume as $t \\to T$ , $a_t \\to 0$ and $b_t \\to 1$ . Thus, $x_T \\sim \\mathcal{N}(0, I)$ . Also, clearly when $t \\to 0$ , $a_t \\to 1$ and $b_t \\to 0$ for this is the boundary condition. More specifically, the Eq. (2) can be viewed as the iterative equation in DDPM [30].",
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+ "type": "text",
+ "text": "From [2], we know $x_{t}$ also satisfy the reverse SDE:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} x _ {t} = \\left(f \\left(x _ {t}, t\\right) - g (t) ^ {2} \\nabla \\log p _ {t} \\left(x _ {t}\\right)\\right) \\mathrm {d} t + g (t) \\mathrm {d} \\widetilde {w} _ {t}, \\tag {3}\n$$\n",
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+ "type": "text",
+ "text": "where $\\widetilde{w}_t \\in \\mathbb{R}^d$ is backward Brownian motion [2], and $\\nabla \\log p_t(x_t)$ is the score function. For convenience, we rewrite the reverse SDE Eq. (3) in a forward version by switching the time direction, replacing $t$ with $T - t$ . Let $\\widetilde{x}_t \\coloneqq x_{T - t}$ . The law of $(\\widetilde{x}_t)_{0 \\leq t \\leq T}$ is identical to the law of $(x_{T - t})_{0 \\leq t \\leq T}$ . We use $q_t$ to denote the density of $\\widetilde{x}_t$ :",
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+ "page_idx": 4
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\mathrm {d} \\widetilde {x} _ {t} = (- f (\\widetilde {x} _ {t}, T - t) + g (T - t) ^ {2} \\nabla \\log p _ {T - t} (\\widetilde {x} _ {t})) \\mathrm {d} t \\\\ + g (T - t) \\mathrm {d} w _ {t}. \\tag {4} \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "The process $(\\widetilde{x}_t)_{0\\leq t\\leq T}$ converts noise into samples from $p_0$ , thereby achieving the objective of generative modeling.",
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+ "type": "text",
+ "text": "Since we can not obtain the score function $\\nabla \\log p_t$ directly, we can use a neural network to approximate it, and we denote the estimated score function by $s_t(x)$ . By replacing the score function $\\nabla \\log p_t$ with our approximated score function $s_t(x)$ , we can rewrite Eq. (4) as:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} y _ {t} = \\left(- f \\left(y _ {t}, T - t\\right) + g (T - t) ^ {2} s _ {T - t} \\left(y _ {t}\\right)\\right) \\mathrm {d} t\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n+ g (T - t) \\mathrm {d} w _ {t}, y _ {0} \\sim p _ {T}, 0 \\leq t \\leq T. \\tag {5}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "where $y_{t}$ is the process we approximate by our SGM $s_t$ . For clarity, we mainly focus on the Ornstein-Uhlenbeck (OU) process, which is a diffusion process with exp coefficient:",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Definition 4.1. The forward SDE of OU process $(f(x_{t},t) = -x_{t}$ , and $g(t)\\equiv \\sqrt{2})$ is: $\\mathrm{d}x_{t} = -x_{t}\\mathrm{d}t + \\sqrt{2}\\mathrm{d}w_{t}$ . The corresponding discrete Markov chain form of OU process is given by: $x_{t} = e^{-t}x_{0} + \\sqrt{1 - e^{-2t}} z$ , where we can see that $a_{t} = e^{-t}$ , $b_{t} = \\sqrt{1 - e^{-2t}}$ in Eq. (2).",
+ "bbox": [
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+ "type": "text",
+ "text": "From Eq. (5) under the OU process, we can have:",
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} y _ {t} = \\left(x _ {t} + 2 s _ {T - t} \\left(y _ {t}\\right)\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} w _ {t}. \\tag {6}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "4.2. Definitions of different solvers",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "In practical applications, it's necessary to adopt a discrete-time approximation for sampling dynamics. We have the following definition.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Definition 4.2 (Time discretization). Define the $N$ discretization points as $\\delta = t_0 \\leq t_1 \\leq \\dots \\leq t_N = T$ , where $\\delta \\geq 0$ is the early stopping parameter, with $\\delta = 0$ presenting the normal setting. For each discretization step $k$ , where $1 \\leq k \\leq N$ , the step size is denoted by $h_k := t_k - t_{k-1}$ .",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Let $\\widehat{y}_t$ be the discrete approximation of $y_{t}$ in Eq. (6) starting from $\\widehat{y}_0\\sim \\mathcal{N}(0,I)$ . We use $\\widehat{q}_t$ to denote the density of $\\widehat{y}_t$ . Let $N$ be defined in Definition 4.2 and $t_k^\\prime = T - t_{N - k}$ . To solve Eq. (6), we have two numerical solvers:",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Definition 4.3. We define EulerMaruyama as the numerical solver satisfying $\\widehat{y}_{T - \\delta} =$ EulerMaruyama(T,s), where $\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d$ is the output, $T\\in \\mathbb{R}^{+}$ is the total time, and $s$ is the score estimates. The Euler-Maruyama scheme is, (Equation 5 in [10]), for $t\\in [t_k',t_{k + 1}']$",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} \\hat {y} _ {t} = \\left(\\hat {y} _ {t _ {k} ^ {\\prime}} + 2 s _ {T - t _ {k} ^ {\\prime}} \\left(\\hat {y} _ {t _ {k} ^ {\\prime}}\\right)\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} w _ {t}. \\tag {7}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Definition 4.4. We define ExponentialIntegrator as the numerical solver satisfying $\\widehat{y}_{T - \\delta} =$ ExponentialIntegrator(T,s), where $\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d$ is the output, $T\\in \\mathbb{R}^{+}$ is the total time, and $s$ is the score estimates. The Exponential Integrator scheme is, (Equation 6 in [10]), for $t\\in [t_k',t_{k + 1}']$",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {d} \\widehat {y} _ {t} = \\left(\\widehat {y} _ {t} + 2 s _ {T - t _ {k} ^ {\\prime}} \\left(\\widehat {y} _ {t _ {k} ^ {\\prime}}\\right)\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} w _ {t}. \\tag {8}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "The two methods above are used for solving SDE. The difference is that in the first term of RHS of Euler-Maruyama uses $\\widehat{y} t_{k}^{\\prime}$ , while Exponential Integrator uses $\\widehat{y}_t$ . The Exponential Integrator scheme has a closed-form solution (see detail in Section 1.1 of [10]).",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "We now introduce two ordinary differential equation (ODE) solvers, DPOM and DPUM, which omit the Brownian motion term in Eq. (6). These solvers, defined in",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "page_number",
+ "text": "11440",
+ "bbox": [
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+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Definitions 4.5 and 4.6, represent distinct approaches using predictor-corrector steps to address the reverse process via probability flow ODEs. Specifically, DPOM employs overdamped Langevin Monte Carlo (LMC), while DPUM uses underdamped LMC, enabling more efficient sampling. We will present their concrete step bounds in Section 5.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Definition 4.5. We define DPOM (Diffusion Predictor with Overdamped Modeling) as Algorithm 1 in [14] satisfying $\\widehat{y}_{T - \\delta} = \\mathsf{DPOM}(T,h_{\\mathrm{pred}},h_{\\mathrm{corr}},s)$ , where $\\delta$ is the early stopping parameter, $\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d$ is the output, $T\\in \\mathbb{R}^{+}$ is the total steps, $h_\\mathrm{pred}$ is the predictor step size, $h_\\mathrm{corr}$ is the corrector step size, (see detailed definition in Algorithm 1 of [14]), and $s$ is the score estimates.",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Definition 4.6. We define DPUM (Diffusion Predictor with Underdamped Modeling) as Algorithm 2 in [14], satisfying $\\widehat{y}_{T - \\delta} = \\mathsf{DPUM}(T,h_{\\mathrm{pred}},h_{\\mathrm{corr}},s)$ , where $\\delta$ is the early stopping parameter, $\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d$ is the output, $T\\in \\mathbb{R}^{+}$ is the total steps, $h_\\mathrm{pred}$ is the predictor step size, $h_\\mathrm{corr}$ is the corrector step size, (see detailed definition in Algorithm 2 of [14]), and $s$ is the score estimates.",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "5. Main Result for Application",
+ "text_level": 1,
+ "bbox": [
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+ 448
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "In this section, we will provide the main results of applications. In Section 5.1, we provide our key definitions and assumptions used. In Section 5.2, we provide our results for the total variation bound. In Section 5.3, we provide our results for the KL divergence bound. In Section 5.4, we provide our results for the probability flow ODE method, including DPOM and DPUM.",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "5.1. Key definitions and assumptions",
+ "text_level": 1,
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "We first assume that the loss of the learned score estimator is upper bounded by $\\epsilon_0^2$ in Assumption 5.1. Then, we can show that we can recover the target/image data distribution under a small total variation or KL divergence gap later.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Assumption 5.1 (Score estimation error, Assumption 1 in [10], page 6, and Assumption 3 in [13], page 6). The learned score function $s_t(x)$ satisfies for any $1 \\leq k \\leq N$ ,",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\frac {1}{T} \\sum_ {k = 1} ^ {N} h _ {k} \\underset {p _ {t _ {k}}} {\\mathbb {E}} [ \\| \\nabla \\log p _ {t _ {k}} (x) - s _ {t _ {k}} (x) \\| _ {2} ^ {2} ] \\leq \\epsilon_ {0} ^ {2}.\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "where $h_k$ is the step size defined in Definition 4.2 for step $k$ , $N$ is the total steps, and $\\sum_{k=1}^{N} h_k = T$ .",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "To avoid ill-distribution $q_{T}$ , we have the below definition follows [10, 14].",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Definition 5.2. We define $\\epsilon$ as total variation distance between $q_{T - \\delta}$ and $q_{T}$ .",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Let the distribution $p_0(x)$ be a $k$ -mixture of Gaussians:",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\np _ {0} (x) := \\sum_ {i = 1} ^ {k} \\alpha_ {i} \\mathcal {N} \\left(\\mu_ {i}, \\Sigma_ {i}\\right). \\tag {9}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Using the Proposition 3.2, we know the pdf of $x_{t}$ at the any time $t$ is given by:",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\np _ {t} (x) = \\sum_ {i = 1} ^ {k} \\alpha_ {i} \\mathcal {N} \\left(a _ {t} \\mu_ {i}, a _ {t} ^ {2} \\Sigma_ {i} + b _ {t} ^ {2} I\\right). \\tag {10}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "We introduce Pinsker's inequality, which relates total variation distance to the Kullback-Leibler divergence.",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Lemma 5.3 (Pinsker's inequality [18]). Let $p, q$ are two probability distributions, then we have $\\mathrm{TV}(\\mathrm{p},\\mathrm{q}) \\leq \\sqrt{\\frac{1}{2}\\mathrm{KL}(p\\|q)}$ .",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "From Lemma 5.3, we can see the total variation is a weaker bound than KL divergence.",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "5.2. Total variation",
+ "text_level": 1,
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Now, we are ready to present our result for total variation bound assuming data distribution is $k$ -mixture of Gaussian $(p_0$ in Eq. (9)). Recall $\\epsilon_0$ is defined in Assumption 5.1, $\\epsilon$ is defined in Definition 5.2 and $h_k$ is defined in Definition 4.2. See the proof in Appendix I.",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Theorem 5.4 (DDPM, total variation, informal version of Theorem I.1). Assume Condition 3.4 and Assumption 5.1 hold. The step size $h_k \\coloneqq T / N$ satisfies $h_k = O(1 / L)$ and $L \\geq 1$ for $k \\in [N]$ . Let $\\widehat{q}$ denote the density of the output of the Euler-Maruyama defined by Definition 4.3. Then, we have",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\mathrm {T V} (\\widehat {q}, p _ {0}) \\lesssim \\underbrace {\\sqrt {\\mathrm {K L} (p _ {0} \\| \\mathcal {N} (0 , I))} \\exp (- T)} _ {\\text {c o n v e r g e n c e o f f o r w a r d p r o c e s s}} \\\\ + \\underbrace {(L \\sqrt {d h} + L m _ {2} h) \\sqrt {T}} _ {\\text {d i s c r e t i z a t i o n e r r o r}} + \\underbrace {\\epsilon_ {0} \\sqrt {T}} _ {\\text {s c o r e e s t i m a t i o n e r r o r}}. \\\\ \\end{array}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "where $L = \\frac{1}{\\sigma_{\\min(p_t)}} + \\frac{2R^2}{\\gamma^2\\sigma_{\\min(p_t)}^2} \\cdot \\left(\\frac{1}{(2\\pi)^d\\operatorname*{det}_{\\min(p_t)}} + \\right.$",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "$\\frac{1}{(2\\pi)^{d / 2}\\operatorname*{det}_{\\min (p_t)}^{1 / 2}}$ $\\exp (-\\frac{\\beta^2}{2\\sigma_{\\max(p_t)}}),\\qquad m_2\\qquad =$",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "$(\\sum_{i=1}^{k} \\alpha_i (\\|\\mu_i\\|_2^2 + \\mathrm{tr}[\\Sigma_i]))^{1/2}$ , and $\\mathrm{KL}(p_0(x) \\| \\mathcal{N}(0, I)) \\leq \\frac{1}{2} (-\\log(\\det_{\\min(p_0)}) + d\\sigma_{\\max(p_0)} + \\mu_{\\max(p_0)} - d)$ .",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "In Theorem 5.4, suppose that $m_2 \\leq d$ and choose $T = \\Theta(\\log(\\mathrm{KL}(p_0 \\| \\mathcal{N}(0, I)) / \\epsilon))$ , $h_k = \\Theta\\left(\\frac{\\epsilon^2}{L^2d}\\right)$ , then we have $\\mathrm{TV}(\\widehat{q}, p_0) \\leq \\widetilde{O}(\\epsilon + \\epsilon_0)$ , for $N = \\widetilde{O}(L^2d / \\epsilon^2)$ . In particular, in order to have $\\mathrm{TV}(\\widehat{q}, p_0) \\leq \\epsilon$ , it suffices to have score error $\\epsilon_0 \\leq \\widetilde{O}(\\epsilon)$ , where $\\widetilde{O}(\\cdot)$ hides $T$ which is a log term. Thus, Theorem 5.4 provides a guarantee for total variation bound between target data distribution $p_0$ and learned output distribution $\\widehat{q}$ with concrete $L$ and $m_2$ .",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "page_number",
+ "text": "11441",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "5.3. KL divergence",
+ "text_level": 1,
+ "bbox": [
+ 89,
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+ 240,
+ 107
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "Similarly, we can present our result for the KL divergence bound in the following two theorems, assuming data distribution is $k$ -mixture of Gaussian. Recall $\\epsilon_0$ is defined in Assumption 5.1, $\\epsilon$ is denied in Definition 5.2 and $h_k$ is defined in Definition 4.2. See the proof in Appendix I.",
+ "bbox": [
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+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "Theorem 5.5 (DDPM, KL divergence, informal version of Theorem I.2). Assume Condition 3.4 and Assumption 5.1 hold. We use uniform discretization points.",
+ "bbox": [
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+ 241
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "(1) Let $\\widehat{q}$ denote the density of the output of the ExponentialIntegrator (Definition 4.4), we have",
+ "bbox": [
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+ 272
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {K L} (p _ {0} \\| \\widehat {q}) \\lesssim (M _ {2} + d) \\exp (- T) + T \\epsilon_ {0} ^ {2} + \\frac {d T ^ {2} L ^ {2}}{N}.\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "In particular, choosing $T = \\Theta (\\log (M_2d / \\epsilon_0))$ and $N = \\Theta (dT^2 L^2 /\\epsilon_0^2)$ , then $\\mathrm{KL}(p_0\\| \\widehat{q}) = \\widetilde{O} (\\epsilon_0^2)$ .",
+ "bbox": [
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+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "(2) Let $\\widehat{q}$ denote the density of the output of the EulerMaruyama (Definition 4.3), we have",
+ "bbox": [
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+ 382
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathrm {K L} (p _ {0} \\| \\widehat {q}) \\lesssim (M _ {2} + d) \\exp (- T) + T \\epsilon_ {0} ^ {2} + \\frac {d T ^ {2} L ^ {2}}{N} + \\frac {T ^ {3} M _ {2}}{N ^ {2}}.\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ 390,
+ 500,
+ 422
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\begin{array}{l l} w h e r e M _ {2} = \\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ]) a n d L = \\\\ \\frac {1}{\\sigma_ {\\min (p _ {t})}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\min (p _ {t})} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\det _ {\\min (p _ {t})}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\det _ {\\min (p _ {t})} ^ {1 / 2}}\\right). \\end{array} \\\\ \\exp \\bigl (- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}} \\bigr). \\\\ \\end{array}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ 483,
+ 498
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "Theorem 5.6 (DDPM, KL divergence for smooth data distribution, informal version of Theorem I.3). Assume Condition 3.4 and Assumption 5.1 hold. We use the exponentially decreasing (then constant) step size $h_k = c \\min \\{ \\max \\{ t_k, 1 / L \\}, 1 \\}$ , $c = \\frac{T + \\log L}{N} \\leq \\frac{1}{Kd}$ . Let $\\widehat{q}$ denote the density of the output of the ExponentialIntegrator defined by Definition 4.4. Then, we have",
+ "bbox": [
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+ 609
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\operatorname {K L} \\left(p _ {0} \\| \\widehat {q}\\right) \\lesssim \\left(M _ {2} + d\\right) \\exp (- T) + T \\epsilon_ {0} ^ {2} + \\frac {d ^ {2} (T + \\log L) ^ {2}}{N},\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 6
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\begin{array}{l l} w h e r e M _ {2} = \\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ]) a n d L = \\\\ \\frac {1}{\\sigma_ {\\min (p _ {t})}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\min (p _ {t})} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\det _ {\\min (p _ {t})}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\det _ {\\min (p _ {t})} ^ {1 / 2}}\\right). \\end{array} \\\\ \\begin{array}{l} \\exp (- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}}). \\quad \\text {I n p a r t i c u l a r , i f w e s e t T =} \\\\ \\Theta (\\log (M _ {2} d / \\epsilon_ {0})) \\text {a n d N = \\Theta (d ^ {2} (T + \\log L) ^ {2} / \\epsilon_ {0} ^ {2}) , t h e n} \\\\ \\mathrm {K L} (p _ {0} \\| \\widehat {q}) \\leq \\widetilde {O} (\\epsilon_ {0} ^ {2}). \\text {I n a d d i t i o n , f o r E u l e r - M a r u y a m a} \\\\ \\text {s c h e m e d e f i n e d i n D e f i n i o n 4 . 3 , t h e s a m e b o u n d s h o l d w i t h} \\\\ \\text {a n a n d i s t i t i o n a l M _ {2} \\sum_ {k = 1} ^ {N} h _ {k} ^ {3} t e r m .} \\end{array} \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "Theorem 5.6 and Theorem 5.5 provide a guarantee for KL divergence bound between target data distribution $p_0$ and learned output distribution $\\widehat{q}$ with concrete $L$ and $M_2$ . Theorem 5.6 has $\\log^2 L$ instead of $L^2$ in the bound for total number of discretization points $N$ , but includes an additional $d$ compared to Theorem 5.5. On the other hand, Theorem 5.6 requires the data distribution $p_0$ is Lipschitz and",
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+ "type": "text",
+ "text": "second-order differentiable [10], allowing a better bound in terms of $L$ , while all other theorems [13, 14] require conditions about Lipschitz on $p_t$ for any $0 \\leq t \\leq T$ . However, our assumption $p_0$ is $k$ -mixture of Gaussians satisfies all conditions they use.",
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+ "type": "text",
+ "text": "From Lemma 5.3, we can compare KL divergence results with total variation results. Notice that $M_2 = m_2^2$ when comparing theorems for total variation and KL divergence. According to Lemma 5.3, the square of the TV distance is comparable to the KL divergence, which explains the squared relationship of the second momentum term.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "5.4. Probability flow ODE",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Notice that in the previous results we are considering SDE based models. However from [63], we know that we can also use ODE to run the reverse process, which has the same marginal distribution with SDE reverse process but is thereby deterministic. In this section, we provide results of DPOM and DPUM (Algorithm 1 and 2 in [14]) algorithms which are based on ODE reverse process.",
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+ "type": "text",
+ "text": "Theorem 5.7 (DPOM, informal version of Theorem I.4). Assume Condition 3.4 and Assumption 5.1 hold. We use the DPOM algorithm defined in Definition 4.5, and let $\\widehat{q}$ be the output density of it. Then, we have",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\mathrm {T V} (\\widehat {q}, p _ {0}) \\lesssim (\\sqrt {d} + m _ {2}) \\exp (- T) + L ^ {2} T d ^ {1 / 2} h _ {\\mathrm {p r e d}} \\\\ + L ^ {3 / 2} T d ^ {1 / 2} h _ {\\mathrm {c o r r}} ^ {1 / 2} + L ^ {1 / 2} T \\epsilon_ {0} + \\epsilon . \\\\ \\end{array}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\begin{array}{l} \\text {w h e r e} m _ {2} = (\\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ])) ^ {1 / 2} \\text {a n d} L = \\\\ \\frac {1}{\\sigma_ {\\min (p _ {t})}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\min (p _ {t})} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\det _ {\\min (p _ {t})}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\det _ {\\min (p _ {t})} ^ {1 / 2}}\\right). \\end{array} \\\\ \\begin{array}{l} \\exp (- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}}). \\quad \\text {I n p a r t i c u l a r , i f w e s e t T =} \\\\ \\Theta (\\log (d m _ {2} / \\epsilon)), h _ {\\text {p r e d}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {2} d ^ {1 / 2}}), h _ {\\text {c o r r}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {3} d}), \\text {a n d} \\\\ \\text {i f t h e s c o r e e s t i m a t i o n e r r o r s a t i s f i e s \\epsilon_ {0} \\leq \\widetilde {O} (\\frac {\\epsilon}{\\sqrt {L}}) , t h e n w e} \\\\ \\widetilde {\\Theta} (L ^ {3} d / \\epsilon^ {2}) \\text {s t e p s .} \\end{array} \\\\ \\end{array}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "Theorem 5.8 (DPUM, informal version of Theorem I.5). Assume Condition 3.4 and Assumption 5.1 hold. We use the DPUM algorithm defined in Definition 4.6, and let $\\widehat{q}$ be the output density of it. Then, we have",
+ "bbox": [
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\mathrm {T V} (\\widehat {q}, p _ {0}) \\lesssim (\\sqrt {d} + m _ {2}) \\exp (- T) + L ^ {2} T d ^ {1 / 2} h _ {\\mathrm {p r e d}} \\\\ + L ^ {3 / 2} T d ^ {1 / 2} h _ {\\mathrm {c o r r}} ^ {1 / 2} + L ^ {1 / 2} T \\epsilon_ {0} + \\epsilon . \\\\ \\end{array}\n$$\n",
+ "text_format": "latex",
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} w h e r e L = \\frac {1}{\\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d}} \\det _ {\\min \\left(p _ {t}\\right)} + \\right. \\\\ \\frac {1}{(2 \\pi) ^ {d / 2} \\operatorname* {d e t} _ {\\min (p _ {t})} ^ {1 / 2}}) \\quad \\cdot \\quad \\exp \\left(- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}}\\right) \\quad a n d \\quad m _ {2} \\quad = \\\\ \\begin{array}{l} (\\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ])) ^ {1 / 2}. \\quad I n \\text {p a r t i c u l a r , i f} \\\\ w e s e t T = \\Theta (\\log (d m _ {2} / \\epsilon)), h _ {\\mathrm {p r e d}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {2} d ^ {1 / 2}}), \\\\ h _ {\\mathrm {c o r r}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {3 / 2} d ^ {1 / 2}}), a n d i f t h e s c o r e e s t i m a t i o n e r r o r \\end{array} \\\\ \\end{array}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "page_number",
+ "text": "11442",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "satisfies $\\epsilon_0\\leq \\widetilde{O} (\\frac{\\epsilon}{\\sqrt{L}})$ , then we can obtain TV error $\\epsilon$ with a total iteration complexity of $\\widetilde{\\Theta} (L^2 d^{1 / 2} / \\epsilon)$ steps.",
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "Theorem 5.7 and Theorem 5.8 provide a guarantee for total variation bound between target data distribution $p_0$ and learned output distribution $\\widehat{q}$ with concrete $L$ and $M_2$ for ODE reverse process. The difference between the DPOM (Theorem 5.7) and DPUM (Theorem 5.8) is the complexity of $h_{\\mathrm{corr}}$ and the final iteration complexity term. Using DPUM algorithm, we can reduce the total iteration complexity from $\\widetilde{\\Theta}(L^3 d / \\epsilon^2)$ to $\\widetilde{\\Theta}(L^2 \\sqrt{d} / \\epsilon)$ .",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "6. Experiments",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "We provide empirical evidence supporting our theoretical results. In Section 6.1, we describe the experimental settings and data configurations used in our study. In Section 6.2, we analyze the correlation between the Lipschitz constant and the performance of the diffusion model.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "6.1. Experiment setup",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "We used a Gaussian dataset with three modes (clusters) in two-dimensional space, each having the same covariance matrix. By adjusting the covariance, we examine the impact of the Lipschitz constant on model performance. The model we use is a one hidden layer MLP with 32 hidden dimensions. We use DDPM algorithm for our forward diffusion process and reverse denoising process. The number of inference steps we use is 200. It is optimized by MSE loss, and the performance metrics are log likelihood and Mahalanobis squared distance. For the training, we use AdamW optimizer with 0.001 learning rate and training epochs 100.",
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+ },
+ {
+ "type": "text",
+ "text": "For the evaluation, we sample 1000 dots from central Gaussian distribution with variance 1. Then calculate the two losses of output and ground truth.",
+ "bbox": [
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+ "page_idx": 7
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+ {
+ "type": "text",
+ "text": "6.2. Correlation study",
+ "text_level": 1,
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "This section explores the relationship between the Lipschitz constant and key performance indicators of the diffusion model. Table 2 shows the average log likelihoods with Lipschitz constants, and Table 3 presents the average Mahalanobis squared distances.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Figure 2 portrays two line charts: the upper panel maps the log likelihood against the Lipschitz constant, and the lower panel charts the Mahalanobis squared distance.",
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+ {
+ "type": "text",
+ "text": "From Table 2, Table 3 and Figure 2, we can conclude the message that a larger covariance leads to a smaller Lipschitz (more smooth) target function, which is easier to learn. This is aligned with our theoretical analysis, i.e., Lemma 3.5, Theorem 5.4, Theorem 5.5, and Theorem 5.6.",
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+ {
+ "type": "text",
+ "text": "7. Conclusion",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "We have presented a theoretical analysis of the Lipschitz continuity and second momentum properties of diffusion",
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+ "type": "table",
+ "img_path": "images/7e28b3a2264a18a522778b61ba4080621756c5e9c9dd75195ddf67b979bb1591.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Covariance | Lipschitz | Avg Log Likelihood |
| 1 | 3.69 × 107 | -9901.2324 |
| 10 | 3.23 × 104 | -1001.9962 |
| 100 | 31.8916 | -106.1019 |
| 200 | 3.9870 | -57.2244 |
| 500 | 0.2567 | -28.0872 |
| 600 | 0.1491 | -24.9577 |
| 700 | 0.0943 | -22.6524 |
| 800 | 0.0634 | -21.0397 |
| 900 | 0.0448 | -19.7688 |
| 1000 | 0.0328 | -18.7532 |
",
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+ "type": "table",
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+ "table_caption": [
+ "Table 2. Log Likelihood Loss for Different Lipschitz. For the Covariance column, the number being $z$ means that the covariance matrix $\\Sigma = zI_{2\\times 2}$ . We compute the corresponding Lipschitz $L$ and report the evaluation loss (Avg Log Likelihood)."
+ ],
+ "table_footnote": [],
+ "table_body": "| Covariance | Lipschitz | Avg Mahalanobis2 |
| 1 | 3.69 × 107 | 19798.7871 |
| 10 | 3.23 × 104 | 1995.7114 |
| 100 | 31.8916 | 199.3178 |
| 200 | 3.9870 | 100.1765 |
| 500 | 0.2567 | 40.0695 |
| 600 | 0.1491 | 33.4458 |
| 700 | 0.0943 | 28.5269 |
| 800 | 0.0634 | 25.0344 |
| 900 | 0.0448 | 22.2571 |
| 1000 | 0.0328 | 20.0152 |
",
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+ "type": "text",
+ "text": "Table 3. Mahalanobis Squared Loss for Different Lipschitz. For the Covariance column, the number being $z$ means that the covariance matrix $\\Sigma = zI_{2\\times 2}$ . We compute the corresponding Lipschitz $L$ and report the evaluation loss (Avg Mahalanobis).",
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+ "img_path": "images/712d927a96b39649212cf578040dfc9584df37d21a88dc5ccaef1240ad169770.jpg",
+ "image_caption": [
+ "Figure 2. Left: Log likelihood vs. Lipschitz constant. Right: Mahalanobis squared distance vs. Lipschitz constant."
+ ],
+ "image_footnote": [],
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+ {
+ "type": "text",
+ "text": "models. Our results provide concrete bounds on key properties of the diffusion process and establish error guarantees for various diffusion solvers. These findings contribute to a deeper understanding of diffusion models and spur further theoretical and practical advancements in this field.",
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+ "type": "text",
+ "text": "References",
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+ "content": "Yingyu Liang\\(^{1,3,\\dagger}\\) Zhizhou Sha\\(^{2}\\) Zhenmei Shi\\(^{3}\\) Zhao Song\\(^{4,*}\\) Mingda Wan\\(^{5}\\) Yufa Zhou\\(^{6}\\) \n\\(^{1}\\)The University of Hong Kong, \\(^{2}\\)University of Texas at Austin, \\(^{3}\\)University of Wisconsin-Madison \n\\(^{4}\\)University of California, Berkeley, \\(^{5}\\)Independent Researcher, \\(^{6}\\)University of Pennsylvania"
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+ "content": "Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking. In this paper, we bridge this gap by providing a detailed examination of these smoothness properties for the case where the target data distribution is a mixture of Gaussians, which serves as a universal approximator for smooth densities such as image data. We prove that if the target distribution is a \\(k\\)-mixture of Gaussians, the density of the entire diffusion process will also be a \\(k\\)-mixture of Gaussians. We then derive tight upper bounds on the Lipschitz constant and second momentum that are independent of the number of mixture components \\(k\\). Finally, we apply our analysis to various diffusion solvers, both SDE and ODE based, to establish concrete error guarantees in terms of the total variation distance and KL divergence between the target and learned distributions. Furthermore, our preliminary experiments support our theoretical analysis. Our results provide deeper theoretical insights into the dynamics of the diffusion process under common data distributions."
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+ "content": "Diffusion models, a prominent generative modeling framework, have rapid progress and garnered significant attention in recent years, due to their potential powerful ability to generate high-quality samples across various domains and diverse applications. Score-based generative diffusion models [30, 63] can generate high-quality image samples comparable to GANs, which require adversarial optimization. Based on the U-Net [50], stable diffusion [49], a conditional multi-modality generation model, can successfully generate business-used images. Based on the Transformer (DiT) [45], OpenAI released a video diffusion model, SORA [44], with a surprising performance."
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+ "content": "However, despite these technological strides, a critical gap persists in the theoretical understanding of diffusion processes, especially concerning the Lipschitz continuity and second momentum properties of these models. Many existing studies ([10, 13, 14, 21, 35] and many more) make simplifying assumptions about these key smoothness properties but lack rigorous formulation or comprehensive analysis. This paper aims to bridge this theoretical gap by providing a detailed examination of the Lipschitz and second momentum characteristics. To make the data distribution analyzable, we consider the mixture of Gaussian data distribution (see illustration in Figure 1), which is a universal approximation (Fact 1.1) for any smooth density, such as complex image and video data distributions."
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+ "content": "Figure 1. An illustration of discrete diffusion process for 8 mixture of Gaussian as shown in Eq. (2). The left figure represents the target 2-dimensional data distribution \\( p_0 \\). The right figure represents the standard normal distribution \\( p_T = \\mathcal{N}(0, I_{2\\times 2}) \\), where \\( T = 3 \\). This experimental setup is also used in [13]."
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+ "content": "- We analyze the Lipschitz and second momentum of \\( k \\)-mixture of Gaussian data distribution and provide a tight upper bound, which is independent of \\( k \\), (Lemma 3.5 and Lemma 3.6), even when \\( k \\) goes to infinity (see more discussion in Section 3.1)."
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+ "content": "- After applying our analysis to DDPM, which is the SDE version of reverse process, we prove the dynamic of the diffusion process satisfies some concrete total variation bound (Theorem 5.4) and concrete KL divergence bound (Theorem 5.5 and Theorem 5.6) under choosing some total discretization steps. See a summary in Table 1."
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+ "content": "There is a rich line of work that studies a mixture of Gaussian data distribution under the diffusion process, sharing a similar popular setting. However, none focuses on the Lipschitz smoothness and second momentum property as ours. We provide a short summary here for convenience. [71] analyses the effect of diffusion guidance and provides theoretical insights on the instillation of task-specific information into the score function and conditional generation, e.g., text-to-image, by studying the mixture of Gaussian data distribution as a case study. [27] propose a new SDE-solver for diffusion models under a mixture of Gaussian data. [26, 53] learn mixtures of Gaussian data using the DDPM objective and gives bound for sample complexity by assuming all covariance matrices are identity but does not use Lipschitz, while our work does not need identity assumptions. [16] mainly focuses on solving \\( k \\)-mixture of Gaussian in diffusion model by leveraging the property of the mixture of Gaussian and polynomial approximation methods and gives bound for sample complexity by assuming the covariance matrices have bounded condition number and that the mean vectors and covariance matrices lie in a bounded ball."
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+ "content": "Diffusion models and score-based models. [30] introduced the concept of denoising diffusion probabilistic models (DDPM), which learn to reverse a gradual noising process to generate samples and have been applied to many area [68-70]. Then, [63] used Stochastic Differential Equations (SDE) to build the diffusion model and explored the equivalence between score-based generative models (SGMs) and diffusion models, generalizing the diffusion model to continuous time. There is a line of works [58] studying the connection between diffusion models and nonequilibrium thermodynamics, providing a theoretical foundation for these models. Another line of work has focused on improving the efficiency and quality of diffusion models [42]. Particularly, [59] leverages score matching to train diffusion models more efficiently; [43] improved architectures and training techniques for diffusion models. Diffusion models have been applied to various domains beyond image generation, achieving impressive results, e.g., text-to-image synthesis [12], audio synthesis [33], image superresolution [51], and so on."
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+ "content": "Mixture of Gaussian. Mixtures of Gaussian are among the most fundamental and widely used statistical models [1, 3-6, 8, 9, 19, 20, 22-25, 37, 41, 55, 56, 66, 72] and studied in neural networks learning [39, 47, 54, 57]. Recently, they have also been widely studied in diffusion models [16, 26, 27, 53, 71] (see detailed discussion in Section 1)."
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+ "content": "Lipschitz and second momentum in score estimation. There is a line of work using bounded Lipschitz and second momentum as their key smoothness assumptions for the whole diffusion process without giving any concrete formulation [7, 10, 11, 13-15, 32, 34, 35, 40, 74], while our work gives a \"close-form\" formulation of Lipschitz and second momentum. [73] primarily identifies the existence of Lipschitz singularities without deriving tight bounds for arbitrary data distributions. In contrast, our analysis provides explicit bounds for the Lipschitz constant in terms of the pa"
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+ "content": "| Type | Error guarantee | Steps for Φ(ε02) error | Reference |
| DDPM [13] | TV(p0, q)2 | Θ(d/ε02) | Theorem 5.4 |
| DDPM [10] | KL(p0, q) | Θ(d/ε02) | Theorem 5.5 |
| DDPM [10] | KL(p0, q) | Θ(d2/ε02) | Theorem 5.6 |
| DPOM [14] | TV(p0, q)2 | Θ(d/ε02) | Theorem 5.7 |
| DPUM [14] | TV(p0, q)2 | Θ(√d/ε0) | Theorem 5.8 |
"
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+ "content": "Table 1. A summary of our applications using our Lipschitz and second momentum bound, when we assume \\(\\sigma_{\\min (pt)}\\) as a constant (defined in Definition 3.3). The third column means the number of discretization points required to guarantee a small total variation/KL divergence distance between the target data distribution \\(p_0\\) and the learned distribution \\(\\widehat{q}\\)"
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+ "content": "rameters of the underlying mixture model. It connects these Lipschitz properties to concrete error guarantees for various solvers. There is another rich line of work studying how to train the diffusion models to have a better theoretical guarantee [11, 14-16, 26-28, 31, 36, 40, 48, 53, 59-62, 64, 65]."
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+ "angle": 0,
+ "content": "3. Lipschitz and Second Momentum of Mixture of Gaussian"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "In this section, we discuss the notations used, several key definitions for \\(k\\) mixtures of Gaussian distributions, and lemmas concerning the Lipschitz continuity and second momentum of these mixtures. We begin by presenting the notations that are used throughout the paper."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.485,
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+ ],
+ "angle": 0,
+ "content": "Notations. For two vectors \\( x \\in \\mathbb{R}^n \\) and \\( y \\in \\mathbb{R}^n \\), we use \\( \\langle x, y \\rangle \\) to denote the inner product between \\( x, y \\), i.e., \\( \\langle x, y \\rangle = \\sum_{i=1}^{n} x_i y_i \\). We use \\( \\operatorname{Pr}[] \\) to denote the probability, we use \\( \\mathbb{E}[] \\) to denote the expectation. We use \\( e_i \\) to denote a vector where only \\( i \\)-th coordinate is 1, and other entries are 0. For each \\( a, b \\in \\mathbb{R}^n \\), we use \\( a \\circ b \\in \\mathbb{R}^n \\) to denote the vector where \\( i \\)-th entry is \\( (a \\circ b)_i = a_i b_i \\) for all \\( i \\in [n] \\), and this is the Hardamard product. We use \\( \\mathbf{1}_n \\) to denote a length-\\( n \\) vector where all the entries are ones. We use \\( x_{i,j} \\) to denote the \\( j \\)-th coordinate of \\( x_i \\in \\mathbb{R}^n \\). We use \\( \\|x\\|_p \\) to denote the \\( \\ell_p \\) norm of a vector \\( x \\in \\mathbb{R}^n \\), i.e. \\( \\|x\\|_1 := \\sum_{i=1}^{n} |x_i| \\), \\( \\|x\\|_2 := (\\sum_{i=1}^{n} x_i^2)^{1/2} \\), and \\( \\|x\\|_\\infty := \\max_{i \\in [n]} |x_i| \\). For \\( k > n \\), for any matrix \\( A \\in \\mathbb{R}^{k \\times n} \\), we use \\( \\|A\\| \\) to denote the spectral norm of \\( A \\), i.e. \\( \\|A\\| := \\sup_{x \\in \\mathbb{R}^n} \\|Ax\\|_2 / \\|x\\|_2 \\). We use \\( \\sigma_{\\min}(A), \\sigma_{\\max}(A) \\) to denote the minimum/maximum singular value of matrix \\( A \\). For a square matrix \\( A \\), we use \\( \\mathrm{tr}[A] \\) to denote the trace of \\( A \\), i.e., \\( \\mathrm{tr}[A] = \\sum_{i=1}^{n} A_{i,i} \\). We use \\( \\det(A) \\) to denote the determinant of matrix \\( A \\). We use \\( f * g \\) to denote the convolution of 2 functions \\( f, g \\). In addition to \\( O(\\cdot) \\) notation, for two functions \\( f, g \\), we use the shorthand \\( f \\lesssim g \\) (resp. \\( \\gtrsim \\)) to indicate that \\( f \\leq Cg \\) (resp. \\( \\geq \\)) for an absolute constant \\( C \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.814,
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+ ],
+ "angle": 0,
+ "content": "\\(k\\) mixtures of Gaussian. Now, we are ready to introduce \\(k\\) mixtures of Gaussian. Formally, we can have the following definition of the pdf for \\(k\\) mixtures of Gaussian."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.87,
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+ 0.903
+ ],
+ "angle": 0,
+ "content": "Definition 3.1 (\\(k\\) mixtures of Gaussian pdf). Let \\(x \\in \\mathbb{R}^d\\), \\(i \\in [k]\\), \\(t \\geq 0 \\in \\mathbb{R}\\). For a fixed timestamp \\(t\\), (1) let \\(\\alpha_i(t) \\in\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.272,
+ 0.907,
+ 0.336
+ ],
+ "angle": 0,
+ "content": "(0,1) be the weight for the \\(i\\)-th Gaussian component at time \\(t\\) and \\(\\sum_{i=1}^{k} \\alpha_i(t) = 1\\); (2) let \\(\\mu_i(t) \\in \\mathbb{R}^d\\) and \\(\\Sigma_i(t) \\in \\mathbb{R}^{d \\times d}\\) be the mean vector and covariance matrix for the \\(i\\)-th Gaussian component at time \\(t\\). Then, we define"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.529,
+ 0.346,
+ 0.888,
+ 0.42
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} p _ {t} (x) := \\sum_ {i = 1} ^ {k} \\frac {\\alpha_ {i} (t)}{(2 \\pi) ^ {d / 2} \\det (\\Sigma_ {i} (t)) ^ {1 / 2}} \\\\ \\cdot \\exp (- \\frac {1}{2} (x - \\mu_ {i} (t)) ^ {\\top} \\Sigma_ {i} (t) ^ {- 1} (x - \\mu_ {i} (t))). \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.429,
+ 0.907,
+ 0.492
+ ],
+ "angle": 0,
+ "content": "Then, the following lemma shows that the linear combination between \\( k \\) mixtures of Gaussian and a single standard Gaussian is still a \\( k \\) mixtures of Gaussian. The proof is in Appendix H."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.5,
+ 0.907,
+ 0.547
+ ],
+ "angle": 0,
+ "content": "Proposition 3.2 (Informal version of Proposition H.1). Let \\(a, b \\in \\mathbb{R}\\). Let \\(\\mathcal{D}\\) be a \\(k\\)-mixture of Gaussian distribution, and let \\(p\\) be its pdf defined in Definition 3.1, i.e.,"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.565,
+ 0.557,
+ 0.852,
+ 0.63
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} p (x) := \\sum_ {i = 1} ^ {k} \\frac {\\alpha_ {i}}{(2 \\pi) ^ {d / 2} \\det (\\Sigma_ {i}) ^ {1 / 2}} \\\\ \\cdot \\exp \\left(- \\frac {1}{2} (x - \\mu_ {i}) ^ {\\top} \\Sigma_ {i} ^ {- 1} (x - \\mu_ {i})\\right) \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.64,
+ 0.907,
+ 0.703
+ ],
+ "angle": 0,
+ "content": "Let \\( x \\in \\mathbb{R}^d \\) sample from \\( \\mathcal{D} \\). Let \\( z \\in \\mathbb{R}^d \\) and \\( z \\sim \\mathcal{N}(0, I) \\) which is independent from \\( x \\). Then, we have a new random variable \\( y = ax + bz \\) which is also a \\( k \\)-mixture of Gaussian distribution \\( \\widetilde{\\mathcal{D}} \\), whose pdf is"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.563,
+ 0.714,
+ 0.856,
+ 0.787
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\widetilde {p} (x) := \\sum_ {i = 1} ^ {k} \\frac {\\alpha_ {i}}{(2 \\pi) ^ {d / 2} \\det (\\widetilde {\\Sigma} _ {i}) ^ {1 / 2}} \\\\ \\cdot \\exp (- \\frac {1}{2} (x - \\widetilde {\\mu} _ {i}) ^ {\\top} \\widetilde {\\Sigma} _ {i} ^ {- 1} (x - \\widetilde {\\mu} _ {i})), \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.798,
+ 0.75,
+ 0.816
+ ],
+ "angle": 0,
+ "content": "where \\(\\widetilde{\\mu}_i = a\\mu_i,\\widetilde{\\Sigma}_i = a^2\\Sigma_i + b^2 I.\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.826,
+ 0.907,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "The Gaussian mixture model is a universal approximator of densities (Fact 1.1). Then, it is natural to assume that the target/image \\((p_0)\\) data distribution as the \\(k\\) mixtures of Gaussian. Proposition 3.2 tells us that if the target data distribution is \\(k\\) mixtures of Gaussian, then by Eq. (2), the pdf"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.48,
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+ ],
+ "angle": 0,
+ "content": "11438"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.482,
+ 0.121
+ ],
+ "angle": 0,
+ "content": "of the whole diffusion process is \\(k\\) mixtures of Gaussian, i.e., the \\(p_t\\) for any \\(t \\in [0, T]\\). See details in Section 4."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.123,
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+ "angle": 0,
+ "content": "Main properties. Thus, we only need to analyze the property, i.e., Lipschitz constant and second momentum, of \\( k \\) mixtures of Gaussian, to have a clear guarantee for the whole diffusion process. In the following two lemmas, we will give concrete bounds of the Lipschitz constant and second momentum of \\( k \\) mixtures of Gaussian. Both proofs can be found in Appendix H."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.23,
+ 0.483,
+ 0.259
+ ],
+ "angle": 0,
+ "content": "First, we define the following conditions of the \\(k\\) mixtures of Gaussian."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.273,
+ 0.484,
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+ ],
+ "angle": 0,
+ "content": "Definition 3.3. The first two definitions here are related to the beginning time density \\( p_0 \\) in Eq. (9). The last two definitions are related to the all time density \\( p_t \\) in Eq. (10), where \\( t \\in [0, T] \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.334,
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+ 0.365
+ ],
+ "angle": 0,
+ "content": "- Let \\(\\sigma_{\\min(p_0)} =: \\min_{i \\in [k]} \\{\\sigma_{\\min}(\\Sigma_i)\\}\\) and \\(\\sigma_{\\max(p_0)} =: \\max_{i \\in [k]} \\{\\sigma_{\\max}(\\Sigma_i)\\}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.365,
+ 0.482,
+ 0.395
+ ],
+ "angle": 0,
+ "content": "- Let \\(\\mu_{\\max(p_0)} =: \\max_{i \\in [k]} \\{ \\| \\mu_i \\|_2^2 \\}\\) and \\(\\operatorname*{det}_{\\min(p_0)} =: \\min_{i \\in [k]} \\{ \\operatorname*{det}(\\Sigma_i) \\}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.395,
+ 0.482,
+ 0.426
+ ],
+ "angle": 0,
+ "content": "- Let \\(\\sigma_{\\min(p_t)} := \\min_{i \\in [k]} \\{ \\sigma_{\\min}(a_t^2 \\Sigma_i + b_t^2 I) \\}\\), \\(\\sigma_{\\max(p_t)} := \\max_{i \\in [k]} \\{ \\sigma_{\\max}(a_t^2 \\Sigma_i + b_t^2 I) \\}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.426,
+ 0.414,
+ 0.442
+ ],
+ "angle": 0,
+ "content": "- Let \\(\\operatorname*{det}_{\\min (p_t)}\\coloneqq \\min_{i\\in [k]}\\{\\operatorname *{det}(a_t^2\\Sigma_i + b_t^2 I)\\} .\\)"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.091,
+ 0.334,
+ 0.483,
+ 0.442
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.454,
+ 0.484,
+ 0.56
+ ],
+ "angle": 0,
+ "content": "Definition 3.3 denotes \\(\\sigma_{\\min(p_0)}\\), \\(\\sigma_{\\max(p_0)}\\), \\(\\sigma_{\\min(p_t)}\\), \\(\\sigma_{\\max(p_t)}\\) as the minimum/maximum singular value between the covariance matrices of \\(k\\)-components at the original distribution \\(p_0\\) and \\(p_t\\). \\(\\mu_{\\max(p_0)}\\) is the maximum \\(\\ell_2^2\\)-norm between mean vectors of the \\(k\\)-components at \\(p_0\\). \\(\\operatorname{det}_{\\min(p_0)}\\) is the minimum determinant between the covariance matrices of \\(k\\)-components at \\(p_0\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.572,
+ 0.484,
+ 0.632
+ ],
+ "angle": 0,
+ "content": "Condition 3.4. All conditions here are related to the all time density \\( p_t \\) in Eq. (10), where \\( t \\in [0, T] \\). Let \\( x \\in \\mathbb{R}^d \\) and \\( a_t, b_t \\) be defined by Definition 4.1. We only consider the \\( x \\) satisfying the following conditions:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "- Let \\(\\beta \\leq \\| x - a_t\\mu_i\\| _2\\leq R\\) , where \\(R\\geq 1\\) and \\(\\beta \\in (0,0.1)\\) for each \\(i\\in [k]\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.664,
+ 0.482,
+ 0.694
+ ],
+ "angle": 0,
+ "content": "- Let \\( p_t(x) \\) be defined as Eq. (10) and \\( p_t(x) \\geq \\gamma \\), where \\( \\gamma \\in (0, 0.1) \\)."
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.091,
+ 0.633,
+ 0.482,
+ 0.694
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.706,
+ 0.484,
+ 0.86
+ ],
+ "angle": 0,
+ "content": "In Condition 3.4, \\(\\beta, R\\) are the lower/upper bound of the \\(\\ell_2\\) distance between the input data \\(x\\) and all \\(k\\) scaled mean vectors \\(a_t\\mu_i\\) at timestep \\(t\\). Let \\(\\gamma\\) be the lower bound of \\(p_t(x)\\), the pdf at time \\(t\\) and \\(\\operatorname*{det}_{\\min(p_t)}\\) be the minimum determinant at \\(p_t\\). We assume \\(\\beta\\) and \\(\\gamma\\) are lower bounded/constant, implying that each Gaussian component in the mixture is well-conditioned. This is a standard assumption in diffusion theory and is consistent with other theoretical findings [16, 17, 26, 38, 53, 71]. Clearly, we have \\(\\sigma_{\\max(p_t)} \\geq \\sigma_{\\max(p_0)}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.871,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Lemma 3.5 (Lipschitz, informal version of Lemma H.3). Assume Condition 3.4 holds. The Lipschitz constant for the"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.514,
+ 0.089,
+ 0.766,
+ 0.11
+ ],
+ "angle": 0,
+ "content": "score function \\(\\frac{\\mathrm{d}\\log(p_t(x))}{\\mathrm{d}x}\\) is given by:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.549,
+ 0.123,
+ 0.868,
+ 0.201
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} L = \\frac {1}{\\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)} ^ {2}} \\cdot \\exp \\left(- \\frac {\\beta^ {2}}{2 \\sigma_ {\\operatorname* {m a x} \\left(p _ {t}\\right)}}\\right) \\\\ \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\operatorname* {d e t} _ {\\min \\left(p _ {t}\\right)}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\operatorname* {d e t} _ {\\min \\left(p _ {t}\\right)} ^ {1 / 2}}\\right). \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.216,
+ 0.907,
+ 0.383
+ ],
+ "angle": 0,
+ "content": "In Lemma 3.5, we can clearly see that roughly \\( L = O(1 / \\mathrm{poly}(\\sigma_{\\min(p_t)})) \\), which means the Lipschitz is only conditioned on the smallest singular value of all Gaussian components but independent of \\( k \\). The bounded region required in Condition 3.4 applies to where most of the probability mass lies, which is a common assumption in diffusion literature (e.g., [16, 26, 73]). Outside this region, the score function indeed may not be Lipschitz, but this affects regions with negligible probability mass, similar to observations in [73]. We provide an additional empirical study in Section 6 to support our analysis."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.399,
+ 0.907,
+ 0.444
+ ],
+ "angle": 0,
+ "content": "Lemma 3.6 (Second momentum, informal version of Lemma H.2). Let \\( x_0 \\sim p_0 \\), where \\( p_0 \\) is defined by Eq. (9). Then, we have"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.55,
+ 0.459,
+ 0.866,
+ 0.527
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} m _ {2} ^ {2} := \\underset {x _ {0} \\sim p _ {0}} {\\mathbb {E}} [ \\| x _ {0} \\| _ {2} ^ {2} ] = \\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ]) \\\\ \\leq \\max _ {i \\in [ k ]} \\left\\{\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} \\left[ \\Sigma_ {i} \\right] \\right\\}. \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.545,
+ 0.907,
+ 0.68
+ ],
+ "angle": 0,
+ "content": "The proof idea of Lemma 3.5 and Lemma 3.6 is that we first consider the case when \\( k = 1 \\) in Appendix D and then we extend to 2 mixtures of Gaussian setting in Appendix E. Finally, we can generalize to \\( k \\) setting in Appendix F and summarize it in Appendix H. In Lemma 3.6, we can see that \\( m_2^2 = O(1) \\) roughly, which is independent of \\( k \\) as well. Later, we will apply our Lemma 3.5 and Lemma 3.6 in Section 5 to get concrete bound for each diffusion process, e.g., DDPM, DPOM and DPUM."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.696,
+ 0.685,
+ 0.712
+ ],
+ "angle": 0,
+ "content": "3.1. Practical insights"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.72,
+ 0.907,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "We believe our results in Lemma 3.5 is non-trivial. First, the Lipschitz bound depends inversely exponential on the dimension \\( d \\). If \\( d \\) grows larger, the Lipschitz constant \\( L \\) becomes much smaller. Second, in practice, the \\( k \\) will be super large for complicated data distribution, e.g., millions of Gaussian components for an image distribution. Many studies need to overcome the large \\( k \\) hardness in learning Gaussian mixture models [5, 8, 47, 57], while our Lipschitz upper-bound is independent with \\( k \\). These theoretical insights can help practitioners make more informed decisions about model architecture, optimization strategies, and computational resources needed for different applications."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "11439"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "4. Score Based Model and Diffusion Model"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.115,
+ 0.484,
+ 0.192
+ ],
+ "angle": 0,
+ "content": "In Section 4.1, we first briefly introduce DDPM [30], a stochastic differential equations (SDE) version of the reverse diffusion process, and score-based generative models (SGMs) [63], a generalization of DDPM. In Section 4.2, we introduce multiple solvers for the reverse process."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.2,
+ 0.462,
+ 0.215
+ ],
+ "angle": 0,
+ "content": "4.1. Background on score based diffusion model"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.221,
+ 0.484,
+ 0.298
+ ],
+ "angle": 0,
+ "content": "First, we denote the input data as \\( x \\in \\mathbb{R}^d \\) and the target original data distribution as \\( p_0(x) \\). Assuming that the noisy latent state of score-based generative models (SGMs) at time \\( t \\) is a stochastic process \\( x_{t} \\) for \\( 0 \\leq t \\leq T \\), we have the forward SDE is defined by:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.105,
+ 0.306,
+ 0.483,
+ 0.323
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} x _ {t} = f \\left(x _ {t}, t\\right) \\mathrm {d} t + g (t) \\mathrm {d} w _ {t}, \\quad x _ {0} \\sim p _ {0}, \\quad 0 \\leq t \\leq T \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.332,
+ 0.484,
+ 0.422
+ ],
+ "angle": 0,
+ "content": "where \\(w_{t}\\in \\mathbb{R}^{d}\\) is the standard Brownian motion, \\(f(\\cdot ,t):\\) \\(\\mathbb{R}^d\\to \\mathbb{R}^d\\) which is called drift coefficient, and \\(g(t):\\mathbb{R}\\rightarrow\\) \\(\\mathbb{R}\\) which is called diffusion coefficient. We use \\(p_t(x)\\) to denote the marginal probability density function of \\(x_{t}\\). The pdf at last time step \\(p_T\\) is the prior distribution which often defined as standard Gaussian \\(p_T(x) = \\mathcal{N}(0,I)\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.423,
+ 0.484,
+ 0.452
+ ],
+ "angle": 0,
+ "content": "The continuous forward SDE Eq. (1) also has the discrete Markov chain form as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.195,
+ 0.463,
+ 0.482,
+ 0.478
+ ],
+ "angle": 0,
+ "content": "\\[\nx _ {t} = a _ {t} x _ {0} + b _ {t} z, \\quad x _ {0} \\sim p _ {0} \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.487,
+ 0.484,
+ 0.576
+ ],
+ "angle": 0,
+ "content": "where \\(x_0 \\sim p_0(x)\\) and \\(z \\sim \\mathcal{N}(0, I)\\), and \\(a_t, b_t \\in \\mathbb{R}\\) are functions of time. Additionally, we assume as \\(t \\to T\\), \\(a_t \\to 0\\) and \\(b_t \\to 1\\). Thus, \\(x_T \\sim \\mathcal{N}(0, I)\\). Also, clearly when \\(t \\to 0\\), \\(a_t \\to 1\\) and \\(b_t \\to 0\\) for this is the boundary condition. More specifically, the Eq. (2) can be viewed as the iterative equation in DDPM [30]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.578,
+ 0.452,
+ 0.593
+ ],
+ "angle": 0,
+ "content": "From [2], we know \\( x_{t} \\) also satisfy the reverse SDE:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.102,
+ 0.6,
+ 0.483,
+ 0.619
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} x _ {t} = \\left(f \\left(x _ {t}, t\\right) - g (t) ^ {2} \\nabla \\log p _ {t} \\left(x _ {t}\\right)\\right) \\mathrm {d} t + g (t) \\mathrm {d} \\widetilde {w} _ {t}, \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.627,
+ 0.484,
+ 0.72
+ ],
+ "angle": 0,
+ "content": "where \\(\\widetilde{w}_t \\in \\mathbb{R}^d\\) is backward Brownian motion [2], and \\(\\nabla \\log p_t(x_t)\\) is the score function. For convenience, we rewrite the reverse SDE Eq. (3) in a forward version by switching the time direction, replacing \\(t\\) with \\(T - t\\). Let \\(\\widetilde{x}_t \\coloneqq x_{T - t}\\). The law of \\((\\widetilde{x}_t)_{0 \\leq t \\leq T}\\) is identical to the law of \\((x_{T - t})_{0 \\leq t \\leq T}\\). We use \\(q_t\\) to denote the density of \\(\\widetilde{x}_t\\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.106,
+ 0.726,
+ 0.482,
+ 0.763
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathrm {d} \\widetilde {x} _ {t} = (- f (\\widetilde {x} _ {t}, T - t) + g (T - t) ^ {2} \\nabla \\log p _ {T - t} (\\widetilde {x} _ {t})) \\mathrm {d} t \\\\ + g (T - t) \\mathrm {d} w _ {t}. \\tag {4} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.771,
+ 0.483,
+ 0.802
+ ],
+ "angle": 0,
+ "content": "The process \\((\\widetilde{x}_t)_{0\\leq t\\leq T}\\) converts noise into samples from \\(p_0\\), thereby achieving the objective of generative modeling."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.802,
+ 0.484,
+ 0.877
+ ],
+ "angle": 0,
+ "content": "Since we can not obtain the score function \\(\\nabla \\log p_t\\) directly, we can use a neural network to approximate it, and we denote the estimated score function by \\(s_t(x)\\). By replacing the score function \\(\\nabla \\log p_t\\) with our approximated score function \\(s_t(x)\\), we can rewrite Eq. (4) as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.128,
+ 0.885,
+ 0.446,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} y _ {t} = \\left(- f \\left(y _ {t}, T - t\\right) + g (T - t) ^ {2} s _ {T - t} \\left(y _ {t}\\right)\\right) \\mathrm {d} t\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.597,
+ 0.092,
+ 0.905,
+ 0.108
+ ],
+ "angle": 0,
+ "content": "\\[\n+ g (T - t) \\mathrm {d} w _ {t}, y _ {0} \\sim p _ {T}, 0 \\leq t \\leq T. \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.118,
+ 0.905,
+ 0.164
+ ],
+ "angle": 0,
+ "content": "where \\( y_{t} \\) is the process we approximate by our SGM \\( s_t \\). For clarity, we mainly focus on the Ornstein-Uhlenbeck (OU) process, which is a diffusion process with exp coefficient:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.171,
+ 0.906,
+ 0.248
+ ],
+ "angle": 0,
+ "content": "Definition 4.1. The forward SDE of OU process \\((f(x_{t},t) = -x_{t}\\), and \\(g(t)\\equiv \\sqrt{2})\\) is: \\(\\mathrm{d}x_{t} = -x_{t}\\mathrm{d}t + \\sqrt{2}\\mathrm{d}w_{t}\\). The corresponding discrete Markov chain form of OU process is given by: \\(x_{t} = e^{-t}x_{0} + \\sqrt{1 - e^{-2t}} z\\), where we can see that \\(a_{t} = e^{-t}\\), \\(b_{t} = \\sqrt{1 - e^{-2t}}\\) in Eq. (2)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.532,
+ 0.256,
+ 0.862,
+ 0.271
+ ],
+ "angle": 0,
+ "content": "From Eq. (5) under the OU process, we can have:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.583,
+ 0.28,
+ 0.905,
+ 0.298
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} y _ {t} = \\left(x _ {t} + 2 s _ {T - t} \\left(y _ {t}\\right)\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} w _ {t}. \\tag {6}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.307,
+ 0.782,
+ 0.321
+ ],
+ "angle": 0,
+ "content": "4.2. Definitions of different solvers"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.329,
+ 0.905,
+ 0.373
+ ],
+ "angle": 0,
+ "content": "In practical applications, it's necessary to adopt a discrete-time approximation for sampling dynamics. We have the following definition."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.382,
+ 0.906,
+ 0.459
+ ],
+ "angle": 0,
+ "content": "Definition 4.2 (Time discretization). Define the \\(N\\) discretization points as \\(\\delta = t_0 \\leq t_1 \\leq \\dots \\leq t_N = T\\), where \\(\\delta \\geq 0\\) is the early stopping parameter, with \\(\\delta = 0\\) presenting the normal setting. For each discretization step \\(k\\), where \\(1 \\leq k \\leq N\\), the step size is denoted by \\(h_k := t_k - t_{k-1}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.466,
+ 0.906,
+ 0.528
+ ],
+ "angle": 0,
+ "content": "Let \\(\\widehat{y}_t\\) be the discrete approximation of \\(y_{t}\\) in Eq. (6) starting from \\(\\widehat{y}_0\\sim \\mathcal{N}(0,I)\\). We use \\(\\widehat{q}_t\\) to denote the density of \\(\\widehat{y}_t\\). Let \\(N\\) be defined in Definition 4.2 and \\(t_k^\\prime = T - t_{N - k}\\). To solve Eq. (6), we have two numerical solvers:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.536,
+ 0.906,
+ 0.613
+ ],
+ "angle": 0,
+ "content": "Definition 4.3. We define EulerMaruyama as the numerical solver satisfying \\(\\widehat{y}_{T - \\delta} =\\) EulerMaruyama(T,s), where \\(\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d\\) is the output, \\(T\\in \\mathbb{R}^{+}\\) is the total time, and \\(s\\) is the score estimates. The Euler-Maruyama scheme is, (Equation 5 in [10]), for \\(t\\in [t_k',t_{k + 1}']\\)"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.573,
+ 0.623,
+ 0.905,
+ 0.643
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} \\hat {y} _ {t} = \\left(\\hat {y} _ {t _ {k} ^ {\\prime}} + 2 s _ {T - t _ {k} ^ {\\prime}} \\left(\\hat {y} _ {t _ {k} ^ {\\prime}}\\right)\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} w _ {t}. \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.65,
+ 0.906,
+ 0.743
+ ],
+ "angle": 0,
+ "content": "Definition 4.4. We define ExponentialIntegrator as the numerical solver satisfying \\(\\widehat{y}_{T - \\delta} =\\) ExponentialIntegrator(T,s), where \\(\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d\\) is the output, \\(T\\in \\mathbb{R}^{+}\\) is the total time, and \\(s\\) is the score estimates. The Exponential Integrator scheme is, (Equation 6 in [10]), for \\(t\\in [t_k',t_{k + 1}']\\)"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.577,
+ 0.753,
+ 0.905,
+ 0.773
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {d} \\widehat {y} _ {t} = \\left(\\widehat {y} _ {t} + 2 s _ {T - t _ {k} ^ {\\prime}} \\left(\\widehat {y} _ {t _ {k} ^ {\\prime}}\\right)\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} w _ {t}. \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.78,
+ 0.906,
+ 0.855
+ ],
+ "angle": 0,
+ "content": "The two methods above are used for solving SDE. The difference is that in the first term of RHS of Euler-Maruyama uses \\(\\widehat{y} t_{k}^{\\prime}\\), while Exponential Integrator uses \\(\\widehat{y}_t\\). The Exponential Integrator scheme has a closed-form solution (see detail in Section 1.1 of [10])."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.856,
+ 0.906,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "We now introduce two ordinary differential equation (ODE) solvers, DPOM and DPUM, which omit the Brownian motion term in Eq. (6). These solvers, defined in"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.945,
+ 0.52,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "11440"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.485,
+ 0.184
+ ],
+ "angle": 0,
+ "content": "Definitions 4.5 and 4.6, represent distinct approaches using predictor-corrector steps to address the reverse process via probability flow ODEs. Specifically, DPOM employs overdamped Langevin Monte Carlo (LMC), while DPUM uses underdamped LMC, enabling more efficient sampling. We will present their concrete step bounds in Section 5."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.193,
+ 0.484,
+ 0.3
+ ],
+ "angle": 0,
+ "content": "Definition 4.5. We define DPOM (Diffusion Predictor with Overdamped Modeling) as Algorithm 1 in [14] satisfying \\(\\widehat{y}_{T - \\delta} = \\mathsf{DPOM}(T,h_{\\mathrm{pred}},h_{\\mathrm{corr}},s)\\), where \\(\\delta\\) is the early stopping parameter, \\(\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d\\) is the output, \\(T\\in \\mathbb{R}^{+}\\) is the total steps, \\(h_\\mathrm{pred}\\) is the predictor step size, \\(h_\\mathrm{corr}\\) is the corrector step size, (see detailed definition in Algorithm 1 of [14]), and \\(s\\) is the score estimates."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.31,
+ 0.484,
+ 0.416
+ ],
+ "angle": 0,
+ "content": "Definition 4.6. We define DPUM (Diffusion Predictor with Underdamped Modeling) as Algorithm 2 in [14], satisfying \\(\\widehat{y}_{T - \\delta} = \\mathsf{DPUM}(T,h_{\\mathrm{pred}},h_{\\mathrm{corr}},s)\\), where \\(\\delta\\) is the early stopping parameter, \\(\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d\\) is the output, \\(T\\in \\mathbb{R}^{+}\\) is the total steps, \\(h_\\mathrm{pred}\\) is the predictor step size, \\(h_\\mathrm{corr}\\) is the corrector step size, (see detailed definition in Algorithm 2 of [14]), and \\(s\\) is the score estimates."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.431,
+ 0.351,
+ 0.449
+ ],
+ "angle": 0,
+ "content": "5. Main Result for Application"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.456,
+ 0.484,
+ 0.562
+ ],
+ "angle": 0,
+ "content": "In this section, we will provide the main results of applications. In Section 5.1, we provide our key definitions and assumptions used. In Section 5.2, we provide our results for the total variation bound. In Section 5.3, we provide our results for the KL divergence bound. In Section 5.4, we provide our results for the probability flow ODE method, including DPOM and DPUM."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.572,
+ 0.376,
+ 0.589
+ ],
+ "angle": 0,
+ "content": "5.1. Key definitions and assumptions"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.595,
+ 0.484,
+ 0.656
+ ],
+ "angle": 0,
+ "content": "We first assume that the loss of the learned score estimator is upper bounded by \\(\\epsilon_0^2\\) in Assumption 5.1. Then, we can show that we can recover the target/image data distribution under a small total variation or KL divergence gap later."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.666,
+ 0.484,
+ 0.713
+ ],
+ "angle": 0,
+ "content": "Assumption 5.1 (Score estimation error, Assumption 1 in [10], page 6, and Assumption 3 in [13], page 6). The learned score function \\( s_t(x) \\) satisfies for any \\( 1 \\leq k \\leq N \\),"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.134,
+ 0.736,
+ 0.443,
+ 0.777
+ ],
+ "angle": 0,
+ "content": "\\[\n\\frac {1}{T} \\sum_ {k = 1} ^ {N} h _ {k} \\underset {p _ {t _ {k}}} {\\mathbb {E}} [ \\| \\nabla \\log p _ {t _ {k}} (x) - s _ {t _ {k}} (x) \\| _ {2} ^ {2} ] \\leq \\epsilon_ {0} ^ {2}.\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.788,
+ 0.483,
+ 0.821
+ ],
+ "angle": 0,
+ "content": "where \\( h_k \\) is the step size defined in Definition 4.2 for step \\( k \\), \\( N \\) is the total steps, and \\( \\sum_{k=1}^{N} h_k = T \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.829,
+ 0.484,
+ 0.86
+ ],
+ "angle": 0,
+ "content": "To avoid ill-distribution \\( q_{T} \\), we have the below definition follows [10, 14]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.871,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Definition 5.2. We define \\(\\epsilon\\) as total variation distance between \\(q_{T - \\delta}\\) and \\(q_{T}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.533,
+ 0.092,
+ 0.905,
+ 0.107
+ ],
+ "angle": 0,
+ "content": "Let the distribution \\(p_0(x)\\) be a \\(k\\)-mixture of Gaussians:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.617,
+ 0.128,
+ 0.905,
+ 0.169
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {0} (x) := \\sum_ {i = 1} ^ {k} \\alpha_ {i} \\mathcal {N} \\left(\\mu_ {i}, \\Sigma_ {i}\\right). \\tag {9}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.175,
+ 0.905,
+ 0.206
+ ],
+ "angle": 0,
+ "content": "Using the Proposition 3.2, we know the pdf of \\( x_{t} \\) at the any time \\( t \\) is given by:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.583,
+ 0.214,
+ 0.905,
+ 0.255
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {t} (x) = \\sum_ {i = 1} ^ {k} \\alpha_ {i} \\mathcal {N} \\left(a _ {t} \\mu_ {i}, a _ {t} ^ {2} \\Sigma_ {i} + b _ {t} ^ {2} I\\right). \\tag {10}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.262,
+ 0.905,
+ 0.292
+ ],
+ "angle": 0,
+ "content": "We introduce Pinsker's inequality, which relates total variation distance to the Kullback-Leibler divergence."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.299,
+ 0.905,
+ 0.354
+ ],
+ "angle": 0,
+ "content": "Lemma 5.3 (Pinsker's inequality [18]). Let \\( p, q \\) are two probability distributions, then we have \\( \\mathrm{TV}(\\mathrm{p},\\mathrm{q}) \\leq \\sqrt{\\frac{1}{2}\\mathrm{KL}(p\\|q)} \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.359,
+ 0.905,
+ 0.39
+ ],
+ "angle": 0,
+ "content": "From Lemma 5.3, we can see the total variation is a weaker bound than KL divergence."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
+ 0.397,
+ 0.665,
+ 0.412
+ ],
+ "angle": 0,
+ "content": "5.2. Total variation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.419,
+ 0.905,
+ 0.495
+ ],
+ "angle": 0,
+ "content": "Now, we are ready to present our result for total variation bound assuming data distribution is \\(k\\)-mixture of Gaussian \\((p_0\\) in Eq. (9)). Recall \\(\\epsilon_0\\) is defined in Assumption 5.1, \\(\\epsilon\\) is defined in Definition 5.2 and \\(h_k\\) is defined in Definition 4.2. See the proof in Appendix I."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.501,
+ 0.907,
+ 0.591
+ ],
+ "angle": 0,
+ "content": "Theorem 5.4 (DDPM, total variation, informal version of Theorem I.1). Assume Condition 3.4 and Assumption 5.1 hold. The step size \\( h_k \\coloneqq T / N \\) satisfies \\( h_k = O(1 / L) \\) and \\( L \\geq 1 \\) for \\( k \\in [N] \\). Let \\( \\widehat{q} \\) denote the density of the output of the Euler-Maruyama defined by Definition 4.3. Then, we have"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.515,
+ 0.598,
+ 0.912,
+ 0.676
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathrm {T V} (\\widehat {q}, p _ {0}) \\lesssim \\underbrace {\\sqrt {\\mathrm {K L} (p _ {0} \\| \\mathcal {N} (0 , I))} \\exp (- T)} _ {\\text {c o n v e r g e n c e o f f o r w a r d p r o c e s s}} \\\\ + \\underbrace {(L \\sqrt {d h} + L m _ {2} h) \\sqrt {T}} _ {\\text {d i s c r e t i z a t i o n e r r o r}} + \\underbrace {\\epsilon_ {0} \\sqrt {T}} _ {\\text {s c o r e e s t i m a t i o n e r r o r}}. \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.515,
+ 0.684,
+ 0.907,
+ 0.709
+ ],
+ "angle": 0,
+ "content": "where \\(L = \\frac{1}{\\sigma_{\\min(p_t)}} + \\frac{2R^2}{\\gamma^2\\sigma_{\\min(p_t)}^2} \\cdot \\left(\\frac{1}{(2\\pi)^d\\operatorname*{det}_{\\min(p_t)}} + \\right.\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.515,
+ 0.709,
+ 0.907,
+ 0.735
+ ],
+ "angle": 0,
+ "content": "\\(\\frac{1}{(2\\pi)^{d / 2}\\operatorname*{det}_{\\min (p_t)}^{1 / 2}}\\) \\(\\exp (-\\frac{\\beta^2}{2\\sigma_{\\max(p_t)}}),\\qquad m_2\\qquad =\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.515,
+ 0.735,
+ 0.905,
+ 0.771
+ ],
+ "angle": 0,
+ "content": "\\((\\sum_{i=1}^{k} \\alpha_i (\\|\\mu_i\\|_2^2 + \\mathrm{tr}[\\Sigma_i]))^{1/2}\\), and \\(\\mathrm{KL}(p_0(x) \\| \\mathcal{N}(0, I)) \\leq \\frac{1}{2} (-\\log(\\det_{\\min(p_0)}) + d\\sigma_{\\max(p_0)} + \\mu_{\\max(p_0)} - d)\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.774,
+ 0.907,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "In Theorem 5.4, suppose that \\(m_2 \\leq d\\) and choose \\(T = \\Theta(\\log(\\mathrm{KL}(p_0 \\| \\mathcal{N}(0, I)) / \\epsilon))\\), \\(h_k = \\Theta\\left(\\frac{\\epsilon^2}{L^2d}\\right)\\), then we have \\(\\mathrm{TV}(\\widehat{q}, p_0) \\leq \\widetilde{O}(\\epsilon + \\epsilon_0)\\), for \\(N = \\widetilde{O}(L^2d / \\epsilon^2)\\). In particular, in order to have \\(\\mathrm{TV}(\\widehat{q}, p_0) \\leq \\epsilon\\), it suffices to have score error \\(\\epsilon_0 \\leq \\widetilde{O}(\\epsilon)\\), where \\(\\widetilde{O}(\\cdot)\\) hides \\(T\\) which is a log term. Thus, Theorem 5.4 provides a guarantee for total variation bound between target data distribution \\(p_0\\) and learned output distribution \\(\\widehat{q}\\) with concrete \\(L\\) and \\(m_2\\)."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.945,
+ 0.518,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "11441"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.091,
+ 0.241,
+ 0.108
+ ],
+ "angle": 0,
+ "content": "5.3. KL divergence"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.113,
+ 0.485,
+ 0.19
+ ],
+ "angle": 0,
+ "content": "Similarly, we can present our result for the KL divergence bound in the following two theorems, assuming data distribution is \\( k \\)-mixture of Gaussian. Recall \\( \\epsilon_0 \\) is defined in Assumption 5.1, \\( \\epsilon \\) is denied in Definition 5.2 and \\( h_k \\) is defined in Definition 4.2. See the proof in Appendix I."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.197,
+ 0.484,
+ 0.242
+ ],
+ "angle": 0,
+ "content": "Theorem 5.5 (DDPM, KL divergence, informal version of Theorem I.2). Assume Condition 3.4 and Assumption 5.1 hold. We use uniform discretization points."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.242,
+ 0.484,
+ 0.273
+ ],
+ "angle": 0,
+ "content": "(1) Let \\(\\widehat{q}\\) denote the density of the output of the ExponentialIntegrator (Definition 4.4), we have"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.115,
+ 0.281,
+ 0.46,
+ 0.312
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {K L} (p _ {0} \\| \\widehat {q}) \\lesssim (M _ {2} + d) \\exp (- T) + T \\epsilon_ {0} ^ {2} + \\frac {d T ^ {2} L ^ {2}}{N}.\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.32,
+ 0.483,
+ 0.354
+ ],
+ "angle": 0,
+ "content": "In particular, choosing \\( T = \\Theta (\\log (M_2d / \\epsilon_0)) \\) and \\( N = \\Theta (dT^2 L^2 /\\epsilon_0^2) \\), then \\( \\mathrm{KL}(p_0\\| \\widehat{q}) = \\widetilde{O} (\\epsilon_0^2) \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.353,
+ 0.484,
+ 0.383
+ ],
+ "angle": 0,
+ "content": "(2) Let \\(\\widehat{q}\\) denote the density of the output of the EulerMaruyama (Definition 4.3), we have"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.09,
+ 0.391,
+ 0.501,
+ 0.424
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathrm {K L} (p _ {0} \\| \\widehat {q}) \\lesssim (M _ {2} + d) \\exp (- T) + T \\epsilon_ {0} ^ {2} + \\frac {d T ^ {2} L ^ {2}}{N} + \\frac {T ^ {3} M _ {2}}{N ^ {2}}.\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.09,
+ 0.431,
+ 0.484,
+ 0.499
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\begin{array}{l l} w h e r e M _ {2} = \\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ]) a n d L = \\\\ \\frac {1}{\\sigma_ {\\min (p _ {t})}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\min (p _ {t})} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\det _ {\\min (p _ {t})}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\det _ {\\min (p _ {t})} ^ {1 / 2}}\\right). \\end{array} \\\\ \\exp \\bigl (- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}} \\bigr). \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.504,
+ 0.484,
+ 0.611
+ ],
+ "angle": 0,
+ "content": "Theorem 5.6 (DDPM, KL divergence for smooth data distribution, informal version of Theorem I.3). Assume Condition 3.4 and Assumption 5.1 hold. We use the exponentially decreasing (then constant) step size \\( h_k = c \\min \\{ \\max \\{ t_k, 1 / L \\}, 1 \\} \\), \\( c = \\frac{T + \\log L}{N} \\leq \\frac{1}{Kd} \\). Let \\( \\widehat{q} \\) denote the density of the output of the ExponentialIntegrator defined by Definition 4.4. Then, we have"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.09,
+ 0.619,
+ 0.49,
+ 0.651
+ ],
+ "angle": 0,
+ "content": "\\[\n\\operatorname {K L} \\left(p _ {0} \\| \\widehat {q}\\right) \\lesssim \\left(M _ {2} + d\\right) \\exp (- T) + T \\epsilon_ {0} ^ {2} + \\frac {d ^ {2} (T + \\log L) ^ {2}}{N},\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.09,
+ 0.658,
+ 0.484,
+ 0.789
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\begin{array}{l l} w h e r e M _ {2} = \\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ]) a n d L = \\\\ \\frac {1}{\\sigma_ {\\min (p _ {t})}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\min (p _ {t})} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\det _ {\\min (p _ {t})}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\det _ {\\min (p _ {t})} ^ {1 / 2}}\\right). \\end{array} \\\\ \\begin{array}{l} \\exp (- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}}). \\quad \\text {I n p a r t i c u l a r , i f w e s e t T =} \\\\ \\Theta (\\log (M _ {2} d / \\epsilon_ {0})) \\text {a n d N = \\Theta (d ^ {2} (T + \\log L) ^ {2} / \\epsilon_ {0} ^ {2}) , t h e n} \\\\ \\mathrm {K L} (p _ {0} \\| \\widehat {q}) \\leq \\widetilde {O} (\\epsilon_ {0} ^ {2}). \\text {I n a d d i t i o n , f o r E u l e r - M a r u y a m a} \\\\ \\text {s c h e m e d e f i n e d i n D e f i n i o n 4 . 3 , t h e s a m e b o u n d s h o l d w i t h} \\\\ \\text {a n a n d i s t i t i o n a l M _ {2} \\sum_ {k = 1} ^ {N} h _ {k} ^ {3} t e r m .} \\end{array} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.795,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Theorem 5.6 and Theorem 5.5 provide a guarantee for KL divergence bound between target data distribution \\( p_0 \\) and learned output distribution \\( \\widehat{q} \\) with concrete \\( L \\) and \\( M_2 \\). Theorem 5.6 has \\( \\log^2 L \\) instead of \\( L^2 \\) in the bound for total number of discretization points \\( N \\), but includes an additional \\( d \\) compared to Theorem 5.5. On the other hand, Theorem 5.6 requires the data distribution \\( p_0 \\) is Lipschitz and"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.906,
+ 0.167
+ ],
+ "angle": 0,
+ "content": "second-order differentiable [10], allowing a better bound in terms of \\( L \\), while all other theorems [13, 14] require conditions about Lipschitz on \\( p_t \\) for any \\( 0 \\leq t \\leq T \\). However, our assumption \\( p_0 \\) is \\( k \\)-mixture of Gaussians satisfies all conditions they use."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.168,
+ 0.907,
+ 0.258
+ ],
+ "angle": 0,
+ "content": "From Lemma 5.3, we can compare KL divergence results with total variation results. Notice that \\( M_2 = m_2^2 \\) when comparing theorems for total variation and KL divergence. According to Lemma 5.3, the square of the TV distance is comparable to the KL divergence, which explains the squared relationship of the second momentum term."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.268,
+ 0.719,
+ 0.284
+ ],
+ "angle": 0,
+ "content": "5.4. Probability flow ODE"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.29,
+ 0.907,
+ 0.397
+ ],
+ "angle": 0,
+ "content": "Notice that in the previous results we are considering SDE based models. However from [63], we know that we can also use ODE to run the reverse process, which has the same marginal distribution with SDE reverse process but is thereby deterministic. In this section, we provide results of DPOM and DPUM (Algorithm 1 and 2 in [14]) algorithms which are based on ODE reverse process."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.406,
+ 0.906,
+ 0.467
+ ],
+ "angle": 0,
+ "content": "Theorem 5.7 (DPOM, informal version of Theorem I.4). Assume Condition 3.4 and Assumption 5.1 hold. We use the DPOM algorithm defined in Definition 4.5, and let \\(\\widehat{q}\\) be the output density of it. Then, we have"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.534,
+ 0.477,
+ 0.884,
+ 0.518
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathrm {T V} (\\widehat {q}, p _ {0}) \\lesssim (\\sqrt {d} + m _ {2}) \\exp (- T) + L ^ {2} T d ^ {1 / 2} h _ {\\mathrm {p r e d}} \\\\ + L ^ {3 / 2} T d ^ {1 / 2} h _ {\\mathrm {c o r r}} ^ {1 / 2} + L ^ {1 / 2} T \\epsilon_ {0} + \\epsilon . \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.513,
+ 0.53,
+ 0.907,
+ 0.664
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\begin{array}{l} \\text {w h e r e} m _ {2} = (\\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ])) ^ {1 / 2} \\text {a n d} L = \\\\ \\frac {1}{\\sigma_ {\\min (p _ {t})}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\min (p _ {t})} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\det _ {\\min (p _ {t})}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\det _ {\\min (p _ {t})} ^ {1 / 2}}\\right). \\end{array} \\\\ \\begin{array}{l} \\exp (- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}}). \\quad \\text {I n p a r t i c u l a r , i f w e s e t T =} \\\\ \\Theta (\\log (d m _ {2} / \\epsilon)), h _ {\\text {p r e d}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {2} d ^ {1 / 2}}), h _ {\\text {c o r r}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {3} d}), \\text {a n d} \\\\ \\text {i f t h e s c o r e e s t i m a t i o n e r r o r s a t i s f i e s \\epsilon_ {0} \\leq \\widetilde {O} (\\frac {\\epsilon}{\\sqrt {L}}) , t h e n w e} \\\\ \\widetilde {\\Theta} (L ^ {3} d / \\epsilon^ {2}) \\text {s t e p s .} \\end{array} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.673,
+ 0.906,
+ 0.735
+ ],
+ "angle": 0,
+ "content": "Theorem 5.8 (DPUM, informal version of Theorem I.5). Assume Condition 3.4 and Assumption 5.1 hold. We use the DPUM algorithm defined in Definition 4.6, and let \\(\\widehat{q}\\) be the output density of it. Then, we have"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.534,
+ 0.744,
+ 0.884,
+ 0.786
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathrm {T V} (\\widehat {q}, p _ {0}) \\lesssim (\\sqrt {d} + m _ {2}) \\exp (- T) + L ^ {2} T d ^ {1 / 2} h _ {\\mathrm {p r e d}} \\\\ + L ^ {3 / 2} T d ^ {1 / 2} h _ {\\mathrm {c o r r}} ^ {1 / 2} + L ^ {1 / 2} T \\epsilon_ {0} + \\epsilon . \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.513,
+ 0.797,
+ 0.908,
+ 0.904
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} w h e r e L = \\frac {1}{\\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d}} \\det _ {\\min \\left(p _ {t}\\right)} + \\right. \\\\ \\frac {1}{(2 \\pi) ^ {d / 2} \\operatorname* {d e t} _ {\\min (p _ {t})} ^ {1 / 2}}) \\quad \\cdot \\quad \\exp \\left(- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}}\\right) \\quad a n d \\quad m _ {2} \\quad = \\\\ \\begin{array}{l} (\\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ])) ^ {1 / 2}. \\quad I n \\text {p a r t i c u l a r , i f} \\\\ w e s e t T = \\Theta (\\log (d m _ {2} / \\epsilon)), h _ {\\mathrm {p r e d}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {2} d ^ {1 / 2}}), \\\\ h _ {\\mathrm {c o r r}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {3 / 2} d ^ {1 / 2}}), a n d i f t h e s c o r e e s t i m a t i o n e r r o r \\end{array} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.48,
+ 0.945,
+ 0.52,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "11442"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.09,
+ 0.486,
+ 0.128
+ ],
+ "angle": 0,
+ "content": "satisfies \\(\\epsilon_0\\leq \\widetilde{O} (\\frac{\\epsilon}{\\sqrt{L}})\\), then we can obtain TV error \\(\\epsilon\\) with a total iteration complexity of \\(\\widetilde{\\Theta} (L^2 d^{1 / 2} / \\epsilon)\\) steps."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.133,
+ 0.486,
+ 0.257
+ ],
+ "angle": 0,
+ "content": "Theorem 5.7 and Theorem 5.8 provide a guarantee for total variation bound between target data distribution \\( p_0 \\) and learned output distribution \\( \\widehat{q} \\) with concrete \\( L \\) and \\( M_2 \\) for ODE reverse process. The difference between the DPOM (Theorem 5.7) and DPUM (Theorem 5.8) is the complexity of \\( h_{\\mathrm{corr}} \\) and the final iteration complexity term. Using DPUM algorithm, we can reduce the total iteration complexity from \\( \\widetilde{\\Theta}(L^3 d / \\epsilon^2) \\) to \\( \\widetilde{\\Theta}(L^2 \\sqrt{d} / \\epsilon) \\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.267,
+ 0.226,
+ 0.284
+ ],
+ "angle": 0,
+ "content": "6. Experiments"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.291,
+ 0.485,
+ 0.368
+ ],
+ "angle": 0,
+ "content": "We provide empirical evidence supporting our theoretical results. In Section 6.1, we describe the experimental settings and data configurations used in our study. In Section 6.2, we analyze the correlation between the Lipschitz constant and the performance of the diffusion model."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.375,
+ 0.266,
+ 0.391
+ ],
+ "angle": 0,
+ "content": "6.1. Experiment setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.396,
+ 0.485,
+ 0.563
+ ],
+ "angle": 0,
+ "content": "We used a Gaussian dataset with three modes (clusters) in two-dimensional space, each having the same covariance matrix. By adjusting the covariance, we examine the impact of the Lipschitz constant on model performance. The model we use is a one hidden layer MLP with 32 hidden dimensions. We use DDPM algorithm for our forward diffusion process and reverse denoising process. The number of inference steps we use is 200. It is optimized by MSE loss, and the performance metrics are log likelihood and Mahalanobis squared distance. For the training, we use AdamW optimizer with 0.001 learning rate and training epochs 100."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.564,
+ 0.485,
+ 0.609
+ ],
+ "angle": 0,
+ "content": "For the evaluation, we sample 1000 dots from central Gaussian distribution with variance 1. Then calculate the two losses of output and ground truth."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.615,
+ 0.266,
+ 0.632
+ ],
+ "angle": 0,
+ "content": "6.2. Correlation study"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.637,
+ 0.483,
+ 0.713
+ ],
+ "angle": 0,
+ "content": "This section explores the relationship between the Lipschitz constant and key performance indicators of the diffusion model. Table 2 shows the average log likelihoods with Lipschitz constants, and Table 3 presents the average Mahalanobis squared distances."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.713,
+ 0.483,
+ 0.759
+ ],
+ "angle": 0,
+ "content": "Figure 2 portrays two line charts: the upper panel maps the log likelihood against the Lipschitz constant, and the lower panel charts the Mahalanobis squared distance."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.759,
+ 0.483,
+ 0.834
+ ],
+ "angle": 0,
+ "content": "From Table 2, Table 3 and Figure 2, we can conclude the message that a larger covariance leads to a smaller Lipschitz (more smooth) target function, which is easier to learn. This is aligned with our theoretical analysis, i.e., Lemma 3.5, Theorem 5.4, Theorem 5.5, and Theorem 5.6."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.845,
+ 0.212,
+ 0.861
+ ],
+ "angle": 0,
+ "content": "7. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.871,
+ 0.485,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "We have presented a theoretical analysis of the Lipschitz continuity and second momentum properties of diffusion"
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.541,
+ 0.089,
+ 0.883,
+ 0.272
+ ],
+ "angle": 0,
+ "content": "| Covariance | Lipschitz | Avg Log Likelihood |
| 1 | 3.69 × 107 | -9901.2324 |
| 10 | 3.23 × 104 | -1001.9962 |
| 100 | 31.8916 | -106.1019 |
| 200 | 3.9870 | -57.2244 |
| 500 | 0.2567 | -28.0872 |
| 600 | 0.1491 | -24.9577 |
| 700 | 0.0943 | -22.6524 |
| 800 | 0.0634 | -21.0397 |
| 900 | 0.0448 | -19.7688 |
| 1000 | 0.0328 | -18.7532 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.513,
+ 0.282,
+ 0.906,
+ 0.34
+ ],
+ "angle": 0,
+ "content": "Table 2. Log Likelihood Loss for Different Lipschitz. For the Covariance column, the number being \\( z \\) means that the covariance matrix \\( \\Sigma = zI_{2\\times 2} \\). We compute the corresponding Lipschitz \\( L \\) and report the evaluation loss (Avg Log Likelihood)."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.546,
+ 0.363,
+ 0.878,
+ 0.545
+ ],
+ "angle": 0,
+ "content": "| Covariance | Lipschitz | Avg Mahalanobis2 |
| 1 | 3.69 × 107 | 19798.7871 |
| 10 | 3.23 × 104 | 1995.7114 |
| 100 | 31.8916 | 199.3178 |
| 200 | 3.9870 | 100.1765 |
| 500 | 0.2567 | 40.0695 |
| 600 | 0.1491 | 33.4458 |
| 700 | 0.0943 | 28.5269 |
| 800 | 0.0634 | 25.0344 |
| 900 | 0.0448 | 22.2571 |
| 1000 | 0.0328 | 20.0152 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.513,
+ 0.556,
+ 0.907,
+ 0.613
+ ],
+ "angle": 0,
+ "content": "Table 3. Mahalanobis Squared Loss for Different Lipschitz. For the Covariance column, the number being \\( z \\) means that the covariance matrix \\( \\Sigma = zI_{2\\times 2} \\). We compute the corresponding Lipschitz \\( L \\) and report the evaluation loss (Avg Mahalanobis)."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.522,
+ 0.64,
+ 0.707,
+ 0.743
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.715,
+ 0.64,
+ 0.899,
+ 0.743
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.513,
+ 0.76,
+ 0.907,
+ 0.789
+ ],
+ "angle": 0,
+ "content": "Figure 2. Left: Log likelihood vs. Lipschitz constant. Right: Mahalanobis squared distance vs. Lipschitz constant."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.826,
+ 0.907,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "models. Our results provide concrete bounds on key properties of the diffusion process and establish error guarantees for various diffusion solvers. These findings contribute to a deeper understanding of diffusion models and spur further theoretical and practical advancements in this field."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.945,
+ 0.52,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "11443"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.093,
+ 0.09,
+ 0.188,
+ 0.106
+ ],
+ "angle": 0,
+ "content": "References"
+ },
+ {
+ "type": "ref_text",
+ "bbox": [
+ 0.101,
+ 0.115,
+ 0.484,
+ 0.184
+ ],
+ "angle": 0,
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+# Unraveling the Smoothness Properties of Diffusion Models: A Gaussian Mixture Perspective
+
+Yingyu Liang $^{1,3,\dagger}$ Zhizhou Sha $^{2}$ Zhenmei Shi $^{3}$ Zhao Song $^{4,*}$ Mingda Wan $^{5}$ Yufa Zhou $^{6}$ $^{1}$ The University of Hong Kong, $^{2}$ University of Texas at Austin, $^{3}$ University of Wisconsin-Madison
+ $^{4}$ University of California, Berkeley, $^{5}$ Independent Researcher, $^{6}$ University of Pennsylvania
+
+*magic.linuxkde@gmail.com, †yliang@cs.wisc.edu,yingyul@hku.hk
+
+# Abstract
+
+Diffusion models have made rapid progress in generating high-quality samples across various domains. However, a theoretical understanding of the Lipschitz continuity and second momentum properties of the diffusion process is still lacking. In this paper, we bridge this gap by providing a detailed examination of these smoothness properties for the case where the target data distribution is a mixture of Gaussians, which serves as a universal approximator for smooth densities such as image data. We prove that if the target distribution is a $k$ -mixture of Gaussians, the density of the entire diffusion process will also be a $k$ -mixture of Gaussians. We then derive tight upper bounds on the Lipschitz constant and second momentum that are independent of the number of mixture components $k$ . Finally, we apply our analysis to various diffusion solvers, both SDE and ODE based, to establish concrete error guarantees in terms of the total variation distance and KL divergence between the target and learned distributions. Furthermore, our preliminary experiments support our theoretical analysis. Our results provide deeper theoretical insights into the dynamics of the diffusion process under common data distributions.
+
+# 1. Introduction
+
+Diffusion models, a prominent generative modeling framework, have rapid progress and garnered significant attention in recent years, due to their potential powerful ability to generate high-quality samples across various domains and diverse applications. Score-based generative diffusion models [30, 63] can generate high-quality image samples comparable to GANs, which require adversarial optimization. Based on the U-Net [50], stable diffusion [49], a conditional multi-modality generation model, can successfully generate business-used images. Based on the Transformer (DiT) [45], OpenAI released a video diffusion model, SORA [44], with a surprising performance.
+
+However, despite these technological strides, a critical gap persists in the theoretical understanding of diffusion processes, especially concerning the Lipschitz continuity and second momentum properties of these models. Many existing studies ([10, 13, 14, 21, 35] and many more) make simplifying assumptions about these key smoothness properties but lack rigorous formulation or comprehensive analysis. This paper aims to bridge this theoretical gap by providing a detailed examination of the Lipschitz and second momentum characteristics. To make the data distribution analyzable, we consider the mixture of Gaussian data distribution (see illustration in Figure 1), which is a universal approximation (Fact 1.1) for any smooth density, such as complex image and video data distributions.
+
+Fact 1.1. A Gaussian mixture model is a universal approximator of densities, in the sense that any smooth density can be approximated with any specific nonzero amount of error by a Gaussian mixture model with enough components [52].
+
+Furthermore, we prove that if the target data distribution is a $k$ -mixture of Gaussian, the density of the whole diffusion process will be a $k$ -mixture of Gaussian (Proposition 3.2). Thus, our focus is studying a mixture of Gaussian target data distribution in the diffusion process, where we can gain a concrete Lipschitz constant and second momentum (Lemma 3.5 and Lemma 3.6). Moreover, we explore the implications of these properties through the lens of various solvers, both Stochastic Differential Equation (SDE) and Ordinary Differential Equation (ODE) based, providing a deeper insight into the dynamic behavior of diffusion processes and concrete guarantees in Table 1. Moreover, our preliminary experiments support our theoretical analysis.
+
+Our main contribution are summarized as follows:
+
+- As the Gaussian mixture model is a universal approximator of densities (Fact 1.1), we assume the target/image data distribution as a $k$ -mixture of Gaussian. Then, we show that the density of the whole diffusion process is a $k$ -mixture of Gaussian (Proposition 3.2).
+
+
+Figure 1. An illustration of discrete diffusion process for 8 mixture of Gaussian as shown in Eq. (2). The left figure represents the target 2-dimensional data distribution $p_0$ . The right figure represents the standard normal distribution $p_T = \mathcal{N}(0, I_{2\times 2})$ , where $T = 3$ . This experimental setup is also used in [13].
+
+
+
+
+
+
+
+- We analyze the Lipschitz and second momentum of $k$ -mixture of Gaussian data distribution and provide a tight upper bound, which is independent of $k$ , (Lemma 3.5 and Lemma 3.6), even when $k$ goes to infinity (see more discussion in Section 3.1).
+- After applying our analysis to DDPM, which is the SDE version of reverse process, we prove the dynamic of the diffusion process satisfies some concrete total variation bound (Theorem 5.4) and concrete KL divergence bound (Theorem 5.5 and Theorem 5.6) under choosing some total discretization steps. See a summary in Table 1.
+- After applying our analysis to DPOM and DPUM, which is the ODE version of the reverse process, we prove the dynamic of the diffusion process satisfies some concrete total variation bound (Theorem 5.7 and Theorem 5.8) under choosing some total discretization steps.
+
+# Studies of the mixture of Gaussian under diffusion.
+
+There is a rich line of work that studies a mixture of Gaussian data distribution under the diffusion process, sharing a similar popular setting. However, none focuses on the Lipschitz smoothness and second momentum property as ours. We provide a short summary here for convenience. [71] analyses the effect of diffusion guidance and provides theoretical insights on the instillation of task-specific information into the score function and conditional generation, e.g., text-to-image, by studying the mixture of Gaussian data distribution as a case study. [27] propose a new SDE-solver for diffusion models under a mixture of Gaussian data. [26, 53] learn mixtures of Gaussian data using the DDPM objective and gives bound for sample complexity by assuming all covariance matrices are identity but does not use Lipschitz, while our work does not need identity assumptions. [16] mainly focuses on solving $k$ -mixture of Gaussian in diffusion model by leveraging the property of the mixture of Gaussian and polynomial approximation methods and gives bound for sample complexity by assuming the covariance matrices have bounded condition number and that the mean vectors and covariance matrices lie in a bounded ball.
+
+# 2. Related Work
+
+Diffusion models and score-based models. [30] introduced the concept of denoising diffusion probabilistic models (DDPM), which learn to reverse a gradual noising process to generate samples and have been applied to many area [68-70]. Then, [63] used Stochastic Differential Equations (SDE) to build the diffusion model and explored the equivalence between score-based generative models (SGMs) and diffusion models, generalizing the diffusion model to continuous time. There is a line of works [58] studying the connection between diffusion models and nonequilibrium thermodynamics, providing a theoretical foundation for these models. Another line of work has focused on improving the efficiency and quality of diffusion models [42]. Particularly, [59] leverages score matching to train diffusion models more efficiently; [43] improved architectures and training techniques for diffusion models. Diffusion models have been applied to various domains beyond image generation, achieving impressive results, e.g., text-to-image synthesis [12], audio synthesis [33], image superresolution [51], and so on.
+
+Mixture of Gaussian. Mixtures of Gaussian are among the most fundamental and widely used statistical models [1, 3-6, 8, 9, 19, 20, 22-25, 37, 41, 55, 56, 66, 72] and studied in neural networks learning [39, 47, 54, 57]. Recently, they have also been widely studied in diffusion models [16, 26, 27, 53, 71] (see detailed discussion in Section 1).
+
+Lipschitz and second momentum in score estimation. There is a line of work using bounded Lipschitz and second momentum as their key smoothness assumptions for the whole diffusion process without giving any concrete formulation [7, 10, 11, 13-15, 32, 34, 35, 40, 74], while our work gives a "close-form" formulation of Lipschitz and second momentum. [73] primarily identifies the existence of Lipschitz singularities without deriving tight bounds for arbitrary data distributions. In contrast, our analysis provides explicit bounds for the Lipschitz constant in terms of the pa
+
+| Type | Error guarantee | Steps for Φ(ε02) error | Reference |
| DDPM [13] | TV(p0, q)2 | Θ(d/ε02) | Theorem 5.4 |
| DDPM [10] | KL(p0, q) | Θ(d/ε02) | Theorem 5.5 |
| DDPM [10] | KL(p0, q) | Θ(d2/ε02) | Theorem 5.6 |
| DPOM [14] | TV(p0, q)2 | Θ(d/ε02) | Theorem 5.7 |
| DPUM [14] | TV(p0, q)2 | Θ(√d/ε0) | Theorem 5.8 |
+
+Table 1. A summary of our applications using our Lipschitz and second momentum bound, when we assume $\sigma_{\min (pt)}$ as a constant (defined in Definition 3.3). The third column means the number of discretization points required to guarantee a small total variation/KL divergence distance between the target data distribution $p_0$ and the learned distribution $\widehat{q}$
+
+rameters of the underlying mixture model. It connects these Lipschitz properties to concrete error guarantees for various solvers. There is another rich line of work studying how to train the diffusion models to have a better theoretical guarantee [11, 14-16, 26-28, 31, 36, 40, 48, 53, 59-62, 64, 65].
+
+# 3. Lipschitz and Second Momentum of Mixture of Gaussian
+
+In this section, we discuss the notations used, several key definitions for $k$ mixtures of Gaussian distributions, and lemmas concerning the Lipschitz continuity and second momentum of these mixtures. We begin by presenting the notations that are used throughout the paper.
+
+Notations. For two vectors $x \in \mathbb{R}^n$ and $y \in \mathbb{R}^n$ , we use $\langle x, y \rangle$ to denote the inner product between $x, y$ , i.e., $\langle x, y \rangle = \sum_{i=1}^{n} x_i y_i$ . We use $\operatorname{Pr}[]$ to denote the probability, we use $\mathbb{E}[]$ to denote the expectation. We use $e_i$ to denote a vector where only $i$ -th coordinate is 1, and other entries are 0. For each $a, b \in \mathbb{R}^n$ , we use $a \circ b \in \mathbb{R}^n$ to denote the vector where $i$ -th entry is $(a \circ b)_i = a_i b_i$ for all $i \in [n]$ , and this is the Hardamard product. We use $\mathbf{1}_n$ to denote a length- $n$ vector where all the entries are ones. We use $x_{i,j}$ to denote the $j$ -th coordinate of $x_i \in \mathbb{R}^n$ . We use $\|x\|_p$ to denote the $\ell_p$ norm of a vector $x \in \mathbb{R}^n$ , i.e. $\|x\|_1 := \sum_{i=1}^{n} |x_i|$ , $\|x\|_2 := (\sum_{i=1}^{n} x_i^2)^{1/2}$ , and $\|x\|_\infty := \max_{i \in [n]} |x_i|$ . For $k > n$ , for any matrix $A \in \mathbb{R}^{k \times n}$ , we use $\|A\|$ to denote the spectral norm of $A$ , i.e. $\|A\| := \sup_{x \in \mathbb{R}^n} \|Ax\|_2 / \|x\|_2$ . We use $\sigma_{\min}(A), \sigma_{\max}(A)$ to denote the minimum/maximum singular value of matrix $A$ . For a square matrix $A$ , we use $\mathrm{tr}[A]$ to denote the trace of $A$ , i.e., $\mathrm{tr}[A] = \sum_{i=1}^{n} A_{i,i}$ . We use $\det(A)$ to denote the determinant of matrix $A$ . We use $f * g$ to denote the convolution of 2 functions $f, g$ . In addition to $O(\cdot)$ notation, for two functions $f, g$ , we use the shorthand $f \lesssim g$ (resp. $\gtrsim$ ) to indicate that $f \leq Cg$ (resp. $\geq$ ) for an absolute constant $C$ .
+
+$k$ mixtures of Gaussian. Now, we are ready to introduce $k$ mixtures of Gaussian. Formally, we can have the following definition of the pdf for $k$ mixtures of Gaussian.
+
+Definition 3.1 ( $k$ mixtures of Gaussian pdf). Let $x \in \mathbb{R}^d$ , $i \in [k]$ , $t \geq 0 \in \mathbb{R}$ . For a fixed timestamp $t$ , (1) let $\alpha_i(t) \in$
+
+(0,1) be the weight for the $i$ -th Gaussian component at time $t$ and $\sum_{i=1}^{k} \alpha_i(t) = 1$ ; (2) let $\mu_i(t) \in \mathbb{R}^d$ and $\Sigma_i(t) \in \mathbb{R}^{d \times d}$ be the mean vector and covariance matrix for the $i$ -th Gaussian component at time $t$ . Then, we define
+
+$$
+\begin{array}{l} p _ {t} (x) := \sum_ {i = 1} ^ {k} \frac {\alpha_ {i} (t)}{(2 \pi) ^ {d / 2} \det (\Sigma_ {i} (t)) ^ {1 / 2}} \\ \cdot \exp (- \frac {1}{2} (x - \mu_ {i} (t)) ^ {\top} \Sigma_ {i} (t) ^ {- 1} (x - \mu_ {i} (t))). \\ \end{array}
+$$
+
+Then, the following lemma shows that the linear combination between $k$ mixtures of Gaussian and a single standard Gaussian is still a $k$ mixtures of Gaussian. The proof is in Appendix H.
+
+Proposition 3.2 (Informal version of Proposition H.1). Let $a, b \in \mathbb{R}$ . Let $\mathcal{D}$ be a $k$ -mixture of Gaussian distribution, and let $p$ be its pdf defined in Definition 3.1, i.e.,
+
+$$
+\begin{array}{l} p (x) := \sum_ {i = 1} ^ {k} \frac {\alpha_ {i}}{(2 \pi) ^ {d / 2} \det (\Sigma_ {i}) ^ {1 / 2}} \\ \cdot \exp \left(- \frac {1}{2} (x - \mu_ {i}) ^ {\top} \Sigma_ {i} ^ {- 1} (x - \mu_ {i})\right) \\ \end{array}
+$$
+
+Let $x \in \mathbb{R}^d$ sample from $\mathcal{D}$ . Let $z \in \mathbb{R}^d$ and $z \sim \mathcal{N}(0, I)$ which is independent from $x$ . Then, we have a new random variable $y = ax + bz$ which is also a $k$ -mixture of Gaussian distribution $\widetilde{\mathcal{D}}$ , whose pdf is
+
+$$
+\begin{array}{l} \widetilde {p} (x) := \sum_ {i = 1} ^ {k} \frac {\alpha_ {i}}{(2 \pi) ^ {d / 2} \det (\widetilde {\Sigma} _ {i}) ^ {1 / 2}} \\ \cdot \exp (- \frac {1}{2} (x - \widetilde {\mu} _ {i}) ^ {\top} \widetilde {\Sigma} _ {i} ^ {- 1} (x - \widetilde {\mu} _ {i})), \\ \end{array}
+$$
+
+where $\widetilde{\mu}_i = a\mu_i,\widetilde{\Sigma}_i = a^2\Sigma_i + b^2 I.$
+
+The Gaussian mixture model is a universal approximator of densities (Fact 1.1). Then, it is natural to assume that the target/image $(p_0)$ data distribution as the $k$ mixtures of Gaussian. Proposition 3.2 tells us that if the target data distribution is $k$ mixtures of Gaussian, then by Eq. (2), the pdf
+
+of the whole diffusion process is $k$ mixtures of Gaussian, i.e., the $p_t$ for any $t \in [0, T]$ . See details in Section 4.
+
+Main properties. Thus, we only need to analyze the property, i.e., Lipschitz constant and second momentum, of $k$ mixtures of Gaussian, to have a clear guarantee for the whole diffusion process. In the following two lemmas, we will give concrete bounds of the Lipschitz constant and second momentum of $k$ mixtures of Gaussian. Both proofs can be found in Appendix H.
+
+First, we define the following conditions of the $k$ mixtures of Gaussian.
+
+Definition 3.3. The first two definitions here are related to the beginning time density $p_0$ in Eq. (9). The last two definitions are related to the all time density $p_t$ in Eq. (10), where $t \in [0, T]$ .
+
+- Let $\sigma_{\min(p_0)} =: \min_{i \in [k]} \{\sigma_{\min}(\Sigma_i)\}$ and $\sigma_{\max(p_0)} =: \max_{i \in [k]} \{\sigma_{\max}(\Sigma_i)\}$ .
+- Let $\mu_{\max(p_0)} =: \max_{i \in [k]} \{ \| \mu_i \|_2^2 \}$ and $\operatorname*{det}_{\min(p_0)} =: \min_{i \in [k]} \{ \operatorname*{det}(\Sigma_i) \}$ .
+- Let $\sigma_{\min(p_t)} := \min_{i \in [k]} \{ \sigma_{\min}(a_t^2 \Sigma_i + b_t^2 I) \}$ , $\sigma_{\max(p_t)} := \max_{i \in [k]} \{ \sigma_{\max}(a_t^2 \Sigma_i + b_t^2 I) \}$ .
+- Let $\operatorname*{det}_{\min (p_t)}\coloneqq \min_{i\in [k]}\{\operatorname *{det}(a_t^2\Sigma_i + b_t^2 I)\} .$
+
+Definition 3.3 denotes $\sigma_{\min(p_0)}$ , $\sigma_{\max(p_0)}$ , $\sigma_{\min(p_t)}$ , $\sigma_{\max(p_t)}$ as the minimum/maximum singular value between the covariance matrices of $k$ -components at the original distribution $p_0$ and $p_t$ . $\mu_{\max(p_0)}$ is the maximum $\ell_2^2$ -norm between mean vectors of the $k$ -components at $p_0$ . $\operatorname{det}_{\min(p_0)}$ is the minimum determinant between the covariance matrices of $k$ -components at $p_0$ .
+
+Condition 3.4. All conditions here are related to the all time density $p_t$ in Eq. (10), where $t \in [0, T]$ . Let $x \in \mathbb{R}^d$ and $a_t, b_t$ be defined by Definition 4.1. We only consider the $x$ satisfying the following conditions:
+
+- Let $\beta \leq \| x - a_t\mu_i\| _2\leq R$ , where $R\geq 1$ and $\beta \in (0,0.1)$ for each $i\in [k]$
+- Let $p_t(x)$ be defined as Eq. (10) and $p_t(x) \geq \gamma$ , where $\gamma \in (0, 0.1)$ .
+
+In Condition 3.4, $\beta, R$ are the lower/upper bound of the $\ell_2$ distance between the input data $x$ and all $k$ scaled mean vectors $a_t\mu_i$ at timestep $t$ . Let $\gamma$ be the lower bound of $p_t(x)$ , the pdf at time $t$ and $\operatorname*{det}_{\min(p_t)}$ be the minimum determinant at $p_t$ . We assume $\beta$ and $\gamma$ are lower bounded/constant, implying that each Gaussian component in the mixture is well-conditioned. This is a standard assumption in diffusion theory and is consistent with other theoretical findings [16, 17, 26, 38, 53, 71]. Clearly, we have $\sigma_{\max(p_t)} \geq \sigma_{\max(p_0)}$ .
+
+Lemma 3.5 (Lipschitz, informal version of Lemma H.3). Assume Condition 3.4 holds. The Lipschitz constant for the
+
+score function $\frac{\mathrm{d}\log(p_t(x))}{\mathrm{d}x}$ is given by:
+
+$$
+\begin{array}{l} L = \frac {1}{\sigma_ {\operatorname* {m i n} \left(p _ {t}\right)}} + \frac {2 R ^ {2}}{\gamma^ {2} \sigma_ {\operatorname* {m i n} \left(p _ {t}\right)} ^ {2}} \cdot \exp \left(- \frac {\beta^ {2}}{2 \sigma_ {\operatorname* {m a x} \left(p _ {t}\right)}}\right) \\ \cdot \left(\frac {1}{(2 \pi) ^ {d} \operatorname* {d e t} _ {\min \left(p _ {t}\right)}} + \frac {1}{(2 \pi) ^ {d / 2} \operatorname* {d e t} _ {\min \left(p _ {t}\right)} ^ {1 / 2}}\right). \\ \end{array}
+$$
+
+In Lemma 3.5, we can clearly see that roughly $L = O(1 / \mathrm{poly}(\sigma_{\min(p_t)}))$ , which means the Lipschitz is only conditioned on the smallest singular value of all Gaussian components but independent of $k$ . The bounded region required in Condition 3.4 applies to where most of the probability mass lies, which is a common assumption in diffusion literature (e.g., [16, 26, 73]). Outside this region, the score function indeed may not be Lipschitz, but this affects regions with negligible probability mass, similar to observations in [73]. We provide an additional empirical study in Section 6 to support our analysis.
+
+Lemma 3.6 (Second momentum, informal version of Lemma H.2). Let $x_0 \sim p_0$ , where $p_0$ is defined by Eq. (9). Then, we have
+
+$$
+\begin{array}{l} m _ {2} ^ {2} := \underset {x _ {0} \sim p _ {0}} {\mathbb {E}} [ \| x _ {0} \| _ {2} ^ {2} ] = \sum_ {i = 1} ^ {k} \alpha_ {i} (\| \mu_ {i} \| _ {2} ^ {2} + \operatorname {t r} [ \Sigma_ {i} ]) \\ \leq \max _ {i \in [ k ]} \left\{\| \mu_ {i} \| _ {2} ^ {2} + \operatorname {t r} \left[ \Sigma_ {i} \right] \right\}. \\ \end{array}
+$$
+
+The proof idea of Lemma 3.5 and Lemma 3.6 is that we first consider the case when $k = 1$ in Appendix D and then we extend to 2 mixtures of Gaussian setting in Appendix E. Finally, we can generalize to $k$ setting in Appendix F and summarize it in Appendix H. In Lemma 3.6, we can see that $m_2^2 = O(1)$ roughly, which is independent of $k$ as well. Later, we will apply our Lemma 3.5 and Lemma 3.6 in Section 5 to get concrete bound for each diffusion process, e.g., DDPM, DPOM and DPUM.
+
+# 3.1. Practical insights
+
+We believe our results in Lemma 3.5 is non-trivial. First, the Lipschitz bound depends inversely exponential on the dimension $d$ . If $d$ grows larger, the Lipschitz constant $L$ becomes much smaller. Second, in practice, the $k$ will be super large for complicated data distribution, e.g., millions of Gaussian components for an image distribution. Many studies need to overcome the large $k$ hardness in learning Gaussian mixture models [5, 8, 47, 57], while our Lipschitz upper-bound is independent with $k$ . These theoretical insights can help practitioners make more informed decisions about model architecture, optimization strategies, and computational resources needed for different applications.
+
+# 4. Score Based Model and Diffusion Model
+
+In Section 4.1, we first briefly introduce DDPM [30], a stochastic differential equations (SDE) version of the reverse diffusion process, and score-based generative models (SGMs) [63], a generalization of DDPM. In Section 4.2, we introduce multiple solvers for the reverse process.
+
+# 4.1. Background on score based diffusion model
+
+First, we denote the input data as $x \in \mathbb{R}^d$ and the target original data distribution as $p_0(x)$ . Assuming that the noisy latent state of score-based generative models (SGMs) at time $t$ is a stochastic process $x_{t}$ for $0 \leq t \leq T$ , we have the forward SDE is defined by:
+
+$$
+\mathrm {d} x _ {t} = f \left(x _ {t}, t\right) \mathrm {d} t + g (t) \mathrm {d} w _ {t}, \quad x _ {0} \sim p _ {0}, \quad 0 \leq t \leq T \tag {1}
+$$
+
+where $w_{t}\in \mathbb{R}^{d}$ is the standard Brownian motion, $f(\cdot ,t):$ $\mathbb{R}^d\to \mathbb{R}^d$ which is called drift coefficient, and $g(t):\mathbb{R}\rightarrow$ $\mathbb{R}$ which is called diffusion coefficient. We use $p_t(x)$ to denote the marginal probability density function of $x_{t}$ . The pdf at last time step $p_T$ is the prior distribution which often defined as standard Gaussian $p_T(x) = \mathcal{N}(0,I)$
+
+The continuous forward SDE Eq. (1) also has the discrete Markov chain form as
+
+$$
+x _ {t} = a _ {t} x _ {0} + b _ {t} z, \quad x _ {0} \sim p _ {0} \tag {2}
+$$
+
+where $x_0 \sim p_0(x)$ and $z \sim \mathcal{N}(0, I)$ , and $a_t, b_t \in \mathbb{R}$ are functions of time. Additionally, we assume as $t \to T$ , $a_t \to 0$ and $b_t \to 1$ . Thus, $x_T \sim \mathcal{N}(0, I)$ . Also, clearly when $t \to 0$ , $a_t \to 1$ and $b_t \to 0$ for this is the boundary condition. More specifically, the Eq. (2) can be viewed as the iterative equation in DDPM [30].
+
+From [2], we know $x_{t}$ also satisfy the reverse SDE:
+
+$$
+\mathrm {d} x _ {t} = \left(f \left(x _ {t}, t\right) - g (t) ^ {2} \nabla \log p _ {t} \left(x _ {t}\right)\right) \mathrm {d} t + g (t) \mathrm {d} \widetilde {w} _ {t}, \tag {3}
+$$
+
+where $\widetilde{w}_t \in \mathbb{R}^d$ is backward Brownian motion [2], and $\nabla \log p_t(x_t)$ is the score function. For convenience, we rewrite the reverse SDE Eq. (3) in a forward version by switching the time direction, replacing $t$ with $T - t$ . Let $\widetilde{x}_t \coloneqq x_{T - t}$ . The law of $(\widetilde{x}_t)_{0 \leq t \leq T}$ is identical to the law of $(x_{T - t})_{0 \leq t \leq T}$ . We use $q_t$ to denote the density of $\widetilde{x}_t$ :
+
+$$
+\begin{array}{l} \mathrm {d} \widetilde {x} _ {t} = (- f (\widetilde {x} _ {t}, T - t) + g (T - t) ^ {2} \nabla \log p _ {T - t} (\widetilde {x} _ {t})) \mathrm {d} t \\ + g (T - t) \mathrm {d} w _ {t}. \tag {4} \\ \end{array}
+$$
+
+The process $(\widetilde{x}_t)_{0\leq t\leq T}$ converts noise into samples from $p_0$ , thereby achieving the objective of generative modeling.
+
+Since we can not obtain the score function $\nabla \log p_t$ directly, we can use a neural network to approximate it, and we denote the estimated score function by $s_t(x)$ . By replacing the score function $\nabla \log p_t$ with our approximated score function $s_t(x)$ , we can rewrite Eq. (4) as:
+
+$$
+\mathrm {d} y _ {t} = \left(- f \left(y _ {t}, T - t\right) + g (T - t) ^ {2} s _ {T - t} \left(y _ {t}\right)\right) \mathrm {d} t
+$$
+
+$$
++ g (T - t) \mathrm {d} w _ {t}, y _ {0} \sim p _ {T}, 0 \leq t \leq T. \tag {5}
+$$
+
+where $y_{t}$ is the process we approximate by our SGM $s_t$ . For clarity, we mainly focus on the Ornstein-Uhlenbeck (OU) process, which is a diffusion process with exp coefficient:
+
+Definition 4.1. The forward SDE of OU process $(f(x_{t},t) = -x_{t}$ , and $g(t)\equiv \sqrt{2})$ is: $\mathrm{d}x_{t} = -x_{t}\mathrm{d}t + \sqrt{2}\mathrm{d}w_{t}$ . The corresponding discrete Markov chain form of OU process is given by: $x_{t} = e^{-t}x_{0} + \sqrt{1 - e^{-2t}} z$ , where we can see that $a_{t} = e^{-t}$ , $b_{t} = \sqrt{1 - e^{-2t}}$ in Eq. (2).
+
+From Eq. (5) under the OU process, we can have:
+
+$$
+\mathrm {d} y _ {t} = \left(x _ {t} + 2 s _ {T - t} \left(y _ {t}\right)\right) \mathrm {d} t + \sqrt {2} \mathrm {d} w _ {t}. \tag {6}
+$$
+
+# 4.2. Definitions of different solvers
+
+In practical applications, it's necessary to adopt a discrete-time approximation for sampling dynamics. We have the following definition.
+
+Definition 4.2 (Time discretization). Define the $N$ discretization points as $\delta = t_0 \leq t_1 \leq \dots \leq t_N = T$ , where $\delta \geq 0$ is the early stopping parameter, with $\delta = 0$ presenting the normal setting. For each discretization step $k$ , where $1 \leq k \leq N$ , the step size is denoted by $h_k := t_k - t_{k-1}$ .
+
+Let $\widehat{y}_t$ be the discrete approximation of $y_{t}$ in Eq. (6) starting from $\widehat{y}_0\sim \mathcal{N}(0,I)$ . We use $\widehat{q}_t$ to denote the density of $\widehat{y}_t$ . Let $N$ be defined in Definition 4.2 and $t_k^\prime = T - t_{N - k}$ . To solve Eq. (6), we have two numerical solvers:
+
+Definition 4.3. We define EulerMaruyama as the numerical solver satisfying $\widehat{y}_{T - \delta} =$ EulerMaruyama(T,s), where $\widehat{y}_{T - \delta}\in \mathbb{R}^d$ is the output, $T\in \mathbb{R}^{+}$ is the total time, and $s$ is the score estimates. The Euler-Maruyama scheme is, (Equation 5 in [10]), for $t\in [t_k',t_{k + 1}']$
+
+$$
+\mathrm {d} \hat {y} _ {t} = \left(\hat {y} _ {t _ {k} ^ {\prime}} + 2 s _ {T - t _ {k} ^ {\prime}} \left(\hat {y} _ {t _ {k} ^ {\prime}}\right)\right) \mathrm {d} t + \sqrt {2} \mathrm {d} w _ {t}. \tag {7}
+$$
+
+Definition 4.4. We define ExponentialIntegrator as the numerical solver satisfying $\widehat{y}_{T - \delta} =$ ExponentialIntegrator(T,s), where $\widehat{y}_{T - \delta}\in \mathbb{R}^d$ is the output, $T\in \mathbb{R}^{+}$ is the total time, and $s$ is the score estimates. The Exponential Integrator scheme is, (Equation 6 in [10]), for $t\in [t_k',t_{k + 1}']$
+
+$$
+\mathrm {d} \widehat {y} _ {t} = \left(\widehat {y} _ {t} + 2 s _ {T - t _ {k} ^ {\prime}} \left(\widehat {y} _ {t _ {k} ^ {\prime}}\right)\right) \mathrm {d} t + \sqrt {2} \mathrm {d} w _ {t}. \tag {8}
+$$
+
+The two methods above are used for solving SDE. The difference is that in the first term of RHS of Euler-Maruyama uses $\widehat{y} t_{k}^{\prime}$ , while Exponential Integrator uses $\widehat{y}_t$ . The Exponential Integrator scheme has a closed-form solution (see detail in Section 1.1 of [10]).
+
+We now introduce two ordinary differential equation (ODE) solvers, DPOM and DPUM, which omit the Brownian motion term in Eq. (6). These solvers, defined in
+
+Definitions 4.5 and 4.6, represent distinct approaches using predictor-corrector steps to address the reverse process via probability flow ODEs. Specifically, DPOM employs overdamped Langevin Monte Carlo (LMC), while DPUM uses underdamped LMC, enabling more efficient sampling. We will present their concrete step bounds in Section 5.
+
+Definition 4.5. We define DPOM (Diffusion Predictor with Overdamped Modeling) as Algorithm 1 in [14] satisfying $\widehat{y}_{T - \delta} = \mathsf{DPOM}(T,h_{\mathrm{pred}},h_{\mathrm{corr}},s)$ , where $\delta$ is the early stopping parameter, $\widehat{y}_{T - \delta}\in \mathbb{R}^d$ is the output, $T\in \mathbb{R}^{+}$ is the total steps, $h_\mathrm{pred}$ is the predictor step size, $h_\mathrm{corr}$ is the corrector step size, (see detailed definition in Algorithm 1 of [14]), and $s$ is the score estimates.
+
+Definition 4.6. We define DPUM (Diffusion Predictor with Underdamped Modeling) as Algorithm 2 in [14], satisfying $\widehat{y}_{T - \delta} = \mathsf{DPUM}(T,h_{\mathrm{pred}},h_{\mathrm{corr}},s)$ , where $\delta$ is the early stopping parameter, $\widehat{y}_{T - \delta}\in \mathbb{R}^d$ is the output, $T\in \mathbb{R}^{+}$ is the total steps, $h_\mathrm{pred}$ is the predictor step size, $h_\mathrm{corr}$ is the corrector step size, (see detailed definition in Algorithm 2 of [14]), and $s$ is the score estimates.
+
+# 5. Main Result for Application
+
+In this section, we will provide the main results of applications. In Section 5.1, we provide our key definitions and assumptions used. In Section 5.2, we provide our results for the total variation bound. In Section 5.3, we provide our results for the KL divergence bound. In Section 5.4, we provide our results for the probability flow ODE method, including DPOM and DPUM.
+
+# 5.1. Key definitions and assumptions
+
+We first assume that the loss of the learned score estimator is upper bounded by $\epsilon_0^2$ in Assumption 5.1. Then, we can show that we can recover the target/image data distribution under a small total variation or KL divergence gap later.
+
+Assumption 5.1 (Score estimation error, Assumption 1 in [10], page 6, and Assumption 3 in [13], page 6). The learned score function $s_t(x)$ satisfies for any $1 \leq k \leq N$ ,
+
+$$
+\frac {1}{T} \sum_ {k = 1} ^ {N} h _ {k} \underset {p _ {t _ {k}}} {\mathbb {E}} [ \| \nabla \log p _ {t _ {k}} (x) - s _ {t _ {k}} (x) \| _ {2} ^ {2} ] \leq \epsilon_ {0} ^ {2}.
+$$
+
+where $h_k$ is the step size defined in Definition 4.2 for step $k$ , $N$ is the total steps, and $\sum_{k=1}^{N} h_k = T$ .
+
+To avoid ill-distribution $q_{T}$ , we have the below definition follows [10, 14].
+
+Definition 5.2. We define $\epsilon$ as total variation distance between $q_{T - \delta}$ and $q_{T}$ .
+
+Let the distribution $p_0(x)$ be a $k$ -mixture of Gaussians:
+
+$$
+p _ {0} (x) := \sum_ {i = 1} ^ {k} \alpha_ {i} \mathcal {N} \left(\mu_ {i}, \Sigma_ {i}\right). \tag {9}
+$$
+
+Using the Proposition 3.2, we know the pdf of $x_{t}$ at the any time $t$ is given by:
+
+$$
+p _ {t} (x) = \sum_ {i = 1} ^ {k} \alpha_ {i} \mathcal {N} \left(a _ {t} \mu_ {i}, a _ {t} ^ {2} \Sigma_ {i} + b _ {t} ^ {2} I\right). \tag {10}
+$$
+
+We introduce Pinsker's inequality, which relates total variation distance to the Kullback-Leibler divergence.
+
+Lemma 5.3 (Pinsker's inequality [18]). Let $p, q$ are two probability distributions, then we have $\mathrm{TV}(\mathrm{p},\mathrm{q}) \leq \sqrt{\frac{1}{2}\mathrm{KL}(p\|q)}$ .
+
+From Lemma 5.3, we can see the total variation is a weaker bound than KL divergence.
+
+# 5.2. Total variation
+
+Now, we are ready to present our result for total variation bound assuming data distribution is $k$ -mixture of Gaussian $(p_0$ in Eq. (9)). Recall $\epsilon_0$ is defined in Assumption 5.1, $\epsilon$ is defined in Definition 5.2 and $h_k$ is defined in Definition 4.2. See the proof in Appendix I.
+
+Theorem 5.4 (DDPM, total variation, informal version of Theorem I.1). Assume Condition 3.4 and Assumption 5.1 hold. The step size $h_k \coloneqq T / N$ satisfies $h_k = O(1 / L)$ and $L \geq 1$ for $k \in [N]$ . Let $\widehat{q}$ denote the density of the output of the Euler-Maruyama defined by Definition 4.3. Then, we have
+
+$$
+\begin{array}{l} \mathrm {T V} (\widehat {q}, p _ {0}) \lesssim \underbrace {\sqrt {\mathrm {K L} (p _ {0} \| \mathcal {N} (0 , I))} \exp (- T)} _ {\text {c o n v e r g e n c e o f f o r w a r d p r o c e s s}} \\ + \underbrace {(L \sqrt {d h} + L m _ {2} h) \sqrt {T}} _ {\text {d i s c r e t i z a t i o n e r r o r}} + \underbrace {\epsilon_ {0} \sqrt {T}} _ {\text {s c o r e e s t i m a t i o n e r r o r}}. \\ \end{array}
+$$
+
+where $L = \frac{1}{\sigma_{\min(p_t)}} + \frac{2R^2}{\gamma^2\sigma_{\min(p_t)}^2} \cdot \left(\frac{1}{(2\pi)^d\operatorname*{det}_{\min(p_t)}} + \right.$
+
+$\frac{1}{(2\pi)^{d / 2}\operatorname*{det}_{\min (p_t)}^{1 / 2}}$ $\exp (-\frac{\beta^2}{2\sigma_{\max(p_t)}}),\qquad m_2\qquad =$
+
+$(\sum_{i=1}^{k} \alpha_i (\|\mu_i\|_2^2 + \mathrm{tr}[\Sigma_i]))^{1/2}$ , and $\mathrm{KL}(p_0(x) \| \mathcal{N}(0, I)) \leq \frac{1}{2} (-\log(\det_{\min(p_0)}) + d\sigma_{\max(p_0)} + \mu_{\max(p_0)} - d)$ .
+
+In Theorem 5.4, suppose that $m_2 \leq d$ and choose $T = \Theta(\log(\mathrm{KL}(p_0 \| \mathcal{N}(0, I)) / \epsilon))$ , $h_k = \Theta\left(\frac{\epsilon^2}{L^2d}\right)$ , then we have $\mathrm{TV}(\widehat{q}, p_0) \leq \widetilde{O}(\epsilon + \epsilon_0)$ , for $N = \widetilde{O}(L^2d / \epsilon^2)$ . In particular, in order to have $\mathrm{TV}(\widehat{q}, p_0) \leq \epsilon$ , it suffices to have score error $\epsilon_0 \leq \widetilde{O}(\epsilon)$ , where $\widetilde{O}(\cdot)$ hides $T$ which is a log term. Thus, Theorem 5.4 provides a guarantee for total variation bound between target data distribution $p_0$ and learned output distribution $\widehat{q}$ with concrete $L$ and $m_2$ .
+
+# 5.3. KL divergence
+
+Similarly, we can present our result for the KL divergence bound in the following two theorems, assuming data distribution is $k$ -mixture of Gaussian. Recall $\epsilon_0$ is defined in Assumption 5.1, $\epsilon$ is denied in Definition 5.2 and $h_k$ is defined in Definition 4.2. See the proof in Appendix I.
+
+Theorem 5.5 (DDPM, KL divergence, informal version of Theorem I.2). Assume Condition 3.4 and Assumption 5.1 hold. We use uniform discretization points.
+
+(1) Let $\widehat{q}$ denote the density of the output of the ExponentialIntegrator (Definition 4.4), we have
+
+$$
+\mathrm {K L} (p _ {0} \| \widehat {q}) \lesssim (M _ {2} + d) \exp (- T) + T \epsilon_ {0} ^ {2} + \frac {d T ^ {2} L ^ {2}}{N}.
+$$
+
+In particular, choosing $T = \Theta (\log (M_2d / \epsilon_0))$ and $N = \Theta (dT^2 L^2 /\epsilon_0^2)$ , then $\mathrm{KL}(p_0\| \widehat{q}) = \widetilde{O} (\epsilon_0^2)$ .
+
+(2) Let $\widehat{q}$ denote the density of the output of the EulerMaruyama (Definition 4.3), we have
+
+$$
+\mathrm {K L} (p _ {0} \| \widehat {q}) \lesssim (M _ {2} + d) \exp (- T) + T \epsilon_ {0} ^ {2} + \frac {d T ^ {2} L ^ {2}}{N} + \frac {T ^ {3} M _ {2}}{N ^ {2}}.
+$$
+
+$$
+\begin{array}{l} \begin{array}{l l} w h e r e M _ {2} = \sum_ {i = 1} ^ {k} \alpha_ {i} (\| \mu_ {i} \| _ {2} ^ {2} + \operatorname {t r} [ \Sigma_ {i} ]) a n d L = \\ \frac {1}{\sigma_ {\min (p _ {t})}} + \frac {2 R ^ {2}}{\gamma^ {2} \sigma_ {\min (p _ {t})} ^ {2}} \cdot \left(\frac {1}{(2 \pi) ^ {d} \det _ {\min (p _ {t})}} + \frac {1}{(2 \pi) ^ {d / 2} \det _ {\min (p _ {t})} ^ {1 / 2}}\right). \end{array} \\ \exp \bigl (- \frac {\beta^ {2}}{2 \sigma_ {\max (p _ {t})}} \bigr). \\ \end{array}
+$$
+
+Theorem 5.6 (DDPM, KL divergence for smooth data distribution, informal version of Theorem I.3). Assume Condition 3.4 and Assumption 5.1 hold. We use the exponentially decreasing (then constant) step size $h_k = c \min \{ \max \{ t_k, 1 / L \}, 1 \}$ , $c = \frac{T + \log L}{N} \leq \frac{1}{Kd}$ . Let $\widehat{q}$ denote the density of the output of the ExponentialIntegrator defined by Definition 4.4. Then, we have
+
+$$
+\operatorname {K L} \left(p _ {0} \| \widehat {q}\right) \lesssim \left(M _ {2} + d\right) \exp (- T) + T \epsilon_ {0} ^ {2} + \frac {d ^ {2} (T + \log L) ^ {2}}{N},
+$$
+
+$$
+\begin{array}{l} \begin{array}{l l} w h e r e M _ {2} = \sum_ {i = 1} ^ {k} \alpha_ {i} (\| \mu_ {i} \| _ {2} ^ {2} + \operatorname {t r} [ \Sigma_ {i} ]) a n d L = \\ \frac {1}{\sigma_ {\min (p _ {t})}} + \frac {2 R ^ {2}}{\gamma^ {2} \sigma_ {\min (p _ {t})} ^ {2}} \cdot \left(\frac {1}{(2 \pi) ^ {d} \det _ {\min (p _ {t})}} + \frac {1}{(2 \pi) ^ {d / 2} \det _ {\min (p _ {t})} ^ {1 / 2}}\right). \end{array} \\ \begin{array}{l} \exp (- \frac {\beta^ {2}}{2 \sigma_ {\max (p _ {t})}}). \quad \text {I n p a r t i c u l a r , i f w e s e t T =} \\ \Theta (\log (M _ {2} d / \epsilon_ {0})) \text {a n d N = \Theta (d ^ {2} (T + \log L) ^ {2} / \epsilon_ {0} ^ {2}) , t h e n} \\ \mathrm {K L} (p _ {0} \| \widehat {q}) \leq \widetilde {O} (\epsilon_ {0} ^ {2}). \text {I n a d d i t i o n , f o r E u l e r - M a r u y a m a} \\ \text {s c h e m e d e f i n e d i n D e f i n i o n 4 . 3 , t h e s a m e b o u n d s h o l d w i t h} \\ \text {a n a n d i s t i t i o n a l M _ {2} \sum_ {k = 1} ^ {N} h _ {k} ^ {3} t e r m .} \end{array} \\ \end{array}
+$$
+
+Theorem 5.6 and Theorem 5.5 provide a guarantee for KL divergence bound between target data distribution $p_0$ and learned output distribution $\widehat{q}$ with concrete $L$ and $M_2$ . Theorem 5.6 has $\log^2 L$ instead of $L^2$ in the bound for total number of discretization points $N$ , but includes an additional $d$ compared to Theorem 5.5. On the other hand, Theorem 5.6 requires the data distribution $p_0$ is Lipschitz and
+
+second-order differentiable [10], allowing a better bound in terms of $L$ , while all other theorems [13, 14] require conditions about Lipschitz on $p_t$ for any $0 \leq t \leq T$ . However, our assumption $p_0$ is $k$ -mixture of Gaussians satisfies all conditions they use.
+
+From Lemma 5.3, we can compare KL divergence results with total variation results. Notice that $M_2 = m_2^2$ when comparing theorems for total variation and KL divergence. According to Lemma 5.3, the square of the TV distance is comparable to the KL divergence, which explains the squared relationship of the second momentum term.
+
+# 5.4. Probability flow ODE
+
+Notice that in the previous results we are considering SDE based models. However from [63], we know that we can also use ODE to run the reverse process, which has the same marginal distribution with SDE reverse process but is thereby deterministic. In this section, we provide results of DPOM and DPUM (Algorithm 1 and 2 in [14]) algorithms which are based on ODE reverse process.
+
+Theorem 5.7 (DPOM, informal version of Theorem I.4). Assume Condition 3.4 and Assumption 5.1 hold. We use the DPOM algorithm defined in Definition 4.5, and let $\widehat{q}$ be the output density of it. Then, we have
+
+$$
+\begin{array}{l} \mathrm {T V} (\widehat {q}, p _ {0}) \lesssim (\sqrt {d} + m _ {2}) \exp (- T) + L ^ {2} T d ^ {1 / 2} h _ {\mathrm {p r e d}} \\ + L ^ {3 / 2} T d ^ {1 / 2} h _ {\mathrm {c o r r}} ^ {1 / 2} + L ^ {1 / 2} T \epsilon_ {0} + \epsilon . \\ \end{array}
+$$
+
+$$
+\begin{array}{l} \begin{array}{l} \text {w h e r e} m _ {2} = (\sum_ {i = 1} ^ {k} \alpha_ {i} (\| \mu_ {i} \| _ {2} ^ {2} + \operatorname {t r} [ \Sigma_ {i} ])) ^ {1 / 2} \text {a n d} L = \\ \frac {1}{\sigma_ {\min (p _ {t})}} + \frac {2 R ^ {2}}{\gamma^ {2} \sigma_ {\min (p _ {t})} ^ {2}} \cdot \left(\frac {1}{(2 \pi) ^ {d} \det _ {\min (p _ {t})}} + \frac {1}{(2 \pi) ^ {d / 2} \det _ {\min (p _ {t})} ^ {1 / 2}}\right). \end{array} \\ \begin{array}{l} \exp (- \frac {\beta^ {2}}{2 \sigma_ {\max (p _ {t})}}). \quad \text {I n p a r t i c u l a r , i f w e s e t T =} \\ \Theta (\log (d m _ {2} / \epsilon)), h _ {\text {p r e d}} = \widetilde {\Theta} (\frac {\epsilon}{L ^ {2} d ^ {1 / 2}}), h _ {\text {c o r r}} = \widetilde {\Theta} (\frac {\epsilon}{L ^ {3} d}), \text {a n d} \\ \text {i f t h e s c o r e e s t i m a t i o n e r r o r s a t i s f i e s \epsilon_ {0} \leq \widetilde {O} (\frac {\epsilon}{\sqrt {L}}) , t h e n w e} \\ \widetilde {\Theta} (L ^ {3} d / \epsilon^ {2}) \text {s t e p s .} \end{array} \\ \end{array}
+$$
+
+Theorem 5.8 (DPUM, informal version of Theorem I.5). Assume Condition 3.4 and Assumption 5.1 hold. We use the DPUM algorithm defined in Definition 4.6, and let $\widehat{q}$ be the output density of it. Then, we have
+
+$$
+\begin{array}{l} \mathrm {T V} (\widehat {q}, p _ {0}) \lesssim (\sqrt {d} + m _ {2}) \exp (- T) + L ^ {2} T d ^ {1 / 2} h _ {\mathrm {p r e d}} \\ + L ^ {3 / 2} T d ^ {1 / 2} h _ {\mathrm {c o r r}} ^ {1 / 2} + L ^ {1 / 2} T \epsilon_ {0} + \epsilon . \\ \end{array}
+$$
+
+$$
+\begin{array}{l} w h e r e L = \frac {1}{\sigma_ {\operatorname* {m i n} \left(p _ {t}\right)}} + \frac {2 R ^ {2}}{\gamma^ {2} \sigma_ {\operatorname* {m i n} \left(p _ {t}\right)} ^ {2}} \cdot \left(\frac {1}{(2 \pi) ^ {d}} \det _ {\min \left(p _ {t}\right)} + \right. \\ \frac {1}{(2 \pi) ^ {d / 2} \operatorname* {d e t} _ {\min (p _ {t})} ^ {1 / 2}}) \quad \cdot \quad \exp \left(- \frac {\beta^ {2}}{2 \sigma_ {\max (p _ {t})}}\right) \quad a n d \quad m _ {2} \quad = \\ \begin{array}{l} (\sum_ {i = 1} ^ {k} \alpha_ {i} (\| \mu_ {i} \| _ {2} ^ {2} + \operatorname {t r} [ \Sigma_ {i} ])) ^ {1 / 2}. \quad I n \text {p a r t i c u l a r , i f} \\ w e s e t T = \Theta (\log (d m _ {2} / \epsilon)), h _ {\mathrm {p r e d}} = \widetilde {\Theta} (\frac {\epsilon}{L ^ {2} d ^ {1 / 2}}), \\ h _ {\mathrm {c o r r}} = \widetilde {\Theta} (\frac {\epsilon}{L ^ {3 / 2} d ^ {1 / 2}}), a n d i f t h e s c o r e e s t i m a t i o n e r r o r \end{array} \\ \end{array}
+$$
+
+satisfies $\epsilon_0\leq \widetilde{O} (\frac{\epsilon}{\sqrt{L}})$ , then we can obtain TV error $\epsilon$ with a total iteration complexity of $\widetilde{\Theta} (L^2 d^{1 / 2} / \epsilon)$ steps.
+
+Theorem 5.7 and Theorem 5.8 provide a guarantee for total variation bound between target data distribution $p_0$ and learned output distribution $\widehat{q}$ with concrete $L$ and $M_2$ for ODE reverse process. The difference between the DPOM (Theorem 5.7) and DPUM (Theorem 5.8) is the complexity of $h_{\mathrm{corr}}$ and the final iteration complexity term. Using DPUM algorithm, we can reduce the total iteration complexity from $\widetilde{\Theta}(L^3 d / \epsilon^2)$ to $\widetilde{\Theta}(L^2 \sqrt{d} / \epsilon)$ .
+
+# 6. Experiments
+
+We provide empirical evidence supporting our theoretical results. In Section 6.1, we describe the experimental settings and data configurations used in our study. In Section 6.2, we analyze the correlation between the Lipschitz constant and the performance of the diffusion model.
+
+# 6.1. Experiment setup
+
+We used a Gaussian dataset with three modes (clusters) in two-dimensional space, each having the same covariance matrix. By adjusting the covariance, we examine the impact of the Lipschitz constant on model performance. The model we use is a one hidden layer MLP with 32 hidden dimensions. We use DDPM algorithm for our forward diffusion process and reverse denoising process. The number of inference steps we use is 200. It is optimized by MSE loss, and the performance metrics are log likelihood and Mahalanobis squared distance. For the training, we use AdamW optimizer with 0.001 learning rate and training epochs 100.
+
+For the evaluation, we sample 1000 dots from central Gaussian distribution with variance 1. Then calculate the two losses of output and ground truth.
+
+# 6.2. Correlation study
+
+This section explores the relationship between the Lipschitz constant and key performance indicators of the diffusion model. Table 2 shows the average log likelihoods with Lipschitz constants, and Table 3 presents the average Mahalanobis squared distances.
+
+Figure 2 portrays two line charts: the upper panel maps the log likelihood against the Lipschitz constant, and the lower panel charts the Mahalanobis squared distance.
+
+From Table 2, Table 3 and Figure 2, we can conclude the message that a larger covariance leads to a smaller Lipschitz (more smooth) target function, which is easier to learn. This is aligned with our theoretical analysis, i.e., Lemma 3.5, Theorem 5.4, Theorem 5.5, and Theorem 5.6.
+
+# 7. Conclusion
+
+We have presented a theoretical analysis of the Lipschitz continuity and second momentum properties of diffusion
+
+| Covariance | Lipschitz | Avg Log Likelihood |
| 1 | 3.69 × 107 | -9901.2324 |
| 10 | 3.23 × 104 | -1001.9962 |
| 100 | 31.8916 | -106.1019 |
| 200 | 3.9870 | -57.2244 |
| 500 | 0.2567 | -28.0872 |
| 600 | 0.1491 | -24.9577 |
| 700 | 0.0943 | -22.6524 |
| 800 | 0.0634 | -21.0397 |
| 900 | 0.0448 | -19.7688 |
| 1000 | 0.0328 | -18.7532 |
+
+Table 2. Log Likelihood Loss for Different Lipschitz. For the Covariance column, the number being $z$ means that the covariance matrix $\Sigma = zI_{2\times 2}$ . We compute the corresponding Lipschitz $L$ and report the evaluation loss (Avg Log Likelihood).
+
+| Covariance | Lipschitz | Avg Mahalanobis2 |
| 1 | 3.69 × 107 | 19798.7871 |
| 10 | 3.23 × 104 | 1995.7114 |
| 100 | 31.8916 | 199.3178 |
| 200 | 3.9870 | 100.1765 |
| 500 | 0.2567 | 40.0695 |
| 600 | 0.1491 | 33.4458 |
| 700 | 0.0943 | 28.5269 |
| 800 | 0.0634 | 25.0344 |
| 900 | 0.0448 | 22.2571 |
| 1000 | 0.0328 | 20.0152 |
+
+Table 3. Mahalanobis Squared Loss for Different Lipschitz. For the Covariance column, the number being $z$ means that the covariance matrix $\Sigma = zI_{2\times 2}$ . We compute the corresponding Lipschitz $L$ and report the evaluation loss (Avg Mahalanobis).
+
+
+Figure 2. Left: Log likelihood vs. Lipschitz constant. Right: Mahalanobis squared distance vs. Lipschitz constant.
+
+
+
+models. Our results provide concrete bounds on key properties of the diffusion process and establish error guarantees for various diffusion solvers. These findings contribute to a deeper understanding of diffusion models and spur further theoretical and practical advancements in this field.
+
+# References
+
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+ "html": "| Type | Error guarantee | Steps for Φ(ε02) error | Reference |
| DDPM [13] | TV(p0, q)2 | Θ(d/ε02) | Theorem 5.4 |
| DDPM [10] | KL(p0, q) | Θ(d/ε02) | Theorem 5.5 |
| DDPM [10] | KL(p0, q) | Θ(d2/ε02) | Theorem 5.6 |
| DPOM [14] | TV(p0, q)2 | Θ(d/ε02) | Theorem 5.7 |
| DPUM [14] | TV(p0, q)2 | Θ(√d/ε0) | Theorem 5.8 |
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+ "content": "Table 1. A summary of our applications using our Lipschitz and second momentum bound, when we assume "
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+ "content": " as a constant (defined in Definition 3.3). The third column means the number of discretization points required to guarantee a small total variation/KL divergence distance between the target data distribution "
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+ "type": "text",
+ "content": "rameters of the underlying mixture model. It connects these Lipschitz properties to concrete error guarantees for various solvers. There is another rich line of work studying how to train the diffusion models to have a better theoretical guarantee [11, 14-16, 26-28, 31, 36, 40, 48, 53, 59-62, 64, 65]."
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+ "type": "text",
+ "content": " mixtures of Gaussian distributions, and lemmas concerning the Lipschitz continuity and second momentum of these mixtures. We begin by presenting the notations that are used throughout the paper."
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+ {
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+ "type": "inline_equation",
+ "content": "y \\in \\mathbb{R}^n"
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+ "content": ", we use "
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+ {
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+ "type": "inline_equation",
+ "content": "\\langle x, y \\rangle"
+ },
+ {
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+ "type": "text",
+ "content": " to denote the inner product between "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "x, y"
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+ "type": "text",
+ "content": ", i.e., "
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+ "type": "inline_equation",
+ "content": "\\langle x, y \\rangle = \\sum_{i=1}^{n} x_i y_i"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ". We use "
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+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "\\operatorname{Pr}[]"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " to denote the probability, we use "
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+ {
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+ "type": "inline_equation",
+ "content": "\\mathbb{E}[]"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " to denote the expectation. We use "
+ },
+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "e_i"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " to denote a vector where only "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "i"
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+ {
+ "bbox": [
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+ "type": "text",
+ "content": "-th coordinate is 1, and other entries are 0. For each "
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+ {
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+ "type": "inline_equation",
+ "content": "a, b \\in \\mathbb{R}^n"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ", we use "
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+ {
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+ "type": "inline_equation",
+ "content": "a \\circ b \\in \\mathbb{R}^n"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " to denote the vector where "
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+ {
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+ "type": "inline_equation",
+ "content": "i"
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+ {
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+ "type": "text",
+ "content": "-th entry is "
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+ "type": "inline_equation",
+ "content": "(a \\circ b)_i = a_i b_i"
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+ {
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+ "type": "text",
+ "content": " for all "
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+ {
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+ "type": "inline_equation",
+ "content": "i \\in [n]"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ", and this is the Hardamard product. We use "
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+ {
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+ "type": "inline_equation",
+ "content": "\\mathbf{1}_n"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " to denote a length-"
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+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "n"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " vector where all the entries are ones. We use "
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+ {
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+ "type": "inline_equation",
+ "content": "x_{i,j}"
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+ {
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+ "type": "text",
+ "content": " to denote the "
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+ "type": "inline_equation",
+ "content": "j"
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+ {
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+ "type": "text",
+ "content": "-th coordinate of "
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+ {
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+ "type": "inline_equation",
+ "content": "x_i \\in \\mathbb{R}^n"
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+ {
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+ "type": "text",
+ "content": ". We use "
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+ {
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+ "type": "inline_equation",
+ "content": "\\|x\\|_p"
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+ {
+ "bbox": [
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+ "type": "text",
+ "content": " to denote the "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "\\ell_p"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " norm of a vector "
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+ {
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+ "type": "inline_equation",
+ "content": "x \\in \\mathbb{R}^n"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ", i.e. "
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+ {
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+ "type": "inline_equation",
+ "content": "\\|x\\|_1 := \\sum_{i=1}^{n} |x_i|"
+ },
+ {
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+ "type": "text",
+ "content": ", "
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+ {
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+ "type": "inline_equation",
+ "content": "\\|x\\|_2 := (\\sum_{i=1}^{n} x_i^2)^{1/2}"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ", and "
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+ {
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+ "type": "inline_equation",
+ "content": "\\|x\\|_\\infty := \\max_{i \\in [n]} |x_i|"
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+ {
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+ "type": "text",
+ "content": ". For "
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+ {
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+ "type": "inline_equation",
+ "content": "k > n"
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+ {
+ "bbox": [
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+ "type": "text",
+ "content": ", for any matrix "
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+ {
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+ "type": "inline_equation",
+ "content": "A \\in \\mathbb{R}^{k \\times n}"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ", we use "
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+ {
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+ "type": "inline_equation",
+ "content": "\\|A\\|"
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+ {
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+ "type": "text",
+ "content": " to denote the spectral norm of "
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+ {
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+ "type": "inline_equation",
+ "content": "A"
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+ {
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+ "type": "text",
+ "content": ", i.e. "
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+ {
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+ "type": "inline_equation",
+ "content": "\\|A\\| := \\sup_{x \\in \\mathbb{R}^n} \\|Ax\\|_2 / \\|x\\|_2"
+ },
+ {
+ "bbox": [
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+ "content": ". We use "
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+ {
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+ ],
+ "type": "inline_equation",
+ "content": "\\sigma_{\\min}(A), \\sigma_{\\max}(A)"
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+ {
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+ "type": "text",
+ "content": " to denote the minimum/maximum singular value of matrix "
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+ {
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+ "type": "inline_equation",
+ "content": "A"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ". For a square matrix "
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+ {
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+ "type": "inline_equation",
+ "content": "A"
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+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", we use "
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+ {
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+ "type": "inline_equation",
+ "content": "\\mathrm{tr}[A]"
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+ {
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+ "type": "text",
+ "content": " to denote the trace of "
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+ {
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+ "type": "inline_equation",
+ "content": "A"
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+ {
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+ "type": "text",
+ "content": ", i.e., "
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+ {
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+ "type": "inline_equation",
+ "content": "\\mathrm{tr}[A] = \\sum_{i=1}^{n} A_{i,i}"
+ },
+ {
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+ "type": "text",
+ "content": ". We use "
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+ {
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+ ],
+ "type": "inline_equation",
+ "content": "\\det(A)"
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+ {
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+ "type": "text",
+ "content": " to denote the determinant of matrix "
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+ {
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+ "type": "inline_equation",
+ "content": "A"
+ },
+ {
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+ "type": "text",
+ "content": ". We use "
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+ {
+ "bbox": [
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+ "type": "inline_equation",
+ "content": "f * g"
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+ {
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+ "type": "text",
+ "content": " to denote the convolution of 2 functions "
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+ {
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+ "type": "inline_equation",
+ "content": "f, g"
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+ "type": "text",
+ "content": ". In addition to "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "O(\\cdot)"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " notation, for two functions "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "f, g"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": ", we use the shorthand "
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+ "type": "inline_equation",
+ "content": "f \\lesssim g"
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+ "type": "text",
+ "content": " (resp. "
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+ "type": "inline_equation",
+ "content": "\\gtrsim"
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+ "type": "text",
+ "content": ") to indicate that "
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+ "type": "inline_equation",
+ "content": "f \\leq Cg"
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+ "type": "text",
+ "content": " (resp. "
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+ "type": "inline_equation",
+ "content": "\\geq"
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+ "type": "text",
+ "content": ") for an absolute constant "
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+ {
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+ "type": "inline_equation",
+ "content": "C"
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+ "type": "text",
+ "content": "."
+ }
+ ]
+ }
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+ "type": "inline_equation",
+ "content": "k"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " mixtures of Gaussian. Now, we are ready to introduce "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "k"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " mixtures of Gaussian. Formally, we can have the following definition of the pdf for "
+ },
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+ "content": "\\begin{array}{l} L = \\frac {1}{\\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)} ^ {2}} \\cdot \\exp \\left(- \\frac {\\beta^ {2}}{2 \\sigma_ {\\operatorname* {m a x} \\left(p _ {t}\\right)}}\\right) \\\\ \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\operatorname* {d e t} _ {\\min \\left(p _ {t}\\right)}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\operatorname* {d e t} _ {\\min \\left(p _ {t}\\right)} ^ {1 / 2}}\\right). \\\\ \\end{array}",
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+ "content": " is defined by Eq. (9). Then, we have"
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+ "content": "\\begin{array}{l} m _ {2} ^ {2} := \\underset {x _ {0} \\sim p _ {0}} {\\mathbb {E}} [ \\| x _ {0} \\| _ {2} ^ {2} ] = \\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ]) \\\\ \\leq \\max _ {i \\in [ k ]} \\left\\{\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} \\left[ \\Sigma_ {i} \\right] \\right\\}. \\\\ \\end{array}",
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+ "content": " in Appendix D and then we extend to 2 mixtures of Gaussian setting in Appendix E. Finally, we can generalize to "
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+ "content": " setting in Appendix F and summarize it in Appendix H. In Lemma 3.6, we can see that "
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+ "content": " as well. Later, we will apply our Lemma 3.5 and Lemma 3.6 in Section 5 to get concrete bound for each diffusion process, e.g., DDPM, DPOM and DPUM."
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+ "content": " will be super large for complicated data distribution, e.g., millions of Gaussian components for an image distribution. Many studies need to overcome the large "
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+ "content": ". These theoretical insights can help practitioners make more informed decisions about model architecture, optimization strategies, and computational resources needed for different applications."
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+ "type": "text",
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+ "bbox": [
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+ "type": "inline_equation",
+ "content": "a_t, b_t \\in \\mathbb{R}"
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+ "type": "text",
+ "content": " are functions of time. Additionally, we assume as "
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+ "type": "text",
+ "content": ". Also, clearly when "
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+ "type": "text",
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+ {
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+ "type": "text",
+ "content": " for this is the boundary condition. More specifically, the Eq. (2) can be viewed as the iterative equation in DDPM [30]."
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+ "type": "text",
+ "content": " also satisfy the reverse SDE:"
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+ "content": "\\mathrm {d} x _ {t} = \\left(f \\left(x _ {t}, t\\right) - g (t) ^ {2} \\nabla \\log p _ {t} \\left(x _ {t}\\right)\\right) \\mathrm {d} t + g (t) \\mathrm {d} \\widetilde {w} _ {t}, \\tag {3}",
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+ "content": " is backward Brownian motion [2], and "
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+ "type": "text",
+ "content": " is the score function. For convenience, we rewrite the reverse SDE Eq. (3) in a forward version by switching the time direction, replacing "
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+ "content": "\\begin{array}{l} \\mathrm {d} \\widetilde {x} _ {t} = (- f (\\widetilde {x} _ {t}, T - t) + g (T - t) ^ {2} \\nabla \\log p _ {T - t} (\\widetilde {x} _ {t})) \\mathrm {d} t \\\\ + g (T - t) \\mathrm {d} w _ {t}. \\tag {4} \\\\ \\end{array}",
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+ "content": " converts noise into samples from "
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+ "type": "text",
+ "content": ", thereby achieving the objective of generative modeling."
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+ "content": "Since we can not obtain the score function "
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+ "content": "\\nabla \\log p_t"
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+ "type": "text",
+ "content": " directly, we can use a neural network to approximate it, and we denote the estimated score function by "
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+ "type": "text",
+ "content": ". By replacing the score function "
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+ "type": "text",
+ "content": " with our approximated score function "
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+ "type": "text",
+ "content": ", we can rewrite Eq. (4) as:"
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+ "type": "interline_equation",
+ "content": "\\mathrm {d} y _ {t} = \\left(- f \\left(y _ {t}, T - t\\right) + g (T - t) ^ {2} s _ {T - t} \\left(y _ {t}\\right)\\right) \\mathrm {d} t",
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+ "content": "+ g (T - t) \\mathrm {d} w _ {t}, y _ {0} \\sim p _ {T}, 0 \\leq t \\leq T. \\tag {5}",
+ "image_path": "9fe86109dfb6470823d48b9251afaeabf8d269de884cdbcb97b69339ea2fd8ba.jpg"
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+ "content": "y_{t}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " is the process we approximate by our SGM "
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+ "content": "s_t"
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+ ],
+ "type": "text",
+ "content": ". For clarity, we mainly focus on the Ornstein-Uhlenbeck (OU) process, which is a diffusion process with exp coefficient:"
+ }
+ ]
+ }
+ ],
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+ "content": "Definition 4.1. The forward SDE of OU process "
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+ "type": "inline_equation",
+ "content": "(f(x_{t},t) = -x_{t}"
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+ "content": ", and "
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+ "type": "inline_equation",
+ "content": "g(t)\\equiv \\sqrt{2})"
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+ "content": " is: "
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+ "type": "inline_equation",
+ "content": "\\mathrm{d}x_{t} = -x_{t}\\mathrm{d}t + \\sqrt{2}\\mathrm{d}w_{t}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ". The corresponding discrete Markov chain form of OU process is given by: "
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+ ],
+ "type": "inline_equation",
+ "content": "x_{t} = e^{-t}x_{0} + \\sqrt{1 - e^{-2t}} z"
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+ {
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+ ],
+ "type": "text",
+ "content": ", where we can see that "
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+ {
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+ ],
+ "type": "inline_equation",
+ "content": "a_{t} = e^{-t}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ", "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "b_{t} = \\sqrt{1 - e^{-2t}}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " in Eq. (2)."
+ }
+ ]
+ }
+ ],
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+ {
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+ "type": "text",
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+ "lines": [
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+ "type": "text",
+ "content": "From Eq. (5) under the OU process, we can have:"
+ }
+ ]
+ }
+ ],
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+ },
+ {
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+ ],
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+ "type": "interline_equation",
+ "content": "\\mathrm {d} y _ {t} = \\left(x _ {t} + 2 s _ {T - t} \\left(y _ {t}\\right)\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} w _ {t}. \\tag {6}",
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+ }
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+ }
+ ],
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+ "type": "text",
+ "content": "4.2. Definitions of different solvers"
+ }
+ ]
+ }
+ ],
+ "index": 21
+ },
+ {
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+ "type": "text",
+ "content": "In practical applications, it's necessary to adopt a discrete-time approximation for sampling dynamics. We have the following definition."
+ }
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+ }
+ ],
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+ "type": "text",
+ "content": "Definition 4.2 (Time discretization). Define the "
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+ {
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+ "type": "inline_equation",
+ "content": "N"
+ },
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+ "type": "text",
+ "content": " discretization points as "
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+ {
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+ "type": "inline_equation",
+ "content": "\\delta = t_0 \\leq t_1 \\leq \\dots \\leq t_N = T"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ", where "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "\\delta \\geq 0"
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+ "type": "text",
+ "content": " presenting the normal setting. For each discretization step "
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+ "type": "text",
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+ "content": " be the discrete approximation of "
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+ "content": " in Eq. (6) starting from "
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+ "type": "text",
+ "content": " to denote the density of "
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+ "content": "\\widehat{y}_t"
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+ {
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+ "type": "text",
+ "content": ". Let "
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+ "content": "N"
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+ "content": " be defined in Definition 4.2 and "
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+ "content": "T\\in \\mathbb{R}^{+}"
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+ "content": " is the total time, and "
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+ "type": "text",
+ "content": " is the score estimates. The Euler-Maruyama scheme is, (Equation 5 in [10]), for "
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+ "type": "inline_equation",
+ "content": "t\\in [t_k',t_{k + 1}']"
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+ ]
+ }
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+ "content": "\\mathrm {d} \\hat {y} _ {t} = \\left(\\hat {y} _ {t _ {k} ^ {\\prime}} + 2 s _ {T - t _ {k} ^ {\\prime}} \\left(\\hat {y} _ {t _ {k} ^ {\\prime}}\\right)\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} w _ {t}. \\tag {7}",
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+ "content": "Definition 4.4. We define ExponentialIntegrator as the numerical solver satisfying "
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+ "type": "inline_equation",
+ "content": "\\widehat{y}_{T - \\delta} ="
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+ "content": " ExponentialIntegrator(T,s), where "
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+ "content": "\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d"
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+ "type": "text",
+ "content": " is the output, "
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+ "type": "inline_equation",
+ "content": "T\\in \\mathbb{R}^{+}"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " is the total time, and "
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+ "type": "inline_equation",
+ "content": "s"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " is the score estimates. The Exponential Integrator scheme is, (Equation 6 in [10]), for "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "t\\in [t_k',t_{k + 1}']"
+ }
+ ]
+ }
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+ "index": 27
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+ "content": "\\mathrm {d} \\widehat {y} _ {t} = \\left(\\widehat {y} _ {t} + 2 s _ {T - t _ {k} ^ {\\prime}} \\left(\\widehat {y} _ {t _ {k} ^ {\\prime}}\\right)\\right) \\mathrm {d} t + \\sqrt {2} \\mathrm {d} w _ {t}. \\tag {8}",
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+ }
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+ "type": "text",
+ "content": "The two methods above are used for solving SDE. The difference is that in the first term of RHS of Euler-Maruyama uses "
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+ "type": "inline_equation",
+ "content": "\\widehat{y} t_{k}^{\\prime}"
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+ "content": ", while Exponential Integrator uses "
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+ "content": "\\widehat{y}_t"
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+ "type": "text",
+ "content": ". The Exponential Integrator scheme has a closed-form solution (see detail in Section 1.1 of [10])."
+ }
+ ]
+ }
+ ],
+ "index": 29
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+ {
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+ "type": "text",
+ "content": "We now introduce two ordinary differential equation (ODE) solvers, DPOM and DPUM, which omit the Brownian motion term in Eq. (6). These solvers, defined in"
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+ ]
+ }
+ ],
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+ }
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+ "content": "Definitions 4.5 and 4.6, represent distinct approaches using predictor-corrector steps to address the reverse process via probability flow ODEs. Specifically, DPOM employs overdamped Langevin Monte Carlo (LMC), while DPUM uses underdamped LMC, enabling more efficient sampling. We will present their concrete step bounds in Section 5."
+ }
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+ }
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+ "content": "Definition 4.5. We define DPOM (Diffusion Predictor with Overdamped Modeling) as Algorithm 1 in [14] satisfying "
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+ "content": "\\widehat{y}_{T - \\delta} = \\mathsf{DPOM}(T,h_{\\mathrm{pred}},h_{\\mathrm{corr}},s)"
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+ "content": ", where "
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+ "content": "\\delta"
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+ "type": "text",
+ "content": " is the early stopping parameter, "
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+ "type": "inline_equation",
+ "content": "\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d"
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+ {
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+ "type": "text",
+ "content": " is the output, "
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+ "type": "inline_equation",
+ "content": "T\\in \\mathbb{R}^{+}"
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+ {
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+ ],
+ "type": "text",
+ "content": " is the total steps, "
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+ "content": "h_\\mathrm{pred}"
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+ "type": "text",
+ "content": " is the predictor step size, "
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+ "content": "h_\\mathrm{corr}"
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+ "type": "text",
+ "content": " is the corrector step size, (see detailed definition in Algorithm 1 of [14]), and "
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+ "type": "inline_equation",
+ "content": "s"
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+ {
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+ "type": "text",
+ "content": " is the score estimates."
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+ }
+ ],
+ "index": 1
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+ "type": "text",
+ "content": "Definition 4.6. We define DPUM (Diffusion Predictor with Underdamped Modeling) as Algorithm 2 in [14], satisfying "
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+ "type": "inline_equation",
+ "content": "\\widehat{y}_{T - \\delta} = \\mathsf{DPUM}(T,h_{\\mathrm{pred}},h_{\\mathrm{corr}},s)"
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+ "content": ", where "
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+ "type": "text",
+ "content": " is the early stopping parameter, "
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+ "type": "inline_equation",
+ "content": "\\widehat{y}_{T - \\delta}\\in \\mathbb{R}^d"
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+ {
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+ "type": "text",
+ "content": " is the output, "
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+ "type": "inline_equation",
+ "content": "T\\in \\mathbb{R}^{+}"
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+ "type": "text",
+ "content": " is the total steps, "
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+ "content": "h_\\mathrm{pred}"
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+ {
+ "bbox": [
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+ "type": "text",
+ "content": " is the predictor step size, "
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+ "type": "inline_equation",
+ "content": "h_\\mathrm{corr}"
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+ {
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+ "type": "text",
+ "content": " is the corrector step size, (see detailed definition in Algorithm 2 of [14]), and "
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+ "content": "s"
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+ {
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+ "type": "text",
+ "content": " is the score estimates."
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+ }
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+ "type": "text",
+ "content": "5. Main Result for Application"
+ }
+ ]
+ }
+ ],
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+ "type": "text",
+ "content": "In this section, we will provide the main results of applications. In Section 5.1, we provide our key definitions and assumptions used. In Section 5.2, we provide our results for the total variation bound. In Section 5.3, we provide our results for the KL divergence bound. In Section 5.4, we provide our results for the probability flow ODE method, including DPOM and DPUM."
+ }
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+ }
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+ "content": "5.1. Key definitions and assumptions"
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+ "content": " in Assumption 5.1. Then, we can show that we can recover the target/image data distribution under a small total variation or KL divergence gap later."
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+ "content": "q_{T - \\delta}"
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+ "content": "p _ {0} (x) := \\sum_ {i = 1} ^ {k} \\alpha_ {i} \\mathcal {N} \\left(\\mu_ {i}, \\Sigma_ {i}\\right). \\tag {9}",
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+ "content": " at the any time "
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+ "type": "text",
+ "content": "We introduce Pinsker's inequality, which relates total variation distance to the Kullback-Leibler divergence."
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+ "type": "text",
+ "content": " in Eq. (9)). Recall "
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+ "content": " is defined in Assumption 5.1, "
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+ "content": " is defined in Definition 5.2 and "
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+ "type": "text",
+ "content": " is defined in Definition 4.2. See the proof in Appendix I."
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+ "type": "text",
+ "content": "Theorem 5.4 (DDPM, total variation, informal version of Theorem I.1). Assume Condition 3.4 and Assumption 5.1 hold. The step size "
+ },
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+ "content": "h_k \\coloneqq T / N"
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+ "content": " satisfies "
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+ "type": "inline_equation",
+ "content": "h_k = O(1 / L)"
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+ "content": "L \\geq 1"
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+ "content": "k \\in [N]"
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+ "type": "text",
+ "content": ". Let "
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+ "type": "inline_equation",
+ "content": "\\widehat{q}"
+ },
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+ "type": "text",
+ "content": " denote the density of the output of the Euler-Maruyama defined by Definition 4.3. Then, we have"
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+ }
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+ "content": "\\begin{array}{l} \\mathrm {T V} (\\widehat {q}, p _ {0}) \\lesssim \\underbrace {\\sqrt {\\mathrm {K L} (p _ {0} \\| \\mathcal {N} (0 , I))} \\exp (- T)} _ {\\text {c o n v e r g e n c e o f f o r w a r d p r o c e s s}} \\\\ + \\underbrace {(L \\sqrt {d h} + L m _ {2} h) \\sqrt {T}} _ {\\text {d i s c r e t i z a t i o n e r r o r}} + \\underbrace {\\epsilon_ {0} \\sqrt {T}} _ {\\text {s c o r e e s t i m a t i o n e r r o r}}. \\\\ \\end{array}",
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+ "content": "L = \\frac{1}{\\sigma_{\\min(p_t)}} + \\frac{2R^2}{\\gamma^2\\sigma_{\\min(p_t)}^2} \\cdot \\left(\\frac{1}{(2\\pi)^d\\operatorname*{det}_{\\min(p_t)}} + \\right."
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+ "content": "\\exp (-\\frac{\\beta^2}{2\\sigma_{\\max(p_t)}}),\\qquad m_2\\qquad ="
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+ "type": "inline_equation",
+ "content": "(\\sum_{i=1}^{k} \\alpha_i (\\|\\mu_i\\|_2^2 + \\mathrm{tr}[\\Sigma_i]))^{1/2}"
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+ "content": "\\mathrm{KL}(p_0(x) \\| \\mathcal{N}(0, I)) \\leq \\frac{1}{2} (-\\log(\\det_{\\min(p_0)}) + d\\sigma_{\\max(p_0)} + \\mu_{\\max(p_0)} - d)"
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+ "content": " and choose "
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+ "type": "inline_equation",
+ "content": "T = \\Theta(\\log(\\mathrm{KL}(p_0 \\| \\mathcal{N}(0, I)) / \\epsilon))"
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+ "type": "inline_equation",
+ "content": "h_k = \\Theta\\left(\\frac{\\epsilon^2}{L^2d}\\right)"
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+ "type": "inline_equation",
+ "content": "\\mathrm{TV}(\\widehat{q}, p_0) \\leq \\widetilde{O}(\\epsilon + \\epsilon_0)"
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+ "type": "inline_equation",
+ "content": "N = \\widetilde{O}(L^2d / \\epsilon^2)"
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+ "type": "text",
+ "content": ". In particular, in order to have "
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+ "type": "inline_equation",
+ "content": "\\mathrm{TV}(\\widehat{q}, p_0) \\leq \\epsilon"
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+ "type": "inline_equation",
+ "content": "\\epsilon_0 \\leq \\widetilde{O}(\\epsilon)"
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+ "type": "text",
+ "content": ", where "
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+ "type": "inline_equation",
+ "content": "\\widetilde{O}(\\cdot)"
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+ "content": " hides "
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+ "type": "text",
+ "content": " which is a log term. Thus, Theorem 5.4 provides a guarantee for total variation bound between target data distribution "
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+ "content": " and learned output distribution "
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+ "content": "\\widehat{q}"
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+ "content": " with concrete "
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+ "content": "Similarly, we can present our result for the KL divergence bound in the following two theorems, assuming data distribution is "
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+ "content": " is defined in Assumption 5.1, "
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+ "content": " is denied in Definition 5.2 and "
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+ "content": " is defined in Definition 4.2. See the proof in Appendix I."
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+ "type": "text",
+ "content": "Theorem 5.5 (DDPM, KL divergence, informal version of Theorem I.2). Assume Condition 3.4 and Assumption 5.1 hold. We use uniform discretization points."
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+ "content": "\\widehat{q}"
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+ "type": "text",
+ "content": " denote the density of the output of the ExponentialIntegrator (Definition 4.4), we have"
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+ "content": "\\mathrm {K L} (p _ {0} \\| \\widehat {q}) \\lesssim (M _ {2} + d) \\exp (- T) + T \\epsilon_ {0} ^ {2} + \\frac {d T ^ {2} L ^ {2}}{N}.",
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+ "content": "\\mathrm{KL}(p_0\\| \\widehat{q}) = \\widetilde{O} (\\epsilon_0^2)"
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+ "content": "(2) Let "
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+ "bbox": [
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+ "content": "\\widehat{q}"
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+ "type": "text",
+ "content": " denote the density of the output of the EulerMaruyama (Definition 4.3), we have"
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+ "content": "\\begin{array}{l} \\begin{array}{l l} w h e r e M _ {2} = \\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ]) a n d L = \\\\ \\frac {1}{\\sigma_ {\\min (p _ {t})}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\min (p _ {t})} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\det _ {\\min (p _ {t})}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\det _ {\\min (p _ {t})} ^ {1 / 2}}\\right). \\end{array} \\\\ \\exp \\bigl (- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}} \\bigr). \\\\ \\end{array}",
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+ "type": "text",
+ "content": "Theorem 5.6 (DDPM, KL divergence for smooth data distribution, informal version of Theorem I.3). Assume Condition 3.4 and Assumption 5.1 hold. We use the exponentially decreasing (then constant) step size "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "h_k = c \\min \\{ \\max \\{ t_k, 1 / L \\}, 1 \\}"
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+ "type": "inline_equation",
+ "content": "c = \\frac{T + \\log L}{N} \\leq \\frac{1}{Kd}"
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+ "type": "text",
+ "content": ". Let "
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+ "type": "inline_equation",
+ "content": "\\widehat{q}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " denote the density of the output of the ExponentialIntegrator defined by Definition 4.4. Then, we have"
+ }
+ ]
+ }
+ ],
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+ "content": "\\operatorname {K L} \\left(p _ {0} \\| \\widehat {q}\\right) \\lesssim \\left(M _ {2} + d\\right) \\exp (- T) + T \\epsilon_ {0} ^ {2} + \\frac {d ^ {2} (T + \\log L) ^ {2}}{N},",
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+ "content": "\\begin{array}{l} \\begin{array}{l l} w h e r e M _ {2} = \\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ]) a n d L = \\\\ \\frac {1}{\\sigma_ {\\min (p _ {t})}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\min (p _ {t})} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\det _ {\\min (p _ {t})}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\det _ {\\min (p _ {t})} ^ {1 / 2}}\\right). \\end{array} \\\\ \\begin{array}{l} \\exp (- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}}). \\quad \\text {I n p a r t i c u l a r , i f w e s e t T =} \\\\ \\Theta (\\log (M _ {2} d / \\epsilon_ {0})) \\text {a n d N = \\Theta (d ^ {2} (T + \\log L) ^ {2} / \\epsilon_ {0} ^ {2}) , t h e n} \\\\ \\mathrm {K L} (p _ {0} \\| \\widehat {q}) \\leq \\widetilde {O} (\\epsilon_ {0} ^ {2}). \\text {I n a d d i t i o n , f o r E u l e r - M a r u y a m a} \\\\ \\text {s c h e m e d e f i n e d i n D e f i n i o n 4 . 3 , t h e s a m e b o u n d s h o l d w i t h} \\\\ \\text {a n a n d i s t i t i o n a l M _ {2} \\sum_ {k = 1} ^ {N} h _ {k} ^ {3} t e r m .} \\end{array} \\\\ \\end{array}",
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+ }
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+ "content": "Theorem 5.6 and Theorem 5.5 provide a guarantee for KL divergence bound between target data distribution "
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+ "content": "p_0"
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+ "content": " and learned output distribution "
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+ "content": "\\widehat{q}"
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+ "content": " with concrete "
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+ "content": "L"
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+ "content": " and "
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+ "content": "M_2"
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+ "type": "text",
+ "content": ". Theorem 5.6 has "
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+ "content": " when comparing theorems for total variation and KL divergence. According to Lemma 5.3, the square of the TV distance is comparable to the KL divergence, which explains the squared relationship of the second momentum term."
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+ "content": "Theorem 5.7 (DPOM, informal version of Theorem I.4). Assume Condition 3.4 and Assumption 5.1 hold. We use the DPOM algorithm defined in Definition 4.5, and let "
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+ "content": "\\begin{array}{l} \\mathrm {T V} (\\widehat {q}, p _ {0}) \\lesssim (\\sqrt {d} + m _ {2}) \\exp (- T) + L ^ {2} T d ^ {1 / 2} h _ {\\mathrm {p r e d}} \\\\ + L ^ {3 / 2} T d ^ {1 / 2} h _ {\\mathrm {c o r r}} ^ {1 / 2} + L ^ {1 / 2} T \\epsilon_ {0} + \\epsilon . \\\\ \\end{array}",
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+ "content": "\\begin{array}{l} \\begin{array}{l} \\text {w h e r e} m _ {2} = (\\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ])) ^ {1 / 2} \\text {a n d} L = \\\\ \\frac {1}{\\sigma_ {\\min (p _ {t})}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\min (p _ {t})} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d} \\det _ {\\min (p _ {t})}} + \\frac {1}{(2 \\pi) ^ {d / 2} \\det _ {\\min (p _ {t})} ^ {1 / 2}}\\right). \\end{array} \\\\ \\begin{array}{l} \\exp (- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}}). \\quad \\text {I n p a r t i c u l a r , i f w e s e t T =} \\\\ \\Theta (\\log (d m _ {2} / \\epsilon)), h _ {\\text {p r e d}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {2} d ^ {1 / 2}}), h _ {\\text {c o r r}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {3} d}), \\text {a n d} \\\\ \\text {i f t h e s c o r e e s t i m a t i o n e r r o r s a t i s f i e s \\epsilon_ {0} \\leq \\widetilde {O} (\\frac {\\epsilon}{\\sqrt {L}}) , t h e n w e} \\\\ \\widetilde {\\Theta} (L ^ {3} d / \\epsilon^ {2}) \\text {s t e p s .} \\end{array} \\\\ \\end{array}",
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+ "content": "Theorem 5.8 (DPUM, informal version of Theorem I.5). Assume Condition 3.4 and Assumption 5.1 hold. We use the DPUM algorithm defined in Definition 4.6, and let "
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+ "content": "\\begin{array}{l} \\mathrm {T V} (\\widehat {q}, p _ {0}) \\lesssim (\\sqrt {d} + m _ {2}) \\exp (- T) + L ^ {2} T d ^ {1 / 2} h _ {\\mathrm {p r e d}} \\\\ + L ^ {3 / 2} T d ^ {1 / 2} h _ {\\mathrm {c o r r}} ^ {1 / 2} + L ^ {1 / 2} T \\epsilon_ {0} + \\epsilon . \\\\ \\end{array}",
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+ "content": "\\begin{array}{l} w h e r e L = \\frac {1}{\\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)}} + \\frac {2 R ^ {2}}{\\gamma^ {2} \\sigma_ {\\operatorname* {m i n} \\left(p _ {t}\\right)} ^ {2}} \\cdot \\left(\\frac {1}{(2 \\pi) ^ {d}} \\det _ {\\min \\left(p _ {t}\\right)} + \\right. \\\\ \\frac {1}{(2 \\pi) ^ {d / 2} \\operatorname* {d e t} _ {\\min (p _ {t})} ^ {1 / 2}}) \\quad \\cdot \\quad \\exp \\left(- \\frac {\\beta^ {2}}{2 \\sigma_ {\\max (p _ {t})}}\\right) \\quad a n d \\quad m _ {2} \\quad = \\\\ \\begin{array}{l} (\\sum_ {i = 1} ^ {k} \\alpha_ {i} (\\| \\mu_ {i} \\| _ {2} ^ {2} + \\operatorname {t r} [ \\Sigma_ {i} ])) ^ {1 / 2}. \\quad I n \\text {p a r t i c u l a r , i f} \\\\ w e s e t T = \\Theta (\\log (d m _ {2} / \\epsilon)), h _ {\\mathrm {p r e d}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {2} d ^ {1 / 2}}), \\\\ h _ {\\mathrm {c o r r}} = \\widetilde {\\Theta} (\\frac {\\epsilon}{L ^ {3 / 2} d ^ {1 / 2}}), a n d i f t h e s c o r e e s t i m a t i o n e r r o r \\end{array} \\\\ \\end{array}",
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+ "content": " for ODE reverse process. The difference between the DPOM (Theorem 5.7) and DPUM (Theorem 5.8) is the complexity of "
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+ "content": "We provide empirical evidence supporting our theoretical results. In Section 6.1, we describe the experimental settings and data configurations used in our study. In Section 6.2, we analyze the correlation between the Lipschitz constant and the performance of the diffusion model."
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+ "content": "We used a Gaussian dataset with three modes (clusters) in two-dimensional space, each having the same covariance matrix. By adjusting the covariance, we examine the impact of the Lipschitz constant on model performance. The model we use is a one hidden layer MLP with 32 hidden dimensions. We use DDPM algorithm for our forward diffusion process and reverse denoising process. The number of inference steps we use is 200. It is optimized by MSE loss, and the performance metrics are log likelihood and Mahalanobis squared distance. For the training, we use AdamW optimizer with 0.001 learning rate and training epochs 100."
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+ "type": "text",
+ "content": "For the evaluation, we sample 1000 dots from central Gaussian distribution with variance 1. Then calculate the two losses of output and ground truth."
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| 200 | 3.9870 | -57.2244 |
| 500 | 0.2567 | -28.0872 |
| 600 | 0.1491 | -24.9577 |
| 700 | 0.0943 | -22.6524 |
| 800 | 0.0634 | -21.0397 |
| 900 | 0.0448 | -19.7688 |
| 1000 | 0.0328 | -18.7532 |
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| 100 | 31.8916 | 199.3178 |
| 200 | 3.9870 | 100.1765 |
| 500 | 0.2567 | 40.0695 |
| 600 | 0.1491 | 33.4458 |
| 700 | 0.0943 | 28.5269 |
| 800 | 0.0634 | 25.0344 |
| 900 | 0.0448 | 22.2571 |
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+ "text": "Fangwei Zhong\\*16 Kui Wu\\*2 Churan Wang\\* Hao Chen\\* Hai Ci\\* Zhoujun Li\\* Yizhou Wang\\* 1 School of Artificial Intelligence, Beijing Normal University",
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+ "Figure 1. UnrealZoo enriches photo-realistic virtual worlds with diverse scenes and playable entities, enabling training of generalizable embodied AI agents for navigation, tracking, and social interactions."
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+ "text": "Abstract",
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+ "text": "We introduce UnrealZoo, a collection of over 100 photorealistic 3D virtual worlds built on Unreal Engine, designed to reflect the complexity and variability of open-world environments. We also provide a rich variety of playable entities, including humans, animals, robots, and vehicles for embodied AI research. We extend UnrealCV with optimized APIs and tools for data collection, environment augmentation, distributed training, and benchmarking. These improvements achieve significant improvements in the efficiency of rendering and communication, enabling advanced",
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+ "text": "applications such as multi-agent interactions. Our experimental evaluation across visual navigation and tracking tasks reveals two key insights: 1) environmental diversity provides substantial benefits for developing generalizable reinforcement learning (RL) agents, and 2) current embodied agents face persistent challenges in open-world scenarios, including navigation in unstructured terrain, adaptation to unseen morphologies, and managing latency in the close-loop control systems for interacting in highly dynamic objects. UnrealZoo thus serves as both a comprehensive testing ground and a pathway toward developing more capable embodied AI systems for real-world deployment.",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "*Equal contribution, ⋅Corresponding author",
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+ "text": "1. Introduction",
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+ "text": "Currently, embodied artificial intelligence (Embodied AI) agents are often homebodies, primarily confined to controlled indoor environments and rarely venturing outside to explore the diversity of the open world. While several simulators [8, 20, 22, 28, 29] have advanced the field, they often focus on specific scenarios, such as daily activities in homes or autonomous driving on urban roads. This narrow focus hinders AI agents' adaptability and generalization in open worlds, such as factories, public areas, and landscapes, which are required by several real-world applications.",
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+ "text": "To bridge this gap, there is a growing demand for simulators that feature diverse open-world environments. First, the diversity of 3D scenes and morphologies is fundamental to developing spatial intelligence [7]. This diversity enables agents to actively perceive, reason, plan, and act while tackling various tasks in complex 3D worlds. Second, the complexity of multi-agent interactions is essential for developing social intelligence [10], such as the theory of mind [17], negotiation [15], cooperation [34], and competition [47], encouraging agents to behave more like humans. Third, virtual worlds that mimic the challenges in open-world scenarios can evaluate agents efficiently and effectively, identifying limitations and preventing hardware losses from real-world deployment failures [18]. Ultimately, these features will inspire researchers to explore new challenges previously overlooked in other simulators [9], facilitating seamless integration into real-world applications.",
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+ "text": "In this work, we introduce UnrealZoo, a comprehensive collection of photo-realistic virtual worlds, based on Unreal Engine and UnrealCV [30]. UnrealZoo features a diverse range of complex open worlds and playable entities to advance research in embodied AI and related domains. This high-quality set includes 100 realistic scenes at varying scales, such as houses, supermarkets, train stations, industrial factories, urban cities, villages, temples, and natural landscapes. Each environment is expertly designed by artists to mimic realistic lighting, textures, and dynamics, closely resembling real-world experiences. Our collection also includes diverse playable entities, including humans, animals, robots, drones, motorbikes, and cars. This diversity enables researchers to investigate the generalization of agents across different embodiments or build complex 3D social worlds with numerous heterogeneous agents. To enhance usability, we further optimize UnrealCV and offer a suite of easy-to-use Python APIs and tools (UnrealCV+), including environment augmentation, demonstration collection, and distributed training/testing. These tools allow for customization and extension of the environments to meet various needs in future applications, ensuring UnrealZoo remains adaptable as the embodied AI agents evolve.",
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+ "text": "We conduct experiments to demonstrate the applicability of UnrealZoo for embodied AI. First, we benchmark",
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+ "text": "frames per second (FPS) across various commands, highlighting the significant improvement in image rendering and multi-agent interactions with the UnrealCV+ API. We use embodied visual navigation [52] and tracking [24, 47] as two example tasks to benchmark embodied vision agents in complex dynamic environments with moving objects and unstructured maps. We also introduce a set of simple yet effective baseline methods for developing embodied vision agents, including distributed online reinforcement learning algorithms [27], offline reinforcement learning algorithms [21], and a reasoning framework for large vision-language models (VLMs). Our evaluations across different settings emphasize the importance of diverse training environments for enhancing agent generalization and robustness, the necessity of low latency in closed-loop control to handle dynamic factors, and the potential of reinforcement learning for training agents to navigate complex scenes.",
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+ "text": "Our contributions can be summarized as follows: 1) We build UnrealZoo, a collection of 100 high-quality photorealistic scenes along with a set of playable entities. These cover the most challenging aspects for embodied AI agents in open-world environments. 2) We optimize the communication efficiency of UnrealCV APIs and provide easy-to-use Gym interfaces with a toolkit to meet diverse requirements. 3) We conduct experiments to demonstrate the usability of UnrealZoo, showing the importance of the diversity of the environments to the embodied agents, and analyzing the limitations of the current RL-based and VLM-based agents in the open worlds.",
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+ "text": "Realistic Simulators for Embodied AI. Realistic simulators are widely adopted in embodied AI research due to their high-quality rendering, cost-effective ground truth generation, and environmental controllability. Specialized 3D simulators have been developed for indoor navigation [20, 28, 36, 37], robot manipulation [4, 11, 43], and autonomous driving [8, 13, 32]. Recent advances in computer graphics have enabled general-purpose virtual worlds with photo-realistic rendering. ThreeDWorlds (TDW) [14] and LEGENT [5] offer multi-modal platforms based on Unity, but their scenes and playable entities remain limited, with performance degrading in large outdoor environments. V-IRL [41] leverages Google Maps' API to simulate agents with real-world street view images, yet lacks physical interaction capabilities due to its static image composition. While the community has begun exploring dynamic environments with social interactions, existing solutions like Habitat 3.0 [29] focus on limited agent interactions in indoor scenes, and HAZARD [51] addresses only single-agent simulations in scenarios like fires and floods. In contrast, UnrealZoo offers a comprehensive collection of diverse scenes across different scales, situations, eras, and",
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+ "table_caption": [
+ "Table 1. The comparison with related photo-realistic virtual worlds for embodied AI. Nav. Sys. specifies whether the agent in the environment includes an autonomous navigation system. We compare the visual realism across different engines and list the descriptions of the symbols in supplementary materials."
+ ],
+ "table_footnote": [],
+ "table_body": "| Virtual Worlds | Scene: Categories | Scene: Scale Level | Scene: Style | Scene: Base Engine | Agent: Body | Agent: Nav. Sys. | Agent: Multi-agent |
| VirtualHome AI2THOR ThreeDWorld OmniGibson Habitat 3.0 CARLA AirSim LEGENT V-IRL | Indoor Indoor Indoor Indoor, Building, Community Indoor Indoor Community, Landscape Community, Landscape Indoor, Building Community, Landscape | Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western | Unity Unity Unity Omniverse - Habitat-Sim UE 4/5 UE 4 Unity Google Map | | ✓ - - - - - | ✓ - - - - - | ✓ - ✓ ✓ ✓ ✓ |
|
|
|
|
|
|
|
|
|
| UnrealZoo | Indoor, Building, Community, Landscape | Ancient, Modern, Sci-Fi Western, Eastern, Nature | UE 4/5 | | ✓ | ✓ | |
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+ "text": "cultural backgrounds with various playable entities. Leveraging Unreal Engine advancements and optimized UnrealCV, our environment achieves real-time performance in large-scale scenes with multiple agents and photo-realistic rendering. A detailed comparison of photo-realistic simulators is presented in Table 1.",
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+ "text": "Embodied Vision Agents. This represents a key frontier in AI research, performing tasks with visual observation, like navigation [16, 23, 42, 52], active object tracking [24, 46-49], and other interactive tasks [2, 6, 33, 35]. Their development involves state representation learning [12, 39, 40, 44], reinforcement learning (RL) [26, 31, 38], and large vision-language models (VLMs) [45, 50], such as GPT-4o and SpatialVLM [3]. Despite advances, significant challenges persist. RL methods require extensive trial-and-error interactions and computational resources, often struggling with generalization. VLM-based methods excel at interpreting instructions and images but may lack fine-grained control and adaptability for real-time interactions. Importantly, previous simulators primarily focus on indoor rooms or urban roads, overlooking critical challenges faced by embodied vision agents in open worlds: unstructured terrain, dynamic factors, perception-control loop costs, and multi-agent social interactions. Therefore, benchmarking agents in expansive, photo-realistic virtual environments is essential to address real-world challenges. In this work, we collect a subset of environments from UnrealZoo and benchmark embodied visual navigation and tracking agents, revealing limitations in current methods that were previously masked by constrained simulation environments.",
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+ "text": "3. UnrealZoo",
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+ "text": "UnrealZoo is a collection of photo-realistic, interactive open-world environments with diverse embodied characters, built on Unreal Engine and UnrealCV [30]. The environments are sourced from the Unreal Engine Marketplace1, which shares high-quality content from artists,",
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+ "text": "and were accumulated over two years at a cost exceeding 10,000. UnrealZoo features a diverse array of scenes with varying sizes and styles. Among them, the largest scene, i.e., Medieval Nature Environment, covers more than $16km^2$ areas. The environments also include a wide range of embodiment, such as human avatars, vehicles, drones, animals, and virtual cameras, all of which can interact with the environment and are equipped with ego-centric sensing systems. We offer easy-to-use Python APIs based on UnrealCV to facilitate interaction between Python programs and the game engine. Note that UnrealCV is optimized for rendering and communication, particularly in large-scale and multi-agent scenarios, namely UnrealCV+. Additionally, we provide OpenAI Gym interfaces to standardize agent-environment interactions. The gym-like interface also contains a set of toolkits, e.g., environment augmentation, population control, time dilation, and JSON-style task configurations to help the user customize the environments for various tasks with minimal effort.",
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+ "text": "UnrealCV Zoo contains 100 scenes based on Unreal Engine 4 and 5. We select the scene based on the public reviews in the marketplace and the difference between the collected scenes, aiming at covering a wide range of styles from ancient to fictional, ensuring diversity. We provide an overview of the environments in the scene gallery, and the detailed statistical distribution is shown in Figure 2.",
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+ "text": "We have tagged the collected scenes with several feature labels, allowing researchers to select appropriate scenes for testing or training based on the tags associated with each scene. Our tags cover the following aspects:",
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+ "text": "- Scene Categories: We categorize scenes into three main types: interior, exterior, and both. The interiors include private houses, museums, supermarkets, train stations, factories, gyms, and caves. The exteriors include various outdoor terrains such as ruins, islands, plazas, neighborhoods, and mountains. Additionally, there are 46 scenes that include both interior and exterior elements, offer",
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+ "text": "1 https://www.unrealengine.com/marketplace",
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+ "Figure 2. The statistical distribution of scene content and scale in UnrealZoo. The bar chart depicts the number of scenarios featuring each type of content, noting that larger scenes may encompass multiple categories. The pie chart classifies these scenes by scale, revealing a predominance of large-scale 'Landscape' environments, followed by 'Community', 'Building', and 'Indoor' levels. The distribution reflects the diversity of UnrealZoo and the balanced composition of scenes of different scales."
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+ "text": "ing a blend of architectural elements and natural landscapes, enhancing the versatility and realism of our collection. More details about the distribution of the scenes are shown in Figure 2.",
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+ "- Scale: Each scene is labeled according to its scale, and categorized into four levels: indoor, building, community, and landscape. The indoor scale is the smallest, typically encompassing one or multiple interior rooms (up to a complete floor), such as apartments and office interiors. The building scale includes a single building and its immediate surroundings, like a museum, supermarket, or gas station. The community scale covers areas with multiple buildings, such as neighborhoods, villages, castles, or container yards. The landscape scale includes vast natural or man-made areas, or parts of a city or an entire small town, such as mountains, forests, islands, and urban districts. Specifically, there are 35 scenes classified as landscape, 28 as community, 23 as building, and 15 as indoor. The largest scene covers 16 square kilometers.",
+ "- Spatial Structure: We also tag the spatial structure of the scenes, including multi-floor, topological, flat, steep, etc. Such categorization is vital for benchmarking the spatial intelligence of embodied agents. Multi-floor structures, for instance, challenge agents with vertical navigation and require advanced path-planning algorithms. Topological features, such as interconnected pathways, test the agent's ability to understand and traverse complex networks.",
+ "- Dynamics: The environment's dynamics include simulating factors like weather, fire, gas, fluid, and interactive objects. These elements enhance the visual and physical diversity of the scene while evaluating agents' adaptability and generalization. Weather variations such as sandstorms, snowfall, and thunderstorms are crucial, as are in"
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+ "image_caption": [
+ "Figure 3. First-person and third-person view images of different entities in different scenes. Note that camera parameters can be reconfigured by UnrealCV APIs."
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+ "text": "teractive objects like doors that agents can interact with. These dynamics are vital for an open-world experience.",
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+ "text": "- Style: The scenesen compass diverse cultural and historical styles, including Asian Temple, Western Church, and Middle Eastern Street. Cultural labels include Western, Asian, and Middle Eastern, while era labels encompass Medieval, Modern, and Science Fiction. Identifying the styles will help us build a new data set to benchmark how social agents adapt to different backgrounds.",
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+ "text": "After categorizing the scenes, we integrate UnrealCV+ (Refer to Section 3.3) into the UE project and add the controllable player assets (Refer to Section 3.2) to each scene. Due to licensing restrictions, content purchased from the marketplace cannot be open-source, so we package the projects into an executable binary for sharing with the community. These executable binaries will be compatible with various operating systems, including Windows, Linux, and macOS, allowing users to download and run them via the Python interface without needing any knowledge of Unreal Engine, which is primarily built on C++ and Blueprint.",
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+ "text": "3.2. Playable Entities",
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+ "text": "UnrealZoo includes seven types of playable entities: humans, animals, cars, motorbikes, drones, mobile robots, and flying cameras (See Figure 1). Specifically, it comprises 19 human entities, 27 animal entities (dog, horse, elephant, pig, bird, turtle, etc), 3 cars, 14 quadruped robots, 3 motorcycles, and 1 quad-copter drone. This diversity, with varying affordances like action space and viewpoint, allows us to explore new challenges in embodied AI, such as cross-embodiment generalization and heterogeneous multi-agent interactions.",
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+ "text": "Each entity includes a skeleton with appropriate meshes and textures, a local motion system, and a navigation system. We offer a set of callable functions for each entity, en",
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+ "text": "abling users to modify attributes like size, appearance, and camera positions, as well as control movements. Each entity can switch between different textures and appearances via UnrealCV API, enhancing visual diversity and adaptability for various scenarios. Each entity is equipped with an ego-centric camera, allowing the users to capture various types of image data such as RGB, depth, surface normal, and instance-level segmentation (object mask) from the agent's ego-centric view. Figure 3 shows examples of the captured first-person view and third-person view images of different entities with varying locomotion. For multi-agent interaction, the population of the entities in a scene can be easily adjusted using the spawn or destroy functions.",
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+ "text": "The locomotion system is built on Smart Locomotion, an animation framework providing natural movement and environmental interactions. Interactions are animation-based rather than physics-based, featuring binary state changes (e.g., opening doors without physical doorknob manipulation) and positional animations (crouching, jumping, climbing), similar to VirtualHome [28]. Interactive objects maintain consistent behavior across all environments and can be spawned at arbitrary locations with customizable visual properties via the API. This approach facilitates research on high-level reasoning and planning without the need for extra implementation of primitive motion control.",
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+ "text": "The navigation system is built on NavMesh (a spatial partitioning system that defines walkable surfaces), allowing agents to autonomously navigate with the built-in AI controller. This includes path-finding and obstacle avoidance capabilities, ensuring smooth and realistic movement throughout diverse terrains and structures. For urban-style maps, we segment the roads to distinguish between pedestrian and vehicle pathways. When agents use the navigation system for autonomous control, they will navigate the shortest path based on the priority of the different areas. For example, pedestrians and animals will prioritize walking on sidewalks, while vehicles and motorcycles will prioritize driving on roadways. An example of the navigation area is shown in Supplementary Materials.",
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+ "text": "3.3. Programming Interface",
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+ "text": "We provide UnrealCV+ as the fundamental interface on Python to capture data and control the entities and scenes, and provide an OpenAI Gym interface for general agent-environment interactions. The architectures of the programming interfaces are shown in Figure 4.",
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+ "text": "UnrealCV+ is our improved version of the UnrealCV [30] for high-throughput interactions. As the original version of UnrealCV primarily focuses on generating synthesis data for computer vision, the frame rates per second (FPS) are not optimized for real-time interactions. We optimize the rendering pipelines in the UnrealCV server and",
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+ "Figure 4. The detailed architecture of UnrealZoo. The Gray box indicates the UE binary, containing the scenes, playable entities, and UnrealCV+ server. We have bolded the names of the optimized or new modules in UnrealCV+ Server and Client. We provide OpenAI Gym Interfaces for agent-environment interaction. Our gym interface supports customizing the task in a configuration file and contains a toolkit with a set of gym wrappers for environment augmentation, population control, and etc."
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+ "text": "the communication protocols between the server and the client to improve the FPS. Specifically, we enable parallel processing while rendering object masks and depth images, which can significantly improve the FPS in large-scale scenes. For multi-agent interactions, we further introduce the batch commands protocol. In this protocol, the client can simultaneously send a batch of commands to the server, processing all the received commands and returning a batch of results. In this way, we can reduce the time spent on server-client communication. Since reinforcement learning requires extensive trial-and-error interactions, often running multiple environments on a computer, we introduce Interprocess communication (IPC) sockets instead of TCP sockets to improve the stability of the server-client communication under high loads. We benchmark the FPS performance in Table 2. To enhance user-friendliness, we have developed high-level Python APIs that are built upon the command systems of UnrealCV. These APIs encapsulate all the request commands and their corresponding data decoders into a callable Python function. This approach significantly simplifies the process for beginners, allowing them to interact with and customize the environment using UnrealCV+.",
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+ "text": "Gym Interface is used to define the interactive tasks and standardize the agent-environment interaction, following Gym-UnrealCV. Even though there are a lot of tasks for agents, they usually share common interaction protocols, i.e., the agent gets observations from the environment and returns actions. The main difference across different tasks is usually the reward functions, the modality of the observation, and the available actions. Hence, we define the basic interaction functions for general usage and list the task-specific configurations, e.g., scene name, and reward function, in a JSON File. In this way, when adding new UE scenes, the users only need to set the parameters in the JSON files. Moreover, we provide a toolkit with a set of gym wrappers for training and testing the agents, such as environment augmentation that has been in previous work for",
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+ "text": "$^{2}$ https://github.com/UnrealZoo/unrealzoo-gym",
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+ "Table 2. Comparison of FPS in Unreal Engine 4.27 with UnrealCV and UnrealCV+. Results represent average performance across 6 typical environments ranging from small-scale scenes $(2,440m^2)$ to expansive landscapes $(16km^2)$ . Benchmarks were conducted on a system with an Nvidia RTX 4090 GPU, Intel i7-14700k CPU, and Windows OS. Performance metrics were collected by executing each Python function 1,000 times and measuring execution duration. Multi-agent interaction testing utilized the gym interface, with all rendered images at $640\\times 480$ resolution. See the supplementary material for the detailed results."
+ ],
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+ "table_body": " | Image Capture | Multi-agent Interaction |
| Color | Object Mask | Surface Normal | Depth | N=2 | N=6 | N=10 |
| UnrealCV | 74 | 70 | 109 | 52 | 35 | 13 | 8 |
| UnrealCV+ | 83(↑ 12%) | 154(↑ 120%) | 131(↑ 20%) | 97(↑ 86%) | 54(↑ 54%) | 25(↑ 92%) | 16(↑ 100%) |
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+ "text": "training generalizable agents [24, 25], population control to adjust the number of agents in the scene, and time dilation to adjust the control frequency in dynamic scenes. In Section 4.3, we demonstrate an example usage of the toolkit to analyze the robustness of social tracking agents to the population of crowds and the impact of the control frequency in such dynamic scenes. We also provide a launch tool to enable the user to run multiple environments with specific GPU IDs within a computer, which is useful for distributed online reinforcement learning.",
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+ "text": "4. Experiments",
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+ "text": "In this section, we conduct experiments involving a series of challenging tasks on UnrealZoo to show its unique features regarding usability, diversity, efficiency, and extensibility. We begin with a visual navigation task to indicate the suitability of UnrealZoo for distributed online reinforcement learning. This task also highlights how the complex spatial structures within our environments introduce new challenges that the off-the-shelf methods struggle to address effectively. Next, we evaluate agents through active visual tracking to validate the necessity of scaling environmental diversity for improving cross-scene generalization. Finally, our social tracking experiments illustrate the exceptional flexibility of UnrealZoo. By enabling easy modification of simulation control frequencies, population scale, and agent morphologies, UnrealZoo reveals previously overlooked challenges in high-dynamic environments and cross-body generalization.",
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+ "text": "4.1. Emergent Challenges in Visual Navigation",
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+ "text": "Taking the visual navigation task as an example, a fundamental skill for embodied agents, we demonstrate the usability of our environments for various approaches, including distributed online reinforcement learning and large vision-language models. Additionally, we highlight the emergent challenges posed by unstructured open-world environments. While traditional approaches often operate within well-defined 3D spatial structures, our environments require agents to navigate through complex, unconstrained terrains. Therefore, agents must execute diverse locomotion skills, including running, climbing, jumping, and crouching, to overcome various environmental obstacles while pursuing target objects. This setting demands sophisticated 3D spatial reasoning capabilities and action selection mechanisms for effective real-time decision-making. The details",
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+ "text": "of the task setting, implementation, and training curve are introduced in the supplementary materials.",
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+ "text": "Evaluation Metrics. We employ two key metrics to evaluate visual navigation agents: 1) Average Episode Length (EL), representing the average number of steps per episode over 50 episodes. 2) Success Rate (SR), measuring the percentage of episodes the agent successfully navigates to the target object out of 50 total episodes, which represents the navigation capability in the wild environment. 3) Success weighted by Path Length (SPL) [1], a standard metric that accounts for both success and path efficiency.",
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+ "text": "Baselines for Navigation. We build simple baselines to demonstrate the applicability of our environments for training reinforcement learning agents and benchmark the agents based on pre-trained large models. 1) Online RL: We train RL-based navigation agents independently in the Roof and Factory environments using a distributed online reinforcement learning (RL) approach, e.g., A3C [27]. The model takes the first-person view segmentation mask and the relative position between the agent and target as input, and outputs discrete actions to navigate. This setup allows the agent to iteratively refine navigation strategies through continuous environmental interaction. 2) GPT-4o: We leverage the multimodal reasoning capabilities of GPT-4o for navigation model. Following a structured prompt template, GPT-4o performs reasoning to select appropriate actions from the action space to guide the agent toward the target location. 3) Human: As a reference, we conduct experiments where human players control agents via keyboard inputs, analogous to first-person video game interactions. The human players use the same action space available to other baselines.",
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+ "text": "Results. In Table 3, we report the performances of different methods in two unstructured scenes. The RL-based agent performs moderately well, achieving better results in the simpler environment (Industrial Area) compared to the Roof, where the target object is located on different levels of stairs. The GPT-4o agent struggles in both scenarios. This implies that the GPT-4o performs poorly in complex 3D scene reasoning. As a reference, the human player completes both tasks with the fewest steps and a 1.00 success rate, underscoring the significant performance gap between current embodied AI agents and humans, indicating substantial room for improvement to navigate in such complex, open-world environments.",
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+ "Table 3. The results (EL/SR/SPL) of visual navigation agents in two unstructured terrains."
+ ],
+ "table_footnote": [],
+ "table_body": " | Online RL | GPT-4o | Human |
| Roof | 1660/0.32/0.10 | 2000/0.00/0.00 | 515/1.00/0.97 |
| Industrial Area | 261/0.52/0.31 | 369/0.20/0.08 | 158/1.00/0.98 |
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+ "Figure 5. An exemplar sequence from the embodied navigation agent in the Roof. The RL agent learned to climb on a box and wall and jump over an obstacle to reach the goal in a short path."
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+ "text": "4.2. Scaling the Diversity for Active Visual Tracking",
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+ "text": "In this section, we aim to analyze the effectiveness of the diversity of the training data on the generalization of the active visual tracking. We collect 3 sets of demonstrations from different numbers of environments in UnrealZoo and train the tracking policy via offline reinforcement learning [49]. We evaluate the tracking performance across 16 unseen environments covering four categories: Interior Scenes, Palaces, Wilds, and Modern Scenes. Each category contains 4 individual environments. The implementation details are introduced in the supplementary materials.",
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+ "text": "Evaluation Metrics. Our evaluation employs three key metrics: (1) Average Episodic Return (ER): calculates the mean episodic return over 50 episodes, providing insights into overall tracking performance; (2) Average Episode Length (EL): represents the average number of steps per episode, which reflects long-term tracking effectiveness; and (3) Success Rate (SR): measures the percentage of episodes that complete 500 steps out of 50 total episodes.",
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+ "text": "Baselines for Active Visual Tracking. 1) PID: A classical control approach that uses a PID controller to adjust agent actions by maximizing IoU between the detected target bounding box and an expected position. 2) RL: We adapt the offline reinforcement learning implementation from Zhong et al. [49], using their network architecture while collecting three distinct offline datasets (100k steps each) with varying environmental diversity: single environment (1 Env.), two environments (2 Envs.), and eight environments (8 Envs.). Notably, FlexibleRoom represents an abstract environment where objects appear as geometric shapes with randomized patterns used in the three settings. 3) OpenVLA: We fine-tune OpenVLA [19], an end-to-end large model originally designed for robotic manipulation with strong generalization capabilities, on our most diverse dataset (8 Envs.) to adapt it for tracking tasks. 4) GPT-4o: We implement a VLM-based agent using GPT-4o",
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+ "image_caption": [
+ "The averaged success rate of embodied tracking agents across four kinds of scenes",
+ "Figure 6. Average success rates across four environment categories: Interior Scenes, Palaces, Wilds, and Modern Urbanity. Results compare Offline RL agents trained on three offline dataset settings with increasing environmental diversity (1 Env., 2 Envs., 8 Envs.). Performance consistently improves with dataset diversity, demonstrating enhanced generalization capabilities. Notably, environments with complex spatial structures (Interior Scenes and Palaces) present greater challenges for navigation and obstacle avoidance, resulting in lower success rates."
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+ "text": "to generate actions directly from observed images. We designed a prompt template to standardize outputs into predefined action commands (moving forward/backward, turning left/right, or maintaining position), which are then mapped to appropriate velocities. Despite GPT-4o's capabilities, we observed poor alignment performance and significant latency issues when processing raw image inputs, limiting its effectiveness for real-time tracking.",
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+ "text": "Result Analysis. We first evaluate the performance of agents trained with offline datasets collected from varying numbers of environments (1 Env., 2 Envs., 8 Envs.) across 16 unseen environmentsTo visualize the performance change of different settings within various scene categories, we calculate the average success rate (SR) of each agent in four categories, and the results are shown in Figure 6. Then we compared the baseline methods' performance, as shown in Table 5 (0D). The results reveal a clear trend: as the number of environments used for training increases, agent long-term tracking performance generally improves across all categories. In the Wilds, a significant increase in success rate is observed with the 8 Envs. dataset, which involves the highest diversity of environments. This demonstrates that diverse environmental exposure plays a crucial role in improving the agent's generalization capabilities in more complex, open-world environments. The lower success rate in the 1 Env. highlights the limitations of training solely in abstract settings like the FlexibleRoom. Similarly, in the Palace, the success rate improves notably from 1 Env. to 8 Envs., suggesting that training with a broader range of environments helps the agent better adapt to intricate 3D spatial structures.",
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+ "text": "4.3. Benchmarking Agents at Variant Settings",
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+ "text": "We augment the environment employed for active tracking by seamlessly integrating the Gym toolkit into diverse settings. We use the population control wrapper to create social tracking scenarios. In this setting, the agent is required to follow the target through crowds. We can also adjust the morphology of the trackers for evaluating the cross-embodiment generalization. Moreover, we employ the time dilation wrapper to simulate a variety of control frequencies. This allows us to analyze the impact of the latency within the perception-control loop on tracking performance.",
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+ "text": "Robustness to Active Distractions. A key challenge in active visual tracking is handling visual distractions and dynamic obstacles, which is crucial for real-world deployment in crowds. We evaluated agents in four representative environments: Storage House, Desert Ruins, TerrainDemo, and SuburbNeighborhoodDay, with varying numbers of human distractors (0D, 4D, 10D) and compared RL-based methods (trained in 8 environments, denoted as RL 8 Envs.) against PID, OpenVLA, and GPT-4o. Table 5 shows that RL-based methods maintain stable success rates, RL 8 Envs. achieving 0.76 SR in 0D, 0.68 in 4D and 0.56 in 10D, benefiting from diverse training data. In contrast, PID, OpenVLA, and GPT-4o struggle, showing significantly lower returns and success rates. PID suffers from delayed reactions when the target is occluded, leading to failures. OpenVLA tracks effectively at short distances but loses accuracy over time due to accumulated errors. Both OpenVLA and GPT-4o are highly prone to distractions, often tracking the wrong target. These results highlight the limitations of large models in dynamic environments with active distractions.",
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+ "text": "Cross-Embodiment Generalization. To investigate whether policies can effectively transfer to agents with different morphologies, we apply the agents (RL and OpenVLA) trained on a human character to a quadrupedal robot dog. This exploration is motivated by the practical necessity in real-world applications where a single policy might need to operate across various embodiments with different perceptual perspectives and movement capabilities. As shown in Table 5, the performance decreases notably, particularly the success rate (from 0.68 to 0.48 with 4D and from 0.56 to 0.40 with 10D for RL 8 Envs.), indicating that the community should pay more attention to the cross-embodiment generalization for real-world deployment.",
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+ "text": "The Impact of Control Frequency. In high-dynamic scenes, the latency of the perception-control loop plays a critical role in managing multiple dynamic factors effectively. To verify this, We employ the time dilation wrapper to simulate different control frequencies during deployment. As shown in Table 4, when the rate drops below 10 FPS, performance significantly declines. Our results show that RL-based agents achieve superior performance in social tracking scenarios when operating at higher control fre",
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+ "table_caption": [
+ "Table 4. The impact of control frequency on tracking performance. We evaluate the RL agent (1 Env.) in the FlexibleRoom using the time dilation wrapper to simulate varying control frequencies."
+ ],
+ "table_footnote": [],
+ "table_body": " | 3 FPS | 10 FPS | 30 FPS | w/o FPS Control |
| ER | 184 | 303 | 368 | 275 |
| EL | 377 | 449 | 482 | 425 |
| SR | 0.34 | 0.62 | 0.92 | 0.74 |
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+ "Table 5. We evaluate different methods in four representative environments: Storage House, Desert Ruins, TerrainDemo, and SuburbNeighborhoodDay, with varying numbers of distractors (0D, 4D, 10D). Each cell presents the averaged values across four environments for three metrics: Episodic Return (ER), Episode Length (EL), and Success Rate (SR). OpenVLA and RL are trained on the dataset collected from 8 environments."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | 0D | 4D | 10D |
| PID | 113/298/0.34 | 107/295/0.30 | 78/105/0.14 |
| GPT-4o | 2/228/0.28 | -102/264/0.16 | -80/240/0.10 |
| OpenVLA | 55/323/0.10 | -39/149/0.02 | -30/156/0.00 |
| RL | 321/468/0.76 | 280/437/0.68 | 187/402/0.56 |
| PID (Robot dog) | 152/245/0.30 | 149/237/0.22 | 100/102/0.16 |
| GPT-4o (Robot dog) | -5/263/0.20 | -98/272/0.16 | -59/223/0.04 |
| OpenVLA(Robot dog) | 42/301/0.08 | -37/142/0.00 | -13/117/0.00 |
| RL (Robot dog) | 279/433/0.60 | 220/409/0.48 | 143/367/0.40 |
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+ "text": "quencies. These findings emphasize the necessity of developing efficient models for embodied agents to successfully execute tasks in dynamic social worlds.",
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+ "text": "5. Conclusions",
+ "text_level": 1,
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+ {
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+ "text": "In conclusion, UnrealZoo addresses critical gaps in embodied AI research by providing unprecedented environmental diversity across 100 scenes and 67 embodiment options. By offering easy-to-use Python APIs and toolkits, we support efficient environmental interactions, distributed training, and task customization in UnrealZoo. The experiments on UnrealZoo reveal the importance of environment diversity for agent generalization capabilities, the necessity of low-latency control in dynamic scenes, and key challenges faced by current methods for embodied agents in open worlds. These findings highlight a clear path forward for developing more robust embodied AI systems capable of navigating the complexity of real-world deployment.",
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+ "text": "Looking forward, UnrealZoo will drive research in several key areas: 1) spatial intelligence development in complex 3D environments; 2) social intelligence research through multi-agent interactions; 3) safe pre-deployment evaluation and limitation identification; 4) cross-embodiment learning and skill transfer; and 5) adaptation to dynamic environments. As we continue to enrich virtual worlds and interaction capabilities, UnrealZoo will play an increasingly vital role in advancing agents from simulation to reality, ultimately fostering harmonious human-AI coexistence.",
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+ "text": "5776",
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+ {
+ "type": "text",
+ "text": "Acknowledgments",
+ "text_level": 1,
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+ {
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+ "text": "This work was supported by the National Science and Technology Major Project (2022ZD0114904), NSFC-6247070125, NSFC-62406010, the Funding Scheme for Research and Innovation of FDCT (Grant No. 0021/2025/ITP1), the Fundamental Research Funds for the Central Universities, and Qualcomm University Research Grant. We express our gratitude to Weichao Qiu for his invaluable support in optimizing UnrealCV and for the insightful discussions. We are also thankful to Tingyun Yan for providing the early version of the human entity and to Jingzhe Lin for his assistance in producing demo videos. Our appreciation extends to the active developers in the open-source community for ensuring UnrealCV's compatibility with the latest Unreal Engine versions, such as UE 5.4. Furthermore, we thank the contributors in the Unreal Engine Marketplace for offering high-quality content and plugins, which have been instrumental in the development of UnrealZoo.",
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+ {
+ "type": "text",
+ "text": "References",
+ "text_level": 1,
+ "bbox": [
+ 91,
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+ 187,
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+ },
+ {
+ "type": "list",
+ "sub_type": "ref_text",
+ "list_items": [
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+ "content": "In this work, we introduce UnrealZoo, a comprehensive collection of photo-realistic virtual worlds, based on Unreal Engine and UnrealCV [30]. UnrealZoo features a diverse range of complex open worlds and playable entities to advance research in embodied AI and related domains. This high-quality set includes 100 realistic scenes at varying scales, such as houses, supermarkets, train stations, industrial factories, urban cities, villages, temples, and natural landscapes. Each environment is expertly designed by artists to mimic realistic lighting, textures, and dynamics, closely resembling real-world experiences. Our collection also includes diverse playable entities, including humans, animals, robots, drones, motorbikes, and cars. This diversity enables researchers to investigate the generalization of agents across different embodiments or build complex 3D social worlds with numerous heterogeneous agents. To enhance usability, we further optimize UnrealCV and offer a suite of easy-to-use Python APIs and tools (UnrealCV+), including environment augmentation, demonstration collection, and distributed training/testing. These tools allow for customization and extension of the environments to meet various needs in future applications, ensuring UnrealZoo remains adaptable as the embodied AI agents evolve."
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+ "content": "Table 1. The comparison with related photo-realistic virtual worlds for embodied AI. Nav. Sys. specifies whether the agent in the environment includes an autonomous navigation system. We compare the visual realism across different engines and list the descriptions of the symbols in supplementary materials."
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+ "content": "| Virtual Worlds | Scene: Categories | Scene: Scale Level | Scene: Style | Scene: Base Engine | Agent: Body | Agent: Nav. Sys. | Agent: Multi-agent |
| VirtualHome AI2THOR ThreeDWorld OmniGibson Habitat 3.0 CARLA AirSim LEGENT V-IRL | Indoor Indoor Indoor Indoor, Building, Community Indoor Indoor Community, Landscape Community, Landscape Indoor, Building Community, Landscape | Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western | Unity Unity Unity Omniverse - Habitat-Sim UE 4/5 UE 4 Unity Google Map | | ✓ - - - - - | ✓ - - - - - | ✓ - ✓ ✓ ✓ ✓ |
|
|
|
|
|
|
|
|
|
| UnrealZoo | Indoor, Building, Community, Landscape | Ancient, Modern, Sci-Fi Western, Eastern, Nature | UE 4/5 | | ✓ | ✓ | |
"
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+ {
+ "type": "text",
+ "bbox": [
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+ "content": "cultural backgrounds with various playable entities. Leveraging Unreal Engine advancements and optimized UnrealCV, our environment achieves real-time performance in large-scale scenes with multiple agents and photo-realistic rendering. A detailed comparison of photo-realistic simulators is presented in Table 1."
+ },
+ {
+ "type": "text",
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+ "content": "Embodied Vision Agents. This represents a key frontier in AI research, performing tasks with visual observation, like navigation [16, 23, 42, 52], active object tracking [24, 46-49], and other interactive tasks [2, 6, 33, 35]. Their development involves state representation learning [12, 39, 40, 44], reinforcement learning (RL) [26, 31, 38], and large vision-language models (VLMs) [45, 50], such as GPT-4o and SpatialVLM [3]. Despite advances, significant challenges persist. RL methods require extensive trial-and-error interactions and computational resources, often struggling with generalization. VLM-based methods excel at interpreting instructions and images but may lack fine-grained control and adaptability for real-time interactions. Importantly, previous simulators primarily focus on indoor rooms or urban roads, overlooking critical challenges faced by embodied vision agents in open worlds: unstructured terrain, dynamic factors, perception-control loop costs, and multi-agent social interactions. Therefore, benchmarking agents in expansive, photo-realistic virtual environments is essential to address real-world challenges. In this work, we collect a subset of environments from UnrealZoo and benchmark embodied visual navigation and tracking agents, revealing limitations in current methods that were previously masked by constrained simulation environments."
+ },
+ {
+ "type": "title",
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+ "content": "3. UnrealZoo"
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+ "content": "UnrealZoo is a collection of photo-realistic, interactive open-world environments with diverse embodied characters, built on Unreal Engine and UnrealCV [30]. The environments are sourced from the Unreal Engine Marketplace1, which shares high-quality content from artists,"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "and were accumulated over two years at a cost exceeding 10,000. UnrealZoo features a diverse array of scenes with varying sizes and styles. Among them, the largest scene, i.e., Medieval Nature Environment, covers more than \\(16km^2\\) areas. The environments also include a wide range of embodiment, such as human avatars, vehicles, drones, animals, and virtual cameras, all of which can interact with the environment and are equipped with ego-centric sensing systems. We offer easy-to-use Python APIs based on UnrealCV to facilitate interaction between Python programs and the game engine. Note that UnrealCV is optimized for rendering and communication, particularly in large-scale and multi-agent scenarios, namely UnrealCV+. Additionally, we provide OpenAI Gym interfaces to standardize agent-environment interactions. The gym-like interface also contains a set of toolkits, e.g., environment augmentation, population control, time dilation, and JSON-style task configurations to help the user customize the environments for various tasks with minimal effort."
+ },
+ {
+ "type": "title",
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+ "content": "3.1. Scene Collection"
+ },
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+ "content": "UnrealCV Zoo contains 100 scenes based on Unreal Engine 4 and 5. We select the scene based on the public reviews in the marketplace and the difference between the collected scenes, aiming at covering a wide range of styles from ancient to fictional, ensuring diversity. We provide an overview of the environments in the scene gallery, and the detailed statistical distribution is shown in Figure 2."
+ },
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+ "content": "We have tagged the collected scenes with several feature labels, allowing researchers to select appropriate scenes for testing or training based on the tags associated with each scene. Our tags cover the following aspects:"
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+ "content": "- Scene Categories: We categorize scenes into three main types: interior, exterior, and both. The interiors include private houses, museums, supermarkets, train stations, factories, gyms, and caves. The exteriors include various outdoor terrains such as ruins, islands, plazas, neighborhoods, and mountains. Additionally, there are 46 scenes that include both interior and exterior elements, offer"
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+ "content": "1 https://www.unrealengine.com/marketplace"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 2. The statistical distribution of scene content and scale in UnrealZoo. The bar chart depicts the number of scenarios featuring each type of content, noting that larger scenes may encompass multiple categories. The pie chart classifies these scenes by scale, revealing a predominance of large-scale 'Landscape' environments, followed by 'Community', 'Building', and 'Indoor' levels. The distribution reflects the diversity of UnrealZoo and the balanced composition of scenes of different scales."
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+ "bbox": [
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+ "angle": 0,
+ "content": "ing a blend of architectural elements and natural landscapes, enhancing the versatility and realism of our collection. More details about the distribution of the scenes are shown in Figure 2."
+ },
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+ "content": "- Scale: Each scene is labeled according to its scale, and categorized into four levels: indoor, building, community, and landscape. The indoor scale is the smallest, typically encompassing one or multiple interior rooms (up to a complete floor), such as apartments and office interiors. The building scale includes a single building and its immediate surroundings, like a museum, supermarket, or gas station. The community scale covers areas with multiple buildings, such as neighborhoods, villages, castles, or container yards. The landscape scale includes vast natural or man-made areas, or parts of a city or an entire small town, such as mountains, forests, islands, and urban districts. Specifically, there are 35 scenes classified as landscape, 28 as community, 23 as building, and 15 as indoor. The largest scene covers 16 square kilometers."
+ },
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+ "content": "- Spatial Structure: We also tag the spatial structure of the scenes, including multi-floor, topological, flat, steep, etc. Such categorization is vital for benchmarking the spatial intelligence of embodied agents. Multi-floor structures, for instance, challenge agents with vertical navigation and require advanced path-planning algorithms. Topological features, such as interconnected pathways, test the agent's ability to understand and traverse complex networks."
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+ "content": "- Dynamics: The environment's dynamics include simulating factors like weather, fire, gas, fluid, and interactive objects. These elements enhance the visual and physical diversity of the scene while evaluating agents' adaptability and generalization. Weather variations such as sandstorms, snowfall, and thunderstorms are crucial, as are in"
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+ "angle": 0,
+ "content": "Figure 3. First-person and third-person view images of different entities in different scenes. Note that camera parameters can be reconfigured by UnrealCV APIs."
+ },
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+ "content": "teractive objects like doors that agents can interact with. These dynamics are vital for an open-world experience."
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+ "content": "- Style: The scenesen compass diverse cultural and historical styles, including Asian Temple, Western Church, and Middle Eastern Street. Cultural labels include Western, Asian, and Middle Eastern, while era labels encompass Medieval, Modern, and Science Fiction. Identifying the styles will help us build a new data set to benchmark how social agents adapt to different backgrounds."
+ },
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+ "content": "After categorizing the scenes, we integrate UnrealCV+ (Refer to Section 3.3) into the UE project and add the controllable player assets (Refer to Section 3.2) to each scene. Due to licensing restrictions, content purchased from the marketplace cannot be open-source, so we package the projects into an executable binary for sharing with the community. These executable binaries will be compatible with various operating systems, including Windows, Linux, and macOS, allowing users to download and run them via the Python interface without needing any knowledge of Unreal Engine, which is primarily built on C++ and Blueprint."
+ },
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+ "content": "3.2. Playable Entities"
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+ "content": "UnrealZoo includes seven types of playable entities: humans, animals, cars, motorbikes, drones, mobile robots, and flying cameras (See Figure 1). Specifically, it comprises 19 human entities, 27 animal entities (dog, horse, elephant, pig, bird, turtle, etc), 3 cars, 14 quadruped robots, 3 motorcycles, and 1 quad-copter drone. This diversity, with varying affordances like action space and viewpoint, allows us to explore new challenges in embodied AI, such as cross-embodiment generalization and heterogeneous multi-agent interactions."
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+ "content": "Each entity includes a skeleton with appropriate meshes and textures, a local motion system, and a navigation system. We offer a set of callable functions for each entity, en"
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+ "bbox": [
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+ "content": "abling users to modify attributes like size, appearance, and camera positions, as well as control movements. Each entity can switch between different textures and appearances via UnrealCV API, enhancing visual diversity and adaptability for various scenarios. Each entity is equipped with an ego-centric camera, allowing the users to capture various types of image data such as RGB, depth, surface normal, and instance-level segmentation (object mask) from the agent's ego-centric view. Figure 3 shows examples of the captured first-person view and third-person view images of different entities with varying locomotion. For multi-agent interaction, the population of the entities in a scene can be easily adjusted using the spawn or destroy functions."
+ },
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+ "angle": 0,
+ "content": "The locomotion system is built on Smart Locomotion, an animation framework providing natural movement and environmental interactions. Interactions are animation-based rather than physics-based, featuring binary state changes (e.g., opening doors without physical doorknob manipulation) and positional animations (crouching, jumping, climbing), similar to VirtualHome [28]. Interactive objects maintain consistent behavior across all environments and can be spawned at arbitrary locations with customizable visual properties via the API. This approach facilitates research on high-level reasoning and planning without the need for extra implementation of primitive motion control."
+ },
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+ "content": "The navigation system is built on NavMesh (a spatial partitioning system that defines walkable surfaces), allowing agents to autonomously navigate with the built-in AI controller. This includes path-finding and obstacle avoidance capabilities, ensuring smooth and realistic movement throughout diverse terrains and structures. For urban-style maps, we segment the roads to distinguish between pedestrian and vehicle pathways. When agents use the navigation system for autonomous control, they will navigate the shortest path based on the priority of the different areas. For example, pedestrians and animals will prioritize walking on sidewalks, while vehicles and motorcycles will prioritize driving on roadways. An example of the navigation area is shown in Supplementary Materials."
+ },
+ {
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+ "content": "3.3. Programming Interface"
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+ "content": "We provide UnrealCV+ as the fundamental interface on Python to capture data and control the entities and scenes, and provide an OpenAI Gym interface for general agent-environment interactions. The architectures of the programming interfaces are shown in Figure 4."
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+ "content": "UnrealCV+ is our improved version of the UnrealCV [30] for high-throughput interactions. As the original version of UnrealCV primarily focuses on generating synthesis data for computer vision, the frame rates per second (FPS) are not optimized for real-time interactions. We optimize the rendering pipelines in the UnrealCV server and"
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+ "content": "Figure 4. The detailed architecture of UnrealZoo. The Gray box indicates the UE binary, containing the scenes, playable entities, and UnrealCV+ server. We have bolded the names of the optimized or new modules in UnrealCV+ Server and Client. We provide OpenAI Gym Interfaces for agent-environment interaction. Our gym interface supports customizing the task in a configuration file and contains a toolkit with a set of gym wrappers for environment augmentation, population control, and etc."
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+ "content": "the communication protocols between the server and the client to improve the FPS. Specifically, we enable parallel processing while rendering object masks and depth images, which can significantly improve the FPS in large-scale scenes. For multi-agent interactions, we further introduce the batch commands protocol. In this protocol, the client can simultaneously send a batch of commands to the server, processing all the received commands and returning a batch of results. In this way, we can reduce the time spent on server-client communication. Since reinforcement learning requires extensive trial-and-error interactions, often running multiple environments on a computer, we introduce Interprocess communication (IPC) sockets instead of TCP sockets to improve the stability of the server-client communication under high loads. We benchmark the FPS performance in Table 2. To enhance user-friendliness, we have developed high-level Python APIs that are built upon the command systems of UnrealCV. These APIs encapsulate all the request commands and their corresponding data decoders into a callable Python function. This approach significantly simplifies the process for beginners, allowing them to interact with and customize the environment using UnrealCV+."
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+ "content": "Gym Interface is used to define the interactive tasks and standardize the agent-environment interaction, following Gym-UnrealCV. Even though there are a lot of tasks for agents, they usually share common interaction protocols, i.e., the agent gets observations from the environment and returns actions. The main difference across different tasks is usually the reward functions, the modality of the observation, and the available actions. Hence, we define the basic interaction functions for general usage and list the task-specific configurations, e.g., scene name, and reward function, in a JSON File. In this way, when adding new UE scenes, the users only need to set the parameters in the JSON files. Moreover, we provide a toolkit with a set of gym wrappers for training and testing the agents, such as environment augmentation that has been in previous work for"
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+ "angle": 0,
+ "content": "\\(^{2}\\)https://github.com/UnrealZoo/unrealzoo-gym"
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+ "content": "Table 2. Comparison of FPS in Unreal Engine 4.27 with UnrealCV and UnrealCV+. Results represent average performance across 6 typical environments ranging from small-scale scenes \\((2,440m^2)\\) to expansive landscapes \\((16km^2)\\). Benchmarks were conducted on a system with an Nvidia RTX 4090 GPU, Intel i7-14700k CPU, and Windows OS. Performance metrics were collected by executing each Python function 1,000 times and measuring execution duration. Multi-agent interaction testing utilized the gym interface, with all rendered images at \\(640\\times 480\\) resolution. See the supplementary material for the detailed results."
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+ "content": " | Image Capture | Multi-agent Interaction |
| Color | Object Mask | Surface Normal | Depth | N=2 | N=6 | N=10 |
| UnrealCV | 74 | 70 | 109 | 52 | 35 | 13 | 8 |
| UnrealCV+ | 83(↑ 12%) | 154(↑ 120%) | 131(↑ 20%) | 97(↑ 86%) | 54(↑ 54%) | 25(↑ 92%) | 16(↑ 100%) |
"
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+ "content": "training generalizable agents [24, 25], population control to adjust the number of agents in the scene, and time dilation to adjust the control frequency in dynamic scenes. In Section 4.3, we demonstrate an example usage of the toolkit to analyze the robustness of social tracking agents to the population of crowds and the impact of the control frequency in such dynamic scenes. We also provide a launch tool to enable the user to run multiple environments with specific GPU IDs within a computer, which is useful for distributed online reinforcement learning."
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+ "content": "4. Experiments"
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+ "content": "In this section, we conduct experiments involving a series of challenging tasks on UnrealZoo to show its unique features regarding usability, diversity, efficiency, and extensibility. We begin with a visual navigation task to indicate the suitability of UnrealZoo for distributed online reinforcement learning. This task also highlights how the complex spatial structures within our environments introduce new challenges that the off-the-shelf methods struggle to address effectively. Next, we evaluate agents through active visual tracking to validate the necessity of scaling environmental diversity for improving cross-scene generalization. Finally, our social tracking experiments illustrate the exceptional flexibility of UnrealZoo. By enabling easy modification of simulation control frequencies, population scale, and agent morphologies, UnrealZoo reveals previously overlooked challenges in high-dynamic environments and cross-body generalization."
+ },
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+ "content": "4.1. Emergent Challenges in Visual Navigation"
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+ "content": "Taking the visual navigation task as an example, a fundamental skill for embodied agents, we demonstrate the usability of our environments for various approaches, including distributed online reinforcement learning and large vision-language models. Additionally, we highlight the emergent challenges posed by unstructured open-world environments. While traditional approaches often operate within well-defined 3D spatial structures, our environments require agents to navigate through complex, unconstrained terrains. Therefore, agents must execute diverse locomotion skills, including running, climbing, jumping, and crouching, to overcome various environmental obstacles while pursuing target objects. This setting demands sophisticated 3D spatial reasoning capabilities and action selection mechanisms for effective real-time decision-making. The details"
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+ "content": "of the task setting, implementation, and training curve are introduced in the supplementary materials."
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+ "content": "Evaluation Metrics. We employ two key metrics to evaluate visual navigation agents: 1) Average Episode Length (EL), representing the average number of steps per episode over 50 episodes. 2) Success Rate (SR), measuring the percentage of episodes the agent successfully navigates to the target object out of 50 total episodes, which represents the navigation capability in the wild environment. 3) Success weighted by Path Length (SPL) [1], a standard metric that accounts for both success and path efficiency."
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+ "content": "Baselines for Navigation. We build simple baselines to demonstrate the applicability of our environments for training reinforcement learning agents and benchmark the agents based on pre-trained large models. 1) Online RL: We train RL-based navigation agents independently in the Roof and Factory environments using a distributed online reinforcement learning (RL) approach, e.g., A3C [27]. The model takes the first-person view segmentation mask and the relative position between the agent and target as input, and outputs discrete actions to navigate. This setup allows the agent to iteratively refine navigation strategies through continuous environmental interaction. 2) GPT-4o: We leverage the multimodal reasoning capabilities of GPT-4o for navigation model. Following a structured prompt template, GPT-4o performs reasoning to select appropriate actions from the action space to guide the agent toward the target location. 3) Human: As a reference, we conduct experiments where human players control agents via keyboard inputs, analogous to first-person video game interactions. The human players use the same action space available to other baselines."
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+ "content": "Results. In Table 3, we report the performances of different methods in two unstructured scenes. The RL-based agent performs moderately well, achieving better results in the simpler environment (Industrial Area) compared to the Roof, where the target object is located on different levels of stairs. The GPT-4o agent struggles in both scenarios. This implies that the GPT-4o performs poorly in complex 3D scene reasoning. As a reference, the human player completes both tasks with the fewest steps and a 1.00 success rate, underscoring the significant performance gap between current embodied AI agents and humans, indicating substantial room for improvement to navigate in such complex, open-world environments."
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+ "content": "Table 3. The results (EL/SR/SPL) of visual navigation agents in two unstructured terrains."
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+ "content": " | Online RL | GPT-4o | Human |
| Roof | 1660/0.32/0.10 | 2000/0.00/0.00 | 515/1.00/0.97 |
| Industrial Area | 261/0.52/0.31 | 369/0.20/0.08 | 158/1.00/0.98 |
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+ "content": "Figure 5. An exemplar sequence from the embodied navigation agent in the Roof. The RL agent learned to climb on a box and wall and jump over an obstacle to reach the goal in a short path."
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+ "content": "4.2. Scaling the Diversity for Active Visual Tracking"
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+ "content": "In this section, we aim to analyze the effectiveness of the diversity of the training data on the generalization of the active visual tracking. We collect 3 sets of demonstrations from different numbers of environments in UnrealZoo and train the tracking policy via offline reinforcement learning [49]. We evaluate the tracking performance across 16 unseen environments covering four categories: Interior Scenes, Palaces, Wilds, and Modern Scenes. Each category contains 4 individual environments. The implementation details are introduced in the supplementary materials."
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+ "content": "Evaluation Metrics. Our evaluation employs three key metrics: (1) Average Episodic Return (ER): calculates the mean episodic return over 50 episodes, providing insights into overall tracking performance; (2) Average Episode Length (EL): represents the average number of steps per episode, which reflects long-term tracking effectiveness; and (3) Success Rate (SR): measures the percentage of episodes that complete 500 steps out of 50 total episodes."
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+ "content": "Baselines for Active Visual Tracking. 1) PID: A classical control approach that uses a PID controller to adjust agent actions by maximizing IoU between the detected target bounding box and an expected position. 2) RL: We adapt the offline reinforcement learning implementation from Zhong et al. [49], using their network architecture while collecting three distinct offline datasets (100k steps each) with varying environmental diversity: single environment (1 Env.), two environments (2 Envs.), and eight environments (8 Envs.). Notably, FlexibleRoom represents an abstract environment where objects appear as geometric shapes with randomized patterns used in the three settings. 3) OpenVLA: We fine-tune OpenVLA [19], an end-to-end large model originally designed for robotic manipulation with strong generalization capabilities, on our most diverse dataset (8 Envs.) to adapt it for tracking tasks. 4) GPT-4o: We implement a VLM-based agent using GPT-4o"
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+ "content": "The averaged success rate of embodied tracking agents across four kinds of scenes"
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+ "content": "Figure 6. Average success rates across four environment categories: Interior Scenes, Palaces, Wilds, and Modern Urbanity. Results compare Offline RL agents trained on three offline dataset settings with increasing environmental diversity (1 Env., 2 Envs., 8 Envs.). Performance consistently improves with dataset diversity, demonstrating enhanced generalization capabilities. Notably, environments with complex spatial structures (Interior Scenes and Palaces) present greater challenges for navigation and obstacle avoidance, resulting in lower success rates."
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+ "content": "to generate actions directly from observed images. We designed a prompt template to standardize outputs into predefined action commands (moving forward/backward, turning left/right, or maintaining position), which are then mapped to appropriate velocities. Despite GPT-4o's capabilities, we observed poor alignment performance and significant latency issues when processing raw image inputs, limiting its effectiveness for real-time tracking."
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+ "content": "Result Analysis. We first evaluate the performance of agents trained with offline datasets collected from varying numbers of environments (1 Env., 2 Envs., 8 Envs.) across 16 unseen environmentsTo visualize the performance change of different settings within various scene categories, we calculate the average success rate (SR) of each agent in four categories, and the results are shown in Figure 6. Then we compared the baseline methods' performance, as shown in Table 5 (0D). The results reveal a clear trend: as the number of environments used for training increases, agent long-term tracking performance generally improves across all categories. In the Wilds, a significant increase in success rate is observed with the 8 Envs. dataset, which involves the highest diversity of environments. This demonstrates that diverse environmental exposure plays a crucial role in improving the agent's generalization capabilities in more complex, open-world environments. The lower success rate in the 1 Env. highlights the limitations of training solely in abstract settings like the FlexibleRoom. Similarly, in the Palace, the success rate improves notably from 1 Env. to 8 Envs., suggesting that training with a broader range of environments helps the agent better adapt to intricate 3D spatial structures."
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+ "content": "4.3. Benchmarking Agents at Variant Settings"
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+ "content": "We augment the environment employed for active tracking by seamlessly integrating the Gym toolkit into diverse settings. We use the population control wrapper to create social tracking scenarios. In this setting, the agent is required to follow the target through crowds. We can also adjust the morphology of the trackers for evaluating the cross-embodiment generalization. Moreover, we employ the time dilation wrapper to simulate a variety of control frequencies. This allows us to analyze the impact of the latency within the perception-control loop on tracking performance."
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+ "content": "Robustness to Active Distractions. A key challenge in active visual tracking is handling visual distractions and dynamic obstacles, which is crucial for real-world deployment in crowds. We evaluated agents in four representative environments: Storage House, Desert Ruins, TerrainDemo, and SuburbNeighborhoodDay, with varying numbers of human distractors (0D, 4D, 10D) and compared RL-based methods (trained in 8 environments, denoted as RL 8 Envs.) against PID, OpenVLA, and GPT-4o. Table 5 shows that RL-based methods maintain stable success rates, RL 8 Envs. achieving 0.76 SR in 0D, 0.68 in 4D and 0.56 in 10D, benefiting from diverse training data. In contrast, PID, OpenVLA, and GPT-4o struggle, showing significantly lower returns and success rates. PID suffers from delayed reactions when the target is occluded, leading to failures. OpenVLA tracks effectively at short distances but loses accuracy over time due to accumulated errors. Both OpenVLA and GPT-4o are highly prone to distractions, often tracking the wrong target. These results highlight the limitations of large models in dynamic environments with active distractions."
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+ "content": "Cross-Embodiment Generalization. To investigate whether policies can effectively transfer to agents with different morphologies, we apply the agents (RL and OpenVLA) trained on a human character to a quadrupedal robot dog. This exploration is motivated by the practical necessity in real-world applications where a single policy might need to operate across various embodiments with different perceptual perspectives and movement capabilities. As shown in Table 5, the performance decreases notably, particularly the success rate (from 0.68 to 0.48 with 4D and from 0.56 to 0.40 with 10D for RL 8 Envs.), indicating that the community should pay more attention to the cross-embodiment generalization for real-world deployment."
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+ "content": "The Impact of Control Frequency. In high-dynamic scenes, the latency of the perception-control loop plays a critical role in managing multiple dynamic factors effectively. To verify this, We employ the time dilation wrapper to simulate different control frequencies during deployment. As shown in Table 4, when the rate drops below 10 FPS, performance significantly declines. Our results show that RL-based agents achieve superior performance in social tracking scenarios when operating at higher control fre"
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+ {
+ "type": "table_caption",
+ "bbox": [
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+ "content": "Table 4. The impact of control frequency on tracking performance. We evaluate the RL agent (1 Env.) in the FlexibleRoom using the time dilation wrapper to simulate varying control frequencies."
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+ "content": " | 3 FPS | 10 FPS | 30 FPS | w/o FPS Control |
| ER | 184 | 303 | 368 | 275 |
| EL | 377 | 449 | 482 | 425 |
| SR | 0.34 | 0.62 | 0.92 | 0.74 |
"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Table 5. We evaluate different methods in four representative environments: Storage House, Desert Ruins, TerrainDemo, and SuburbNeighborhoodDay, with varying numbers of distractors (0D, 4D, 10D). Each cell presents the averaged values across four environments for three metrics: Episodic Return (ER), Episode Length (EL), and Success Rate (SR). OpenVLA and RL are trained on the dataset collected from 8 environments."
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+ "angle": 0,
+ "content": "| Method | 0D | 4D | 10D |
| PID | 113/298/0.34 | 107/295/0.30 | 78/105/0.14 |
| GPT-4o | 2/228/0.28 | -102/264/0.16 | -80/240/0.10 |
| OpenVLA | 55/323/0.10 | -39/149/0.02 | -30/156/0.00 |
| RL | 321/468/0.76 | 280/437/0.68 | 187/402/0.56 |
| PID (Robot dog) | 152/245/0.30 | 149/237/0.22 | 100/102/0.16 |
| GPT-4o (Robot dog) | -5/263/0.20 | -98/272/0.16 | -59/223/0.04 |
| OpenVLA(Robot dog) | 42/301/0.08 | -37/142/0.00 | -13/117/0.00 |
| RL (Robot dog) | 279/433/0.60 | 220/409/0.48 | 143/367/0.40 |
"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "quencies. These findings emphasize the necessity of developing efficient models for embodied agents to successfully execute tasks in dynamic social worlds."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "5. Conclusions"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In conclusion, UnrealZoo addresses critical gaps in embodied AI research by providing unprecedented environmental diversity across 100 scenes and 67 embodiment options. By offering easy-to-use Python APIs and toolkits, we support efficient environmental interactions, distributed training, and task customization in UnrealZoo. The experiments on UnrealZoo reveal the importance of environment diversity for agent generalization capabilities, the necessity of low-latency control in dynamic scenes, and key challenges faced by current methods for embodied agents in open worlds. These findings highlight a clear path forward for developing more robust embodied AI systems capable of navigating the complexity of real-world deployment."
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Looking forward, UnrealZoo will drive research in several key areas: 1) spatial intelligence development in complex 3D environments; 2) social intelligence research through multi-agent interactions; 3) safe pre-deployment evaluation and limitation identification; 4) cross-embodiment learning and skill transfer; and 5) adaptation to dynamic environments. As we continue to enrich virtual worlds and interaction capabilities, UnrealZoo will play an increasingly vital role in advancing agents from simulation to reality, ultimately fostering harmonious human-AI coexistence."
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+ "type": "title",
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+ "angle": 0,
+ "content": "Acknowledgments"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "This work was supported by the National Science and Technology Major Project (2022ZD0114904), NSFC-6247070125, NSFC-62406010, the Funding Scheme for Research and Innovation of FDCT (Grant No. 0021/2025/ITP1), the Fundamental Research Funds for the Central Universities, and Qualcomm University Research Grant. We express our gratitude to Weichao Qiu for his invaluable support in optimizing UnrealCV and for the insightful discussions. We are also thankful to Tingyun Yan for providing the early version of the human entity and to Jingzhe Lin for his assistance in producing demo videos. Our appreciation extends to the active developers in the open-source community for ensuring UnrealCV's compatibility with the latest Unreal Engine versions, such as UE 5.4. Furthermore, we thank the contributors in the Unreal Engine Marketplace for offering high-quality content and plugins, which have been instrumental in the development of UnrealZoo."
+ },
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+ "content": "References"
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+# UnrealZoo: Enriching Photo-realistic Virtual Worlds for Embodied AI
+
+Fangwei Zhong\*16 Kui Wu\*2 Churan Wang\* Hao Chen\* Hai Ci\* Zhoujun Li\* Yizhou Wang\* 1 School of Artificial Intelligence, Beijing Normal University
+
+$^{2}$ State Key Laboratory of Complex & Critical Software Environment, Beihang University
+
+$^{3}$ School of Computer Science, Institute for Artificial Intelligence, State Key Laboratory of General Artificial Intelligence, Peking University
+
+$^{4}$ City University of Macau $^{5}$ National University of Singapore
+
+$^{6}$ Beijing Institute for General Artificial Intelligence (BIGAI)
+
+fangweizhong@bnu.edu.cn, wukui@buaa.edu.cn
+
+
+Figure 1. UnrealZoo enriches photo-realistic virtual worlds with diverse scenes and playable entities, enabling training of generalizable embodied AI agents for navigation, tracking, and social interactions.
+
+# Abstract
+
+We introduce UnrealZoo, a collection of over 100 photorealistic 3D virtual worlds built on Unreal Engine, designed to reflect the complexity and variability of open-world environments. We also provide a rich variety of playable entities, including humans, animals, robots, and vehicles for embodied AI research. We extend UnrealCV with optimized APIs and tools for data collection, environment augmentation, distributed training, and benchmarking. These improvements achieve significant improvements in the efficiency of rendering and communication, enabling advanced
+
+applications such as multi-agent interactions. Our experimental evaluation across visual navigation and tracking tasks reveals two key insights: 1) environmental diversity provides substantial benefits for developing generalizable reinforcement learning (RL) agents, and 2) current embodied agents face persistent challenges in open-world scenarios, including navigation in unstructured terrain, adaptation to unseen morphologies, and managing latency in the close-loop control systems for interacting in highly dynamic objects. UnrealZoo thus serves as both a comprehensive testing ground and a pathway toward developing more capable embodied AI systems for real-world deployment.
+
+# 1. Introduction
+
+Currently, embodied artificial intelligence (Embodied AI) agents are often homebodies, primarily confined to controlled indoor environments and rarely venturing outside to explore the diversity of the open world. While several simulators [8, 20, 22, 28, 29] have advanced the field, they often focus on specific scenarios, such as daily activities in homes or autonomous driving on urban roads. This narrow focus hinders AI agents' adaptability and generalization in open worlds, such as factories, public areas, and landscapes, which are required by several real-world applications.
+
+To bridge this gap, there is a growing demand for simulators that feature diverse open-world environments. First, the diversity of 3D scenes and morphologies is fundamental to developing spatial intelligence [7]. This diversity enables agents to actively perceive, reason, plan, and act while tackling various tasks in complex 3D worlds. Second, the complexity of multi-agent interactions is essential for developing social intelligence [10], such as the theory of mind [17], negotiation [15], cooperation [34], and competition [47], encouraging agents to behave more like humans. Third, virtual worlds that mimic the challenges in open-world scenarios can evaluate agents efficiently and effectively, identifying limitations and preventing hardware losses from real-world deployment failures [18]. Ultimately, these features will inspire researchers to explore new challenges previously overlooked in other simulators [9], facilitating seamless integration into real-world applications.
+
+In this work, we introduce UnrealZoo, a comprehensive collection of photo-realistic virtual worlds, based on Unreal Engine and UnrealCV [30]. UnrealZoo features a diverse range of complex open worlds and playable entities to advance research in embodied AI and related domains. This high-quality set includes 100 realistic scenes at varying scales, such as houses, supermarkets, train stations, industrial factories, urban cities, villages, temples, and natural landscapes. Each environment is expertly designed by artists to mimic realistic lighting, textures, and dynamics, closely resembling real-world experiences. Our collection also includes diverse playable entities, including humans, animals, robots, drones, motorbikes, and cars. This diversity enables researchers to investigate the generalization of agents across different embodiments or build complex 3D social worlds with numerous heterogeneous agents. To enhance usability, we further optimize UnrealCV and offer a suite of easy-to-use Python APIs and tools (UnrealCV+), including environment augmentation, demonstration collection, and distributed training/testing. These tools allow for customization and extension of the environments to meet various needs in future applications, ensuring UnrealZoo remains adaptable as the embodied AI agents evolve.
+
+We conduct experiments to demonstrate the applicability of UnrealZoo for embodied AI. First, we benchmark
+
+frames per second (FPS) across various commands, highlighting the significant improvement in image rendering and multi-agent interactions with the UnrealCV+ API. We use embodied visual navigation [52] and tracking [24, 47] as two example tasks to benchmark embodied vision agents in complex dynamic environments with moving objects and unstructured maps. We also introduce a set of simple yet effective baseline methods for developing embodied vision agents, including distributed online reinforcement learning algorithms [27], offline reinforcement learning algorithms [21], and a reasoning framework for large vision-language models (VLMs). Our evaluations across different settings emphasize the importance of diverse training environments for enhancing agent generalization and robustness, the necessity of low latency in closed-loop control to handle dynamic factors, and the potential of reinforcement learning for training agents to navigate complex scenes.
+
+Our contributions can be summarized as follows: 1) We build UnrealZoo, a collection of 100 high-quality photorealistic scenes along with a set of playable entities. These cover the most challenging aspects for embodied AI agents in open-world environments. 2) We optimize the communication efficiency of UnrealCV APIs and provide easy-to-use Gym interfaces with a toolkit to meet diverse requirements. 3) We conduct experiments to demonstrate the usability of UnrealZoo, showing the importance of the diversity of the environments to the embodied agents, and analyzing the limitations of the current RL-based and VLM-based agents in the open worlds.
+
+# 2. Related Works
+
+Realistic Simulators for Embodied AI. Realistic simulators are widely adopted in embodied AI research due to their high-quality rendering, cost-effective ground truth generation, and environmental controllability. Specialized 3D simulators have been developed for indoor navigation [20, 28, 36, 37], robot manipulation [4, 11, 43], and autonomous driving [8, 13, 32]. Recent advances in computer graphics have enabled general-purpose virtual worlds with photo-realistic rendering. ThreeDWorlds (TDW) [14] and LEGENT [5] offer multi-modal platforms based on Unity, but their scenes and playable entities remain limited, with performance degrading in large outdoor environments. V-IRL [41] leverages Google Maps' API to simulate agents with real-world street view images, yet lacks physical interaction capabilities due to its static image composition. While the community has begun exploring dynamic environments with social interactions, existing solutions like Habitat 3.0 [29] focus on limited agent interactions in indoor scenes, and HAZARD [51] addresses only single-agent simulations in scenarios like fires and floods. In contrast, UnrealZoo offers a comprehensive collection of diverse scenes across different scales, situations, eras, and
+
+Table 1. The comparison with related photo-realistic virtual worlds for embodied AI. Nav. Sys. specifies whether the agent in the environment includes an autonomous navigation system. We compare the visual realism across different engines and list the descriptions of the symbols in supplementary materials.
+
+| Virtual Worlds | Scene: Categories | Scene: Scale Level | Scene: Style | Scene: Base Engine | Agent: Body | Agent: Nav. Sys. | Agent: Multi-agent |
| VirtualHome AI2THOR ThreeDWorld OmniGibson Habitat 3.0 CARLA AirSim LEGENT V-IRL | Indoor Indoor Indoor Indoor, Building, Community Indoor Indoor Community, Landscape Community, Landscape Indoor, Building Community, Landscape | Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western | Unity Unity Unity Omniverse - Habitat-Sim UE 4/5 UE 4 Unity Google Map | | ✓ - - - - - | ✓ - - - - - | ✓ - ✓ ✓ ✓ ✓ |
|
|
|
|
|
|
|
|
|
| UnrealZoo | Indoor, Building, Community, Landscape | Ancient, Modern, Sci-Fi Western, Eastern, Nature | UE 4/5 | | ✓ | ✓ | |
+
+cultural backgrounds with various playable entities. Leveraging Unreal Engine advancements and optimized UnrealCV, our environment achieves real-time performance in large-scale scenes with multiple agents and photo-realistic rendering. A detailed comparison of photo-realistic simulators is presented in Table 1.
+
+Embodied Vision Agents. This represents a key frontier in AI research, performing tasks with visual observation, like navigation [16, 23, 42, 52], active object tracking [24, 46-49], and other interactive tasks [2, 6, 33, 35]. Their development involves state representation learning [12, 39, 40, 44], reinforcement learning (RL) [26, 31, 38], and large vision-language models (VLMs) [45, 50], such as GPT-4o and SpatialVLM [3]. Despite advances, significant challenges persist. RL methods require extensive trial-and-error interactions and computational resources, often struggling with generalization. VLM-based methods excel at interpreting instructions and images but may lack fine-grained control and adaptability for real-time interactions. Importantly, previous simulators primarily focus on indoor rooms or urban roads, overlooking critical challenges faced by embodied vision agents in open worlds: unstructured terrain, dynamic factors, perception-control loop costs, and multi-agent social interactions. Therefore, benchmarking agents in expansive, photo-realistic virtual environments is essential to address real-world challenges. In this work, we collect a subset of environments from UnrealZoo and benchmark embodied visual navigation and tracking agents, revealing limitations in current methods that were previously masked by constrained simulation environments.
+
+# 3. UnrealZoo
+
+UnrealZoo is a collection of photo-realistic, interactive open-world environments with diverse embodied characters, built on Unreal Engine and UnrealCV [30]. The environments are sourced from the Unreal Engine Marketplace1, which shares high-quality content from artists,
+
+and were accumulated over two years at a cost exceeding 10,000. UnrealZoo features a diverse array of scenes with varying sizes and styles. Among them, the largest scene, i.e., Medieval Nature Environment, covers more than $16km^2$ areas. The environments also include a wide range of embodiment, such as human avatars, vehicles, drones, animals, and virtual cameras, all of which can interact with the environment and are equipped with ego-centric sensing systems. We offer easy-to-use Python APIs based on UnrealCV to facilitate interaction between Python programs and the game engine. Note that UnrealCV is optimized for rendering and communication, particularly in large-scale and multi-agent scenarios, namely UnrealCV+. Additionally, we provide OpenAI Gym interfaces to standardize agent-environment interactions. The gym-like interface also contains a set of toolkits, e.g., environment augmentation, population control, time dilation, and JSON-style task configurations to help the user customize the environments for various tasks with minimal effort.
+
+# 3.1. Scene Collection
+
+UnrealCV Zoo contains 100 scenes based on Unreal Engine 4 and 5. We select the scene based on the public reviews in the marketplace and the difference between the collected scenes, aiming at covering a wide range of styles from ancient to fictional, ensuring diversity. We provide an overview of the environments in the scene gallery, and the detailed statistical distribution is shown in Figure 2.
+
+We have tagged the collected scenes with several feature labels, allowing researchers to select appropriate scenes for testing or training based on the tags associated with each scene. Our tags cover the following aspects:
+
+- Scene Categories: We categorize scenes into three main types: interior, exterior, and both. The interiors include private houses, museums, supermarkets, train stations, factories, gyms, and caves. The exteriors include various outdoor terrains such as ruins, islands, plazas, neighborhoods, and mountains. Additionally, there are 46 scenes that include both interior and exterior elements, offer
+
+
+Figure 2. The statistical distribution of scene content and scale in UnrealZoo. The bar chart depicts the number of scenarios featuring each type of content, noting that larger scenes may encompass multiple categories. The pie chart classifies these scenes by scale, revealing a predominance of large-scale 'Landscape' environments, followed by 'Community', 'Building', and 'Indoor' levels. The distribution reflects the diversity of UnrealZoo and the balanced composition of scenes of different scales.
+
+ing a blend of architectural elements and natural landscapes, enhancing the versatility and realism of our collection. More details about the distribution of the scenes are shown in Figure 2.
+
+- Scale: Each scene is labeled according to its scale, and categorized into four levels: indoor, building, community, and landscape. The indoor scale is the smallest, typically encompassing one or multiple interior rooms (up to a complete floor), such as apartments and office interiors. The building scale includes a single building and its immediate surroundings, like a museum, supermarket, or gas station. The community scale covers areas with multiple buildings, such as neighborhoods, villages, castles, or container yards. The landscape scale includes vast natural or man-made areas, or parts of a city or an entire small town, such as mountains, forests, islands, and urban districts. Specifically, there are 35 scenes classified as landscape, 28 as community, 23 as building, and 15 as indoor. The largest scene covers 16 square kilometers.
+- Spatial Structure: We also tag the spatial structure of the scenes, including multi-floor, topological, flat, steep, etc. Such categorization is vital for benchmarking the spatial intelligence of embodied agents. Multi-floor structures, for instance, challenge agents with vertical navigation and require advanced path-planning algorithms. Topological features, such as interconnected pathways, test the agent's ability to understand and traverse complex networks.
+- Dynamics: The environment's dynamics include simulating factors like weather, fire, gas, fluid, and interactive objects. These elements enhance the visual and physical diversity of the scene while evaluating agents' adaptability and generalization. Weather variations such as sandstorms, snowfall, and thunderstorms are crucial, as are in
+
+
+Figure 3. First-person and third-person view images of different entities in different scenes. Note that camera parameters can be reconfigured by UnrealCV APIs.
+
+teractive objects like doors that agents can interact with. These dynamics are vital for an open-world experience.
+
+- Style: The scenesen compass diverse cultural and historical styles, including Asian Temple, Western Church, and Middle Eastern Street. Cultural labels include Western, Asian, and Middle Eastern, while era labels encompass Medieval, Modern, and Science Fiction. Identifying the styles will help us build a new data set to benchmark how social agents adapt to different backgrounds.
+
+After categorizing the scenes, we integrate UnrealCV+ (Refer to Section 3.3) into the UE project and add the controllable player assets (Refer to Section 3.2) to each scene. Due to licensing restrictions, content purchased from the marketplace cannot be open-source, so we package the projects into an executable binary for sharing with the community. These executable binaries will be compatible with various operating systems, including Windows, Linux, and macOS, allowing users to download and run them via the Python interface without needing any knowledge of Unreal Engine, which is primarily built on C++ and Blueprint.
+
+# 3.2. Playable Entities
+
+UnrealZoo includes seven types of playable entities: humans, animals, cars, motorbikes, drones, mobile robots, and flying cameras (See Figure 1). Specifically, it comprises 19 human entities, 27 animal entities (dog, horse, elephant, pig, bird, turtle, etc), 3 cars, 14 quadruped robots, 3 motorcycles, and 1 quad-copter drone. This diversity, with varying affordances like action space and viewpoint, allows us to explore new challenges in embodied AI, such as cross-embodiment generalization and heterogeneous multi-agent interactions.
+
+Each entity includes a skeleton with appropriate meshes and textures, a local motion system, and a navigation system. We offer a set of callable functions for each entity, en
+
+abling users to modify attributes like size, appearance, and camera positions, as well as control movements. Each entity can switch between different textures and appearances via UnrealCV API, enhancing visual diversity and adaptability for various scenarios. Each entity is equipped with an ego-centric camera, allowing the users to capture various types of image data such as RGB, depth, surface normal, and instance-level segmentation (object mask) from the agent's ego-centric view. Figure 3 shows examples of the captured first-person view and third-person view images of different entities with varying locomotion. For multi-agent interaction, the population of the entities in a scene can be easily adjusted using the spawn or destroy functions.
+
+The locomotion system is built on Smart Locomotion, an animation framework providing natural movement and environmental interactions. Interactions are animation-based rather than physics-based, featuring binary state changes (e.g., opening doors without physical doorknob manipulation) and positional animations (crouching, jumping, climbing), similar to VirtualHome [28]. Interactive objects maintain consistent behavior across all environments and can be spawned at arbitrary locations with customizable visual properties via the API. This approach facilitates research on high-level reasoning and planning without the need for extra implementation of primitive motion control.
+
+The navigation system is built on NavMesh (a spatial partitioning system that defines walkable surfaces), allowing agents to autonomously navigate with the built-in AI controller. This includes path-finding and obstacle avoidance capabilities, ensuring smooth and realistic movement throughout diverse terrains and structures. For urban-style maps, we segment the roads to distinguish between pedestrian and vehicle pathways. When agents use the navigation system for autonomous control, they will navigate the shortest path based on the priority of the different areas. For example, pedestrians and animals will prioritize walking on sidewalks, while vehicles and motorcycles will prioritize driving on roadways. An example of the navigation area is shown in Supplementary Materials.
+
+# 3.3. Programming Interface
+
+We provide UnrealCV+ as the fundamental interface on Python to capture data and control the entities and scenes, and provide an OpenAI Gym interface for general agent-environment interactions. The architectures of the programming interfaces are shown in Figure 4.
+
+UnrealCV+ is our improved version of the UnrealCV [30] for high-throughput interactions. As the original version of UnrealCV primarily focuses on generating synthesis data for computer vision, the frame rates per second (FPS) are not optimized for real-time interactions. We optimize the rendering pipelines in the UnrealCV server and
+
+
+Figure 4. The detailed architecture of UnrealZoo. The Gray box indicates the UE binary, containing the scenes, playable entities, and UnrealCV+ server. We have bolded the names of the optimized or new modules in UnrealCV+ Server and Client. We provide OpenAI Gym Interfaces for agent-environment interaction. Our gym interface supports customizing the task in a configuration file and contains a toolkit with a set of gym wrappers for environment augmentation, population control, and etc.
+
+the communication protocols between the server and the client to improve the FPS. Specifically, we enable parallel processing while rendering object masks and depth images, which can significantly improve the FPS in large-scale scenes. For multi-agent interactions, we further introduce the batch commands protocol. In this protocol, the client can simultaneously send a batch of commands to the server, processing all the received commands and returning a batch of results. In this way, we can reduce the time spent on server-client communication. Since reinforcement learning requires extensive trial-and-error interactions, often running multiple environments on a computer, we introduce Interprocess communication (IPC) sockets instead of TCP sockets to improve the stability of the server-client communication under high loads. We benchmark the FPS performance in Table 2. To enhance user-friendliness, we have developed high-level Python APIs that are built upon the command systems of UnrealCV. These APIs encapsulate all the request commands and their corresponding data decoders into a callable Python function. This approach significantly simplifies the process for beginners, allowing them to interact with and customize the environment using UnrealCV+.
+
+Gym Interface is used to define the interactive tasks and standardize the agent-environment interaction, following Gym-UnrealCV. Even though there are a lot of tasks for agents, they usually share common interaction protocols, i.e., the agent gets observations from the environment and returns actions. The main difference across different tasks is usually the reward functions, the modality of the observation, and the available actions. Hence, we define the basic interaction functions for general usage and list the task-specific configurations, e.g., scene name, and reward function, in a JSON File. In this way, when adding new UE scenes, the users only need to set the parameters in the JSON files. Moreover, we provide a toolkit with a set of gym wrappers for training and testing the agents, such as environment augmentation that has been in previous work for
+
+Table 2. Comparison of FPS in Unreal Engine 4.27 with UnrealCV and UnrealCV+. Results represent average performance across 6 typical environments ranging from small-scale scenes $(2,440m^2)$ to expansive landscapes $(16km^2)$ . Benchmarks were conducted on a system with an Nvidia RTX 4090 GPU, Intel i7-14700k CPU, and Windows OS. Performance metrics were collected by executing each Python function 1,000 times and measuring execution duration. Multi-agent interaction testing utilized the gym interface, with all rendered images at $640\times 480$ resolution. See the supplementary material for the detailed results.
+
+ | Image Capture | Multi-agent Interaction |
| Color | Object Mask | Surface Normal | Depth | N=2 | N=6 | N=10 |
| UnrealCV | 74 | 70 | 109 | 52 | 35 | 13 | 8 |
| UnrealCV+ | 83(↑ 12%) | 154(↑ 120%) | 131(↑ 20%) | 97(↑ 86%) | 54(↑ 54%) | 25(↑ 92%) | 16(↑ 100%) |
+
+training generalizable agents [24, 25], population control to adjust the number of agents in the scene, and time dilation to adjust the control frequency in dynamic scenes. In Section 4.3, we demonstrate an example usage of the toolkit to analyze the robustness of social tracking agents to the population of crowds and the impact of the control frequency in such dynamic scenes. We also provide a launch tool to enable the user to run multiple environments with specific GPU IDs within a computer, which is useful for distributed online reinforcement learning.
+
+# 4. Experiments
+
+In this section, we conduct experiments involving a series of challenging tasks on UnrealZoo to show its unique features regarding usability, diversity, efficiency, and extensibility. We begin with a visual navigation task to indicate the suitability of UnrealZoo for distributed online reinforcement learning. This task also highlights how the complex spatial structures within our environments introduce new challenges that the off-the-shelf methods struggle to address effectively. Next, we evaluate agents through active visual tracking to validate the necessity of scaling environmental diversity for improving cross-scene generalization. Finally, our social tracking experiments illustrate the exceptional flexibility of UnrealZoo. By enabling easy modification of simulation control frequencies, population scale, and agent morphologies, UnrealZoo reveals previously overlooked challenges in high-dynamic environments and cross-body generalization.
+
+# 4.1. Emergent Challenges in Visual Navigation
+
+Taking the visual navigation task as an example, a fundamental skill for embodied agents, we demonstrate the usability of our environments for various approaches, including distributed online reinforcement learning and large vision-language models. Additionally, we highlight the emergent challenges posed by unstructured open-world environments. While traditional approaches often operate within well-defined 3D spatial structures, our environments require agents to navigate through complex, unconstrained terrains. Therefore, agents must execute diverse locomotion skills, including running, climbing, jumping, and crouching, to overcome various environmental obstacles while pursuing target objects. This setting demands sophisticated 3D spatial reasoning capabilities and action selection mechanisms for effective real-time decision-making. The details
+
+of the task setting, implementation, and training curve are introduced in the supplementary materials.
+
+Evaluation Metrics. We employ two key metrics to evaluate visual navigation agents: 1) Average Episode Length (EL), representing the average number of steps per episode over 50 episodes. 2) Success Rate (SR), measuring the percentage of episodes the agent successfully navigates to the target object out of 50 total episodes, which represents the navigation capability in the wild environment. 3) Success weighted by Path Length (SPL) [1], a standard metric that accounts for both success and path efficiency.
+
+Baselines for Navigation. We build simple baselines to demonstrate the applicability of our environments for training reinforcement learning agents and benchmark the agents based on pre-trained large models. 1) Online RL: We train RL-based navigation agents independently in the Roof and Factory environments using a distributed online reinforcement learning (RL) approach, e.g., A3C [27]. The model takes the first-person view segmentation mask and the relative position between the agent and target as input, and outputs discrete actions to navigate. This setup allows the agent to iteratively refine navigation strategies through continuous environmental interaction. 2) GPT-4o: We leverage the multimodal reasoning capabilities of GPT-4o for navigation model. Following a structured prompt template, GPT-4o performs reasoning to select appropriate actions from the action space to guide the agent toward the target location. 3) Human: As a reference, we conduct experiments where human players control agents via keyboard inputs, analogous to first-person video game interactions. The human players use the same action space available to other baselines.
+
+Results. In Table 3, we report the performances of different methods in two unstructured scenes. The RL-based agent performs moderately well, achieving better results in the simpler environment (Industrial Area) compared to the Roof, where the target object is located on different levels of stairs. The GPT-4o agent struggles in both scenarios. This implies that the GPT-4o performs poorly in complex 3D scene reasoning. As a reference, the human player completes both tasks with the fewest steps and a 1.00 success rate, underscoring the significant performance gap between current embodied AI agents and humans, indicating substantial room for improvement to navigate in such complex, open-world environments.
+
+Table 3. The results (EL/SR/SPL) of visual navigation agents in two unstructured terrains.
+
+ | Online RL | GPT-4o | Human |
| Roof | 1660/0.32/0.10 | 2000/0.00/0.00 | 515/1.00/0.97 |
| Industrial Area | 261/0.52/0.31 | 369/0.20/0.08 | 158/1.00/0.98 |
+
+
+Figure 5. An exemplar sequence from the embodied navigation agent in the Roof. The RL agent learned to climb on a box and wall and jump over an obstacle to reach the goal in a short path.
+
+# 4.2. Scaling the Diversity for Active Visual Tracking
+
+In this section, we aim to analyze the effectiveness of the diversity of the training data on the generalization of the active visual tracking. We collect 3 sets of demonstrations from different numbers of environments in UnrealZoo and train the tracking policy via offline reinforcement learning [49]. We evaluate the tracking performance across 16 unseen environments covering four categories: Interior Scenes, Palaces, Wilds, and Modern Scenes. Each category contains 4 individual environments. The implementation details are introduced in the supplementary materials.
+
+Evaluation Metrics. Our evaluation employs three key metrics: (1) Average Episodic Return (ER): calculates the mean episodic return over 50 episodes, providing insights into overall tracking performance; (2) Average Episode Length (EL): represents the average number of steps per episode, which reflects long-term tracking effectiveness; and (3) Success Rate (SR): measures the percentage of episodes that complete 500 steps out of 50 total episodes.
+
+Baselines for Active Visual Tracking. 1) PID: A classical control approach that uses a PID controller to adjust agent actions by maximizing IoU between the detected target bounding box and an expected position. 2) RL: We adapt the offline reinforcement learning implementation from Zhong et al. [49], using their network architecture while collecting three distinct offline datasets (100k steps each) with varying environmental diversity: single environment (1 Env.), two environments (2 Envs.), and eight environments (8 Envs.). Notably, FlexibleRoom represents an abstract environment where objects appear as geometric shapes with randomized patterns used in the three settings. 3) OpenVLA: We fine-tune OpenVLA [19], an end-to-end large model originally designed for robotic manipulation with strong generalization capabilities, on our most diverse dataset (8 Envs.) to adapt it for tracking tasks. 4) GPT-4o: We implement a VLM-based agent using GPT-4o
+
+
+The averaged success rate of embodied tracking agents across four kinds of scenes
+Figure 6. Average success rates across four environment categories: Interior Scenes, Palaces, Wilds, and Modern Urbanity. Results compare Offline RL agents trained on three offline dataset settings with increasing environmental diversity (1 Env., 2 Envs., 8 Envs.). Performance consistently improves with dataset diversity, demonstrating enhanced generalization capabilities. Notably, environments with complex spatial structures (Interior Scenes and Palaces) present greater challenges for navigation and obstacle avoidance, resulting in lower success rates.
+
+to generate actions directly from observed images. We designed a prompt template to standardize outputs into predefined action commands (moving forward/backward, turning left/right, or maintaining position), which are then mapped to appropriate velocities. Despite GPT-4o's capabilities, we observed poor alignment performance and significant latency issues when processing raw image inputs, limiting its effectiveness for real-time tracking.
+
+Result Analysis. We first evaluate the performance of agents trained with offline datasets collected from varying numbers of environments (1 Env., 2 Envs., 8 Envs.) across 16 unseen environmentsTo visualize the performance change of different settings within various scene categories, we calculate the average success rate (SR) of each agent in four categories, and the results are shown in Figure 6. Then we compared the baseline methods' performance, as shown in Table 5 (0D). The results reveal a clear trend: as the number of environments used for training increases, agent long-term tracking performance generally improves across all categories. In the Wilds, a significant increase in success rate is observed with the 8 Envs. dataset, which involves the highest diversity of environments. This demonstrates that diverse environmental exposure plays a crucial role in improving the agent's generalization capabilities in more complex, open-world environments. The lower success rate in the 1 Env. highlights the limitations of training solely in abstract settings like the FlexibleRoom. Similarly, in the Palace, the success rate improves notably from 1 Env. to 8 Envs., suggesting that training with a broader range of environments helps the agent better adapt to intricate 3D spatial structures.
+
+# 4.3. Benchmarking Agents at Variant Settings
+
+We augment the environment employed for active tracking by seamlessly integrating the Gym toolkit into diverse settings. We use the population control wrapper to create social tracking scenarios. In this setting, the agent is required to follow the target through crowds. We can also adjust the morphology of the trackers for evaluating the cross-embodiment generalization. Moreover, we employ the time dilation wrapper to simulate a variety of control frequencies. This allows us to analyze the impact of the latency within the perception-control loop on tracking performance.
+
+Robustness to Active Distractions. A key challenge in active visual tracking is handling visual distractions and dynamic obstacles, which is crucial for real-world deployment in crowds. We evaluated agents in four representative environments: Storage House, Desert Ruins, TerrainDemo, and SuburbNeighborhoodDay, with varying numbers of human distractors (0D, 4D, 10D) and compared RL-based methods (trained in 8 environments, denoted as RL 8 Envs.) against PID, OpenVLA, and GPT-4o. Table 5 shows that RL-based methods maintain stable success rates, RL 8 Envs. achieving 0.76 SR in 0D, 0.68 in 4D and 0.56 in 10D, benefiting from diverse training data. In contrast, PID, OpenVLA, and GPT-4o struggle, showing significantly lower returns and success rates. PID suffers from delayed reactions when the target is occluded, leading to failures. OpenVLA tracks effectively at short distances but loses accuracy over time due to accumulated errors. Both OpenVLA and GPT-4o are highly prone to distractions, often tracking the wrong target. These results highlight the limitations of large models in dynamic environments with active distractions.
+
+Cross-Embodiment Generalization. To investigate whether policies can effectively transfer to agents with different morphologies, we apply the agents (RL and OpenVLA) trained on a human character to a quadrupedal robot dog. This exploration is motivated by the practical necessity in real-world applications where a single policy might need to operate across various embodiments with different perceptual perspectives and movement capabilities. As shown in Table 5, the performance decreases notably, particularly the success rate (from 0.68 to 0.48 with 4D and from 0.56 to 0.40 with 10D for RL 8 Envs.), indicating that the community should pay more attention to the cross-embodiment generalization for real-world deployment.
+
+The Impact of Control Frequency. In high-dynamic scenes, the latency of the perception-control loop plays a critical role in managing multiple dynamic factors effectively. To verify this, We employ the time dilation wrapper to simulate different control frequencies during deployment. As shown in Table 4, when the rate drops below 10 FPS, performance significantly declines. Our results show that RL-based agents achieve superior performance in social tracking scenarios when operating at higher control fre
+
+Table 4. The impact of control frequency on tracking performance. We evaluate the RL agent (1 Env.) in the FlexibleRoom using the time dilation wrapper to simulate varying control frequencies.
+
+ | 3 FPS | 10 FPS | 30 FPS | w/o FPS Control |
| ER | 184 | 303 | 368 | 275 |
| EL | 377 | 449 | 482 | 425 |
| SR | 0.34 | 0.62 | 0.92 | 0.74 |
+
+Table 5. We evaluate different methods in four representative environments: Storage House, Desert Ruins, TerrainDemo, and SuburbNeighborhoodDay, with varying numbers of distractors (0D, 4D, 10D). Each cell presents the averaged values across four environments for three metrics: Episodic Return (ER), Episode Length (EL), and Success Rate (SR). OpenVLA and RL are trained on the dataset collected from 8 environments.
+
+| Method | 0D | 4D | 10D |
| PID | 113/298/0.34 | 107/295/0.30 | 78/105/0.14 |
| GPT-4o | 2/228/0.28 | -102/264/0.16 | -80/240/0.10 |
| OpenVLA | 55/323/0.10 | -39/149/0.02 | -30/156/0.00 |
| RL | 321/468/0.76 | 280/437/0.68 | 187/402/0.56 |
| PID (Robot dog) | 152/245/0.30 | 149/237/0.22 | 100/102/0.16 |
| GPT-4o (Robot dog) | -5/263/0.20 | -98/272/0.16 | -59/223/0.04 |
| OpenVLA(Robot dog) | 42/301/0.08 | -37/142/0.00 | -13/117/0.00 |
| RL (Robot dog) | 279/433/0.60 | 220/409/0.48 | 143/367/0.40 |
+
+quencies. These findings emphasize the necessity of developing efficient models for embodied agents to successfully execute tasks in dynamic social worlds.
+
+# 5. Conclusions
+
+In conclusion, UnrealZoo addresses critical gaps in embodied AI research by providing unprecedented environmental diversity across 100 scenes and 67 embodiment options. By offering easy-to-use Python APIs and toolkits, we support efficient environmental interactions, distributed training, and task customization in UnrealZoo. The experiments on UnrealZoo reveal the importance of environment diversity for agent generalization capabilities, the necessity of low-latency control in dynamic scenes, and key challenges faced by current methods for embodied agents in open worlds. These findings highlight a clear path forward for developing more robust embodied AI systems capable of navigating the complexity of real-world deployment.
+
+Looking forward, UnrealZoo will drive research in several key areas: 1) spatial intelligence development in complex 3D environments; 2) social intelligence research through multi-agent interactions; 3) safe pre-deployment evaluation and limitation identification; 4) cross-embodiment learning and skill transfer; and 5) adaptation to dynamic environments. As we continue to enrich virtual worlds and interaction capabilities, UnrealZoo will play an increasingly vital role in advancing agents from simulation to reality, ultimately fostering harmonious human-AI coexistence.
+
+# Acknowledgments
+
+This work was supported by the National Science and Technology Major Project (2022ZD0114904), NSFC-6247070125, NSFC-62406010, the Funding Scheme for Research and Innovation of FDCT (Grant No. 0021/2025/ITP1), the Fundamental Research Funds for the Central Universities, and Qualcomm University Research Grant. We express our gratitude to Weichao Qiu for his invaluable support in optimizing UnrealCV and for the insightful discussions. We are also thankful to Tingyun Yan for providing the early version of the human entity and to Jingzhe Lin for his assistance in producing demo videos. Our appreciation extends to the active developers in the open-source community for ensuring UnrealCV's compatibility with the latest Unreal Engine versions, such as UE 5.4. Furthermore, we thank the contributors in the Unreal Engine Marketplace for offering high-quality content and plugins, which have been instrumental in the development of UnrealZoo.
+
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+
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| VirtualHome AI2THOR ThreeDWorld OmniGibson Habitat 3.0 CARLA AirSim LEGENT V-IRL | Indoor Indoor Indoor Indoor, Building, Community Indoor Indoor Community, Landscape Community, Landscape Indoor, Building Community, Landscape | Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western Modern, Western | Unity Unity Unity Omniverse - Habitat-Sim UE 4/5 UE 4 Unity Google Map | | ✓ - - - - - | ✓ - - - - - | ✓ - ✓ ✓ ✓ ✓ |
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| UnrealZoo | Indoor, Building, Community, Landscape | Ancient, Modern, Sci-Fi Western, Eastern, Nature | UE 4/5 | | ✓ | ✓ | |
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| Color | Object Mask | Surface Normal | Depth | N=2 | N=6 | N=10 |
| UnrealCV | 74 | 70 | 109 | 52 | 35 | 13 | 8 |
| UnrealCV+ | 83(↑ 12%) | 154(↑ 120%) | 131(↑ 20%) | 97(↑ 86%) | 54(↑ 54%) | 25(↑ 92%) | 16(↑ 100%) |
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| ER | 184 | 303 | 368 | 275 |
| EL | 377 | 449 | 482 | 425 |
| SR | 0.34 | 0.62 | 0.92 | 0.74 |
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| PID | 113/298/0.34 | 107/295/0.30 | 78/105/0.14 |
| GPT-4o | 2/228/0.28 | -102/264/0.16 | -80/240/0.10 |
| OpenVLA | 55/323/0.10 | -39/149/0.02 | -30/156/0.00 |
| RL | 321/468/0.76 | 280/437/0.68 | 187/402/0.56 |
| PID (Robot dog) | 152/245/0.30 | 149/237/0.22 | 100/102/0.16 |
| GPT-4o (Robot dog) | -5/263/0.20 | -98/272/0.16 | -59/223/0.04 |
| OpenVLA(Robot dog) | 42/301/0.08 | -37/142/0.00 | -13/117/0.00 |
| RL (Robot dog) | 279/433/0.60 | 220/409/0.48 | 143/367/0.40 |
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diff --git a/2025/Unsupervised Histopathological Image Semantic Segmentation with Overlapping Patches Consistency Constraint/c7ca9d94-b46a-45fa-8735-814dc1aec4fe_content_list.json b/2025/Unsupervised Histopathological Image Semantic Segmentation with Overlapping Patches Consistency Constraint/c7ca9d94-b46a-45fa-8735-814dc1aec4fe_content_list.json
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+ "text": "Abstract",
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+ "text": "Massive requirement for pixel-wise annotations in histopathological image segmentation poses a significant challenge, leading to increasing interest in Unsupervised Semantic Segmentation (USS) as a viable alternative. Pre-trained model-based methods have been widely used in USS, achieving promising segmentation performance. However, these methods are less capable for medical image USS tasks due to their limited ability in encoding task-specific contextual information. In this paper, we propose a context-based Overlapping Patches Consistency Constraint (OPCC), which employs the consistency constraint between the local overlapping region's similarity and global context similarity, achieving consistent class representation in similar environments. Additionally, we introduce an InterLayer Self-Attention Fusion (ILSAF) module that employs a multi-head self-attention mechanism along with InterLayer Importance-Weighting to generate context-aware and semantically discriminative pixel representations, improving pixel clustering accuracy. Extensive experiments on two public histopathological image segmentation datasets demonstrate that our approach significantly outperforms state-of-the-art methods by a large margin, with mIoU surpassing previous leading work by 5.74 and 8.38 percentage points on the two datasets, respectively.",
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+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
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+ "text": "Semantic segmentation is an important research topic in medical image analysis [3, 26, 30, 32, 35], which supports critical tasks in disease diagnosis and treatment planning by accurately delineating regions of tumors or lesions. How-",
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+ "text": "ever, deep learning-based segmentation methods typically require pixel-level annotations from pathologists, which is costly in terms of time and expertise [12, 20, 39]. As a result, researchers have turned their attention to weakly supervised [6, 10, 17, 22, 25, 45] and unsupervised semantic segmentation (USS) [11, 16, 18, 19, 21, 31, 33, 34, 36-38, 42] approaches, which can train segmentation models without pixel-level annotations and thus reduce the burden of manual labeling. In this paper, we focus on the unsupervised semantic segmentation of histopathological images, where we aim to capture the structural properties of tissue sections using only unlabeled data.",
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+ "text": "Clustering-based strategies have been proposed to tackle this problem and have become a common choice for USS. Early methods [11, 19, 36] generally train the segmentation network from scratch via self-supervised feature learning to maximize the mutual information between an image and its augmentations. This approach helps the model learn meaningful representations for clustering without relying on labeled data. More recently, STEGO [16] proposed a method that separates feature learning from cluster compactification, leveraging large-scale pre-trained backbones and contrastive objectives to distill semantic relationships between image patches. Based on this idea, many follow-up works [21, 33, 34] focus on obtaining more semantically meaningful and compact patch features to aid subsequent clustering. However, we point out their limitations in that they inevitably rely on the frozen backbone features, which are inadequate for digital pathology image USS tasks due to the lack of task-specific contextual information.",
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+ "text": "To alleviate this, in this paper, we propose a context-based Overlapping Patches Consistency Constraint (OPCC), to achieve consistent class representation in similar environments. Motivated by clinical experience [4, 8], which indicates that contextual information plays a critical role in the interpretation of pathological images, we observe that referring to the structure and morphology of the",
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+ "type": "header",
+ "text": "CVF",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "type": "page_footnote",
+ "text": "*These authors contributed equally to this work.",
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+ "type": "page_footnote",
+ "text": "†Corresponding authors: Ying Gao (gaoying@scut.edu.cn), Ping Gao (gaoping8599@gdph.org.cn).",
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+ "type": "page_number",
+ "text": "23332",
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+ "text": "surrounding regions can reveal lesion characteristics more accurately. Specifically, the representation of a pathological image depends on its context: the same tissue should exhibit more similar representations when situated in similar environments, whereas different contexts yield dissimilar representations. Based on this observation, our OPCC module extracts overlapping sub-images from the input image. After encoding these sub-images with the backbone, we obtain representations for both the locally overlapping regions and the global context. The similarity of the overlapping region's representations is then used as prior knowledge to guide the backbone, facilitating consistency between the local overlapping region's similarity and global context similarity. This promotes uniform global features across structurally similar images, aiding in maintaining consistent class representation in similar environments and facilitating pixel-level clustering.",
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+ "text": "In addition, to obtain more robust and discriminative pixel-level representations, we propose an attention-based multi-layer feature fusion method, termed Inter-Layer Self-Attention Fusion (ILSAF). Specifically, self-attention with multiple fixed attention heads is introduced to compute feature correlations from different perspectives. Furthermore, an importance-weighted fusion mechanism is designed to dynamically adjust the aggregation process based on the specific features at each position and for each sample, ensuring the fused features capture both global context and local details.",
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+ "type": "text",
+ "text": "To summarize our major contributions:",
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+ "type": "list",
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+ "list_items": [
+ "- We propose a context-based Overlapping Patches Consistency Constraint (OPCC) module, achieving consistent global contextual features encoding across structurally similar images, enforcing the backbone's ability in extracting consistent contextual information.",
+ "- We propose an Inter-Layer Self-Attention Fusion (IL-SAF) module that adaptively integrates multi-level features, obtaining context-aware and semantically discriminative pixel representations",
+ "- Extensive experiments on two public histopathological image segmentation datasets demonstrate that our method achieves state-of-the-art performance in unsupervised semantic segmentation."
+ ],
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "2. Related works",
+ "text_level": 1,
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+ "type": "text",
+ "text": "2.1. Unsupervised Semantic Segmentation",
+ "text_level": 1,
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+ "text": "Semantic segmentation classifiers every pixel in an image into specific categories, with wide-ranging applications across various scenarios [30, 41]. However, training semantic segmentation models requires a large number of pixel-level labels, the acquisition of which is costly [6]. To address this, numerous researchers have explored training semantic segmentation models without labels [9, 11, 16, 19,",
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+ "type": "text",
+ "text": "21, 33, 34, 38].",
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+ "text": "Early studies primarily focused on pixel clustering based on invariance. For instance, IIC [19] introduced a novel clustering objective based on maximizing mutual information between different augmented versions of an image, while PiCIE [11] proposed an unsupervised semantic segmentation (USS) framework that incorporates geometric consistency as an inductive bias for pixel-level clustering.",
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+ "text": "More recently, clustering using pre-trained models has become the mainstream approach. DINO-pretrained ViT [9] plays a crucial role in USS methods and serves as a classic USS approach, where the semantically relevant features encoded by the backbone can be directly clustered to generate segmentation maps. Building on this, STEGO [16] separates feature learning from cluster compactification by introducing a novel contrastive loss to distill unsupervised features into discrete semantic labels, achieving significant performance improvements. HP [33] leverages contrastive learning to discover both global and local hidden positives, ensuring rich semantic relationships and local semantic consistency. EAGLE [21] emphasizes object-centric representation learning through a spectral technique (EiCue) and an object-centric contrastive loss. DepthG [34] incorporates depth information to learn scene structure through depth-feature correlation and 3D farthest-point sampling. ReCLIP [38] explicitly models and rectifies the inherent spatial and class biases in CLIP-based USS by employing learnable reference text inputs and a logit-subtraction mechanism, leading to enhanced unsupervised semantic segmentation performance.",
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+ "type": "text",
+ "text": "However, despite the performance improvements achieved by these methods, the inherent limitations in spatial contextual modeling of features derived from fixed backbone architectures, hinder further advancements in medical domain.",
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+ {
+ "type": "text",
+ "text": "2.2. Consistency Constraints in Computer Vision",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Consistency constraints have become a pivotal technique in various computer vision tasks, enhancing model performance by ensuring alignment and coherence across different representations or predictions [14, 15, 27-29, 40, 43, 44]. In segmentation tasks, consistency constraints play a crucial role in improving the robustness and accuracy of models.",
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+ "text": "For instance, CTVIS [43] proposed a consistency training framework for video instance segmentation tackles occlusion and deformation, which employs contrastive learning to align instance features across frames, enforcing temporal consistency for robust tracking. RAC-Net [40] is designed for weakly-supervised point cloud segmentation, where it identifies reliable pseudo-labels and applies different consistency constraints based on their reliability.",
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+ {
+ "type": "text",
+ "text": "Unsupervised learning also benefits significantly from",
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+ {
+ "type": "page_number",
+ "text": "23333",
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+ "type": "text",
+ "text": "consistency constraints. In unsupervised monocular depth estimation, left-right consistency constraints [14] ensure that depth maps estimated from different views are aligned. Contrastive clustering with graph consistency constraints [44] further enhances image clustering performance by ensuring consistency in the representation of similar data points.",
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "Consistency constraints have proven to be a versatile and effective approach across various computer vision tasks. In our method, we design a Overlapping Patches Consistency Constraint and apply it to unsupervised semantic segmentation.",
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+ "type": "text",
+ "text": "3. Methodology",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Before detailing our full pipeline shown in Fig. 1, we first introduce the core USS framework based on pre-trained models as in prior works [16, 21, 34].",
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+ "type": "text",
+ "text": "3.1. Preliminaries",
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+ "text": "Our approach builds upon STEGO [16], where a frozen DINO-pretrained ViT backbone $\\mathcal{F}_{\\xi}$ is introduced to extract image features. Specifically, the input image $x \\in \\mathbb{R}^{3 \\times H_{\\mathrm{in}} \\times W_{\\mathrm{in}}}$ is encoded into a more compact feature space, resulting in a feature map $f = \\mathcal{F}_{\\xi}(x) \\in \\mathbb{R}^{HW \\times C}$ , where $C$ is the feature dimension, and $H$ and $W$ are the height and width of the feature map. Subsequently, a trainable segmentation head $S$ , which includes both linear and nonlinear transformations, further transforms these features into the code space, yielding the feature encoding $s = S(f) \\in \\mathbb{R}^{HW \\times Q}$ , where $Q$ represents the encoding dimension.",
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+ "type": "text",
+ "text": "3.1.1. Feature Compactification",
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+ "text": "During the training process, a feature correlation loss is introduced to construct more compact feature encodings. Specifically, given a pair of input images $x_{i}$ and $x_{j}$ (where $x_{j}$ could be selected as $x_{i}$ itself, from KNN of $x_{i}$ , or randomly [16]), their corresponding feature maps $f_{i}$ and $f_{j}$ , as well as feature encodings $s_{i}$ and $s_{j}$ , are obtained through the backbone $\\mathcal{F}_{\\xi}$ and the segmentation head $S$ . The feature correlation between $f_{i}$ and $f_{j}$ is computed as follows:",
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+ "text": "\n$$\n\\operatorname {C o r r} \\left(f _ {i}, f _ {j}\\right) = \\frac {f _ {i} ^ {h w} \\cdot f _ {j} ^ {u v}}{\\| f _ {i} ^ {h w} \\| _ {2} \\| f _ {j} ^ {u v} \\| _ {2}}, \\tag {1}\n$$\n",
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+ "text": "where $\\cdot$ represents the dot product, and $\\| \\cdot \\| _2$ denotes the $L_{2}$ -norm. Similarly, the correlation between $s_i$ and $s_j$ is obtained through Equation 1. The Correspondence Distillation Loss is then calculated as:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\text {d i s t i l l}} = - \\sum_ {h w, u v} \\left(\\operatorname {C o r r} \\left(f _ {i}, f _ {j}\\right) - b\\right) \\max \\left(\\operatorname {C o r r} \\left(s _ {i}, s _ {j}\\right), 0\\right), \\tag {2}\n$$\n",
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+ "text": "where $b$ is a scalar bias hyperparameter that adjusts the influence of the correlation term. This loss encourages the",
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+ "type": "text",
+ "text": "feature encodings to maintain high correlation for semantically similar regions while discouraging spurious associations, thereby promoting compact and discriminative feature representations.",
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+ "type": "text",
+ "text": "3.1.2. Clustering",
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+ "type": "text",
+ "text": "Additionally, a cluster head is introduced with $K$ parameterized cluster centers $\\{\\mu_k\\}_{k=1}^K$ , where $K$ corresponds to the number of classes. The inner products between the feature encodings $s$ and the cluster centers $\\mu_k$ are computed as follows:",
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+ "text": "\n$$\n\\operatorname {I n n e r P r o d u c t} (\\mathbf {s}, \\boldsymbol {\\mu} _ {k}) = \\mathbf {s} \\cdot \\boldsymbol {\\mu} _ {k}. \\tag {3}\n$$\n",
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+ "text": "After computing the inner products, the softmax function is applied to obtain the cluster probability maps $M \\in \\mathbb{R}^{K \\times H \\times W}$ . The k-means clustering loss is then calculated as:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\text {c l u s t e r}} = - \\sum_ {k = 1} ^ {K} M _ {k} \\cdot \\text {I n n e r P r o d u c t} (s, \\mu_ {k}). \\tag {4}\n$$\n",
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+ "text": "The evaluation process of the model is detailed in Section 4.2.",
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+ "type": "text",
+ "text": "3.2. Overlapping Patches Consistency Constraint",
+ "text_level": 1,
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+ "type": "text",
+ "text": "This work is motivated by the observation that the same tissue should exhibit more similar representations when situated in similar environments, whereas different contexts yield dissimilar representations. Based on this observation, an Overlapping Patches Consistency Constraint (OPCC) module is proposed, which leverages the similarity of overlapping sub-image features from the input image as a prior to strengthen the consistency between the local overlapping region's similarity and global context similarity.",
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+ "type": "text",
+ "text": "3.2.1. Overlapping Region Extraction",
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+ "text": "First, given an input image $x \\in \\mathbb{R}^{3 \\times H_{\\mathrm{in}} \\times W_{\\mathrm{in}}}$ , we impose a 5-crop on the image, which yields five sub-images:",
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+ "text": "\n$$\nx _ {k} = \\mathcal {C} (x, p _ {k}), \\quad \\forall k \\in \\{\\text {c e n t e r}, \\mathrm {T L}, \\mathrm {T R}, \\mathrm {B L}, \\mathrm {B R} \\} \\tag {5}\n$$\n",
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+ "text": "where $\\mathcal{C}(x,p)$ denotes the cropping operator applied to image $x$ at the region $p$ , in which center, TL, TR, BL, BR denote the sub-images in the center, top-left, top-right, bottom-left, and bottom-right region respectively. Each resulting crop $x_{k}$ belongs to $\\mathbb{R}^{3\\times H_{crop}\\times W_{crop}}$ .",
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+ "text": "Next, these cropped sub-images are fed into the gradient update encoder $\\mathcal{F}_{\\theta}$ to obtain feature representations. Formally, for each crop $x_{k}$ , we compute",
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+ "text": "\n$$\nr _ {k} = \\mathcal {F} _ {\\theta} \\left(x _ {k}\\right), \\tag {6}\n$$\n",
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+ "text": "where $r_k$ denotes the representation corresponding to $x_{k}$",
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+ "img_path": "images/838e1ca6c1cc5181f1f036cf310be9170e8a5906f87548f295f0e690d14e3866.jpg",
+ "image_caption": [
+ "Figure 1. Main architecture of our proposed method. The input image is first subjected to an overlapping crop operation to generate five overlapping sub-images. These sub-images are then processed by the proposed (a) Overlapping Patches Consistency Constraint module, which guides the gradient update encoder $\\mathcal{F}_{\\theta}$ to consistently encode global contextual features across structurally similar images using overlapping patch similarity as a prior (Sec. 3.2). The parameters of $\\mathcal{F}_{\\theta}$ are then updated via EMA to the momentum encoder $\\mathcal{F}_{\\xi}$ . Next, multi-layer representations are extracted from the momentum encoder $\\mathcal{F}_{\\xi}$ and fed into the proposed (b) Inter-Layer Self-Attention Fusion (ILSAF) module to generate context-aware and semantically discriminative pixel representations (Sec. 3.3). Finally, following the previous pipeline, feature compactification and clustering are performed to obtain the final pixel-level segmentation results (Sec. 3.1)."
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+ "type": "text",
+ "text": "Then we extract patch-level features from overlapping region between two sub-images. Let $x_{m}, x_{n} \\in x_{k}$ be the pair of overlapping sub-images cropped from $x$ , $P_{m} = \\{p_{m}^{1}, p_{m}^{2}, \\ldots, p_{m}^{HW}\\}$ and $P_{n} = \\{p_{n}^{1}, p_{n}^{2}, \\ldots, p_{n}^{HW}\\}$ be the sets of patch tokens in $x_{m}, x_{n}$ . The patches in the overlapping region between $x_{m}$ and $x_{n}$ are denoted as:",
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+ "text": "\n$$\nP _ {\\text {o v e r l a p}} = P _ {m} \\cap P _ {n}. \\tag {7}\n$$\n",
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+ "text": "For each overlapping patch $p_{\\mathrm{overlap}_i} \\in P_{\\mathrm{overlap}}$ , we retrieve its feature representations $r$ from both feature maps:",
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+ "text": "\n$$\nr _ {m} ^ {\\text {o v e r l a p} _ {i}} = \\mathcal {F} _ {\\theta} \\left(x _ {m}\\right) \\left[ p _ {\\text {o v e r l a p} _ {i}} \\right], \\tag {8}\n$$\n",
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+ {
+ "type": "equation",
+ "text": "\n$$\nr _ {n} ^ {\\text {o v e r l a p} _ {i}} = \\mathcal {F} _ {\\theta} (x _ {n}) \\left[ p _ {\\text {o v e r l a p} _ {i}} \\right].\n$$\n",
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+ {
+ "type": "text",
+ "text": "Afterward, we compute the cosine similarity between the corresponding patches from the overlapping region. Specifically, the similarity for each overlapping patch $p_{\\mathrm{overlap}_i}$ is defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nS _ {\\text {o v e r l a p} _ {i}} = \\frac {r _ {m} ^ {\\text {o v e r l a p} _ {i}} \\cdot r _ {n} ^ {\\text {o v e r l a p} _ {i}}}{\\left\\| r _ {m} ^ {\\text {o v e r l a p} _ {i}} \\right\\| _ {2} \\left\\| r _ {n} ^ {\\text {o v e r l a p} _ {i}} \\right\\| _ {2}}, \\tag {9}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where $\\cdot$ represents the dot product, and $\\| \\cdot \\| _2$ denotes the $L_{2}$ -norm. The overall similarity of the overlapping region is then obtained by averaging the similarities of all overlapping patches:",
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+ "type": "equation",
+ "text": "\n$$\nS _ {\\text {o v e r l a p}} = \\frac {1}{\\left| P _ {\\text {o v e r l a p}} \\right|} \\sum_ {i = 1} ^ {\\left| P _ {\\text {o v e r l a p}} \\right|} S _ {\\text {o v e r l a p} _ {i}}. \\tag {10}\n$$\n",
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+ "bbox": [
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+ {
+ "type": "text",
+ "text": "3.2.3. Contextual Information Encoding",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "To effectively capture contextual information, we introduce a context token $t_{\\mathrm{ctx}}$ into the encoder $\\mathcal{F}_{\\theta}$ , which serves as a global representation that aggregates spatial and semantic information from the input feature maps. Formally, we append $t_{\\mathrm{ctx}}$ to the input sequence before passing it through the transformer layers:",
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+ "type": "equation",
+ "text": "\n$$\nt _ {\\mathrm {c t x}, k}, r _ {k} = \\mathcal {F} _ {\\theta} \\left(t _ {\\mathrm {c t x}}, x _ {k}\\right). \\tag {11}\n$$\n",
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+ {
+ "type": "text",
+ "text": "3.2.4. Similarity Consistency Constraint",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Following this, the obtained overlapping patches similarity $S_{\\mathrm{overlap}}$ is used as prior knowledge, indicating the degree of difference between the contexts of the overlapping subimages. To align the contextual representations with this prior, an $L_{1}$ loss is introduced between $S_{\\mathrm{overlap}}$ and the similarity of the context token embeddings from $x_{m}$ and $x_{n}$ .",
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+ {
+ "type": "text",
+ "text": "Let $S_{\\mathrm{ctx}}$ denote the similarity between the context token embeddings $t_{\\mathrm{ctx},m}$ and $t_{\\mathrm{ctx},n}$ , computed in the same manner as in Eq. (9). The Overlapping Patches Consistency Constraint loss is then defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {O P C C}} = \\left| S _ {\\mathrm {c t x}} - S _ {\\text {o v e r l a p}} \\right|. \\tag {12}\n$$\n",
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+ "type": "text",
+ "text": "This loss aligns the contextual similarity $S_{\\mathrm{ctx}}$ with the overlapping patches $S_{\\mathrm{overlap}}$ , ensuring that structurally similar images share a consistent global context feature.",
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+ {
+ "type": "page_number",
+ "text": "23335",
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+ },
+ {
+ "type": "image",
+ "img_path": "images/723d6e62f7134173b7f14898e8dd102b5a033389324af73539d92a2ae0ed7a48.jpg",
+ "image_caption": [
+ "Figure 2. Illustration of our proposed Inter-Layer Self-Attention Fusion (ILSAF) module. Multi-layer representations are extracted from the momentum encoder $\\mathcal{F}_{\\xi}$ and fed into the proposed ILSAF module, which leverages a (a) Multi-Head Self-Attention mechanism to capture correlations between pixel features and employs (b) Inter-Layer Importance-Weighting to adaptively fuse features from different layers, enhancing the overall feature representations."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "3.2.5. EMA Update of the Backbone",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "Finally, the parameters of $\\mathcal{F}_{\\theta}$ are updated to the frozen ViT backbone $\\mathcal{F}_{\\xi}$ using an exponential moving average (EMA) mechanism [1, 7], which is defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\xi \\leftarrow \\alpha \\xi + (1 - \\alpha) \\theta , \\tag {13}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "where $\\alpha$ is the momentum coefficient controlling the update rate, which is set to 0.99 in practice. This EMA update allows the contextual information encoding ability, learned by $\\mathcal{F}_{\\theta}$ , to be stably transferred to the unsupervised feature extraction backbone $\\mathcal{F}_{\\xi}$ , improving the accuracy of pixel clustering.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "3.3. Inter-Layer Self-Attention Fusion",
+ "text_level": 1,
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "In order to enhance the representation capability of both fine-grained details and semantic information for unsupervised semantic segmentation in digital pathology images, we propose a Inter-Layer Self-Attention Fusion (ILSAF) module, as illustrated in Fig. 2.",
+ "bbox": [
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+ "page_idx": 4
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+ {
+ "type": "text",
+ "text": "Specifically, we first extract the output features from the last three Transformer blocks of the ViT backbone $\\mathcal{F}_{\\xi}$ , denoted as $f_{L-2}, f_{L-1}$ , and $f_{L} \\in \\mathbb{R}^{HW \\times C}$ , where $HW$ represents the total number of patches in the image, and $C$ denotes the number of feature channels. To mitigate the scale discrepancy among features from different layers, channel-wise normalization is performed on each feature map.",
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+ },
+ {
+ "type": "text",
+ "text": "3.3.1. Multi-Head Self-Attention",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "As shown in Fig. 2 (a), to capture the interactions among multi-level features, we employ multiple fixed attention heads to compute the feature correlations from different perspectives. First, the normalized features are stacked into a tensor $F \\in \\mathbb{R}^{L \\times HW \\times C}$ , where $L = 3$ . Then, fixed linear projections are applied to generate the Query, Key, and Value matrices:",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\nQ = F W _ {Q}, \\quad K = F W _ {K}, \\quad V = F W _ {V}, \\tag {14}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "where $W_{Q}, W_{K}, W_{V} \\in \\mathbb{R}^{C \\times C}$ are initialized as identity matrices. The self-attention output is directly computed as",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\nF _ {\\text {a t t n}} = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {C}}\\right) V, \\tag {15}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "resulting in features of shape $\\mathbb{R}^{L\\times HW\\times C}$ . This process captures the similarity relationships between patches within different Transformer layers and extracts inter-layer interactions from multiple perspectives. Then the fused feature representation $F_{\\mathrm{attn}}$ is unstacked along the first dimension to restore individual layer features $f_l^{\\prime}\\in \\mathbb{R}^{HW\\times C}$ , where $l\\in \\{L - 2,L - 1,L\\}$ .",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "3.3.2. Inter-Layer Importance-Weighting",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "As depicted in Fig. 2 (b), To further adaptively distinguish the importance of different layer features, we compute the norm of each layer's feature along the channel dimension, obtaining the inter-layer weight:",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\alpha_ {l} = \\operatorname {s o f t m a x} \\left(\\| f _ {l} ^ {\\prime} \\| _ {2}\\right), \\tag {16}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "where $\\| f_l^{\\prime}\\| _2\\in \\mathbb{R}^C$ represents the $L_{2}$ norm computed at each patch position for the $l$ -th layer. Finally, the features from different layers $l$ are fused by a weighted summation:",
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\nf _ {\\text {f u s e}} = \\sum_ {l} \\alpha_ {l} \\odot f _ {l} ^ {\\prime}, \\tag {17}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "where $\\odot$ denotes element-wise multiplication. Lastly, normalization and nonlinear activation are applied to the fused features.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "3.4. Model Optimization",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "After obtaining the fused features $f_{\\mathrm{fuse}}$ , we can obtain the segmentation feature encoding $s_{\\mathrm{fuse}}$ through $s_{\\mathrm{fuse}} = S(f_{\\mathrm{fuse}})$ . Consequently, the correspondence distillation loss, mentioned in Eq. 2, can be written as:",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {d i s t i l l}} ^ {\\text {I L S A F}} = \\mathcal {L} _ {\\text {d i s t i l l}} \\left(f _ {\\text {f u s e}, i}, f _ {\\text {f u s e}, j}, s _ {\\text {f u s e}, i}, s _ {\\text {f u s e}, j}\\right). \\tag {18}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "page_number",
+ "text": "23336",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "The final training objective is formulated as follows:",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {O P C C}} + \\lambda_ {2} \\mathcal {L} _ {\\text {d i s t i l l}} ^ {\\text {I L S A F}} + \\mathcal {L} _ {\\text {c l u s t e r}}, \\tag {19}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
+ 153,
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "where $\\lambda_{1}$ and $\\lambda_{2}$ are weights that control the contribution of each loss component, which are set to 0.5 and 1 in practice.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4. Experiment",
+ "text_level": 1,
+ "bbox": [
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+ 209
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4.1. Datasets",
+ "text_level": 1,
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "We evaluate the proposed method on two public datasets. The first dataset is the LUng ADenocarcinoma (LUAD) [17] tissue segmentation dataset, and the second is the Breast Cancer Semantic Segmentation (BCSS) [2] dataset.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4.1.1. LUAD Dataset",
+ "text_level": 1,
+ "bbox": [
+ 89,
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+ 321
+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "The LUAD dataset includes whole slide images (WSIs) from 54 patients, covering four tissue types: tumor epithelial (TE), tumor-associated stroma (TAS), necrosis (NEC), and lymphocyte (LYM). The WSIs are split into 29 for training and 25 for validation/testing. From each WSI, 800 random patches are sampled at $10\\mathrm{X}$ magnification, with a resolution of $224\\times 224$ . After removing low-quality patches, the dataset includes 16,678 patches for training, 300 for validation, and 307 for testing. The training set is unlabeled, while the validation and test sets include pixel-level annotations.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4.1.2. BCSS Dataset",
+ "text_level": 1,
+ "bbox": [
+ 89,
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Following [17], we test our method on the BCSS dataset [2], which contains 151 Regions of Interest (ROIs) extracted from H&E stained WSIs of breast cancer, covering five classes: Tumor (TUM), Stroma (STR), Lymphocytic infiltrate (LYM), Necrosis (NEC), and Other (OTR). Random crops of $224 \\times 224$ resolution are taken from the ROIs, yielding 31,826 patches. These are split into 23,422 patches for training without annotations, 3,418 for validation, and 4,986 for testing.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4.2. Evaluation Protocols and Metrics",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Similar to related works [16, 21], we evaluate our model in the unsupervised, clustering-based setting. Specifically, the output of our model is a pixel-level representation map, which is processed through clustering to generate a probability map indicating the likelihood of each pixel belonging to each cluster center. After applying argmax and upsampling, we obtain a class-agnostic segmentation map. To assign semantic labels to the class-agnostic segmentation map, we align the pseudo-labeled clusters with ground-truth labels across the entire validation set using Hungarian matching [23, 24].",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "To verify the performance of our proposed method and compare with the state-of-the-art methods, we use Mean Intersection over Union (MIoU), Frequency Weighted Intersection over Union (FWIoU) and mean Pixel Accuracy",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "(Acc), as the evaluation metrics. MIoU is computed as the average IoU across all classes, where IoU for each class is defined as the ratio between the intersection and union of the predicted and ground truth regions. FwIoU weights the IoU of each class by its frequency in the dataset, providing a measure that emphasizes performance on more prevalent classes. Acc is the average ratio of correctly classified pixels over all classes, reflecting overall pixel-level accuracy.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4.3. Implementation Details",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Our proposed method and comparison are all implemented using PyTorch 2.4.0 with CUDA 12.3 on one NVIDIA GeForce RTX 3090 GPU. For fair comparisons, we used a DINO pre-trained ViT-S/8 from ImageNet [13] as the backbone. For data preprocessing, we followed previous work [16, 21, 33], adopting geometric transforms as well as photometric transforms. The input image resolution during training is $224 \\times 224$ , while images for validation and testing are resized to $320 \\times 320$ . Each method is trained for one epoch with a batch size of 16. The Adam optimizer is applied with the learning rate set to 5e-4 for the segmentation head and 5e-3 for the clustering head.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "To select optimal hyperparameters, we used Wandb's [5] Sweep agent to perform 50 Bayesian hyperparameter searches for both the compared methods and our method. The best hyperparameters and model were chosen based on the mIoU on the validation set, and these were then evaluated on the test set.",
+ "bbox": [
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+ "page_idx": 5
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+ {
+ "type": "text",
+ "text": "4.4. Quantitative Comparison and Analysis",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "To verify the effectiveness of our proposed method, we compare it with several leading approaches, including STEGO [16], EAGLE [21], HP [33], DepthG [34], and ReCLIP [38], on the LUAD and BCSS datasets. The experimental results on both the validation and test sets are presented in Table 1 and Table 2, respectively.",
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4.4.1. Results on LUAD dataset",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "From Table 1 we can see that our method achieves consistent improvements across multiple metrics. On the validation set, our method outperforms the best-performing baseline by $2.61\\%$ in pixel accuracy, $10.26\\%$ in mIoU, and $1.63\\%$ in FwIoU. Notably, while existing methods struggle to balance performance across various foreground classes, our method demonstrates a marked improvement, particularly in the segmentation of the TE and NEC classes. On the test set, our approach continues to demonstrate superior performance, improving the best baseline by around $6.7\\%$ in pixel accuracy, $5.7\\%$ in mIoU, and $5.3\\%$ in FwIoU. Our method significantly enhances segmentation in TE and NEC categories, with NEC showing an increase of over 12 percentage points compared to the next best-performing method. The segmentation of LYM also benefits from our",
+ "bbox": [
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+ {
+ "type": "page_number",
+ "text": "23337",
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+ {
+ "type": "table",
+ "img_path": "images/624acb949e86aba6414938170bdf8bd062e6de32cd58b020442be18600b7d073.jpg",
+ "table_caption": [
+ "Table 1. Performance evaluation on LUAD dataset. The best result is shown in bold, and the second best result is underlined."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | Validation | Test |
| Foreground IoUs | Acc | mIoU | FwIoU | Foreground IoUs | Acc | mIoU | FwIoU |
| TE | NEC | LYM | TAS | TE | NEC | LYM | TAS |
| DINO ICCV2021 | 37.75 | 0.47 | 13.64 | 24.31 | 39.4 | 19.04 | 22.02 | 31.91 | 11.34 | 26.41 | 20.71 | 38.77 | 22.59 | 23.48 |
| STEGO ICLR2022 | 29.17 | 7.78 | 16.07 | 38.11 | 43.27 | 22.78 | 24.64 | 24.54 | 16.28 | 31.41 | 29.79 | 41.63 | 25.51 | 26.2 |
| HP CVPR2023 | 25.67 | 15.09 | 14.32 | 36.57 | 38.22 | 22.92 | 21.6 | 24.16 | 24.16 | 31.06 | 30.81 | 40.2 | 28.01 | 25.27 |
| ReCLIP CVPR2024 | 21.37 | 2.47 | 3.63 | 34.8 | 38.9 | 15.57 | 24.11 | 18.53 | 5.68 | 6.25 | 30.81 | 34.17 | 15.32 | 22.37 |
| DepthCVPR2024 | 31.35 | 7.91 | 11.66 | 35.36 | 44.41 | 21.57 | 26.76 | 23.71 | 1.84 | 12.3 | 34.18 | 37.93 | 18.01 | 23.85 |
| EAGLE CVPR2024 | 26.4 | 0.09 | 27.91 | 47.99 | 54.32 | 25.6 | 40.54 | 21.93 | 0.28 | 38.72 | 40.85 | 48.47 | 25.44 | 36.43 |
| Ours | 50.72 | 36.73 | 26.78 | 29.21 | 56.93 | 35.86 | 42.17 | 49.94 | 24.43 | 37.48 | 23.15 | 55.16 | 33.75 | 41.73 |
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+ "img_path": "images/452ff0bc53254f1afb308ee92c8fb53a0edc11e0991074f81a84c77e14106ad1.jpg",
+ "table_caption": [
+ "Table 2. Performance evaluation on BCSS dataset. The best result is shown in bold, and the second best result is underlined."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | Validation | Test |
| Foreground IoUs | Acc | mIoU | FwIoU | Foreground IoUs | Acc | mIoU | FwIoU |
| TUM | STR | LYM | NEC | TUM | STR | LYM | NEC |
| DINO ICCV2021 | 25.54 | 33.88 | 14.91 | 5.48 | 37.36 | 19.95 | 21.21 | 25.27 | 33.04 | 12.92 | 3.84 | 36.79 | 18.77 | 20.48 |
| STEGO ICLR2022 | 57.97 | 50.05 | 37.59 | 12.86 | 63.45 | 39.62 | 46.34 | 45.52 | 43.89 | 24.49 | 3.79 | 51.81 | 29.42 | 32.13 |
| HP CVPR2023 | 26.99 | 44.48 | 36.35 | 12.26 | 43.83 | 30.02 | 26.13 | 16.23 | 41.61 | 34.55 | 3.23 | 41.28 | 23.91 | 28.33 |
| ReCLIP CVPR2024 | 22.02 | 33.14 | 3.87 | 3.53 | 38.47 | 15.64 | 26.25 | 22.76 | 33.63 | 3.78 | 2.68 | 40.0 | 15.71 | 27.0 |
| DepthCVPR2024 | 25.7 | 31.71 | 19.07 | 17.09 | 41.39 | 23.39 | 25.73 | 32.42 | 31.58 | 14.48 | 16.38 | 45.0 | 23.72 | 29.1 |
| EAGLE CVPR2024 | 24.32 | 38.55 | 14.86 | 4.63 | 41.29 | 20.59 | 26.3 | 22.42 | 37.74 | 13.78 | 3.83 | 40.69 | 19.45 | 25.87 |
| Ours | 52.08 | 54.49 | 35.52 | 9.84 | 63.65 | 37.99 | 47.22 | 46.11 | 55.51 | 39.3 | 10.28 | 61.54 | 37.8 | 43.46 |
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+ "type": "text",
+ "text": "approach, with a notable gain over most baselines. Moreover, the methods ReCLIP and DepthG achieve the lowest mIoU on the test set among all compared methods. We hypothesize that this is due to their additional incorporation of pre-trained knowledge from CLIP and depth estimation, which may be incompatible with the medical domain. These results highlight the effectiveness of our proposed framework in capturing robust and discriminative representations for unsupervised histopathological segmentation.",
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+ "text": "4.4.2. Results on BCSS dataset",
+ "text_level": 1,
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+ "text": "We further evaluate our method on the BCSS dataset, the quantitative results are shown in Table 2. From the validation set results, our method achieves competitive performance across all evaluation metrics. On the test set, our method consistently outperforms all baselines in every metric. Compared to the best-performing baseline, we observe significant improvements of approximately $9.73\\%$ in pixel accuracy, $8.38\\%$ in mIoU, and $11.33\\%$ in FwIoU. Our model achieves the best IoU scores across all four foreground categories, with particularly notable gains in STR and LYM, surpassing the second-best results by over $11.62\\%$ and $4.75\\%$ , respectively.",
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+ "text": "4.5. Ablation Studies",
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+ "text": "To further validate the contributions of different components in our approach, we conduct ablation studies on the",
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+ "table_caption": [
+ "Table 3. Ablation studies on LUAD dataset. S, O, E and I denote our baseline STEGO [16], OPCC, EMA and ILSAF respectively."
+ ],
+ "table_footnote": [],
+ "table_body": "| Modules | Validation | Test |
| S | O | E | I | Acc | mIoU | FwIoU | Acc | mIoU |
| ✓ | | | | 43.27 | 22.78 | 24.64 | 41.63 | 25.51 |
| ✓ | ✓ | | | 50.73 | 27.54 | 31.70 | 48.17 | 30.20 |
| ✓ | ✓ | ✓ | | 55.27 | 30.07 | 37.56 | 51.95 | 32.53 |
| ✓ | | | ✓ | 55.58 | 31.65 | 39.5 | 45.66 | 29.27 |
| ✓ | ✓ | ✓ | ✓ | 56.93 | 35.86 | 42.17 | 55.16 | 33.75 |
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+ "text": "LUAD dataset by progressively incorporating the Overlapping Patches Consistency Constraint (OPCC) and InterLayer Self-Attention Fusion (ILSAF) into the baseline STEGO framework. The results are summarized in Table 3.",
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+ "text": "4.5.1. Effectiveness of OPCC",
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+ "text": "Starting with the baseline STEGO model, we observe relatively lower segmentation performance on the validation and test sets. When the Overlap module is introduced, it leads to noticeable improvements, increasing mIoU by $4.76\\%$ on the validation set and $4.69\\%$ on the test set. This demonstrates the effectiveness of the OPCC in enforcing the backbone's ability in extracting consistent contextual information. Furthermore, when the EMA is incorporated, the segmentation performance continues to improve, with an mIoU increase to $30.07\\%$ on the validation set and $32.53\\%$",
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+ "text": "on the test set.",
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+ "text": "4.5.2. Effectiveness of ILSAF",
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+ "text": "Similarly, incorporating the ILSAF module alone results in a significant performance gain, improving mIoU by $8.87\\%$ on the validation set and $3.76\\%$ on the test set compared to the baseline. This highlights the advantage of leveraging multi-level feature interactions through inter-layer self-attention to enhance feature representations for unsupervised semantic segmentation.",
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+ "text": "Finally, integrating both OPCC and ILSAF modules leads to the best performance across all evaluation metrics, confirming that these two components work synergistically to enhance segmentation quality.",
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+ "text": "4.5.3. Different feature fusion strategies",
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+ "img_path": "images/a737d539f797ee44485251d7fadaa61e3e347f4688821f81100667c29aa65525.jpg",
+ "table_caption": [
+ "Table 4. Different multi-layer feature fusion strategies on the LUAD dataset."
+ ],
+ "table_footnote": [],
+ "table_body": "| Fusion | Validation | Test |
| Acc | mIoU | FwIoU | Acc | mIoU | FwIoU |
| w/o | 43.27 | 22.78 | 24.64 | 41.63 | 25.51 | 26.2 |
| Add | 46.63 | 28.08 | 29.35 | 44.31 | 25.78 | 28.43 |
| Mul | 51.21 | 22.31 | 34.11 | 42.91 | 20.36 | 28.49 |
| Cat | 47.01 | 27.54 | 31.94 | 42.11 | 26.6 | 27.18 |
| ILSAF | 55.58 | 31.65 | 39.5 | 45.66 | 29.27 | 29.6 |
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+ "text": "As shown in Table 4, we first conduct simple multi-layer feature fusion approaches (Add, Mul, and Cat). The experimental results indicate that employing multi-layer features can improve certain metrics relative to the baseline. However, these methods do not fully capture the relationships among different feature levels. In contrast, our proposed ILSAF strategy utilizes self-attention plus importance-weighting to adaptively highlight the features from different Transformer layers, which allows the model to focus on meaningful correlations rather than simply mixing or stacking feature maps in a hand-crafted manner, leading to consistently higher performance on both the validation and test sets.",
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+ "text": "4.6. Visual Comparison",
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+ "type": "text",
+ "text": "To evaluate our method, we conducted visual comparisons with leading approaches, including DINO [9], STEGO [16], EAGLE [21], and HP [33], on the LUAD test set (Fig. 3). The baseline methods showed varying levels of misidentification, introducing non-existent categories like NEC and TAS, particularly in the fifth row where only TE and LYM are present in the ground truth. In contrast, our method accurately identified the correct categories with superior precision.",
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+ {
+ "type": "text",
+ "text": "Visualizations of the BCSS dataset are shown in Fig. 4. By aligning contextual representations during training,",
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+ "text": "our method outperforms the others in maintaining structural continuity. For example, DINO and EAGLE produce fragmented results with erroneous categories. Our model, however, consistently produces continuous segmentation regions, demonstrating its enhanced ability to preserve topological integrity and outperform the leading methods.",
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+ "img_path": "images/a290aa716b23b8600246078f6f059e6c58084c35c986a70bf63ec69d0816dce1.jpg",
+ "image_caption": [
+ "Figure 3. Visual comparison of segmentation results on LUAD dataset."
+ ],
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+ "img_path": "images/c133348c87c1c5d446da6265c3492a65c7f69021a10c084becfde07432ef8a4c.jpg",
+ "image_caption": [
+ "Figure 4. Visual comparison of segmentation results on BCSS dataset."
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+ "text": "5. Conclusion",
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+ {
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+ "text": "Unsupervised Semantic Segmentation is a highly challenging task in computer vision. Most existing methods are incompatible for digital pathology image USS tasks due to their limited capacity in encoding task-specific contextual information within digital pathology images. To alleviate this, we propose OPCC to capture consistent global contextual features across structurally similar images. Additionally, an ILSAF modules is proposed to generate discriminative pixel representations with fine-grained details and semantic information for pixel clustering. Extensive experiments on two public pathology image segmentation datasets demonstrate the effectiveness and superiority of our approach in medical USS tasks.",
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+ "text": "Acknowledgements",
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+ "text": "This work was supported in part by the Key Area Research and Development Program of Guangzhou (Industry Chain) under Grant No. 2024B01W0029, the Science and Technology Project of the Guangzhou Economic and Technological Development Zone under Grant No. 2023GH18, and the Guangdong Provincial Key Laboratory of Artificial Intelligence in Medical Image Analysis and Application under Grant No. 2022B1212010011.",
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+ {
+ "type": "text",
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+ "[39] Shanshan Wang, Cheng Li, Rongpin Wang, Zaiyi Liu, Meiyun Wang, Hongna Tan, Yaping Wu, Xinfeng Liu, Hui Sun, Rui Yang, et al. Annotation-efficient deep learning for automatic medical image segmentation. Nature communications, 12(1):5915, 2021. 1",
+ "[40] Zhonghua Wu, Yicheng Wu, Guosheng Lin, and Jianfei Cai. Reliability-adaptive consistency regularization for weakly-supervised point cloud segmentation. International Journal of Computer Vision, 132(6):2276-2289, 2024. 2",
+ "[41] Linsen Xie, Wentian Cai, and Ying Gao. Dmcgnet: A novel network for medical image segmentation with dense self-mimic and channel grouping mechanism. IEEE Journal of Biomedical and Health Informatics, 26(10):5013-5024, 2022. 2",
+ "[42] Zhaoyuan Yin, Pichao Wang, Fan Wang, Xianzhe Xu, Hanling Zhang, Hao Li, and Rong Jin. Transfgu: a top-down approach to fine-grained unsupervised semantic segmentation. In European conference on computer vision, pages 73-89. Springer, 2022. 1",
+ "[43] Kaining Ying, Qing Zhong, Weian Mao, Zhenhua Wang, Hao Chen, Lin Yuanbo Wu, Yifan Liu, Chengxiang Fan, Yunzhi Zhuge, and Chunhua Shen. Ctvis: Consistent training for online video instance segmentation. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 899-908, 2023. 2",
+ "[44] Yunxiao Zhao and Liang Bai. Contrastive clustering with a graph consistency constraint. Pattern Recognition, 146: 110032, 2024. 2, 3",
+ "[45] Yuan Zhong, Chenhui Tang, Yumeng Yang, Ruoxi Qi, Kang Zhou, Yuqi Gong, Pheng Ann Heng, Janet H Hsiao, and Qi Dou. Weakly-supervised medical image segmentation with gaze annotations. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 530-540. Springer, 2024. 1"
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diff --git a/2025/Unsupervised Histopathological Image Semantic Segmentation with Overlapping Patches Consistency Constraint/c7ca9d94-b46a-45fa-8735-814dc1aec4fe_model.json b/2025/Unsupervised Histopathological Image Semantic Segmentation with Overlapping Patches Consistency Constraint/c7ca9d94-b46a-45fa-8735-814dc1aec4fe_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..109ab92bb9ee59fd0dbb64e518a2104dc2296104
--- /dev/null
+++ b/2025/Unsupervised Histopathological Image Semantic Segmentation with Overlapping Patches Consistency Constraint/c7ca9d94-b46a-45fa-8735-814dc1aec4fe_model.json
@@ -0,0 +1,2453 @@
+[
+ [
+ {
+ "type": "header",
+ "bbox": [
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+ "angle": 0,
+ "content": "CVF"
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+ "type": "header",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.093,
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+ "angle": 0,
+ "content": "Unsupervised Histopathological Image Semantic Segmentation with Overlapping Patches Consistency Constraint"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Wentian Cai\\(^{1,2,*}\\) Weizhao Weng\\(^{1,*}\\) Zihao Huang\\(^{1}\\) Yandan Chen\\(^{1}\\) Siquan Huang\\(^{1}\\) Ping Gao\\(^{3,\\dagger}\\) Victor C. M. Leung\\(^{4}\\) Ying Gao\\(^{1,2,\\dagger}\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\(^{1}\\)School of Computer Science and Engineering, South China University of Technology \n\\(^{2}\\)Guangdong Provincial Key Laboratory of Artificial Intelligence in Medical Image Analysis and Application \n\\(^{3}\\)Department of Geriatric Respiratory Medicine, Guangdong Provincial People's Hospital \n\\(^{4}\\)Department of Electrical and Computer Engineering, University of British Columbia"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.327,
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+ ],
+ "angle": 0,
+ "content": "Abstract"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Massive requirement for pixel-wise annotations in histopathological image segmentation poses a significant challenge, leading to increasing interest in Unsupervised Semantic Segmentation (USS) as a viable alternative. Pre-trained model-based methods have been widely used in USS, achieving promising segmentation performance. However, these methods are less capable for medical image USS tasks due to their limited ability in encoding task-specific contextual information. In this paper, we propose a context-based Overlapping Patches Consistency Constraint (OPCC), which employs the consistency constraint between the local overlapping region's similarity and global context similarity, achieving consistent class representation in similar environments. Additionally, we introduce an InterLayer Self-Attention Fusion (ILSAF) module that employs a multi-head self-attention mechanism along with InterLayer Importance-Weighting to generate context-aware and semantically discriminative pixel representations, improving pixel clustering accuracy. Extensive experiments on two public histopathological image segmentation datasets demonstrate that our approach significantly outperforms state-of-the-art methods by a large margin, with mIoU surpassing previous leading work by 5.74 and 8.38 percentage points on the two datasets, respectively."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.484,
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+ "angle": 0,
+ "content": "Semantic segmentation is an important research topic in medical image analysis [3, 26, 30, 32, 35], which supports critical tasks in disease diagnosis and treatment planning by accurately delineating regions of tumors or lesions. How-"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.34,
+ 0.908,
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+ "angle": 0,
+ "content": "ever, deep learning-based segmentation methods typically require pixel-level annotations from pathologists, which is costly in terms of time and expertise [12, 20, 39]. As a result, researchers have turned their attention to weakly supervised [6, 10, 17, 22, 25, 45] and unsupervised semantic segmentation (USS) [11, 16, 18, 19, 21, 31, 33, 34, 36-38, 42] approaches, which can train segmentation models without pixel-level annotations and thus reduce the burden of manual labeling. In this paper, we focus on the unsupervised semantic segmentation of histopathological images, where we aim to capture the structural properties of tissue sections using only unlabeled data."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Clustering-based strategies have been proposed to tackle this problem and have become a common choice for USS. Early methods [11, 19, 36] generally train the segmentation network from scratch via self-supervised feature learning to maximize the mutual information between an image and its augmentations. This approach helps the model learn meaningful representations for clustering without relying on labeled data. More recently, STEGO [16] proposed a method that separates feature learning from cluster compactification, leveraging large-scale pre-trained backbones and contrastive objectives to distill semantic relationships between image patches. Based on this idea, many follow-up works [21, 33, 34] focus on obtaining more semantically meaningful and compact patch features to aid subsequent clustering. However, we point out their limitations in that they inevitably rely on the frozen backbone features, which are inadequate for digital pathology image USS tasks due to the lack of task-specific contextual information."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To alleviate this, in this paper, we propose a context-based Overlapping Patches Consistency Constraint (OPCC), to achieve consistent class representation in similar environments. Motivated by clinical experience [4, 8], which indicates that contextual information plays a critical role in the interpretation of pathological images, we observe that referring to the structure and morphology of the"
+ },
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+ "type": "page_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "*These authors contributed equally to this work."
+ },
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+ "type": "page_footnote",
+ "bbox": [
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+ "content": "†Corresponding authors: Ying Gao (gaoying@scut.edu.cn), Ping Gao (gaoping8599@gdph.org.cn)."
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+ [
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "surrounding regions can reveal lesion characteristics more accurately. Specifically, the representation of a pathological image depends on its context: the same tissue should exhibit more similar representations when situated in similar environments, whereas different contexts yield dissimilar representations. Based on this observation, our OPCC module extracts overlapping sub-images from the input image. After encoding these sub-images with the backbone, we obtain representations for both the locally overlapping regions and the global context. The similarity of the overlapping region's representations is then used as prior knowledge to guide the backbone, facilitating consistency between the local overlapping region's similarity and global context similarity. This promotes uniform global features across structurally similar images, aiding in maintaining consistent class representation in similar environments and facilitating pixel-level clustering."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In addition, to obtain more robust and discriminative pixel-level representations, we propose an attention-based multi-layer feature fusion method, termed Inter-Layer Self-Attention Fusion (ILSAF). Specifically, self-attention with multiple fixed attention heads is introduced to compute feature correlations from different perspectives. Furthermore, an importance-weighted fusion mechanism is designed to dynamically adjust the aggregation process based on the specific features at each position and for each sample, ensuring the fused features capture both global context and local details."
+ },
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+ "type": "text",
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+ "content": "To summarize our major contributions:"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We propose a context-based Overlapping Patches Consistency Constraint (OPCC) module, achieving consistent global contextual features encoding across structurally similar images, enforcing the backbone's ability in extracting consistent contextual information."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "- We propose an Inter-Layer Self-Attention Fusion (IL-SAF) module that adaptively integrates multi-level features, obtaining context-aware and semantically discriminative pixel representations"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- Extensive experiments on two public histopathological image segmentation datasets demonstrate that our method achieves state-of-the-art performance in unsupervised semantic segmentation."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "content": "2. Related works"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.1. Unsupervised Semantic Segmentation"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Semantic segmentation classifiers every pixel in an image into specific categories, with wide-ranging applications across various scenarios [30, 41]. However, training semantic segmentation models requires a large number of pixel-level labels, the acquisition of which is costly [6]. To address this, numerous researchers have explored training semantic segmentation models without labels [9, 11, 16, 19,"
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "21, 33, 34, 38]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Early studies primarily focused on pixel clustering based on invariance. For instance, IIC [19] introduced a novel clustering objective based on maximizing mutual information between different augmented versions of an image, while PiCIE [11] proposed an unsupervised semantic segmentation (USS) framework that incorporates geometric consistency as an inductive bias for pixel-level clustering."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "More recently, clustering using pre-trained models has become the mainstream approach. DINO-pretrained ViT [9] plays a crucial role in USS methods and serves as a classic USS approach, where the semantically relevant features encoded by the backbone can be directly clustered to generate segmentation maps. Building on this, STEGO [16] separates feature learning from cluster compactification by introducing a novel contrastive loss to distill unsupervised features into discrete semantic labels, achieving significant performance improvements. HP [33] leverages contrastive learning to discover both global and local hidden positives, ensuring rich semantic relationships and local semantic consistency. EAGLE [21] emphasizes object-centric representation learning through a spectral technique (EiCue) and an object-centric contrastive loss. DepthG [34] incorporates depth information to learn scene structure through depth-feature correlation and 3D farthest-point sampling. ReCLIP [38] explicitly models and rectifies the inherent spatial and class biases in CLIP-based USS by employing learnable reference text inputs and a logit-subtraction mechanism, leading to enhanced unsupervised semantic segmentation performance."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "However, despite the performance improvements achieved by these methods, the inherent limitations in spatial contextual modeling of features derived from fixed backbone architectures, hinder further advancements in medical domain."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "2.2. Consistency Constraints in Computer Vision"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Consistency constraints have become a pivotal technique in various computer vision tasks, enhancing model performance by ensuring alignment and coherence across different representations or predictions [14, 15, 27-29, 40, 43, 44]. In segmentation tasks, consistency constraints play a crucial role in improving the robustness and accuracy of models."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "For instance, CTVIS [43] proposed a consistency training framework for video instance segmentation tackles occlusion and deformation, which employs contrastive learning to align instance features across frames, enforcing temporal consistency for robust tracking. RAC-Net [40] is designed for weakly-supervised point cloud segmentation, where it identifies reliable pseudo-labels and applies different consistency constraints based on their reliability."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Unsupervised learning also benefits significantly from"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "23333"
+ }
+ ],
+ [
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+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.196
+ ],
+ "angle": 0,
+ "content": "consistency constraints. In unsupervised monocular depth estimation, left-right consistency constraints [14] ensure that depth maps estimated from different views are aligned. Contrastive clustering with graph consistency constraints [44] further enhances image clustering performance by ensuring consistency in the representation of similar data points."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.197,
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+ ],
+ "angle": 0,
+ "content": "Consistency constraints have proven to be a versatile and effective approach across various computer vision tasks. In our method, we design a Overlapping Patches Consistency Constraint and apply it to unsupervised semantic segmentation."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3. Methodology"
+ },
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+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Before detailing our full pipeline shown in Fig. 1, we first introduce the core USS framework based on pre-trained models as in prior works [16, 21, 34]."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.1. Preliminaries"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Our approach builds upon STEGO [16], where a frozen DINO-pretrained ViT backbone \\(\\mathcal{F}_{\\xi}\\) is introduced to extract image features. Specifically, the input image \\(x \\in \\mathbb{R}^{3 \\times H_{\\mathrm{in}} \\times W_{\\mathrm{in}}}\\) is encoded into a more compact feature space, resulting in a feature map \\(f = \\mathcal{F}_{\\xi}(x) \\in \\mathbb{R}^{HW \\times C}\\), where \\(C\\) is the feature dimension, and \\(H\\) and \\(W\\) are the height and width of the feature map. Subsequently, a trainable segmentation head \\(S\\), which includes both linear and nonlinear transformations, further transforms these features into the code space, yielding the feature encoding \\(s = S(f) \\in \\mathbb{R}^{HW \\times Q}\\), where \\(Q\\) represents the encoding dimension."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.1.1. Feature Compactification"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "During the training process, a feature correlation loss is introduced to construct more compact feature encodings. Specifically, given a pair of input images \\( x_{i} \\) and \\( x_{j} \\) (where \\( x_{j} \\) could be selected as \\( x_{i} \\) itself, from KNN of \\( x_{i} \\), or randomly [16]), their corresponding feature maps \\( f_{i} \\) and \\( f_{j} \\), as well as feature encodings \\( s_{i} \\) and \\( s_{j} \\), are obtained through the backbone \\( \\mathcal{F}_{\\xi} \\) and the segmentation head \\( S \\). The feature correlation between \\( f_{i} \\) and \\( f_{j} \\) is computed as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ 0.712,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\operatorname {C o r r} \\left(f _ {i}, f _ {j}\\right) = \\frac {f _ {i} ^ {h w} \\cdot f _ {j} ^ {u v}}{\\| f _ {i} ^ {h w} \\| _ {2} \\| f _ {j} ^ {u v} \\| _ {2}}, \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(\\cdot\\) represents the dot product, and \\(\\| \\cdot \\| _2\\) denotes the \\(L_{2}\\)-norm. Similarly, the correlation between \\(s_i\\) and \\(s_j\\) is obtained through Equation 1. The Correspondence Distillation Loss is then calculated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {d i s t i l l}} = - \\sum_ {h w, u v} \\left(\\operatorname {C o r r} \\left(f _ {i}, f _ {j}\\right) - b\\right) \\max \\left(\\operatorname {C o r r} \\left(s _ {i}, s _ {j}\\right), 0\\right), \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "where \\( b \\) is a scalar bias hyperparameter that adjusts the influence of the correlation term. This loss encourages the"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "feature encodings to maintain high correlation for semantically similar regions while discouraging spurious associations, thereby promoting compact and discriminative feature representations."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3.1.2. Clustering"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Additionally, a cluster head is introduced with \\( K \\) parameterized cluster centers \\( \\{\\mu_k\\}_{k=1}^K \\), where \\( K \\) corresponds to the number of classes. The inner products between the feature encodings \\( s \\) and the cluster centers \\( \\mu_k \\) are computed as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.608,
+ 0.269,
+ 0.905,
+ 0.285
+ ],
+ "angle": 0,
+ "content": "\\[\n\\operatorname {I n n e r P r o d u c t} (\\mathbf {s}, \\boldsymbol {\\mu} _ {k}) = \\mathbf {s} \\cdot \\boldsymbol {\\mu} _ {k}. \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "After computing the inner products, the softmax function is applied to obtain the cluster probability maps \\( M \\in \\mathbb{R}^{K \\times H \\times W} \\). The k-means clustering loss is then calculated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.568,
+ 0.358,
+ 0.905,
+ 0.4
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {c l u s t e r}} = - \\sum_ {k = 1} ^ {K} M _ {k} \\cdot \\text {I n n e r P r o d u c t} (s, \\mu_ {k}). \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "The evaluation process of the model is detailed in Section 4.2."
+ },
+ {
+ "type": "title",
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+ ],
+ "angle": 0,
+ "content": "3.2. Overlapping Patches Consistency Constraint"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This work is motivated by the observation that the same tissue should exhibit more similar representations when situated in similar environments, whereas different contexts yield dissimilar representations. Based on this observation, an Overlapping Patches Consistency Constraint (OPCC) module is proposed, which leverages the similarity of overlapping sub-image features from the input image as a prior to strengthen the consistency between the local overlapping region's similarity and global context similarity."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.614,
+ 0.78,
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+ ],
+ "angle": 0,
+ "content": "3.2.1. Overlapping Region Extraction"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.632,
+ 0.905,
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+ ],
+ "angle": 0,
+ "content": "First, given an input image \\( x \\in \\mathbb{R}^{3 \\times H_{\\mathrm{in}} \\times W_{\\mathrm{in}}} \\), we impose a 5-crop on the image, which yields five sub-images:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.535,
+ 0.674,
+ 0.905,
+ 0.691
+ ],
+ "angle": 0,
+ "content": "\\[\nx _ {k} = \\mathcal {C} (x, p _ {k}), \\quad \\forall k \\in \\{\\text {c e n t e r}, \\mathrm {T L}, \\mathrm {T R}, \\mathrm {B L}, \\mathrm {B R} \\} \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.701,
+ 0.905,
+ 0.777
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathcal{C}(x,p)\\) denotes the cropping operator applied to image \\(x\\) at the region \\(p\\), in which center, TL, TR, BL, BR denote the sub-images in the center, top-left, top-right, bottom-left, and bottom-right region respectively. Each resulting crop \\(x_{k}\\) belongs to \\(\\mathbb{R}^{3\\times H_{crop}\\times W_{crop}}\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.784,
+ 0.791,
+ 0.799
+ ],
+ "angle": 0,
+ "content": "3.2.2. Overlapping Patches Correlation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.802,
+ 0.905,
+ 0.848
+ ],
+ "angle": 0,
+ "content": "Next, these cropped sub-images are fed into the gradient update encoder \\(\\mathcal{F}_{\\theta}\\) to obtain feature representations. Formally, for each crop \\(x_{k}\\), we compute"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.661,
+ 0.859,
+ 0.905,
+ 0.876
+ ],
+ "angle": 0,
+ "content": "\\[\nr _ {k} = \\mathcal {F} _ {\\theta} \\left(x _ {k}\\right), \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.886,
+ 0.891,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "where \\(r_k\\) denotes the representation corresponding to \\(x_{k}\\)"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
+ 0.945,
+ 0.519,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "23334"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.16,
+ 0.089,
+ 0.845,
+ 0.351
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
+ 0.36,
+ 0.908,
+ 0.459
+ ],
+ "angle": 0,
+ "content": "Figure 1. Main architecture of our proposed method. The input image is first subjected to an overlapping crop operation to generate five overlapping sub-images. These sub-images are then processed by the proposed (a) Overlapping Patches Consistency Constraint module, which guides the gradient update encoder \\(\\mathcal{F}_{\\theta}\\) to consistently encode global contextual features across structurally similar images using overlapping patch similarity as a prior (Sec. 3.2). The parameters of \\(\\mathcal{F}_{\\theta}\\) are then updated via EMA to the momentum encoder \\(\\mathcal{F}_{\\xi}\\). Next, multi-layer representations are extracted from the momentum encoder \\(\\mathcal{F}_{\\xi}\\) and fed into the proposed (b) Inter-Layer Self-Attention Fusion (ILSAF) module to generate context-aware and semantically discriminative pixel representations (Sec. 3.3). Finally, following the previous pipeline, feature compactification and clustering are performed to obtain the final pixel-level segmentation results (Sec. 3.1)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.485,
+ 0.484,
+ 0.576
+ ],
+ "angle": 0,
+ "content": "Then we extract patch-level features from overlapping region between two sub-images. Let \\( x_{m}, x_{n} \\in x_{k} \\) be the pair of overlapping sub-images cropped from \\( x \\), \\( P_{m} = \\{p_{m}^{1}, p_{m}^{2}, \\ldots, p_{m}^{HW}\\} \\) and \\( P_{n} = \\{p_{n}^{1}, p_{n}^{2}, \\ldots, p_{n}^{HW}\\} \\) be the sets of patch tokens in \\( x_{m}, x_{n} \\). The patches in the overlapping region between \\( x_{m} \\) and \\( x_{n} \\) are denoted as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.219,
+ 0.582,
+ 0.482,
+ 0.598
+ ],
+ "angle": 0,
+ "content": "\\[\nP _ {\\text {o v e r l a p}} = P _ {m} \\cap P _ {n}. \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.604,
+ 0.484,
+ 0.634
+ ],
+ "angle": 0,
+ "content": "For each overlapping patch \\( p_{\\mathrm{overlap}_i} \\in P_{\\mathrm{overlap}} \\), we retrieve its feature representations \\( r \\) from both feature maps:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.191,
+ 0.645,
+ 0.483,
+ 0.671
+ ],
+ "angle": 0,
+ "content": "\\[\nr _ {m} ^ {\\text {o v e r l a p} _ {i}} = \\mathcal {F} _ {\\theta} \\left(x _ {m}\\right) \\left[ p _ {\\text {o v e r l a p} _ {i}} \\right], \\tag {8}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.194,
+ 0.67,
+ 0.377,
+ 0.687
+ ],
+ "angle": 0,
+ "content": "\\[\nr _ {n} ^ {\\text {o v e r l a p} _ {i}} = \\mathcal {F} _ {\\theta} (x _ {n}) \\left[ p _ {\\text {o v e r l a p} _ {i}} \\right].\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.689,
+ 0.484,
+ 0.748
+ ],
+ "angle": 0,
+ "content": "Afterward, we compute the cosine similarity between the corresponding patches from the overlapping region. Specifically, the similarity for each overlapping patch \\( p_{\\mathrm{overlap}_i} \\) is defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.173,
+ 0.751,
+ 0.483,
+ 0.79
+ ],
+ "angle": 0,
+ "content": "\\[\nS _ {\\text {o v e r l a p} _ {i}} = \\frac {r _ {m} ^ {\\text {o v e r l a p} _ {i}} \\cdot r _ {n} ^ {\\text {o v e r l a p} _ {i}}}{\\left\\| r _ {m} ^ {\\text {o v e r l a p} _ {i}} \\right\\| _ {2} \\left\\| r _ {n} ^ {\\text {o v e r l a p} _ {i}} \\right\\| _ {2}}, \\tag {9}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.795,
+ 0.484,
+ 0.856
+ ],
+ "angle": 0,
+ "content": "where \\(\\cdot\\) represents the dot product, and \\(\\| \\cdot \\| _2\\) denotes the \\(L_{2}\\)-norm. The overall similarity of the overlapping region is then obtained by averaging the similarities of all overlapping patches:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.171,
+ 0.861,
+ 0.483,
+ 0.905
+ ],
+ "angle": 0,
+ "content": "\\[\nS _ {\\text {o v e r l a p}} = \\frac {1}{\\left| P _ {\\text {o v e r l a p}} \\right|} \\sum_ {i = 1} ^ {\\left| P _ {\\text {o v e r l a p}} \\right|} S _ {\\text {o v e r l a p} _ {i}}. \\tag {10}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.485,
+ 0.796,
+ 0.5
+ ],
+ "angle": 0,
+ "content": "3.2.3. Contextual Information Encoding"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.503,
+ 0.907,
+ 0.595
+ ],
+ "angle": 0,
+ "content": "To effectively capture contextual information, we introduce a context token \\( t_{\\mathrm{ctx}} \\) into the encoder \\( \\mathcal{F}_{\\theta} \\), which serves as a global representation that aggregates spatial and semantic information from the input feature maps. Formally, we append \\( t_{\\mathrm{ctx}} \\) to the input sequence before passing it through the transformer layers:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.627,
+ 0.607,
+ 0.907,
+ 0.624
+ ],
+ "angle": 0,
+ "content": "\\[\nt _ {\\mathrm {c t x}, k}, r _ {k} = \\mathcal {F} _ {\\theta} \\left(t _ {\\mathrm {c t x}}, x _ {k}\\right). \\tag {11}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.644,
+ 0.798,
+ 0.659
+ ],
+ "angle": 0,
+ "content": "3.2.4. Similarity Consistency Constraint"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.663,
+ 0.906,
+ 0.754
+ ],
+ "angle": 0,
+ "content": "Following this, the obtained overlapping patches similarity \\( S_{\\mathrm{overlap}} \\) is used as prior knowledge, indicating the degree of difference between the contexts of the overlapping subimages. To align the contextual representations with this prior, an \\( L_{1} \\) loss is introduced between \\( S_{\\mathrm{overlap}} \\) and the similarity of the context token embeddings from \\( x_{m} \\) and \\( x_{n} \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.755,
+ 0.907,
+ 0.813
+ ],
+ "angle": 0,
+ "content": "Let \\( S_{\\mathrm{ctx}} \\) denote the similarity between the context token embeddings \\( t_{\\mathrm{ctx},m} \\) and \\( t_{\\mathrm{ctx},n} \\), computed in the same manner as in Eq. (9). The Overlapping Patches Consistency Constraint loss is then defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.623,
+ 0.828,
+ 0.905,
+ 0.844
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {O P C C}} = \\left| S _ {\\mathrm {c t x}} - S _ {\\text {o v e r l a p}} \\right|. \\tag {12}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.856,
+ 0.906,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "This loss aligns the contextual similarity \\( S_{\\mathrm{ctx}} \\) with the overlapping patches \\( S_{\\mathrm{overlap}} \\), ensuring that structurally similar images share a consistent global context feature."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
+ 0.945,
+ 0.518,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "23335"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.195,
+ 0.089,
+ 0.805,
+ 0.24
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
+ 0.249,
+ 0.908,
+ 0.306
+ ],
+ "angle": 0,
+ "content": "Figure 2. Illustration of our proposed Inter-Layer Self-Attention Fusion (ILSAF) module. Multi-layer representations are extracted from the momentum encoder \\(\\mathcal{F}_{\\xi}\\) and fed into the proposed ILSAF module, which leverages a (a) Multi-Head Self-Attention mechanism to capture correlations between pixel features and employs (b) Inter-Layer Importance-Weighting to adaptively fuse features from different layers, enhancing the overall feature representations."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.331,
+ 0.347,
+ 0.347
+ ],
+ "angle": 0,
+ "content": "3.2.5. EMA Update of the Backbone"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.35,
+ 0.484,
+ 0.397
+ ],
+ "angle": 0,
+ "content": "Finally, the parameters of \\(\\mathcal{F}_{\\theta}\\) are updated to the frozen ViT backbone \\(\\mathcal{F}_{\\xi}\\) using an exponential moving average (EMA) mechanism [1, 7], which is defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.216,
+ 0.409,
+ 0.482,
+ 0.426
+ ],
+ "angle": 0,
+ "content": "\\[\n\\xi \\leftarrow \\alpha \\xi + (1 - \\alpha) \\theta , \\tag {13}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.437,
+ 0.484,
+ 0.528
+ ],
+ "angle": 0,
+ "content": "where \\(\\alpha\\) is the momentum coefficient controlling the update rate, which is set to 0.99 in practice. This EMA update allows the contextual information encoding ability, learned by \\(\\mathcal{F}_{\\theta}\\), to be stably transferred to the unsupervised feature extraction backbone \\(\\mathcal{F}_{\\xi}\\), improving the accuracy of pixel clustering."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.537,
+ 0.387,
+ 0.553
+ ],
+ "angle": 0,
+ "content": "3.3. Inter-Layer Self-Attention Fusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.559,
+ 0.484,
+ 0.635
+ ],
+ "angle": 0,
+ "content": "In order to enhance the representation capability of both fine-grained details and semantic information for unsupervised semantic segmentation in digital pathology images, we propose a Inter-Layer Self-Attention Fusion (ILSAF) module, as illustrated in Fig. 2."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.635,
+ 0.484,
+ 0.742
+ ],
+ "angle": 0,
+ "content": "Specifically, we first extract the output features from the last three Transformer blocks of the ViT backbone \\(\\mathcal{F}_{\\xi}\\), denoted as \\(f_{L-2}, f_{L-1}\\), and \\(f_{L} \\in \\mathbb{R}^{HW \\times C}\\), where \\(HW\\) represents the total number of patches in the image, and \\(C\\) denotes the number of feature channels. To mitigate the scale discrepancy among features from different layers, channel-wise normalization is performed on each feature map."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.748,
+ 0.322,
+ 0.763
+ ],
+ "angle": 0,
+ "content": "3.3.1. Multi-Head Self-Attention"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.767,
+ 0.484,
+ 0.873
+ ],
+ "angle": 0,
+ "content": "As shown in Fig. 2 (a), to capture the interactions among multi-level features, we employ multiple fixed attention heads to compute the feature correlations from different perspectives. First, the normalized features are stacked into a tensor \\( F \\in \\mathbb{R}^{L \\times HW \\times C} \\), where \\( L = 3 \\). Then, fixed linear projections are applied to generate the Query, Key, and Value matrices:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.145,
+ 0.885,
+ 0.484,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "\\[\nQ = F W _ {Q}, \\quad K = F W _ {K}, \\quad V = F W _ {V}, \\tag {14}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.33,
+ 0.907,
+ 0.363
+ ],
+ "angle": 0,
+ "content": "where \\(W_{Q}, W_{K}, W_{V} \\in \\mathbb{R}^{C \\times C}\\) are initialized as identity matrices. The self-attention output is directly computed as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.617,
+ 0.369,
+ 0.907,
+ 0.405
+ ],
+ "angle": 0,
+ "content": "\\[\nF _ {\\text {a t t n}} = \\operatorname {s o f t m a x} \\left(\\frac {Q K ^ {\\top}}{\\sqrt {C}}\\right) V, \\tag {15}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.412,
+ 0.907,
+ 0.52
+ ],
+ "angle": 0,
+ "content": "resulting in features of shape \\(\\mathbb{R}^{L\\times HW\\times C}\\). This process captures the similarity relationships between patches within different Transformer layers and extracts inter-layer interactions from multiple perspectives. Then the fused feature representation \\(F_{\\mathrm{attn}}\\) is unstacked along the first dimension to restore individual layer features \\(f_l^{\\prime}\\in \\mathbb{R}^{HW\\times C}\\), where \\(l\\in \\{L - 2,L - 1,L\\}\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.525,
+ 0.806,
+ 0.541
+ ],
+ "angle": 0,
+ "content": "3.3.2. Inter-Layer Importance-Weighting"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.543,
+ 0.907,
+ 0.605
+ ],
+ "angle": 0,
+ "content": "As depicted in Fig. 2 (b), To further adaptively distinguish the importance of different layer features, we compute the norm of each layer's feature along the channel dimension, obtaining the inter-layer weight:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.631,
+ 0.612,
+ 0.906,
+ 0.639
+ ],
+ "angle": 0,
+ "content": "\\[\n\\alpha_ {l} = \\operatorname {s o f t m a x} \\left(\\| f _ {l} ^ {\\prime} \\| _ {2}\\right), \\tag {16}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.646,
+ 0.908,
+ 0.693
+ ],
+ "angle": 0,
+ "content": "where \\(\\| f_l^{\\prime}\\| _2\\in \\mathbb{R}^C\\) represents the \\(L_{2}\\) norm computed at each patch position for the \\(l\\)-th layer. Finally, the features from different layers \\(l\\) are fused by a weighted summation:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.642,
+ 0.701,
+ 0.907,
+ 0.733
+ ],
+ "angle": 0,
+ "content": "\\[\nf _ {\\text {f u s e}} = \\sum_ {l} \\alpha_ {l} \\odot f _ {l} ^ {\\prime}, \\tag {17}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.74,
+ 0.908,
+ 0.785
+ ],
+ "angle": 0,
+ "content": "where \\(\\odot\\) denotes element-wise multiplication. Lastly, normalization and nonlinear activation are applied to the fused features."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.794,
+ 0.707,
+ 0.81
+ ],
+ "angle": 0,
+ "content": "3.4. Model Optimization"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.816,
+ 0.907,
+ 0.877
+ ],
+ "angle": 0,
+ "content": "After obtaining the fused features \\( f_{\\mathrm{fuse}} \\), we can obtain the segmentation feature encoding \\( s_{\\mathrm{fuse}} \\) through \\( s_{\\mathrm{fuse}} = S(f_{\\mathrm{fuse}}) \\). Consequently, the correspondence distillation loss, mentioned in Eq. 2, can be written as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.546,
+ 0.884,
+ 0.907,
+ 0.904
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {d i s t i l l}} ^ {\\text {I L S A F}} = \\mathcal {L} _ {\\text {d i s t i l l}} \\left(f _ {\\text {f u s e}, i}, f _ {\\text {f u s e}, j}, s _ {\\text {f u s e}, i}, s _ {\\text {f u s e}, j}\\right). \\tag {18}\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
+ 0.945,
+ 0.521,
+ 0.958
+ ],
+ "angle": 0,
+ "content": "23336"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.111,
+ 0.092,
+ 0.457,
+ 0.107
+ ],
+ "angle": 0,
+ "content": "The final training objective is formulated as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.154,
+ 0.117,
+ 0.482,
+ 0.136
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {O P C C}} + \\lambda_ {2} \\mathcal {L} _ {\\text {d i s t i l l}} ^ {\\text {I L S A F}} + \\mathcal {L} _ {\\text {c l u s t e r}}, \\tag {19}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.148,
+ 0.483,
+ 0.179
+ ],
+ "angle": 0,
+ "content": "where \\(\\lambda_{1}\\) and \\(\\lambda_{2}\\) are weights that control the contribution of each loss component, which are set to 0.5 and 1 in practice."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.193,
+ 0.216,
+ 0.21
+ ],
+ "angle": 0,
+ "content": "4. Experiment"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.218,
+ 0.194,
+ 0.233
+ ],
+ "angle": 0,
+ "content": "4.1. Datasets"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.24,
+ 0.483,
+ 0.302
+ ],
+ "angle": 0,
+ "content": "We evaluate the proposed method on two public datasets. The first dataset is the LUng ADenocarcinoma (LUAD) [17] tissue segmentation dataset, and the second is the Breast Cancer Semantic Segmentation (BCSS) [2] dataset."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.309,
+ 0.24,
+ 0.323
+ ],
+ "angle": 0,
+ "content": "4.1.1. LUAD Dataset"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.327,
+ 0.483,
+ 0.48
+ ],
+ "angle": 0,
+ "content": "The LUAD dataset includes whole slide images (WSIs) from 54 patients, covering four tissue types: tumor epithelial (TE), tumor-associated stroma (TAS), necrosis (NEC), and lymphocyte (LYM). The WSIs are split into 29 for training and 25 for validation/testing. From each WSI, 800 random patches are sampled at \\(10\\mathrm{X}\\) magnification, with a resolution of \\(224\\times 224\\). After removing low-quality patches, the dataset includes 16,678 patches for training, 300 for validation, and 307 for testing. The training set is unlabeled, while the validation and test sets include pixel-level annotations."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.487,
+ 0.236,
+ 0.501
+ ],
+ "angle": 0,
+ "content": "4.1.2. BCSS Dataset"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.506,
+ 0.483,
+ 0.643
+ ],
+ "angle": 0,
+ "content": "Following [17], we test our method on the BCSS dataset [2], which contains 151 Regions of Interest (ROIs) extracted from H&E stained WSIs of breast cancer, covering five classes: Tumor (TUM), Stroma (STR), Lymphocytic infiltrate (LYM), Necrosis (NEC), and Other (OTR). Random crops of \\(224 \\times 224\\) resolution are taken from the ROIs, yielding 31,826 patches. These are split into 23,422 patches for training without annotations, 3,418 for validation, and 4,986 for testing."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Evaluation Protocols and Metrics"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "Similar to related works [16, 21], we evaluate our model in the unsupervised, clustering-based setting. Specifically, the output of our model is a pixel-level representation map, which is processed through clustering to generate a probability map indicating the likelihood of each pixel belonging to each cluster center. After applying argmax and upsampling, we obtain a class-agnostic segmentation map. To assign semantic labels to the class-agnostic segmentation map, we align the pseudo-labeled clusters with ground-truth labels across the entire validation set using Hungarian matching [23, 24]."
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "To verify the performance of our proposed method and compare with the state-of-the-art methods, we use Mean Intersection over Union (MIoU), Frequency Weighted Intersection over Union (FWIoU) and mean Pixel Accuracy"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "(Acc), as the evaluation metrics. MIoU is computed as the average IoU across all classes, where IoU for each class is defined as the ratio between the intersection and union of the predicted and ground truth regions. FwIoU weights the IoU of each class by its frequency in the dataset, providing a measure that emphasizes performance on more prevalent classes. Acc is the average ratio of correctly classified pixels over all classes, reflecting overall pixel-level accuracy."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "4.3. Implementation Details"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Our proposed method and comparison are all implemented using PyTorch 2.4.0 with CUDA 12.3 on one NVIDIA GeForce RTX 3090 GPU. For fair comparisons, we used a DINO pre-trained ViT-S/8 from ImageNet [13] as the backbone. For data preprocessing, we followed previous work [16, 21, 33], adopting geometric transforms as well as photometric transforms. The input image resolution during training is \\(224 \\times 224\\), while images for validation and testing are resized to \\(320 \\times 320\\). Each method is trained for one epoch with a batch size of 16. The Adam optimizer is applied with the learning rate set to 5e-4 for the segmentation head and 5e-3 for the clustering head."
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "To select optimal hyperparameters, we used Wandb's [5] Sweep agent to perform 50 Bayesian hyperparameter searches for both the compared methods and our method. The best hyperparameters and model were chosen based on the mIoU on the validation set, and these were then evaluated on the test set."
+ },
+ {
+ "type": "title",
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+ "content": "4.4. Quantitative Comparison and Analysis"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "To verify the effectiveness of our proposed method, we compare it with several leading approaches, including STEGO [16], EAGLE [21], HP [33], DepthG [34], and ReCLIP [38], on the LUAD and BCSS datasets. The experimental results on both the validation and test sets are presented in Table 1 and Table 2, respectively."
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+ "content": "4.4.1. Results on LUAD dataset"
+ },
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+ "content": "From Table 1 we can see that our method achieves consistent improvements across multiple metrics. On the validation set, our method outperforms the best-performing baseline by \\(2.61\\%\\) in pixel accuracy, \\(10.26\\%\\) in mIoU, and \\(1.63\\%\\) in FwIoU. Notably, while existing methods struggle to balance performance across various foreground classes, our method demonstrates a marked improvement, particularly in the segmentation of the TE and NEC classes. On the test set, our approach continues to demonstrate superior performance, improving the best baseline by around \\(6.7\\%\\) in pixel accuracy, \\(5.7\\%\\) in mIoU, and \\(5.3\\%\\) in FwIoU. Our method significantly enhances segmentation in TE and NEC categories, with NEC showing an increase of over 12 percentage points compared to the next best-performing method. The segmentation of LYM also benefits from our"
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+ "content": "Table 1. Performance evaluation on LUAD dataset. The best result is shown in bold, and the second best result is underlined."
+ },
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+ "content": "| Method | Validation | Test |
| Foreground IoUs | Acc | mIoU | FwIoU | Foreground IoUs | Acc | mIoU | FwIoU |
| TE | NEC | LYM | TAS | TE | NEC | LYM | TAS |
| DINO ICCV2021 | 37.75 | 0.47 | 13.64 | 24.31 | 39.4 | 19.04 | 22.02 | 31.91 | 11.34 | 26.41 | 20.71 | 38.77 | 22.59 | 23.48 |
| STEGO ICLR2022 | 29.17 | 7.78 | 16.07 | 38.11 | 43.27 | 22.78 | 24.64 | 24.54 | 16.28 | 31.41 | 29.79 | 41.63 | 25.51 | 26.2 |
| HP CVPR2023 | 25.67 | 15.09 | 14.32 | 36.57 | 38.22 | 22.92 | 21.6 | 24.16 | 24.16 | 31.06 | 30.81 | 40.2 | 28.01 | 25.27 |
| ReCLIP CVPR2024 | 21.37 | 2.47 | 3.63 | 34.8 | 38.9 | 15.57 | 24.11 | 18.53 | 5.68 | 6.25 | 30.81 | 34.17 | 15.32 | 22.37 |
| DepthCVPR2024 | 31.35 | 7.91 | 11.66 | 35.36 | 44.41 | 21.57 | 26.76 | 23.71 | 1.84 | 12.3 | 34.18 | 37.93 | 18.01 | 23.85 |
| EAGLE CVPR2024 | 26.4 | 0.09 | 27.91 | 47.99 | 54.32 | 25.6 | 40.54 | 21.93 | 0.28 | 38.72 | 40.85 | 48.47 | 25.44 | 36.43 |
| Ours | 50.72 | 36.73 | 26.78 | 29.21 | 56.93 | 35.86 | 42.17 | 49.94 | 24.43 | 37.48 | 23.15 | 55.16 | 33.75 | 41.73 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Performance evaluation on BCSS dataset. The best result is shown in bold, and the second best result is underlined."
+ },
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+ "content": "| Method | Validation | Test |
| Foreground IoUs | Acc | mIoU | FwIoU | Foreground IoUs | Acc | mIoU | FwIoU |
| TUM | STR | LYM | NEC | TUM | STR | LYM | NEC |
| DINO ICCV2021 | 25.54 | 33.88 | 14.91 | 5.48 | 37.36 | 19.95 | 21.21 | 25.27 | 33.04 | 12.92 | 3.84 | 36.79 | 18.77 | 20.48 |
| STEGO ICLR2022 | 57.97 | 50.05 | 37.59 | 12.86 | 63.45 | 39.62 | 46.34 | 45.52 | 43.89 | 24.49 | 3.79 | 51.81 | 29.42 | 32.13 |
| HP CVPR2023 | 26.99 | 44.48 | 36.35 | 12.26 | 43.83 | 30.02 | 26.13 | 16.23 | 41.61 | 34.55 | 3.23 | 41.28 | 23.91 | 28.33 |
| ReCLIP CVPR2024 | 22.02 | 33.14 | 3.87 | 3.53 | 38.47 | 15.64 | 26.25 | 22.76 | 33.63 | 3.78 | 2.68 | 40.0 | 15.71 | 27.0 |
| DepthCVPR2024 | 25.7 | 31.71 | 19.07 | 17.09 | 41.39 | 23.39 | 25.73 | 32.42 | 31.58 | 14.48 | 16.38 | 45.0 | 23.72 | 29.1 |
| EAGLE CVPR2024 | 24.32 | 38.55 | 14.86 | 4.63 | 41.29 | 20.59 | 26.3 | 22.42 | 37.74 | 13.78 | 3.83 | 40.69 | 19.45 | 25.87 |
| Ours | 52.08 | 54.49 | 35.52 | 9.84 | 63.65 | 37.99 | 47.22 | 46.11 | 55.51 | 39.3 | 10.28 | 61.54 | 37.8 | 43.46 |
"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "approach, with a notable gain over most baselines. Moreover, the methods ReCLIP and DepthG achieve the lowest mIoU on the test set among all compared methods. We hypothesize that this is due to their additional incorporation of pre-trained knowledge from CLIP and depth estimation, which may be incompatible with the medical domain. These results highlight the effectiveness of our proposed framework in capturing robust and discriminative representations for unsupervised histopathological segmentation."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "4.4.2. Results on BCSS dataset"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We further evaluate our method on the BCSS dataset, the quantitative results are shown in Table 2. From the validation set results, our method achieves competitive performance across all evaluation metrics. On the test set, our method consistently outperforms all baselines in every metric. Compared to the best-performing baseline, we observe significant improvements of approximately \\(9.73\\%\\) in pixel accuracy, \\(8.38\\%\\) in mIoU, and \\(11.33\\%\\) in FwIoU. Our model achieves the best IoU scores across all four foreground categories, with particularly notable gains in STR and LYM, surpassing the second-best results by over \\(11.62\\%\\) and \\(4.75\\%\\), respectively."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.5. Ablation Studies"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "To further validate the contributions of different components in our approach, we conduct ablation studies on the"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Ablation studies on LUAD dataset. S, O, E and I denote our baseline STEGO [16], OPCC, EMA and ILSAF respectively."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Modules | Validation | Test |
| S | O | E | I | Acc | mIoU | FwIoU | Acc | mIoU |
| ✓ | | | | 43.27 | 22.78 | 24.64 | 41.63 | 25.51 |
| ✓ | ✓ | | | 50.73 | 27.54 | 31.70 | 48.17 | 30.20 |
| ✓ | ✓ | ✓ | | 55.27 | 30.07 | 37.56 | 51.95 | 32.53 |
| ✓ | | | ✓ | 55.58 | 31.65 | 39.5 | 45.66 | 29.27 |
| ✓ | ✓ | ✓ | ✓ | 56.93 | 35.86 | 42.17 | 55.16 | 33.75 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "LUAD dataset by progressively incorporating the Overlapping Patches Consistency Constraint (OPCC) and InterLayer Self-Attention Fusion (ILSAF) into the baseline STEGO framework. The results are summarized in Table 3."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.5.1. Effectiveness of OPCC"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ 0.901
+ ],
+ "angle": 0,
+ "content": "Starting with the baseline STEGO model, we observe relatively lower segmentation performance on the validation and test sets. When the Overlap module is introduced, it leads to noticeable improvements, increasing mIoU by \\(4.76\\%\\) on the validation set and \\(4.69\\%\\) on the test set. This demonstrates the effectiveness of the OPCC in enforcing the backbone's ability in extracting consistent contextual information. Furthermore, when the EMA is incorporated, the segmentation performance continues to improve, with an mIoU increase to \\(30.07\\%\\) on the validation set and \\(32.53\\%\\)"
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+ {
+ "type": "page_number",
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+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "on the test set."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
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+ ],
+ "angle": 0,
+ "content": "4.5.2. Effectiveness of ILSAF"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Similarly, incorporating the ILSAF module alone results in a significant performance gain, improving mIoU by \\(8.87\\%\\) on the validation set and \\(3.76\\%\\) on the test set compared to the baseline. This highlights the advantage of leveraging multi-level feature interactions through inter-layer self-attention to enhance feature representations for unsupervised semantic segmentation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Finally, integrating both OPCC and ILSAF modules leads to the best performance across all evaluation metrics, confirming that these two components work synergistically to enhance segmentation quality."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.5.3. Different feature fusion strategies"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Different multi-layer feature fusion strategies on the LUAD dataset."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Fusion | Validation | Test |
| Acc | mIoU | FwIoU | Acc | mIoU | FwIoU |
| w/o | 43.27 | 22.78 | 24.64 | 41.63 | 25.51 | 26.2 |
| Add | 46.63 | 28.08 | 29.35 | 44.31 | 25.78 | 28.43 |
| Mul | 51.21 | 22.31 | 34.11 | 42.91 | 20.36 | 28.49 |
| Cat | 47.01 | 27.54 | 31.94 | 42.11 | 26.6 | 27.18 |
| ILSAF | 55.58 | 31.65 | 39.5 | 45.66 | 29.27 | 29.6 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "As shown in Table 4, we first conduct simple multi-layer feature fusion approaches (Add, Mul, and Cat). The experimental results indicate that employing multi-layer features can improve certain metrics relative to the baseline. However, these methods do not fully capture the relationships among different feature levels. In contrast, our proposed ILSAF strategy utilizes self-attention plus importance-weighting to adaptively highlight the features from different Transformer layers, which allows the model to focus on meaningful correlations rather than simply mixing or stacking feature maps in a hand-crafted manner, leading to consistently higher performance on both the validation and test sets."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.276,
+ 0.729
+ ],
+ "angle": 0,
+ "content": "4.6. Visual Comparison"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "To evaluate our method, we conducted visual comparisons with leading approaches, including DINO [9], STEGO [16], EAGLE [21], and HP [33], on the LUAD test set (Fig. 3). The baseline methods showed varying levels of misidentification, introducing non-existent categories like NEC and TAS, particularly in the fifth row where only TE and LYM are present in the ground truth. In contrast, our method accurately identified the correct categories with superior precision."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.871,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Visualizations of the BCSS dataset are shown in Fig. 4. By aligning contextual representations during training,"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.906,
+ 0.183
+ ],
+ "angle": 0,
+ "content": "our method outperforms the others in maintaining structural continuity. For example, DINO and EAGLE produce fragmented results with erroneous categories. Our model, however, consistently produces continuous segmentation regions, demonstrating its enhanced ability to preserve topological integrity and outperform the leading methods."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.519,
+ 0.195,
+ 0.905,
+ 0.387
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.513,
+ 0.398,
+ 0.907,
+ 0.424
+ ],
+ "angle": 0,
+ "content": "Figure 3. Visual comparison of segmentation results on LUAD dataset."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.518,
+ 0.435,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. Visual comparison of segmentation results on BCSS dataset."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.704,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Unsupervised Semantic Segmentation is a highly challenging task in computer vision. Most existing methods are incompatible for digital pathology image USS tasks due to their limited capacity in encoding task-specific contextual information within digital pathology images. To alleviate this, we propose OPCC to capture consistent global contextual features across structurally similar images. Additionally, an ILSAF modules is proposed to generate discriminative pixel representations with fine-grained details and semantic information for pixel clustering. Extensive experiments on two public pathology image segmentation datasets demonstrate the effectiveness and superiority of our approach in medical USS tasks."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "23339"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.092,
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+ 0.259,
+ 0.108
+ ],
+ "angle": 0,
+ "content": "Acknowledgements"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.116,
+ 0.484,
+ 0.237
+ ],
+ "angle": 0,
+ "content": "This work was supported in part by the Key Area Research and Development Program of Guangzhou (Industry Chain) under Grant No. 2024B01W0029, the Science and Technology Project of the Guangzhou Economic and Technological Development Zone under Grant No. 2023GH18, and the Guangdong Provincial Key Laboratory of Artificial Intelligence in Medical Image Analysis and Application under Grant No. 2022B1212010011."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.093,
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+ 0.268
+ ],
+ "angle": 0,
+ "content": "References"
+ },
+ {
+ "type": "ref_text",
+ "bbox": [
+ 0.1,
+ 0.277,
+ 0.484,
+ 0.332
+ ],
+ "angle": 0,
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+# Unsupervised Histopathological Image Semantic Segmentation with Overlapping Patches Consistency Constraint
+
+Wentian Cai $^{1,2,*}$ Weizhao Weng $^{1,*}$ Zihao Huang $^{1}$ Yandan Chen $^{1}$ Siquan Huang $^{1}$ Ping Gao $^{3,\dagger}$ Victor C. M. Leung $^{4}$ Ying Gao $^{1,2,\dagger}$
+
+$^{1}$ School of Computer Science and Engineering, South China University of Technology
+ $^{2}$ Guangdong Provincial Key Laboratory of Artificial Intelligence in Medical Image Analysis and Application
+ $^{3}$ Department of Geriatric Respiratory Medicine, Guangdong Provincial People's Hospital
+ $^{4}$ Department of Electrical and Computer Engineering, University of British Columbia
+
+# Abstract
+
+Massive requirement for pixel-wise annotations in histopathological image segmentation poses a significant challenge, leading to increasing interest in Unsupervised Semantic Segmentation (USS) as a viable alternative. Pre-trained model-based methods have been widely used in USS, achieving promising segmentation performance. However, these methods are less capable for medical image USS tasks due to their limited ability in encoding task-specific contextual information. In this paper, we propose a context-based Overlapping Patches Consistency Constraint (OPCC), which employs the consistency constraint between the local overlapping region's similarity and global context similarity, achieving consistent class representation in similar environments. Additionally, we introduce an InterLayer Self-Attention Fusion (ILSAF) module that employs a multi-head self-attention mechanism along with InterLayer Importance-Weighting to generate context-aware and semantically discriminative pixel representations, improving pixel clustering accuracy. Extensive experiments on two public histopathological image segmentation datasets demonstrate that our approach significantly outperforms state-of-the-art methods by a large margin, with mIoU surpassing previous leading work by 5.74 and 8.38 percentage points on the two datasets, respectively.
+
+# 1. Introduction
+
+Semantic segmentation is an important research topic in medical image analysis [3, 26, 30, 32, 35], which supports critical tasks in disease diagnosis and treatment planning by accurately delineating regions of tumors or lesions. How-
+
+ever, deep learning-based segmentation methods typically require pixel-level annotations from pathologists, which is costly in terms of time and expertise [12, 20, 39]. As a result, researchers have turned their attention to weakly supervised [6, 10, 17, 22, 25, 45] and unsupervised semantic segmentation (USS) [11, 16, 18, 19, 21, 31, 33, 34, 36-38, 42] approaches, which can train segmentation models without pixel-level annotations and thus reduce the burden of manual labeling. In this paper, we focus on the unsupervised semantic segmentation of histopathological images, where we aim to capture the structural properties of tissue sections using only unlabeled data.
+
+Clustering-based strategies have been proposed to tackle this problem and have become a common choice for USS. Early methods [11, 19, 36] generally train the segmentation network from scratch via self-supervised feature learning to maximize the mutual information between an image and its augmentations. This approach helps the model learn meaningful representations for clustering without relying on labeled data. More recently, STEGO [16] proposed a method that separates feature learning from cluster compactification, leveraging large-scale pre-trained backbones and contrastive objectives to distill semantic relationships between image patches. Based on this idea, many follow-up works [21, 33, 34] focus on obtaining more semantically meaningful and compact patch features to aid subsequent clustering. However, we point out their limitations in that they inevitably rely on the frozen backbone features, which are inadequate for digital pathology image USS tasks due to the lack of task-specific contextual information.
+
+To alleviate this, in this paper, we propose a context-based Overlapping Patches Consistency Constraint (OPCC), to achieve consistent class representation in similar environments. Motivated by clinical experience [4, 8], which indicates that contextual information plays a critical role in the interpretation of pathological images, we observe that referring to the structure and morphology of the
+
+surrounding regions can reveal lesion characteristics more accurately. Specifically, the representation of a pathological image depends on its context: the same tissue should exhibit more similar representations when situated in similar environments, whereas different contexts yield dissimilar representations. Based on this observation, our OPCC module extracts overlapping sub-images from the input image. After encoding these sub-images with the backbone, we obtain representations for both the locally overlapping regions and the global context. The similarity of the overlapping region's representations is then used as prior knowledge to guide the backbone, facilitating consistency between the local overlapping region's similarity and global context similarity. This promotes uniform global features across structurally similar images, aiding in maintaining consistent class representation in similar environments and facilitating pixel-level clustering.
+
+In addition, to obtain more robust and discriminative pixel-level representations, we propose an attention-based multi-layer feature fusion method, termed Inter-Layer Self-Attention Fusion (ILSAF). Specifically, self-attention with multiple fixed attention heads is introduced to compute feature correlations from different perspectives. Furthermore, an importance-weighted fusion mechanism is designed to dynamically adjust the aggregation process based on the specific features at each position and for each sample, ensuring the fused features capture both global context and local details.
+
+To summarize our major contributions:
+
+- We propose a context-based Overlapping Patches Consistency Constraint (OPCC) module, achieving consistent global contextual features encoding across structurally similar images, enforcing the backbone's ability in extracting consistent contextual information.
+- We propose an Inter-Layer Self-Attention Fusion (IL-SAF) module that adaptively integrates multi-level features, obtaining context-aware and semantically discriminative pixel representations
+- Extensive experiments on two public histopathological image segmentation datasets demonstrate that our method achieves state-of-the-art performance in unsupervised semantic segmentation.
+
+# 2. Related works
+
+# 2.1. Unsupervised Semantic Segmentation
+
+Semantic segmentation classifiers every pixel in an image into specific categories, with wide-ranging applications across various scenarios [30, 41]. However, training semantic segmentation models requires a large number of pixel-level labels, the acquisition of which is costly [6]. To address this, numerous researchers have explored training semantic segmentation models without labels [9, 11, 16, 19,
+
+21, 33, 34, 38].
+
+Early studies primarily focused on pixel clustering based on invariance. For instance, IIC [19] introduced a novel clustering objective based on maximizing mutual information between different augmented versions of an image, while PiCIE [11] proposed an unsupervised semantic segmentation (USS) framework that incorporates geometric consistency as an inductive bias for pixel-level clustering.
+
+More recently, clustering using pre-trained models has become the mainstream approach. DINO-pretrained ViT [9] plays a crucial role in USS methods and serves as a classic USS approach, where the semantically relevant features encoded by the backbone can be directly clustered to generate segmentation maps. Building on this, STEGO [16] separates feature learning from cluster compactification by introducing a novel contrastive loss to distill unsupervised features into discrete semantic labels, achieving significant performance improvements. HP [33] leverages contrastive learning to discover both global and local hidden positives, ensuring rich semantic relationships and local semantic consistency. EAGLE [21] emphasizes object-centric representation learning through a spectral technique (EiCue) and an object-centric contrastive loss. DepthG [34] incorporates depth information to learn scene structure through depth-feature correlation and 3D farthest-point sampling. ReCLIP [38] explicitly models and rectifies the inherent spatial and class biases in CLIP-based USS by employing learnable reference text inputs and a logit-subtraction mechanism, leading to enhanced unsupervised semantic segmentation performance.
+
+However, despite the performance improvements achieved by these methods, the inherent limitations in spatial contextual modeling of features derived from fixed backbone architectures, hinder further advancements in medical domain.
+
+# 2.2. Consistency Constraints in Computer Vision
+
+Consistency constraints have become a pivotal technique in various computer vision tasks, enhancing model performance by ensuring alignment and coherence across different representations or predictions [14, 15, 27-29, 40, 43, 44]. In segmentation tasks, consistency constraints play a crucial role in improving the robustness and accuracy of models.
+
+For instance, CTVIS [43] proposed a consistency training framework for video instance segmentation tackles occlusion and deformation, which employs contrastive learning to align instance features across frames, enforcing temporal consistency for robust tracking. RAC-Net [40] is designed for weakly-supervised point cloud segmentation, where it identifies reliable pseudo-labels and applies different consistency constraints based on their reliability.
+
+Unsupervised learning also benefits significantly from
+
+consistency constraints. In unsupervised monocular depth estimation, left-right consistency constraints [14] ensure that depth maps estimated from different views are aligned. Contrastive clustering with graph consistency constraints [44] further enhances image clustering performance by ensuring consistency in the representation of similar data points.
+
+Consistency constraints have proven to be a versatile and effective approach across various computer vision tasks. In our method, we design a Overlapping Patches Consistency Constraint and apply it to unsupervised semantic segmentation.
+
+# 3. Methodology
+
+Before detailing our full pipeline shown in Fig. 1, we first introduce the core USS framework based on pre-trained models as in prior works [16, 21, 34].
+
+# 3.1. Preliminaries
+
+Our approach builds upon STEGO [16], where a frozen DINO-pretrained ViT backbone $\mathcal{F}_{\xi}$ is introduced to extract image features. Specifically, the input image $x \in \mathbb{R}^{3 \times H_{\mathrm{in}} \times W_{\mathrm{in}}}$ is encoded into a more compact feature space, resulting in a feature map $f = \mathcal{F}_{\xi}(x) \in \mathbb{R}^{HW \times C}$ , where $C$ is the feature dimension, and $H$ and $W$ are the height and width of the feature map. Subsequently, a trainable segmentation head $S$ , which includes both linear and nonlinear transformations, further transforms these features into the code space, yielding the feature encoding $s = S(f) \in \mathbb{R}^{HW \times Q}$ , where $Q$ represents the encoding dimension.
+
+# 3.1.1. Feature Compactification
+
+During the training process, a feature correlation loss is introduced to construct more compact feature encodings. Specifically, given a pair of input images $x_{i}$ and $x_{j}$ (where $x_{j}$ could be selected as $x_{i}$ itself, from KNN of $x_{i}$ , or randomly [16]), their corresponding feature maps $f_{i}$ and $f_{j}$ , as well as feature encodings $s_{i}$ and $s_{j}$ , are obtained through the backbone $\mathcal{F}_{\xi}$ and the segmentation head $S$ . The feature correlation between $f_{i}$ and $f_{j}$ is computed as follows:
+
+$$
+\operatorname {C o r r} \left(f _ {i}, f _ {j}\right) = \frac {f _ {i} ^ {h w} \cdot f _ {j} ^ {u v}}{\| f _ {i} ^ {h w} \| _ {2} \| f _ {j} ^ {u v} \| _ {2}}, \tag {1}
+$$
+
+where $\cdot$ represents the dot product, and $\| \cdot \| _2$ denotes the $L_{2}$ -norm. Similarly, the correlation between $s_i$ and $s_j$ is obtained through Equation 1. The Correspondence Distillation Loss is then calculated as:
+
+$$
+\mathcal {L} _ {\text {d i s t i l l}} = - \sum_ {h w, u v} \left(\operatorname {C o r r} \left(f _ {i}, f _ {j}\right) - b\right) \max \left(\operatorname {C o r r} \left(s _ {i}, s _ {j}\right), 0\right), \tag {2}
+$$
+
+where $b$ is a scalar bias hyperparameter that adjusts the influence of the correlation term. This loss encourages the
+
+feature encodings to maintain high correlation for semantically similar regions while discouraging spurious associations, thereby promoting compact and discriminative feature representations.
+
+# 3.1.2. Clustering
+
+Additionally, a cluster head is introduced with $K$ parameterized cluster centers $\{\mu_k\}_{k=1}^K$ , where $K$ corresponds to the number of classes. The inner products between the feature encodings $s$ and the cluster centers $\mu_k$ are computed as follows:
+
+$$
+\operatorname {I n n e r P r o d u c t} (\mathbf {s}, \boldsymbol {\mu} _ {k}) = \mathbf {s} \cdot \boldsymbol {\mu} _ {k}. \tag {3}
+$$
+
+After computing the inner products, the softmax function is applied to obtain the cluster probability maps $M \in \mathbb{R}^{K \times H \times W}$ . The k-means clustering loss is then calculated as:
+
+$$
+\mathcal {L} _ {\text {c l u s t e r}} = - \sum_ {k = 1} ^ {K} M _ {k} \cdot \text {I n n e r P r o d u c t} (s, \mu_ {k}). \tag {4}
+$$
+
+The evaluation process of the model is detailed in Section 4.2.
+
+# 3.2. Overlapping Patches Consistency Constraint
+
+This work is motivated by the observation that the same tissue should exhibit more similar representations when situated in similar environments, whereas different contexts yield dissimilar representations. Based on this observation, an Overlapping Patches Consistency Constraint (OPCC) module is proposed, which leverages the similarity of overlapping sub-image features from the input image as a prior to strengthen the consistency between the local overlapping region's similarity and global context similarity.
+
+# 3.2.1. Overlapping Region Extraction
+
+First, given an input image $x \in \mathbb{R}^{3 \times H_{\mathrm{in}} \times W_{\mathrm{in}}}$ , we impose a 5-crop on the image, which yields five sub-images:
+
+$$
+x _ {k} = \mathcal {C} (x, p _ {k}), \quad \forall k \in \{\text {c e n t e r}, \mathrm {T L}, \mathrm {T R}, \mathrm {B L}, \mathrm {B R} \} \tag {5}
+$$
+
+where $\mathcal{C}(x,p)$ denotes the cropping operator applied to image $x$ at the region $p$ , in which center, TL, TR, BL, BR denote the sub-images in the center, top-left, top-right, bottom-left, and bottom-right region respectively. Each resulting crop $x_{k}$ belongs to $\mathbb{R}^{3\times H_{crop}\times W_{crop}}$ .
+
+# 3.2.2. Overlapping Patches Correlation
+
+Next, these cropped sub-images are fed into the gradient update encoder $\mathcal{F}_{\theta}$ to obtain feature representations. Formally, for each crop $x_{k}$ , we compute
+
+$$
+r _ {k} = \mathcal {F} _ {\theta} \left(x _ {k}\right), \tag {6}
+$$
+
+where $r_k$ denotes the representation corresponding to $x_{k}$
+
+
+Figure 1. Main architecture of our proposed method. The input image is first subjected to an overlapping crop operation to generate five overlapping sub-images. These sub-images are then processed by the proposed (a) Overlapping Patches Consistency Constraint module, which guides the gradient update encoder $\mathcal{F}_{\theta}$ to consistently encode global contextual features across structurally similar images using overlapping patch similarity as a prior (Sec. 3.2). The parameters of $\mathcal{F}_{\theta}$ are then updated via EMA to the momentum encoder $\mathcal{F}_{\xi}$ . Next, multi-layer representations are extracted from the momentum encoder $\mathcal{F}_{\xi}$ and fed into the proposed (b) Inter-Layer Self-Attention Fusion (ILSAF) module to generate context-aware and semantically discriminative pixel representations (Sec. 3.3). Finally, following the previous pipeline, feature compactification and clustering are performed to obtain the final pixel-level segmentation results (Sec. 3.1).
+
+Then we extract patch-level features from overlapping region between two sub-images. Let $x_{m}, x_{n} \in x_{k}$ be the pair of overlapping sub-images cropped from $x$ , $P_{m} = \{p_{m}^{1}, p_{m}^{2}, \ldots, p_{m}^{HW}\}$ and $P_{n} = \{p_{n}^{1}, p_{n}^{2}, \ldots, p_{n}^{HW}\}$ be the sets of patch tokens in $x_{m}, x_{n}$ . The patches in the overlapping region between $x_{m}$ and $x_{n}$ are denoted as:
+
+$$
+P _ {\text {o v e r l a p}} = P _ {m} \cap P _ {n}. \tag {7}
+$$
+
+For each overlapping patch $p_{\mathrm{overlap}_i} \in P_{\mathrm{overlap}}$ , we retrieve its feature representations $r$ from both feature maps:
+
+$$
+r _ {m} ^ {\text {o v e r l a p} _ {i}} = \mathcal {F} _ {\theta} \left(x _ {m}\right) \left[ p _ {\text {o v e r l a p} _ {i}} \right], \tag {8}
+$$
+
+$$
+r _ {n} ^ {\text {o v e r l a p} _ {i}} = \mathcal {F} _ {\theta} (x _ {n}) \left[ p _ {\text {o v e r l a p} _ {i}} \right].
+$$
+
+Afterward, we compute the cosine similarity between the corresponding patches from the overlapping region. Specifically, the similarity for each overlapping patch $p_{\mathrm{overlap}_i}$ is defined as:
+
+$$
+S _ {\text {o v e r l a p} _ {i}} = \frac {r _ {m} ^ {\text {o v e r l a p} _ {i}} \cdot r _ {n} ^ {\text {o v e r l a p} _ {i}}}{\left\| r _ {m} ^ {\text {o v e r l a p} _ {i}} \right\| _ {2} \left\| r _ {n} ^ {\text {o v e r l a p} _ {i}} \right\| _ {2}}, \tag {9}
+$$
+
+where $\cdot$ represents the dot product, and $\| \cdot \| _2$ denotes the $L_{2}$ -norm. The overall similarity of the overlapping region is then obtained by averaging the similarities of all overlapping patches:
+
+$$
+S _ {\text {o v e r l a p}} = \frac {1}{\left| P _ {\text {o v e r l a p}} \right|} \sum_ {i = 1} ^ {\left| P _ {\text {o v e r l a p}} \right|} S _ {\text {o v e r l a p} _ {i}}. \tag {10}
+$$
+
+# 3.2.3. Contextual Information Encoding
+
+To effectively capture contextual information, we introduce a context token $t_{\mathrm{ctx}}$ into the encoder $\mathcal{F}_{\theta}$ , which serves as a global representation that aggregates spatial and semantic information from the input feature maps. Formally, we append $t_{\mathrm{ctx}}$ to the input sequence before passing it through the transformer layers:
+
+$$
+t _ {\mathrm {c t x}, k}, r _ {k} = \mathcal {F} _ {\theta} \left(t _ {\mathrm {c t x}}, x _ {k}\right). \tag {11}
+$$
+
+# 3.2.4. Similarity Consistency Constraint
+
+Following this, the obtained overlapping patches similarity $S_{\mathrm{overlap}}$ is used as prior knowledge, indicating the degree of difference between the contexts of the overlapping subimages. To align the contextual representations with this prior, an $L_{1}$ loss is introduced between $S_{\mathrm{overlap}}$ and the similarity of the context token embeddings from $x_{m}$ and $x_{n}$ .
+
+Let $S_{\mathrm{ctx}}$ denote the similarity between the context token embeddings $t_{\mathrm{ctx},m}$ and $t_{\mathrm{ctx},n}$ , computed in the same manner as in Eq. (9). The Overlapping Patches Consistency Constraint loss is then defined as:
+
+$$
+\mathcal {L} _ {\mathrm {O P C C}} = \left| S _ {\mathrm {c t x}} - S _ {\text {o v e r l a p}} \right|. \tag {12}
+$$
+
+This loss aligns the contextual similarity $S_{\mathrm{ctx}}$ with the overlapping patches $S_{\mathrm{overlap}}$ , ensuring that structurally similar images share a consistent global context feature.
+
+
+Figure 2. Illustration of our proposed Inter-Layer Self-Attention Fusion (ILSAF) module. Multi-layer representations are extracted from the momentum encoder $\mathcal{F}_{\xi}$ and fed into the proposed ILSAF module, which leverages a (a) Multi-Head Self-Attention mechanism to capture correlations between pixel features and employs (b) Inter-Layer Importance-Weighting to adaptively fuse features from different layers, enhancing the overall feature representations.
+
+# 3.2.5. EMA Update of the Backbone
+
+Finally, the parameters of $\mathcal{F}_{\theta}$ are updated to the frozen ViT backbone $\mathcal{F}_{\xi}$ using an exponential moving average (EMA) mechanism [1, 7], which is defined as:
+
+$$
+\xi \leftarrow \alpha \xi + (1 - \alpha) \theta , \tag {13}
+$$
+
+where $\alpha$ is the momentum coefficient controlling the update rate, which is set to 0.99 in practice. This EMA update allows the contextual information encoding ability, learned by $\mathcal{F}_{\theta}$ , to be stably transferred to the unsupervised feature extraction backbone $\mathcal{F}_{\xi}$ , improving the accuracy of pixel clustering.
+
+# 3.3. Inter-Layer Self-Attention Fusion
+
+In order to enhance the representation capability of both fine-grained details and semantic information for unsupervised semantic segmentation in digital pathology images, we propose a Inter-Layer Self-Attention Fusion (ILSAF) module, as illustrated in Fig. 2.
+
+Specifically, we first extract the output features from the last three Transformer blocks of the ViT backbone $\mathcal{F}_{\xi}$ , denoted as $f_{L-2}, f_{L-1}$ , and $f_{L} \in \mathbb{R}^{HW \times C}$ , where $HW$ represents the total number of patches in the image, and $C$ denotes the number of feature channels. To mitigate the scale discrepancy among features from different layers, channel-wise normalization is performed on each feature map.
+
+# 3.3.1. Multi-Head Self-Attention
+
+As shown in Fig. 2 (a), to capture the interactions among multi-level features, we employ multiple fixed attention heads to compute the feature correlations from different perspectives. First, the normalized features are stacked into a tensor $F \in \mathbb{R}^{L \times HW \times C}$ , where $L = 3$ . Then, fixed linear projections are applied to generate the Query, Key, and Value matrices:
+
+$$
+Q = F W _ {Q}, \quad K = F W _ {K}, \quad V = F W _ {V}, \tag {14}
+$$
+
+where $W_{Q}, W_{K}, W_{V} \in \mathbb{R}^{C \times C}$ are initialized as identity matrices. The self-attention output is directly computed as
+
+$$
+F _ {\text {a t t n}} = \operatorname {s o f t m a x} \left(\frac {Q K ^ {\top}}{\sqrt {C}}\right) V, \tag {15}
+$$
+
+resulting in features of shape $\mathbb{R}^{L\times HW\times C}$ . This process captures the similarity relationships between patches within different Transformer layers and extracts inter-layer interactions from multiple perspectives. Then the fused feature representation $F_{\mathrm{attn}}$ is unstacked along the first dimension to restore individual layer features $f_l^{\prime}\in \mathbb{R}^{HW\times C}$ , where $l\in \{L - 2,L - 1,L\}$ .
+
+# 3.3.2. Inter-Layer Importance-Weighting
+
+As depicted in Fig. 2 (b), To further adaptively distinguish the importance of different layer features, we compute the norm of each layer's feature along the channel dimension, obtaining the inter-layer weight:
+
+$$
+\alpha_ {l} = \operatorname {s o f t m a x} \left(\| f _ {l} ^ {\prime} \| _ {2}\right), \tag {16}
+$$
+
+where $\| f_l^{\prime}\| _2\in \mathbb{R}^C$ represents the $L_{2}$ norm computed at each patch position for the $l$ -th layer. Finally, the features from different layers $l$ are fused by a weighted summation:
+
+$$
+f _ {\text {f u s e}} = \sum_ {l} \alpha_ {l} \odot f _ {l} ^ {\prime}, \tag {17}
+$$
+
+where $\odot$ denotes element-wise multiplication. Lastly, normalization and nonlinear activation are applied to the fused features.
+
+# 3.4. Model Optimization
+
+After obtaining the fused features $f_{\mathrm{fuse}}$ , we can obtain the segmentation feature encoding $s_{\mathrm{fuse}}$ through $s_{\mathrm{fuse}} = S(f_{\mathrm{fuse}})$ . Consequently, the correspondence distillation loss, mentioned in Eq. 2, can be written as:
+
+$$
+\mathcal {L} _ {\text {d i s t i l l}} ^ {\text {I L S A F}} = \mathcal {L} _ {\text {d i s t i l l}} \left(f _ {\text {f u s e}, i}, f _ {\text {f u s e}, j}, s _ {\text {f u s e}, i}, s _ {\text {f u s e}, j}\right). \tag {18}
+$$
+
+The final training objective is formulated as follows:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {\text {O P C C}} + \lambda_ {2} \mathcal {L} _ {\text {d i s t i l l}} ^ {\text {I L S A F}} + \mathcal {L} _ {\text {c l u s t e r}}, \tag {19}
+$$
+
+where $\lambda_{1}$ and $\lambda_{2}$ are weights that control the contribution of each loss component, which are set to 0.5 and 1 in practice.
+
+# 4. Experiment
+
+# 4.1. Datasets
+
+We evaluate the proposed method on two public datasets. The first dataset is the LUng ADenocarcinoma (LUAD) [17] tissue segmentation dataset, and the second is the Breast Cancer Semantic Segmentation (BCSS) [2] dataset.
+
+# 4.1.1. LUAD Dataset
+
+The LUAD dataset includes whole slide images (WSIs) from 54 patients, covering four tissue types: tumor epithelial (TE), tumor-associated stroma (TAS), necrosis (NEC), and lymphocyte (LYM). The WSIs are split into 29 for training and 25 for validation/testing. From each WSI, 800 random patches are sampled at $10\mathrm{X}$ magnification, with a resolution of $224\times 224$ . After removing low-quality patches, the dataset includes 16,678 patches for training, 300 for validation, and 307 for testing. The training set is unlabeled, while the validation and test sets include pixel-level annotations.
+
+# 4.1.2. BCSS Dataset
+
+Following [17], we test our method on the BCSS dataset [2], which contains 151 Regions of Interest (ROIs) extracted from H&E stained WSIs of breast cancer, covering five classes: Tumor (TUM), Stroma (STR), Lymphocytic infiltrate (LYM), Necrosis (NEC), and Other (OTR). Random crops of $224 \times 224$ resolution are taken from the ROIs, yielding 31,826 patches. These are split into 23,422 patches for training without annotations, 3,418 for validation, and 4,986 for testing.
+
+# 4.2. Evaluation Protocols and Metrics
+
+Similar to related works [16, 21], we evaluate our model in the unsupervised, clustering-based setting. Specifically, the output of our model is a pixel-level representation map, which is processed through clustering to generate a probability map indicating the likelihood of each pixel belonging to each cluster center. After applying argmax and upsampling, we obtain a class-agnostic segmentation map. To assign semantic labels to the class-agnostic segmentation map, we align the pseudo-labeled clusters with ground-truth labels across the entire validation set using Hungarian matching [23, 24].
+
+To verify the performance of our proposed method and compare with the state-of-the-art methods, we use Mean Intersection over Union (MIoU), Frequency Weighted Intersection over Union (FWIoU) and mean Pixel Accuracy
+
+(Acc), as the evaluation metrics. MIoU is computed as the average IoU across all classes, where IoU for each class is defined as the ratio between the intersection and union of the predicted and ground truth regions. FwIoU weights the IoU of each class by its frequency in the dataset, providing a measure that emphasizes performance on more prevalent classes. Acc is the average ratio of correctly classified pixels over all classes, reflecting overall pixel-level accuracy.
+
+# 4.3. Implementation Details
+
+Our proposed method and comparison are all implemented using PyTorch 2.4.0 with CUDA 12.3 on one NVIDIA GeForce RTX 3090 GPU. For fair comparisons, we used a DINO pre-trained ViT-S/8 from ImageNet [13] as the backbone. For data preprocessing, we followed previous work [16, 21, 33], adopting geometric transforms as well as photometric transforms. The input image resolution during training is $224 \times 224$ , while images for validation and testing are resized to $320 \times 320$ . Each method is trained for one epoch with a batch size of 16. The Adam optimizer is applied with the learning rate set to 5e-4 for the segmentation head and 5e-3 for the clustering head.
+
+To select optimal hyperparameters, we used Wandb's [5] Sweep agent to perform 50 Bayesian hyperparameter searches for both the compared methods and our method. The best hyperparameters and model were chosen based on the mIoU on the validation set, and these were then evaluated on the test set.
+
+# 4.4. Quantitative Comparison and Analysis
+
+To verify the effectiveness of our proposed method, we compare it with several leading approaches, including STEGO [16], EAGLE [21], HP [33], DepthG [34], and ReCLIP [38], on the LUAD and BCSS datasets. The experimental results on both the validation and test sets are presented in Table 1 and Table 2, respectively.
+
+# 4.4.1. Results on LUAD dataset
+
+From Table 1 we can see that our method achieves consistent improvements across multiple metrics. On the validation set, our method outperforms the best-performing baseline by $2.61\%$ in pixel accuracy, $10.26\%$ in mIoU, and $1.63\%$ in FwIoU. Notably, while existing methods struggle to balance performance across various foreground classes, our method demonstrates a marked improvement, particularly in the segmentation of the TE and NEC classes. On the test set, our approach continues to demonstrate superior performance, improving the best baseline by around $6.7\%$ in pixel accuracy, $5.7\%$ in mIoU, and $5.3\%$ in FwIoU. Our method significantly enhances segmentation in TE and NEC categories, with NEC showing an increase of over 12 percentage points compared to the next best-performing method. The segmentation of LYM also benefits from our
+
+Table 1. Performance evaluation on LUAD dataset. The best result is shown in bold, and the second best result is underlined.
+
+| Method | Validation | Test |
| Foreground IoUs | Acc | mIoU | FwIoU | Foreground IoUs | Acc | mIoU | FwIoU |
| TE | NEC | LYM | TAS | TE | NEC | LYM | TAS |
| DINO ICCV2021 | 37.75 | 0.47 | 13.64 | 24.31 | 39.4 | 19.04 | 22.02 | 31.91 | 11.34 | 26.41 | 20.71 | 38.77 | 22.59 | 23.48 |
| STEGO ICLR2022 | 29.17 | 7.78 | 16.07 | 38.11 | 43.27 | 22.78 | 24.64 | 24.54 | 16.28 | 31.41 | 29.79 | 41.63 | 25.51 | 26.2 |
| HP CVPR2023 | 25.67 | 15.09 | 14.32 | 36.57 | 38.22 | 22.92 | 21.6 | 24.16 | 24.16 | 31.06 | 30.81 | 40.2 | 28.01 | 25.27 |
| ReCLIP CVPR2024 | 21.37 | 2.47 | 3.63 | 34.8 | 38.9 | 15.57 | 24.11 | 18.53 | 5.68 | 6.25 | 30.81 | 34.17 | 15.32 | 22.37 |
| DepthCVPR2024 | 31.35 | 7.91 | 11.66 | 35.36 | 44.41 | 21.57 | 26.76 | 23.71 | 1.84 | 12.3 | 34.18 | 37.93 | 18.01 | 23.85 |
| EAGLE CVPR2024 | 26.4 | 0.09 | 27.91 | 47.99 | 54.32 | 25.6 | 40.54 | 21.93 | 0.28 | 38.72 | 40.85 | 48.47 | 25.44 | 36.43 |
| Ours | 50.72 | 36.73 | 26.78 | 29.21 | 56.93 | 35.86 | 42.17 | 49.94 | 24.43 | 37.48 | 23.15 | 55.16 | 33.75 | 41.73 |
+
+Table 2. Performance evaluation on BCSS dataset. The best result is shown in bold, and the second best result is underlined.
+
+| Method | Validation | Test |
| Foreground IoUs | Acc | mIoU | FwIoU | Foreground IoUs | Acc | mIoU | FwIoU |
| TUM | STR | LYM | NEC | TUM | STR | LYM | NEC |
| DINO ICCV2021 | 25.54 | 33.88 | 14.91 | 5.48 | 37.36 | 19.95 | 21.21 | 25.27 | 33.04 | 12.92 | 3.84 | 36.79 | 18.77 | 20.48 |
| STEGO ICLR2022 | 57.97 | 50.05 | 37.59 | 12.86 | 63.45 | 39.62 | 46.34 | 45.52 | 43.89 | 24.49 | 3.79 | 51.81 | 29.42 | 32.13 |
| HP CVPR2023 | 26.99 | 44.48 | 36.35 | 12.26 | 43.83 | 30.02 | 26.13 | 16.23 | 41.61 | 34.55 | 3.23 | 41.28 | 23.91 | 28.33 |
| ReCLIP CVPR2024 | 22.02 | 33.14 | 3.87 | 3.53 | 38.47 | 15.64 | 26.25 | 22.76 | 33.63 | 3.78 | 2.68 | 40.0 | 15.71 | 27.0 |
| DepthCVPR2024 | 25.7 | 31.71 | 19.07 | 17.09 | 41.39 | 23.39 | 25.73 | 32.42 | 31.58 | 14.48 | 16.38 | 45.0 | 23.72 | 29.1 |
| EAGLE CVPR2024 | 24.32 | 38.55 | 14.86 | 4.63 | 41.29 | 20.59 | 26.3 | 22.42 | 37.74 | 13.78 | 3.83 | 40.69 | 19.45 | 25.87 |
| Ours | 52.08 | 54.49 | 35.52 | 9.84 | 63.65 | 37.99 | 47.22 | 46.11 | 55.51 | 39.3 | 10.28 | 61.54 | 37.8 | 43.46 |
+
+approach, with a notable gain over most baselines. Moreover, the methods ReCLIP and DepthG achieve the lowest mIoU on the test set among all compared methods. We hypothesize that this is due to their additional incorporation of pre-trained knowledge from CLIP and depth estimation, which may be incompatible with the medical domain. These results highlight the effectiveness of our proposed framework in capturing robust and discriminative representations for unsupervised histopathological segmentation.
+
+# 4.4.2. Results on BCSS dataset
+
+We further evaluate our method on the BCSS dataset, the quantitative results are shown in Table 2. From the validation set results, our method achieves competitive performance across all evaluation metrics. On the test set, our method consistently outperforms all baselines in every metric. Compared to the best-performing baseline, we observe significant improvements of approximately $9.73\%$ in pixel accuracy, $8.38\%$ in mIoU, and $11.33\%$ in FwIoU. Our model achieves the best IoU scores across all four foreground categories, with particularly notable gains in STR and LYM, surpassing the second-best results by over $11.62\%$ and $4.75\%$ , respectively.
+
+# 4.5. Ablation Studies
+
+To further validate the contributions of different components in our approach, we conduct ablation studies on the
+
+Table 3. Ablation studies on LUAD dataset. S, O, E and I denote our baseline STEGO [16], OPCC, EMA and ILSAF respectively.
+
+| Modules | Validation | Test |
| S | O | E | I | Acc | mIoU | FwIoU | Acc | mIoU |
| ✓ | | | | 43.27 | 22.78 | 24.64 | 41.63 | 25.51 |
| ✓ | ✓ | | | 50.73 | 27.54 | 31.70 | 48.17 | 30.20 |
| ✓ | ✓ | ✓ | | 55.27 | 30.07 | 37.56 | 51.95 | 32.53 |
| ✓ | | | ✓ | 55.58 | 31.65 | 39.5 | 45.66 | 29.27 |
| ✓ | ✓ | ✓ | ✓ | 56.93 | 35.86 | 42.17 | 55.16 | 33.75 |
+
+LUAD dataset by progressively incorporating the Overlapping Patches Consistency Constraint (OPCC) and InterLayer Self-Attention Fusion (ILSAF) into the baseline STEGO framework. The results are summarized in Table 3.
+
+# 4.5.1. Effectiveness of OPCC
+
+Starting with the baseline STEGO model, we observe relatively lower segmentation performance on the validation and test sets. When the Overlap module is introduced, it leads to noticeable improvements, increasing mIoU by $4.76\%$ on the validation set and $4.69\%$ on the test set. This demonstrates the effectiveness of the OPCC in enforcing the backbone's ability in extracting consistent contextual information. Furthermore, when the EMA is incorporated, the segmentation performance continues to improve, with an mIoU increase to $30.07\%$ on the validation set and $32.53\%$
+
+on the test set.
+
+# 4.5.2. Effectiveness of ILSAF
+
+Similarly, incorporating the ILSAF module alone results in a significant performance gain, improving mIoU by $8.87\%$ on the validation set and $3.76\%$ on the test set compared to the baseline. This highlights the advantage of leveraging multi-level feature interactions through inter-layer self-attention to enhance feature representations for unsupervised semantic segmentation.
+
+Finally, integrating both OPCC and ILSAF modules leads to the best performance across all evaluation metrics, confirming that these two components work synergistically to enhance segmentation quality.
+
+# 4.5.3. Different feature fusion strategies
+
+Table 4. Different multi-layer feature fusion strategies on the LUAD dataset.
+
+| Fusion | Validation | Test |
| Acc | mIoU | FwIoU | Acc | mIoU | FwIoU |
| w/o | 43.27 | 22.78 | 24.64 | 41.63 | 25.51 | 26.2 |
| Add | 46.63 | 28.08 | 29.35 | 44.31 | 25.78 | 28.43 |
| Mul | 51.21 | 22.31 | 34.11 | 42.91 | 20.36 | 28.49 |
| Cat | 47.01 | 27.54 | 31.94 | 42.11 | 26.6 | 27.18 |
| ILSAF | 55.58 | 31.65 | 39.5 | 45.66 | 29.27 | 29.6 |
+
+As shown in Table 4, we first conduct simple multi-layer feature fusion approaches (Add, Mul, and Cat). The experimental results indicate that employing multi-layer features can improve certain metrics relative to the baseline. However, these methods do not fully capture the relationships among different feature levels. In contrast, our proposed ILSAF strategy utilizes self-attention plus importance-weighting to adaptively highlight the features from different Transformer layers, which allows the model to focus on meaningful correlations rather than simply mixing or stacking feature maps in a hand-crafted manner, leading to consistently higher performance on both the validation and test sets.
+
+# 4.6. Visual Comparison
+
+To evaluate our method, we conducted visual comparisons with leading approaches, including DINO [9], STEGO [16], EAGLE [21], and HP [33], on the LUAD test set (Fig. 3). The baseline methods showed varying levels of misidentification, introducing non-existent categories like NEC and TAS, particularly in the fifth row where only TE and LYM are present in the ground truth. In contrast, our method accurately identified the correct categories with superior precision.
+
+Visualizations of the BCSS dataset are shown in Fig. 4. By aligning contextual representations during training,
+
+our method outperforms the others in maintaining structural continuity. For example, DINO and EAGLE produce fragmented results with erroneous categories. Our model, however, consistently produces continuous segmentation regions, demonstrating its enhanced ability to preserve topological integrity and outperform the leading methods.
+
+
+Figure 3. Visual comparison of segmentation results on LUAD dataset.
+
+
+Figure 4. Visual comparison of segmentation results on BCSS dataset.
+
+# 5. Conclusion
+
+Unsupervised Semantic Segmentation is a highly challenging task in computer vision. Most existing methods are incompatible for digital pathology image USS tasks due to their limited capacity in encoding task-specific contextual information within digital pathology images. To alleviate this, we propose OPCC to capture consistent global contextual features across structurally similar images. Additionally, an ILSAF modules is proposed to generate discriminative pixel representations with fine-grained details and semantic information for pixel clustering. Extensive experiments on two public pathology image segmentation datasets demonstrate the effectiveness and superiority of our approach in medical USS tasks.
+
+# Acknowledgements
+
+This work was supported in part by the Key Area Research and Development Program of Guangzhou (Industry Chain) under Grant No. 2024B01W0029, the Science and Technology Project of the Guangzhou Economic and Technological Development Zone under Grant No. 2023GH18, and the Guangdong Provincial Key Laboratory of Artificial Intelligence in Medical Image Analysis and Application under Grant No. 2022B1212010011.
+
+# References
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\ No newline at end of file
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+ "content": "- Extensive experiments on two public histopathological image segmentation datasets demonstrate that our method achieves state-of-the-art performance in unsupervised semantic segmentation."
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+ "content": "We evaluate the proposed method on two public datasets. The first dataset is the LUng ADenocarcinoma (LUAD) [17] tissue segmentation dataset, and the second is the Breast Cancer Semantic Segmentation (BCSS) [2] dataset."
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+ "content": ". After removing low-quality patches, the dataset includes 16,678 patches for training, 300 for validation, and 307 for testing. The training set is unlabeled, while the validation and test sets include pixel-level annotations."
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+ "content": "Similar to related works [16, 21], we evaluate our model in the unsupervised, clustering-based setting. Specifically, the output of our model is a pixel-level representation map, which is processed through clustering to generate a probability map indicating the likelihood of each pixel belonging to each cluster center. After applying argmax and upsampling, we obtain a class-agnostic segmentation map. To assign semantic labels to the class-agnostic segmentation map, we align the pseudo-labeled clusters with ground-truth labels across the entire validation set using Hungarian matching [23, 24]."
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+ "content": "To verify the performance of our proposed method and compare with the state-of-the-art methods, we use Mean Intersection over Union (MIoU), Frequency Weighted Intersection over Union (FWIoU) and mean Pixel Accuracy"
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| Foreground IoUs | Acc | mIoU | FwIoU | Foreground IoUs | Acc | mIoU | FwIoU |
| TE | NEC | LYM | TAS | TE | NEC | LYM | TAS |
| DINO ICCV2021 | 37.75 | 0.47 | 13.64 | 24.31 | 39.4 | 19.04 | 22.02 | 31.91 | 11.34 | 26.41 | 20.71 | 38.77 | 22.59 | 23.48 |
| STEGO ICLR2022 | 29.17 | 7.78 | 16.07 | 38.11 | 43.27 | 22.78 | 24.64 | 24.54 | 16.28 | 31.41 | 29.79 | 41.63 | 25.51 | 26.2 |
| HP CVPR2023 | 25.67 | 15.09 | 14.32 | 36.57 | 38.22 | 22.92 | 21.6 | 24.16 | 24.16 | 31.06 | 30.81 | 40.2 | 28.01 | 25.27 |
| ReCLIP CVPR2024 | 21.37 | 2.47 | 3.63 | 34.8 | 38.9 | 15.57 | 24.11 | 18.53 | 5.68 | 6.25 | 30.81 | 34.17 | 15.32 | 22.37 |
| DepthCVPR2024 | 31.35 | 7.91 | 11.66 | 35.36 | 44.41 | 21.57 | 26.76 | 23.71 | 1.84 | 12.3 | 34.18 | 37.93 | 18.01 | 23.85 |
| EAGLE CVPR2024 | 26.4 | 0.09 | 27.91 | 47.99 | 54.32 | 25.6 | 40.54 | 21.93 | 0.28 | 38.72 | 40.85 | 48.47 | 25.44 | 36.43 |
| Ours | 50.72 | 36.73 | 26.78 | 29.21 | 56.93 | 35.86 | 42.17 | 49.94 | 24.43 | 37.48 | 23.15 | 55.16 | 33.75 | 41.73 |
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| Foreground IoUs | Acc | mIoU | FwIoU | Foreground IoUs | Acc | mIoU | FwIoU |
| TUM | STR | LYM | NEC | TUM | STR | LYM | NEC |
| DINO ICCV2021 | 25.54 | 33.88 | 14.91 | 5.48 | 37.36 | 19.95 | 21.21 | 25.27 | 33.04 | 12.92 | 3.84 | 36.79 | 18.77 | 20.48 |
| STEGO ICLR2022 | 57.97 | 50.05 | 37.59 | 12.86 | 63.45 | 39.62 | 46.34 | 45.52 | 43.89 | 24.49 | 3.79 | 51.81 | 29.42 | 32.13 |
| HP CVPR2023 | 26.99 | 44.48 | 36.35 | 12.26 | 43.83 | 30.02 | 26.13 | 16.23 | 41.61 | 34.55 | 3.23 | 41.28 | 23.91 | 28.33 |
| ReCLIP CVPR2024 | 22.02 | 33.14 | 3.87 | 3.53 | 38.47 | 15.64 | 26.25 | 22.76 | 33.63 | 3.78 | 2.68 | 40.0 | 15.71 | 27.0 |
| DepthCVPR2024 | 25.7 | 31.71 | 19.07 | 17.09 | 41.39 | 23.39 | 25.73 | 32.42 | 31.58 | 14.48 | 16.38 | 45.0 | 23.72 | 29.1 |
| EAGLE CVPR2024 | 24.32 | 38.55 | 14.86 | 4.63 | 41.29 | 20.59 | 26.3 | 22.42 | 37.74 | 13.78 | 3.83 | 40.69 | 19.45 | 25.87 |
| Ours | 52.08 | 54.49 | 35.52 | 9.84 | 63.65 | 37.99 | 47.22 | 46.11 | 55.51 | 39.3 | 10.28 | 61.54 | 37.8 | 43.46 |
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| S | O | E | I | Acc | mIoU | FwIoU | Acc | mIoU |
| ✓ | | | | 43.27 | 22.78 | 24.64 | 41.63 | 25.51 |
| ✓ | ✓ | | | 50.73 | 27.54 | 31.70 | 48.17 | 30.20 |
| ✓ | ✓ | ✓ | | 55.27 | 30.07 | 37.56 | 51.95 | 32.53 |
| ✓ | | | ✓ | 55.58 | 31.65 | 39.5 | 45.66 | 29.27 |
| ✓ | ✓ | ✓ | ✓ | 56.93 | 35.86 | 42.17 | 55.16 | 33.75 |
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| Acc | mIoU | FwIoU | Acc | mIoU | FwIoU |
| w/o | 43.27 | 22.78 | 24.64 | 41.63 | 25.51 | 26.2 |
| Add | 46.63 | 28.08 | 29.35 | 44.31 | 25.78 | 28.43 |
| Mul | 51.21 | 22.31 | 34.11 | 42.91 | 20.36 | 28.49 |
| Cat | 47.01 | 27.54 | 31.94 | 42.11 | 26.6 | 27.18 |
| ILSAF | 55.58 | 31.65 | 39.5 | 45.66 | 29.27 | 29.6 |
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+ "text": "Unsupervised Identification of Protein Compositions and Conformations via Implicit Content-Transformation Disentanglement",
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+ "text": "Mostofa Rafid Uddin",
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+ "text": "Pittsburgh, PA 15213, USA.",
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+ "text": "Identifying different protein compositions and conformations from microscopic images of protein mixtures is a challenging open problem. We address this through disentangled representation learning, where separating protein compositions and conformations in an intermediate latent space enables accurate identification. By modeling compositions and conformations as content and transformation, the task can be reduced to disentangling content and transformation. The existing disentangling methods require an explicit parametric form for the transformation, which is unavailable for conformation, making these methods unsuitable. To overcome this limitation, we propose Dual-Contrast, a novel contrastive learning-based method that implicitly parameterizes and disentangles both transformation and content. DualContrast achieves this by generating positive and negative pairs for content and transformation in both data and latent spaces. We demonstrate that existing self-supervised approaches fail under similar implicit parameterization, underscoring the necessity of our method. Through extensive experiments on 3D microscopic images of protein mixtures and additional shape-focused datasets beyond microscopy, we validate our claims and demonstrate the first in-principle fully unsupervised identification of different protein compositions and conformations in 3D microscopic images.",
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+ "text": "Proteins are fundamental building blocks of life, and their structures and functions have been extensively studied for decades [18, 42]. A protein's structure is characterized by its composition (form of a protein), while its function is dictated by which conformation (specific state of the protein's form) it adopts within a system. Historically,",
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+ "text": "a range of experimental and computational methods separately addressed protein composition and conformation [24, 29, 38, 46]. Now, with the emerging technology of cellular cryo-electron tomography (cryo-ET), it is, in principle, possible to simultaneously determine diverse protein compositions and conformations through direct 3D visualization inside cells [50]. In this paper, we pursue the ambitious goal of identifying diverse protein compositions and conformations from such data using a fully unsupervised, data-driven approach.",
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+ "text": "Identifying protein composition and conformations from cellular cryo-ET image datasets requires separating the intrinsic features that define a protein's composition from those that describe its conformation. From an image analysis perspective, protein conformations can be regarded as data transformations that cause changes in the spatial arrangement of protein shape components (Figure 1b). On the other hand, protein compositions are regarded as the overall shape of the protein that is unaltered by such transformations (Figure 1a). In such a manner, the structural features can be disentangled into content factors and transformation factors. Changing the transformation factor changes the conformation of the protein while preserving the protein identity (i.e., composition). Conversely, changing the content factor is analogous to changing the proteins from one identity to another through compositional change (Fig. 1). Thus, disentangling protein composition and conformation becomes the problem of unsupervised disentanglement of content and transformation factors in images.",
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+ "text": "Currently, a few methods exist for unsupervised disentanglement of semantic content and transformation. Among them, [47] performed explicit parameterization of the transformation factor as diffeomorphic transformations and achieved notable disentanglement of content and transformation in several image datasets. [3] and [51] focus on representing known transformation types as transformation codes. [3] performed disentanglement of two-dimensional",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "Figure 1. (a) Different Compositions (change of shape components, overall shape change) (b) Different Conformations (change of spatial arrangement of shape components) (c) Disentangling composition-conformation through content-transformation"
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+ "text": "translation and rotation, while [51] demonstrated disentanglement of a broader set of transformations that can be explicitly parameterized. All of these explicit parameterization methods require that the data transformations have an explicit functional form parameterized by a fixed number of parameters. However, conformation transformations do not have such a well-defined functional form. Moreover, these methods often struggle to accurately recover contents when conformation-like transformations are present in the datasets (Table 1).",
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+ "text": "Given the above-mentioned issues of explicit disentanglement of transformations, we explore the potential of self-supervised learning (SSL) to implicitly represent them. Previous work by [52] theoretically demonstrated that contrastive learning with data augmentation can disentangle the transformations used in augmentation from the semantic content of the data. However, they experimentally observed that this approach also disentangles generative factors beyond the augmentation itself. In other words, using data augmentation with SSL implicitly disentangles several transformations outside of the augmentation used. For instance, in experiments on Causal3DIndent objects, using only rotation as augmentation in an SSL framework also disentangled object position and class labels [52]. While this phenomenon of implicit disentanglement has been observed experimentally to some extent, it remains largely unexplored.",
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+ "text": "Inspired by such findings, in this work, we aim to implicitly disentangle conformation-like transformations from semantic contents for the unsupervised identification of protein composition and conformation. We found that popular SSL methods [6] with geometric data augmentation fail to disentangle conformation-like transformations in shape-focused images of interest (Table 1), often discarding content as transformation and vice versa. This suggests that existing contrastive strategies with data augmentation are insufficient to disentangle conformation-like transformations, highlighting the need for a novel contrastive strategy to achieve the desired results.",
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+ "text": "learning method for implicit content-transformation disentanglement, termed “DualContrast” (Fig. 2). Unlike existing contrastive strategies, DualContrast creates “positive” and “negative” contrastive pairs with respect to both content and transformation latent codes. Specifically, we create negative pairs for transformation and positive pairs for content by simply rotating the samples. Creating positive pairs for transformation codes directly from the input samples is not possible without prior knowledge. We assume that two images with the same transformation should have transformation factors drawn from the same distribution. Consequently, we sample transformation factors from an identical distribution in the transformation space and generate image samples with those transformation factors to create positive pairs for transformation. Given our observation, this encourages the disentanglement of conformation-like transformations in our datasets. In addition, we perform batch permutation during training to create negative pairs for a batch of samples with respect to content. Upon creating both “positive” and “negative” pairs for content and transformation codes, we penalize similarity between negative pairs and distance between positive pairs for each code. Finally, we incorporate these contrastive losses in a Variational Autoencoder (VAE) based architecture with VAE reconstruction loss and train the model in an end-to-end manner.",
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+ "text": "With such a strategy to create contrastive pairs in the VAE-based framework, DualContrast effectively disentangles conformational-like transformations. These include viewpoint variations in Linemod and several writing styles in MNIST. We then applied DualContrast to disentangle protein compositions and conformations in simulated cellular cryo-ET images of proteins with diverse compositions and conformations. This enabled unsupervised identification of protein compositions and conformations directly from 3D cryo-ET images of proteins. This is not achievable by any of the previous methods, and we are the first to achieve such success.",
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+ "Figure 2. Our proposed contrastive learning-based unsupervised content-transformation disentanglement pipeline. (a) The variational inference of content and transformation codes with $L_{\\mathrm{VAE}}$ . (b) contrastive losses between contrastive pairs for content and transformation codes. (c, d) Contrastive pair creation strategy for both content and transformation. Additional visualization available in Appendix Fig. 8."
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+ "- We developed a novel contrastive modeling strategy that creates positive-negative pairs for both content- and transformation-latent factors. We introduced a novel way of designing contrastive pairs for transformation.",
+ "- We demonstrate that DualContrast effectively disentangles conformation-like transformations from semantic content across various shape-focused image datasets."
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+ "text": "Unsupervised Content-Transformation Disentanglement: There are a few [3, 47, 51, 52] approaches that deal with the unsupervised disentanglement of content and transformation. However, these methods perform explicit parameterization of the transformation codes as affine or some specific parameterized transformation. In contrast, our method does not impose any explicit parameterization on the transformation latent codes and does not face the issues of the explicit methods (Section 1).",
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+ "text": "Contrastive Learning based Disentanglement: Contrastive learning is the primary building block of our method. Contrastive Learning with data augmentation with existing approaches, e.g., InfoNCE loss-based SimCLR [6], has been previously used by [25, 52] to isolate content from style. Though in several scenarios, style in shape focused images can be referred to as transformations, these works do not specifically focus on shape focused real-world images. Moreover, our experiments demonstrate that SimCLR with rotation augmentation in a standard encoder-decoder framework leads to very poor disentanglement of content and transformation (Table 1). Also, [52] only creates positive pairs for content and negative pair for style with data augmentation in SimCLR. We have observed this scheme does not work well in our scenario. Unlike these works,",
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+ "text": "our approach uses a novel strategy to create \"negative\" and \"positive\" pairs for both content and transformation of latent codes without any InfoNCE loss.",
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+ "text": "Composition-Conformation Disentanglement: Our method disentangles protein composition and conformation as content and transformation factors from 3D cryo-electron tomography (cryo-ET) subtomograms. Previously, Harmony [51] was used to disentangle large compositional variability in cellular subtomograms. HEMNMA-3D [14] and TomoFlow [15] were used to disentangle conformational variability in subtomograms using known templates. SpatialVAE [3] disentangled conformational variability from 2D cryo-EM images. However, none of them deals with both composition and conformation. Very recently, a method termed Hydra [34], has been developed to reconstruct multiple protein compositions and conformations from 2D cryo-EM images. Our work is the first to directly address both compositional and conformational variability in two different latent spaces for 3D cryo-ET subtomograms.",
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+ "text": "Further discussions on the related works can be found in Appendix—section A.1. in the supplementary document.",
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+ "type": "text",
+ "text": "3. Method",
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+ "type": "text",
+ "text": "3.1. Disentangling Content and Transformation",
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+ "text": "Disentangling content and transformation refers to learning one mapping $h: \\mathcal{X} \\to \\mathcal{C} \\times \\mathcal{Z}$ , where $\\mathcal{X}$ is an input space, $\\mathcal{C}$ and $\\mathcal{Z}$ are the intermediary content and transformation representation spaces respectively. Here, $h$ can be decomposed as $h_c: \\mathcal{X} \\to \\mathcal{C}$ and $h_z: \\mathcal{X} \\to \\mathcal{Z}$ representing the content and transformation mapping, respectively. In an unsupervised setting, distinguishing between content and transformation can be tricky. In this paper, we distinguish between content and transformation with respect to a family of trans",
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+ "text": "7485",
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+ "type": "text",
+ "text": "formations $\\mathcal{T}:\\mathcal{X}\\to \\mathcal{X}$ such that the following two conditions hold:",
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+ "list_items": [
+ "- Condition 1: $\\forall T \\in \\mathcal{T}$ and $\\forall \\mathbf{x} \\in \\mathcal{X}$ , $h_c(T(\\mathbf{x})) = h_c(\\mathbf{x})$ .",
+ "- Condition 2: $\\exists T \\in \\mathcal{T}$ and $\\forall \\mathbf{x}^{(1)},\\mathbf{x}^{(2)} \\in \\mathcal{X}, h_z(T(\\mathbf{x}^{(1)})) = h_z(\\mathbf{x}^{(2)})$"
+ ],
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+ "type": "text",
+ "text": "Condition 1 defines content space which is invariant w.r.t. $\\mathcal{T}$ . On the other hand, condition 2 states that there is a $T\\in \\mathcal{T}$ that can make the transformation of any two samples equal when applied to any one of them. Thus it defines transformation space which is informative of $\\mathcal{T}$ .",
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+ "type": "text",
+ "text": "For content-transformation $(\\mathbf{c} - \\mathbf{z})$ disentangling, changes in $\\mathcal{C}$ must be unaffected by changes in $\\mathcal{Z}$ and vice versa. In our problem setting, no labels associated with the content space $\\mathcal{C}$ or the transformation space $\\mathcal{Z}$ are known. The exact family of transformation $\\mathcal{T}$ is also not known beforehand. Thus, we aim to simultaneously learn the family of transformations $\\mathcal{T}$ and the content factors unaltered by $\\mathcal{T}$ . In our case, $\\mathcal{T}$ must include conformation-modulating transformation.",
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+ "type": "text",
+ "text": "3.2. Method Overview and Notation",
+ "text_level": 1,
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+ "text": "Our method is built upon a variational auto-encoder (VAE) based architecture (Fig. 2), where we perform inference of the content and transformation factors in the data. Consider, a sample space $\\mathcal{X}$ , two latent distribution spaces $\\Phi_Z$ and $\\Phi_C$ , two latent spaces $\\mathcal{Z}$ and $\\mathcal{C}$ . We apply an encoder network $q_{\\psi}:\\mathcal{X}\\to \\mathcal{C}\\times \\mathcal{Z}$ on a sample space $\\mathbf{x}\\in \\mathcal{X}$ to encode content distribution $\\phi_c\\in \\Phi_c$ and transformation distribution $\\phi_z\\in \\Phi_z$ , where $(\\phi_c,\\phi_z) = q_{\\psi}(\\mathbf{x})$ . Latent parameters $\\mathbf{c}\\in \\mathcal{C}$ , $\\mathbf{z}\\in \\mathcal{Z}$ are drawn from distributions $\\phi_c$ and $\\phi_z$ respectively. These parameters are then decoded using a decoder network $p_{\\theta}:\\mathcal{C}\\times \\mathcal{Z}\\rightarrow \\mathcal{X}$ to produce $x_{\\mathrm{recon}} = p_{\\theta}(\\mathbf{c},\\mathbf{z})$ .",
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+ "type": "text",
+ "text": "3.3. Variational Inference of Content and Transformation Codes",
+ "text_level": 1,
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+ "text": "Similar to a variational auto-encoder (VAE) setting, the encoder and decoder network parameters are simultaneously optimized to maximize the variational lower bound to the likelihood $p(\\mathbf{x})$ called the evidence lower bound (ELBO). ELBO maximizes the log-likelihood of the data and minimizes the KL divergence between latent distributions and a prior distribution. Further details on ELBO objective function can be found in Appendix A.2. The log-likelihood term in ELBO is maximized using a reconstruction loss $L_{\\mathrm{recon}}$ . The prior for $\\mathbf{c}$ and $\\mathbf{z}$ , $p(\\mathbf{c})$ and $p(\\mathbf{z})$ respectively are assumed to be standard normal distribution. In short, we write the KL terms as $L_{\\mathrm{KL}(c)}$ and $L_{\\mathrm{KL}(z)}$ . To regularize the effect of prior on the final objective separately for two latent codes, we scale the two losses with two hyperparameters $\\gamma_c$ and $\\gamma_z$ . Our loss function for variational inference becomes:",
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+ "type": "equation",
+ "text": "\n$$\nL _ {\\mathrm {v a e}} = L _ {\\mathrm {r e c}} + \\gamma_ {c} L _ {\\mathrm {K L} (\\mathbf {c})} + \\gamma_ {z} L _ {\\mathrm {K L} (\\mathbf {z})}. \\tag {1}\n$$\n",
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+ "text": "We observed that by deactivating the KL term associated with any one of the codes, the likelihood tends to be optimized through the other latent code. For instance, if $\\gamma_{c}$ is set as 0 and $\\gamma_{z}$ has a large value, then the $L_{\\mathrm{rec}}$ is optimized through $\\mathbf{c}$ only. As a consequence, $\\mathbf{c}$ captures all the information in $\\mathbf{x}$ , whereas $\\mathbf{z}$ becomes totally independent of the data. In such a scenario, $\\mathbf{z}$ will be a random code with no relation to the transformation of the data, which is not desirable.",
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+ "type": "text",
+ "text": "3.4. Creating Contrastive Pair with respect to Content",
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+ "type": "text",
+ "text": "We adopt a contrastive strategy for $\\mathbf{c} - \\mathbf{z}$ disentanglement. We first develop a strategy to impose a structure to the content latent code with contrastive learning. To this end, we create negative and positive pairs for each data sample w.r.t. the content code. Hence, for a batch of samples $\\mathbf{x}$ , we randomize the order of samples or permute the samples in $x$ to obtain $\\mathbf{x}_{\\mathrm{neg}(\\mathbf{c})}$ , and regard them as negative pairs of each other w.r.t the content code. Such strategy is commonly used in traditional self-supervised learning approaches [6, 16]. This approach accounts for the inherent sample heterogeneity in the data. To generate positive pairs w.r.t. the content code for $\\mathbf{x}$ , we transform it with a transformation $T \\in \\mathcal{T}$ to generate $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{c})}$ . We use the encoder $q_{\\psi}$ to generate content codes $\\mathbf{c}$ , $\\mathbf{c}_{\\mathrm{pos}}$ , and $\\mathbf{c}_{\\mathrm{neg}}$ respectively from $\\mathbf{x}$ , $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{c})}$ , and $\\mathbf{x}_{\\mathrm{neg}(\\mathbf{c})}$ . We use a contrastive loss to penalize the distance between $\\mathbf{c}$ and $\\mathbf{c}_{\\mathrm{pos}}$ and the similarity between $\\mathbf{c}$ and $\\mathbf{c}_{\\mathrm{neg}}$ . Our contrastive loss for content latent code can be written as: $L_{\\mathrm{con}(\\mathbf{c})} = L_{\\mathrm{dist}}(\\mathbf{c}, \\mathbf{c}_{\\mathrm{pos}}) + L_{\\mathrm{sim}}(\\mathbf{c}, \\mathbf{c}_{\\mathrm{neg}})$ . To implement $L_{\\mathrm{dist}}$ and $L_{\\mathrm{sim}}$ , we use mean absolute cosine distance and mean absolute cosine similarity, respectively.",
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+ "type": "text",
+ "text": "3.5. Creating Contrastive Pair with respect to Transformation",
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+ "text": "Imposing contrastive loss only on the content code satisfies condition 1 of the c-z disentanglement (Section 3.1), but not the condition 2. In experiments, doing so optimizes the log likelihood through the transformation code, making the content code uninformative. To this end, we also design contrastive losses w.r.t. the transformation code.",
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+ "type": "text",
+ "text": "The negative pair of sample $\\mathbf{x} \\in \\mathcal{X}$ w.r.t. transformation is generated while creating a positive pair of it w.r.t content. This is because a transformation $T$ on $\\mathbf{x}$ alters its transformation, but not its contents. So, we regard $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{c})}$ as $\\mathbf{x}_{\\mathrm{neg}(\\mathbf{z})}$ .",
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+ "type": "text",
+ "text": "However, creating positive pairs of samples w.r.t. transformation is very challenging as they can not be created in the input space, unlike others. To this end, we assume that two samples have the same transformation code if they are generated using an identical transformation factor. This also implicitly satisfies the condition 2 of the $\\mathbf{c} - \\mathbf{z}$ disentanglement (Section 3.1), making $\\mathbf{z}$ code informative of transformation family $\\mathcal{T}$ . We randomly sample $\\mathbf{z}^{(1)}$ and $\\mathbf{z}^{(2)}$",
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+ "type": "page_number",
+ "text": "7486",
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+ "type": "text",
+ "text": "from $\\mathcal{N}(0,1)$ and use the decoder $p_{\\theta}$ to generate samples $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(1)}$ and $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(2)}$ from them (Fig. 2 (c)). In the decoder, as content input, we use content codes $\\mathbf{c}^{(1)}$ and $\\mathbf{c}^{(2)}$ obtained from encoding $\\mathbf{x}^{(1)}$ and $\\mathbf{x}^{(2)}$ , two random samples obtained by permuting the orders in $\\mathbf{x}$ . Consequently, $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(1)} = p_{\\theta}(\\mathbf{c}^{(1)},\\mathbf{z}^{(1)})$ and $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(2)} = p_{\\theta}(\\mathbf{c}^{(2)},\\mathbf{z}^{(2)})$ serve as the positive pairs w.r.t. transformation. We then use the encoder $q_{\\psi}$ to generate $\\mathbf{z}$ , $\\mathbf{z}_{\\mathrm{neg}}$ , $\\mathbf{z}_{\\mathrm{pos}}^{(1)}$ , and $\\mathbf{z}_{\\mathrm{pos}}^{(2)}$ from $\\mathbf{x}$ , $\\mathbf{x}_{\\mathrm{neg}(\\mathbf{z})}$ , $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(1)}$ , and $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(2)}$ respectively. This process can be best described with following pseudocode:",
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+ },
+ {
+ "type": "code",
+ "sub_type": "code",
+ "code_caption": [],
+ "code_body": "x1, x2 = batch.permute(x) # permuted views (c1, ), (c2, ) = Enc(x1), Enc(x2) # encode content z = sample_normal() #z ~ N(0,I) \nx1_pos_z, x2_pos_z = Dec(c1, z), Dec(c2, z)",
+ "guess_lang": "python",
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+ {
+ "type": "text",
+ "text": "We use a contrastive loss to penalize the distance between $\\mathbf{z}_{\\mathrm{pos}}^{(1)}$ and $\\mathbf{z}_{\\mathrm{pos}}^{(2)}$ and similarity between $\\mathbf{z}$ and $\\mathbf{z}_{\\mathrm{neg}}$ . Our contrastive loss for transformation can be written as: $L_{\\mathrm{con(z)}} = L_{\\mathrm{dist}}(\\mathbf{z}_{\\mathrm{pos}}^{(1)},\\mathbf{z}_{\\mathrm{pos}}^{(2)}) + L_{\\mathrm{sim}}(\\mathbf{z},\\mathbf{z}_{\\mathrm{neg}})$ . Similar to $L_{\\mathrm{con(c)}}$ , we use mean absolute cosine distance and mean absolute cosine similarity to implement $L_{\\mathrm{dist}}$ and $L_{\\mathrm{sim}}$ , respectively.",
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+ "type": "text",
+ "text": "Why rotation?: We used rotation as a transformation to create contrastive pairs because only rotation provided our desired disentanglement of conformation-like transformations in the dataset, compared to other transformations such as translation, scale, blur, or color-based transformations (Details in Appendix A.2.4).",
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+ "type": "text",
+ "text": "Objective Function: In summary, we train the encoder and decoder networks by simultaneously minimizing the loss components. Our overall objective function to minimize is:",
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+ "type": "equation",
+ "text": "\n$$\nL = L _ {\\text {v a e}} + L _ {\\text {c o n (c)}} + L _ {\\text {c o n (z)}} \\tag {2}\n$$\n",
+ "text_format": "latex",
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+ "type": "text",
+ "text": "We optimize $L_{\\mathrm{vae}}$ for both $\\mathbf{x}$ and the transformed image $\\mathbf{x}_{\\mathrm{pos}(\\mathbf{c})}$ (same as $\\mathbf{x}_{\\mathrm{neg}(\\mathbf{z})}$ ), which yielded better experimental result.",
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+ {
+ "type": "text",
+ "text": "4. Experiments & Results",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Implementation Details: We implemented the encoder using a Convolutional Neural Network (CNN) and the decoder using a Fully Connected Network (FCN). Our experiments used the same latent dimension for content and transformation codes. We trained our models using NVIDIA RTX A5000 GPUs and AMD Raedon GPUs. We optimized the model parameters with Adam optimizer. The hyperparameters $\\gamma_z$ and $\\gamma_c$ controls how close the $\\mathbf{z}$ and $\\mathbf{c}$ distribution will be to $\\mathcal{N}(0, I)$ . In our experiments, setting a small value ( $\\approx 0.01$ ) for both provided optimal results. Further details of the overall implementation are provided in the Appendix A.3.",
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+ "type": "text",
+ "text": "Evaluation: We evaluated the methods based on two criteria: (1) the informativeness of the predicted $\\mathbf{c}$ and $\\mathbf{z}$",
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+ "text": "codes w.r.t the relevant ground truth $\\mathbf{c}$ and $\\mathbf{z}$ factors, (2) the separateness of the predicted $\\mathbf{c}$ and $\\mathbf{z}$ codes. We performed these evaluations both quantitatively and qualitatively.",
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+ "text": "To this end, we used $D_{\\mathrm{score}}$ and SAP score. $D_{\\mathrm{score}}$ is simply a measurement of how well the ground truth (gt) factors can be predicted from the corresponding latent codes. In our scenario, there are four such quantities - (a) predictivity of content gt given c code $D_{\\mathrm{score}}(c|c)$ or z code $D_{\\mathrm{score}}(c|z)$ (b) predictivity of transformation gt given c code $D_{\\mathrm{score}}(z|c)$ or z code $D_{\\mathrm{score}}(z|z)$ . Similar to [52], we used linear Logistic Regression Classifiers to measure predictivity ( $D_{\\mathrm{score}}$ ). The higher $D_{\\mathrm{score}}$ , the more informative the latent code is with respect to the gt. SAP score for a gt factor is defined as the difference between the highest and second highest predictivities for it given any latent codes. In our case, SAP(c) can be defined as $|D_{\\mathrm{score}}(c|c) - D_{\\mathrm{score}}(c|z)|$ and SAP(z) as $|D_{\\mathrm{score}}(z|z) - D_{\\mathrm{score}}(z|c)|$ . The higher the SAP score, higher the separateness of the latent codes. For qualitative evaluations, we performed downstream tasks like generating images through unsupervised content-transformer transfer and latent space visualization.",
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+ "text": "For protein subtomograms, we performed coarse refinement step of subtomogram averaging [4] to identify proteins resulting from the latent space clusters. We also quantitatively evaluate the latent space clustering result with Adjusted Rand Index (ARI) and the structure resulting from coarse refinement with per-class AUC-FSC (Area Under the Curve of Fourier Shell Correlation) [23]. Further details on these metrics are provided in the Appendix A.3.",
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+ "type": "text",
+ "text": "4.1. DualContrast disentangles conformation-alike transformations from MNIST and LineMod",
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+ "text": "We first examined whether DualContrast can disentangle conformation- alike transformations in simple shape-focused image datasets. To this end, we selected the MNIST handwritten digits dataset and the RGB LineMod singleobject dataset [54], both of which exhibited such transformations. In MNIST, these transformations arise primarily from variations in writing styles, while in LineMod, they are viewpoint changes. Similar to conformations, both transformations cause changes in the arrangement of shape components in the objects, making them suitable for evaluating our method's effectiveness. Details on the MNIST and LineMod RGB dataset are provided in the Appendix.",
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+ "type": "text",
+ "text": "We applied DualContrast and other unsupervised $\\mathbf{c} - \\mathbf{z}$ disentanglement methods (SpatialVAE [3], Harmony [51], VI-TAE [47]) against these datasets. We also tested the existing self-supervised methods, e.g., SimSiam [8], SimCLR [7], Barlow Twins [55], and MoCo [17] with rotation augmentation to assess their implicit disentanglement ability. We evaluated the quantitative scores $D(c|c)$ , $D(c|z)$ , and $\\mathrm{SAP}(c)$ . We used digit classes in MNIST and the object identities in LineMod as ground-truth content factors, re",
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+ "type": "table",
+ "img_path": "images/b15b625f646400fca62ecb5301a3445f1dded821b18dfff31a8b0d8d0d90646e.jpg",
+ "table_caption": [
+ "Table 1. Quantitative disentanglement results of unsupervised content-transformation disentangling methods. Among these methods, SpatialVAE and Harmony put constraints on the z code dimension given their explicit parameterization; others do not. The std. dev. over model training by setting 3 different random seeds remains within $\\pm 0.04$ . $D_{\\mathrm{score}}$ is written as $D$ . ( $\\uparrow$ ) indicates higher score is better. ( $\\downarrow$ ) indicates lower score is better."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | LineMod | Simulated Protein Subtomogram |
| D(c|c) (↑) | D(c|z) (↓), S(z) (↓) | SAP(c) (↑) | D(c|c) (↑) | D(c|z) (↓) | SAP(c) (↑) | D(z|z) (↑) | D(z|c) (↓) | SAP(z) (↑) |
| SpatialVAE | 0.95 | 0.32, 1.0 | 0.63 | 0.69 | 0.93 | 0.24 | 0.71 | 0.57 | 0.14 |
| Harmony | 0.90 | 0.56, 1.0 | 0.34 | 0.95 | 0.01 | 0.94 | 0.52 | 0.90 | 0.38 |
| SimCLR (Discriminative) | 0.62 | 0.40, 0.99 | 0.22 | 0.39 | 0.69 | 0.30 | 0.51 | 0.52 | 0.01 |
| SimCLR (Generative) | 0.61 | 0.79, 0.70 | 0.18 | 0.53 | 0.59 | 0.06 | 0.55 | 0.54 | 0.01 |
| SimSiam | 0.90 | 0.87, 0.70 | 0.03 | 0.31 | 0.52 | 0.21 | 0.80 | 0.75 | 0.04 |
| MoCo | 0.62 | 0.89, 0.74 | 0.27 | 0.76 | 0.59 | 0.17 | 0.55 | 0.58 | 0.02 |
| Barlow Twins | 0.92 | 0.87, 0.71 | 0.05 | 0.95 | 0.80 | 0.15 | 0.82 | 0.5 | 0.32 |
| VAE with 2 latent space | 0.87 | 0.87, 0.72 | 0.0 | 0.79 | 0.82 | 0.03 | 0.85 | 0.85 | 0.0 |
| VITAE | 0.92 | 0.90, 0.99 | 0.02 | - | - | - | - | - | - |
| DualContrast (w/o Lcon(c)) | 0.86 | 0.31, 0.98 | 0.55 | 0.93 | 0.81 | 0.13 | 0.78 | 0.81 | 0.03 |
| DualContrast (w/o Lcon(z)) | 0.79 | 0.86, 0.69 | 0.07 | 0.99 | 0.86 | 0.13 | 0.86 | 0.63 | 0.23 |
| DualContrast | 0.95 | 0.48, 0.77 | 0.47 | 1.00 | 0.56 | 0.44 | 0.86 | 0.64 | 0.22 |
",
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+ "type": "text",
+ "text": "spectively. Since these datasets do not have ground truth transformation factors, $D(z|c)$ , $D(z|z)$ , and $\\mathrm{SAP}(z)$ could not be calculated. To measure whether the transformation factor is really capturing conformation-alike transformation, we introduced a new metric $S(z)$ . To estimate it, we generated paired images by altering the $z$ code while keeping $c$ fixed. After aligning pairs via rotation and translation, we computed their similarity as their average, which was further SSIM normalized between [0, 1] range. We refer to this value as $S(z)$ . $S(z) = 1$ indicates the $z$ code represents only rotation and translation. However, we want it to capture additional conformation-like transformations, so a lower value of $S(z)$ is preferred, similar to $D(c|z)$ .",
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+ "type": "text",
+ "text": "Our quantitative results (Table 1) for LineMod demonstrate the superior performance of DualContrast compared to the baselines. It also shows that the $\\mathbf{z}$ factor in DualContrast contains information other than rotation (low $S(z)$ ), but is also separated from content (low $D(c|z)$ and high $D(c|c)$ . The results on MNIST, presented in the Appendix Section A.4, also yield similar findings.",
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+ "text": "We then performed a qualitative evaluation of image generation with varying $\\mathbf{c}$ and $\\mathbf{z}$ codes in LineMod (Figure 3). We observe that VITAE [47] significantly distorts the images when performing image generation with $\\mathbf{c} - \\mathbf{z}$ transfer. SpatialVAE and Harmony only disentangle in-plane rotation given their design; so changing the $\\mathbf{z}$ code in these methods only rotates the content sample. Due to this, their $S(z) = 1$ . We provided the results obtained with the existing self-supervised methods, e.g., SimCLR, SimSiam, Barlow Twins, etc., with rotation augmentation in the Appendix, whereas none of them yielded satisfactory results. Only DualContrast disentangled different viewpoints or perspectives of the objects as the $\\mathbf{z}$ code, and changing $\\mathbf{z}$ changes the viewpoint of the objects, reflecting the actual conformational-like transformation present in the dataset.",
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+ "text": "We created a realistically simulated [35] cellular cryo-ET subtomogram dataset of 18,000 samples belonging to 4 different protein compositions: nucleosome, pre-fusion, and post-fusion Sars-Cov-2 spike proteins, and Fatty Acid Synthase (FAS) unit. We collected 6 different conformations for Nucleosome, 5 different conformations of pre-fusion spike protein, 1 conformation of post-fusion spike protein, and 6 different conformations of FAS from RCSB PDB [43]. After collecting the PDB templates, we filtered them to 10 Åresolution. Among the filtered structures, only nucleosome conformations has subtly visible differences among them. For the other proteins, conformational differences were visually indistinguishable in the filtered volumes. For each filtered PDB template, 1,000 subtomograms were generated. Each subtomogram is of size $32^{3}$ and contains a protein in random orientation and shift with a very low signal-to-noise (SNR) ratio (Fig. 4). Further details on the dataset properties are provided in the Appendix A.4.",
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+ "Figure 3. Qualitative results of unsupervised $\\mathbf{c} - \\mathbf{z}$ disentanglement on LineMod obtained by (a) VITAE, (b) SpatialVAE, (c) Harmony, and (d) DualContrast, respectively. Images are generated by the Decoders given $\\mathbf{c}$ code from the leftmost column images and $\\mathbf{z}$ code from the topmost row images. For Harmony and Dualcontrast, we also provide a zoomed-in view of several generated images. Additional content-transformation transfer results are available on Appendix Fig. 11."
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+ "Figure 4. Protein composition latent space with sample visualization. (a) Slice-by-slice visualization of x-y slices in 4 sample subtomograms with 4 different compositions. UMAP embedding of c codes in (b) SpatialVAE, (c) SimSiam, (d) Harmony, and (e) DualContrast."
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+ "text": "Siam (Fig. 4(c)), or Harmony (Fig. 4(d)). We further performed coarse refinement step of subtomogram averaging (STA) to identify the protein structures from latent space clusters. STA obtains readily identifiable high-SNR structure from multiple low-SNR subtomograms of a homogenous structure with varying orientations through iterative alignment and averaging [4]. In our experiments, Gaussian Mixture Models (GMM) (with $\\mathrm{K} = 4$ ) were applied to content (c) codes predicted by models, generating clusters of subtomograms. We evaluated the clustering accuracy with ARI scores (Table 2) where DualContrast shows best performance.",
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+ "text": "Afterwards, we refined each cluster of subtomograms using RELION [58] (Fig. 5). SpatialVAE failed to identify any protein compositions, while Harmony identified the FAS, nucleosome, and 2 spike proteins, though 1 spike protein appeared as an unrealistic mixture of FAS and spike",
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+ "text": "protein. RELION's maximum likelihood based classification was unable to identify the post-fusion spike protein. DualContrast successfully identified the FAS, nucleosome, and 2 distinct spike protein compositions. We further reported the average and minimum per-class AUC-FSCs of the refined structures by each methods on Table 2, where DualContrast demonstrates superior performance, supporting our qualitative results.",
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+ "text": "We then investigated the effectiveness of the $\\mathbf{z}$ factor to obtain different protein compositions. One way with the existing approaches was to cluster Harmony's c codes for nucleosome cluster subtomograms. However, this revealed only 1 nucleosome conformation but mistakenly included a spike protein (Fig. 6), suggesting that Harmony [51] cannot be used for conformation identification. RELION's maximum likelihood classification on the nucleosome cluster subtomograms also did not yield distinct conformational",
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+ "image_caption": [
+ "Figure 5. Structures obtained with each method. RELION refinement for each (4) cluster of subtomograms, whereas the clustering is performed using Gaussian Mixture Modeling (GMM) on c codes, predicted by (a) SpatialVAE (d) Harmony, and (e) DualContrast. (b) shows the different protein compositions reconstructed from Hydra (with $\\mathrm{K} = 4$ ). (c) RELION's initial 3D model generation results."
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+ "text": "classes of nucleosome. However, clustering DualContrast's $\\mathbf{z}$ codes followed by RELION averaging identified 4 out of 6 distinct nucleosome conformations with subtle structural changes (Fig. 6), showcasing its ability to disentangle protein composition and conformation, which is unattained by the other existing methods. This finding is further quantitatively validated with ARI scores and per-class AUC-FSCs reported in Table 2.",
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+ "image_caption": [
+ "Figure 6. (a, b) Structures obtained with RELION refinement for the nucleosome subtomograms (identified with previous step Fig. 4) using GMM on (a) Harmony content codes, and (b) DualContrast transformation codes."
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+ "text": "We also trained the recent composition-conformation reconstruction method Hydra [34] using the projection sum (along the z-axis) of the subtomograms, which serves as a rough equivalent to the 2D cryo-EM images that Hydra typically requires as input. Our goal was to determine whether",
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+ "Table 2. Quantitative evaluation of latent space clustering with ARI and protein structures obtained by coarse refinement with per-class AUC-FSC. $(\\uparrow)$ indicates higher score are better."
+ ],
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+ "table_body": "| Method | Composition | Conformation |
| AUC-FSC | ARI (↑) | AUC-FSC | ARI (↑) |
| avg(↑) | min(↑) | avg (↑) | min(↑) |
| SimCLR | 0.42 | 0.32 | 0.55 | 0.18 | 0.10 | 0.01 |
| MoCo | 0.42 | 0.32 | 0.55 | 0.19 | 0.10 | 0.04 |
| Barlow-Twins | 0.50 | 0.44 | 0.30 | 0.28 | 0.18 | 0.05 |
| SimSiam | 0.42 | 0.24 | 0.63 | 0.25 | 0.12 | 0.10 |
| SpatialVAE | 0.09 | 0.07 | 0.01 | 0.10 | 0.04 | 0.01 |
| Hydra | 0.07 | 0.02 | 0.01 | 0.06 | 0.04 | 0.01 |
| Relion | 0.40 | 0.10 | 0.75 | 0.35 | 0.32 | 0.01 |
| Harmony | 0.43 | 0.17 | 0.72 | 0.35 | 0.13 | 0.12 |
| DualContrast | 0.56 | 0.51 | 0.99 | 0.49 | 0.39 | 0.22 |
",
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+ "text": "Hydra could accurately reconstruct protein conformations and compositions. During training, we set $K = 4$ . We provided details on the Hydra training in the Appendix A.4. However, we found that Hydra was unable to reconstruct the correct protein compositions, let alone their conformations (Fig. 5). Instead, it generated artificial proteins with mixed compositions, such as hybrids of nucleosome and FAS or FAS and spike protein. This issue likely arose from Hydra's reliance on 2D projections rather than actual 3D subtomograms, which hindered its ability to distinguish between different 3D protein compositions in our dataset that have overlapping 2D projections.",
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+ "text": "Ablation Study: To evaluate the individual contribution of the contrastive losses, we conducted both quantitative and qualitative ablation analyses of DualContrast. We trained (1) DualContrast without any contrastive loss, which is basically a VAE with two latent spaces, (2) DualContrast with only $L = L_{\\mathrm{VAE}} + L_{\\mathrm{con(z)}}$ , and (3) $L = L_{\\mathrm{VAE}} + L_{\\mathrm{con(c)}}$ . We qualitatively and quantitatively evaluated each model. We show the quantitative results in Table 1 and qualitative results of MNIST in Appendix A.4.4 with additional discussion.",
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+ "text": "5. Conclusion",
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+ "text": "Motivated by the challenge of unsupervised identification of protein compositions and conformations from cryo-ET subtomograms, we propose a method called DualContrast that solves this problem through unsupervised content-transformation disentanglement. DualContrast is a reconstructive method that employs a novel contrastive learning strategy that creates positive and negative pairs for both content and transformation codes, which enables implicit unsupervised disentanglement of conformation-like transformations in images and subtomograms. Our experiments on simulated datasets showcased that DualContrast can in principle disentangle protein compositions and conformations in a fully unsupervised manner, a capability not previously demonstrated. While the additional complexities of experimental data remain a challenge, DualContrast lays a strong foundation and opens an exciting new avenue for advancing this frontier.",
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+ "text": "Acknowledgement",
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+ "text": "This work was supported in part by U.S. NIH grants R35GM158094, R01GM134020 and P41GM103712, NSF grants DBI-1949629, DBI-2238093, IIS-2007595, IIS-2211597, and MCB-2205148. This work was supported in part by Oracle Cloud credits and related resources provided by Oracle for Research, and the computational resources support from AMD HPC Fund. MRU were supported in part by a fellowship from CMU CMLH.",
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+ "[55] Jure Zbontar, Li Jing, Ishan Misra, Yann LeCun, and Stéphane Deny. Barlow twins: Self-supervised learning via redundancy reduction. In International conference on machine learning, pages 12310-12320. PMLR, 2021. 5",
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+ "[57] Keyang Zhou, Bharat Lal Bhatnagar, and Gerard Pons-Moll. Unsupervised shape and pose disentanglement for 3d meshes. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part XXII 16, pages 341-357. Springer, 2020. 12",
+ "[58] Jasenko Zivanov, Takanori Nakane, Björn O Forsberg, Dari Kimanius, Wim JH Hagen, Erik Lindahl, and Sjors HW Scheres. New tools for automated high-resolution cryo-em structure determination in relation-3. elife, 7:e42166, 2018. 7"
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+ "content": "Identifying different protein compositions and conformations from microscopic images of protein mixtures is a challenging open problem. We address this through disentangled representation learning, where separating protein compositions and conformations in an intermediate latent space enables accurate identification. By modeling compositions and conformations as content and transformation, the task can be reduced to disentangling content and transformation. The existing disentangling methods require an explicit parametric form for the transformation, which is unavailable for conformation, making these methods unsuitable. To overcome this limitation, we propose Dual-Contrast, a novel contrastive learning-based method that implicitly parameterizes and disentangles both transformation and content. DualContrast achieves this by generating positive and negative pairs for content and transformation in both data and latent spaces. We demonstrate that existing self-supervised approaches fail under similar implicit parameterization, underscoring the necessity of our method. Through extensive experiments on 3D microscopic images of protein mixtures and additional shape-focused datasets beyond microscopy, we validate our claims and demonstrate the first in-principle fully unsupervised identification of different protein compositions and conformations in 3D microscopic images."
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+ "content": "Proteins are fundamental building blocks of life, and their structures and functions have been extensively studied for decades [18, 42]. A protein's structure is characterized by its composition (form of a protein), while its function is dictated by which conformation (specific state of the protein's form) it adopts within a system. Historically,"
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+ "content": "a range of experimental and computational methods separately addressed protein composition and conformation [24, 29, 38, 46]. Now, with the emerging technology of cellular cryo-electron tomography (cryo-ET), it is, in principle, possible to simultaneously determine diverse protein compositions and conformations through direct 3D visualization inside cells [50]. In this paper, we pursue the ambitious goal of identifying diverse protein compositions and conformations from such data using a fully unsupervised, data-driven approach."
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+ "content": "Identifying protein composition and conformations from cellular cryo-ET image datasets requires separating the intrinsic features that define a protein's composition from those that describe its conformation. From an image analysis perspective, protein conformations can be regarded as data transformations that cause changes in the spatial arrangement of protein shape components (Figure 1b). On the other hand, protein compositions are regarded as the overall shape of the protein that is unaltered by such transformations (Figure 1a). In such a manner, the structural features can be disentangled into content factors and transformation factors. Changing the transformation factor changes the conformation of the protein while preserving the protein identity (i.e., composition). Conversely, changing the content factor is analogous to changing the proteins from one identity to another through compositional change (Fig. 1). Thus, disentangling protein composition and conformation becomes the problem of unsupervised disentanglement of content and transformation factors in images."
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+ "content": "translation and rotation, while [51] demonstrated disentanglement of a broader set of transformations that can be explicitly parameterized. All of these explicit parameterization methods require that the data transformations have an explicit functional form parameterized by a fixed number of parameters. However, conformation transformations do not have such a well-defined functional form. Moreover, these methods often struggle to accurately recover contents when conformation-like transformations are present in the datasets (Table 1)."
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+ "content": "Given the above-mentioned issues of explicit disentanglement of transformations, we explore the potential of self-supervised learning (SSL) to implicitly represent them. Previous work by [52] theoretically demonstrated that contrastive learning with data augmentation can disentangle the transformations used in augmentation from the semantic content of the data. However, they experimentally observed that this approach also disentangles generative factors beyond the augmentation itself. In other words, using data augmentation with SSL implicitly disentangles several transformations outside of the augmentation used. For instance, in experiments on Causal3DIndent objects, using only rotation as augmentation in an SSL framework also disentangled object position and class labels [52]. While this phenomenon of implicit disentanglement has been observed experimentally to some extent, it remains largely unexplored."
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+ "content": "Inspired by such findings, in this work, we aim to implicitly disentangle conformation-like transformations from semantic contents for the unsupervised identification of protein composition and conformation. We found that popular SSL methods [6] with geometric data augmentation fail to disentangle conformation-like transformations in shape-focused images of interest (Table 1), often discarding content as transformation and vice versa. This suggests that existing contrastive strategies with data augmentation are insufficient to disentangle conformation-like transformations, highlighting the need for a novel contrastive strategy to achieve the desired results."
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+ "content": "learning method for implicit content-transformation disentanglement, termed “DualContrast” (Fig. 2). Unlike existing contrastive strategies, DualContrast creates “positive” and “negative” contrastive pairs with respect to both content and transformation latent codes. Specifically, we create negative pairs for transformation and positive pairs for content by simply rotating the samples. Creating positive pairs for transformation codes directly from the input samples is not possible without prior knowledge. We assume that two images with the same transformation should have transformation factors drawn from the same distribution. Consequently, we sample transformation factors from an identical distribution in the transformation space and generate image samples with those transformation factors to create positive pairs for transformation. Given our observation, this encourages the disentanglement of conformation-like transformations in our datasets. In addition, we perform batch permutation during training to create negative pairs for a batch of samples with respect to content. Upon creating both “positive” and “negative” pairs for content and transformation codes, we penalize similarity between negative pairs and distance between positive pairs for each code. Finally, we incorporate these contrastive losses in a Variational Autoencoder (VAE) based architecture with VAE reconstruction loss and train the model in an end-to-end manner."
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+ "content": "With such a strategy to create contrastive pairs in the VAE-based framework, DualContrast effectively disentangles conformational-like transformations. These include viewpoint variations in Linemod and several writing styles in MNIST. We then applied DualContrast to disentangle protein compositions and conformations in simulated cellular cryo-ET images of proteins with diverse compositions and conformations. This enabled unsupervised identification of protein compositions and conformations directly from 3D cryo-ET images of proteins. This is not achievable by any of the previous methods, and we are the first to achieve such success."
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+ "content": "Figure 2. Our proposed contrastive learning-based unsupervised content-transformation disentanglement pipeline. (a) The variational inference of content and transformation codes with \\( L_{\\mathrm{VAE}} \\). (b) contrastive losses between contrastive pairs for content and transformation codes. (c, d) Contrastive pair creation strategy for both content and transformation. Additional visualization available in Appendix Fig. 8."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Unsupervised Content-Transformation Disentanglement: There are a few [3, 47, 51, 52] approaches that deal with the unsupervised disentanglement of content and transformation. However, these methods perform explicit parameterization of the transformation codes as affine or some specific parameterized transformation. In contrast, our method does not impose any explicit parameterization on the transformation latent codes and does not face the issues of the explicit methods (Section 1)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Contrastive Learning based Disentanglement: Contrastive learning is the primary building block of our method. Contrastive Learning with data augmentation with existing approaches, e.g., InfoNCE loss-based SimCLR [6], has been previously used by [25, 52] to isolate content from style. Though in several scenarios, style in shape focused images can be referred to as transformations, these works do not specifically focus on shape focused real-world images. Moreover, our experiments demonstrate that SimCLR with rotation augmentation in a standard encoder-decoder framework leads to very poor disentanglement of content and transformation (Table 1). Also, [52] only creates positive pairs for content and negative pair for style with data augmentation in SimCLR. We have observed this scheme does not work well in our scenario. Unlike these works,"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.365,
+ 0.907,
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+ ],
+ "angle": 0,
+ "content": "our approach uses a novel strategy to create \"negative\" and \"positive\" pairs for both content and transformation of latent codes without any InfoNCE loss."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Composition-Conformation Disentanglement: Our method disentangles protein composition and conformation as content and transformation factors from 3D cryo-electron tomography (cryo-ET) subtomograms. Previously, Harmony [51] was used to disentangle large compositional variability in cellular subtomograms. HEMNMA-3D [14] and TomoFlow [15] were used to disentangle conformational variability in subtomograms using known templates. SpatialVAE [3] disentangled conformational variability from 2D cryo-EM images. However, none of them deals with both composition and conformation. Very recently, a method termed Hydra [34], has been developed to reconstruct multiple protein compositions and conformations from 2D cryo-EM images. Our work is the first to directly address both compositional and conformational variability in two different latent spaces for 3D cryo-ET subtomograms."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Further discussions on the related works can be found in Appendix—section A.1. in the supplementary document."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "3. Method"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.1. Disentangling Content and Transformation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ "angle": 0,
+ "content": "Disentangling content and transformation refers to learning one mapping \\( h: \\mathcal{X} \\to \\mathcal{C} \\times \\mathcal{Z} \\), where \\( \\mathcal{X} \\) is an input space, \\( \\mathcal{C} \\) and \\( \\mathcal{Z} \\) are the intermediary content and transformation representation spaces respectively. Here, \\( h \\) can be decomposed as \\( h_c: \\mathcal{X} \\to \\mathcal{C} \\) and \\( h_z: \\mathcal{X} \\to \\mathcal{Z} \\) representing the content and transformation mapping, respectively. In an unsupervised setting, distinguishing between content and transformation can be tricky. In this paper, we distinguish between content and transformation with respect to a family of trans"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "7485"
+ }
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+ [
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "formations \\(\\mathcal{T}:\\mathcal{X}\\to \\mathcal{X}\\) such that the following two conditions hold:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "- Condition 1: \\(\\forall T \\in \\mathcal{T}\\) and \\(\\forall \\mathbf{x} \\in \\mathcal{X}\\), \\(h_c(T(\\mathbf{x})) = h_c(\\mathbf{x})\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- Condition 2: \\(\\exists T \\in \\mathcal{T}\\) and \\(\\forall \\mathbf{x}^{(1)},\\mathbf{x}^{(2)} \\in \\mathcal{X}, h_z(T(\\mathbf{x}^{(1)})) = h_z(\\mathbf{x}^{(2)})\\)"
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Condition 1 defines content space which is invariant w.r.t. \\(\\mathcal{T}\\). On the other hand, condition 2 states that there is a \\(T\\in \\mathcal{T}\\) that can make the transformation of any two samples equal when applied to any one of them. Thus it defines transformation space which is informative of \\(\\mathcal{T}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "For content-transformation \\((\\mathbf{c} - \\mathbf{z})\\) disentangling, changes in \\(\\mathcal{C}\\) must be unaffected by changes in \\(\\mathcal{Z}\\) and vice versa. In our problem setting, no labels associated with the content space \\(\\mathcal{C}\\) or the transformation space \\(\\mathcal{Z}\\) are known. The exact family of transformation \\(\\mathcal{T}\\) is also not known beforehand. Thus, we aim to simultaneously learn the family of transformations \\(\\mathcal{T}\\) and the content factors unaltered by \\(\\mathcal{T}\\). In our case, \\(\\mathcal{T}\\) must include conformation-modulating transformation."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.2. Method Overview and Notation"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Our method is built upon a variational auto-encoder (VAE) based architecture (Fig. 2), where we perform inference of the content and transformation factors in the data. Consider, a sample space \\(\\mathcal{X}\\), two latent distribution spaces \\(\\Phi_Z\\) and \\(\\Phi_C\\), two latent spaces \\(\\mathcal{Z}\\) and \\(\\mathcal{C}\\). We apply an encoder network \\(q_{\\psi}:\\mathcal{X}\\to \\mathcal{C}\\times \\mathcal{Z}\\) on a sample space \\(\\mathbf{x}\\in \\mathcal{X}\\) to encode content distribution \\(\\phi_c\\in \\Phi_c\\) and transformation distribution \\(\\phi_z\\in \\Phi_z\\), where \\((\\phi_c,\\phi_z) = q_{\\psi}(\\mathbf{x})\\). Latent parameters \\(\\mathbf{c}\\in \\mathcal{C}\\), \\(\\mathbf{z}\\in \\mathcal{Z}\\) are drawn from distributions \\(\\phi_c\\) and \\(\\phi_z\\) respectively. These parameters are then decoded using a decoder network \\(p_{\\theta}:\\mathcal{C}\\times \\mathcal{Z}\\rightarrow \\mathcal{X}\\) to produce \\(x_{\\mathrm{recon}} = p_{\\theta}(\\mathbf{c},\\mathbf{z})\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.3. Variational Inference of Content and Transformation Codes"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Similar to a variational auto-encoder (VAE) setting, the encoder and decoder network parameters are simultaneously optimized to maximize the variational lower bound to the likelihood \\( p(\\mathbf{x}) \\) called the evidence lower bound (ELBO). ELBO maximizes the log-likelihood of the data and minimizes the KL divergence between latent distributions and a prior distribution. Further details on ELBO objective function can be found in Appendix A.2. The log-likelihood term in ELBO is maximized using a reconstruction loss \\( L_{\\mathrm{recon}} \\). The prior for \\( \\mathbf{c} \\) and \\( \\mathbf{z} \\), \\( p(\\mathbf{c}) \\) and \\( p(\\mathbf{z}) \\) respectively are assumed to be standard normal distribution. In short, we write the KL terms as \\( L_{\\mathrm{KL}(c)} \\) and \\( L_{\\mathrm{KL}(z)} \\). To regularize the effect of prior on the final objective separately for two latent codes, we scale the two losses with two hyperparameters \\( \\gamma_c \\) and \\( \\gamma_z \\). Our loss function for variational inference becomes:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.166,
+ 0.881,
+ 0.483,
+ 0.898
+ ],
+ "angle": 0,
+ "content": "\\[\nL _ {\\mathrm {v a e}} = L _ {\\mathrm {r e c}} + \\gamma_ {c} L _ {\\mathrm {K L} (\\mathbf {c})} + \\gamma_ {z} L _ {\\mathrm {K L} (\\mathbf {z})}. \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.907,
+ 0.227
+ ],
+ "angle": 0,
+ "content": "We observed that by deactivating the KL term associated with any one of the codes, the likelihood tends to be optimized through the other latent code. For instance, if \\(\\gamma_{c}\\) is set as 0 and \\(\\gamma_{z}\\) has a large value, then the \\(L_{\\mathrm{rec}}\\) is optimized through \\(\\mathbf{c}\\) only. As a consequence, \\(\\mathbf{c}\\) captures all the information in \\(\\mathbf{x}\\), whereas \\(\\mathbf{z}\\) becomes totally independent of the data. In such a scenario, \\(\\mathbf{z}\\) will be a random code with no relation to the transformation of the data, which is not desirable."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.239,
+ 0.907,
+ 0.268
+ ],
+ "angle": 0,
+ "content": "3.4. Creating Contrastive Pair with respect to Content"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.277,
+ 0.908,
+ 0.58
+ ],
+ "angle": 0,
+ "content": "We adopt a contrastive strategy for \\(\\mathbf{c} - \\mathbf{z}\\) disentanglement. We first develop a strategy to impose a structure to the content latent code with contrastive learning. To this end, we create negative and positive pairs for each data sample w.r.t. the content code. Hence, for a batch of samples \\(\\mathbf{x}\\), we randomize the order of samples or permute the samples in \\(x\\) to obtain \\(\\mathbf{x}_{\\mathrm{neg}(\\mathbf{c})}\\), and regard them as negative pairs of each other w.r.t the content code. Such strategy is commonly used in traditional self-supervised learning approaches [6, 16]. This approach accounts for the inherent sample heterogeneity in the data. To generate positive pairs w.r.t. the content code for \\(\\mathbf{x}\\), we transform it with a transformation \\(T \\in \\mathcal{T}\\) to generate \\(\\mathbf{x}_{\\mathrm{pos}(\\mathbf{c})}\\). We use the encoder \\(q_{\\psi}\\) to generate content codes \\(\\mathbf{c}\\), \\(\\mathbf{c}_{\\mathrm{pos}}\\), and \\(\\mathbf{c}_{\\mathrm{neg}}\\) respectively from \\(\\mathbf{x}\\), \\(\\mathbf{x}_{\\mathrm{pos}(\\mathbf{c})}\\), and \\(\\mathbf{x}_{\\mathrm{neg}(\\mathbf{c})}\\). We use a contrastive loss to penalize the distance between \\(\\mathbf{c}\\) and \\(\\mathbf{c}_{\\mathrm{pos}}\\) and the similarity between \\(\\mathbf{c}\\) and \\(\\mathbf{c}_{\\mathrm{neg}}\\). Our contrastive loss for content latent code can be written as: \\(L_{\\mathrm{con}(\\mathbf{c})} = L_{\\mathrm{dist}}(\\mathbf{c}, \\mathbf{c}_{\\mathrm{pos}}) + L_{\\mathrm{sim}}(\\mathbf{c}, \\mathbf{c}_{\\mathrm{neg}})\\). To implement \\(L_{\\mathrm{dist}}\\) and \\(L_{\\mathrm{sim}}\\), we use mean absolute cosine distance and mean absolute cosine similarity, respectively."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.59,
+ 0.907,
+ 0.62
+ ],
+ "angle": 0,
+ "content": "3.5. Creating Contrastive Pair with respect to Transformation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.628,
+ 0.906,
+ 0.718
+ ],
+ "angle": 0,
+ "content": "Imposing contrastive loss only on the content code satisfies condition 1 of the c-z disentanglement (Section 3.1), but not the condition 2. In experiments, doing so optimizes the log likelihood through the transformation code, making the content code uninformative. To this end, we also design contrastive losses w.r.t. the transformation code."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.719,
+ 0.906,
+ 0.781
+ ],
+ "angle": 0,
+ "content": "The negative pair of sample \\(\\mathbf{x} \\in \\mathcal{X}\\) w.r.t. transformation is generated while creating a positive pair of it w.r.t content. This is because a transformation \\(T\\) on \\(\\mathbf{x}\\) alters its transformation, but not its contents. So, we regard \\(\\mathbf{x}_{\\mathrm{pos}(\\mathbf{c})}\\) as \\(\\mathbf{x}_{\\mathrm{neg}(\\mathbf{z})}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.781,
+ 0.909,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "However, creating positive pairs of samples w.r.t. transformation is very challenging as they can not be created in the input space, unlike others. To this end, we assume that two samples have the same transformation code if they are generated using an identical transformation factor. This also implicitly satisfies the condition 2 of the \\(\\mathbf{c} - \\mathbf{z}\\) disentanglement (Section 3.1), making \\(\\mathbf{z}\\) code informative of transformation family \\(\\mathcal{T}\\). We randomly sample \\(\\mathbf{z}^{(1)}\\) and \\(\\mathbf{z}^{(2)}\\)"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
+ 0.945,
+ 0.516,
+ 0.956
+ ],
+ "angle": 0,
+ "content": "7486"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.091,
+ 0.485,
+ 0.258
+ ],
+ "angle": 0,
+ "content": "from \\(\\mathcal{N}(0,1)\\) and use the decoder \\(p_{\\theta}\\) to generate samples \\(\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(1)}\\) and \\(\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(2)}\\) from them (Fig. 2 (c)). In the decoder, as content input, we use content codes \\(\\mathbf{c}^{(1)}\\) and \\(\\mathbf{c}^{(2)}\\) obtained from encoding \\(\\mathbf{x}^{(1)}\\) and \\(\\mathbf{x}^{(2)}\\), two random samples obtained by permuting the orders in \\(\\mathbf{x}\\). Consequently, \\(\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(1)} = p_{\\theta}(\\mathbf{c}^{(1)},\\mathbf{z}^{(1)})\\) and \\(\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(2)} = p_{\\theta}(\\mathbf{c}^{(2)},\\mathbf{z}^{(2)})\\) serve as the positive pairs w.r.t. transformation. We then use the encoder \\(q_{\\psi}\\) to generate \\(\\mathbf{z}\\), \\(\\mathbf{z}_{\\mathrm{neg}}\\), \\(\\mathbf{z}_{\\mathrm{pos}}^{(1)}\\), and \\(\\mathbf{z}_{\\mathrm{pos}}^{(2)}\\) from \\(\\mathbf{x}\\), \\(\\mathbf{x}_{\\mathrm{neg}(\\mathbf{z})}\\), \\(\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(1)}\\), and \\(\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(2)}\\) respectively. This process can be best described with following pseudocode:"
+ },
+ {
+ "type": "code",
+ "bbox": [
+ 0.09,
+ 0.263,
+ 0.48,
+ 0.313
+ ],
+ "angle": 0,
+ "content": "x1, x2 = batch.permute(x) # permuted views (c1, ), (c2, ) = Enc(x1), Enc(x2) # encode content z = sample_normal() #z ~ N(0,I) \nx1_pos_z, x2_pos_z = Dec(c1, z), Dec(c2, z)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.319,
+ 0.484,
+ 0.412
+ ],
+ "angle": 0,
+ "content": "We use a contrastive loss to penalize the distance between \\(\\mathbf{z}_{\\mathrm{pos}}^{(1)}\\) and \\(\\mathbf{z}_{\\mathrm{pos}}^{(2)}\\) and similarity between \\(\\mathbf{z}\\) and \\(\\mathbf{z}_{\\mathrm{neg}}\\). Our contrastive loss for transformation can be written as: \\(L_{\\mathrm{con(z)}} = L_{\\mathrm{dist}}(\\mathbf{z}_{\\mathrm{pos}}^{(1)},\\mathbf{z}_{\\mathrm{pos}}^{(2)}) + L_{\\mathrm{sim}}(\\mathbf{z},\\mathbf{z}_{\\mathrm{neg}})\\). Similar to \\(L_{\\mathrm{con(c)}}\\), we use mean absolute cosine distance and mean absolute cosine similarity to implement \\(L_{\\mathrm{dist}}\\) and \\(L_{\\mathrm{sim}}\\), respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.412,
+ 0.484,
+ 0.502
+ ],
+ "angle": 0,
+ "content": "Why rotation?: We used rotation as a transformation to create contrastive pairs because only rotation provided our desired disentanglement of conformation-like transformations in the dataset, compared to other transformations such as translation, scale, blur, or color-based transformations (Details in Appendix A.2.4)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.503,
+ 0.484,
+ 0.562
+ ],
+ "angle": 0,
+ "content": "Objective Function: In summary, we train the encoder and decoder networks by simultaneously minimizing the loss components. Our overall objective function to minimize is:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.193,
+ 0.576,
+ 0.483,
+ 0.593
+ ],
+ "angle": 0,
+ "content": "\\[\nL = L _ {\\text {v a e}} + L _ {\\text {c o n (c)}} + L _ {\\text {c o n (z)}} \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.604,
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+ ],
+ "angle": 0,
+ "content": "We optimize \\( L_{\\mathrm{vae}} \\) for both \\( \\mathbf{x} \\) and the transformed image \\( \\mathbf{x}_{\\mathrm{pos}(\\mathbf{c})} \\) (same as \\( \\mathbf{x}_{\\mathrm{neg}(\\mathbf{z})} \\)), which yielded better experimental result."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "4. Experiments & Results"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.689,
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+ ],
+ "angle": 0,
+ "content": "Implementation Details: We implemented the encoder using a Convolutional Neural Network (CNN) and the decoder using a Fully Connected Network (FCN). Our experiments used the same latent dimension for content and transformation codes. We trained our models using NVIDIA RTX A5000 GPUs and AMD Raedon GPUs. We optimized the model parameters with Adam optimizer. The hyperparameters \\(\\gamma_z\\) and \\(\\gamma_c\\) controls how close the \\(\\mathbf{z}\\) and \\(\\mathbf{c}\\) distribution will be to \\(\\mathcal{N}(0, I)\\). In our experiments, setting a small value (\\(\\approx 0.01\\)) for both provided optimal results. Further details of the overall implementation are provided in the Appendix A.3."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.871,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Evaluation: We evaluated the methods based on two criteria: (1) the informativeness of the predicted \\(\\mathbf{c}\\) and \\(\\mathbf{z}\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.137
+ ],
+ "angle": 0,
+ "content": "codes w.r.t the relevant ground truth \\(\\mathbf{c}\\) and \\(\\mathbf{z}\\) factors, (2) the separateness of the predicted \\(\\mathbf{c}\\) and \\(\\mathbf{z}\\) codes. We performed these evaluations both quantitatively and qualitatively."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.138,
+ 0.907,
+ 0.409
+ ],
+ "angle": 0,
+ "content": "To this end, we used \\( D_{\\mathrm{score}} \\) and SAP score. \\( D_{\\mathrm{score}} \\) is simply a measurement of how well the ground truth (gt) factors can be predicted from the corresponding latent codes. In our scenario, there are four such quantities - (a) predictivity of content gt given c code \\( D_{\\mathrm{score}}(c|c) \\) or z code \\( D_{\\mathrm{score}}(c|z) \\) (b) predictivity of transformation gt given c code \\( D_{\\mathrm{score}}(z|c) \\) or z code \\( D_{\\mathrm{score}}(z|z) \\). Similar to [52], we used linear Logistic Regression Classifiers to measure predictivity (\\( D_{\\mathrm{score}} \\)). The higher \\( D_{\\mathrm{score}} \\), the more informative the latent code is with respect to the gt. SAP score for a gt factor is defined as the difference between the highest and second highest predictivities for it given any latent codes. In our case, SAP(c) can be defined as \\( |D_{\\mathrm{score}}(c|c) - D_{\\mathrm{score}}(c|z)| \\) and SAP(z) as \\( |D_{\\mathrm{score}}(z|z) - D_{\\mathrm{score}}(z|c)| \\). The higher the SAP score, higher the separateness of the latent codes. For qualitative evaluations, we performed downstream tasks like generating images through unsupervised content-transformer transfer and latent space visualization."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.411,
+ 0.906,
+ 0.533
+ ],
+ "angle": 0,
+ "content": "For protein subtomograms, we performed coarse refinement step of subtomogram averaging [4] to identify proteins resulting from the latent space clusters. We also quantitatively evaluate the latent space clustering result with Adjusted Rand Index (ARI) and the structure resulting from coarse refinement with per-class AUC-FSC (Area Under the Curve of Fourier Shell Correlation) [23]. Further details on these metrics are provided in the Appendix A.3."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.545,
+ 0.905,
+ 0.575
+ ],
+ "angle": 0,
+ "content": "4.1. DualContrast disentangles conformation-alike transformations from MNIST and LineMod"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.583,
+ 0.906,
+ 0.765
+ ],
+ "angle": 0,
+ "content": "We first examined whether DualContrast can disentangle conformation- alike transformations in simple shape-focused image datasets. To this end, we selected the MNIST handwritten digits dataset and the RGB LineMod singleobject dataset [54], both of which exhibited such transformations. In MNIST, these transformations arise primarily from variations in writing styles, while in LineMod, they are viewpoint changes. Similar to conformations, both transformations cause changes in the arrangement of shape components in the objects, making them suitable for evaluating our method's effectiveness. Details on the MNIST and LineMod RGB dataset are provided in the Appendix."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.765,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "We applied DualContrast and other unsupervised \\(\\mathbf{c} - \\mathbf{z}\\) disentanglement methods (SpatialVAE [3], Harmony [51], VI-TAE [47]) against these datasets. We also tested the existing self-supervised methods, e.g., SimSiam [8], SimCLR [7], Barlow Twins [55], and MoCo [17] with rotation augmentation to assess their implicit disentanglement ability. We evaluated the quantitative scores \\(D(c|c)\\), \\(D(c|z)\\), and \\(\\mathrm{SAP}(c)\\). We used digit classes in MNIST and the object identities in LineMod as ground-truth content factors, re"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "7487"
+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
+ 0.089,
+ 0.907,
+ 0.145
+ ],
+ "angle": 0,
+ "content": "Table 1. Quantitative disentanglement results of unsupervised content-transformation disentangling methods. Among these methods, SpatialVAE and Harmony put constraints on the z code dimension given their explicit parameterization; others do not. The std. dev. over model training by setting 3 different random seeds remains within \\(\\pm 0.04\\). \\(D_{\\mathrm{score}}\\) is written as \\(D\\). (\\(\\uparrow\\)) indicates higher score is better. (\\(\\downarrow\\)) indicates lower score is better."
+ },
+ {
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+ "content": "| Method | LineMod | Simulated Protein Subtomogram |
| D(c|c) (↑) | D(c|z) (↓), S(z) (↓) | SAP(c) (↑) | D(c|c) (↑) | D(c|z) (↓) | SAP(c) (↑) | D(z|z) (↑) | D(z|c) (↓) | SAP(z) (↑) |
| SpatialVAE | 0.95 | 0.32, 1.0 | 0.63 | 0.69 | 0.93 | 0.24 | 0.71 | 0.57 | 0.14 |
| Harmony | 0.90 | 0.56, 1.0 | 0.34 | 0.95 | 0.01 | 0.94 | 0.52 | 0.90 | 0.38 |
| SimCLR (Discriminative) | 0.62 | 0.40, 0.99 | 0.22 | 0.39 | 0.69 | 0.30 | 0.51 | 0.52 | 0.01 |
| SimCLR (Generative) | 0.61 | 0.79, 0.70 | 0.18 | 0.53 | 0.59 | 0.06 | 0.55 | 0.54 | 0.01 |
| SimSiam | 0.90 | 0.87, 0.70 | 0.03 | 0.31 | 0.52 | 0.21 | 0.80 | 0.75 | 0.04 |
| MoCo | 0.62 | 0.89, 0.74 | 0.27 | 0.76 | 0.59 | 0.17 | 0.55 | 0.58 | 0.02 |
| Barlow Twins | 0.92 | 0.87, 0.71 | 0.05 | 0.95 | 0.80 | 0.15 | 0.82 | 0.5 | 0.32 |
| VAE with 2 latent space | 0.87 | 0.87, 0.72 | 0.0 | 0.79 | 0.82 | 0.03 | 0.85 | 0.85 | 0.0 |
| VITAE | 0.92 | 0.90, 0.99 | 0.02 | - | - | - | - | - | - |
| DualContrast (w/o Lcon(c)) | 0.86 | 0.31, 0.98 | 0.55 | 0.93 | 0.81 | 0.13 | 0.78 | 0.81 | 0.03 |
| DualContrast (w/o Lcon(z)) | 0.79 | 0.86, 0.69 | 0.07 | 0.99 | 0.86 | 0.13 | 0.86 | 0.63 | 0.23 |
| DualContrast | 0.95 | 0.48, 0.77 | 0.47 | 1.00 | 0.56 | 0.44 | 0.86 | 0.64 | 0.22 |
"
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+ "content": "spectively. Since these datasets do not have ground truth transformation factors, \\( D(z|c) \\), \\( D(z|z) \\), and \\( \\mathrm{SAP}(z) \\) could not be calculated. To measure whether the transformation factor is really capturing conformation-alike transformation, we introduced a new metric \\( S(z) \\). To estimate it, we generated paired images by altering the \\( z \\) code while keeping \\( c \\) fixed. After aligning pairs via rotation and translation, we computed their similarity as their average, which was further SSIM normalized between [0, 1] range. We refer to this value as \\( S(z) \\). \\( S(z) = 1 \\) indicates the \\( z \\) code represents only rotation and translation. However, we want it to capture additional conformation-like transformations, so a lower value of \\( S(z) \\) is preferred, similar to \\( D(c|z) \\)."
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+ "content": "Our quantitative results (Table 1) for LineMod demonstrate the superior performance of DualContrast compared to the baselines. It also shows that the \\(\\mathbf{z}\\) factor in DualContrast contains information other than rotation (low \\(S(z)\\)), but is also separated from content (low \\(D(c|z)\\) and high \\(D(c|c)\\). The results on MNIST, presented in the Appendix Section A.4, also yield similar findings."
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+ "content": "We then performed a qualitative evaluation of image generation with varying \\(\\mathbf{c}\\) and \\(\\mathbf{z}\\) codes in LineMod (Figure 3). We observe that VITAE [47] significantly distorts the images when performing image generation with \\(\\mathbf{c} - \\mathbf{z}\\) transfer. SpatialVAE and Harmony only disentangle in-plane rotation given their design; so changing the \\(\\mathbf{z}\\) code in these methods only rotates the content sample. Due to this, their \\(S(z) = 1\\). We provided the results obtained with the existing self-supervised methods, e.g., SimCLR, SimSiam, Barlow Twins, etc., with rotation augmentation in the Appendix, whereas none of them yielded satisfactory results. Only DualContrast disentangled different viewpoints or perspectives of the objects as the \\(\\mathbf{z}\\) code, and changing \\(\\mathbf{z}\\) changes the viewpoint of the objects, reflecting the actual conformational-like transformation present in the dataset."
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+ "content": "We included additional qualitative results, particularly"
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+ "content": "for MNIST, in the Appendix A.4."
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+ "content": "4.2. DualContrast disentangles protein composition from conformations in simulated Cryo-ET subtomograms and enables their precise identification"
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+ "content": "We created a realistically simulated [35] cellular cryo-ET subtomogram dataset of 18,000 samples belonging to 4 different protein compositions: nucleosome, pre-fusion, and post-fusion Sars-Cov-2 spike proteins, and Fatty Acid Synthase (FAS) unit. We collected 6 different conformations for Nucleosome, 5 different conformations of pre-fusion spike protein, 1 conformation of post-fusion spike protein, and 6 different conformations of FAS from RCSB PDB [43]. After collecting the PDB templates, we filtered them to 10 Åresolution. Among the filtered structures, only nucleosome conformations has subtly visible differences among them. For the other proteins, conformational differences were visually indistinguishable in the filtered volumes. For each filtered PDB template, 1,000 subtomograms were generated. Each subtomogram is of size \\(32^{3}\\) and contains a protein in random orientation and shift with a very low signal-to-noise (SNR) ratio (Fig. 4). Further details on the dataset properties are provided in the Appendix A.4."
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+ "content": "We trained DualContrast and the other approaches (except VITAE, since it could not be trained without designing a 3D CPAB transformation) against the protein subtomogram dataset. We provided the quantitative results in Table 1 and Table 2 and qualitative results in Fig. 4, Fig. 5, and Fig. 6 respectively."
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+ "content": "For qualitative results, we first performed UMAP visualization of the latent codes obtained by the models. We observed that the UMAP of \\(\\mathbf{c}\\) codes in DualContrast perfectly clustered the protein identities from the dataset, profoundly disentangling the transformations (Fig. 4(e)). We did not see such clustering for SpatialVAE (Fig. 4(b)), Sim"
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+ "content": "Figure 3. Qualitative results of unsupervised \\(\\mathbf{c} - \\mathbf{z}\\) disentanglement on LineMod obtained by (a) VITAE, (b) SpatialVAE, (c) Harmony, and (d) DualContrast, respectively. Images are generated by the Decoders given \\(\\mathbf{c}\\) code from the leftmost column images and \\(\\mathbf{z}\\) code from the topmost row images. For Harmony and Dualcontrast, we also provide a zoomed-in view of several generated images. Additional content-transformation transfer results are available on Appendix Fig. 11."
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+ "bbox": [
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+ "content": "Figure 4. Protein composition latent space with sample visualization. (a) Slice-by-slice visualization of x-y slices in 4 sample subtomograms with 4 different compositions. UMAP embedding of c codes in (b) SpatialVAE, (c) SimSiam, (d) Harmony, and (e) DualContrast."
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "Siam (Fig. 4(c)), or Harmony (Fig. 4(d)). We further performed coarse refinement step of subtomogram averaging (STA) to identify the protein structures from latent space clusters. STA obtains readily identifiable high-SNR structure from multiple low-SNR subtomograms of a homogenous structure with varying orientations through iterative alignment and averaging [4]. In our experiments, Gaussian Mixture Models (GMM) (with \\( \\mathrm{K} = 4 \\)) were applied to content (c) codes predicted by models, generating clusters of subtomograms. We evaluated the clustering accuracy with ARI scores (Table 2) where DualContrast shows best performance."
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+ "content": "Afterwards, we refined each cluster of subtomograms using RELION [58] (Fig. 5). SpatialVAE failed to identify any protein compositions, while Harmony identified the FAS, nucleosome, and 2 spike proteins, though 1 spike protein appeared as an unrealistic mixture of FAS and spike"
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+ "content": "protein. RELION's maximum likelihood based classification was unable to identify the post-fusion spike protein. DualContrast successfully identified the FAS, nucleosome, and 2 distinct spike protein compositions. We further reported the average and minimum per-class AUC-FSCs of the refined structures by each methods on Table 2, where DualContrast demonstrates superior performance, supporting our qualitative results."
+ },
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+ "angle": 0,
+ "content": "We then investigated the effectiveness of the \\(\\mathbf{z}\\) factor to obtain different protein compositions. One way with the existing approaches was to cluster Harmony's c codes for nucleosome cluster subtomograms. However, this revealed only 1 nucleosome conformation but mistakenly included a spike protein (Fig. 6), suggesting that Harmony [51] cannot be used for conformation identification. RELION's maximum likelihood classification on the nucleosome cluster subtomograms also did not yield distinct conformational"
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+ "angle": 0,
+ "content": "Figure 5. Structures obtained with each method. RELION refinement for each (4) cluster of subtomograms, whereas the clustering is performed using Gaussian Mixture Modeling (GMM) on c codes, predicted by (a) SpatialVAE (d) Harmony, and (e) DualContrast. (b) shows the different protein compositions reconstructed from Hydra (with \\( \\mathrm{K} = 4 \\)). (c) RELION's initial 3D model generation results."
+ },
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+ "bbox": [
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+ "content": "classes of nucleosome. However, clustering DualContrast's \\(\\mathbf{z}\\) codes followed by RELION averaging identified 4 out of 6 distinct nucleosome conformations with subtle structural changes (Fig. 6), showcasing its ability to disentangle protein composition and conformation, which is unattained by the other existing methods. This finding is further quantitatively validated with ARI scores and per-class AUC-FSCs reported in Table 2."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ {
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+ "bbox": [
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+ "content": "Figure 6. (a, b) Structures obtained with RELION refinement for the nucleosome subtomograms (identified with previous step Fig. 4) using GMM on (a) Harmony content codes, and (b) DualContrast transformation codes."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "We also trained the recent composition-conformation reconstruction method Hydra [34] using the projection sum (along the z-axis) of the subtomograms, which serves as a rough equivalent to the 2D cryo-EM images that Hydra typically requires as input. Our goal was to determine whether"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Quantitative evaluation of latent space clustering with ARI and protein structures obtained by coarse refinement with per-class AUC-FSC. \\((\\uparrow)\\) indicates higher score are better."
+ },
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+ "content": "| Method | Composition | Conformation |
| AUC-FSC | ARI (↑) | AUC-FSC | ARI (↑) |
| avg(↑) | min(↑) | avg (↑) | min(↑) |
| SimCLR | 0.42 | 0.32 | 0.55 | 0.18 | 0.10 | 0.01 |
| MoCo | 0.42 | 0.32 | 0.55 | 0.19 | 0.10 | 0.04 |
| Barlow-Twins | 0.50 | 0.44 | 0.30 | 0.28 | 0.18 | 0.05 |
| SimSiam | 0.42 | 0.24 | 0.63 | 0.25 | 0.12 | 0.10 |
| SpatialVAE | 0.09 | 0.07 | 0.01 | 0.10 | 0.04 | 0.01 |
| Hydra | 0.07 | 0.02 | 0.01 | 0.06 | 0.04 | 0.01 |
| Relion | 0.40 | 0.10 | 0.75 | 0.35 | 0.32 | 0.01 |
| Harmony | 0.43 | 0.17 | 0.72 | 0.35 | 0.13 | 0.12 |
| DualContrast | 0.56 | 0.51 | 0.99 | 0.49 | 0.39 | 0.22 |
"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Hydra could accurately reconstruct protein conformations and compositions. During training, we set \\( K = 4 \\). We provided details on the Hydra training in the Appendix A.4. However, we found that Hydra was unable to reconstruct the correct protein compositions, let alone their conformations (Fig. 5). Instead, it generated artificial proteins with mixed compositions, such as hybrids of nucleosome and FAS or FAS and spike protein. This issue likely arose from Hydra's reliance on 2D projections rather than actual 3D subtomograms, which hindered its ability to distinguish between different 3D protein compositions in our dataset that have overlapping 2D projections."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Ablation Study: To evaluate the individual contribution of the contrastive losses, we conducted both quantitative and qualitative ablation analyses of DualContrast. We trained (1) DualContrast without any contrastive loss, which is basically a VAE with two latent spaces, (2) DualContrast with only \\( L = L_{\\mathrm{VAE}} + L_{\\mathrm{con(z)}} \\), and (3) \\( L = L_{\\mathrm{VAE}} + L_{\\mathrm{con(c)}} \\). We qualitatively and quantitatively evaluated each model. We show the quantitative results in Table 1 and qualitative results of MNIST in Appendix A.4.4 with additional discussion."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.644,
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+ ],
+ "angle": 0,
+ "content": "Motivated by the challenge of unsupervised identification of protein compositions and conformations from cryo-ET subtomograms, we propose a method called DualContrast that solves this problem through unsupervised content-transformation disentanglement. DualContrast is a reconstructive method that employs a novel contrastive learning strategy that creates positive and negative pairs for both content and transformation codes, which enables implicit unsupervised disentanglement of conformation-like transformations in images and subtomograms. Our experiments on simulated datasets showcased that DualContrast can in principle disentangle protein compositions and conformations in a fully unsupervised manner, a capability not previously demonstrated. While the additional complexities of experimental data remain a challenge, DualContrast lays a strong foundation and opens an exciting new avenue for advancing this frontier."
+ },
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+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "Acknowledgement"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.114,
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+ ],
+ "angle": 0,
+ "content": "This work was supported in part by U.S. NIH grants R35GM158094, R01GM134020 and P41GM103712, NSF grants DBI-1949629, DBI-2238093, IIS-2007595, IIS-2211597, and MCB-2205148. This work was supported in part by Oracle Cloud credits and related resources provided by Oracle for Research, and the computational resources support from AMD HPC Fund. MRU were supported in part by a fellowship from CMU CMLH."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "References"
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+ {
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+# Unsupervised Identification of Protein Compositions and Conformations via Implicit Content-Transformation Disentanglement
+
+Mostofa Rafid Uddin
+
+Jana Armouti
+
+Min Xu*
+
+Carnegie Mellon University
+
+Pittsburgh, PA 15213, USA.
+
+mru@andrew.cmu.edu
+
+jarmouti@andrew.cmu.edu
+
+mxul@cs.cmu.edu
+
+# Abstract
+
+Identifying different protein compositions and conformations from microscopic images of protein mixtures is a challenging open problem. We address this through disentangled representation learning, where separating protein compositions and conformations in an intermediate latent space enables accurate identification. By modeling compositions and conformations as content and transformation, the task can be reduced to disentangling content and transformation. The existing disentangling methods require an explicit parametric form for the transformation, which is unavailable for conformation, making these methods unsuitable. To overcome this limitation, we propose Dual-Contrast, a novel contrastive learning-based method that implicitly parameterizes and disentangles both transformation and content. DualContrast achieves this by generating positive and negative pairs for content and transformation in both data and latent spaces. We demonstrate that existing self-supervised approaches fail under similar implicit parameterization, underscoring the necessity of our method. Through extensive experiments on 3D microscopic images of protein mixtures and additional shape-focused datasets beyond microscopy, we validate our claims and demonstrate the first in-principle fully unsupervised identification of different protein compositions and conformations in 3D microscopic images.
+
+# 1. Introduction
+
+Proteins are fundamental building blocks of life, and their structures and functions have been extensively studied for decades [18, 42]. A protein's structure is characterized by its composition (form of a protein), while its function is dictated by which conformation (specific state of the protein's form) it adopts within a system. Historically,
+
+a range of experimental and computational methods separately addressed protein composition and conformation [24, 29, 38, 46]. Now, with the emerging technology of cellular cryo-electron tomography (cryo-ET), it is, in principle, possible to simultaneously determine diverse protein compositions and conformations through direct 3D visualization inside cells [50]. In this paper, we pursue the ambitious goal of identifying diverse protein compositions and conformations from such data using a fully unsupervised, data-driven approach.
+
+Identifying protein composition and conformations from cellular cryo-ET image datasets requires separating the intrinsic features that define a protein's composition from those that describe its conformation. From an image analysis perspective, protein conformations can be regarded as data transformations that cause changes in the spatial arrangement of protein shape components (Figure 1b). On the other hand, protein compositions are regarded as the overall shape of the protein that is unaltered by such transformations (Figure 1a). In such a manner, the structural features can be disentangled into content factors and transformation factors. Changing the transformation factor changes the conformation of the protein while preserving the protein identity (i.e., composition). Conversely, changing the content factor is analogous to changing the proteins from one identity to another through compositional change (Fig. 1). Thus, disentangling protein composition and conformation becomes the problem of unsupervised disentanglement of content and transformation factors in images.
+
+Currently, a few methods exist for unsupervised disentanglement of semantic content and transformation. Among them, [47] performed explicit parameterization of the transformation factor as diffeomorphic transformations and achieved notable disentanglement of content and transformation in several image datasets. [3] and [51] focus on representing known transformation types as transformation codes. [3] performed disentanglement of two-dimensional
+
+
+(a)
+
+
+Figure 1. (a) Different Compositions (change of shape components, overall shape change) (b) Different Conformations (change of spatial arrangement of shape components) (c) Disentangling composition-conformation through content-transformation
+
+
+
+
+
+
+
+
+(b)
+
+
+
+
+(c)
+
+translation and rotation, while [51] demonstrated disentanglement of a broader set of transformations that can be explicitly parameterized. All of these explicit parameterization methods require that the data transformations have an explicit functional form parameterized by a fixed number of parameters. However, conformation transformations do not have such a well-defined functional form. Moreover, these methods often struggle to accurately recover contents when conformation-like transformations are present in the datasets (Table 1).
+
+Given the above-mentioned issues of explicit disentanglement of transformations, we explore the potential of self-supervised learning (SSL) to implicitly represent them. Previous work by [52] theoretically demonstrated that contrastive learning with data augmentation can disentangle the transformations used in augmentation from the semantic content of the data. However, they experimentally observed that this approach also disentangles generative factors beyond the augmentation itself. In other words, using data augmentation with SSL implicitly disentangles several transformations outside of the augmentation used. For instance, in experiments on Causal3DIndent objects, using only rotation as augmentation in an SSL framework also disentangled object position and class labels [52]. While this phenomenon of implicit disentanglement has been observed experimentally to some extent, it remains largely unexplored.
+
+Inspired by such findings, in this work, we aim to implicitly disentangle conformation-like transformations from semantic contents for the unsupervised identification of protein composition and conformation. We found that popular SSL methods [6] with geometric data augmentation fail to disentangle conformation-like transformations in shape-focused images of interest (Table 1), often discarding content as transformation and vice versa. This suggests that existing contrastive strategies with data augmentation are insufficient to disentangle conformation-like transformations, highlighting the need for a novel contrastive strategy to achieve the desired results.
+
+In this work, we develop a novel generative contrastive
+
+learning method for implicit content-transformation disentanglement, termed “DualContrast” (Fig. 2). Unlike existing contrastive strategies, DualContrast creates “positive” and “negative” contrastive pairs with respect to both content and transformation latent codes. Specifically, we create negative pairs for transformation and positive pairs for content by simply rotating the samples. Creating positive pairs for transformation codes directly from the input samples is not possible without prior knowledge. We assume that two images with the same transformation should have transformation factors drawn from the same distribution. Consequently, we sample transformation factors from an identical distribution in the transformation space and generate image samples with those transformation factors to create positive pairs for transformation. Given our observation, this encourages the disentanglement of conformation-like transformations in our datasets. In addition, we perform batch permutation during training to create negative pairs for a batch of samples with respect to content. Upon creating both “positive” and “negative” pairs for content and transformation codes, we penalize similarity between negative pairs and distance between positive pairs for each code. Finally, we incorporate these contrastive losses in a Variational Autoencoder (VAE) based architecture with VAE reconstruction loss and train the model in an end-to-end manner.
+
+With such a strategy to create contrastive pairs in the VAE-based framework, DualContrast effectively disentangles conformational-like transformations. These include viewpoint variations in Linemod and several writing styles in MNIST. We then applied DualContrast to disentangle protein compositions and conformations in simulated cellular cryo-ET images of proteins with diverse compositions and conformations. This enabled unsupervised identification of protein compositions and conformations directly from 3D cryo-ET images of proteins. This is not achievable by any of the previous methods, and we are the first to achieve such success.
+
+A summary of our contributions is as follows:
+
+- We developed the first unsupervised approach to identify
+
+
+
+
+
+
+Figure 2. Our proposed contrastive learning-based unsupervised content-transformation disentanglement pipeline. (a) The variational inference of content and transformation codes with $L_{\mathrm{VAE}}$ . (b) contrastive losses between contrastive pairs for content and transformation codes. (c, d) Contrastive pair creation strategy for both content and transformation. Additional visualization available in Appendix Fig. 8.
+
+
+
+protein compositions and conformations via implicit disentanglement of content and transformation.
+
+- We developed a novel contrastive modeling strategy that creates positive-negative pairs for both content- and transformation-latent factors. We introduced a novel way of designing contrastive pairs for transformation.
+- We demonstrate that DualContrast effectively disentangles conformation-like transformations from semantic content across various shape-focused image datasets.
+
+# 2. Related Works
+
+Unsupervised Content-Transformation Disentanglement: There are a few [3, 47, 51, 52] approaches that deal with the unsupervised disentanglement of content and transformation. However, these methods perform explicit parameterization of the transformation codes as affine or some specific parameterized transformation. In contrast, our method does not impose any explicit parameterization on the transformation latent codes and does not face the issues of the explicit methods (Section 1).
+
+Contrastive Learning based Disentanglement: Contrastive learning is the primary building block of our method. Contrastive Learning with data augmentation with existing approaches, e.g., InfoNCE loss-based SimCLR [6], has been previously used by [25, 52] to isolate content from style. Though in several scenarios, style in shape focused images can be referred to as transformations, these works do not specifically focus on shape focused real-world images. Moreover, our experiments demonstrate that SimCLR with rotation augmentation in a standard encoder-decoder framework leads to very poor disentanglement of content and transformation (Table 1). Also, [52] only creates positive pairs for content and negative pair for style with data augmentation in SimCLR. We have observed this scheme does not work well in our scenario. Unlike these works,
+
+our approach uses a novel strategy to create "negative" and "positive" pairs for both content and transformation of latent codes without any InfoNCE loss.
+
+Composition-Conformation Disentanglement: Our method disentangles protein composition and conformation as content and transformation factors from 3D cryo-electron tomography (cryo-ET) subtomograms. Previously, Harmony [51] was used to disentangle large compositional variability in cellular subtomograms. HEMNMA-3D [14] and TomoFlow [15] were used to disentangle conformational variability in subtomograms using known templates. SpatialVAE [3] disentangled conformational variability from 2D cryo-EM images. However, none of them deals with both composition and conformation. Very recently, a method termed Hydra [34], has been developed to reconstruct multiple protein compositions and conformations from 2D cryo-EM images. Our work is the first to directly address both compositional and conformational variability in two different latent spaces for 3D cryo-ET subtomograms.
+
+Further discussions on the related works can be found in Appendix—section A.1. in the supplementary document.
+
+# 3. Method
+
+# 3.1. Disentangling Content and Transformation
+
+Disentangling content and transformation refers to learning one mapping $h: \mathcal{X} \to \mathcal{C} \times \mathcal{Z}$ , where $\mathcal{X}$ is an input space, $\mathcal{C}$ and $\mathcal{Z}$ are the intermediary content and transformation representation spaces respectively. Here, $h$ can be decomposed as $h_c: \mathcal{X} \to \mathcal{C}$ and $h_z: \mathcal{X} \to \mathcal{Z}$ representing the content and transformation mapping, respectively. In an unsupervised setting, distinguishing between content and transformation can be tricky. In this paper, we distinguish between content and transformation with respect to a family of trans
+
+formations $\mathcal{T}:\mathcal{X}\to \mathcal{X}$ such that the following two conditions hold:
+
+- Condition 1: $\forall T \in \mathcal{T}$ and $\forall \mathbf{x} \in \mathcal{X}$ , $h_c(T(\mathbf{x})) = h_c(\mathbf{x})$ .
+- Condition 2: $\exists T \in \mathcal{T}$ and $\forall \mathbf{x}^{(1)},\mathbf{x}^{(2)} \in \mathcal{X}, h_z(T(\mathbf{x}^{(1)})) = h_z(\mathbf{x}^{(2)})$
+
+Condition 1 defines content space which is invariant w.r.t. $\mathcal{T}$ . On the other hand, condition 2 states that there is a $T\in \mathcal{T}$ that can make the transformation of any two samples equal when applied to any one of them. Thus it defines transformation space which is informative of $\mathcal{T}$ .
+
+For content-transformation $(\mathbf{c} - \mathbf{z})$ disentangling, changes in $\mathcal{C}$ must be unaffected by changes in $\mathcal{Z}$ and vice versa. In our problem setting, no labels associated with the content space $\mathcal{C}$ or the transformation space $\mathcal{Z}$ are known. The exact family of transformation $\mathcal{T}$ is also not known beforehand. Thus, we aim to simultaneously learn the family of transformations $\mathcal{T}$ and the content factors unaltered by $\mathcal{T}$ . In our case, $\mathcal{T}$ must include conformation-modulating transformation.
+
+# 3.2. Method Overview and Notation
+
+Our method is built upon a variational auto-encoder (VAE) based architecture (Fig. 2), where we perform inference of the content and transformation factors in the data. Consider, a sample space $\mathcal{X}$ , two latent distribution spaces $\Phi_Z$ and $\Phi_C$ , two latent spaces $\mathcal{Z}$ and $\mathcal{C}$ . We apply an encoder network $q_{\psi}:\mathcal{X}\to \mathcal{C}\times \mathcal{Z}$ on a sample space $\mathbf{x}\in \mathcal{X}$ to encode content distribution $\phi_c\in \Phi_c$ and transformation distribution $\phi_z\in \Phi_z$ , where $(\phi_c,\phi_z) = q_{\psi}(\mathbf{x})$ . Latent parameters $\mathbf{c}\in \mathcal{C}$ , $\mathbf{z}\in \mathcal{Z}$ are drawn from distributions $\phi_c$ and $\phi_z$ respectively. These parameters are then decoded using a decoder network $p_{\theta}:\mathcal{C}\times \mathcal{Z}\rightarrow \mathcal{X}$ to produce $x_{\mathrm{recon}} = p_{\theta}(\mathbf{c},\mathbf{z})$ .
+
+# 3.3. Variational Inference of Content and Transformation Codes
+
+Similar to a variational auto-encoder (VAE) setting, the encoder and decoder network parameters are simultaneously optimized to maximize the variational lower bound to the likelihood $p(\mathbf{x})$ called the evidence lower bound (ELBO). ELBO maximizes the log-likelihood of the data and minimizes the KL divergence between latent distributions and a prior distribution. Further details on ELBO objective function can be found in Appendix A.2. The log-likelihood term in ELBO is maximized using a reconstruction loss $L_{\mathrm{recon}}$ . The prior for $\mathbf{c}$ and $\mathbf{z}$ , $p(\mathbf{c})$ and $p(\mathbf{z})$ respectively are assumed to be standard normal distribution. In short, we write the KL terms as $L_{\mathrm{KL}(c)}$ and $L_{\mathrm{KL}(z)}$ . To regularize the effect of prior on the final objective separately for two latent codes, we scale the two losses with two hyperparameters $\gamma_c$ and $\gamma_z$ . Our loss function for variational inference becomes:
+
+$$
+L _ {\mathrm {v a e}} = L _ {\mathrm {r e c}} + \gamma_ {c} L _ {\mathrm {K L} (\mathbf {c})} + \gamma_ {z} L _ {\mathrm {K L} (\mathbf {z})}. \tag {1}
+$$
+
+We observed that by deactivating the KL term associated with any one of the codes, the likelihood tends to be optimized through the other latent code. For instance, if $\gamma_{c}$ is set as 0 and $\gamma_{z}$ has a large value, then the $L_{\mathrm{rec}}$ is optimized through $\mathbf{c}$ only. As a consequence, $\mathbf{c}$ captures all the information in $\mathbf{x}$ , whereas $\mathbf{z}$ becomes totally independent of the data. In such a scenario, $\mathbf{z}$ will be a random code with no relation to the transformation of the data, which is not desirable.
+
+# 3.4. Creating Contrastive Pair with respect to Content
+
+We adopt a contrastive strategy for $\mathbf{c} - \mathbf{z}$ disentanglement. We first develop a strategy to impose a structure to the content latent code with contrastive learning. To this end, we create negative and positive pairs for each data sample w.r.t. the content code. Hence, for a batch of samples $\mathbf{x}$ , we randomize the order of samples or permute the samples in $x$ to obtain $\mathbf{x}_{\mathrm{neg}(\mathbf{c})}$ , and regard them as negative pairs of each other w.r.t the content code. Such strategy is commonly used in traditional self-supervised learning approaches [6, 16]. This approach accounts for the inherent sample heterogeneity in the data. To generate positive pairs w.r.t. the content code for $\mathbf{x}$ , we transform it with a transformation $T \in \mathcal{T}$ to generate $\mathbf{x}_{\mathrm{pos}(\mathbf{c})}$ . We use the encoder $q_{\psi}$ to generate content codes $\mathbf{c}$ , $\mathbf{c}_{\mathrm{pos}}$ , and $\mathbf{c}_{\mathrm{neg}}$ respectively from $\mathbf{x}$ , $\mathbf{x}_{\mathrm{pos}(\mathbf{c})}$ , and $\mathbf{x}_{\mathrm{neg}(\mathbf{c})}$ . We use a contrastive loss to penalize the distance between $\mathbf{c}$ and $\mathbf{c}_{\mathrm{pos}}$ and the similarity between $\mathbf{c}$ and $\mathbf{c}_{\mathrm{neg}}$ . Our contrastive loss for content latent code can be written as: $L_{\mathrm{con}(\mathbf{c})} = L_{\mathrm{dist}}(\mathbf{c}, \mathbf{c}_{\mathrm{pos}}) + L_{\mathrm{sim}}(\mathbf{c}, \mathbf{c}_{\mathrm{neg}})$ . To implement $L_{\mathrm{dist}}$ and $L_{\mathrm{sim}}$ , we use mean absolute cosine distance and mean absolute cosine similarity, respectively.
+
+# 3.5. Creating Contrastive Pair with respect to Transformation
+
+Imposing contrastive loss only on the content code satisfies condition 1 of the c-z disentanglement (Section 3.1), but not the condition 2. In experiments, doing so optimizes the log likelihood through the transformation code, making the content code uninformative. To this end, we also design contrastive losses w.r.t. the transformation code.
+
+The negative pair of sample $\mathbf{x} \in \mathcal{X}$ w.r.t. transformation is generated while creating a positive pair of it w.r.t content. This is because a transformation $T$ on $\mathbf{x}$ alters its transformation, but not its contents. So, we regard $\mathbf{x}_{\mathrm{pos}(\mathbf{c})}$ as $\mathbf{x}_{\mathrm{neg}(\mathbf{z})}$ .
+
+However, creating positive pairs of samples w.r.t. transformation is very challenging as they can not be created in the input space, unlike others. To this end, we assume that two samples have the same transformation code if they are generated using an identical transformation factor. This also implicitly satisfies the condition 2 of the $\mathbf{c} - \mathbf{z}$ disentanglement (Section 3.1), making $\mathbf{z}$ code informative of transformation family $\mathcal{T}$ . We randomly sample $\mathbf{z}^{(1)}$ and $\mathbf{z}^{(2)}$
+
+from $\mathcal{N}(0,1)$ and use the decoder $p_{\theta}$ to generate samples $\mathbf{x}_{\mathrm{pos}(\mathbf{z})}^{(1)}$ and $\mathbf{x}_{\mathrm{pos}(\mathbf{z})}^{(2)}$ from them (Fig. 2 (c)). In the decoder, as content input, we use content codes $\mathbf{c}^{(1)}$ and $\mathbf{c}^{(2)}$ obtained from encoding $\mathbf{x}^{(1)}$ and $\mathbf{x}^{(2)}$ , two random samples obtained by permuting the orders in $\mathbf{x}$ . Consequently, $\mathbf{x}_{\mathrm{pos}(\mathbf{z})}^{(1)} = p_{\theta}(\mathbf{c}^{(1)},\mathbf{z}^{(1)})$ and $\mathbf{x}_{\mathrm{pos}(\mathbf{z})}^{(2)} = p_{\theta}(\mathbf{c}^{(2)},\mathbf{z}^{(2)})$ serve as the positive pairs w.r.t. transformation. We then use the encoder $q_{\psi}$ to generate $\mathbf{z}$ , $\mathbf{z}_{\mathrm{neg}}$ , $\mathbf{z}_{\mathrm{pos}}^{(1)}$ , and $\mathbf{z}_{\mathrm{pos}}^{(2)}$ from $\mathbf{x}$ , $\mathbf{x}_{\mathrm{neg}(\mathbf{z})}$ , $\mathbf{x}_{\mathrm{pos}(\mathbf{z})}^{(1)}$ , and $\mathbf{x}_{\mathrm{pos}(\mathbf{z})}^{(2)}$ respectively. This process can be best described with following pseudocode:
+
+```python
+x1, x2 = batch.permute(x) # permuted views (c1, ), (c2, ) = Enc(x1), Enc(x2) # encode content z = sample_normal() #z ~ N(0,I)
+x1_pos_z, x2_pos_z = Dec(c1, z), Dec(c2, z)
+```
+
+We use a contrastive loss to penalize the distance between $\mathbf{z}_{\mathrm{pos}}^{(1)}$ and $\mathbf{z}_{\mathrm{pos}}^{(2)}$ and similarity between $\mathbf{z}$ and $\mathbf{z}_{\mathrm{neg}}$ . Our contrastive loss for transformation can be written as: $L_{\mathrm{con(z)}} = L_{\mathrm{dist}}(\mathbf{z}_{\mathrm{pos}}^{(1)},\mathbf{z}_{\mathrm{pos}}^{(2)}) + L_{\mathrm{sim}}(\mathbf{z},\mathbf{z}_{\mathrm{neg}})$ . Similar to $L_{\mathrm{con(c)}}$ , we use mean absolute cosine distance and mean absolute cosine similarity to implement $L_{\mathrm{dist}}$ and $L_{\mathrm{sim}}$ , respectively.
+
+Why rotation?: We used rotation as a transformation to create contrastive pairs because only rotation provided our desired disentanglement of conformation-like transformations in the dataset, compared to other transformations such as translation, scale, blur, or color-based transformations (Details in Appendix A.2.4).
+
+Objective Function: In summary, we train the encoder and decoder networks by simultaneously minimizing the loss components. Our overall objective function to minimize is:
+
+$$
+L = L _ {\text {v a e}} + L _ {\text {c o n (c)}} + L _ {\text {c o n (z)}} \tag {2}
+$$
+
+We optimize $L_{\mathrm{vae}}$ for both $\mathbf{x}$ and the transformed image $\mathbf{x}_{\mathrm{pos}(\mathbf{c})}$ (same as $\mathbf{x}_{\mathrm{neg}(\mathbf{z})}$ ), which yielded better experimental result.
+
+# 4. Experiments & Results
+
+Implementation Details: We implemented the encoder using a Convolutional Neural Network (CNN) and the decoder using a Fully Connected Network (FCN). Our experiments used the same latent dimension for content and transformation codes. We trained our models using NVIDIA RTX A5000 GPUs and AMD Raedon GPUs. We optimized the model parameters with Adam optimizer. The hyperparameters $\gamma_z$ and $\gamma_c$ controls how close the $\mathbf{z}$ and $\mathbf{c}$ distribution will be to $\mathcal{N}(0, I)$ . In our experiments, setting a small value ( $\approx 0.01$ ) for both provided optimal results. Further details of the overall implementation are provided in the Appendix A.3.
+
+Evaluation: We evaluated the methods based on two criteria: (1) the informativeness of the predicted $\mathbf{c}$ and $\mathbf{z}$
+
+codes w.r.t the relevant ground truth $\mathbf{c}$ and $\mathbf{z}$ factors, (2) the separateness of the predicted $\mathbf{c}$ and $\mathbf{z}$ codes. We performed these evaluations both quantitatively and qualitatively.
+
+To this end, we used $D_{\mathrm{score}}$ and SAP score. $D_{\mathrm{score}}$ is simply a measurement of how well the ground truth (gt) factors can be predicted from the corresponding latent codes. In our scenario, there are four such quantities - (a) predictivity of content gt given c code $D_{\mathrm{score}}(c|c)$ or z code $D_{\mathrm{score}}(c|z)$ (b) predictivity of transformation gt given c code $D_{\mathrm{score}}(z|c)$ or z code $D_{\mathrm{score}}(z|z)$ . Similar to [52], we used linear Logistic Regression Classifiers to measure predictivity ( $D_{\mathrm{score}}$ ). The higher $D_{\mathrm{score}}$ , the more informative the latent code is with respect to the gt. SAP score for a gt factor is defined as the difference between the highest and second highest predictivities for it given any latent codes. In our case, SAP(c) can be defined as $|D_{\mathrm{score}}(c|c) - D_{\mathrm{score}}(c|z)|$ and SAP(z) as $|D_{\mathrm{score}}(z|z) - D_{\mathrm{score}}(z|c)|$ . The higher the SAP score, higher the separateness of the latent codes. For qualitative evaluations, we performed downstream tasks like generating images through unsupervised content-transformer transfer and latent space visualization.
+
+For protein subtomograms, we performed coarse refinement step of subtomogram averaging [4] to identify proteins resulting from the latent space clusters. We also quantitatively evaluate the latent space clustering result with Adjusted Rand Index (ARI) and the structure resulting from coarse refinement with per-class AUC-FSC (Area Under the Curve of Fourier Shell Correlation) [23]. Further details on these metrics are provided in the Appendix A.3.
+
+# 4.1. DualContrast disentangles conformation-alike transformations from MNIST and LineMod
+
+We first examined whether DualContrast can disentangle conformation- alike transformations in simple shape-focused image datasets. To this end, we selected the MNIST handwritten digits dataset and the RGB LineMod singleobject dataset [54], both of which exhibited such transformations. In MNIST, these transformations arise primarily from variations in writing styles, while in LineMod, they are viewpoint changes. Similar to conformations, both transformations cause changes in the arrangement of shape components in the objects, making them suitable for evaluating our method's effectiveness. Details on the MNIST and LineMod RGB dataset are provided in the Appendix.
+
+We applied DualContrast and other unsupervised $\mathbf{c} - \mathbf{z}$ disentanglement methods (SpatialVAE [3], Harmony [51], VI-TAE [47]) against these datasets. We also tested the existing self-supervised methods, e.g., SimSiam [8], SimCLR [7], Barlow Twins [55], and MoCo [17] with rotation augmentation to assess their implicit disentanglement ability. We evaluated the quantitative scores $D(c|c)$ , $D(c|z)$ , and $\mathrm{SAP}(c)$ . We used digit classes in MNIST and the object identities in LineMod as ground-truth content factors, re
+
+Table 1. Quantitative disentanglement results of unsupervised content-transformation disentangling methods. Among these methods, SpatialVAE and Harmony put constraints on the z code dimension given their explicit parameterization; others do not. The std. dev. over model training by setting 3 different random seeds remains within $\pm 0.04$ . $D_{\mathrm{score}}$ is written as $D$ . ( $\uparrow$ ) indicates higher score is better. ( $\downarrow$ ) indicates lower score is better.
+
+| Method | LineMod | Simulated Protein Subtomogram |
| D(c|c) (↑) | D(c|z) (↓), S(z) (↓) | SAP(c) (↑) | D(c|c) (↑) | D(c|z) (↓) | SAP(c) (↑) | D(z|z) (↑) | D(z|c) (↓) | SAP(z) (↑) |
| SpatialVAE | 0.95 | 0.32, 1.0 | 0.63 | 0.69 | 0.93 | 0.24 | 0.71 | 0.57 | 0.14 |
| Harmony | 0.90 | 0.56, 1.0 | 0.34 | 0.95 | 0.01 | 0.94 | 0.52 | 0.90 | 0.38 |
| SimCLR (Discriminative) | 0.62 | 0.40, 0.99 | 0.22 | 0.39 | 0.69 | 0.30 | 0.51 | 0.52 | 0.01 |
| SimCLR (Generative) | 0.61 | 0.79, 0.70 | 0.18 | 0.53 | 0.59 | 0.06 | 0.55 | 0.54 | 0.01 |
| SimSiam | 0.90 | 0.87, 0.70 | 0.03 | 0.31 | 0.52 | 0.21 | 0.80 | 0.75 | 0.04 |
| MoCo | 0.62 | 0.89, 0.74 | 0.27 | 0.76 | 0.59 | 0.17 | 0.55 | 0.58 | 0.02 |
| Barlow Twins | 0.92 | 0.87, 0.71 | 0.05 | 0.95 | 0.80 | 0.15 | 0.82 | 0.5 | 0.32 |
| VAE with 2 latent space | 0.87 | 0.87, 0.72 | 0.0 | 0.79 | 0.82 | 0.03 | 0.85 | 0.85 | 0.0 |
| VITAE | 0.92 | 0.90, 0.99 | 0.02 | - | - | - | - | - | - |
| DualContrast (w/o Lcon(c)) | 0.86 | 0.31, 0.98 | 0.55 | 0.93 | 0.81 | 0.13 | 0.78 | 0.81 | 0.03 |
| DualContrast (w/o Lcon(z)) | 0.79 | 0.86, 0.69 | 0.07 | 0.99 | 0.86 | 0.13 | 0.86 | 0.63 | 0.23 |
| DualContrast | 0.95 | 0.48, 0.77 | 0.47 | 1.00 | 0.56 | 0.44 | 0.86 | 0.64 | 0.22 |
+
+spectively. Since these datasets do not have ground truth transformation factors, $D(z|c)$ , $D(z|z)$ , and $\mathrm{SAP}(z)$ could not be calculated. To measure whether the transformation factor is really capturing conformation-alike transformation, we introduced a new metric $S(z)$ . To estimate it, we generated paired images by altering the $z$ code while keeping $c$ fixed. After aligning pairs via rotation and translation, we computed their similarity as their average, which was further SSIM normalized between [0, 1] range. We refer to this value as $S(z)$ . $S(z) = 1$ indicates the $z$ code represents only rotation and translation. However, we want it to capture additional conformation-like transformations, so a lower value of $S(z)$ is preferred, similar to $D(c|z)$ .
+
+Our quantitative results (Table 1) for LineMod demonstrate the superior performance of DualContrast compared to the baselines. It also shows that the $\mathbf{z}$ factor in DualContrast contains information other than rotation (low $S(z)$ ), but is also separated from content (low $D(c|z)$ and high $D(c|c)$ . The results on MNIST, presented in the Appendix Section A.4, also yield similar findings.
+
+We then performed a qualitative evaluation of image generation with varying $\mathbf{c}$ and $\mathbf{z}$ codes in LineMod (Figure 3). We observe that VITAE [47] significantly distorts the images when performing image generation with $\mathbf{c} - \mathbf{z}$ transfer. SpatialVAE and Harmony only disentangle in-plane rotation given their design; so changing the $\mathbf{z}$ code in these methods only rotates the content sample. Due to this, their $S(z) = 1$ . We provided the results obtained with the existing self-supervised methods, e.g., SimCLR, SimSiam, Barlow Twins, etc., with rotation augmentation in the Appendix, whereas none of them yielded satisfactory results. Only DualContrast disentangled different viewpoints or perspectives of the objects as the $\mathbf{z}$ code, and changing $\mathbf{z}$ changes the viewpoint of the objects, reflecting the actual conformational-like transformation present in the dataset.
+
+We included additional qualitative results, particularly
+
+for MNIST, in the Appendix A.4.
+
+# 4.2. DualContrast disentangles protein composition from conformations in simulated Cryo-ET subtomograms and enables their precise identification
+
+We created a realistically simulated [35] cellular cryo-ET subtomogram dataset of 18,000 samples belonging to 4 different protein compositions: nucleosome, pre-fusion, and post-fusion Sars-Cov-2 spike proteins, and Fatty Acid Synthase (FAS) unit. We collected 6 different conformations for Nucleosome, 5 different conformations of pre-fusion spike protein, 1 conformation of post-fusion spike protein, and 6 different conformations of FAS from RCSB PDB [43]. After collecting the PDB templates, we filtered them to 10 Åresolution. Among the filtered structures, only nucleosome conformations has subtly visible differences among them. For the other proteins, conformational differences were visually indistinguishable in the filtered volumes. For each filtered PDB template, 1,000 subtomograms were generated. Each subtomogram is of size $32^{3}$ and contains a protein in random orientation and shift with a very low signal-to-noise (SNR) ratio (Fig. 4). Further details on the dataset properties are provided in the Appendix A.4.
+
+We trained DualContrast and the other approaches (except VITAE, since it could not be trained without designing a 3D CPAB transformation) against the protein subtomogram dataset. We provided the quantitative results in Table 1 and Table 2 and qualitative results in Fig. 4, Fig. 5, and Fig. 6 respectively.
+
+For qualitative results, we first performed UMAP visualization of the latent codes obtained by the models. We observed that the UMAP of $\mathbf{c}$ codes in DualContrast perfectly clustered the protein identities from the dataset, profoundly disentangling the transformations (Fig. 4(e)). We did not see such clustering for SpatialVAE (Fig. 4(b)), Sim
+
+
+Figure 3. Qualitative results of unsupervised $\mathbf{c} - \mathbf{z}$ disentanglement on LineMod obtained by (a) VITAE, (b) SpatialVAE, (c) Harmony, and (d) DualContrast, respectively. Images are generated by the Decoders given $\mathbf{c}$ code from the leftmost column images and $\mathbf{z}$ code from the topmost row images. For Harmony and Dualcontrast, we also provide a zoomed-in view of several generated images. Additional content-transformation transfer results are available on Appendix Fig. 11.
+
+
+
+
+
+
+
+
+
+
+
+
+Figure 4. Protein composition latent space with sample visualization. (a) Slice-by-slice visualization of x-y slices in 4 sample subtomograms with 4 different compositions. UMAP embedding of c codes in (b) SpatialVAE, (c) SimSiam, (d) Harmony, and (e) DualContrast.
+
+
+
+
+
+
+
+Siam (Fig. 4(c)), or Harmony (Fig. 4(d)). We further performed coarse refinement step of subtomogram averaging (STA) to identify the protein structures from latent space clusters. STA obtains readily identifiable high-SNR structure from multiple low-SNR subtomograms of a homogenous structure with varying orientations through iterative alignment and averaging [4]. In our experiments, Gaussian Mixture Models (GMM) (with $\mathrm{K} = 4$ ) were applied to content (c) codes predicted by models, generating clusters of subtomograms. We evaluated the clustering accuracy with ARI scores (Table 2) where DualContrast shows best performance.
+
+Afterwards, we refined each cluster of subtomograms using RELION [58] (Fig. 5). SpatialVAE failed to identify any protein compositions, while Harmony identified the FAS, nucleosome, and 2 spike proteins, though 1 spike protein appeared as an unrealistic mixture of FAS and spike
+
+protein. RELION's maximum likelihood based classification was unable to identify the post-fusion spike protein. DualContrast successfully identified the FAS, nucleosome, and 2 distinct spike protein compositions. We further reported the average and minimum per-class AUC-FSCs of the refined structures by each methods on Table 2, where DualContrast demonstrates superior performance, supporting our qualitative results.
+
+We then investigated the effectiveness of the $\mathbf{z}$ factor to obtain different protein compositions. One way with the existing approaches was to cluster Harmony's c codes for nucleosome cluster subtomograms. However, this revealed only 1 nucleosome conformation but mistakenly included a spike protein (Fig. 6), suggesting that Harmony [51] cannot be used for conformation identification. RELION's maximum likelihood classification on the nucleosome cluster subtomograms also did not yield distinct conformational
+
+
+Figure 5. Structures obtained with each method. RELION refinement for each (4) cluster of subtomograms, whereas the clustering is performed using Gaussian Mixture Modeling (GMM) on c codes, predicted by (a) SpatialVAE (d) Harmony, and (e) DualContrast. (b) shows the different protein compositions reconstructed from Hydra (with $\mathrm{K} = 4$ ). (c) RELION's initial 3D model generation results.
+
+classes of nucleosome. However, clustering DualContrast's $\mathbf{z}$ codes followed by RELION averaging identified 4 out of 6 distinct nucleosome conformations with subtle structural changes (Fig. 6), showcasing its ability to disentangle protein composition and conformation, which is unattained by the other existing methods. This finding is further quantitatively validated with ARI scores and per-class AUC-FSCs reported in Table 2.
+
+
+Figure 6. (a, b) Structures obtained with RELION refinement for the nucleosome subtomograms (identified with previous step Fig. 4) using GMM on (a) Harmony content codes, and (b) DualContrast transformation codes.
+
+We also trained the recent composition-conformation reconstruction method Hydra [34] using the projection sum (along the z-axis) of the subtomograms, which serves as a rough equivalent to the 2D cryo-EM images that Hydra typically requires as input. Our goal was to determine whether
+
+Table 2. Quantitative evaluation of latent space clustering with ARI and protein structures obtained by coarse refinement with per-class AUC-FSC. $(\uparrow)$ indicates higher score are better.
+
+| Method | Composition | Conformation |
| AUC-FSC | ARI (↑) | AUC-FSC | ARI (↑) |
| avg(↑) | min(↑) | avg (↑) | min(↑) |
| SimCLR | 0.42 | 0.32 | 0.55 | 0.18 | 0.10 | 0.01 |
| MoCo | 0.42 | 0.32 | 0.55 | 0.19 | 0.10 | 0.04 |
| Barlow-Twins | 0.50 | 0.44 | 0.30 | 0.28 | 0.18 | 0.05 |
| SimSiam | 0.42 | 0.24 | 0.63 | 0.25 | 0.12 | 0.10 |
| SpatialVAE | 0.09 | 0.07 | 0.01 | 0.10 | 0.04 | 0.01 |
| Hydra | 0.07 | 0.02 | 0.01 | 0.06 | 0.04 | 0.01 |
| Relion | 0.40 | 0.10 | 0.75 | 0.35 | 0.32 | 0.01 |
| Harmony | 0.43 | 0.17 | 0.72 | 0.35 | 0.13 | 0.12 |
| DualContrast | 0.56 | 0.51 | 0.99 | 0.49 | 0.39 | 0.22 |
+
+Hydra could accurately reconstruct protein conformations and compositions. During training, we set $K = 4$ . We provided details on the Hydra training in the Appendix A.4. However, we found that Hydra was unable to reconstruct the correct protein compositions, let alone their conformations (Fig. 5). Instead, it generated artificial proteins with mixed compositions, such as hybrids of nucleosome and FAS or FAS and spike protein. This issue likely arose from Hydra's reliance on 2D projections rather than actual 3D subtomograms, which hindered its ability to distinguish between different 3D protein compositions in our dataset that have overlapping 2D projections.
+
+Ablation Study: To evaluate the individual contribution of the contrastive losses, we conducted both quantitative and qualitative ablation analyses of DualContrast. We trained (1) DualContrast without any contrastive loss, which is basically a VAE with two latent spaces, (2) DualContrast with only $L = L_{\mathrm{VAE}} + L_{\mathrm{con(z)}}$ , and (3) $L = L_{\mathrm{VAE}} + L_{\mathrm{con(c)}}$ . We qualitatively and quantitatively evaluated each model. We show the quantitative results in Table 1 and qualitative results of MNIST in Appendix A.4.4 with additional discussion.
+
+# 5. Conclusion
+
+Motivated by the challenge of unsupervised identification of protein compositions and conformations from cryo-ET subtomograms, we propose a method called DualContrast that solves this problem through unsupervised content-transformation disentanglement. DualContrast is a reconstructive method that employs a novel contrastive learning strategy that creates positive and negative pairs for both content and transformation codes, which enables implicit unsupervised disentanglement of conformation-like transformations in images and subtomograms. Our experiments on simulated datasets showcased that DualContrast can in principle disentangle protein compositions and conformations in a fully unsupervised manner, a capability not previously demonstrated. While the additional complexities of experimental data remain a challenge, DualContrast lays a strong foundation and opens an exciting new avenue for advancing this frontier.
+
+# Acknowledgement
+
+This work was supported in part by U.S. NIH grants R35GM158094, R01GM134020 and P41GM103712, NSF grants DBI-1949629, DBI-2238093, IIS-2007595, IIS-2211597, and MCB-2205148. This work was supported in part by Oracle Cloud credits and related resources provided by Oracle for Research, and the computational resources support from AMD HPC Fund. MRU were supported in part by a fellowship from CMU CMLH.
+
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+ "type": "inline_equation",
+ "content": "\\mathcal{Z}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " are known. The exact family of transformation "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "\\mathcal{T}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " is also not known beforehand. Thus, we aim to simultaneously learn the family of transformations "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "\\mathcal{T}"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " and the content factors unaltered by "
+ },
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+ "content": "\\mathcal{T}"
+ },
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+ ],
+ "type": "text",
+ "content": ". In our case, "
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+ },
+ {
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+ ],
+ "type": "text",
+ "content": " must include conformation-modulating transformation."
+ }
+ ]
+ }
+ ],
+ "index": 5
+ },
+ {
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+ "type": "text",
+ "content": "3.2. Method Overview and Notation"
+ }
+ ]
+ }
+ ],
+ "index": 6
+ },
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+ "type": "text",
+ "content": "Our method is built upon a variational auto-encoder (VAE) based architecture (Fig. 2), where we perform inference of the content and transformation factors in the data. Consider, a sample space "
+ },
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+ "type": "text",
+ "content": ", two latent distribution spaces "
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+ "type": "text",
+ "content": " and "
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+ "content": "\\Phi_C"
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+ "type": "text",
+ "content": ", two latent spaces "
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+ "type": "inline_equation",
+ "content": "\\mathcal{Z}"
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+ "type": "text",
+ "content": " and "
+ },
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+ "type": "inline_equation",
+ "content": "\\mathcal{C}"
+ },
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+ "type": "text",
+ "content": ". We apply an encoder network "
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+ "type": "inline_equation",
+ "content": "q_{\\psi}:\\mathcal{X}\\to \\mathcal{C}\\times \\mathcal{Z}"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " on a sample space "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "\\mathbf{x}\\in \\mathcal{X}"
+ },
+ {
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+ "type": "text",
+ "content": " to encode content distribution "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "\\phi_c\\in \\Phi_c"
+ },
+ {
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+ "type": "text",
+ "content": " and transformation distribution "
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+ "type": "inline_equation",
+ "content": "\\phi_z\\in \\Phi_z"
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+ "type": "text",
+ "content": ", where "
+ },
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+ "type": "inline_equation",
+ "content": "(\\phi_c,\\phi_z) = q_{\\psi}(\\mathbf{x})"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". Latent parameters "
+ },
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+ "type": "inline_equation",
+ "content": "\\mathbf{c}\\in \\mathcal{C}"
+ },
+ {
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+ "type": "text",
+ "content": ", "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "\\mathbf{z}\\in \\mathcal{Z}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " are drawn from distributions "
+ },
+ {
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+ },
+ {
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+ "type": "text",
+ "content": " and "
+ },
+ {
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+ "content": "\\phi_z"
+ },
+ {
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+ "type": "text",
+ "content": " respectively. These parameters are then decoded using a decoder network "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "p_{\\theta}:\\mathcal{C}\\times \\mathcal{Z}\\rightarrow \\mathcal{X}"
+ },
+ {
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+ "type": "text",
+ "content": " to produce "
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+ "type": "inline_equation",
+ "content": "x_{\\mathrm{recon}} = p_{\\theta}(\\mathbf{c},\\mathbf{z})"
+ },
+ {
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+ "type": "text",
+ "content": "."
+ }
+ ]
+ }
+ ],
+ "index": 7
+ },
+ {
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+ "type": "text",
+ "content": "3.3. Variational Inference of Content and Transformation Codes"
+ }
+ ]
+ }
+ ],
+ "index": 8
+ },
+ {
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+ "type": "text",
+ "content": "Similar to a variational auto-encoder (VAE) setting, the encoder and decoder network parameters are simultaneously optimized to maximize the variational lower bound to the likelihood "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "p(\\mathbf{x})"
+ },
+ {
+ "bbox": [
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+ "type": "text",
+ "content": " called the evidence lower bound (ELBO). ELBO maximizes the log-likelihood of the data and minimizes the KL divergence between latent distributions and a prior distribution. Further details on ELBO objective function can be found in Appendix A.2. The log-likelihood term in ELBO is maximized using a reconstruction loss "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "L_{\\mathrm{recon}}"
+ },
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+ "type": "text",
+ "content": ". The prior for "
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+ "type": "inline_equation",
+ "content": "\\mathbf{c}"
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+ "type": "text",
+ "content": " and "
+ },
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+ "content": "\\mathbf{z}"
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+ "type": "text",
+ "content": ", "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "p(\\mathbf{c})"
+ },
+ {
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+ "type": "text",
+ "content": " and "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "p(\\mathbf{z})"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " respectively are assumed to be standard normal distribution. In short, we write the KL terms as "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "L_{\\mathrm{KL}(c)}"
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+ "content": " and "
+ },
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+ "type": "inline_equation",
+ "content": "L_{\\mathrm{KL}(z)}"
+ },
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+ "type": "text",
+ "content": ". To regularize the effect of prior on the final objective separately for two latent codes, we scale the two losses with two hyperparameters "
+ },
+ {
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+ "type": "inline_equation",
+ "content": "\\gamma_c"
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+ "type": "text",
+ "content": " and "
+ },
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+ "type": "inline_equation",
+ "content": "\\gamma_z"
+ },
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+ "type": "text",
+ "content": ". Our loss function for variational inference becomes:"
+ }
+ ]
+ }
+ ],
+ "index": 9
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+ "type": "interline_equation",
+ "content": "L _ {\\mathrm {v a e}} = L _ {\\mathrm {r e c}} + \\gamma_ {c} L _ {\\mathrm {K L} (\\mathbf {c})} + \\gamma_ {z} L _ {\\mathrm {K L} (\\mathbf {z})}. \\tag {1}",
+ "image_path": "c5cc427f65266b1747d38db2de150753cef124d24be6ace1a7d0ab5aea63d743.jpg"
+ }
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+ }
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+ "type": "text",
+ "content": "We observed that by deactivating the KL term associated with any one of the codes, the likelihood tends to be optimized through the other latent code. For instance, if "
+ },
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+ "content": " is set as 0 and "
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+ "type": "text",
+ "content": " has a large value, then the "
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+ "type": "inline_equation",
+ "content": "L_{\\mathrm{rec}}"
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+ "content": " is optimized through "
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+ "type": "text",
+ "content": " only. As a consequence, "
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+ "type": "inline_equation",
+ "content": "\\mathbf{c}"
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+ "type": "text",
+ "content": " captures all the information in "
+ },
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+ "type": "inline_equation",
+ "content": "\\mathbf{x}"
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+ "type": "text",
+ "content": ", whereas "
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+ "type": "text",
+ "content": " becomes totally independent of the data. In such a scenario, "
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+ "content": "\\mathbf{z}"
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+ "type": "text",
+ "content": " will be a random code with no relation to the transformation of the data, which is not desirable."
+ }
+ ]
+ }
+ ],
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+ },
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+ "type": "text",
+ "content": "3.4. Creating Contrastive Pair with respect to Content"
+ }
+ ]
+ }
+ ],
+ "index": 12
+ },
+ {
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+ "type": "text",
+ "content": "We adopt a contrastive strategy for "
+ },
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+ ],
+ "type": "inline_equation",
+ "content": "\\mathbf{c} - \\mathbf{z}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " disentanglement. We first develop a strategy to impose a structure to the content latent code with contrastive learning. To this end, we create negative and positive pairs for each data sample w.r.t. the content code. Hence, for a batch of samples "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "\\mathbf{x}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", we randomize the order of samples or permute the samples in "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "x"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": " to obtain "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "\\mathbf{x}_{\\mathrm{neg}(\\mathbf{c})}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", and regard them as negative pairs of each other w.r.t the content code. Such strategy is commonly used in traditional self-supervised learning approaches [6, 16]. This approach accounts for the inherent sample heterogeneity in the data. To generate positive pairs w.r.t. the content code for "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "\\mathbf{x}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", we transform it with a transformation "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "T \\in \\mathcal{T}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " to generate "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "\\mathbf{x}_{\\mathrm{pos}(\\mathbf{c})}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ". We use the encoder "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "q_{\\psi}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": " to generate content codes "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "\\mathbf{c}"
+ },
+ {
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+ ],
+ "type": "text",
+ "content": ", "
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "inline_equation",
+ "content": "\\mathbf{c}_{\\mathrm{pos}}"
+ },
+ {
+ "bbox": [
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+ ],
+ "type": "text",
+ "content": ", and "
+ },
+ {
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+ ],
+ "type": "inline_equation",
+ "content": "\\mathbf{c}_{\\mathrm{neg}}"
+ },
+ {
+ "bbox": [
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+ ],
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+ "content": " respectively from "
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+ "content": ". We use a contrastive loss to penalize the distance between "
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+ "type": "text",
+ "content": ". Our contrastive loss for content latent code can be written as: "
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+ "content": "L_{\\mathrm{con}(\\mathbf{c})} = L_{\\mathrm{dist}}(\\mathbf{c}, \\mathbf{c}_{\\mathrm{pos}}) + L_{\\mathrm{sim}}(\\mathbf{c}, \\mathbf{c}_{\\mathrm{neg}})"
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+ "content": ". To implement "
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+ "type": "inline_equation",
+ "content": "L_{\\mathrm{dist}}"
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+ "content": " and "
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+ "type": "inline_equation",
+ "content": "L_{\\mathrm{sim}}"
+ },
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+ "type": "text",
+ "content": ", we use mean absolute cosine distance and mean absolute cosine similarity, respectively."
+ }
+ ]
+ }
+ ],
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+ "content": "3.5. Creating Contrastive Pair with respect to Transformation"
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+ "content": "Imposing contrastive loss only on the content code satisfies condition 1 of the c-z disentanglement (Section 3.1), but not the condition 2. In experiments, doing so optimizes the log likelihood through the transformation code, making the content code uninformative. To this end, we also design contrastive losses w.r.t. the transformation code."
+ }
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+ "content": " w.r.t. transformation is generated while creating a positive pair of it w.r.t content. This is because a transformation "
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+ "content": " alters its transformation, but not its contents. So, we regard "
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+ "type": "text",
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+ "content": "However, creating positive pairs of samples w.r.t. transformation is very challenging as they can not be created in the input space, unlike others. To this end, we assume that two samples have the same transformation code if they are generated using an identical transformation factor. This also implicitly satisfies the condition 2 of the "
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+ "type": "text",
+ "content": " from them (Fig. 2 (c)). In the decoder, as content input, we use content codes "
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+ "content": "\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(1)} = p_{\\theta}(\\mathbf{c}^{(1)},\\mathbf{z}^{(1)})"
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+ "content": "\\mathbf{x}_{\\mathrm{pos}(\\mathbf{z})}^{(2)} = p_{\\theta}(\\mathbf{c}^{(2)},\\mathbf{z}^{(2)})"
+ },
+ {
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+ "type": "text",
+ "content": " serve as the positive pairs w.r.t. transformation. We then use the encoder "
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+ "type": "text",
+ "content": " respectively. This process can be best described with following pseudocode:"
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+ ]
+ }
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+ "content": "x1, x2 = batch.permute(x) # permuted views (c1, ), (c2, ) = Enc(x1), Enc(x2) # encode content z = sample_normal() #z ~ N(0,I) \nx1_pos_z, x2_pos_z = Dec(c1, z), Dec(c2, z)"
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+ "content": "We use a contrastive loss to penalize the distance between "
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+ "type": "inline_equation",
+ "content": "\\mathbf{z}_{\\mathrm{pos}}^{(1)}"
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+ "content": " and "
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+ },
+ {
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+ "type": "text",
+ "content": ". Our contrastive loss for transformation can be written as: "
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+ "type": "inline_equation",
+ "content": "L_{\\mathrm{con(z)}} = L_{\\mathrm{dist}}(\\mathbf{z}_{\\mathrm{pos}}^{(1)},\\mathbf{z}_{\\mathrm{pos}}^{(2)}) + L_{\\mathrm{sim}}(\\mathbf{z},\\mathbf{z}_{\\mathrm{neg}})"
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+ "content": ". Similar to "
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+ "type": "inline_equation",
+ "content": "L_{\\mathrm{con(c)}}"
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+ ],
+ "type": "text",
+ "content": ", we use mean absolute cosine distance and mean absolute cosine similarity to implement "
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+ {
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+ "type": "inline_equation",
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+ "type": "text",
+ "content": ", respectively."
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+ "content": "For protein subtomograms, we performed coarse refinement step of subtomogram averaging [4] to identify proteins resulting from the latent space clusters. We also quantitatively evaluate the latent space clustering result with Adjusted Rand Index (ARI) and the structure resulting from coarse refinement with per-class AUC-FSC (Area Under the Curve of Fourier Shell Correlation) [23]. Further details on these metrics are provided in the Appendix A.3."
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+ "content": "4.1. DualContrast disentangles conformation-alike transformations from MNIST and LineMod"
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+ "content": "We first examined whether DualContrast can disentangle conformation- alike transformations in simple shape-focused image datasets. To this end, we selected the MNIST handwritten digits dataset and the RGB LineMod singleobject dataset [54], both of which exhibited such transformations. In MNIST, these transformations arise primarily from variations in writing styles, while in LineMod, they are viewpoint changes. Similar to conformations, both transformations cause changes in the arrangement of shape components in the objects, making them suitable for evaluating our method's effectiveness. Details on the MNIST and LineMod RGB dataset are provided in the Appendix."
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+ "content": " disentanglement methods (SpatialVAE [3], Harmony [51], VI-TAE [47]) against these datasets. We also tested the existing self-supervised methods, e.g., SimSiam [8], SimCLR [7], Barlow Twins [55], and MoCo [17] with rotation augmentation to assess their implicit disentanglement ability. We evaluated the quantitative scores "
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+ "content": ". We used digit classes in MNIST and the object identities in LineMod as ground-truth content factors, re"
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| D(c|c) (↑) | D(c|z) (↓), S(z) (↓) | SAP(c) (↑) | D(c|c) (↑) | D(c|z) (↓) | SAP(c) (↑) | D(z|z) (↑) | D(z|c) (↓) | SAP(z) (↑) |
| SpatialVAE | 0.95 | 0.32, 1.0 | 0.63 | 0.69 | 0.93 | 0.24 | 0.71 | 0.57 | 0.14 |
| Harmony | 0.90 | 0.56, 1.0 | 0.34 | 0.95 | 0.01 | 0.94 | 0.52 | 0.90 | 0.38 |
| SimCLR (Discriminative) | 0.62 | 0.40, 0.99 | 0.22 | 0.39 | 0.69 | 0.30 | 0.51 | 0.52 | 0.01 |
| SimCLR (Generative) | 0.61 | 0.79, 0.70 | 0.18 | 0.53 | 0.59 | 0.06 | 0.55 | 0.54 | 0.01 |
| SimSiam | 0.90 | 0.87, 0.70 | 0.03 | 0.31 | 0.52 | 0.21 | 0.80 | 0.75 | 0.04 |
| MoCo | 0.62 | 0.89, 0.74 | 0.27 | 0.76 | 0.59 | 0.17 | 0.55 | 0.58 | 0.02 |
| Barlow Twins | 0.92 | 0.87, 0.71 | 0.05 | 0.95 | 0.80 | 0.15 | 0.82 | 0.5 | 0.32 |
| VAE with 2 latent space | 0.87 | 0.87, 0.72 | 0.0 | 0.79 | 0.82 | 0.03 | 0.85 | 0.85 | 0.0 |
| VITAE | 0.92 | 0.90, 0.99 | 0.02 | - | - | - | - | - | - |
| DualContrast (w/o Lcon(c)) | 0.86 | 0.31, 0.98 | 0.55 | 0.93 | 0.81 | 0.13 | 0.78 | 0.81 | 0.03 |
| DualContrast (w/o Lcon(z)) | 0.79 | 0.86, 0.69 | 0.07 | 0.99 | 0.86 | 0.13 | 0.86 | 0.63 | 0.23 |
| DualContrast | 0.95 | 0.48, 0.77 | 0.47 | 1.00 | 0.56 | 0.44 | 0.86 | 0.64 | 0.22 |
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+ "html": "| Method | Composition | Conformation |
| AUC-FSC | ARI (↑) | AUC-FSC | ARI (↑) |
| avg(↑) | min(↑) | avg (↑) | min(↑) |
| SimCLR | 0.42 | 0.32 | 0.55 | 0.18 | 0.10 | 0.01 |
| MoCo | 0.42 | 0.32 | 0.55 | 0.19 | 0.10 | 0.04 |
| Barlow-Twins | 0.50 | 0.44 | 0.30 | 0.28 | 0.18 | 0.05 |
| SimSiam | 0.42 | 0.24 | 0.63 | 0.25 | 0.12 | 0.10 |
| SpatialVAE | 0.09 | 0.07 | 0.01 | 0.10 | 0.04 | 0.01 |
| Hydra | 0.07 | 0.02 | 0.01 | 0.06 | 0.04 | 0.01 |
| Relion | 0.40 | 0.10 | 0.75 | 0.35 | 0.32 | 0.01 |
| Harmony | 0.43 | 0.17 | 0.72 | 0.35 | 0.13 | 0.12 |
| DualContrast | 0.56 | 0.51 | 0.99 | 0.49 | 0.39 | 0.22 |
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+ "content": ". We provided details on the Hydra training in the Appendix A.4. However, we found that Hydra was unable to reconstruct the correct protein compositions, let alone their conformations (Fig. 5). Instead, it generated artificial proteins with mixed compositions, such as hybrids of nucleosome and FAS or FAS and spike protein. This issue likely arose from Hydra's reliance on 2D projections rather than actual 3D subtomograms, which hindered its ability to distinguish between different 3D protein compositions in our dataset that have overlapping 2D projections."
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+ {
+ "type": "text",
+ "text": "Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Giacomo Meanti Thomas Ryckeboer Michael Arbel Julien Mairal Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France firstname.lastname@inria.fr",
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+ "page_idx": 0
+ },
+ {
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+ "img_path": "images/4684ce93a49e5b01ee492fff365b2bb297150a8c21557dba54b42635bdeb9662.jpg",
+ "image_caption": [
+ "Figure 1. Learning degradation operators by matching distributions."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "Abstract",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches—which typically assume full knowledge of the forward model or access to paired degraded and ground-truth images—the proposed method operates under minimal assumptions and relies only on small, unpaired datasets. This makes it particularly well-suited for real-world scenarios, where the forward model is often unknown or mis-specified, and collecting paired data is costly or infeasible. The method leverages conditional flow matching to model the distribution of degraded observations, while simultaneously learning the forward model via a distribution-matching loss that arises naturally from the framework. Empirically, it outperforms both single-image blind and unsupervised approaches on deblurring and non-uniform point spread function (PSF) calibration tasks. It also matches state-of-the-art performance on blind super-resolution. We also showcase the effectiveness of our method with a proof of concept for lens calibration: a real-world application traditionally requiring time-consuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort. Code available: https://github.com/inria-thoth/ddm4ip.",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Inverse problems arise in many domains where observed data is the result of a noisy and potentially lossy transfor",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "mation of an underlying signal we wish to recover. More formally, the degradation process is modeled as follows:",
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+ "page_idx": 0
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\ny = \\mathcal {A} (x) + \\epsilon , \\quad \\epsilon \\sim \\mathcal {N} (0, \\sigma^ {2} I), \\tag {1}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "where $\\mathcal{A}$ is the forward operator and $\\epsilon$ denotes additive Gaussian noise. The objective is to recover the original signal $x$ from the measurements $y$ . In practice, $\\mathcal{A}$ may represent a wide range of linear or nonlinear transformations, such as blur kernels, inpainting masks, the Radon transform, and many others.",
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+ {
+ "type": "text",
+ "text": "To introduce the setting of the current work, we categorize the reconstruction methods based on i) the type and availability of data, ii) the extent of prior knowledge about $\\mathcal{A}$ . When $\\mathcal{A}$ is fully known, two main classes of reconstruction approaches are typically used. The first is plug-and-play (PnP) methods, which apply iterative algorithms to recover signal $x$ from a single measurement $y$ by maximizing the posterior distribution $p(x\\mid y,\\mathcal{A})\\propto p(y\\mid x,\\mathcal{A})p(x)$ . These methods alternate between a data-fidelity term (dependent on $\\mathcal{A}$ ) and a prior term. The second class leverages supervised learning: if a clean dataset is available, it can be paired with synthetic measurements generated via $\\mathcal{A}$ to train a reconstruction model in a supervised fashion.",
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+ {
+ "type": "text",
+ "text": "However, complete knowledge of the forward operator $\\mathcal{A}$ is rarely available in practice. For instance, in superresolution it is common to assume bicubic downsampling to generate low-resolution images from high-resolution ones, yet models trained under this assumption often fail on real-world images where the actual downsampling kernel differs [18, 59].",
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+ {
+ "type": "text",
+ "text": "When $\\mathcal{A}$ is unknown or only partially specified, the",
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+ {
+ "type": "header",
+ "text": "CVF",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
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+ {
+ "type": "page_number",
+ "text": "28364",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "problem becomes more challenging and is called blind. One strategy is to collect (or synthetically generate) a dataset that includes corrupted samples produced from a range of possible $\\mathcal{A}$ instances. A supervised model is then trained to generalize across these degradations. An alternative approach is to jointly infer both the clean signal and the unknown operator by maximizing the joint posterior $p(x, \\mathcal{A} \\mid y) \\propto p(y \\mid x)p(x)p(\\mathcal{A})$ which requires priors on both the data distribution and the corruption process. Both approaches implicitly rely on some prior knowledge or assumptions about $\\mathcal{A}$ , either through heuristic degradation models or learned probabilistic priors. Consequently, when the true degradation deviates from these assumptions—which is often the case in real-world scenarios—the reconstruction performance degrades significantly. Although these methods typically require very little input data at test time (sometimes even a single image), their robustness to real-world variations is far from guaranteed.",
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+ {
+ "type": "text",
+ "text": "The natural alternative, which we adopt in this work, is to learn information about $\\mathcal{A}$ directly from data: specifically, from one dataset of corrupted images and a separate dataset of clean images. Crucially, these datasets do not need to contain corresponding clean-corrupted pairs, which significantly simplifies data collection. During training, the unpaired clean images serve as a reference for what the restored outputs should resemble—effectively providing a model for $p(x)$ . This unpaired training setup is often referred to as unsupervised, and has been successfully applied to in-the-wild image restoration tasks [31, 45, 51], where the degradation process is unknown and may involve multiple, complex transformations. Most existing algorithms operating in this unpaired regime use an implicit model of the degradation process: a neural network is trained to map corrupted inputs to clean outputs, without explicitly modeling the underlying forward operator.",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "The method we propose learns the correct degradation by learning an explicit operator $\\mathcal{A}$ and needs a relatively small (hundreds to thousands) number of training points. By using diffusion models and an efficient distribution matching algorithm it outperforms both single-image methods and other unsupervised ones. It comprises two distinct steps: the first one learns a representation of the noisy distribution, the second learns the best degradation operator $\\mathcal{A}$ such that the clean samples corrupted by $\\mathcal{A}$ match in distribution the noisy data prior. Finally the learned corruption can be used in a third step for non-blind restoration. Our contributions are threefold: we begin by devising a principled method for solving inverse problems which only relies on unpaired image data from clean and corrupted distributions, without knowledge of the degradation operator. We prove that under a non-degeneracy assumption on the clean distribution, the true operator can be identified. We then show how this method can provide precise estimates of the degradation operator, without making any distributional assumptions on the operator itself. In particular we focus on the tasks of uniform and non-uniform deblurring. Finally,",
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+ {
+ "type": "text",
+ "text": "Table 1. Summary of tasks for solving inverse problems without knowing the forward operator. The headings refer to what is known about the data and the forward operator. Regarding the latter, we note when the method works on data corrupted by a single (unknown) operator, operators from a predefined distribution, or by a collection of unknown operators. The references are not meant to be exhaustive but just to provide examples.",
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+ "type": "table",
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+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Data | A | Method | References |
| prior on X | single known | PnP | [42, 47, 57, 62] |
| paired | single unknown | supervised | [49] |
| prior on X | prior on A | blind PnP | [12, 23, 44, 52] |
| paired | prior on A | supervised | [18, 50, 58] |
| unpaired | multiple unknown | unsupervised | [34, 45, 51] |
| unpaired | functional form | this paper |
",
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+ {
+ "type": "text",
+ "text": "since the estimates we obtain are considerably more precise than those of single-image methods, we show how they can be used as part of a pipeline for camera lens calibration – where accuracy is essential.",
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+ "text": "The rest of the paper is organized as follows. In Sec. 2, we provide some necessary background on inverse problems with unknown degradations and on our algorithm. In Sec. 3, we detail the different steps of our algorithm, whereas the last section is devoted to experiments of increasing complexity on estimating blur kernels.",
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+ "type": "text",
+ "text": "2. Background",
+ "text_level": 1,
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "We briefly review the literature on blind and unsupervised inverse problems in imaging, along with the various forms of deblurring addressed in this work.",
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+ {
+ "type": "text",
+ "text": "2.1. Unsupervised inverse problems",
+ "text_level": 1,
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "Solving inverse problems without access to the forward operator is inherently challenging and can be approached from multiple perspectives. In Tab. 1 we provide a framework to clarify the various settings considered in the literature. Unlike many of the methods discussed below, our approach assumes a fixed degradation operator $\\mathcal{A}$ which does not vary across measurements $y$ . While this restricts generality, it enables higher reconstruction accuracy in specific settings compared to other unpaired methods. We focus on unpaired algorithms, particularly for deblurring and super-resolution tasks, where $\\mathcal{A}$ typically corresponds to a blur kernel. Data augmentation-based approaches [50, 58] construct synthetic supervised datasets using heuristically designed degradation pipelines which mimic diverse real-world corruptions. To improve adaptability to specific degradations, Zhang et al. [59] propose learning some of the pipeline parameters from a small dataset of noisy reference images. For better alignment with the degradation of each individual image, a line of work tackles the blind MAP inference problem using deep priors over both clean images and degradation operators. These methods are typically coupled with test-time optimization algorithms such as alternating minimization [41], expectation-maximization (EM) [17, 23], or proximal gradient methods [48]. Recent",
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+ {
+ "type": "page_number",
+ "text": "28365",
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+ {
+ "type": "text",
+ "text": "approaches [12, 23, 44] incorporate diffusion models as priors for the blur kernel, jointly estimating $\\mathcal{A}$ and $x$ via plug-and-play algorithms [47]. Closely related methods include FKP [27], which uses a pretrained normalizing flow as a kernel prior, and DKP [52], which employs MCMC to iteratively refine the blur estimate. GibbsDDRM [38], by contrast, uses a diffusion prior on the clean image and a simpler total variation (TV) prior on the blur kernel.",
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "In contrast to this class of methods, which require only a single degraded image at test time, our approach does not rely on any pretrained priors—neither on clean images nor on the degradation operator. Instead, it learns to adapt directly to the specific corruption process represented in the training data. While it does require a small dataset of degraded images from the same corruption distribution, this targeted adaptation enables significantly improved reconstruction accuracy.",
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "Domain transfer approaches based on variations of the cycle-consistency loss [61] are conceptually closer to our method. Given a noisy image $y$ and an unpaired clean image $x$ , a clean-image generator $\\mathcal{G}$ and a noisy-image generator $\\mathcal{F}$ are jointly trained under the constraint that $\\mathcal{G}(\\mathcal{F}(x)) \\approx x$ and $\\mathcal{F}(\\mathcal{G}(y)) \\approx y$ . For instance, CinCGAN [36, 53] translates images downsampled with an unknown kernel into bicubically downsampled images, which can then be more effectively upscaled using standard super-resolution models. Several related methods [9, 30, 34, 37, 45, 51] employ generative models to synthesize corrupted images from clean ones, thereby enabling the construction of supervised training datasets. This synthesis can be done in a two-stage pipeline or directly in an end-to-end manner [11, 43]. Notably, Sim et al. [45] address a setting similar to ours, where a model is trained to deblur microscopy images in an unpaired setup. Compared to these approaches, our method leverages a novel loss function derived from diffusion models—a technique not previously applied in this context. Unlike adversarial losses, our formulation is more stable and easier to train. Moreover, by learning an explicit representation of the degradation kernel rather than an implicit one, our method offers significantly improved interpretability. Furthermore, under certain assumptions, we are able to prove the identifiability of the true operator (see Sec. 3).",
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+ "type": "text",
+ "text": "We also briefly note that many methods aim to learn the degradation operator in a single-image fashion, but still require paired training data—typically synthetic—for supervision. For instance, IKC [18] iteratively refines kernel estimates in alternation with clean-image predictions. DAN [35] extends this idea by unrolling the refinement process into an end-to-end trainable network. In contrast, KernelGAN [6] learns the degradation operator directly from a single input image, followed by a separate non-blind model to reconstruct the clean image $x$ .",
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+ "type": "text",
+ "text": "2.2. Distribution matching",
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+ "type": "text",
+ "text": "Our method minimizes the distance between two probability distributions over images: the distribution of the",
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+ {
+ "type": "text",
+ "text": "observed noisy data $p(y)$ and that of clean data corrupted by a learned degradation operator, i.e., $p(\\mathcal{A}(x))$ . A common strategy for such distribution matching is to use generative adversarial networks (GANs), which optimize an adversarial loss. GANs have been extensively applied to image restoration tasks, as discussed in the previous section [34, 45], and can simultaneously learn both the degradation operator and its inverse within a unified training framework. However, training GANs is notoriously challenging due to instability and sensitivity to hyperparameters [8]. Alternative approaches include normalizing flows, which provide exact likelihoods and invertible mappings. These have been used by DeFlow [51] for matching clean and noisy distributions, and by FKP [27] to generate plausible blur kernels from single images.",
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+ "type": "text",
+ "text": "More recently, diffusion models – like GANs and normalizing flows – have emerged as powerful tools for modeling empirical distributions and have been used in a range of distribution-matching tasks. For example, DreamFusion [39] learns 3D representations whose 2D projections are consistent with a pretrained diffusion model, while DiffInstruct [32] trains a single-step generator to match the distribution of a multi-step diffusion model. Both approaches rely on a loss function that approximates the KL divergence integrated over all diffusion time steps.",
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+ "type": "text",
+ "text": "In our work, we use conditional flow matching (CFM) models [28, 29] as a more conceptually straightforward alternative to standard diffusion models. We adapt the integrated KL divergence loss to the CFM framework for learning the degradation operator.",
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+ "type": "text",
+ "text": "2.3. Camera lens calibration",
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+ "type": "text",
+ "text": "After preliminary experiments on synthetic deblurring, we focus on non-uniform deblurring in the context of a camera calibration pipeline. Camera calibration is a multifaceted task typically broken down into subtasks such as distortion, chromatic aberration, and vignetting corrections among others. In this work, we concentrate solely on compensating for blur induced by lens imperfections, with the goal of obtaining maximally sharp images. These lens aberrations can be characterized by the point spread function (PSF) of the lens-camera system: the blur kernel that transforms an ideal point light source into a spread of colored spots in the image. PSFs are often non-uniform across the image plane and differ across RGB channels, resulting in chromatic aberrations. Correcting such distortions computationally is particularly appealing, as it enables the use of lower-cost lenses without sacrificing image quality.",
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+ "text": "Traditional non-blind correction methods require precise knowledge of the PSF, which can only be obtained through laborious procedures involving printed calibration patterns or specialized screens [5, 21]. In contrast, blind lens aberration correction remains an understudied problem, although it shares many similarities with non-uniform deblurring. It is more commonly approached under the umbrella of defocus deblurring [2, 24, 40, 54], where blur magnitude varies with scene depth. In aberration correction, however,",
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+ "type": "text",
+ "text": "the blur is dependent on spatial location in the image plane rather than depth. Nonetheless, defocus deblurring methods may still be partially effective for lens aberration correction, especially when the induced blur is close to isotropic. As a starting point, we use the PSF dataset from Bauer et al. [5], which provides ground-truth PSFs, and later move to a realistic calibration scenario using a Panasonic Micro 4/3 camera. In this setting, we acquire a small set of images and aim to learn the lens PSFs without access to ground-truth measurements. Our main comparison will be with the blind method proposed by Eboli et al. [16], which performs deblurring followed by color-fringe removal in a two-stage pipeline [10, 15].",
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+ "text": "3. Method",
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+ "type": "text",
+ "text": "Given an inverse problem of the form $y = \\mathcal{A}_{\\omega_{*}}(x) + \\epsilon$ , with known noise level $\\sigma$ and an unknown forward operator $\\mathcal{A}_{\\omega_{*}}$ parameterized by a vector $\\omega_{*}$ , we propose an algorithm to estimate $\\omega_{*}$ using unpaired data. On the one hand, we assume access to a clean dataset $\\mathcal{X} = \\{x_i\\}_{i=1}^n$ of images drawn from a distribution $\\mathbb{X}$ . On the other hand, we have access to a corrupted dataset $\\mathcal{Y} = \\{y_j\\}_{j=1}^m$ of images, generated from unknown clean samples via the forward model $\\mathcal{A}_{\\omega_{*}}$ . We denote by $\\mathbb{Y}_{\\omega_{*}}$ the distribution of such corrupted images, and by $\\mathbb{Y}_{\\omega}$ the distribution induced by applying an arbitrary forward operator $\\mathcal{A}_{\\omega}$ (with additive noise) to samples from $\\mathbb{X}$ .",
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+ "type": "text",
+ "text": "Noting that $\\mathbb{Y}_{\\omega_*}$ is empirically accessible through $\\mathcal{V}$ while $\\mathbb{Y}_{\\omega}$ can be approximated via $\\mathcal{X}$ and a candidate forward operator $\\mathcal{A}_{\\omega}$ , we hypothesize that minimizing the distance between $\\mathbb{Y}_{\\omega_*}$ and $\\mathbb{Y}_{\\omega}$ with respect to $\\mathcal{A}_{\\omega}$ yields a good approximation of the true forward model parameters:",
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+ "type": "equation",
+ "text": "\n$$\n\\hat {\\omega} = \\underset {\\omega} {\\arg \\min } \\mathcal {D} \\left(\\mathbb {Y} _ {\\omega_ {*}}, \\mathbb {Y} _ {\\omega}\\right) \\Rightarrow \\mathcal {A} _ {\\hat {\\omega}} \\approx \\mathcal {A} _ {\\omega_ {*}}, \\tag {2}\n$$\n",
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+ "text": "where $\\mathcal{D}$ is a distance between distribution that will be specified in detail later. We prove this rigorously in a simplified setting in Proposition 3.1, with the full proof provided in the supplementary material, and we assume that the result generalizes when the distributions are only approximately equal, as is typically the case in practice.",
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+ "text": "Proposition 3.1: For any set of forward model parameters $\\omega$ , let $p_{\\omega}(y) = \\int p_{\\omega}(y \\mid x)p(x)dx$ where $p_{\\omega}(y \\mid x) = \\mathcal{N}(y \\mid A_{\\omega}x, \\sigma^2 I)$ . Let $\\omega_*$ be a specific set of parameters which we consider to be the optimal set. Then, assuming the data covariance $\\Sigma = \\mathbb{E}_x[xx^\\top]$ is invertible, there exists an orthogonal matrix $P$ such that",
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+ "type": "equation",
+ "text": "\n$$\np _ {\\omega} (y) = p _ {\\omega_ {*}} (y) \\Longrightarrow \\mathcal {A} _ {\\omega} = \\mathcal {A} _ {\\omega_ {*}} \\Sigma^ {1 / 2} P \\Sigma^ {- 1 / 2} \\tag {3}\n$$\n",
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+ "text": "That is, if the probability distributions $p_{\\omega}$ and $p_{\\omega_*}$ are equal, it is possible to identify $\\mathcal{A}_{\\omega_*}$ up to rotations $P$ .",
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+ "text": "Since neither $\\mathbb{Y}_{\\omega_*}$ nor $\\mathbb{Y}_{\\omega}$ are explicitly available we will use CFM models to act as tractable representations of probability distributions on images.",
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+ "text": "3.1. Distribution matching with diffusion",
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+ "text": "A CFM model $v_{\\theta}(z^{(t)}, t)$ trained on data from a distribution $\\mathbb{Y}_{\\omega}$ allows one to sample from $\\mathbb{Y}_{\\omega}$ by solving an ODE between times 0 and 1, defined as",
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+ "type": "equation",
+ "text": "\n$$\nd z ^ {(t)} = v _ {\\theta} \\left(z ^ {(t)}, t\\right) d t, \\quad z ^ {(0)} \\sim \\mathcal {N} (0, I).\n$$\n",
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+ "type": "text",
+ "text": "such that $z^{(t = 1)}\\sim \\mathbb{Y}_{\\omega}$ . This conditional flow matching [28, 29] perspective is connected to standard Langevin diffusion since the velocity field $v_{\\theta}(x^{(t)},t)$ is related to the score of a diffusion model: $v_{\\theta}(z^{(t)},t) + z^{(t)}\\propto$ $\\nabla_z\\log p_{\\mathbb{Y}_\\omega^{(t)}}(z_\\omega^{(t)})$ [60], assuming the neural network model of the velocity field to be exact. Each $z^{(t)}$ follows an intermediate distribution between Gaussian noise and the data $\\mathbb{Y}_{\\omega}^{(t)}$ for $t\\in [0,1]$ . Hence, instead of computing a distance between two distributions, we will compute it between two sequences of distributions $\\mathbb{Y}_{\\omega}^{(t)}$ and $\\mathbb{Y}_{\\omega_*}^{(t)}$ which arise from two CFM models. In particular we will use the KL divergence integrated over time, and follow the derivation proposed by DiffInstruct [32] to compute its gradient with respect to $\\omega$ . The integrated KL divergence is defined as",
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+ "text": "\n$$\n\\operatorname {I K L} \\left(\\mathbb {Y} _ {\\omega_ {*}} \\| \\mathbb {Y} _ {\\omega}\\right) = \\int_ {t = 0} ^ {1} \\operatorname {K L} \\left(\\mathbb {Y} _ {\\omega_ {*}} ^ {(t)} \\| \\mathbb {Y} _ {\\omega} ^ {(t)}\\right) d t. \\tag {4}\n$$\n",
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+ "type": "text",
+ "text": "Assuming that the score terms for both probability distributions (i.e. $s_{\\theta, \\omega_*(y,t)} \\approx \\nabla_y \\log p_{\\mathbb{Y}_{\\omega_*}^{(t)}}(y)$ and $s_{\\phi, \\omega}(y,t) \\approx \\nabla_y \\log p_{\\mathbb{Y}_{\\omega^*}^{(t)}}(y)$ ) can be computed, it is possible to efficiently differentiate the IKL with respect to $\\omega$ :",
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+ "type": "equation",
+ "text": "\n$$\n\\nabla_ {\\omega} \\operatorname {I K L} \\left(\\mathbb {Y} _ {\\omega_ {*}} \\| \\mathbb {Y} _ {\\omega}\\right) =\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\int_ {t = 0} ^ {1} \\mathbb {E} \\left[ s _ {\\theta , \\omega_ {*}} \\left(y _ {\\omega} ^ {(t)}, t\\right) - s _ {\\phi , \\omega} \\left(y _ {\\omega} ^ {(t)}, t\\right) \\right] ^ {\\top} \\nabla_ {\\omega} y _ {\\omega} ^ {(t)} d t, \\tag {5}\n$$\n",
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+ "type": "text",
+ "text": "where the expectation is over $y_{\\omega}^{(0)} \\sim \\mathcal{N}(0, I), x \\sim \\mathcal{X}, y_{\\omega}^{(1)} = \\mathcal{A}_{\\omega}(x) + \\epsilon$ and $y_{\\omega}^{(t)} = (1 - t)y_{\\omega}^{(0)} + ty_{\\omega}^{(1)}$ . Note that eq. (5) has in fact been originally introduced to optimize a 3D scene consistent with a diffusion model's outputs [39] and in [32] was used to learn a distilled model. Here we are showing it can be used effectively on conditional flow matching models as well, and in a completely different setting. The loss gradient shown in eq. (5) needs certain quantities to be computed: the score of $p_{\\mathbb{Y}_{\\omega_*}}$ can be obtained beforehand by training a flow-matching model $v_{\\theta, \\omega_*}$ on the available noisy data $\\mathcal{V}$ . The score of $p_{\\mathbb{Y}_\\omega}$ however depends on a distribution which changes with every change in $\\omega$ . Therefore the strategy we use is to alternately optimize i) an auxiliary flow-matching model $v_{\\psi, \\omega}$ for a fixed $\\omega$ with a standard diffusion loss and ii) forward model parameters $\\omega$ with the IKL loss keeping the auxiliary model fixed [32]. By changing the parametrization of $\\mathcal{A}_{\\omega}$ eq. (5) can be used to learn the degradation of a variety of different inverse problems. We will now go into the details of the algorithm for the task of learning blur operators.",
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+ "type": "text",
+ "text": "3.2. Learning the forward operator",
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+ "text": "In deblurring, $\\mathcal{A}_{\\omega}$ corresponds to a convolution with kernel $\\omega$ . The algorithm we propose proceeds in three distinct",
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+ "text": "28367",
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+ "img_path": "images/97007ede18321d3a9b2c2fc76e4cbf1c459870b7f18ac1cc990a5b093bffcc58.jpg",
+ "image_caption": [
+ "Figure 2. Samples generated by the flow matching model with motion-blur kernel. While the model is average at generating faces, it correctly represents the degradation."
+ ],
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+ "bbox": [
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+ "type": "text",
+ "text": "steps: i) learn the corrupted data distribution, ii) approximate the forward operator $\\mathcal{A}_{\\omega_*}$ and iii) solve the non-blind inverse problem.",
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+ "text": "Step 1: Learning $\\mathbb{Y}_{\\omega_*}$ . In more detail, the first step uses the noisy dataset $\\{y_j\\}_{j=1}^m$ to train a conditional flow matching (CFM) model $v_{\\theta, \\omega_*}$ that transports Gaussian noise samples at time $t = 0$ , $z^{(0)} \\sim \\mathcal{N}(0, I)$ , to samples from the corrupted data distribution $\\mathbb{Y}_{\\omega_*}$ at time $t = 1$ , i.e., $z^{(1)} \\sim \\mathbb{Y}_{\\omega_*}$ . The training objective is the standard conditional flow matching loss [28, 29]:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C F M}} = \\mathbb {E} _ {t, z ^ {(0)}, z ^ {(1)}} \\left[ \\left\\| v _ {\\theta , \\omega_ {*}} (z ^ {(t)}, t) - (z ^ {(1)} - z ^ {(0)}) \\right\\| \\right].\n$$\n",
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+ "text": "Importantly, for the overall success of our method, it is not necessary for $v_{\\theta, \\omega_*}$ to achieve state-of-the-art generative quality; it only needs to effectively capture the degradation process, which we found to be significantly easier than precisely modeling image content. See Fig. 2 for sample outputs produced by a model at this stage.",
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+ "text": "Step 2: distribution matching. The second step uses the clean dataset $\\mathcal{X}$ to learn the corruption operator $\\hat{\\mathcal{A}}_{\\omega} \\approx \\mathcal{A}_{\\omega_*}$ by minimizing the IKL loss (4). This involves two alternating optimization steps: first, training an auxiliary diffusion model $v_{\\phi,\\omega}(z^{(t)}, t)$ using the standard flow-matching loss, where $z^{(t)} = (1 - t)z^{(0)} + t\\mathcal{A}_{\\omega}(x)$ ; second, updating $\\hat{\\mathcal{A}}_{\\omega}$ by following the gradient in eq. (5).",
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+ "type": "text",
+ "text": "To encourage fast convergence, the auxiliary model $v_{\\phi,\\omega}$ is initialized with the pretrained weights from $v_{\\theta,\\omega_*(z^{(t)},t)}$ . The parameterization of $\\hat{\\mathcal{A}}_{\\omega}$ is flexible: it may depend on the clean image $x$ —which limits certain options for the final step—or be independent of $x$ . For instance, we consider modeling non-uniform blur with an operator $\\hat{\\mathcal{A}}_{\\omega}$ that varies with pixel location. The framework is general, but $\\hat{\\mathcal{A}}_{\\omega}$ should not depend on corrupted images, as these are unavailable in the unpaired training setting. The distribution matching step can also be regularized in various ways to introduce prior knowledge about the forward model and improve the quality of results. For example, when $\\mathcal{V}$ and $\\mathcal{X}$ consist of patch data, their distribution will be invariant to translation: an image patch translated by some amount in any direction will still follow the same distribution. This invariant can easily lead to learning blur filters which are off-center as shown in Fig. 3. To counter this we add a regularizer which constrains the center of mass of the learned kernels to be in the middle of the filter itself.",
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+ "type": "text",
+ "text": "Step 3: solve the inverse problem. The third and final step is to use the learned forward model $\\hat{A}_{\\omega}$ to solve the inverse problem. At this point the non-blind setting applies,",
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+ "img_path": "images/eda72e53b6bdada176402e36da3be203d7a8e9f9dda7aa5d1bff4cce0b385de5.jpg",
+ "image_caption": [
+ "Figure 3. Effect of center regularization on reconstruction quality. Without regularization the learned blur filter may be shifted leading to larger reconstruction errors (second row of the plot). A moderate amount of regularization fixes this."
+ ],
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+ "text": "hence multiple strategies can be chosen depending on the specific problem and on the type of data which is available. When a larger clean-image dataset is available, by leveraging $\\hat{A}_{\\omega}$ it is possible to generate a paired noisy-clean dataset on which to train a supervised image restoration model [49, 54]. The second option is to use a plug and play algorithm [47] which leverages a pretrained prior on clean images (classically this could have been a prior such as total-variation instead) to iteratively convert a noisy image into a clean one. In Sec. 4 we will use ESRGAN [49] from the first option and DPIR [55], DiffPIR [62] from the second one. Of course classical alternatives such as Wiener deconvolution can be used depending on the specific inverse problem.",
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+ "type": "text",
+ "text": "4. Experiments",
+ "text_level": 1,
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+ "type": "text",
+ "text": "4.1. Deblurring",
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+ "text": "We used subsets of the FFHQ dataset [19] to compare with blind deblurring methods. In particular, for each of two degradation operators we train a small CFM model on 1000 images from FFHQ corrupted by the blurring operator $\\mathcal{A}_{\\omega_*}$ and subsequently utilize 100 different clean images to learn $\\hat{\\mathcal{A}}_{\\omega}$ with distribution matching. We use an isotropic Gaussian blur with standard deviation 1 and a motion blur kernel generated following Borodenko [7]. In both cases, Gaussian noise is added with standard deviation of 0.02. We finally use plug and play algorithm DiffPIR [62] to solve the inverse problem $\\hat{\\mathcal{A}}_{\\omega}$ . The natural upper baseline for this experiment is to run the same PnP algorithm with the ground-truth kernel. In addition to this, we compare with some lower baselines which learn the correct kernel from a single image, and simultaneously perform deblurring: diffusion based methods BlindDPS [12], FastDiffusionEM [23] and KernelDiff [44]. These latter blind algorithms require two priors (in the form of pretrained diffusion models): one on the image dataset and one on the kernels. BlindDPS and FastDiffusionEM use FFHQ as image prior while KernelDiff uses several natural image datasets [14]. All three methods assume the blur kernels to be motion-blur, generated using the same stochastic procedure [7] as the true one. BlindDPS additionally includes isotropic Gaussian",
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+ "type": "table",
+ "img_path": "images/163a275fdb8be9feb173942ddfdbd31107daa965ac5b5c347ff2d43e95921aef.jpg",
+ "table_caption": [
+ "Table 2. Reconstruction error on FFHQ. KernelDiff was run with no noise. FastEM was run with 16 samples and IIGDM."
+ ],
+ "table_footnote": [],
+ "table_body": " | Gaussian blur | Motion blur |
| PSNR | LPIPS | PSNR | LPIPS |
| Non-blind (true kernel available) |
| DiffPIR | 32.7 | 0.031 | 29.3 | 0.068 |
| Blind, multi-image |
| Ours + DiffPIR | 32.7 | 0.031 | 28.8 | 0.069 |
| Blind, single-image |
| Blind-DPS [12] | 29.8 | 0.077 | 25.5 | 0.122 |
| FastEM (n=16) [23] | - | - | 24.9 | 0.130 |
| KernelDiff [44] | - | - | 21.7 | 0.194 |
",
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+ "type": "text",
+ "text": "kernels in its kernel prior, which is why in Tab. 2 we also test it on a Gaussian kernel. It is important to stress that our algorithm works in a different setting from the single-image methods: we require a dataset of clean and noisy images for each degradation, while the single-image algorithms only require a single noisy image. However, note that all single-image algorithms rely strongly on the image and kernel priors on which they were trained: for example we could not successfully run the method from Laroche et al. [23] on a simple Gaussian kernel without first retraining the kernel prior, and KernelDiff which uses a different image prior than FFHQ performs poorly in this setting. The results in Tab. 2 demonstrate two things: first, even when the problem is purely in-distribution, the gap between blind and non-blind algorithms is large. In second instance, the algorithm we propose significantly reduces this gap by using more data from the same distribution to learn the necessary information about the degradation operator. To increase the robustness of our experiments we compute the standard deviation over 5 different random seeds for the 2nd step of our pipeline (thus keeping the 1st step fixed). For the motion blur kernel, we find a standard deviation of 0.02 for PSNR and 0.0005 for LPIPS which are both negligible.",
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+ "type": "text",
+ "text": "4.2. Space-varying blur",
+ "text_level": 1,
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+ "text": "In practice image blur may come from a variety of sources such as camera shake/motion, out-of-focus objects or lens distortions. We focus on the latter which better fits the our framework: it is easy to collect a set of noisy images with equal distribution, but it is not really possible to collect paired datasets (note that paired datasets can be generated synthetically through software camera models [26]). Every imaging system is imperfect, which can be characterized by a spatially varying point spread function (PSF) at every location in the image plane. It can thus be modeled as a per-pixel blur where the blur kernel depends on the image plane location. Since the PSFs are intrinsically connected to the imaging system, multiple pictures taken with the same camera and camera settings will have the same degradation.",
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+ "type": "table",
+ "img_path": "images/8de2c91663ad53c9d898ae7c3f4528202650d2d33dad3ded7457135fd27d8603.jpg",
+ "table_caption": [
+ "Table 3. Reconstruction error for non-uniform deblurring on DPDD. The degradation is a spatially varying blur with additive Gaussian noise ( $\\sigma = 0.01$ )."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| Non-blind (true kernel available) |
| ESRGAN [49] | 32.53 | 0.906 | 0.058 |
| DPIR [55] | 34.89 | 0.933 | 0.112 |
| Blind, multi-image |
| DeFlow+ESRGAN [51] | 27.92 | 0.818 | 0.206 |
| Ours+ESRGAN | 32.38 | 0.911 | 0.061 |
| Ours+DPIR | 33.84 | 0.933 | 0.099 |
| Blind, single-image |
| INIKNet [40] | 29.45 | 0.874 | 0.160 |
| Restormer [54] | 28.59 | 0.859 | 0.203 |
",
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+ "text": "For the first experiment we use real PSFs, taken from a subset of those identified in a real camera system [5] but synthetically applied to a clean dataset. In particular we use the green channel PSFs from the Canon EF 24mm f/1.4L II USM lens at 1.4 aperture, and subsample them to a $8 \\times 8$ grid, shown in Fig. 10 (top-left). This grid is then mapped to images from DIV2K [3] and DPDD [1], and applied as a per-pixel blur by linearly interpolating the kernels to each image location. We use the degraded DIV2K training-set (subdivided into patches 128 pixels wide) to train the diffusion model in the first stage of our algorithm, and the clean DDPD training-set for the second stage – thus ensuring the data is strictly unpaired. For the third and final stage we experiment with two procedures: the plug and play algorithm DPIR [55] which uses a CNN as regularizing prior and can be applied directly to the learned kernels, and supervised method ESRGAN [49] for which we generate a paired clean-noisy dataset using the learned degradation. In order to condition the kernels on image location, we add two positional encoding channels to our images such that the diffusion model learns different distributions based on the patch location. For the degradation prediction we directly learn the 64 kernels without any additional parametrization; both at train and at test time the correct kernels are picked by using the positional encoding and linearly interpolating between the kernels. For this experiment we used the centering regularization and also introduced an isotropic Gaussian regularization which helped stabilize training.",
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+ "text": "We compare the results obtained on the \"target\" testset of DPDD (corrupted with the camera PSFs and not with the original defocus degradations) against two pretrained methods tailored for real-world defocus deblurring: Restormer [54] and INIKNet [40], against unpaired algorithm DeFlow [51] which we retrain for the current task and couple with ESRGAN (DeFlow does not provide explicit degradations hence cannot be coupled with DPIR) and against the upper baselines ESRGAN and DPIR trained with the true degradation. While Restormer and INIKNet were trained on a different degradation domain, defocus",
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+ "DPIR* [55]"
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+ "Figure 4. Sample reconstructions on DDPD. INIKNet and Restormer are single image, DPIR is non-blind.",
+ "Figure 5. Different aberrations in parking lot data. While images taken at f/5.6 are sharp, chromatic aberrations are still present outside of the center portion as evidenced by the middle panel."
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+ "text": "blur is also spatially varying and should not be too far from the mostly isotropic kernels of the camera PSF. Nevertheless, their inferior performance compared to our method shows how even small changes to the degradation distribution can have a large impact on reconstruction performance. Table 3 shows the quantitative evaluation on DPDD while the qualitative results are shown in Fig. 4. DeFlow does not manage to learn the correct blur distribution, and simply introduces a small amount of noise in the generated degraded images, thus garnering the worst results. Both INIKNet and Restormer perform similarly and succeed at removing some of the blur, but the results are not as sharp as the reconstructions obtained with our method. Both non-blind methods perform very well, with ESRGAN being better under perceptual metrics and DPIR under distortion metrics. Importantly, and like we showed for the first round of experiments on FFHQ, our method is very close to its upper limit given by the non-blind counterpart. In the supplementary material we plot the predicted kernels which capture the spread and anisotropy of the true kernels.",
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+ "text": "As a final experiment we attempt to tackle the same lens-aberrations of the previous task, but this time on real data. We used a Panasonic DC-GX9 camera in aperture priority mode with a Leica DG Summilux $25\\mathrm{mm}$ f/1.4 II lens to take 22 pictures in our parking lot at different apertures. Our goal was to learn the PSF of the lens at an extreme aperture (e.g. f/16) in order to correct it using the clean distribution of images taken at a reasonable aperture (e.g. f/5.6). To",
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+ "Figure 6. Sample reconstructions on the parking lot dataset. Color differences in DxO are likely due to a different white-balancing algorithm. Eboli [15] correctly removes chromatic aberrations but introduces some noise artifacts. Our method results visually pleasing and significantly sharper than the original image."
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+ "text": "avoid confounding factors we tried to keep all the image-plane in focus and had ample light to obtain sharp images. Note that while the images at different f-stops were taken using a tripod from the same location no additional care was taken to align them, and they would not be suitable for a supervised learning algorithm. Images were minimally postprocessed, by devignetting and converting to sRGB using lensfunpy [25], in order to preserve the blurry artifacts. Then they were split into patches and fed through our algorithm: an initial diffusion model was trained on the \"noisy\" images at f/16, and then used as a guide to learn the degradation operator on the center part of f/5.6 images. By using the central part of f/5.6 images we should be able to fix the chromatic aberrations which appears around sharp edges but much less in central part of images. By inspecting the data (see Fig. 5) there is a noticeable increase in blurriness between clean and noisy samples, which nevertheless is not very strong. Unlike the previous experiments where we knew the amount of additive Gaussian noise $\\sigma$ used in the forward model, now the noise distribution is completely unknown. For simplicity we again use a Gaussian noise model and treat its standard deviation as a trainable parameter of $\\hat{A}_{\\omega}$ . Having a good noise estimate can be very useful in guiding the final reconstruction with plug-and-play methods. In Fig. 6 we compare our results with the algorithm from Eboli et al. [16] which is a two-step approach to first estimate and remove the blur, and then remove colored fringes using a specialized procedure [15]. For fairness we must note that the algorithm we're comparing against [16]",
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+ "text": "works with single images, and doesn't need retraining for different lenses, partly thanks to strong inductive priors on the blur kernel (Gaussian with 7 parameters) and on the color aberrations. We also compare to commercial solution DxO PhotoLab [22] which exploits information about the specific lens used. We used the web version of the software and applied chromatic aberration filter followed by deblurring with strength 1.23. More comparisons as well as training details are available in the supplementary.",
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+ "text": "4.4. Single image super-resolution",
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+ "text": "Up to now we have dealt with the task of deblurring, matching clean and corrupted distributions across datasets. Interestingly, there is a very related task whose properties allow us to work on single images, instead of across datasets. Super-resolution is commonly modeled as the composition of blurring with kernel $k$ and subsampling $y = (x \\otimes k) \\downarrow s$ , hence its close relationship to deblurring. In this setting our algorithm works on single low-resolution images, split into small patches. First, the noisy distribution $\\mathbb{Y}_{\\omega_*}$ is learned with a diffusion model on the patches. Then we learn a kernel $\\hat{k}$ such that",
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+ "text": "\n$$\np \\left(\\left(y * \\hat {k}\\right) \\downarrow_ {s}\\right) \\approx \\mathbb {Y} _ {\\omega_ {*}}. \\tag {6}\n$$\n",
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+ "text": "Note that in eq. (6) the low-resolution image $y$ is further downscaled using kernel $\\hat{k}$ which is the current estimator of the true kernel. This twice-downscaled image is compared in distribution to the once-downscaled image. Thanks to the scale-invariance of natural images the distributions (once-downscaled and twice-downscaled) will match when the kernels used for downscaling are the same, leading to the recovery of the true kernel. The downscaling step is crucial for this to work: if we omitted it (i.e. pure deblurring), we would always recover the identity kernel. For a quantitative experiment on single image super-resolution we adopt the setting from Bell-Kligler et al. [6] who also introduced the DIV2KRK dataset consisting of 100 images from DIV2K [3] downscaled with random anisotropic Gaussian kernels. After learning $\\hat{k}$ using the proposed algorithm, we tested three non-blind solvers: ZSSR [4] which requires no pretraining and USRNet [56] for which we used the tiny pretrained model and DANv2 [35] from which we took just the Restorer module plugged with $\\hat{k}$ . In Tab. 4 we compare our approach with: i) Two end-to-end solutions [33, 35] which jointly learn super-resolution and kernel-estimation by pre-training on DIV2K + Flickr2K [46] datasets, ii) two non-blind super-resolution algorithms [4, 56] which are natural upper-bounds for our method and iii) three kernel-estimation algorithms [6, 27, 52] which are directly comparable to the proposed method. Note that both DANv2 and DCLS outperform the non-blind methods. We hypothesize this may be due to the strong prior the methods have learned during training on a dataset which is very similar to the one used in testing. To analyze kernel estimation performance in isolation we look at kernel metrics k-PSNR and k-NCC (not available for DCLS which operates in a",
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+ "table_caption": [
+ "Table 4. x2 super-resolution on DIV2RKK dataset. Methods are grouped by the respective non-blind solver. NCC is the normalized cross-correlation metric."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | Y-PSNR | SSIM | LPIPS | kernel PSNR | kernel NCC |
| End to end (kernel estimator trained on external data) |
| DANv2 [35] | 32.12 | 0.8954 | 0.148 | 56.8 | 0.97 |
| DCLS [33] | 32.31 | 0.9006 | 0.147 | - | - |
| Non-blind (true kernel available) |
| ZSSR | 32.04 | 0.8885 | 0.196 | ∞ | 1 |
| USRNet | 32.06 | 0.8923 | 0.158 | ∞ | 1 |
| DANv2 | 31.94 | 0.8957 | 0.147 | ∞ | 1 |
| Two-step (kernel estimate from single image) |
| KernelGAN [6] | 29.65 | 0.8465 | 0.248 | 51.5 | 0.92 |
| Ours + ZSSR | 31.61 | 0.8837 | 0.200 | 64.2 | 0.96 |
| DKP [52] | 23.18 | 0.6245 | 0.226 | 53.6 | 0.92 |
| DIP-FKP [27] | 29.52 | 0.8530 | 0.249 | 50.4 | 0.95 |
| Ours + USRNet | 31.11 | 0.8838 | 0.167 | 64.2 | 0.96 |
| Ours + DANv2 | 31.86 | 0.8938 | 0.149 | 64.2 | 0.96 |
",
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+ "type": "text",
+ "text": "different kernel space) which show that the proposed algorithm performs the same as DANv2. This can be further corroborated by plugging in the learned kernels with the DANv2 super-resolution module on its own, which significantly reduces the performance gap to the end-to-end DANv2. When compared to the other 2-step methods, the proposed algorithm emerges as the clear winner both on image and kernel metrics.",
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+ "type": "text",
+ "text": "5. Conclusions",
+ "text_level": 1,
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+ "text": "Solving blind inverse problems from unpaired data is highly relevant for practical real-world image restoration tasks. In this work, we proposed an algorithm which learns the degradation operator directly from data, making minimal assumptions about the operator itself. Through extensive experiments on uniform and non-uniform deblurring, we have shown that it is possible to reduce the performance gap between blind single-image methods and non-blind methods by leveraging multiple images from the same degradation process. Built-in interpretability and flexibility in its design make the proposed algorithm applicable to solving diverse problems. On the other hand, having multiple images belonging to the same noisy-data distribution may not be realistic for all situations, where single-image methods work best – this single-image setting can be handled with our methods only in specific problems such as superresolution. Furthermore, while our framework is designed to deal with unpaired data, if the clean and noisy distributions are known through highly unrelated datasets, the matching procedure will struggle to learn a degradation operator to reconcile the two. The domain shift between clean and noisy distributions hinders training as it becomes larger. Future directions include tackling problems from different domains such as microscopy or medical imaging, as well improving the noise-modeling to be more realistic (e.g. to handle Poisson-Gaussian noise).",
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+ "text": "Acknowledgements",
+ "text_level": 1,
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+ "text": "This work was supported by ERC grant number 101087696 (APHELEIA project). This work was granted access to the HPC resources of IDRIS under the allocation AD011015445 made by GENCI.",
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+ "text": "References",
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+ },
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+ "Feng Gao, Ying Nian Wu et al. Flow priors for linear inverse problems via iterative corrupted trajectory matching. In Neural Information Processing Systems (NeurIPS), 2024. 4",
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diff --git a/2025/Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching/463f2cdf-f627-4efe-affd-1ebc9f1c243d_model.json b/2025/Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching/463f2cdf-f627-4efe-affd-1ebc9f1c243d_model.json
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+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "content": "Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching"
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+ "content": "Giacomo Meanti Thomas Ryckeboer Michael Arbel Julien Mairal Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France firstname.lastname@inria.fr"
+ },
+ {
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+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 1. Learning degradation operators by matching distributions."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "Abstract"
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+ "type": "text",
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+ "angle": 0,
+ "content": "This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches—which typically assume full knowledge of the forward model or access to paired degraded and ground-truth images—the proposed method operates under minimal assumptions and relies only on small, unpaired datasets. This makes it particularly well-suited for real-world scenarios, where the forward model is often unknown or mis-specified, and collecting paired data is costly or infeasible. The method leverages conditional flow matching to model the distribution of degraded observations, while simultaneously learning the forward model via a distribution-matching loss that arises naturally from the framework. Empirically, it outperforms both single-image blind and unsupervised approaches on deblurring and non-uniform point spread function (PSF) calibration tasks. It also matches state-of-the-art performance on blind super-resolution. We also showcase the effectiveness of our method with a proof of concept for lens calibration: a real-world application traditionally requiring time-consuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort. Code available: https://github.com/inria-thoth/ddm4ip."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "1. Introduction"
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+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "Inverse problems arise in many domains where observed data is the result of a noisy and potentially lossy transfor"
+ },
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+ "type": "text",
+ "bbox": [
+ 0.525,
+ 0.455,
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+ "angle": 0,
+ "content": "mation of an underlying signal we wish to recover. More formally, the degradation process is modeled as follows:"
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+ {
+ "type": "equation",
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+ "content": "\\[\ny = \\mathcal {A} (x) + \\epsilon , \\quad \\epsilon \\sim \\mathcal {N} (0, \\sigma^ {2} I), \\tag {1}\n\\]"
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+ {
+ "type": "text",
+ "bbox": [
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+ "content": "where \\(\\mathcal{A}\\) is the forward operator and \\(\\epsilon\\) denotes additive Gaussian noise. The objective is to recover the original signal \\(x\\) from the measurements \\(y\\). In practice, \\(\\mathcal{A}\\) may represent a wide range of linear or nonlinear transformations, such as blur kernels, inpainting masks, the Radon transform, and many others."
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+ "content": "To introduce the setting of the current work, we categorize the reconstruction methods based on i) the type and availability of data, ii) the extent of prior knowledge about \\(\\mathcal{A}\\). When \\(\\mathcal{A}\\) is fully known, two main classes of reconstruction approaches are typically used. The first is plug-and-play (PnP) methods, which apply iterative algorithms to recover signal \\(x\\) from a single measurement \\(y\\) by maximizing the posterior distribution \\(p(x\\mid y,\\mathcal{A})\\propto p(y\\mid x,\\mathcal{A})p(x)\\). These methods alternate between a data-fidelity term (dependent on \\(\\mathcal{A}\\)) and a prior term. The second class leverages supervised learning: if a clean dataset is available, it can be paired with synthetic measurements generated via \\(\\mathcal{A}\\) to train a reconstruction model in a supervised fashion."
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+ "content": "However, complete knowledge of the forward operator \\(\\mathcal{A}\\) is rarely available in practice. For instance, in superresolution it is common to assume bicubic downsampling to generate low-resolution images from high-resolution ones, yet models trained under this assumption often fail on real-world images where the actual downsampling kernel differs [18, 59]."
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+ "content": "When \\(\\mathcal{A}\\) is unknown or only partially specified, the"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "problem becomes more challenging and is called blind. One strategy is to collect (or synthetically generate) a dataset that includes corrupted samples produced from a range of possible \\(\\mathcal{A}\\) instances. A supervised model is then trained to generalize across these degradations. An alternative approach is to jointly infer both the clean signal and the unknown operator by maximizing the joint posterior \\(p(x, \\mathcal{A} \\mid y) \\propto p(y \\mid x)p(x)p(\\mathcal{A})\\) which requires priors on both the data distribution and the corruption process. Both approaches implicitly rely on some prior knowledge or assumptions about \\(\\mathcal{A}\\), either through heuristic degradation models or learned probabilistic priors. Consequently, when the true degradation deviates from these assumptions—which is often the case in real-world scenarios—the reconstruction performance degrades significantly. Although these methods typically require very little input data at test time (sometimes even a single image), their robustness to real-world variations is far from guaranteed."
+ },
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+ "type": "text",
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+ "content": "The natural alternative, which we adopt in this work, is to learn information about \\(\\mathcal{A}\\) directly from data: specifically, from one dataset of corrupted images and a separate dataset of clean images. Crucially, these datasets do not need to contain corresponding clean-corrupted pairs, which significantly simplifies data collection. During training, the unpaired clean images serve as a reference for what the restored outputs should resemble—effectively providing a model for \\(p(x)\\). This unpaired training setup is often referred to as unsupervised, and has been successfully applied to in-the-wild image restoration tasks [31, 45, 51], where the degradation process is unknown and may involve multiple, complex transformations. Most existing algorithms operating in this unpaired regime use an implicit model of the degradation process: a neural network is trained to map corrupted inputs to clean outputs, without explicitly modeling the underlying forward operator."
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+ "type": "text",
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+ "content": "The method we propose learns the correct degradation by learning an explicit operator \\(\\mathcal{A}\\) and needs a relatively small (hundreds to thousands) number of training points. By using diffusion models and an efficient distribution matching algorithm it outperforms both single-image methods and other unsupervised ones. It comprises two distinct steps: the first one learns a representation of the noisy distribution, the second learns the best degradation operator \\(\\mathcal{A}\\) such that the clean samples corrupted by \\(\\mathcal{A}\\) match in distribution the noisy data prior. Finally the learned corruption can be used in a third step for non-blind restoration. Our contributions are threefold: we begin by devising a principled method for solving inverse problems which only relies on unpaired image data from clean and corrupted distributions, without knowledge of the degradation operator. We prove that under a non-degeneracy assumption on the clean distribution, the true operator can be identified. We then show how this method can provide precise estimates of the degradation operator, without making any distributional assumptions on the operator itself. In particular we focus on the tasks of uniform and non-uniform deblurring. Finally,"
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+ "content": "Table 1. Summary of tasks for solving inverse problems without knowing the forward operator. The headings refer to what is known about the data and the forward operator. Regarding the latter, we note when the method works on data corrupted by a single (unknown) operator, operators from a predefined distribution, or by a collection of unknown operators. The references are not meant to be exhaustive but just to provide examples."
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+ "content": "| Data | A | Method | References |
| prior on X | single known | PnP | [42, 47, 57, 62] |
| paired | single unknown | supervised | [49] |
| prior on X | prior on A | blind PnP | [12, 23, 44, 52] |
| paired | prior on A | supervised | [18, 50, 58] |
| unpaired | multiple unknown | unsupervised | [34, 45, 51] |
| unpaired | functional form | this paper |
"
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+ "content": "since the estimates we obtain are considerably more precise than those of single-image methods, we show how they can be used as part of a pipeline for camera lens calibration – where accuracy is essential."
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+ "content": "The rest of the paper is organized as follows. In Sec. 2, we provide some necessary background on inverse problems with unknown degradations and on our algorithm. In Sec. 3, we detail the different steps of our algorithm, whereas the last section is devoted to experiments of increasing complexity on estimating blur kernels."
+ },
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+ "type": "title",
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+ "content": "2. Background"
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+ "type": "text",
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+ "angle": 0,
+ "content": "We briefly review the literature on blind and unsupervised inverse problems in imaging, along with the various forms of deblurring addressed in this work."
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+ "content": "2.1. Unsupervised inverse problems"
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+ "content": "Solving inverse problems without access to the forward operator is inherently challenging and can be approached from multiple perspectives. In Tab. 1 we provide a framework to clarify the various settings considered in the literature. Unlike many of the methods discussed below, our approach assumes a fixed degradation operator \\(\\mathcal{A}\\) which does not vary across measurements \\(y\\). While this restricts generality, it enables higher reconstruction accuracy in specific settings compared to other unpaired methods. We focus on unpaired algorithms, particularly for deblurring and super-resolution tasks, where \\(\\mathcal{A}\\) typically corresponds to a blur kernel. Data augmentation-based approaches [50, 58] construct synthetic supervised datasets using heuristically designed degradation pipelines which mimic diverse real-world corruptions. To improve adaptability to specific degradations, Zhang et al. [59] propose learning some of the pipeline parameters from a small dataset of noisy reference images. For better alignment with the degradation of each individual image, a line of work tackles the blind MAP inference problem using deep priors over both clean images and degradation operators. These methods are typically coupled with test-time optimization algorithms such as alternating minimization [41], expectation-maximization (EM) [17, 23], or proximal gradient methods [48]. Recent"
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+ "angle": 0,
+ "content": "approaches [12, 23, 44] incorporate diffusion models as priors for the blur kernel, jointly estimating \\(\\mathcal{A}\\) and \\(x\\) via plug-and-play algorithms [47]. Closely related methods include FKP [27], which uses a pretrained normalizing flow as a kernel prior, and DKP [52], which employs MCMC to iteratively refine the blur estimate. GibbsDDRM [38], by contrast, uses a diffusion prior on the clean image and a simpler total variation (TV) prior on the blur kernel."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In contrast to this class of methods, which require only a single degraded image at test time, our approach does not rely on any pretrained priors—neither on clean images nor on the degradation operator. Instead, it learns to adapt directly to the specific corruption process represented in the training data. While it does require a small dataset of degraded images from the same corruption distribution, this targeted adaptation enables significantly improved reconstruction accuracy."
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+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "Domain transfer approaches based on variations of the cycle-consistency loss [61] are conceptually closer to our method. Given a noisy image \\( y \\) and an unpaired clean image \\( x \\), a clean-image generator \\( \\mathcal{G} \\) and a noisy-image generator \\( \\mathcal{F} \\) are jointly trained under the constraint that \\( \\mathcal{G}(\\mathcal{F}(x)) \\approx x \\) and \\( \\mathcal{F}(\\mathcal{G}(y)) \\approx y \\). For instance, CinCGAN [36, 53] translates images downsampled with an unknown kernel into bicubically downsampled images, which can then be more effectively upscaled using standard super-resolution models. Several related methods [9, 30, 34, 37, 45, 51] employ generative models to synthesize corrupted images from clean ones, thereby enabling the construction of supervised training datasets. This synthesis can be done in a two-stage pipeline or directly in an end-to-end manner [11, 43]. Notably, Sim et al. [45] address a setting similar to ours, where a model is trained to deblur microscopy images in an unpaired setup. Compared to these approaches, our method leverages a novel loss function derived from diffusion models—a technique not previously applied in this context. Unlike adversarial losses, our formulation is more stable and easier to train. Moreover, by learning an explicit representation of the degradation kernel rather than an implicit one, our method offers significantly improved interpretability. Furthermore, under certain assumptions, we are able to prove the identifiability of the true operator (see Sec. 3)."
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+ "content": "We also briefly note that many methods aim to learn the degradation operator in a single-image fashion, but still require paired training data—typically synthetic—for supervision. For instance, IKC [18] iteratively refines kernel estimates in alternation with clean-image predictions. DAN [35] extends this idea by unrolling the refinement process into an end-to-end trainable network. In contrast, KernelGAN [6] learns the degradation operator directly from a single input image, followed by a separate non-blind model to reconstruct the clean image \\( x \\)."
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+ "content": "2.2. Distribution matching"
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+ "content": "Our method minimizes the distance between two probability distributions over images: the distribution of the"
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+ ],
+ "angle": 0,
+ "content": "observed noisy data \\( p(y) \\) and that of clean data corrupted by a learned degradation operator, i.e., \\( p(\\mathcal{A}(x)) \\). A common strategy for such distribution matching is to use generative adversarial networks (GANs), which optimize an adversarial loss. GANs have been extensively applied to image restoration tasks, as discussed in the previous section [34, 45], and can simultaneously learn both the degradation operator and its inverse within a unified training framework. However, training GANs is notoriously challenging due to instability and sensitivity to hyperparameters [8]. Alternative approaches include normalizing flows, which provide exact likelihoods and invertible mappings. These have been used by DeFlow [51] for matching clean and noisy distributions, and by FKP [27] to generate plausible blur kernels from single images."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.522,
+ 0.299,
+ 0.911,
+ 0.45
+ ],
+ "angle": 0,
+ "content": "More recently, diffusion models – like GANs and normalizing flows – have emerged as powerful tools for modeling empirical distributions and have been used in a range of distribution-matching tasks. For example, DreamFusion [39] learns 3D representations whose 2D projections are consistent with a pretrained diffusion model, while DiffInstruct [32] trains a single-step generator to match the distribution of a multi-step diffusion model. Both approaches rely on a loss function that approximates the KL divergence integrated over all diffusion time steps."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.522,
+ 0.45,
+ 0.91,
+ 0.526
+ ],
+ "angle": 0,
+ "content": "In our work, we use conditional flow matching (CFM) models [28, 29] as a more conceptually straightforward alternative to standard diffusion models. We adapt the integrated KL divergence loss to the CFM framework for learning the degradation operator."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.525,
+ 0.533,
+ 0.747,
+ 0.547
+ ],
+ "angle": 0,
+ "content": "2.3. Camera lens calibration"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.522,
+ 0.555,
+ 0.91,
+ 0.796
+ ],
+ "angle": 0,
+ "content": "After preliminary experiments on synthetic deblurring, we focus on non-uniform deblurring in the context of a camera calibration pipeline. Camera calibration is a multifaceted task typically broken down into subtasks such as distortion, chromatic aberration, and vignetting corrections among others. In this work, we concentrate solely on compensating for blur induced by lens imperfections, with the goal of obtaining maximally sharp images. These lens aberrations can be characterized by the point spread function (PSF) of the lens-camera system: the blur kernel that transforms an ideal point light source into a spread of colored spots in the image. PSFs are often non-uniform across the image plane and differ across RGB channels, resulting in chromatic aberrations. Correcting such distortions computationally is particularly appealing, as it enables the use of lower-cost lenses without sacrificing image quality."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.522,
+ 0.797,
+ 0.911,
+ 0.932
+ ],
+ "angle": 0,
+ "content": "Traditional non-blind correction methods require precise knowledge of the PSF, which can only be obtained through laborious procedures involving printed calibration patterns or specialized screens [5, 21]. In contrast, blind lens aberration correction remains an understudied problem, although it shares many similarities with non-uniform deblurring. It is more commonly approached under the umbrella of defocus deblurring [2, 24, 40, 54], where blur magnitude varies with scene depth. In aberration correction, however,"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.48,
+ 0.961,
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+ 0.972
+ ],
+ "angle": 0,
+ "content": "28366"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.072,
+ 0.498,
+ 0.27
+ ],
+ "angle": 0,
+ "content": "the blur is dependent on spatial location in the image plane rather than depth. Nonetheless, defocus deblurring methods may still be partially effective for lens aberration correction, especially when the induced blur is close to isotropic. As a starting point, we use the PSF dataset from Bauer et al. [5], which provides ground-truth PSFs, and later move to a realistic calibration scenario using a Panasonic Micro 4/3 camera. In this setting, we acquire a small set of images and aim to learn the lens PSFs without access to ground-truth measurements. Our main comparison will be with the blind method proposed by Eboli et al. [16], which performs deblurring followed by color-fringe removal in a two-stage pipeline [10, 15]."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.111,
+ 0.283,
+ 0.203,
+ 0.3
+ ],
+ "angle": 0,
+ "content": "3. Method"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.309,
+ 0.497,
+ 0.49
+ ],
+ "angle": 0,
+ "content": "Given an inverse problem of the form \\( y = \\mathcal{A}_{\\omega_{*}}(x) + \\epsilon \\), with known noise level \\( \\sigma \\) and an unknown forward operator \\( \\mathcal{A}_{\\omega_{*}} \\) parameterized by a vector \\( \\omega_{*} \\), we propose an algorithm to estimate \\( \\omega_{*} \\) using unpaired data. On the one hand, we assume access to a clean dataset \\( \\mathcal{X} = \\{x_i\\}_{i=1}^n \\) of images drawn from a distribution \\( \\mathbb{X} \\). On the other hand, we have access to a corrupted dataset \\( \\mathcal{Y} = \\{y_j\\}_{j=1}^m \\) of images, generated from unknown clean samples via the forward model \\( \\mathcal{A}_{\\omega_{*}} \\). We denote by \\( \\mathbb{Y}_{\\omega_{*}} \\) the distribution of such corrupted images, and by \\( \\mathbb{Y}_{\\omega} \\) the distribution induced by applying an arbitrary forward operator \\( \\mathcal{A}_{\\omega} \\) (with additive noise) to samples from \\( \\mathbb{X} \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.491,
+ 0.497,
+ 0.567
+ ],
+ "angle": 0,
+ "content": "Noting that \\(\\mathbb{Y}_{\\omega_*}\\) is empirically accessible through \\(\\mathcal{V}\\) while \\(\\mathbb{Y}_{\\omega}\\) can be approximated via \\(\\mathcal{X}\\) and a candidate forward operator \\(\\mathcal{A}_{\\omega}\\), we hypothesize that minimizing the distance between \\(\\mathbb{Y}_{\\omega_*}\\) and \\(\\mathbb{Y}_{\\omega}\\) with respect to \\(\\mathcal{A}_{\\omega}\\) yields a good approximation of the true forward model parameters:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.153,
+ 0.582,
+ 0.496,
+ 0.607
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\omega} = \\underset {\\omega} {\\arg \\min } \\mathcal {D} \\left(\\mathbb {Y} _ {\\omega_ {*}}, \\mathbb {Y} _ {\\omega}\\right) \\Rightarrow \\mathcal {A} _ {\\hat {\\omega}} \\approx \\mathcal {A} _ {\\omega_ {*}}, \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.613,
+ 0.497,
+ 0.705
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathcal{D}\\) is a distance between distribution that will be specified in detail later. We prove this rigorously in a simplified setting in Proposition 3.1, with the full proof provided in the supplementary material, and we assume that the result generalizes when the distributions are only approximately equal, as is typically the case in practice."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.714,
+ 0.493,
+ 0.807
+ ],
+ "angle": 0,
+ "content": "Proposition 3.1: For any set of forward model parameters \\(\\omega\\), let \\(p_{\\omega}(y) = \\int p_{\\omega}(y \\mid x)p(x)dx\\) where \\(p_{\\omega}(y \\mid x) = \\mathcal{N}(y \\mid A_{\\omega}x, \\sigma^2 I)\\). Let \\(\\omega_*\\) be a specific set of parameters which we consider to be the optimal set. Then, assuming the data covariance \\(\\Sigma = \\mathbb{E}_x[xx^\\top]\\) is invertible, there exists an orthogonal matrix \\(P\\) such that"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.133,
+ 0.815,
+ 0.49,
+ 0.836
+ ],
+ "angle": 0,
+ "content": "\\[\np _ {\\omega} (y) = p _ {\\omega_ {*}} (y) \\Longrightarrow \\mathcal {A} _ {\\omega} = \\mathcal {A} _ {\\omega_ {*}} \\Sigma^ {1 / 2} P \\Sigma^ {- 1 / 2} \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.845,
+ 0.49,
+ 0.876
+ ],
+ "angle": 0,
+ "content": "That is, if the probability distributions \\( p_{\\omega} \\) and \\( p_{\\omega_*} \\) are equal, it is possible to identify \\( \\mathcal{A}_{\\omega_*} \\) up to rotations \\( P \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.887,
+ 0.497,
+ 0.933
+ ],
+ "angle": 0,
+ "content": "Since neither \\(\\mathbb{Y}_{\\omega_*}\\) nor \\(\\mathbb{Y}_{\\omega}\\) are explicitly available we will use CFM models to act as tractable representations of probability distributions on images."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.525,
+ 0.072,
+ 0.843,
+ 0.088
+ ],
+ "angle": 0,
+ "content": "3.1. Distribution matching with diffusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.524,
+ 0.093,
+ 0.91,
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+ ],
+ "angle": 0,
+ "content": "A CFM model \\( v_{\\theta}(z^{(t)}, t) \\) trained on data from a distribution \\( \\mathbb{Y}_{\\omega} \\) allows one to sample from \\( \\mathbb{Y}_{\\omega} \\) by solving an ODE between times 0 and 1, defined as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.583,
+ 0.144,
+ 0.851,
+ 0.162
+ ],
+ "angle": 0,
+ "content": "\\[\nd z ^ {(t)} = v _ {\\theta} \\left(z ^ {(t)}, t\\right) d t, \\quad z ^ {(0)} \\sim \\mathcal {N} (0, I).\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.524,
+ 0.168,
+ 0.912,
+ 0.39
+ ],
+ "angle": 0,
+ "content": "such that \\(z^{(t = 1)}\\sim \\mathbb{Y}_{\\omega}\\) . This conditional flow matching [28, 29] perspective is connected to standard Langevin diffusion since the velocity field \\(v_{\\theta}(x^{(t)},t)\\) is related to the score of a diffusion model: \\(v_{\\theta}(z^{(t)},t) + z^{(t)}\\propto\\) \\(\\nabla_z\\log p_{\\mathbb{Y}_\\omega^{(t)}}(z_\\omega^{(t)})\\) [60], assuming the neural network model of the velocity field to be exact. Each \\(z^{(t)}\\) follows an intermediate distribution between Gaussian noise and the data \\(\\mathbb{Y}_{\\omega}^{(t)}\\) for \\(t\\in [0,1]\\) . Hence, instead of computing a distance between two distributions, we will compute it between two sequences of distributions \\(\\mathbb{Y}_{\\omega}^{(t)}\\) and \\(\\mathbb{Y}_{\\omega_*}^{(t)}\\) which arise from two CFM models. In particular we will use the KL divergence integrated over time, and follow the derivation proposed by DiffInstruct [32] to compute its gradient with respect to \\(\\omega\\) . The integrated KL divergence is defined as"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.569,
+ 0.395,
+ 0.91,
+ 0.43
+ ],
+ "angle": 0,
+ "content": "\\[\n\\operatorname {I K L} \\left(\\mathbb {Y} _ {\\omega_ {*}} \\| \\mathbb {Y} _ {\\omega}\\right) = \\int_ {t = 0} ^ {1} \\operatorname {K L} \\left(\\mathbb {Y} _ {\\omega_ {*}} ^ {(t)} \\| \\mathbb {Y} _ {\\omega} ^ {(t)}\\right) d t. \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.524,
+ 0.434,
+ 0.912,
+ 0.498
+ ],
+ "angle": 0,
+ "content": "Assuming that the score terms for both probability distributions (i.e. \\(s_{\\theta, \\omega_*(y,t)} \\approx \\nabla_y \\log p_{\\mathbb{Y}_{\\omega_*}^{(t)}}(y)\\) and \\(s_{\\phi, \\omega}(y,t) \\approx \\nabla_y \\log p_{\\mathbb{Y}_{\\omega^*}^{(t)}}(y)\\)) can be computed, it is possible to efficiently differentiate the IKL with respect to \\(\\omega\\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.544,
+ 0.504,
+ 0.701,
+ 0.521
+ ],
+ "angle": 0,
+ "content": "\\[\n\\nabla_ {\\omega} \\operatorname {I K L} \\left(\\mathbb {Y} _ {\\omega_ {*}} \\| \\mathbb {Y} _ {\\omega}\\right) =\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.549,
+ 0.523,
+ 0.91,
+ 0.559
+ ],
+ "angle": 0,
+ "content": "\\[\n\\int_ {t = 0} ^ {1} \\mathbb {E} \\left[ s _ {\\theta , \\omega_ {*}} \\left(y _ {\\omega} ^ {(t)}, t\\right) - s _ {\\phi , \\omega} \\left(y _ {\\omega} ^ {(t)}, t\\right) \\right] ^ {\\top} \\nabla_ {\\omega} y _ {\\omega} ^ {(t)} d t, \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.524,
+ 0.566,
+ 0.912,
+ 0.873
+ ],
+ "angle": 0,
+ "content": "where the expectation is over \\(y_{\\omega}^{(0)} \\sim \\mathcal{N}(0, I), x \\sim \\mathcal{X}, y_{\\omega}^{(1)} = \\mathcal{A}_{\\omega}(x) + \\epsilon\\) and \\(y_{\\omega}^{(t)} = (1 - t)y_{\\omega}^{(0)} + ty_{\\omega}^{(1)}\\). Note that eq. (5) has in fact been originally introduced to optimize a 3D scene consistent with a diffusion model's outputs [39] and in [32] was used to learn a distilled model. Here we are showing it can be used effectively on conditional flow matching models as well, and in a completely different setting. The loss gradient shown in eq. (5) needs certain quantities to be computed: the score of \\(p_{\\mathbb{Y}_{\\omega_*}}\\) can be obtained beforehand by training a flow-matching model \\(v_{\\theta, \\omega_*}\\) on the available noisy data \\(\\mathcal{V}\\). The score of \\(p_{\\mathbb{Y}_\\omega}\\) however depends on a distribution which changes with every change in \\(\\omega\\). Therefore the strategy we use is to alternately optimize i) an auxiliary flow-matching model \\(v_{\\psi, \\omega}\\) for a fixed \\(\\omega\\) with a standard diffusion loss and ii) forward model parameters \\(\\omega\\) with the IKL loss keeping the auxiliary model fixed [32]. By changing the parametrization of \\(\\mathcal{A}_{\\omega}\\) eq. (5) can be used to learn the degradation of a variety of different inverse problems. We will now go into the details of the algorithm for the task of learning blur operators."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.525,
+ 0.88,
+ 0.8,
+ 0.896
+ ],
+ "angle": 0,
+ "content": "3.2. Learning the forward operator"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.524,
+ 0.902,
+ 0.91,
+ 0.933
+ ],
+ "angle": 0,
+ "content": "In deblurring, \\(\\mathcal{A}_{\\omega}\\) corresponds to a convolution with kernel \\(\\omega\\). The algorithm we propose proceeds in three distinct"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
+ 0.96,
+ 0.519,
+ 0.972
+ ],
+ "angle": 0,
+ "content": "28367"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.123,
+ 0.069,
+ 0.487,
+ 0.142
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.11,
+ 0.152,
+ 0.496,
+ 0.194
+ ],
+ "angle": 0,
+ "content": "Figure 2. Samples generated by the flow matching model with motion-blur kernel. While the model is average at generating faces, it correctly represents the degradation."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.211,
+ 0.496,
+ 0.256
+ ],
+ "angle": 0,
+ "content": "steps: i) learn the corrupted data distribution, ii) approximate the forward operator \\(\\mathcal{A}_{\\omega_*}\\) and iii) solve the non-blind inverse problem."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.257,
+ 0.497,
+ 0.363
+ ],
+ "angle": 0,
+ "content": "Step 1: Learning \\(\\mathbb{Y}_{\\omega_*}\\). In more detail, the first step uses the noisy dataset \\(\\{y_j\\}_{j=1}^m\\) to train a conditional flow matching (CFM) model \\(v_{\\theta, \\omega_*}\\) that transports Gaussian noise samples at time \\(t = 0\\), \\(z^{(0)} \\sim \\mathcal{N}(0, I)\\), to samples from the corrupted data distribution \\(\\mathbb{Y}_{\\omega_*}\\) at time \\(t = 1\\), i.e., \\(z^{(1)} \\sim \\mathbb{Y}_{\\omega_*}\\). The training objective is the standard conditional flow matching loss [28, 29]:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.123,
+ 0.372,
+ 0.483,
+ 0.393
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {C F M}} = \\mathbb {E} _ {t, z ^ {(0)}, z ^ {(1)}} \\left[ \\left\\| v _ {\\theta , \\omega_ {*}} (z ^ {(t)}, t) - (z ^ {(1)} - z ^ {(0)}) \\right\\| \\right].\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.402,
+ 0.495,
+ 0.492
+ ],
+ "angle": 0,
+ "content": "Importantly, for the overall success of our method, it is not necessary for \\( v_{\\theta, \\omega_*} \\) to achieve state-of-the-art generative quality; it only needs to effectively capture the degradation process, which we found to be significantly easier than precisely modeling image content. See Fig. 2 for sample outputs produced by a model at this stage."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.492,
+ 0.496,
+ 0.598
+ ],
+ "angle": 0,
+ "content": "Step 2: distribution matching. The second step uses the clean dataset \\(\\mathcal{X}\\) to learn the corruption operator \\(\\hat{\\mathcal{A}}_{\\omega} \\approx \\mathcal{A}_{\\omega_*}\\) by minimizing the IKL loss (4). This involves two alternating optimization steps: first, training an auxiliary diffusion model \\(v_{\\phi,\\omega}(z^{(t)}, t)\\) using the standard flow-matching loss, where \\(z^{(t)} = (1 - t)z^{(0)} + t\\mathcal{A}_{\\omega}(x)\\); second, updating \\(\\hat{\\mathcal{A}}_{\\omega}\\) by following the gradient in eq. (5)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.599,
+ 0.497,
+ 0.885
+ ],
+ "angle": 0,
+ "content": "To encourage fast convergence, the auxiliary model \\( v_{\\phi,\\omega} \\) is initialized with the pretrained weights from \\( v_{\\theta,\\omega_*(z^{(t)},t)} \\). The parameterization of \\( \\hat{\\mathcal{A}}_{\\omega} \\) is flexible: it may depend on the clean image \\( x \\) —which limits certain options for the final step—or be independent of \\( x \\). For instance, we consider modeling non-uniform blur with an operator \\( \\hat{\\mathcal{A}}_{\\omega} \\) that varies with pixel location. The framework is general, but \\( \\hat{\\mathcal{A}}_{\\omega} \\) should not depend on corrupted images, as these are unavailable in the unpaired training setting. The distribution matching step can also be regularized in various ways to introduce prior knowledge about the forward model and improve the quality of results. For example, when \\( \\mathcal{V} \\) and \\( \\mathcal{X} \\) consist of patch data, their distribution will be invariant to translation: an image patch translated by some amount in any direction will still follow the same distribution. This invariant can easily lead to learning blur filters which are off-center as shown in Fig. 3. To counter this we add a regularizer which constrains the center of mass of the learned kernels to be in the middle of the filter itself."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.887,
+ 0.497,
+ 0.933
+ ],
+ "angle": 0,
+ "content": "Step 3: solve the inverse problem. The third and final step is to use the learned forward model \\(\\hat{A}_{\\omega}\\) to solve the inverse problem. At this point the non-blind setting applies,"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.587,
+ 0.073,
+ 0.852,
+ 0.207
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.524,
+ 0.22,
+ 0.912,
+ 0.275
+ ],
+ "angle": 0,
+ "content": "Figure 3. Effect of center regularization on reconstruction quality. Without regularization the learned blur filter may be shifted leading to larger reconstruction errors (second row of the plot). A moderate amount of regularization fixes this."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.524,
+ 0.295,
+ 0.912,
+ 0.506
+ ],
+ "angle": 0,
+ "content": "hence multiple strategies can be chosen depending on the specific problem and on the type of data which is available. When a larger clean-image dataset is available, by leveraging \\(\\hat{A}_{\\omega}\\) it is possible to generate a paired noisy-clean dataset on which to train a supervised image restoration model [49, 54]. The second option is to use a plug and play algorithm [47] which leverages a pretrained prior on clean images (classically this could have been a prior such as total-variation instead) to iteratively convert a noisy image into a clean one. In Sec. 4 we will use ESRGAN [49] from the first option and DPIR [55], DiffPIR [62] from the second one. Of course classical alternatives such as Wiener deconvolution can be used depending on the specific inverse problem."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.525,
+ 0.521,
+ 0.658,
+ 0.539
+ ],
+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.525,
+ 0.547,
+ 0.65,
+ 0.563
+ ],
+ "angle": 0,
+ "content": "4.1. Deblurring"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.524,
+ 0.569,
+ 0.912,
+ 0.932
+ ],
+ "angle": 0,
+ "content": "We used subsets of the FFHQ dataset [19] to compare with blind deblurring methods. In particular, for each of two degradation operators we train a small CFM model on 1000 images from FFHQ corrupted by the blurring operator \\(\\mathcal{A}_{\\omega_*}\\) and subsequently utilize 100 different clean images to learn \\(\\hat{\\mathcal{A}}_{\\omega}\\) with distribution matching. We use an isotropic Gaussian blur with standard deviation 1 and a motion blur kernel generated following Borodenko [7]. In both cases, Gaussian noise is added with standard deviation of 0.02. We finally use plug and play algorithm DiffPIR [62] to solve the inverse problem \\(\\hat{\\mathcal{A}}_{\\omega}\\). The natural upper baseline for this experiment is to run the same PnP algorithm with the ground-truth kernel. In addition to this, we compare with some lower baselines which learn the correct kernel from a single image, and simultaneously perform deblurring: diffusion based methods BlindDPS [12], FastDiffusionEM [23] and KernelDiff [44]. These latter blind algorithms require two priors (in the form of pretrained diffusion models): one on the image dataset and one on the kernels. BlindDPS and FastDiffusionEM use FFHQ as image prior while KernelDiff uses several natural image datasets [14]. All three methods assume the blur kernels to be motion-blur, generated using the same stochastic procedure [7] as the true one. BlindDPS additionally includes isotropic Gaussian"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.48,
+ 0.961,
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+ 0.972
+ ],
+ "angle": 0,
+ "content": "28368"
+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.111,
+ 0.07,
+ 0.496,
+ 0.098
+ ],
+ "angle": 0,
+ "content": "Table 2. Reconstruction error on FFHQ. KernelDiff was run with no noise. FastEM was run with 16 samples and IIGDM."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.126,
+ 0.108,
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+ 0.317
+ ],
+ "angle": 0,
+ "content": " | Gaussian blur | Motion blur |
| PSNR | LPIPS | PSNR | LPIPS |
| Non-blind (true kernel available) |
| DiffPIR | 32.7 | 0.031 | 29.3 | 0.068 |
| Blind, multi-image |
| Ours + DiffPIR | 32.7 | 0.031 | 28.8 | 0.069 |
| Blind, single-image |
| Blind-DPS [12] | 29.8 | 0.077 | 25.5 | 0.122 |
| FastEM (n=16) [23] | - | - | 24.9 | 0.130 |
| KernelDiff [44] | - | - | 21.7 | 0.194 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "kernels in its kernel prior, which is why in Tab. 2 we also test it on a Gaussian kernel. It is important to stress that our algorithm works in a different setting from the single-image methods: we require a dataset of clean and noisy images for each degradation, while the single-image algorithms only require a single noisy image. However, note that all single-image algorithms rely strongly on the image and kernel priors on which they were trained: for example we could not successfully run the method from Laroche et al. [23] on a simple Gaussian kernel without first retraining the kernel prior, and KernelDiff which uses a different image prior than FFHQ performs poorly in this setting. The results in Tab. 2 demonstrate two things: first, even when the problem is purely in-distribution, the gap between blind and non-blind algorithms is large. In second instance, the algorithm we propose significantly reduces this gap by using more data from the same distribution to learn the necessary information about the degradation operator. To increase the robustness of our experiments we compute the standard deviation over 5 different random seeds for the 2nd step of our pipeline (thus keeping the 1st step fixed). For the motion blur kernel, we find a standard deviation of 0.02 for PSNR and 0.0005 for LPIPS which are both negligible."
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+ "content": "4.2. Space-varying blur"
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+ "content": "In practice image blur may come from a variety of sources such as camera shake/motion, out-of-focus objects or lens distortions. We focus on the latter which better fits the our framework: it is easy to collect a set of noisy images with equal distribution, but it is not really possible to collect paired datasets (note that paired datasets can be generated synthetically through software camera models [26]). Every imaging system is imperfect, which can be characterized by a spatially varying point spread function (PSF) at every location in the image plane. It can thus be modeled as a per-pixel blur where the blur kernel depends on the image plane location. Since the PSFs are intrinsically connected to the imaging system, multiple pictures taken with the same camera and camera settings will have the same degradation."
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+ "content": "Table 3. Reconstruction error for non-uniform deblurring on DPDD. The degradation is a spatially varying blur with additive Gaussian noise (\\(\\sigma = 0.01\\))."
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+ "content": "| Method | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| Non-blind (true kernel available) |
| ESRGAN [49] | 32.53 | 0.906 | 0.058 |
| DPIR [55] | 34.89 | 0.933 | 0.112 |
| Blind, multi-image |
| DeFlow+ESRGAN [51] | 27.92 | 0.818 | 0.206 |
| Ours+ESRGAN | 32.38 | 0.911 | 0.061 |
| Ours+DPIR | 33.84 | 0.933 | 0.099 |
| Blind, single-image |
| INIKNet [40] | 29.45 | 0.874 | 0.160 |
| Restormer [54] | 28.59 | 0.859 | 0.203 |
"
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+ "content": "For the first experiment we use real PSFs, taken from a subset of those identified in a real camera system [5] but synthetically applied to a clean dataset. In particular we use the green channel PSFs from the Canon EF 24mm f/1.4L II USM lens at 1.4 aperture, and subsample them to a \\(8 \\times 8\\) grid, shown in Fig. 10 (top-left). This grid is then mapped to images from DIV2K [3] and DPDD [1], and applied as a per-pixel blur by linearly interpolating the kernels to each image location. We use the degraded DIV2K training-set (subdivided into patches 128 pixels wide) to train the diffusion model in the first stage of our algorithm, and the clean DDPD training-set for the second stage – thus ensuring the data is strictly unpaired. For the third and final stage we experiment with two procedures: the plug and play algorithm DPIR [55] which uses a CNN as regularizing prior and can be applied directly to the learned kernels, and supervised method ESRGAN [49] for which we generate a paired clean-noisy dataset using the learned degradation. In order to condition the kernels on image location, we add two positional encoding channels to our images such that the diffusion model learns different distributions based on the patch location. For the degradation prediction we directly learn the 64 kernels without any additional parametrization; both at train and at test time the correct kernels are picked by using the positional encoding and linearly interpolating between the kernels. For this experiment we used the centering regularization and also introduced an isotropic Gaussian regularization which helped stabilize training."
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+ "content": "We compare the results obtained on the \"target\" testset of DPDD (corrupted with the camera PSFs and not with the original defocus degradations) against two pretrained methods tailored for real-world defocus deblurring: Restormer [54] and INIKNet [40], against unpaired algorithm DeFlow [51] which we retrain for the current task and couple with ESRGAN (DeFlow does not provide explicit degradations hence cannot be coupled with DPIR) and against the upper baselines ESRGAN and DPIR trained with the true degradation. While Restormer and INIKNet were trained on a different degradation domain, defocus"
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+ "content": "Figure 4. Sample reconstructions on DDPD. INIKNet and Restormer are single image, DPIR is non-blind."
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. Different aberrations in parking lot data. While images taken at f/5.6 are sharp, chromatic aberrations are still present outside of the center portion as evidenced by the middle panel."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "blur is also spatially varying and should not be too far from the mostly isotropic kernels of the camera PSF. Nevertheless, their inferior performance compared to our method shows how even small changes to the degradation distribution can have a large impact on reconstruction performance. Table 3 shows the quantitative evaluation on DPDD while the qualitative results are shown in Fig. 4. DeFlow does not manage to learn the correct blur distribution, and simply introduces a small amount of noise in the generated degraded images, thus garnering the worst results. Both INIKNet and Restormer perform similarly and succeed at removing some of the blur, but the results are not as sharp as the reconstructions obtained with our method. Both non-blind methods perform very well, with ESRGAN being better under perceptual metrics and DPIR under distortion metrics. Importantly, and like we showed for the first round of experiments on FFHQ, our method is very close to its upper limit given by the non-blind counterpart. In the supplementary material we plot the predicted kernels which capture the spread and anisotropy of the true kernels."
+ },
+ {
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+ "bbox": [
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+ "content": "4.3. Real-world camera lens calibration"
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+ "content": "As a final experiment we attempt to tackle the same lens-aberrations of the previous task, but this time on real data. We used a Panasonic DC-GX9 camera in aperture priority mode with a Leica DG Summilux \\(25\\mathrm{mm}\\) f/1.4 II lens to take 22 pictures in our parking lot at different apertures. Our goal was to learn the PSF of the lens at an extreme aperture (e.g. f/16) in order to correct it using the clean distribution of images taken at a reasonable aperture (e.g. f/5.6). To"
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+ "bbox": [
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+ "content": "f/16.0 (original)"
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+ "bbox": [
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+ "angle": 0,
+ "content": "DxO"
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+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Eboli"
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+ {
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+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.524,
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+ ],
+ "angle": 0,
+ "content": "Figure 6. Sample reconstructions on the parking lot dataset. Color differences in DxO are likely due to a different white-balancing algorithm. Eboli [15] correctly removes chromatic aberrations but introduces some noise artifacts. Our method results visually pleasing and significantly sharper than the original image."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.524,
+ 0.494,
+ 0.912,
+ 0.933
+ ],
+ "angle": 0,
+ "content": "avoid confounding factors we tried to keep all the image-plane in focus and had ample light to obtain sharp images. Note that while the images at different f-stops were taken using a tripod from the same location no additional care was taken to align them, and they would not be suitable for a supervised learning algorithm. Images were minimally postprocessed, by devignetting and converting to sRGB using lensfunpy [25], in order to preserve the blurry artifacts. Then they were split into patches and fed through our algorithm: an initial diffusion model was trained on the \"noisy\" images at f/16, and then used as a guide to learn the degradation operator on the center part of f/5.6 images. By using the central part of f/5.6 images we should be able to fix the chromatic aberrations which appears around sharp edges but much less in central part of images. By inspecting the data (see Fig. 5) there is a noticeable increase in blurriness between clean and noisy samples, which nevertheless is not very strong. Unlike the previous experiments where we knew the amount of additive Gaussian noise \\(\\sigma\\) used in the forward model, now the noise distribution is completely unknown. For simplicity we again use a Gaussian noise model and treat its standard deviation as a trainable parameter of \\(\\hat{A}_{\\omega}\\). Having a good noise estimate can be very useful in guiding the final reconstruction with plug-and-play methods. In Fig. 6 we compare our results with the algorithm from Eboli et al. [16] which is a two-step approach to first estimate and remove the blur, and then remove colored fringes using a specialized procedure [15]. For fairness we must note that the algorithm we're comparing against [16]"
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+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "28370"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.072,
+ 0.496,
+ 0.209
+ ],
+ "angle": 0,
+ "content": "works with single images, and doesn't need retraining for different lenses, partly thanks to strong inductive priors on the blur kernel (Gaussian with 7 parameters) and on the color aberrations. We also compare to commercial solution DxO PhotoLab [22] which exploits information about the specific lens used. We used the web version of the software and applied chromatic aberration filter followed by deblurring with strength 1.23. More comparisons as well as training details are available in the supplementary."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Single image super-resolution"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Up to now we have dealt with the task of deblurring, matching clean and corrupted distributions across datasets. Interestingly, there is a very related task whose properties allow us to work on single images, instead of across datasets. Super-resolution is commonly modeled as the composition of blurring with kernel \\( k \\) and subsampling \\( y = (x \\otimes k) \\downarrow s \\), hence its close relationship to deblurring. In this setting our algorithm works on single low-resolution images, split into small patches. First, the noisy distribution \\( \\mathbb{Y}_{\\omega_*} \\) is learned with a diffusion model on the patches. Then we learn a kernel \\( \\hat{k} \\) such that"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\np \\left(\\left(y * \\hat {k}\\right) \\downarrow_ {s}\\right) \\approx \\mathbb {Y} _ {\\omega_ {*}}. \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Note that in eq. (6) the low-resolution image \\( y \\) is further downscaled using kernel \\( \\hat{k} \\) which is the current estimator of the true kernel. This twice-downscaled image is compared in distribution to the once-downscaled image. Thanks to the scale-invariance of natural images the distributions (once-downscaled and twice-downscaled) will match when the kernels used for downscaling are the same, leading to the recovery of the true kernel. The downscaling step is crucial for this to work: if we omitted it (i.e. pure deblurring), we would always recover the identity kernel. For a quantitative experiment on single image super-resolution we adopt the setting from Bell-Kligler et al. [6] who also introduced the DIV2KRK dataset consisting of 100 images from DIV2K [3] downscaled with random anisotropic Gaussian kernels. After learning \\( \\hat{k} \\) using the proposed algorithm, we tested three non-blind solvers: ZSSR [4] which requires no pretraining and USRNet [56] for which we used the tiny pretrained model and DANv2 [35] from which we took just the Restorer module plugged with \\( \\hat{k} \\). In Tab. 4 we compare our approach with: i) Two end-to-end solutions [33, 35] which jointly learn super-resolution and kernel-estimation by pre-training on DIV2K + Flickr2K [46] datasets, ii) two non-blind super-resolution algorithms [4, 56] which are natural upper-bounds for our method and iii) three kernel-estimation algorithms [6, 27, 52] which are directly comparable to the proposed method. Note that both DANv2 and DCLS outperform the non-blind methods. We hypothesize this may be due to the strong prior the methods have learned during training on a dataset which is very similar to the one used in testing. To analyze kernel estimation performance in isolation we look at kernel metrics k-PSNR and k-NCC (not available for DCLS which operates in a"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. x2 super-resolution on DIV2RKK dataset. Methods are grouped by the respective non-blind solver. NCC is the normalized cross-correlation metric."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Method | Y-PSNR | SSIM | LPIPS | kernel PSNR | kernel NCC |
| End to end (kernel estimator trained on external data) |
| DANv2 [35] | 32.12 | 0.8954 | 0.148 | 56.8 | 0.97 |
| DCLS [33] | 32.31 | 0.9006 | 0.147 | - | - |
| Non-blind (true kernel available) |
| ZSSR | 32.04 | 0.8885 | 0.196 | ∞ | 1 |
| USRNet | 32.06 | 0.8923 | 0.158 | ∞ | 1 |
| DANv2 | 31.94 | 0.8957 | 0.147 | ∞ | 1 |
| Two-step (kernel estimate from single image) |
| KernelGAN [6] | 29.65 | 0.8465 | 0.248 | 51.5 | 0.92 |
| Ours + ZSSR | 31.61 | 0.8837 | 0.200 | 64.2 | 0.96 |
| DKP [52] | 23.18 | 0.6245 | 0.226 | 53.6 | 0.92 |
| DIP-FKP [27] | 29.52 | 0.8530 | 0.249 | 50.4 | 0.95 |
| Ours + USRNet | 31.11 | 0.8838 | 0.167 | 64.2 | 0.96 |
| Ours + DANv2 | 31.86 | 0.8938 | 0.149 | 64.2 | 0.96 |
"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "different kernel space) which show that the proposed algorithm performs the same as DANv2. This can be further corroborated by plugging in the learned kernels with the DANv2 super-resolution module on its own, which significantly reduces the performance gap to the end-to-end DANv2. When compared to the other 2-step methods, the proposed algorithm emerges as the clear winner both on image and kernel metrics."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "5. Conclusions"
+ },
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+ "type": "text",
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+ "content": "Solving blind inverse problems from unpaired data is highly relevant for practical real-world image restoration tasks. In this work, we proposed an algorithm which learns the degradation operator directly from data, making minimal assumptions about the operator itself. Through extensive experiments on uniform and non-uniform deblurring, we have shown that it is possible to reduce the performance gap between blind single-image methods and non-blind methods by leveraging multiple images from the same degradation process. Built-in interpretability and flexibility in its design make the proposed algorithm applicable to solving diverse problems. On the other hand, having multiple images belonging to the same noisy-data distribution may not be realistic for all situations, where single-image methods work best – this single-image setting can be handled with our methods only in specific problems such as superresolution. Furthermore, while our framework is designed to deal with unpaired data, if the clean and noisy distributions are known through highly unrelated datasets, the matching procedure will struggle to learn a degradation operator to reconcile the two. The domain shift between clean and noisy distributions hinders training as it becomes larger. Future directions include tackling problems from different domains such as microscopy or medical imaging, as well improving the noise-modeling to be more realistic (e.g. to handle Poisson-Gaussian noise)."
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+ "content": "This work was supported by ERC grant number 101087696 (APHELEIA project). This work was granted access to the HPC resources of IDRIS under the allocation AD011015445 made by GENCI."
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+# Unsupervised Imaging Inverse Problems with Diffusion Distribution Matching
+
+Giacomo Meanti Thomas Ryckeboer Michael Arbel Julien Mairal Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP, LJK, 38000 Grenoble, France firstname.lastname@inria.fr
+
+
+Figure 1. Learning degradation operators by matching distributions.
+
+# Abstract
+
+This work addresses image restoration tasks through the lens of inverse problems using unpaired datasets. In contrast to traditional approaches—which typically assume full knowledge of the forward model or access to paired degraded and ground-truth images—the proposed method operates under minimal assumptions and relies only on small, unpaired datasets. This makes it particularly well-suited for real-world scenarios, where the forward model is often unknown or mis-specified, and collecting paired data is costly or infeasible. The method leverages conditional flow matching to model the distribution of degraded observations, while simultaneously learning the forward model via a distribution-matching loss that arises naturally from the framework. Empirically, it outperforms both single-image blind and unsupervised approaches on deblurring and non-uniform point spread function (PSF) calibration tasks. It also matches state-of-the-art performance on blind super-resolution. We also showcase the effectiveness of our method with a proof of concept for lens calibration: a real-world application traditionally requiring time-consuming experiments and specialized equipment. In contrast, our approach achieves this with minimal data acquisition effort. Code available: https://github.com/inria-thoth/ddm4ip.
+
+# 1. Introduction
+
+Inverse problems arise in many domains where observed data is the result of a noisy and potentially lossy transfor
+
+mation of an underlying signal we wish to recover. More formally, the degradation process is modeled as follows:
+
+$$
+y = \mathcal {A} (x) + \epsilon , \quad \epsilon \sim \mathcal {N} (0, \sigma^ {2} I), \tag {1}
+$$
+
+where $\mathcal{A}$ is the forward operator and $\epsilon$ denotes additive Gaussian noise. The objective is to recover the original signal $x$ from the measurements $y$ . In practice, $\mathcal{A}$ may represent a wide range of linear or nonlinear transformations, such as blur kernels, inpainting masks, the Radon transform, and many others.
+
+To introduce the setting of the current work, we categorize the reconstruction methods based on i) the type and availability of data, ii) the extent of prior knowledge about $\mathcal{A}$ . When $\mathcal{A}$ is fully known, two main classes of reconstruction approaches are typically used. The first is plug-and-play (PnP) methods, which apply iterative algorithms to recover signal $x$ from a single measurement $y$ by maximizing the posterior distribution $p(x\mid y,\mathcal{A})\propto p(y\mid x,\mathcal{A})p(x)$ . These methods alternate between a data-fidelity term (dependent on $\mathcal{A}$ ) and a prior term. The second class leverages supervised learning: if a clean dataset is available, it can be paired with synthetic measurements generated via $\mathcal{A}$ to train a reconstruction model in a supervised fashion.
+
+However, complete knowledge of the forward operator $\mathcal{A}$ is rarely available in practice. For instance, in superresolution it is common to assume bicubic downsampling to generate low-resolution images from high-resolution ones, yet models trained under this assumption often fail on real-world images where the actual downsampling kernel differs [18, 59].
+
+When $\mathcal{A}$ is unknown or only partially specified, the
+
+problem becomes more challenging and is called blind. One strategy is to collect (or synthetically generate) a dataset that includes corrupted samples produced from a range of possible $\mathcal{A}$ instances. A supervised model is then trained to generalize across these degradations. An alternative approach is to jointly infer both the clean signal and the unknown operator by maximizing the joint posterior $p(x, \mathcal{A} \mid y) \propto p(y \mid x)p(x)p(\mathcal{A})$ which requires priors on both the data distribution and the corruption process. Both approaches implicitly rely on some prior knowledge or assumptions about $\mathcal{A}$ , either through heuristic degradation models or learned probabilistic priors. Consequently, when the true degradation deviates from these assumptions—which is often the case in real-world scenarios—the reconstruction performance degrades significantly. Although these methods typically require very little input data at test time (sometimes even a single image), their robustness to real-world variations is far from guaranteed.
+
+The natural alternative, which we adopt in this work, is to learn information about $\mathcal{A}$ directly from data: specifically, from one dataset of corrupted images and a separate dataset of clean images. Crucially, these datasets do not need to contain corresponding clean-corrupted pairs, which significantly simplifies data collection. During training, the unpaired clean images serve as a reference for what the restored outputs should resemble—effectively providing a model for $p(x)$ . This unpaired training setup is often referred to as unsupervised, and has been successfully applied to in-the-wild image restoration tasks [31, 45, 51], where the degradation process is unknown and may involve multiple, complex transformations. Most existing algorithms operating in this unpaired regime use an implicit model of the degradation process: a neural network is trained to map corrupted inputs to clean outputs, without explicitly modeling the underlying forward operator.
+
+The method we propose learns the correct degradation by learning an explicit operator $\mathcal{A}$ and needs a relatively small (hundreds to thousands) number of training points. By using diffusion models and an efficient distribution matching algorithm it outperforms both single-image methods and other unsupervised ones. It comprises two distinct steps: the first one learns a representation of the noisy distribution, the second learns the best degradation operator $\mathcal{A}$ such that the clean samples corrupted by $\mathcal{A}$ match in distribution the noisy data prior. Finally the learned corruption can be used in a third step for non-blind restoration. Our contributions are threefold: we begin by devising a principled method for solving inverse problems which only relies on unpaired image data from clean and corrupted distributions, without knowledge of the degradation operator. We prove that under a non-degeneracy assumption on the clean distribution, the true operator can be identified. We then show how this method can provide precise estimates of the degradation operator, without making any distributional assumptions on the operator itself. In particular we focus on the tasks of uniform and non-uniform deblurring. Finally,
+
+Table 1. Summary of tasks for solving inverse problems without knowing the forward operator. The headings refer to what is known about the data and the forward operator. Regarding the latter, we note when the method works on data corrupted by a single (unknown) operator, operators from a predefined distribution, or by a collection of unknown operators. The references are not meant to be exhaustive but just to provide examples.
+
+| Data | A | Method | References |
| prior on X | single known | PnP | [42, 47, 57, 62] |
| paired | single unknown | supervised | [49] |
| prior on X | prior on A | blind PnP | [12, 23, 44, 52] |
| paired | prior on A | supervised | [18, 50, 58] |
| unpaired | multiple unknown | unsupervised | [34, 45, 51] |
| unpaired | functional form | this paper |
+
+since the estimates we obtain are considerably more precise than those of single-image methods, we show how they can be used as part of a pipeline for camera lens calibration – where accuracy is essential.
+
+The rest of the paper is organized as follows. In Sec. 2, we provide some necessary background on inverse problems with unknown degradations and on our algorithm. In Sec. 3, we detail the different steps of our algorithm, whereas the last section is devoted to experiments of increasing complexity on estimating blur kernels.
+
+# 2. Background
+
+We briefly review the literature on blind and unsupervised inverse problems in imaging, along with the various forms of deblurring addressed in this work.
+
+# 2.1. Unsupervised inverse problems
+
+Solving inverse problems without access to the forward operator is inherently challenging and can be approached from multiple perspectives. In Tab. 1 we provide a framework to clarify the various settings considered in the literature. Unlike many of the methods discussed below, our approach assumes a fixed degradation operator $\mathcal{A}$ which does not vary across measurements $y$ . While this restricts generality, it enables higher reconstruction accuracy in specific settings compared to other unpaired methods. We focus on unpaired algorithms, particularly for deblurring and super-resolution tasks, where $\mathcal{A}$ typically corresponds to a blur kernel. Data augmentation-based approaches [50, 58] construct synthetic supervised datasets using heuristically designed degradation pipelines which mimic diverse real-world corruptions. To improve adaptability to specific degradations, Zhang et al. [59] propose learning some of the pipeline parameters from a small dataset of noisy reference images. For better alignment with the degradation of each individual image, a line of work tackles the blind MAP inference problem using deep priors over both clean images and degradation operators. These methods are typically coupled with test-time optimization algorithms such as alternating minimization [41], expectation-maximization (EM) [17, 23], or proximal gradient methods [48]. Recent
+
+approaches [12, 23, 44] incorporate diffusion models as priors for the blur kernel, jointly estimating $\mathcal{A}$ and $x$ via plug-and-play algorithms [47]. Closely related methods include FKP [27], which uses a pretrained normalizing flow as a kernel prior, and DKP [52], which employs MCMC to iteratively refine the blur estimate. GibbsDDRM [38], by contrast, uses a diffusion prior on the clean image and a simpler total variation (TV) prior on the blur kernel.
+
+In contrast to this class of methods, which require only a single degraded image at test time, our approach does not rely on any pretrained priors—neither on clean images nor on the degradation operator. Instead, it learns to adapt directly to the specific corruption process represented in the training data. While it does require a small dataset of degraded images from the same corruption distribution, this targeted adaptation enables significantly improved reconstruction accuracy.
+
+Domain transfer approaches based on variations of the cycle-consistency loss [61] are conceptually closer to our method. Given a noisy image $y$ and an unpaired clean image $x$ , a clean-image generator $\mathcal{G}$ and a noisy-image generator $\mathcal{F}$ are jointly trained under the constraint that $\mathcal{G}(\mathcal{F}(x)) \approx x$ and $\mathcal{F}(\mathcal{G}(y)) \approx y$ . For instance, CinCGAN [36, 53] translates images downsampled with an unknown kernel into bicubically downsampled images, which can then be more effectively upscaled using standard super-resolution models. Several related methods [9, 30, 34, 37, 45, 51] employ generative models to synthesize corrupted images from clean ones, thereby enabling the construction of supervised training datasets. This synthesis can be done in a two-stage pipeline or directly in an end-to-end manner [11, 43]. Notably, Sim et al. [45] address a setting similar to ours, where a model is trained to deblur microscopy images in an unpaired setup. Compared to these approaches, our method leverages a novel loss function derived from diffusion models—a technique not previously applied in this context. Unlike adversarial losses, our formulation is more stable and easier to train. Moreover, by learning an explicit representation of the degradation kernel rather than an implicit one, our method offers significantly improved interpretability. Furthermore, under certain assumptions, we are able to prove the identifiability of the true operator (see Sec. 3).
+
+We also briefly note that many methods aim to learn the degradation operator in a single-image fashion, but still require paired training data—typically synthetic—for supervision. For instance, IKC [18] iteratively refines kernel estimates in alternation with clean-image predictions. DAN [35] extends this idea by unrolling the refinement process into an end-to-end trainable network. In contrast, KernelGAN [6] learns the degradation operator directly from a single input image, followed by a separate non-blind model to reconstruct the clean image $x$ .
+
+# 2.2. Distribution matching
+
+Our method minimizes the distance between two probability distributions over images: the distribution of the
+
+observed noisy data $p(y)$ and that of clean data corrupted by a learned degradation operator, i.e., $p(\mathcal{A}(x))$ . A common strategy for such distribution matching is to use generative adversarial networks (GANs), which optimize an adversarial loss. GANs have been extensively applied to image restoration tasks, as discussed in the previous section [34, 45], and can simultaneously learn both the degradation operator and its inverse within a unified training framework. However, training GANs is notoriously challenging due to instability and sensitivity to hyperparameters [8]. Alternative approaches include normalizing flows, which provide exact likelihoods and invertible mappings. These have been used by DeFlow [51] for matching clean and noisy distributions, and by FKP [27] to generate plausible blur kernels from single images.
+
+More recently, diffusion models – like GANs and normalizing flows – have emerged as powerful tools for modeling empirical distributions and have been used in a range of distribution-matching tasks. For example, DreamFusion [39] learns 3D representations whose 2D projections are consistent with a pretrained diffusion model, while DiffInstruct [32] trains a single-step generator to match the distribution of a multi-step diffusion model. Both approaches rely on a loss function that approximates the KL divergence integrated over all diffusion time steps.
+
+In our work, we use conditional flow matching (CFM) models [28, 29] as a more conceptually straightforward alternative to standard diffusion models. We adapt the integrated KL divergence loss to the CFM framework for learning the degradation operator.
+
+# 2.3. Camera lens calibration
+
+After preliminary experiments on synthetic deblurring, we focus on non-uniform deblurring in the context of a camera calibration pipeline. Camera calibration is a multifaceted task typically broken down into subtasks such as distortion, chromatic aberration, and vignetting corrections among others. In this work, we concentrate solely on compensating for blur induced by lens imperfections, with the goal of obtaining maximally sharp images. These lens aberrations can be characterized by the point spread function (PSF) of the lens-camera system: the blur kernel that transforms an ideal point light source into a spread of colored spots in the image. PSFs are often non-uniform across the image plane and differ across RGB channels, resulting in chromatic aberrations. Correcting such distortions computationally is particularly appealing, as it enables the use of lower-cost lenses without sacrificing image quality.
+
+Traditional non-blind correction methods require precise knowledge of the PSF, which can only be obtained through laborious procedures involving printed calibration patterns or specialized screens [5, 21]. In contrast, blind lens aberration correction remains an understudied problem, although it shares many similarities with non-uniform deblurring. It is more commonly approached under the umbrella of defocus deblurring [2, 24, 40, 54], where blur magnitude varies with scene depth. In aberration correction, however,
+
+the blur is dependent on spatial location in the image plane rather than depth. Nonetheless, defocus deblurring methods may still be partially effective for lens aberration correction, especially when the induced blur is close to isotropic. As a starting point, we use the PSF dataset from Bauer et al. [5], which provides ground-truth PSFs, and later move to a realistic calibration scenario using a Panasonic Micro 4/3 camera. In this setting, we acquire a small set of images and aim to learn the lens PSFs without access to ground-truth measurements. Our main comparison will be with the blind method proposed by Eboli et al. [16], which performs deblurring followed by color-fringe removal in a two-stage pipeline [10, 15].
+
+# 3. Method
+
+Given an inverse problem of the form $y = \mathcal{A}_{\omega_{*}}(x) + \epsilon$ , with known noise level $\sigma$ and an unknown forward operator $\mathcal{A}_{\omega_{*}}$ parameterized by a vector $\omega_{*}$ , we propose an algorithm to estimate $\omega_{*}$ using unpaired data. On the one hand, we assume access to a clean dataset $\mathcal{X} = \{x_i\}_{i=1}^n$ of images drawn from a distribution $\mathbb{X}$ . On the other hand, we have access to a corrupted dataset $\mathcal{Y} = \{y_j\}_{j=1}^m$ of images, generated from unknown clean samples via the forward model $\mathcal{A}_{\omega_{*}}$ . We denote by $\mathbb{Y}_{\omega_{*}}$ the distribution of such corrupted images, and by $\mathbb{Y}_{\omega}$ the distribution induced by applying an arbitrary forward operator $\mathcal{A}_{\omega}$ (with additive noise) to samples from $\mathbb{X}$ .
+
+Noting that $\mathbb{Y}_{\omega_*}$ is empirically accessible through $\mathcal{V}$ while $\mathbb{Y}_{\omega}$ can be approximated via $\mathcal{X}$ and a candidate forward operator $\mathcal{A}_{\omega}$ , we hypothesize that minimizing the distance between $\mathbb{Y}_{\omega_*}$ and $\mathbb{Y}_{\omega}$ with respect to $\mathcal{A}_{\omega}$ yields a good approximation of the true forward model parameters:
+
+$$
+\hat {\omega} = \underset {\omega} {\arg \min } \mathcal {D} \left(\mathbb {Y} _ {\omega_ {*}}, \mathbb {Y} _ {\omega}\right) \Rightarrow \mathcal {A} _ {\hat {\omega}} \approx \mathcal {A} _ {\omega_ {*}}, \tag {2}
+$$
+
+where $\mathcal{D}$ is a distance between distribution that will be specified in detail later. We prove this rigorously in a simplified setting in Proposition 3.1, with the full proof provided in the supplementary material, and we assume that the result generalizes when the distributions are only approximately equal, as is typically the case in practice.
+
+Proposition 3.1: For any set of forward model parameters $\omega$ , let $p_{\omega}(y) = \int p_{\omega}(y \mid x)p(x)dx$ where $p_{\omega}(y \mid x) = \mathcal{N}(y \mid A_{\omega}x, \sigma^2 I)$ . Let $\omega_*$ be a specific set of parameters which we consider to be the optimal set. Then, assuming the data covariance $\Sigma = \mathbb{E}_x[xx^\top]$ is invertible, there exists an orthogonal matrix $P$ such that
+
+$$
+p _ {\omega} (y) = p _ {\omega_ {*}} (y) \Longrightarrow \mathcal {A} _ {\omega} = \mathcal {A} _ {\omega_ {*}} \Sigma^ {1 / 2} P \Sigma^ {- 1 / 2} \tag {3}
+$$
+
+That is, if the probability distributions $p_{\omega}$ and $p_{\omega_*}$ are equal, it is possible to identify $\mathcal{A}_{\omega_*}$ up to rotations $P$ .
+
+Since neither $\mathbb{Y}_{\omega_*}$ nor $\mathbb{Y}_{\omega}$ are explicitly available we will use CFM models to act as tractable representations of probability distributions on images.
+
+# 3.1. Distribution matching with diffusion
+
+A CFM model $v_{\theta}(z^{(t)}, t)$ trained on data from a distribution $\mathbb{Y}_{\omega}$ allows one to sample from $\mathbb{Y}_{\omega}$ by solving an ODE between times 0 and 1, defined as
+
+$$
+d z ^ {(t)} = v _ {\theta} \left(z ^ {(t)}, t\right) d t, \quad z ^ {(0)} \sim \mathcal {N} (0, I).
+$$
+
+such that $z^{(t = 1)}\sim \mathbb{Y}_{\omega}$ . This conditional flow matching [28, 29] perspective is connected to standard Langevin diffusion since the velocity field $v_{\theta}(x^{(t)},t)$ is related to the score of a diffusion model: $v_{\theta}(z^{(t)},t) + z^{(t)}\propto$ $\nabla_z\log p_{\mathbb{Y}_\omega^{(t)}}(z_\omega^{(t)})$ [60], assuming the neural network model of the velocity field to be exact. Each $z^{(t)}$ follows an intermediate distribution between Gaussian noise and the data $\mathbb{Y}_{\omega}^{(t)}$ for $t\in [0,1]$ . Hence, instead of computing a distance between two distributions, we will compute it between two sequences of distributions $\mathbb{Y}_{\omega}^{(t)}$ and $\mathbb{Y}_{\omega_*}^{(t)}$ which arise from two CFM models. In particular we will use the KL divergence integrated over time, and follow the derivation proposed by DiffInstruct [32] to compute its gradient with respect to $\omega$ . The integrated KL divergence is defined as
+
+$$
+\operatorname {I K L} \left(\mathbb {Y} _ {\omega_ {*}} \| \mathbb {Y} _ {\omega}\right) = \int_ {t = 0} ^ {1} \operatorname {K L} \left(\mathbb {Y} _ {\omega_ {*}} ^ {(t)} \| \mathbb {Y} _ {\omega} ^ {(t)}\right) d t. \tag {4}
+$$
+
+Assuming that the score terms for both probability distributions (i.e. $s_{\theta, \omega_*(y,t)} \approx \nabla_y \log p_{\mathbb{Y}_{\omega_*}^{(t)}}(y)$ and $s_{\phi, \omega}(y,t) \approx \nabla_y \log p_{\mathbb{Y}_{\omega^*}^{(t)}}(y)$ ) can be computed, it is possible to efficiently differentiate the IKL with respect to $\omega$ :
+
+$$
+\nabla_ {\omega} \operatorname {I K L} \left(\mathbb {Y} _ {\omega_ {*}} \| \mathbb {Y} _ {\omega}\right) =
+$$
+
+$$
+\int_ {t = 0} ^ {1} \mathbb {E} \left[ s _ {\theta , \omega_ {*}} \left(y _ {\omega} ^ {(t)}, t\right) - s _ {\phi , \omega} \left(y _ {\omega} ^ {(t)}, t\right) \right] ^ {\top} \nabla_ {\omega} y _ {\omega} ^ {(t)} d t, \tag {5}
+$$
+
+where the expectation is over $y_{\omega}^{(0)} \sim \mathcal{N}(0, I), x \sim \mathcal{X}, y_{\omega}^{(1)} = \mathcal{A}_{\omega}(x) + \epsilon$ and $y_{\omega}^{(t)} = (1 - t)y_{\omega}^{(0)} + ty_{\omega}^{(1)}$ . Note that eq. (5) has in fact been originally introduced to optimize a 3D scene consistent with a diffusion model's outputs [39] and in [32] was used to learn a distilled model. Here we are showing it can be used effectively on conditional flow matching models as well, and in a completely different setting. The loss gradient shown in eq. (5) needs certain quantities to be computed: the score of $p_{\mathbb{Y}_{\omega_*}}$ can be obtained beforehand by training a flow-matching model $v_{\theta, \omega_*}$ on the available noisy data $\mathcal{V}$ . The score of $p_{\mathbb{Y}_\omega}$ however depends on a distribution which changes with every change in $\omega$ . Therefore the strategy we use is to alternately optimize i) an auxiliary flow-matching model $v_{\psi, \omega}$ for a fixed $\omega$ with a standard diffusion loss and ii) forward model parameters $\omega$ with the IKL loss keeping the auxiliary model fixed [32]. By changing the parametrization of $\mathcal{A}_{\omega}$ eq. (5) can be used to learn the degradation of a variety of different inverse problems. We will now go into the details of the algorithm for the task of learning blur operators.
+
+# 3.2. Learning the forward operator
+
+In deblurring, $\mathcal{A}_{\omega}$ corresponds to a convolution with kernel $\omega$ . The algorithm we propose proceeds in three distinct
+
+
+Figure 2. Samples generated by the flow matching model with motion-blur kernel. While the model is average at generating faces, it correctly represents the degradation.
+
+steps: i) learn the corrupted data distribution, ii) approximate the forward operator $\mathcal{A}_{\omega_*}$ and iii) solve the non-blind inverse problem.
+
+Step 1: Learning $\mathbb{Y}_{\omega_*}$ . In more detail, the first step uses the noisy dataset $\{y_j\}_{j=1}^m$ to train a conditional flow matching (CFM) model $v_{\theta, \omega_*}$ that transports Gaussian noise samples at time $t = 0$ , $z^{(0)} \sim \mathcal{N}(0, I)$ , to samples from the corrupted data distribution $\mathbb{Y}_{\omega_*}$ at time $t = 1$ , i.e., $z^{(1)} \sim \mathbb{Y}_{\omega_*}$ . The training objective is the standard conditional flow matching loss [28, 29]:
+
+$$
+\mathcal {L} _ {\mathrm {C F M}} = \mathbb {E} _ {t, z ^ {(0)}, z ^ {(1)}} \left[ \left\| v _ {\theta , \omega_ {*}} (z ^ {(t)}, t) - (z ^ {(1)} - z ^ {(0)}) \right\| \right].
+$$
+
+Importantly, for the overall success of our method, it is not necessary for $v_{\theta, \omega_*}$ to achieve state-of-the-art generative quality; it only needs to effectively capture the degradation process, which we found to be significantly easier than precisely modeling image content. See Fig. 2 for sample outputs produced by a model at this stage.
+
+Step 2: distribution matching. The second step uses the clean dataset $\mathcal{X}$ to learn the corruption operator $\hat{\mathcal{A}}_{\omega} \approx \mathcal{A}_{\omega_*}$ by minimizing the IKL loss (4). This involves two alternating optimization steps: first, training an auxiliary diffusion model $v_{\phi,\omega}(z^{(t)}, t)$ using the standard flow-matching loss, where $z^{(t)} = (1 - t)z^{(0)} + t\mathcal{A}_{\omega}(x)$ ; second, updating $\hat{\mathcal{A}}_{\omega}$ by following the gradient in eq. (5).
+
+To encourage fast convergence, the auxiliary model $v_{\phi,\omega}$ is initialized with the pretrained weights from $v_{\theta,\omega_*(z^{(t)},t)}$ . The parameterization of $\hat{\mathcal{A}}_{\omega}$ is flexible: it may depend on the clean image $x$ —which limits certain options for the final step—or be independent of $x$ . For instance, we consider modeling non-uniform blur with an operator $\hat{\mathcal{A}}_{\omega}$ that varies with pixel location. The framework is general, but $\hat{\mathcal{A}}_{\omega}$ should not depend on corrupted images, as these are unavailable in the unpaired training setting. The distribution matching step can also be regularized in various ways to introduce prior knowledge about the forward model and improve the quality of results. For example, when $\mathcal{V}$ and $\mathcal{X}$ consist of patch data, their distribution will be invariant to translation: an image patch translated by some amount in any direction will still follow the same distribution. This invariant can easily lead to learning blur filters which are off-center as shown in Fig. 3. To counter this we add a regularizer which constrains the center of mass of the learned kernels to be in the middle of the filter itself.
+
+Step 3: solve the inverse problem. The third and final step is to use the learned forward model $\hat{A}_{\omega}$ to solve the inverse problem. At this point the non-blind setting applies,
+
+
+Figure 3. Effect of center regularization on reconstruction quality. Without regularization the learned blur filter may be shifted leading to larger reconstruction errors (second row of the plot). A moderate amount of regularization fixes this.
+
+hence multiple strategies can be chosen depending on the specific problem and on the type of data which is available. When a larger clean-image dataset is available, by leveraging $\hat{A}_{\omega}$ it is possible to generate a paired noisy-clean dataset on which to train a supervised image restoration model [49, 54]. The second option is to use a plug and play algorithm [47] which leverages a pretrained prior on clean images (classically this could have been a prior such as total-variation instead) to iteratively convert a noisy image into a clean one. In Sec. 4 we will use ESRGAN [49] from the first option and DPIR [55], DiffPIR [62] from the second one. Of course classical alternatives such as Wiener deconvolution can be used depending on the specific inverse problem.
+
+# 4. Experiments
+
+# 4.1. Deblurring
+
+We used subsets of the FFHQ dataset [19] to compare with blind deblurring methods. In particular, for each of two degradation operators we train a small CFM model on 1000 images from FFHQ corrupted by the blurring operator $\mathcal{A}_{\omega_*}$ and subsequently utilize 100 different clean images to learn $\hat{\mathcal{A}}_{\omega}$ with distribution matching. We use an isotropic Gaussian blur with standard deviation 1 and a motion blur kernel generated following Borodenko [7]. In both cases, Gaussian noise is added with standard deviation of 0.02. We finally use plug and play algorithm DiffPIR [62] to solve the inverse problem $\hat{\mathcal{A}}_{\omega}$ . The natural upper baseline for this experiment is to run the same PnP algorithm with the ground-truth kernel. In addition to this, we compare with some lower baselines which learn the correct kernel from a single image, and simultaneously perform deblurring: diffusion based methods BlindDPS [12], FastDiffusionEM [23] and KernelDiff [44]. These latter blind algorithms require two priors (in the form of pretrained diffusion models): one on the image dataset and one on the kernels. BlindDPS and FastDiffusionEM use FFHQ as image prior while KernelDiff uses several natural image datasets [14]. All three methods assume the blur kernels to be motion-blur, generated using the same stochastic procedure [7] as the true one. BlindDPS additionally includes isotropic Gaussian
+
+Table 2. Reconstruction error on FFHQ. KernelDiff was run with no noise. FastEM was run with 16 samples and IIGDM.
+
+ | Gaussian blur | Motion blur |
| PSNR | LPIPS | PSNR | LPIPS |
| Non-blind (true kernel available) |
| DiffPIR | 32.7 | 0.031 | 29.3 | 0.068 |
| Blind, multi-image |
| Ours + DiffPIR | 32.7 | 0.031 | 28.8 | 0.069 |
| Blind, single-image |
| Blind-DPS [12] | 29.8 | 0.077 | 25.5 | 0.122 |
| FastEM (n=16) [23] | - | - | 24.9 | 0.130 |
| KernelDiff [44] | - | - | 21.7 | 0.194 |
+
+kernels in its kernel prior, which is why in Tab. 2 we also test it on a Gaussian kernel. It is important to stress that our algorithm works in a different setting from the single-image methods: we require a dataset of clean and noisy images for each degradation, while the single-image algorithms only require a single noisy image. However, note that all single-image algorithms rely strongly on the image and kernel priors on which they were trained: for example we could not successfully run the method from Laroche et al. [23] on a simple Gaussian kernel without first retraining the kernel prior, and KernelDiff which uses a different image prior than FFHQ performs poorly in this setting. The results in Tab. 2 demonstrate two things: first, even when the problem is purely in-distribution, the gap between blind and non-blind algorithms is large. In second instance, the algorithm we propose significantly reduces this gap by using more data from the same distribution to learn the necessary information about the degradation operator. To increase the robustness of our experiments we compute the standard deviation over 5 different random seeds for the 2nd step of our pipeline (thus keeping the 1st step fixed). For the motion blur kernel, we find a standard deviation of 0.02 for PSNR and 0.0005 for LPIPS which are both negligible.
+
+# 4.2. Space-varying blur
+
+In practice image blur may come from a variety of sources such as camera shake/motion, out-of-focus objects or lens distortions. We focus on the latter which better fits the our framework: it is easy to collect a set of noisy images with equal distribution, but it is not really possible to collect paired datasets (note that paired datasets can be generated synthetically through software camera models [26]). Every imaging system is imperfect, which can be characterized by a spatially varying point spread function (PSF) at every location in the image plane. It can thus be modeled as a per-pixel blur where the blur kernel depends on the image plane location. Since the PSFs are intrinsically connected to the imaging system, multiple pictures taken with the same camera and camera settings will have the same degradation.
+
+Table 3. Reconstruction error for non-uniform deblurring on DPDD. The degradation is a spatially varying blur with additive Gaussian noise ( $\sigma = 0.01$ ).
+
+| Method | PSNR ↑ | SSIM ↑ | LPIPS ↓ |
| Non-blind (true kernel available) |
| ESRGAN [49] | 32.53 | 0.906 | 0.058 |
| DPIR [55] | 34.89 | 0.933 | 0.112 |
| Blind, multi-image |
| DeFlow+ESRGAN [51] | 27.92 | 0.818 | 0.206 |
| Ours+ESRGAN | 32.38 | 0.911 | 0.061 |
| Ours+DPIR | 33.84 | 0.933 | 0.099 |
| Blind, single-image |
| INIKNet [40] | 29.45 | 0.874 | 0.160 |
| Restormer [54] | 28.59 | 0.859 | 0.203 |
+
+For the first experiment we use real PSFs, taken from a subset of those identified in a real camera system [5] but synthetically applied to a clean dataset. In particular we use the green channel PSFs from the Canon EF 24mm f/1.4L II USM lens at 1.4 aperture, and subsample them to a $8 \times 8$ grid, shown in Fig. 10 (top-left). This grid is then mapped to images from DIV2K [3] and DPDD [1], and applied as a per-pixel blur by linearly interpolating the kernels to each image location. We use the degraded DIV2K training-set (subdivided into patches 128 pixels wide) to train the diffusion model in the first stage of our algorithm, and the clean DDPD training-set for the second stage – thus ensuring the data is strictly unpaired. For the third and final stage we experiment with two procedures: the plug and play algorithm DPIR [55] which uses a CNN as regularizing prior and can be applied directly to the learned kernels, and supervised method ESRGAN [49] for which we generate a paired clean-noisy dataset using the learned degradation. In order to condition the kernels on image location, we add two positional encoding channels to our images such that the diffusion model learns different distributions based on the patch location. For the degradation prediction we directly learn the 64 kernels without any additional parametrization; both at train and at test time the correct kernels are picked by using the positional encoding and linearly interpolating between the kernels. For this experiment we used the centering regularization and also introduced an isotropic Gaussian regularization which helped stabilize training.
+
+We compare the results obtained on the "target" testset of DPDD (corrupted with the camera PSFs and not with the original defocus degradations) against two pretrained methods tailored for real-world defocus deblurring: Restormer [54] and INIKNet [40], against unpaired algorithm DeFlow [51] which we retrain for the current task and couple with ESRGAN (DeFlow does not provide explicit degradations hence cannot be coupled with DPIR) and against the upper baselines ESRGAN and DPIR trained with the true degradation. While Restormer and INIKNet were trained on a different degradation domain, defocus
+
+
+Full ours
+
+
+
+
+Measurement
+
+
+
+
+INIKNet [40]
+
+
+
+
+Restormer [54]
+
+
+
+
+DeFlow [51]
+
+
+Ours+DPIR
+
+
+DPIR* [55]
+
+
+Figure 4. Sample reconstructions on DDPD. INIKNet and Restormer are single image, DPIR is non-blind.
+Figure 5. Different aberrations in parking lot data. While images taken at f/5.6 are sharp, chromatic aberrations are still present outside of the center portion as evidenced by the middle panel.
+
+blur is also spatially varying and should not be too far from the mostly isotropic kernels of the camera PSF. Nevertheless, their inferior performance compared to our method shows how even small changes to the degradation distribution can have a large impact on reconstruction performance. Table 3 shows the quantitative evaluation on DPDD while the qualitative results are shown in Fig. 4. DeFlow does not manage to learn the correct blur distribution, and simply introduces a small amount of noise in the generated degraded images, thus garnering the worst results. Both INIKNet and Restormer perform similarly and succeed at removing some of the blur, but the results are not as sharp as the reconstructions obtained with our method. Both non-blind methods perform very well, with ESRGAN being better under perceptual metrics and DPIR under distortion metrics. Importantly, and like we showed for the first round of experiments on FFHQ, our method is very close to its upper limit given by the non-blind counterpart. In the supplementary material we plot the predicted kernels which capture the spread and anisotropy of the true kernels.
+
+# 4.3. Real-world camera lens calibration
+
+As a final experiment we attempt to tackle the same lens-aberrations of the previous task, but this time on real data. We used a Panasonic DC-GX9 camera in aperture priority mode with a Leica DG Summilux $25\mathrm{mm}$ f/1.4 II lens to take 22 pictures in our parking lot at different apertures. Our goal was to learn the PSF of the lens at an extreme aperture (e.g. f/16) in order to correct it using the clean distribution of images taken at a reasonable aperture (e.g. f/5.6). To
+
+
+f/16.0 (original)
+
+
+DxO
+
+
+Eboli
+
+
+
+
+Ours
+
+
+
+
+
+
+
+
+
+
+
+
+Figure 6. Sample reconstructions on the parking lot dataset. Color differences in DxO are likely due to a different white-balancing algorithm. Eboli [15] correctly removes chromatic aberrations but introduces some noise artifacts. Our method results visually pleasing and significantly sharper than the original image.
+
+
+
+
+
+
+
+
+
+avoid confounding factors we tried to keep all the image-plane in focus and had ample light to obtain sharp images. Note that while the images at different f-stops were taken using a tripod from the same location no additional care was taken to align them, and they would not be suitable for a supervised learning algorithm. Images were minimally postprocessed, by devignetting and converting to sRGB using lensfunpy [25], in order to preserve the blurry artifacts. Then they were split into patches and fed through our algorithm: an initial diffusion model was trained on the "noisy" images at f/16, and then used as a guide to learn the degradation operator on the center part of f/5.6 images. By using the central part of f/5.6 images we should be able to fix the chromatic aberrations which appears around sharp edges but much less in central part of images. By inspecting the data (see Fig. 5) there is a noticeable increase in blurriness between clean and noisy samples, which nevertheless is not very strong. Unlike the previous experiments where we knew the amount of additive Gaussian noise $\sigma$ used in the forward model, now the noise distribution is completely unknown. For simplicity we again use a Gaussian noise model and treat its standard deviation as a trainable parameter of $\hat{A}_{\omega}$ . Having a good noise estimate can be very useful in guiding the final reconstruction with plug-and-play methods. In Fig. 6 we compare our results with the algorithm from Eboli et al. [16] which is a two-step approach to first estimate and remove the blur, and then remove colored fringes using a specialized procedure [15]. For fairness we must note that the algorithm we're comparing against [16]
+
+works with single images, and doesn't need retraining for different lenses, partly thanks to strong inductive priors on the blur kernel (Gaussian with 7 parameters) and on the color aberrations. We also compare to commercial solution DxO PhotoLab [22] which exploits information about the specific lens used. We used the web version of the software and applied chromatic aberration filter followed by deblurring with strength 1.23. More comparisons as well as training details are available in the supplementary.
+
+# 4.4. Single image super-resolution
+
+Up to now we have dealt with the task of deblurring, matching clean and corrupted distributions across datasets. Interestingly, there is a very related task whose properties allow us to work on single images, instead of across datasets. Super-resolution is commonly modeled as the composition of blurring with kernel $k$ and subsampling $y = (x \otimes k) \downarrow s$ , hence its close relationship to deblurring. In this setting our algorithm works on single low-resolution images, split into small patches. First, the noisy distribution $\mathbb{Y}_{\omega_*}$ is learned with a diffusion model on the patches. Then we learn a kernel $\hat{k}$ such that
+
+$$
+p \left(\left(y * \hat {k}\right) \downarrow_ {s}\right) \approx \mathbb {Y} _ {\omega_ {*}}. \tag {6}
+$$
+
+Note that in eq. (6) the low-resolution image $y$ is further downscaled using kernel $\hat{k}$ which is the current estimator of the true kernel. This twice-downscaled image is compared in distribution to the once-downscaled image. Thanks to the scale-invariance of natural images the distributions (once-downscaled and twice-downscaled) will match when the kernels used for downscaling are the same, leading to the recovery of the true kernel. The downscaling step is crucial for this to work: if we omitted it (i.e. pure deblurring), we would always recover the identity kernel. For a quantitative experiment on single image super-resolution we adopt the setting from Bell-Kligler et al. [6] who also introduced the DIV2KRK dataset consisting of 100 images from DIV2K [3] downscaled with random anisotropic Gaussian kernels. After learning $\hat{k}$ using the proposed algorithm, we tested three non-blind solvers: ZSSR [4] which requires no pretraining and USRNet [56] for which we used the tiny pretrained model and DANv2 [35] from which we took just the Restorer module plugged with $\hat{k}$ . In Tab. 4 we compare our approach with: i) Two end-to-end solutions [33, 35] which jointly learn super-resolution and kernel-estimation by pre-training on DIV2K + Flickr2K [46] datasets, ii) two non-blind super-resolution algorithms [4, 56] which are natural upper-bounds for our method and iii) three kernel-estimation algorithms [6, 27, 52] which are directly comparable to the proposed method. Note that both DANv2 and DCLS outperform the non-blind methods. We hypothesize this may be due to the strong prior the methods have learned during training on a dataset which is very similar to the one used in testing. To analyze kernel estimation performance in isolation we look at kernel metrics k-PSNR and k-NCC (not available for DCLS which operates in a
+
+Table 4. x2 super-resolution on DIV2RKK dataset. Methods are grouped by the respective non-blind solver. NCC is the normalized cross-correlation metric.
+
+| Method | Y-PSNR | SSIM | LPIPS | kernel PSNR | kernel NCC |
| End to end (kernel estimator trained on external data) |
| DANv2 [35] | 32.12 | 0.8954 | 0.148 | 56.8 | 0.97 |
| DCLS [33] | 32.31 | 0.9006 | 0.147 | - | - |
| Non-blind (true kernel available) |
| ZSSR | 32.04 | 0.8885 | 0.196 | ∞ | 1 |
| USRNet | 32.06 | 0.8923 | 0.158 | ∞ | 1 |
| DANv2 | 31.94 | 0.8957 | 0.147 | ∞ | 1 |
| Two-step (kernel estimate from single image) |
| KernelGAN [6] | 29.65 | 0.8465 | 0.248 | 51.5 | 0.92 |
| Ours + ZSSR | 31.61 | 0.8837 | 0.200 | 64.2 | 0.96 |
| DKP [52] | 23.18 | 0.6245 | 0.226 | 53.6 | 0.92 |
| DIP-FKP [27] | 29.52 | 0.8530 | 0.249 | 50.4 | 0.95 |
| Ours + USRNet | 31.11 | 0.8838 | 0.167 | 64.2 | 0.96 |
| Ours + DANv2 | 31.86 | 0.8938 | 0.149 | 64.2 | 0.96 |
+
+different kernel space) which show that the proposed algorithm performs the same as DANv2. This can be further corroborated by plugging in the learned kernels with the DANv2 super-resolution module on its own, which significantly reduces the performance gap to the end-to-end DANv2. When compared to the other 2-step methods, the proposed algorithm emerges as the clear winner both on image and kernel metrics.
+
+# 5. Conclusions
+
+Solving blind inverse problems from unpaired data is highly relevant for practical real-world image restoration tasks. In this work, we proposed an algorithm which learns the degradation operator directly from data, making minimal assumptions about the operator itself. Through extensive experiments on uniform and non-uniform deblurring, we have shown that it is possible to reduce the performance gap between blind single-image methods and non-blind methods by leveraging multiple images from the same degradation process. Built-in interpretability and flexibility in its design make the proposed algorithm applicable to solving diverse problems. On the other hand, having multiple images belonging to the same noisy-data distribution may not be realistic for all situations, where single-image methods work best – this single-image setting can be handled with our methods only in specific problems such as superresolution. Furthermore, while our framework is designed to deal with unpaired data, if the clean and noisy distributions are known through highly unrelated datasets, the matching procedure will struggle to learn a degradation operator to reconcile the two. The domain shift between clean and noisy distributions hinders training as it becomes larger. Future directions include tackling problems from different domains such as microscopy or medical imaging, as well improving the noise-modeling to be more realistic (e.g. to handle Poisson-Gaussian noise).
+
+# Acknowledgements
+
+This work was supported by ERC grant number 101087696 (APHELEIA project). This work was granted access to the HPC resources of IDRIS under the allocation AD011015445 made by GENCI.
+
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+[51] Valentin Wolf, Andreas Lugmayr, Martin Danelljan, Luc Van Gool, and Radu Timofte. DeFlow: Learning complex image degradations from unpaired data with conditional flows. In IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR, 2021. 2, 3, 6, 7, 14
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+[55] Kai Zhang, Wangmeng Zuo, Shuhang Gu, and Lei Zhang. Learning deep CNN denoiser prior for image restoration. In IEEE Conference on Computer Vision and Pattern Recognition, pages 3929-3938, 2017. 5, 6, 7
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+Feng Gao, Ying Nian Wu et al. Flow priors for linear inverse problems via iterative corrupted trajectory matching. In Neural Information Processing Systems (NeurIPS), 2024. 4
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| prior on X | single known | PnP | [42, 47, 57, 62] |
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| paired | prior on A | supervised | [18, 50, 58] |
| unpaired | multiple unknown | unsupervised | [34, 45, 51] |
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+ "content": " be a specific set of parameters which we consider to be the optimal set. Then, assuming the data covariance "
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| DPIR [55] | 34.89 | 0.933 | 0.112 |
| Blind, multi-image |
| DeFlow+ESRGAN [51] | 27.92 | 0.818 | 0.206 |
| Ours+ESRGAN | 32.38 | 0.911 | 0.061 |
| Ours+DPIR | 33.84 | 0.933 | 0.099 |
| Blind, single-image |
| INIKNet [40] | 29.45 | 0.874 | 0.160 |
| Restormer [54] | 28.59 | 0.859 | 0.203 |
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| End to end (kernel estimator trained on external data) |
| DANv2 [35] | 32.12 | 0.8954 | 0.148 | 56.8 | 0.97 |
| DCLS [33] | 32.31 | 0.9006 | 0.147 | - | - |
| Non-blind (true kernel available) |
| ZSSR | 32.04 | 0.8885 | 0.196 | ∞ | 1 |
| USRNet | 32.06 | 0.8923 | 0.158 | ∞ | 1 |
| DANv2 | 31.94 | 0.8957 | 0.147 | ∞ | 1 |
| Two-step (kernel estimate from single image) |
| KernelGAN [6] | 29.65 | 0.8465 | 0.248 | 51.5 | 0.92 |
| Ours + ZSSR | 31.61 | 0.8837 | 0.200 | 64.2 | 0.96 |
| DKP [52] | 23.18 | 0.6245 | 0.226 | 53.6 | 0.92 |
| DIP-FKP [27] | 29.52 | 0.8530 | 0.249 | 50.4 | 0.95 |
| Ours + USRNet | 31.11 | 0.8838 | 0.167 | 64.2 | 0.96 |
| Ours + DANv2 | 31.86 | 0.8938 | 0.149 | 64.2 | 0.96 |
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diff --git a/2025/Unsupervised Joint Learning of Optical Flow and Intensity with Event Cameras/92edc20b-e741-4fac-9960-c5dbfdfad535_content_list.json b/2025/Unsupervised Joint Learning of Optical Flow and Intensity with Event Cameras/92edc20b-e741-4fac-9960-c5dbfdfad535_content_list.json
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+ "type": "text",
+ "text": "Unsupervised Joint Learning of Optical Flow and Intensity with Event Cameras",
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+ "text": "Shuang Guo $^{1}$ , Friedhelm Hamann $^{1,2}$ and Guillermo Gallego $^{1,2,3}$ .",
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+ "text": "TU Berlin and Robotics Institute Germany,",
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+ "text": "$^{2}$ Science of Intelligence Excellence Cluster, $^{3}$ Einstein Center for Digital Future.",
+ "bbox": [
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+ "text": "Event cameras rely on motion to obtain information about scene appearance. This means that appearance and motion are inherently linked: either both are present and recorded in the event data, or neither is captured. Previous works treat the recovery of these two visual quantities as separate tasks, which does not fit with the above-mentioned nature of event cameras and overlooks the inherent relations between them. We propose an unsupervised learning framework that jointly estimates optical flow (motion) and image intensity (appearance) using a single network. From the data generation model, we newly derive the event-based photometric error as a function of optical flow and image intensity. This error is further combined with the contrast maximization framework to form a comprehensive loss function that provides proper constraints for both flow and intensity estimation. Exhaustive experiments show our method's state-of-the-art performance: in optical flow estimation, it reduces EPE by $20\\%$ and AE by $25\\%$ compared to unsupervised approaches, while delivering competitive intensity estimation results, particularly in high dynamic range scenarios. Our method also achieves shorter inference time than all other optical flow methods and many of the image reconstruction methods, while they output only one quantity. Project page: https://github.com/tub-rip/E2FAI",
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+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
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+ "page_idx": 0
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+ {
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+ "text": "Event cameras [18, 30] are novel bio-inspired vision sensors that offer attractive properties compared to traditional cameras: high temporal resolution, very high dynamic range (HDR), low power consumption and high pixel bandwidth, resulting in reduced motion blur. Hence, event cameras have a large potential for computer vision and robotics applications in challenging scenarios for traditional cameras, such as high speed motion and HDR illumination. However, novel methods are required to process the unconventional output of these sensors (a stream of asynchronous per-pixel brightness changes instead of conventional images) in order to unlock their potential [9].",
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+ "image_caption": [
+ "Figure 1. Our method computes accurate optical flow and intensity images from event-camera data despite complex scenarios, fast motion and high dynamic range. The above result is obtained using data from interlaken_00_b sequence of DSEC [13]."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "text": "In the past decade, a variety of computer vision algorithms have been developed to recover fundamental visual quantities from event streams [4, 9, 14, 50], such as EV-FlowNet [52] for optical flow estimation, and E2VID [31] for image intensity reconstruction. Despite achieving good performance, most of these methods are designed to estimate a single visual quantity: optical flow or image intensity. This philosophy does not fit well with the fact that, under constant illumination, motion and appearance are inherently entangled in the input data, since events are produced by moving intensity patterns on the image plane (e.g., Fig. 1a). More accurate and robust estimation becomes possible when the synergies between both visual quantities are properly leveraged.",
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+ "text": "To achieve this goal, we newly derive the event-based photometric error (PhE) as a function of optical flow and image intensity, and combine it with the state-of-the-art contrast maximization (CMax) framework [7], yielding a comprehensive loss function. Both PhE and CMax provide constraints on scene appearance and motion. The former focuses more on appearance (i.e., intensity) while the latter focuses more on motion (i.e., optical flow). Their complementary properties give rise to a well-behaved loss in both aspects. In addition, our loss function also includes a full consideration of the internal synergies between esti",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
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+ "type": "text",
+ "text": "mated visual quantities: during training, the predicted flow is leveraged to warp the predicted image intensity to the adjacent interval so that a temporal consistency (TC) loss can be calculated, which significantly encourages consistency and robustness. We train a deep neural network (DNN) with this loss function in an unsupervised manner. The resulting model can predict precise optical flow and image intensity simultaneously from event data (see Fig. 1).",
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+ "text": "To the best of our knowledge, this paper presents the first unsupervised learning-based approach that jointly recovers optical flow and image intensity from event data, with a single network (Tab. 1). In the experiments, we evaluate our method in terms of optical flow and intensity on a variety of public datasets. For optical flow, our method achieves the best accuracy in the unsupervised learning category in the DSEC benchmark [13], with $20\\%$ and $25\\%$ improvements in terms of EPE and AE, respectively. For intensity, our method reports competitive results with respect to other unsupervised methods and even some supervised ones, especially in HDR scenarios. In terms of speed, our method reports minimal inference time to obtain both visual quantities. Our method robustly predicts precise flow and intensity on unseen data recorded in different scenarios and with different event cameras, thus demonstrating generalization. Our contributions can be summarized as follows:",
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+ "1. We propose the first unsupervised learning framework for the joint estimation, with a single network, of event-based optical flow and image intensity. Its working principle fits naturally with the characteristics of event data.",
+ "2. We derive event-based PhD, and combine it with CMax, yielding a comprehensive and well-behaved loss function for the estimation of motion and scene appearance. It can be directly adapted to various optimization and learning-based solutions for similar problems.",
+ "3. We conduct comprehensive experiments on public datasets, where our method shows state-of-the-art performance on optical flow, image intensity and inference time. Furthermore, our method shows excellent generalization on unseen data recorded in different scenarios (HDR and fast motion) and with different event cameras."
+ ],
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+ "text": "We hope the clear advantages of our approach and the source code provided will make its adoption appealing, thus bringing the tasks of optical flow estimation and intensity reconstruction closer than they currently are (until now, they have mostly been treated as independent problems).",
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+ "text": "2. Related Work",
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+ "text": "Given the high-speed and HDR properties of event cameras, extensive research has been carried out to utilize them for the estimation of optical flow and image intensity. Let us review the literature on each of these tasks in Sec. 2.1 and Sec. 2.2, respectively, and summarize the approaches that solve for both quantities in Sec. 2.3.",
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+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Method | Year | Type | DOFs | Joint | Loss function |
| IVM [5] | 2011 | MB | 3 | ✓ | “Consistency” of the data (Max. Likelihood) |
| SOFIE [1] | 2016 | MB | 6 | ✓ | Pixel-wise brightness change + TC |
| E-cGAN [25] | 2021 | SL | 6 | ✗ | Supervised: Error w.r.t. ground truth |
| BTEB [28] | 2021 | USL | 6 | ✗ | FlowNet: IWE sharpness; ReconNet: LEGM |
| Ours | 2025 | USL | 6 | ✓ | CMax + PhE of Flow and Intensity + TC |
",
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+ "type": "text",
+ "text": "Table 1. Event-based optical flow and intensity estimation methods. The columns indicate: the method type, the number of degrees of freedom (DOFs) of the camera motion that the method can handle (3 ≡ rotation, 6 ≡ free motion), whether the method estimates flow and intensity jointly or separately, and the loss used.",
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+ "type": "text",
+ "text": "2.1. Event-based Optical Flow Estimation",
+ "text_level": 1,
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+ "text": "Previous works can be categorized into model-based (MB), supervised learning (SL) or unsupervised learning (USL). State-of-the-art MB methods [3, 39] formulate the problem using an objective function, and solve for optical flow through optimization. The most commonly-used objective is the sharpness of images of warped events (IWEs), such as the CMax loss [7, 8] used in [39], and the flow warping loss (FWL) [41] used in [3]. The optimization usually takes a number of iterations to converge, and it repeatedly warps all the involved events in every iteration, which makes these methods costly. Furthermore, the objectives derived from IWE sharpness may suffer from the issue of event collapse [36, 38], which affects flow accuracy and requires strong regularization to mitigate it.",
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+ "text": "Due to the better fitting capabilities and short inference times of DNNs, researchers have adopted them to compute optical flow. SL approaches [11, 13, 17, 19, 21, 45] train DNNs to learn the mapping from event data to the ground truth (GT) optical flow. However, the acquisition of GT relies on either simulation [17, 21] or calculation from external depth sensors using the motion field equation [13, 51]. Both are expensive. The former suffers from the sim-to-real gap, that is, the trained model may not perform well on real-world data, while the latter suffers from sensor inaccuracy and data sparsity [16, 39]. Although SL methods are generally ahead in optical flow benchmarks, the above issues about GT data are inherited by the trained model.",
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+ "type": "text",
+ "text": "In contrast, USL methods [16, 29, 47, 52] forego costly data labeling, shifting the focus to the data and the loss function to learn optical flow patterns. Similarly to MB methods, current mainstream loss functions are still based on IWE sharpness [8]. For instance, EV-FlowNet [52] quantifies sharpness in terms of average timestamp images [22]. More recently, [16, 29, 39] adopted the CMax loss to train DNNs, which achieved obvious improvements with respect to MB methods that used the same loss functions. In addition, USL performs expensive event warping only during training, hence it has much shorter and more constant inference time than equivalent MB methods.",
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+ "type": "page_number",
+ "text": "7981",
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+ "type": "text",
+ "text": "2.2. Event-based Image Intensity Reconstruction",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Similarly, intensity estimation methods can be classified into MB, SL and USL categories. For the MB category, early works recovered brightness from events by means of temporal filtering [34] or temporal integration with manifold denoising [27]. A recent work [49] formulated this task as a linear inverse problem with image regularization and solved for intensity using ADMM [2]. However, it required accurate optical flow as input, which limits its applicability.",
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+ "type": "text",
+ "text": "SL approaches [10, 31, 35, 44] trained DNNs using synthetic data to learn the mapping from event data to image intensity. In this way, the models were prevented from learning motion blur and under/over-exposure that happens in traditional cameras. Besides, these methods were aimed at video reconstruction and therefore adopted recurrent network architectures while introducing temporal consistency loss to guarantee the continuity of sequential images. However, they suffer from the sim-to-real gap and sometimes perform poorly in HDR scenarios (see, e.g., Fig. 4).",
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+ "text": "USL methods for intensity reconstruction are underexplored. Recent work [28] proposed to supervise the training with event-based photometric consistency. The loss was defined using the linearized event generation model (LEGM), as the error between brightness increments measured by event data and those obtained from the spatial gradient of the predicted image. However, this method requires accurate optical flow provided externally for both training and inference, for which the authors had to train a separate network to estimate optical flow (see details of the flow part in Sec. 2.3). The need to infer sequentially with two separate models takes more time and amplifies error propagation, thus significantly limiting practicality.",
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+ "type": "text",
+ "text": "2.3. Event-based Flow-Intensity Estimation",
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+ "type": "text",
+ "text": "Table 1 summarizes the main works that estimate both optical flow and image intensity with event cameras. The earliest work [5] proposed a joint estimation approach recovering optical flow, image intensity and camera ego-motion. However, it was limited to pure rotational motion. Bardow et al. [1] developed a variational algorithm that simultaneously optimized optical flow and image intensity. However, optical flow was only constrained by the brightness constancy between estimated intensity images, while the motion information in event data was not utilized. Hence, the resulting intensity and optical flow showed poor accuracy.",
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+ "text": "In the learning-based category, [25] presented an SL method for image reconstruction from events using conditional generative adversarial networks (cGANs), and also showed the applicability to predict depth and optical flow. The networks were trained and performed inference for each quantity separately, so the bonds between them were ignored. More recently, [28] proposed training an intensity reconstruction DNN (same architecture as [31]), but in an",
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+ "type": "text",
+ "text": "unsupervised manner. To do so, they separately trained a network for optical flow estimation using the same loss as [52], and subsequently fed its output flow into a second network for intensity reconstruction (see Sec. 2.2).",
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+ "type": "text",
+ "text": "Our method overcomes and simplifies previous designs: it jointly estimates intensity and flow in an unsupervised manner by leveraging their synergies via the proposed loss function and architecture (i.e., using a single DNN).",
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+ "type": "text",
+ "text": "3. Method",
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+ "text": "In this section, we first explain the preliminaries (Sec. 3.1), then introduce our proposed comprehensive loss function, including newly derived event-based PhE (Sec. 3.2), CMax loss (Sec. 3.3) and regularization terms (Sec. 3.4). Finally, we present the training pipeline in Sec. 3.5.",
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+ "text": "3.1. Preliminaries",
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+ "text": "Event Generation Model (EGM). Every pixel of an event camera independently measures brightness changes, generating an event $e_k \\doteq (\\mathbf{x}_k, t_k, p_k)$ when the logarithmic brightness change $\\Delta L$ reaches a contrast threshold $C$ [9]:",
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+ "text": "\n$$\n\\Delta L \\doteq L (\\mathbf {x} _ {k}, t _ {k}) - L (\\mathbf {x} _ {k}, t _ {k} - \\Delta t _ {k}) = p _ {k} C, \\tag {1}\n$$\n",
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+ "text": "where $p_k \\in \\{+1, -1\\}$ indicates the polarity of the intensity increment, and $\\Delta t_k$ is the time elapsed since the previous event at the same pixel $\\mathbf{x}_k$ .",
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+ "text": "Event warping. Given a set of events $\\mathcal{E} \\doteq \\{e_k\\}_{k=1}^{N_e}$ , we can warp them to a reference time $t_{\\mathrm{ref}}$ with a motion model $\\mathbf{W}$ , yielding a set of warped events $\\mathcal{E}_{t_{\\mathrm{ref}}}^{\\prime} \\doteq \\{e_k^{\\prime}\\}_{k=1}^{N_e}$ , where: $e_k \\doteq (\\mathbf{x}_k, t_k, p_k) \\to e_k^{\\prime} \\doteq (\\mathbf{x}_k^{\\prime}, t_{\\mathrm{ref}}, p_k)$ . Provided that the time span of $\\mathcal{E}$ is small, we can assume all pixels move with constant but different velocities on the image plane, that is, the motion model $\\mathbf{W}$ is given by:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {x} _ {k} ^ {\\prime} = \\mathbf {x} _ {k} + \\left(t _ {\\text {r e f}} - t _ {k}\\right) F (\\mathbf {x} _ {k}), \\tag {2}\n$$\n",
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+ "text": "where $F(\\mathbf{x}_k)$ is the optical flow at $\\mathbf{x}_k$ [39].",
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+ "text": "3.2. Event-based Photometric Error (PhE)",
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+ "text": "We leverage the original EGM to derive the event-based PhE. Starting from (1), we warp an event $e_k \\doteq (\\mathbf{x}_k, t_k, p_k)$ and its predecessor (at the same pixel) $e_{k-1} \\doteq (\\mathbf{x}_k, t_k - \\Delta t_k, p_{k-1})$ to a reference time $t_\\mathrm{ref}$ . According to (2), their warped locations on the camera plane at $t_\\mathrm{ref}$ are:",
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+ "text": "\n$$\n\\begin{array}{l} \\mathbf {x} _ {k} ^ {\\prime} = \\mathbf {x} _ {k} + \\left(t _ {\\text {r e f}} - t _ {k}\\right) F (\\mathbf {x} _ {k}), \\\\ \\mathbf {x} _ {k - 1} ^ {\\prime} = \\mathbf {x} _ {k} + \\left(t _ {\\text {r e f}} - \\left(t _ {k} - \\Delta t _ {k}\\right)\\right) F (\\mathbf {x} _ {k}). \\tag {3} \\\\ \\end{array}\n$$\n",
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+ "text": "Let the image intensity at $t_{\\mathrm{ref}}$ be $L(\\mathbf{x})$ , then we substitute (3) into (1) to obtain the PhE for the event $e_k$ :",
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+ "text": "\n$$\n\\epsilon_ {k} \\doteq \\left(L \\left(\\mathbf {x} _ {k} ^ {\\prime}\\right) - L \\left(\\mathbf {x} _ {k - 1} ^ {\\prime}\\right)\\right) - p _ {k} C, \\tag {4}\n$$\n",
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+ "type": "page_footnote",
+ "text": "1We omit \"logarithmic\" in the following text for simplification.",
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+ "text": "7982",
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+ "Figure 2. The training pipeline of our proposed flow-intensity joint estimation method. In every training step, two consecutive event data samples are input to the network, respectively. The CMax and PhE losses for each sample are calculated with the output optical flow and image intensity. The TC loss is defined by the photometric error between the predicted $L_{i+1}$ and the one warped from $L_i$ through $F_{i\\rightarrow i+1}$ ."
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+ "type": "text",
+ "text": "which is the difference between the predicted intensity increment and the measured one. In practice, $\\mathbf{x}_k^{\\prime}$ and $\\mathbf{x}_{k - 1}^{\\prime}$ have sub-pixel precision, so we use bilinear interpolation to compute $L(\\mathbf{x}_k^{\\prime})$ and $L(\\mathbf{x}_{k - 1}^{\\prime})$ . Therefore, every PhE term (4) provides constraints for the intensity values at up to eight pixels around $\\mathbf{x}_k^\\prime$ and $\\mathbf{x}_{k - 1}^{\\prime}$ , as well as the optical flow value at one pixel $\\mathbf{x}_k$ . Finally, we sum the photometric error terms of all events in $\\mathcal{E}$ , obtaining the PhE loss:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {P h E}} (L, F) \\doteq \\frac {1}{N _ {e}} \\sum_ {k = 1} ^ {N _ {e}} | \\epsilon_ {k} |. \\tag {5}\n$$\n",
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+ "text": "It is an objective function of both intensity and flow, which opens the door to the joint estimation of both quantities. It is worth emphasizing that the PhE loss does not have the event collapse problem [36, 38] that CMax suffers from.",
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+ "type": "text",
+ "text": "3.3. Contrast Maximization (CMax)",
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+ "text": "The CMax framework [7, 8] assumes events are triggered by moving edges, so that optical flow estimation can be determined by seeking the best motion compensation. Specifically, warped events $\\mathcal{E}_{t_{\\mathrm{ref}}}^{\\prime}$ are aggregated on the image plane at $t_\\mathrm{ref}$ , forming an image of warped events:",
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+ "text": "\n$$\n\\operatorname {I W E} (\\mathbf {x}; \\mathcal {E} _ {t _ {\\text {r e f}}} ^ {\\prime}, F) \\doteq \\sum_ {k = 1} ^ {N _ {e}} \\mathcal {N} \\left(\\mathbf {x}; \\mathbf {x} _ {k} ^ {\\prime}, \\sigma^ {2} = 1 \\mathrm {p x}\\right), \\tag {6}\n$$\n",
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+ "type": "text",
+ "text": "where every pixel $\\mathbf{x}$ counts its number of warped events.",
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+ "text": "In this work, we adopt the inverse of the $L^1$ magnitude of the gradient to quantify the CMax loss:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C M a x}} (F) \\doteq 1 / \\left(\\frac {1}{| \\Omega |} \\int_ {\\Omega} \\| \\nabla \\mathrm {I W E} (\\mathbf {x}) \\| _ {1} d \\mathbf {x}\\right). \\tag {7}\n$$\n",
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+ "text": "In contrast to PhD, the CMax loss recovers scene appearance in the form of a sharp edge map, which is the objective instead of the variable. The only estimizable variable is optical flow, which reflects that CMax loss focuses more on motion parameters, as mentioned in Sec. 1.",
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+ "text": "3.4. Regularization",
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+ "type": "text",
+ "text": "Smoothness of Flow and Intensity. As stated in Sec. 3.2, the PhE loss only provides supervisory constraints on pixels that contain events (called valid pixels). To infer the values of the remaining pixels, regularization is needed; we use the total variation (TV) [33] to encourage smoothness of optical flow and intensity predictions: $\\mathcal{L}_{\\mathrm{FTV}}(F)\\doteq \\frac{1}{|\\Omega|}\\int_{\\Omega}\\| \\nabla F(\\mathbf{x})\\| _1d\\mathbf{x}$ , and $\\mathcal{L}_{\\mathrm{ITV}}(L)\\doteq \\frac{1}{|\\Omega|}\\int_{\\Omega}\\| \\nabla L(\\mathbf{x})\\| _1d\\mathbf{x}$ . Additionally, the smoothness of the flow mitigates the event collapse caused by the CMax loss.",
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+ "type": "text",
+ "text": "Temporal Consistency (TC). A key advantage of joint estimation (over a separate one) is being able to leverage the synergies between the quantities for better consistency. We achieve this by establishing associations between temporally consecutive predictions. As depicted in Fig. 2, in each training step, the network takes as input two consecutive data samples to predict the corresponding optical flow and image intensity. We leverage flow $F_{i\\rightarrow i + 1}$ to transport $L_{i}$ to $t_{i + 1}$ , yielding $L_{i + 1}^{\\prime}$ , whose photometric error with respect to $L_{i + 1}$ (predicted from the other data sample) is calculated to encourage temporal consistency (TC):",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {T C}} \\doteq \\frac {1}{| \\Omega |} \\int_ {\\Omega} \\left| L _ {i + 1} (\\mathbf {x}) - \\mathcal {W} (\\mathbf {x}; L _ {i}, F _ {i \\rightarrow i + 1}) \\right| d \\mathbf {x}, \\tag {8}\n$$\n",
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+ "type": "text",
+ "text": "where $\\mathcal{W}$ warps an image according to the optical flow. The introduction of the TC loss greatly improves the prediction quality, especially in image intensity (see Sec. 4.4).",
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+ "type": "text",
+ "text": "3.5. Training Pipeline",
+ "text_level": 1,
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+ "type": "text",
+ "text": "An overview of the training pipeline is displayed in Fig. 2. During training, the loss terms (5), (7), etc. are evaluated with the predictions of each sample, while the TC loss (8), between consecutive samples. Consequently, the total loss is the weighted sum of all these terms:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {P h E}} + \\lambda_ {2} \\mathcal {L} _ {\\text {C M a x}} + \\lambda_ {3} \\mathcal {L} _ {\\text {F T V}} + \\lambda_ {4} \\mathcal {L} _ {\\text {I T V}} + \\lambda_ {5} \\mathcal {L} _ {\\text {T C}},\n$$\n",
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+ "type": "text",
+ "text": "where the first four terms are the sum for the two data samples (Fig. 2). For every sample, the reference time of CMax is set to a random number within the time span of the event set [16], that is, keeping the IWE sharp at any time, which helps reduce the possibility of event collapse, while that of PhE is always set to the end time of the sample. For inference, users just need to input one event voxel grid $\\mathcal{V}(t_{i-1}, t_i)$ to predict flow $F_{i-1 \\to i}$ and intensity $L_i$ .",
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+ "type": "text",
+ "text": "4. Experiments",
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+ "type": "text",
+ "text": "We begin by describing the experimental setup (Sec. 4.1), then present the results of optical flow evaluation (Sec. 4.2) and of image intensity evaluation (Sec. 4.3), before finally introducing the ablation study (Sec. 4.4).",
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+ "text": "4.1. Experimental setup",
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+ "type": "text",
+ "text": "Datasets. Table 2 summarizes the datasets used in our experiments. The ECD dataset [26] is collected with a handheld DAVIS240C camera in indoor scenarios, where the motion speed varies from slow to fast. The DSEC dataset [13] features urban and highway driving scenarios in daylight and night. It is recorded with an on-board Prophesee Gen3 camera, and the GT optical flow is computed from the LiDAR disparity data. The HDR dataset [31] contains event data captured in HDR illumination conditions, such as the Sun and a car driving out of a tunnel. It highlights the HDR property of event cameras. The BS-ERGB dataset [42] provides high-resolution event data recorded by a handheld co-capture system composed of a Prophesee Gen4 camera (1 megapixel) and a FLIR RGB camera, in complex outdoor scenes. The high quality of the GT frames makes them suitable for the evaluation of event-based intensity reconstruction. For intensity evaluation, we use the EVREAL tool [6], and adopt its sequence selection. The sole change made is the removal of the last seconds of the may29_rooftop sequences from the evaluation, where the camera does not move and event data consists of pure noise.",
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+ "text": "Metrics. For optical flow, we adopt standard metrics: end-point error (EPE), angular error (AE) and $\\% \\mathrm{Out}$ (the percentage of flow estimates whose EPE $>3\\mathrm{px}$ ). We also report the flow warp loss (FWL) proposed in [41]. For image intensity, we report full-reference metrics when GT images are available (e.g., BS-ERGB dataset): mean square error (MSE), structure similarity index (SSIM) [43]",
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+ "type": "table",
+ "img_path": "images/9e2b31c490169fd627f4d514ecd9c204f06aec89fd64ce874cf0af1e1af679c0.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Dataset | Camera | Pixels | Scenarios & Features |
| ECD [26] | DAVIS240C | 240 × 180 | Indoor handheld, varying speed |
| DSEC [12] | Prophesee Gen3 | 640 × 480 | Outdoor driving, daylight & night |
| HDR [31] | Samsung DVS Gen3 | 640 × 480 | Indoor & outdoor, handheld & driving, HDR |
| BS-ERGB [42] | PSEE Gen4 & FLIR | 970 × 625 | Outdoor handheld motion, HDR |
",
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+ "type": "text",
+ "text": "Table 2. Configurations of the datasets used in the experiments. The BS-ERGB data is cropped; its resolution is a bit smaller than the event camera resolution.",
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+ "type": "text",
+ "text": "and perceptual similarity (LPIPS) [48]. Otherwise, we use no-reference metrics: BRISQUE [23], NIQE [24], MANIQA [46] (e.g., HDR dataset).",
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+ "type": "text",
+ "text": "Implementation Details. We train our model only on the DSEC training split for 130 epochs with an AdamW optimizer [20], whose learning rate is $10^{-3}$ for the first 100 epochs and then decays to $10^{-4}$ . The training is carried out on four NVIDIA RTX A6000 GPUs with a total batch size of 24. This trained model is used for the evaluation of optical flow on the test split of DSEC and those of image intensity on BS-ERGB and HDR datasets, without fine-tuning. The weights of the loss terms are: $\\lambda_1 = 30$ , $\\lambda_2 = 1$ , $\\lambda_3 = 10$ , $\\lambda_4 = 0.001$ , $\\lambda_5 = 1$ . The contrast threshold $C$ is set to 0.2. We adopt the classical U-Net architecture [32], which has 15 input channels (number of time bins in the event voxel grid [52]) and three output channels (first two: optical flow, third one: intensity).",
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+ "text": "During training and inference, we first apply average pooling with a kernel size of 16 to the raw output flow, and then perform bilinear interpolation to recover the original resolution for the output flow, to further guarantee flow smoothness. For inference, like [28], we convert the predicted logarithmic intensity into the linear scale through $I = \\exp (L)$ , then perform the robust min/max normalization before evaluation and visualization: $\\hat{I} = (I - m) / (M - m)$ , where $m$ and $M$ are the $1\\%$ and $99\\%$ percentiles of $I$ , respectively. The inference time reported in Tabs. 3 and 5 is measured on a single GPU of the same type (NVIDIA RTX A6000).",
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+ "text": "4.2. Optical Flow Evaluation",
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+ "text": "Accuracy. Table 3 presents a comprehensive comparison between our method and baseline approaches, where the methods that require GT optical flow (SL) and those that do not (MB/USL) are compared respectively in two categories. As mentioned in Sec. 2.1, SL methods achieve smaller errors because they are not only trained with GT, but also the GT of training and test sequences are from the same sensor (no distribution gap). In the MB/USL category, our method significantly outperforms all others in the summarized metrics (\"All\" columns) and the per-sequence values. The only exception is that our value of %Out on interlaken_00_b is slightly bigger than that of MotionPriorCM. Overall, our",
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+ "table_body": "| Type | Method | \\(t_{\\text{inf}}[\\text{ms}]\\) | All | interlaken_00_b | interlaken_01_a | thun_01_a |
| EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ |
| SL | E-RAFT [13] | 46.33 | 0.79 | 10.56 | 2.68 | 1.29 | 1.39 | 6.22 | 6.19 | 1.32 | 0.90 | 6.88 | 3.91 | 1.42 | 0.65 | 9.75 | 1.87 | 1.20 |
| IDNet [45] | | 0.72 | 2.72 | 2.04 | - | 1.25 | 2.11 | 4.35 | - | 0.77 | 2.25 | 2.60 | - | 0.57 | 2.66 | 1.47 | - |
| MB/USL | RTEF [3] | | 4.88 | - | 41.95 | 2.51 | 8.59 | - | 59.84 | 2.89 | 5.94 | - | 47.33 | 2.92 | 3.01 | - | 29.70 | 2.39 |
| MultiCM [37] | \\(9.9 \\cdot 10^3\\) | 3.47 | 13.98 | 30.86 | 1.37 | 5.74 | 9.19 | 38.93 | 1.50 | 3.74 | 9.77 | 31.37 | 1.51 | 2.12 | 11.06 | 17.68 | 1.24 |
| BTEB [28] | | 3.86 | - | 31.45 | 1.30 | 6.32 | - | 47.95 | 1.46 | 4.91 | - | 36.07 | 1.42 | 2.33 | - | 20.92 | 1.32 |
| Paredes et al. [29] | 40.1 | 2.33 | 10.56 | 17.77 | - | 3.34 | 6.22 | 25.72 | - | 2.49 | 6.88 | 19.15 | - | 1.73 | 9.75 | 10.39 | - |
| EV-FlowNet [52] | | 3.86 | - | 31.45 | 1.30 | 6.32 | - | 47.95 | 1.46 | 4.91 | - | 36.07 | 1.42 | 2.33 | - | 20.92 | 1.32 |
| MotionPriorCM [16] | 17.86 | 3.20 | 8.53 | 15.21 | 1.46 | 3.21 | 4.89 | 20.45 | 1.58 | 2.38 | 5.46 | 17.40 | 1.70 | 1.39 | 6.99 | 7.36 | 1.30 |
| VSA-SM [47] | | 2.22 | 8.86 | 16.83 | - | 3.20 | 6.23 | 24.61 | - | 2.46 | 7.00 | 20.23 | - | 1.55 | 6.63 | 10.67 | - |
| Ours | 15.12 | 1.78 | 6.44 | 11.24 | 1.79 | 3.08 | 3.87 | 20.76 | 1.92 | 1.90 | 4.11 | 12.62 | 2.06 | 1.26 | 5.69 | 6.61 | 1.56 |
",
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+ "table_body": "| Type | Method | thun_01_b | zurich_city_12_a | zurich_city_14_c | zurich_city_15_a |
| EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ |
| SL | E-RAFT [13] | 0.58 | 8.41 | 1.52 | 1.18 | 0.61 | 23.16 | 1.06 | 1.12 | 0.71 | 10.23 | 1.91 | 1.47 | 0.59 | 8.88 | 1.30 | 1.34 |
| IDNet [45] | 0.55 | 2.07 | 1.35 | - | 0.60 | 4.56 | 1.16 | - | 0.76 | 3.74 | 2.74 | - | 0.55 | 2.55 | 1.02 | - |
| MB/USL | RTEF [3] | 3.91 | - | 34.69 | 2.48 | 3.14 | - | 34.08 | 1.42 | 4.00 | - | 45.67 | 2.67 | 3.78 | - | 37.99 | 2.82 |
| MultiCM [37] | 2.48 | 12.05 | 23.56 | 1.24 | 3.86 | 28.61 | 43.96 | 1.14 | 2.72 | 12.62 | 30.53 | 1.50 | 2.35 | 11.82 | 20.99 | 1.41 |
| BTEB [28] | 3.04 | - | 25.41 | 1.33 | 2.62 | - | 25.80 | 1.03 | 3.36 | - | 36.34 | 1.24 | 2.97 | - | 25.53 | 1.33 |
| Paredes et al. [29] | 1.66 | 8.41 | 9.34 | - | 2.72 | 23.16 | 26.65 | - | 2.64 | 10.23 | 23.01 | - | 1.69 | 8.88 | 9.98 | - |
| EV-FlowNet [52] | 3.04 | - | 25.41 | 1.33 | 2.62 | - | 25.80 | 1.03 | 3.36 | - | 36.34 | 1.24 | 2.97 | - | 25.53 | 1.33 |
| MotionPriorCM [16] | 1.54 | 6.55 | 9.69 | 1.33 | 8.33 | 20.16 | 22.39 | 1.13 | 1.78 | 8.79 | 12.99 | 1.56 | 1.45 | 6.27 | 8.34 | 1.51 |
| VSA-SM [47] | 1.74 | 6.76 | 13.07 | - | 2.19 | 17.13 | 15.24 | - | 1.69 | 7.57 | 11.02 | - | 1.85 | 8.06 | 13.55 | - |
| Ours | 1.15 | 4.89 | 5.81 | 1.63 | 1.92 | 14.35 | 13.31 | 1.40 | 1.50 | 6.93 | 10.51 | 1.92 | 1.26 | 5.46 | 6.41 | 1.89 |
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+ "text": "Table 3. Optical flow evaluation. Results on the DSEC optical flow benchmark [13]. Bold is the best in each category, except the column of $t_{\\mathrm{inf}}$ , where only the shortest $t_{\\mathrm{inf}}$ is marked. Note that our model predicts both flow and intensity, while others only predicts the former.",
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+ "image_caption": [
+ "Figure 3. Qualitative comparisons on DSEC. From left to right: (a) input events; (b) image of warped events (IWE) with our predicted flow; (c) our predicted intensity; (d) our predicted flow; (e)-(f) two baseline methods that predict optical flow (USL and SL, respectively)."
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+ "text": "method achieves great improvements of $20\\%$ , $25\\%$ and $26\\%$ in terms of EPE, AE and $\\% \\text{Out}$ , respectively. Note that our method even outperforms E-RAFT (SL) in terms of AE, with a reduction of $39\\%$ . RTEF directly adopts FWL as the objective function to optimize, so it has the highest FWL scores on all sequences, followed by our method in the second place. Note that a high FWL value may not always be good, as it can be indicative of event collapse [39]. In addition to the overall metrics, our method shows the best performance on all individual sequences that are recorded in various scenarios (urban and highway) and various illumination conditions (daylight and night). This demonstrates the robustness and versatility of the proposed approach.",
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+ {
+ "type": "text",
+ "text": "Figure 3 presents a qualitative comparison on the DSEC",
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+ {
+ "type": "text",
+ "text": "dataset. It is clear that the output flow maps (column d) of our method are more precise than those of the most recent USL method (MotionPriorCM, column e). Regarding scene appearance, our method not only generates sharp edge maps using the predicted flow (column b) –like flow-based methods–, but also simultaneously produces detailed intensity images (column c).",
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+ "text": "Runtime. We also compare the inference time of some methods in Tab. 3 (\" $t_{\\mathrm{inf}}$ \" column). Our method shows the best efficiency despite predicting two quantities (flow and intensity). Note that MotionPriorCM also uses a U-Net architecture, where the only difference from ours is the way of up-sampling features in the decoder (we use bilinear interpolation whereas [16] uses 2D transposed convolutions).",
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+ "img_path": "images/e6e33d926c8f612338ab86a474d78425ebdb17e49bb4ec8ae3b8adedffb58a8b.jpg",
+ "image_caption": [
+ "Figure 4. Qualitative image-intensity comparisons on ECD, BS-ERGB, HDR and ECD-fast data. Best viewed when zoomed in."
+ ],
+ "image_footnote": [],
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+ "text": "4.3. Evaluation of Image Intensity Reconstruction",
+ "text_level": 1,
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+ "text": "The results of the benchmarks with and without GT reference images on the BS-ERGB and HDR datasets are presented in Tab. 4. In addition, the inference times of all methods are reported in Tab. 5.",
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+ "text": "Among supervised-learning (SL) approaches, ET-Net achieves the best image quality in five out of six metrics, but it is the slowest by a margin. Conversely, FireNet reports the shortest inference time, but its quality metrics are not as good as other methods.",
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+ "text": "In the unsupervised-learning (USL) category, our method reports comparable results in full-reference metrics as those of BTEB [28]. However, our method significantly outperforms BTEB in all three metrics on the HDR dataset, with an improvement of around $50\\%$ , where many SL methods are also surpassed. In particular, we achieve the best MANIQA value compared to all baselines. This implies that our method better unlocks the HDR properties of event cameras. In terms of inference time, our model stands in the middle of the ranking; however, our model outputs both flow and intensity, while the others only output intensity.",
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+ "text": "An important remark to make is that the above metrics have limitations: as analyzed in [49], different metrics often lead to divergent conclusions, where discrepancies occur. For example, some methods achieve better MSE just by darkening the predictions (as GT images are dark). Our method reports better LPIPS, but worse MSE and SSIM values than BTEB; E2VID reports better BRISQUE than ET-Net, but it performs worse in terms of NIQE and MANIQA. The numbers do not seem to entirely reflect visual quality from a human perspective, as we present in the qualitative comparisons of Fig. 4. From the images, it is clear that",
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+ "table_body": "| Type | Method | BS-ERGB | HDR |
| MSE↓ | SSIM↑ | LPIPS↓ | BRISQUE↓ | NIQE↓ | MANIQA↑ |
| SL | E2VID [31] | 0.14 | 0.33 | 0.56 | 12.63 | 4.27 | 0.30 |
| FireNet [35] | 0.10 | 0.34 | 0.53 | 18.57 | 3.85 | 0.30 |
| SPADE-E2VID [10] | 0.09 | 0.35 | 0.63 | 24.51 | 7.17 | 0.28 |
| ET-Net [44] | 0.07 | 0.37 | 0.44 | 19.20 | 3.45 | 0.32 |
| USL | BTEB [28] | 0.09 | 0.36 | 0.62 | 51.47 | 6.24 | 0.18 |
| Ours | 0.10 | 0.31 | 0.56 | 25.03 | 3.78 | 0.40 |
",
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+ "img_path": "images/5bc3da66ae5487ee11bf398ee576072262929e27585acbc1dd368ff0c39f3bb0.jpg",
+ "table_caption": [
+ "Table 4. Image-intensity quality assessment. Full-reference evaluation results on the BS-ERGB [42] dataset (left), and nonreference evaluation results on the HDR [31] dataset (right). Bold is the best in each category. The between-frame event slicing is used for BS-ERGB while the fixed-duration slicing ( $\\Delta t = 100\\mathrm{ms}$ ) is used for HDR, where no frame is available."
+ ],
+ "table_footnote": [],
+ "table_body": "| Resolution | E2VID (2019) | FireNet (2020) | SPADE-E2VID (2021) | ET-Net (2021) | BTEB (2021) | Ours (2024) |
| 640 × 480 | 10.95 | 4.94 | 36.07 | 173.56 | 10.59 | 15.11 |
| 1280 × 720 | 31.04 | 14.67 | 105.87 | 1606.33 | 29.89 | 40.78 |
",
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+ "text": "Table 5. Runtime evaluation [ms] of event-based intensity estimation methods at VGA and HD resolutions. Note that our model infers both flow and intensity, while others only infer intensity.",
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+ {
+ "type": "text",
+ "text": "our approach is able to recover fine details (sharp image) of scene appearance despite the HDR illumination (selfie) and fast motion (poster fast). Figure 4 also illustrates the shortcomings of the above quantitative metrics. All images from SPADE-E2VID are visually blurred, but it reports better MSE and SSIM than FireNet and our method, whose images are markedly sharper and cleaner.",
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+ "text": "4.4. Ablation Study",
+ "text_level": 1,
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+ "text": "We conduct an ablation study to illustrate the effects of some loss terms and the superiority of joint flow-intensity",
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+ {
+ "type": "text",
+ "text": "estimation over flow-only estimation. The quantitative and qualitative results are presented in Tab. 6 and Fig. 5. Please refer to the supplementary for the ablation studies on loss weights and camera contrast threshold $C$ .",
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+ "text": "TC Loss. First, we disable the TC loss $(\\lambda_5 = 0)$ . Although flow accuracy does not decrease dramatically (around $10\\%$ ), intensity accuracy is reduced significantly (Tab. 6, 1st row). This is also revealed in Fig. 5 (column a), where texture at valid pixels is recovered, while invalid pixels are filled with markedly incorrect values due to the lack of constraints. This confirms our claim in Sec. 1, that better estimation for both visual quantities is achieved by leveraging their synergies.",
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+ "text": "TV regularization. Next, we disable the TV regularization of both flow and intensity ( $\\lambda_3 = \\lambda_4 = 0$ ). Contrary to the previous test, intensity accuracy remains while flow accuracy drops considerably (Tab. 6, 2nd row). The same conclusion can be drawn from Fig. 5 (column b), where the estimated flow shows artifacts, mostly at invalid pixels. As a consequence, the output image intensity at such pixels is not as smooth as that of our main model (column c).",
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+ "text": "Flow-only Estimation. Finally, we train the network to predict only optical flow ( $\\lambda_{1} = \\lambda_{4} = \\lambda_{5} = 0$ , thus changing the number of output channels from three to two). In this case, the loss function basically reduces to the one used by recent purely CMax-based optical flow estimation methods [16, 37]. As reported in the third row of Tab. 6, the flow accuracy is slightly better than that of w/o TV reg., but still falls far behind our main model, with respective gaps of $43\\%$ , $33\\%$ , $53\\%$ in terms of EPE, AE and %Out. This again confirms the advantages of our proposed joint estimation method over the separate ones.",
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+ "type": "text",
+ "text": "4.5. Single Network vs. Dual Network",
+ "text_level": 1,
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+ "text": "To illustrate the superiority of joint learning with a single network, we compare it to a dual network (two U-Nets, one for optical flow prediction and the other for intensity reconstruction), with configuration identical to ours (loss function, loss weights and training settings). Table 6 show that the estimation results of the dual network (4th row) are considerably worse than those of the single U-Net model (last row). Our joint learning scheme enables one single network to learn the motion and appearance, as well as their synergies, thus achieving better performance than separately.",
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+ "type": "text",
+ "text": "5. Limitations",
+ "text_level": 1,
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+ "text": "The event camera output depends on scene texture and camera motion. In regions where no events are produced, it is thus difficult to recover motion parameters and/or scene appearance. In this case, regularization is used to fill in those pixels by encouraging spatial smoothness. However, this may cause inaccuracies. This issue could be overcome by combining two visual modalities (events and frames),",
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+ "img_path": "images/7e1dcf2237aff08f3e42be2bda6cf9ad583b5734325fe00fe13d9ea0bfce6284.jpg",
+ "image_caption": [
+ "(a) w/o TC loss"
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+ {
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+ "img_path": "images/454193e2a9ef81f3bbf20eac08b9ecbb14ed8b05eaf12cf1823ccd09056b26b9.jpg",
+ "image_caption": [
+ "(b) w/o TV reg."
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+ {
+ "type": "image",
+ "img_path": "images/00bc54714f4b123a8f85030d78100899d56aed93f8a00e6b0935e593c445af98.jpg",
+ "image_caption": [
+ "(c) Ours",
+ "Figure 5. Qualitative results of ablation study. The above are results from the thun_01_b sequence of DSEC. The reference optical flow is generated using E-RAFT [13]."
+ ],
+ "image_footnote": [],
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+ {
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+ "img_path": "images/6b8537e96f6427123d7975103a695860f2ecfb114ca567f0cac67306be699f2b.jpg",
+ "image_caption": [
+ "(d) References"
+ ],
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+ {
+ "type": "table",
+ "img_path": "images/c7a6096615a07665fa54151df27ed6c3b70ce29580381a652ae636c32f2c4560.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Ablation | Flow | Intensity |
| EPE↓ | AE↓ | %Out↓ | MSE↓ | SSIM↑ | LPIPS↓ |
| w/o TC loss | 2.01 | 7.92 | 13.96 | 0.16 | 0.23 | 0.64 |
| w/o TV reg. | 3.30 | 14.93 | 24.95 | 0.10 | 0.30 | 0.55 |
| Flow-only | 3.13 | 9.61 | 23.56 | - | - | - |
| Dual network | 3.30 | 10.15 | 22.85 | 0.11 | 0.29 | 0.59 |
| Ours | 1.78 | 6.44 | 11.24 | 0.10 | 0.31 | 0.56 |
",
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+ "type": "text",
+ "text": "Table 6. Quantitative results of an ablation study. Flow evaluation is performed on the DSEC dataset and intensity evaluation is done on the BS-ERGB dataset.",
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+ {
+ "type": "text",
+ "text": "not without considering data fusion challenges, and/or by adding recurrent connections (at the expense of increasing the initialization time and inertia of the system [31]).",
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+ {
+ "type": "text",
+ "text": "Events triggered by flickering lights or hot pixels do not satisfy the brightness constancy assumption, which is the basis of all involved MB/USL methods. As outliers, they can undermine estimation accuracy. Learning-based methods have some capacity to deal with such outliers. However outliers would be more sensibly treated in pre-processing by some denoising method, or more recently, jointly [40].",
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+ "text": "We have presented the first unsupervised joint learning framework for optical flow and image intensity estimation with event cameras. This enabled us to train a single and lightweight network for predicting both visual quantities simultaneously, exploiting their synergies. It is designed to match the natural sensing principle of event cameras, that is, that motion and appearance are intertwined and, therefore, shall be jointly estimated. A comprehensive and well-behaved loss function is proposed by combining the event generation model, photometric consistency, event alignment and regularization. The experiments demonstrate that our method is accurate and efficient: (i) it achieves the highest accuracy among MB/USL optical flow methods; (ii) it shows competitive intensity quality, especially in HDR conditions; and (iii) it reports very short inference time while predicting both flow and image intensity.",
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+ "type": "list",
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+ "[51] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. EV-FlowNet: Self-supervised optical flow estimation for event-based cameras. In Robotics: Science and Systems (RSS), pages 1–9, 2018.",
+ "[52] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. Unsupervised event-based learning of optical flow, depth, and egomotion. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), pages 989-997, 2019."
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+ "content": "Shuang Guo\\(^{1}\\), Friedhelm Hamann\\(^{1,2}\\) and Guillermo Gallego\\(^{1,2,3}\\)."
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+ "content": "\\(^{2}\\) Science of Intelligence Excellence Cluster, \\(^{3}\\) Einstein Center for Digital Future."
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+ "content": "Event cameras rely on motion to obtain information about scene appearance. This means that appearance and motion are inherently linked: either both are present and recorded in the event data, or neither is captured. Previous works treat the recovery of these two visual quantities as separate tasks, which does not fit with the above-mentioned nature of event cameras and overlooks the inherent relations between them. We propose an unsupervised learning framework that jointly estimates optical flow (motion) and image intensity (appearance) using a single network. From the data generation model, we newly derive the event-based photometric error as a function of optical flow and image intensity. This error is further combined with the contrast maximization framework to form a comprehensive loss function that provides proper constraints for both flow and intensity estimation. Exhaustive experiments show our method's state-of-the-art performance: in optical flow estimation, it reduces EPE by \\(20\\%\\) and AE by \\(25\\%\\) compared to unsupervised approaches, while delivering competitive intensity estimation results, particularly in high dynamic range scenarios. Our method also achieves shorter inference time than all other optical flow methods and many of the image reconstruction methods, while they output only one quantity. Project page: https://github.com/tub-rip/E2FAI"
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+ "content": "1. Introduction"
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+ "content": "Event cameras [18, 30] are novel bio-inspired vision sensors that offer attractive properties compared to traditional cameras: high temporal resolution, very high dynamic range (HDR), low power consumption and high pixel bandwidth, resulting in reduced motion blur. Hence, event cameras have a large potential for computer vision and robotics applications in challenging scenarios for traditional cameras, such as high speed motion and HDR illumination. However, novel methods are required to process the unconventional output of these sensors (a stream of asynchronous per-pixel brightness changes instead of conventional images) in order to unlock their potential [9]."
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+ "content": "Figure 1. Our method computes accurate optical flow and intensity images from event-camera data despite complex scenarios, fast motion and high dynamic range. The above result is obtained using data from interlaken_00_b sequence of DSEC [13]."
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+ "content": "In the past decade, a variety of computer vision algorithms have been developed to recover fundamental visual quantities from event streams [4, 9, 14, 50], such as EV-FlowNet [52] for optical flow estimation, and E2VID [31] for image intensity reconstruction. Despite achieving good performance, most of these methods are designed to estimate a single visual quantity: optical flow or image intensity. This philosophy does not fit well with the fact that, under constant illumination, motion and appearance are inherently entangled in the input data, since events are produced by moving intensity patterns on the image plane (e.g., Fig. 1a). More accurate and robust estimation becomes possible when the synergies between both visual quantities are properly leveraged."
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+ "content": "To achieve this goal, we newly derive the event-based photometric error (PhE) as a function of optical flow and image intensity, and combine it with the state-of-the-art contrast maximization (CMax) framework [7], yielding a comprehensive loss function. Both PhE and CMax provide constraints on scene appearance and motion. The former focuses more on appearance (i.e., intensity) while the latter focuses more on motion (i.e., optical flow). Their complementary properties give rise to a well-behaved loss in both aspects. In addition, our loss function also includes a full consideration of the internal synergies between esti"
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+ "content": "mated visual quantities: during training, the predicted flow is leveraged to warp the predicted image intensity to the adjacent interval so that a temporal consistency (TC) loss can be calculated, which significantly encourages consistency and robustness. We train a deep neural network (DNN) with this loss function in an unsupervised manner. The resulting model can predict precise optical flow and image intensity simultaneously from event data (see Fig. 1)."
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+ "content": "To the best of our knowledge, this paper presents the first unsupervised learning-based approach that jointly recovers optical flow and image intensity from event data, with a single network (Tab. 1). In the experiments, we evaluate our method in terms of optical flow and intensity on a variety of public datasets. For optical flow, our method achieves the best accuracy in the unsupervised learning category in the DSEC benchmark [13], with \\(20\\%\\) and \\(25\\%\\) improvements in terms of EPE and AE, respectively. For intensity, our method reports competitive results with respect to other unsupervised methods and even some supervised ones, especially in HDR scenarios. In terms of speed, our method reports minimal inference time to obtain both visual quantities. Our method robustly predicts precise flow and intensity on unseen data recorded in different scenarios and with different event cameras, thus demonstrating generalization. Our contributions can be summarized as follows:"
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+ "content": "1. We propose the first unsupervised learning framework for the joint estimation, with a single network, of event-based optical flow and image intensity. Its working principle fits naturally with the characteristics of event data."
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+ "content": "2. We derive event-based PhD, and combine it with CMax, yielding a comprehensive and well-behaved loss function for the estimation of motion and scene appearance. It can be directly adapted to various optimization and learning-based solutions for similar problems."
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+ "content": "3. We conduct comprehensive experiments on public datasets, where our method shows state-of-the-art performance on optical flow, image intensity and inference time. Furthermore, our method shows excellent generalization on unseen data recorded in different scenarios (HDR and fast motion) and with different event cameras."
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+ "content": "We hope the clear advantages of our approach and the source code provided will make its adoption appealing, thus bringing the tasks of optical flow estimation and intensity reconstruction closer than they currently are (until now, they have mostly been treated as independent problems)."
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+ "content": "2. Related Work"
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+ "content": "Given the high-speed and HDR properties of event cameras, extensive research has been carried out to utilize them for the estimation of optical flow and image intensity. Let us review the literature on each of these tasks in Sec. 2.1 and Sec. 2.2, respectively, and summarize the approaches that solve for both quantities in Sec. 2.3."
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+ "content": "| Method | Year | Type | DOFs | Joint | Loss function |
| IVM [5] | 2011 | MB | 3 | ✓ | “Consistency” of the data (Max. Likelihood) |
| SOFIE [1] | 2016 | MB | 6 | ✓ | Pixel-wise brightness change + TC |
| E-cGAN [25] | 2021 | SL | 6 | ✗ | Supervised: Error w.r.t. ground truth |
| BTEB [28] | 2021 | USL | 6 | ✗ | FlowNet: IWE sharpness; ReconNet: LEGM |
| Ours | 2025 | USL | 6 | ✓ | CMax + PhE of Flow and Intensity + TC |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. Event-based optical flow and intensity estimation methods. The columns indicate: the method type, the number of degrees of freedom (DOFs) of the camera motion that the method can handle (3 ≡ rotation, 6 ≡ free motion), whether the method estimates flow and intensity jointly or separately, and the loss used."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.1. Event-based Optical Flow Estimation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.305,
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+ "angle": 0,
+ "content": "Previous works can be categorized into model-based (MB), supervised learning (SL) or unsupervised learning (USL). State-of-the-art MB methods [3, 39] formulate the problem using an objective function, and solve for optical flow through optimization. The most commonly-used objective is the sharpness of images of warped events (IWEs), such as the CMax loss [7, 8] used in [39], and the flow warping loss (FWL) [41] used in [3]. The optimization usually takes a number of iterations to converge, and it repeatedly warps all the involved events in every iteration, which makes these methods costly. Furthermore, the objectives derived from IWE sharpness may suffer from the issue of event collapse [36, 38], which affects flow accuracy and requires strong regularization to mitigate it."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.52,
+ 0.906,
+ 0.716
+ ],
+ "angle": 0,
+ "content": "Due to the better fitting capabilities and short inference times of DNNs, researchers have adopted them to compute optical flow. SL approaches [11, 13, 17, 19, 21, 45] train DNNs to learn the mapping from event data to the ground truth (GT) optical flow. However, the acquisition of GT relies on either simulation [17, 21] or calculation from external depth sensors using the motion field equation [13, 51]. Both are expensive. The former suffers from the sim-to-real gap, that is, the trained model may not perform well on real-world data, while the latter suffers from sensor inaccuracy and data sparsity [16, 39]. Although SL methods are generally ahead in optical flow benchmarks, the above issues about GT data are inherited by the trained model."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.72,
+ 0.906,
+ 0.901
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+ "angle": 0,
+ "content": "In contrast, USL methods [16, 29, 47, 52] forego costly data labeling, shifting the focus to the data and the loss function to learn optical flow patterns. Similarly to MB methods, current mainstream loss functions are still based on IWE sharpness [8]. For instance, EV-FlowNet [52] quantifies sharpness in terms of average timestamp images [22]. More recently, [16, 29, 39] adopted the CMax loss to train DNNs, which achieved obvious improvements with respect to MB methods that used the same loss functions. In addition, USL performs expensive event warping only during training, hence it has much shorter and more constant inference time than equivalent MB methods."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "7981"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ 0.091,
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+ ],
+ "angle": 0,
+ "content": "2.2. Event-based Image Intensity Reconstruction"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.113,
+ 0.484,
+ 0.234
+ ],
+ "angle": 0,
+ "content": "Similarly, intensity estimation methods can be classified into MB, SL and USL categories. For the MB category, early works recovered brightness from events by means of temporal filtering [34] or temporal integration with manifold denoising [27]. A recent work [49] formulated this task as a linear inverse problem with image regularization and solved for intensity using ADMM [2]. However, it required accurate optical flow as input, which limits its applicability."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.234,
+ 0.483,
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+ ],
+ "angle": 0,
+ "content": "SL approaches [10, 31, 35, 44] trained DNNs using synthetic data to learn the mapping from event data to image intensity. In this way, the models were prevented from learning motion blur and under/over-exposure that happens in traditional cameras. Besides, these methods were aimed at video reconstruction and therefore adopted recurrent network architectures while introducing temporal consistency loss to guarantee the continuity of sequential images. However, they suffer from the sim-to-real gap and sometimes perform poorly in HDR scenarios (see, e.g., Fig. 4)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.386,
+ 0.484,
+ 0.582
+ ],
+ "angle": 0,
+ "content": "USL methods for intensity reconstruction are underexplored. Recent work [28] proposed to supervise the training with event-based photometric consistency. The loss was defined using the linearized event generation model (LEGM), as the error between brightness increments measured by event data and those obtained from the spatial gradient of the predicted image. However, this method requires accurate optical flow provided externally for both training and inference, for which the authors had to train a separate network to estimate optical flow (see details of the flow part in Sec. 2.3). The need to infer sequentially with two separate models takes more time and amplifies error propagation, thus significantly limiting practicality."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
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+ "angle": 0,
+ "content": "2.3. Event-based Flow-Intensity Estimation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Table 1 summarizes the main works that estimate both optical flow and image intensity with event cameras. The earliest work [5] proposed a joint estimation approach recovering optical flow, image intensity and camera ego-motion. However, it was limited to pure rotational motion. Bardow et al. [1] developed a variational algorithm that simultaneously optimized optical flow and image intensity. However, optical flow was only constrained by the brightness constancy between estimated intensity images, while the motion information in event data was not utilized. Hence, the resulting intensity and optical flow showed poor accuracy."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.781,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "In the learning-based category, [25] presented an SL method for image reconstruction from events using conditional generative adversarial networks (cGANs), and also showed the applicability to predict depth and optical flow. The networks were trained and performed inference for each quantity separately, so the bonds between them were ignored. More recently, [28] proposed training an intensity reconstruction DNN (same architecture as [31]), but in an"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.906,
+ 0.152
+ ],
+ "angle": 0,
+ "content": "unsupervised manner. To do so, they separately trained a network for optical flow estimation using the same loss as [52], and subsequently fed its output flow into a second network for intensity reconstruction (see Sec. 2.2)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.152,
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+ 0.213
+ ],
+ "angle": 0,
+ "content": "Our method overcomes and simplifies previous designs: it jointly estimates intensity and flow in an unsupervised manner by leveraging their synergies via the proposed loss function and architecture (i.e., using a single DNN)."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3. Method"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.251,
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+ "angle": 0,
+ "content": "In this section, we first explain the preliminaries (Sec. 3.1), then introduce our proposed comprehensive loss function, including newly derived event-based PhE (Sec. 3.2), CMax loss (Sec. 3.3) and regularization terms (Sec. 3.4). Finally, we present the training pipeline in Sec. 3.5."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.1. Preliminaries"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.357,
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+ ],
+ "angle": 0,
+ "content": "Event Generation Model (EGM). Every pixel of an event camera independently measures brightness changes, generating an event \\( e_k \\doteq (\\mathbf{x}_k, t_k, p_k) \\) when the logarithmic brightness change \\( \\Delta L \\) reaches a contrast threshold \\( C \\) [9]:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.56,
+ 0.432,
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+ 0.449
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+ "angle": 0,
+ "content": "\\[\n\\Delta L \\doteq L (\\mathbf {x} _ {k}, t _ {k}) - L (\\mathbf {x} _ {k}, t _ {k} - \\Delta t _ {k}) = p _ {k} C, \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.454,
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+ 0.498
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+ "angle": 0,
+ "content": "where \\(p_k \\in \\{+1, -1\\}\\) indicates the polarity of the intensity increment, and \\(\\Delta t_k\\) is the time elapsed since the previous event at the same pixel \\(\\mathbf{x}_k\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Event warping. Given a set of events \\(\\mathcal{E} \\doteq \\{e_k\\}_{k=1}^{N_e}\\), we can warp them to a reference time \\(t_{\\mathrm{ref}}\\) with a motion model \\(\\mathbf{W}\\), yielding a set of warped events \\(\\mathcal{E}_{t_{\\mathrm{ref}}}^{\\prime} \\doteq \\{e_k^{\\prime}\\}_{k=1}^{N_e}\\), where: \\(e_k \\doteq (\\mathbf{x}_k, t_k, p_k) \\to e_k^{\\prime} \\doteq (\\mathbf{x}_k^{\\prime}, t_{\\mathrm{ref}}, p_k)\\). Provided that the time span of \\(\\mathcal{E}\\) is small, we can assume all pixels move with constant but different velocities on the image plane, that is, the motion model \\(\\mathbf{W}\\) is given by:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.611,
+ 0.618,
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+ 0.634
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {x} _ {k} ^ {\\prime} = \\mathbf {x} _ {k} + \\left(t _ {\\text {r e f}} - t _ {k}\\right) F (\\mathbf {x} _ {k}), \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "where \\(F(\\mathbf{x}_k)\\) is the optical flow at \\(\\mathbf{x}_k\\) [39]."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.2. Event-based Photometric Error (PhE)"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We leverage the original EGM to derive the event-based PhE. Starting from (1), we warp an event \\( e_k \\doteq (\\mathbf{x}_k, t_k, p_k) \\) and its predecessor (at the same pixel) \\( e_{k-1} \\doteq (\\mathbf{x}_k, t_k - \\Delta t_k, p_{k-1}) \\) to a reference time \\( t_\\mathrm{ref} \\). According to (2), their warped locations on the camera plane at \\( t_\\mathrm{ref} \\) are:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ 0.775,
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+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathbf {x} _ {k} ^ {\\prime} = \\mathbf {x} _ {k} + \\left(t _ {\\text {r e f}} - t _ {k}\\right) F (\\mathbf {x} _ {k}), \\\\ \\mathbf {x} _ {k - 1} ^ {\\prime} = \\mathbf {x} _ {k} + \\left(t _ {\\text {r e f}} - \\left(t _ {k} - \\Delta t _ {k}\\right)\\right) F (\\mathbf {x} _ {k}). \\tag {3} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Let the image intensity at \\( t_{\\mathrm{ref}} \\) be \\( L(\\mathbf{x}) \\), then we substitute (3) into (1) to obtain the PhE for the event \\( e_k \\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.597,
+ 0.862,
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+ 0.879
+ ],
+ "angle": 0,
+ "content": "\\[\n\\epsilon_ {k} \\doteq \\left(L \\left(\\mathbf {x} _ {k} ^ {\\prime}\\right) - L \\left(\\mathbf {x} _ {k - 1} ^ {\\prime}\\right)\\right) - p _ {k} C, \\tag {4}\n\\]"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
+ 0.532,
+ 0.887,
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+ 0.901
+ ],
+ "angle": 0,
+ "content": "1We omit \"logarithmic\" in the following text for simplification."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "7982"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
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+ ],
+ "angle": 0,
+ "content": "Figure 2. The training pipeline of our proposed flow-intensity joint estimation method. In every training step, two consecutive event data samples are input to the network, respectively. The CMax and PhE losses for each sample are calculated with the output optical flow and image intensity. The TC loss is defined by the photometric error between the predicted \\( L_{i+1} \\) and the one warped from \\( L_i \\) through \\( F_{i\\rightarrow i+1} \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.406,
+ 0.484,
+ 0.527
+ ],
+ "angle": 0,
+ "content": "which is the difference between the predicted intensity increment and the measured one. In practice, \\(\\mathbf{x}_k^{\\prime}\\) and \\(\\mathbf{x}_{k - 1}^{\\prime}\\) have sub-pixel precision, so we use bilinear interpolation to compute \\(L(\\mathbf{x}_k^{\\prime})\\) and \\(L(\\mathbf{x}_{k - 1}^{\\prime})\\). Therefore, every PhE term (4) provides constraints for the intensity values at up to eight pixels around \\(\\mathbf{x}_k^\\prime\\) and \\(\\mathbf{x}_{k - 1}^{\\prime}\\), as well as the optical flow value at one pixel \\(\\mathbf{x}_k\\). Finally, we sum the photometric error terms of all events in \\(\\mathcal{E}\\), obtaining the PhE loss:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ 0.538,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {P h E}} (L, F) \\doteq \\frac {1}{N _ {e}} \\sum_ {k = 1} ^ {N _ {e}} | \\epsilon_ {k} |. \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "It is an objective function of both intensity and flow, which opens the door to the joint estimation of both quantities. It is worth emphasizing that the PhE loss does not have the event collapse problem [36, 38] that CMax suffers from."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.3. Contrast Maximization (CMax)"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The CMax framework [7, 8] assumes events are triggered by moving edges, so that optical flow estimation can be determined by seeking the best motion compensation. Specifically, warped events \\(\\mathcal{E}_{t_{\\mathrm{ref}}}^{\\prime}\\) are aggregated on the image plane at \\(t_\\mathrm{ref}\\), forming an image of warped events:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\operatorname {I W E} (\\mathbf {x}; \\mathcal {E} _ {t _ {\\text {r e f}}} ^ {\\prime}, F) \\doteq \\sum_ {k = 1} ^ {N _ {e}} \\mathcal {N} \\left(\\mathbf {x}; \\mathbf {x} _ {k} ^ {\\prime}, \\sigma^ {2} = 1 \\mathrm {p x}\\right), \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.817,
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+ ],
+ "angle": 0,
+ "content": "where every pixel \\( \\mathbf{x} \\) counts its number of warped events."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "In this work, we adopt the inverse of the \\(L^1\\) magnitude of the gradient to quantify the CMax loss:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.131,
+ 0.871,
+ 0.483,
+ 0.906
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {C M a x}} (F) \\doteq 1 / \\left(\\frac {1}{| \\Omega |} \\int_ {\\Omega} \\| \\nabla \\mathrm {I W E} (\\mathbf {x}) \\| _ {1} d \\mathbf {x}\\right). \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.406,
+ 0.906,
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+ ],
+ "angle": 0,
+ "content": "In contrast to PhD, the CMax loss recovers scene appearance in the form of a sharp edge map, which is the objective instead of the variable. The only estimizable variable is optical flow, which reflects that CMax loss focuses more on motion parameters, as mentioned in Sec. 1."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.4. Regularization"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.511,
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+ ],
+ "angle": 0,
+ "content": "Smoothness of Flow and Intensity. As stated in Sec. 3.2, the PhE loss only provides supervisory constraints on pixels that contain events (called valid pixels). To infer the values of the remaining pixels, regularization is needed; we use the total variation (TV) [33] to encourage smoothness of optical flow and intensity predictions: \\(\\mathcal{L}_{\\mathrm{FTV}}(F)\\doteq \\frac{1}{|\\Omega|}\\int_{\\Omega}\\| \\nabla F(\\mathbf{x})\\| _1d\\mathbf{x}\\), and \\(\\mathcal{L}_{\\mathrm{ITV}}(L)\\doteq \\frac{1}{|\\Omega|}\\int_{\\Omega}\\| \\nabla L(\\mathbf{x})\\| _1d\\mathbf{x}\\). Additionally, the smoothness of the flow mitigates the event collapse caused by the CMax loss."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.649,
+ 0.907,
+ 0.815
+ ],
+ "angle": 0,
+ "content": "Temporal Consistency (TC). A key advantage of joint estimation (over a separate one) is being able to leverage the synergies between the quantities for better consistency. We achieve this by establishing associations between temporally consecutive predictions. As depicted in Fig. 2, in each training step, the network takes as input two consecutive data samples to predict the corresponding optical flow and image intensity. We leverage flow \\( F_{i\\rightarrow i + 1} \\) to transport \\( L_{i} \\) to \\( t_{i + 1} \\), yielding \\( L_{i + 1}^{\\prime} \\), whose photometric error with respect to \\( L_{i + 1} \\) (predicted from the other data sample) is calculated to encourage temporal consistency (TC):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.533,
+ 0.819,
+ 0.905,
+ 0.851
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {T C}} \\doteq \\frac {1}{| \\Omega |} \\int_ {\\Omega} \\left| L _ {i + 1} (\\mathbf {x}) - \\mathcal {W} (\\mathbf {x}; L _ {i}, F _ {i \\rightarrow i + 1}) \\right| d \\mathbf {x}, \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.856,
+ 0.906,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathcal{W}\\) warps an image according to the optical flow. The introduction of the TC loss greatly improves the prediction quality, especially in image intensity (see Sec. 4.4)."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "7983"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.5. Training Pipeline"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.113,
+ 0.485,
+ 0.189
+ ],
+ "angle": 0,
+ "content": "An overview of the training pipeline is displayed in Fig. 2. During training, the loss terms (5), (7), etc. are evaluated with the predictions of each sample, while the TC loss (8), between consecutive samples. Consequently, the total loss is the weighted sum of all these terms:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.092,
+ 0.2,
+ 0.483,
+ 0.217
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\lambda_ {1} \\mathcal {L} _ {\\text {P h E}} + \\lambda_ {2} \\mathcal {L} _ {\\text {C M a x}} + \\lambda_ {3} \\mathcal {L} _ {\\text {F T V}} + \\lambda_ {4} \\mathcal {L} _ {\\text {I T V}} + \\lambda_ {5} \\mathcal {L} _ {\\text {T C}},\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.227,
+ 0.484,
+ 0.349
+ ],
+ "angle": 0,
+ "content": "where the first four terms are the sum for the two data samples (Fig. 2). For every sample, the reference time of CMax is set to a random number within the time span of the event set [16], that is, keeping the IWE sharp at any time, which helps reduce the possibility of event collapse, while that of PhE is always set to the end time of the sample. For inference, users just need to input one event voxel grid \\(\\mathcal{V}(t_{i-1}, t_i)\\) to predict flow \\(F_{i-1 \\to i}\\) and intensity \\(L_i\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.361,
+ 0.223,
+ 0.379
+ ],
+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.387,
+ 0.484,
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+ ],
+ "angle": 0,
+ "content": "We begin by describing the experimental setup (Sec. 4.1), then present the results of optical flow evaluation (Sec. 4.2) and of image intensity evaluation (Sec. 4.3), before finally introducing the ablation study (Sec. 4.4)."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.456,
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+ 0.473
+ ],
+ "angle": 0,
+ "content": "4.1. Experimental setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Datasets. Table 2 summarizes the datasets used in our experiments. The ECD dataset [26] is collected with a handheld DAVIS240C camera in indoor scenarios, where the motion speed varies from slow to fast. The DSEC dataset [13] features urban and highway driving scenarios in daylight and night. It is recorded with an on-board Prophesee Gen3 camera, and the GT optical flow is computed from the LiDAR disparity data. The HDR dataset [31] contains event data captured in HDR illumination conditions, such as the Sun and a car driving out of a tunnel. It highlights the HDR property of event cameras. The BS-ERGB dataset [42] provides high-resolution event data recorded by a handheld co-capture system composed of a Prophesee Gen4 camera (1 megapixel) and a FLIR RGB camera, in complex outdoor scenes. The high quality of the GT frames makes them suitable for the evaluation of event-based intensity reconstruction. For intensity evaluation, we use the EVREAL tool [6], and adopt its sequence selection. The sole change made is the removal of the last seconds of the may29_rooftop sequences from the evaluation, where the camera does not move and event data consists of pure noise."
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+ "content": "Metrics. For optical flow, we adopt standard metrics: end-point error (EPE), angular error (AE) and \\(\\% \\mathrm{Out}\\) (the percentage of flow estimates whose EPE \\(>3\\mathrm{px}\\)). We also report the flow warp loss (FWL) proposed in [41]. For image intensity, we report full-reference metrics when GT images are available (e.g., BS-ERGB dataset): mean square error (MSE), structure similarity index (SSIM) [43]"
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+ "content": "| Dataset | Camera | Pixels | Scenarios & Features |
| ECD [26] | DAVIS240C | 240 × 180 | Indoor handheld, varying speed |
| DSEC [12] | Prophesee Gen3 | 640 × 480 | Outdoor driving, daylight & night |
| HDR [31] | Samsung DVS Gen3 | 640 × 480 | Indoor & outdoor, handheld & driving, HDR |
| BS-ERGB [42] | PSEE Gen4 & FLIR | 970 × 625 | Outdoor handheld motion, HDR |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Configurations of the datasets used in the experiments. The BS-ERGB data is cropped; its resolution is a bit smaller than the event camera resolution."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "and perceptual similarity (LPIPS) [48]. Otherwise, we use no-reference metrics: BRISQUE [23], NIQE [24], MANIQA [46] (e.g., HDR dataset)."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "Implementation Details. We train our model only on the DSEC training split for 130 epochs with an AdamW optimizer [20], whose learning rate is \\(10^{-3}\\) for the first 100 epochs and then decays to \\(10^{-4}\\). The training is carried out on four NVIDIA RTX A6000 GPUs with a total batch size of 24. This trained model is used for the evaluation of optical flow on the test split of DSEC and those of image intensity on BS-ERGB and HDR datasets, without fine-tuning. The weights of the loss terms are: \\(\\lambda_1 = 30\\), \\(\\lambda_2 = 1\\), \\(\\lambda_3 = 10\\), \\(\\lambda_4 = 0.001\\), \\(\\lambda_5 = 1\\). The contrast threshold \\(C\\) is set to 0.2. We adopt the classical U-Net architecture [32], which has 15 input channels (number of time bins in the event voxel grid [52]) and three output channels (first two: optical flow, third one: intensity)."
+ },
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+ "content": "During training and inference, we first apply average pooling with a kernel size of 16 to the raw output flow, and then perform bilinear interpolation to recover the original resolution for the output flow, to further guarantee flow smoothness. For inference, like [28], we convert the predicted logarithmic intensity into the linear scale through \\( I = \\exp (L) \\), then perform the robust min/max normalization before evaluation and visualization: \\( \\hat{I} = (I - m) / (M - m) \\), where \\( m \\) and \\( M \\) are the \\( 1\\% \\) and \\( 99\\% \\) percentiles of \\( I \\), respectively. The inference time reported in Tabs. 3 and 5 is measured on a single GPU of the same type (NVIDIA RTX A6000)."
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+ "content": "4.2. Optical Flow Evaluation"
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+ "content": "Accuracy. Table 3 presents a comprehensive comparison between our method and baseline approaches, where the methods that require GT optical flow (SL) and those that do not (MB/USL) are compared respectively in two categories. As mentioned in Sec. 2.1, SL methods achieve smaller errors because they are not only trained with GT, but also the GT of training and test sequences are from the same sensor (no distribution gap). In the MB/USL category, our method significantly outperforms all others in the summarized metrics (\"All\" columns) and the per-sequence values. The only exception is that our value of %Out on interlaken_00_b is slightly bigger than that of MotionPriorCM. Overall, our"
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+ "content": "| Type | Method | \\(t_{\\text{inf}}[\\text{ms}]\\) | All | interlaken_00_b | interlaken_01_a | thun_01_a |
| EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ |
| SL | E-RAFT [13] | 46.33 | 0.79 | 10.56 | 2.68 | 1.29 | 1.39 | 6.22 | 6.19 | 1.32 | 0.90 | 6.88 | 3.91 | 1.42 | 0.65 | 9.75 | 1.87 | 1.20 |
| IDNet [45] | | 0.72 | 2.72 | 2.04 | - | 1.25 | 2.11 | 4.35 | - | 0.77 | 2.25 | 2.60 | - | 0.57 | 2.66 | 1.47 | - |
| MB/USL | RTEF [3] | | 4.88 | - | 41.95 | 2.51 | 8.59 | - | 59.84 | 2.89 | 5.94 | - | 47.33 | 2.92 | 3.01 | - | 29.70 | 2.39 |
| MultiCM [37] | \\(9.9 \\cdot 10^3\\) | 3.47 | 13.98 | 30.86 | 1.37 | 5.74 | 9.19 | 38.93 | 1.50 | 3.74 | 9.77 | 31.37 | 1.51 | 2.12 | 11.06 | 17.68 | 1.24 |
| BTEB [28] | | 3.86 | - | 31.45 | 1.30 | 6.32 | - | 47.95 | 1.46 | 4.91 | - | 36.07 | 1.42 | 2.33 | - | 20.92 | 1.32 |
| Paredes et al. [29] | 40.1 | 2.33 | 10.56 | 17.77 | - | 3.34 | 6.22 | 25.72 | - | 2.49 | 6.88 | 19.15 | - | 1.73 | 9.75 | 10.39 | - |
| EV-FlowNet [52] | | 3.86 | - | 31.45 | 1.30 | 6.32 | - | 47.95 | 1.46 | 4.91 | - | 36.07 | 1.42 | 2.33 | - | 20.92 | 1.32 |
| MotionPriorCM [16] | 17.86 | 3.20 | 8.53 | 15.21 | 1.46 | 3.21 | 4.89 | 20.45 | 1.58 | 2.38 | 5.46 | 17.40 | 1.70 | 1.39 | 6.99 | 7.36 | 1.30 |
| VSA-SM [47] | | 2.22 | 8.86 | 16.83 | - | 3.20 | 6.23 | 24.61 | - | 2.46 | 7.00 | 20.23 | - | 1.55 | 6.63 | 10.67 | - |
| Ours | 15.12 | 1.78 | 6.44 | 11.24 | 1.79 | 3.08 | 3.87 | 20.76 | 1.92 | 1.90 | 4.11 | 12.62 | 2.06 | 1.26 | 5.69 | 6.61 | 1.56 |
"
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+ "content": "| Type | Method | thun_01_b | zurich_city_12_a | zurich_city_14_c | zurich_city_15_a |
| EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ |
| SL | E-RAFT [13] | 0.58 | 8.41 | 1.52 | 1.18 | 0.61 | 23.16 | 1.06 | 1.12 | 0.71 | 10.23 | 1.91 | 1.47 | 0.59 | 8.88 | 1.30 | 1.34 |
| IDNet [45] | 0.55 | 2.07 | 1.35 | - | 0.60 | 4.56 | 1.16 | - | 0.76 | 3.74 | 2.74 | - | 0.55 | 2.55 | 1.02 | - |
| MB/USL | RTEF [3] | 3.91 | - | 34.69 | 2.48 | 3.14 | - | 34.08 | 1.42 | 4.00 | - | 45.67 | 2.67 | 3.78 | - | 37.99 | 2.82 |
| MultiCM [37] | 2.48 | 12.05 | 23.56 | 1.24 | 3.86 | 28.61 | 43.96 | 1.14 | 2.72 | 12.62 | 30.53 | 1.50 | 2.35 | 11.82 | 20.99 | 1.41 |
| BTEB [28] | 3.04 | - | 25.41 | 1.33 | 2.62 | - | 25.80 | 1.03 | 3.36 | - | 36.34 | 1.24 | 2.97 | - | 25.53 | 1.33 |
| Paredes et al. [29] | 1.66 | 8.41 | 9.34 | - | 2.72 | 23.16 | 26.65 | - | 2.64 | 10.23 | 23.01 | - | 1.69 | 8.88 | 9.98 | - |
| EV-FlowNet [52] | 3.04 | - | 25.41 | 1.33 | 2.62 | - | 25.80 | 1.03 | 3.36 | - | 36.34 | 1.24 | 2.97 | - | 25.53 | 1.33 |
| MotionPriorCM [16] | 1.54 | 6.55 | 9.69 | 1.33 | 8.33 | 20.16 | 22.39 | 1.13 | 1.78 | 8.79 | 12.99 | 1.56 | 1.45 | 6.27 | 8.34 | 1.51 |
| VSA-SM [47] | 1.74 | 6.76 | 13.07 | - | 2.19 | 17.13 | 15.24 | - | 1.69 | 7.57 | 11.02 | - | 1.85 | 8.06 | 13.55 | - |
| Ours | 1.15 | 4.89 | 5.81 | 1.63 | 1.92 | 14.35 | 13.31 | 1.40 | 1.50 | 6.93 | 10.51 | 1.92 | 1.26 | 5.46 | 6.41 | 1.89 |
"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Optical flow evaluation. Results on the DSEC optical flow benchmark [13]. Bold is the best in each category, except the column of \\( t_{\\mathrm{inf}} \\), where only the shortest \\( t_{\\mathrm{inf}} \\) is marked. Note that our model predicts both flow and intensity, while others only predicts the former."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 3. Qualitative comparisons on DSEC. From left to right: (a) input events; (b) image of warped events (IWE) with our predicted flow; (c) our predicted intensity; (d) our predicted flow; (e)-(f) two baseline methods that predict optical flow (USL and SL, respectively)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "method achieves great improvements of \\(20\\%\\), \\(25\\%\\) and \\(26\\%\\) in terms of EPE, AE and \\(\\% \\text{Out}\\), respectively. Note that our method even outperforms E-RAFT (SL) in terms of AE, with a reduction of \\(39\\%\\). RTEF directly adopts FWL as the objective function to optimize, so it has the highest FWL scores on all sequences, followed by our method in the second place. Note that a high FWL value may not always be good, as it can be indicative of event collapse [39]. In addition to the overall metrics, our method shows the best performance on all individual sequences that are recorded in various scenarios (urban and highway) and various illumination conditions (daylight and night). This demonstrates the robustness and versatility of the proposed approach."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 3 presents a qualitative comparison on the DSEC"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ "angle": 0,
+ "content": "dataset. It is clear that the output flow maps (column d) of our method are more precise than those of the most recent USL method (MotionPriorCM, column e). Regarding scene appearance, our method not only generates sharp edge maps using the predicted flow (column b) –like flow-based methods–, but also simultaneously produces detailed intensity images (column c)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Runtime. We also compare the inference time of some methods in Tab. 3 (\"\\(t_{\\mathrm{inf}}\\)\" column). Our method shows the best efficiency despite predicting two quantities (flow and intensity). Note that MotionPriorCM also uses a U-Net architecture, where the only difference from ours is the way of up-sampling features in the decoder (we use bilinear interpolation whereas [16] uses 2D transposed convolutions)."
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+ [
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+ "bbox": [
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. Qualitative image-intensity comparisons on ECD, BS-ERGB, HDR and ECD-fast data. Best viewed when zoomed in."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.3. Evaluation of Image Intensity Reconstruction"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The results of the benchmarks with and without GT reference images on the BS-ERGB and HDR datasets are presented in Tab. 4. In addition, the inference times of all methods are reported in Tab. 5."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Among supervised-learning (SL) approaches, ET-Net achieves the best image quality in five out of six metrics, but it is the slowest by a margin. Conversely, FireNet reports the shortest inference time, but its quality metrics are not as good as other methods."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In the unsupervised-learning (USL) category, our method reports comparable results in full-reference metrics as those of BTEB [28]. However, our method significantly outperforms BTEB in all three metrics on the HDR dataset, with an improvement of around \\(50\\%\\), where many SL methods are also surpassed. In particular, we achieve the best MANIQA value compared to all baselines. This implies that our method better unlocks the HDR properties of event cameras. In terms of inference time, our model stands in the middle of the ranking; however, our model outputs both flow and intensity, while the others only output intensity."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "An important remark to make is that the above metrics have limitations: as analyzed in [49], different metrics often lead to divergent conclusions, where discrepancies occur. For example, some methods achieve better MSE just by darkening the predictions (as GT images are dark). Our method reports better LPIPS, but worse MSE and SSIM values than BTEB; E2VID reports better BRISQUE than ET-Net, but it performs worse in terms of NIQE and MANIQA. The numbers do not seem to entirely reflect visual quality from a human perspective, as we present in the qualitative comparisons of Fig. 4. From the images, it is clear that"
+ },
+ {
+ "type": "table",
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+ "angle": 0,
+ "content": "| Type | Method | BS-ERGB | HDR |
| MSE↓ | SSIM↑ | LPIPS↓ | BRISQUE↓ | NIQE↓ | MANIQA↑ |
| SL | E2VID [31] | 0.14 | 0.33 | 0.56 | 12.63 | 4.27 | 0.30 |
| FireNet [35] | 0.10 | 0.34 | 0.53 | 18.57 | 3.85 | 0.30 |
| SPADE-E2VID [10] | 0.09 | 0.35 | 0.63 | 24.51 | 7.17 | 0.28 |
| ET-Net [44] | 0.07 | 0.37 | 0.44 | 19.20 | 3.45 | 0.32 |
| USL | BTEB [28] | 0.09 | 0.36 | 0.62 | 51.47 | 6.24 | 0.18 |
| Ours | 0.10 | 0.31 | 0.56 | 25.03 | 3.78 | 0.40 |
"
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+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Image-intensity quality assessment. Full-reference evaluation results on the BS-ERGB [42] dataset (left), and nonreference evaluation results on the HDR [31] dataset (right). Bold is the best in each category. The between-frame event slicing is used for BS-ERGB while the fixed-duration slicing (\\(\\Delta t = 100\\mathrm{ms}\\)) is used for HDR, where no frame is available."
+ },
+ {
+ "type": "table",
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+ "angle": 0,
+ "content": "| Resolution | E2VID (2019) | FireNet (2020) | SPADE-E2VID (2021) | ET-Net (2021) | BTEB (2021) | Ours (2024) |
| 640 × 480 | 10.95 | 4.94 | 36.07 | 173.56 | 10.59 | 15.11 |
| 1280 × 720 | 31.04 | 14.67 | 105.87 | 1606.33 | 29.89 | 40.78 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 5. Runtime evaluation [ms] of event-based intensity estimation methods at VGA and HD resolutions. Note that our model infers both flow and intensity, while others only infer intensity."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ 0.84
+ ],
+ "angle": 0,
+ "content": "our approach is able to recover fine details (sharp image) of scene appearance despite the HDR illumination (selfie) and fast motion (poster fast). Figure 4 also illustrates the shortcomings of the above quantitative metrics. All images from SPADE-E2VID are visually blurred, but it reports better MSE and SSIM than FireNet and our method, whose images are markedly sharper and cleaner."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Ablation Study"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "We conduct an ablation study to illustrate the effects of some loss terms and the superiority of joint flow-intensity"
+ },
+ {
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+ "bbox": [
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+ "content": "7986"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "estimation over flow-only estimation. The quantitative and qualitative results are presented in Tab. 6 and Fig. 5. Please refer to the supplementary for the ablation studies on loss weights and camera contrast threshold \\( C \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "TC Loss. First, we disable the TC loss \\((\\lambda_5 = 0)\\). Although flow accuracy does not decrease dramatically (around \\(10\\%\\)), intensity accuracy is reduced significantly (Tab. 6, 1st row). This is also revealed in Fig. 5 (column a), where texture at valid pixels is recovered, while invalid pixels are filled with markedly incorrect values due to the lack of constraints. This confirms our claim in Sec. 1, that better estimation for both visual quantities is achieved by leveraging their synergies."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "TV regularization. Next, we disable the TV regularization of both flow and intensity (\\(\\lambda_3 = \\lambda_4 = 0\\)). Contrary to the previous test, intensity accuracy remains while flow accuracy drops considerably (Tab. 6, 2nd row). The same conclusion can be drawn from Fig. 5 (column b), where the estimated flow shows artifacts, mostly at invalid pixels. As a consequence, the output image intensity at such pixels is not as smooth as that of our main model (column c)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.409,
+ 0.483,
+ 0.575
+ ],
+ "angle": 0,
+ "content": "Flow-only Estimation. Finally, we train the network to predict only optical flow (\\(\\lambda_{1} = \\lambda_{4} = \\lambda_{5} = 0\\), thus changing the number of output channels from three to two). In this case, the loss function basically reduces to the one used by recent purely CMax-based optical flow estimation methods [16, 37]. As reported in the third row of Tab. 6, the flow accuracy is slightly better than that of w/o TV reg., but still falls far behind our main model, with respective gaps of \\(43\\%\\), \\(33\\%\\), \\(53\\%\\) in terms of EPE, AE and %Out. This again confirms the advantages of our proposed joint estimation method over the separate ones."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.5. Single Network vs. Dual Network"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To illustrate the superiority of joint learning with a single network, we compare it to a dual network (two U-Nets, one for optical flow prediction and the other for intensity reconstruction), with configuration identical to ours (loss function, loss weights and training settings). Table 6 show that the estimation results of the dual network (4th row) are considerably worse than those of the single U-Net model (last row). Our joint learning scheme enables one single network to learn the motion and appearance, as well as their synergies, thus achieving better performance than separately."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ 0.785
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+ "angle": 0,
+ "content": "5. Limitations"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "The event camera output depends on scene texture and camera motion. In regions where no events are produced, it is thus difficult to recover motion parameters and/or scene appearance. In this case, regularization is used to fill in those pixels by encouraging spatial smoothness. However, this may cause inaccuracies. This issue could be overcome by combining two visual modalities (events and frames),"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "content": "Figure 5. Qualitative results of ablation study. The above are results from the thun_01_b sequence of DSEC. The reference optical flow is generated using E-RAFT [13]."
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+ "content": "| Ablation | Flow | Intensity |
| EPE↓ | AE↓ | %Out↓ | MSE↓ | SSIM↑ | LPIPS↓ |
| w/o TC loss | 2.01 | 7.92 | 13.96 | 0.16 | 0.23 | 0.64 |
| w/o TV reg. | 3.30 | 14.93 | 24.95 | 0.10 | 0.30 | 0.55 |
| Flow-only | 3.13 | 9.61 | 23.56 | - | - | - |
| Dual network | 3.30 | 10.15 | 22.85 | 0.11 | 0.29 | 0.59 |
| Ours | 1.78 | 6.44 | 11.24 | 0.10 | 0.31 | 0.56 |
"
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+ "content": "Table 6. Quantitative results of an ablation study. Flow evaluation is performed on the DSEC dataset and intensity evaluation is done on the BS-ERGB dataset."
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+ "content": "not without considering data fusion challenges, and/or by adding recurrent connections (at the expense of increasing the initialization time and inertia of the system [31])."
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+ "content": "Events triggered by flickering lights or hot pixels do not satisfy the brightness constancy assumption, which is the basis of all involved MB/USL methods. As outliers, they can undermine estimation accuracy. Learning-based methods have some capacity to deal with such outliers. However outliers would be more sensibly treated in pre-processing by some denoising method, or more recently, jointly [40]."
+ },
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+ "content": "We have presented the first unsupervised joint learning framework for optical flow and image intensity estimation with event cameras. This enabled us to train a single and lightweight network for predicting both visual quantities simultaneously, exploiting their synergies. It is designed to match the natural sensing principle of event cameras, that is, that motion and appearance are intertwined and, therefore, shall be jointly estimated. A comprehensive and well-behaved loss function is proposed by combining the event generation model, photometric consistency, event alignment and regularization. The experiments demonstrate that our method is accurate and efficient: (i) it achieves the highest accuracy among MB/USL optical flow methods; (ii) it shows competitive intensity quality, especially in HDR conditions; and (iii) it reports very short inference time while predicting both flow and image intensity."
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+ "content": "Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC 2002/1 \"Science of Intelligence\" - project number 390523135."
+ },
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+ "type": "title",
+ "bbox": [
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+ "content": "References"
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+# Unsupervised Joint Learning of Optical Flow and Intensity with Event Cameras
+
+Shuang Guo $^{1}$ , Friedhelm Hamann $^{1,2}$ and Guillermo Gallego $^{1,2,3}$ .
+
+TU Berlin and Robotics Institute Germany,
+
+$^{2}$ Science of Intelligence Excellence Cluster, $^{3}$ Einstein Center for Digital Future.
+
+# Abstract
+
+Event cameras rely on motion to obtain information about scene appearance. This means that appearance and motion are inherently linked: either both are present and recorded in the event data, or neither is captured. Previous works treat the recovery of these two visual quantities as separate tasks, which does not fit with the above-mentioned nature of event cameras and overlooks the inherent relations between them. We propose an unsupervised learning framework that jointly estimates optical flow (motion) and image intensity (appearance) using a single network. From the data generation model, we newly derive the event-based photometric error as a function of optical flow and image intensity. This error is further combined with the contrast maximization framework to form a comprehensive loss function that provides proper constraints for both flow and intensity estimation. Exhaustive experiments show our method's state-of-the-art performance: in optical flow estimation, it reduces EPE by $20\%$ and AE by $25\%$ compared to unsupervised approaches, while delivering competitive intensity estimation results, particularly in high dynamic range scenarios. Our method also achieves shorter inference time than all other optical flow methods and many of the image reconstruction methods, while they output only one quantity. Project page: https://github.com/tub-rip/E2FAI
+
+# 1. Introduction
+
+Event cameras [18, 30] are novel bio-inspired vision sensors that offer attractive properties compared to traditional cameras: high temporal resolution, very high dynamic range (HDR), low power consumption and high pixel bandwidth, resulting in reduced motion blur. Hence, event cameras have a large potential for computer vision and robotics applications in challenging scenarios for traditional cameras, such as high speed motion and HDR illumination. However, novel methods are required to process the unconventional output of these sensors (a stream of asynchronous per-pixel brightness changes instead of conventional images) in order to unlock their potential [9].
+
+
+Figure 1. Our method computes accurate optical flow and intensity images from event-camera data despite complex scenarios, fast motion and high dynamic range. The above result is obtained using data from interlaken_00_b sequence of DSEC [13].
+
+In the past decade, a variety of computer vision algorithms have been developed to recover fundamental visual quantities from event streams [4, 9, 14, 50], such as EV-FlowNet [52] for optical flow estimation, and E2VID [31] for image intensity reconstruction. Despite achieving good performance, most of these methods are designed to estimate a single visual quantity: optical flow or image intensity. This philosophy does not fit well with the fact that, under constant illumination, motion and appearance are inherently entangled in the input data, since events are produced by moving intensity patterns on the image plane (e.g., Fig. 1a). More accurate and robust estimation becomes possible when the synergies between both visual quantities are properly leveraged.
+
+To achieve this goal, we newly derive the event-based photometric error (PhE) as a function of optical flow and image intensity, and combine it with the state-of-the-art contrast maximization (CMax) framework [7], yielding a comprehensive loss function. Both PhE and CMax provide constraints on scene appearance and motion. The former focuses more on appearance (i.e., intensity) while the latter focuses more on motion (i.e., optical flow). Their complementary properties give rise to a well-behaved loss in both aspects. In addition, our loss function also includes a full consideration of the internal synergies between esti
+
+mated visual quantities: during training, the predicted flow is leveraged to warp the predicted image intensity to the adjacent interval so that a temporal consistency (TC) loss can be calculated, which significantly encourages consistency and robustness. We train a deep neural network (DNN) with this loss function in an unsupervised manner. The resulting model can predict precise optical flow and image intensity simultaneously from event data (see Fig. 1).
+
+To the best of our knowledge, this paper presents the first unsupervised learning-based approach that jointly recovers optical flow and image intensity from event data, with a single network (Tab. 1). In the experiments, we evaluate our method in terms of optical flow and intensity on a variety of public datasets. For optical flow, our method achieves the best accuracy in the unsupervised learning category in the DSEC benchmark [13], with $20\%$ and $25\%$ improvements in terms of EPE and AE, respectively. For intensity, our method reports competitive results with respect to other unsupervised methods and even some supervised ones, especially in HDR scenarios. In terms of speed, our method reports minimal inference time to obtain both visual quantities. Our method robustly predicts precise flow and intensity on unseen data recorded in different scenarios and with different event cameras, thus demonstrating generalization. Our contributions can be summarized as follows:
+
+1. We propose the first unsupervised learning framework for the joint estimation, with a single network, of event-based optical flow and image intensity. Its working principle fits naturally with the characteristics of event data.
+2. We derive event-based PhD, and combine it with CMax, yielding a comprehensive and well-behaved loss function for the estimation of motion and scene appearance. It can be directly adapted to various optimization and learning-based solutions for similar problems.
+3. We conduct comprehensive experiments on public datasets, where our method shows state-of-the-art performance on optical flow, image intensity and inference time. Furthermore, our method shows excellent generalization on unseen data recorded in different scenarios (HDR and fast motion) and with different event cameras.
+
+We hope the clear advantages of our approach and the source code provided will make its adoption appealing, thus bringing the tasks of optical flow estimation and intensity reconstruction closer than they currently are (until now, they have mostly been treated as independent problems).
+
+# 2. Related Work
+
+Given the high-speed and HDR properties of event cameras, extensive research has been carried out to utilize them for the estimation of optical flow and image intensity. Let us review the literature on each of these tasks in Sec. 2.1 and Sec. 2.2, respectively, and summarize the approaches that solve for both quantities in Sec. 2.3.
+
+| Method | Year | Type | DOFs | Joint | Loss function |
| IVM [5] | 2011 | MB | 3 | ✓ | “Consistency” of the data (Max. Likelihood) |
| SOFIE [1] | 2016 | MB | 6 | ✓ | Pixel-wise brightness change + TC |
| E-cGAN [25] | 2021 | SL | 6 | ✗ | Supervised: Error w.r.t. ground truth |
| BTEB [28] | 2021 | USL | 6 | ✗ | FlowNet: IWE sharpness; ReconNet: LEGM |
| Ours | 2025 | USL | 6 | ✓ | CMax + PhE of Flow and Intensity + TC |
+
+Table 1. Event-based optical flow and intensity estimation methods. The columns indicate: the method type, the number of degrees of freedom (DOFs) of the camera motion that the method can handle (3 ≡ rotation, 6 ≡ free motion), whether the method estimates flow and intensity jointly or separately, and the loss used.
+
+# 2.1. Event-based Optical Flow Estimation
+
+Previous works can be categorized into model-based (MB), supervised learning (SL) or unsupervised learning (USL). State-of-the-art MB methods [3, 39] formulate the problem using an objective function, and solve for optical flow through optimization. The most commonly-used objective is the sharpness of images of warped events (IWEs), such as the CMax loss [7, 8] used in [39], and the flow warping loss (FWL) [41] used in [3]. The optimization usually takes a number of iterations to converge, and it repeatedly warps all the involved events in every iteration, which makes these methods costly. Furthermore, the objectives derived from IWE sharpness may suffer from the issue of event collapse [36, 38], which affects flow accuracy and requires strong regularization to mitigate it.
+
+Due to the better fitting capabilities and short inference times of DNNs, researchers have adopted them to compute optical flow. SL approaches [11, 13, 17, 19, 21, 45] train DNNs to learn the mapping from event data to the ground truth (GT) optical flow. However, the acquisition of GT relies on either simulation [17, 21] or calculation from external depth sensors using the motion field equation [13, 51]. Both are expensive. The former suffers from the sim-to-real gap, that is, the trained model may not perform well on real-world data, while the latter suffers from sensor inaccuracy and data sparsity [16, 39]. Although SL methods are generally ahead in optical flow benchmarks, the above issues about GT data are inherited by the trained model.
+
+In contrast, USL methods [16, 29, 47, 52] forego costly data labeling, shifting the focus to the data and the loss function to learn optical flow patterns. Similarly to MB methods, current mainstream loss functions are still based on IWE sharpness [8]. For instance, EV-FlowNet [52] quantifies sharpness in terms of average timestamp images [22]. More recently, [16, 29, 39] adopted the CMax loss to train DNNs, which achieved obvious improvements with respect to MB methods that used the same loss functions. In addition, USL performs expensive event warping only during training, hence it has much shorter and more constant inference time than equivalent MB methods.
+
+# 2.2. Event-based Image Intensity Reconstruction
+
+Similarly, intensity estimation methods can be classified into MB, SL and USL categories. For the MB category, early works recovered brightness from events by means of temporal filtering [34] or temporal integration with manifold denoising [27]. A recent work [49] formulated this task as a linear inverse problem with image regularization and solved for intensity using ADMM [2]. However, it required accurate optical flow as input, which limits its applicability.
+
+SL approaches [10, 31, 35, 44] trained DNNs using synthetic data to learn the mapping from event data to image intensity. In this way, the models were prevented from learning motion blur and under/over-exposure that happens in traditional cameras. Besides, these methods were aimed at video reconstruction and therefore adopted recurrent network architectures while introducing temporal consistency loss to guarantee the continuity of sequential images. However, they suffer from the sim-to-real gap and sometimes perform poorly in HDR scenarios (see, e.g., Fig. 4).
+
+USL methods for intensity reconstruction are underexplored. Recent work [28] proposed to supervise the training with event-based photometric consistency. The loss was defined using the linearized event generation model (LEGM), as the error between brightness increments measured by event data and those obtained from the spatial gradient of the predicted image. However, this method requires accurate optical flow provided externally for both training and inference, for which the authors had to train a separate network to estimate optical flow (see details of the flow part in Sec. 2.3). The need to infer sequentially with two separate models takes more time and amplifies error propagation, thus significantly limiting practicality.
+
+# 2.3. Event-based Flow-Intensity Estimation
+
+Table 1 summarizes the main works that estimate both optical flow and image intensity with event cameras. The earliest work [5] proposed a joint estimation approach recovering optical flow, image intensity and camera ego-motion. However, it was limited to pure rotational motion. Bardow et al. [1] developed a variational algorithm that simultaneously optimized optical flow and image intensity. However, optical flow was only constrained by the brightness constancy between estimated intensity images, while the motion information in event data was not utilized. Hence, the resulting intensity and optical flow showed poor accuracy.
+
+In the learning-based category, [25] presented an SL method for image reconstruction from events using conditional generative adversarial networks (cGANs), and also showed the applicability to predict depth and optical flow. The networks were trained and performed inference for each quantity separately, so the bonds between them were ignored. More recently, [28] proposed training an intensity reconstruction DNN (same architecture as [31]), but in an
+
+unsupervised manner. To do so, they separately trained a network for optical flow estimation using the same loss as [52], and subsequently fed its output flow into a second network for intensity reconstruction (see Sec. 2.2).
+
+Our method overcomes and simplifies previous designs: it jointly estimates intensity and flow in an unsupervised manner by leveraging their synergies via the proposed loss function and architecture (i.e., using a single DNN).
+
+# 3. Method
+
+In this section, we first explain the preliminaries (Sec. 3.1), then introduce our proposed comprehensive loss function, including newly derived event-based PhE (Sec. 3.2), CMax loss (Sec. 3.3) and regularization terms (Sec. 3.4). Finally, we present the training pipeline in Sec. 3.5.
+
+# 3.1. Preliminaries
+
+Event Generation Model (EGM). Every pixel of an event camera independently measures brightness changes, generating an event $e_k \doteq (\mathbf{x}_k, t_k, p_k)$ when the logarithmic brightness change $\Delta L$ reaches a contrast threshold $C$ [9]:
+
+$$
+\Delta L \doteq L (\mathbf {x} _ {k}, t _ {k}) - L (\mathbf {x} _ {k}, t _ {k} - \Delta t _ {k}) = p _ {k} C, \tag {1}
+$$
+
+where $p_k \in \{+1, -1\}$ indicates the polarity of the intensity increment, and $\Delta t_k$ is the time elapsed since the previous event at the same pixel $\mathbf{x}_k$ .
+
+Event warping. Given a set of events $\mathcal{E} \doteq \{e_k\}_{k=1}^{N_e}$ , we can warp them to a reference time $t_{\mathrm{ref}}$ with a motion model $\mathbf{W}$ , yielding a set of warped events $\mathcal{E}_{t_{\mathrm{ref}}}^{\prime} \doteq \{e_k^{\prime}\}_{k=1}^{N_e}$ , where: $e_k \doteq (\mathbf{x}_k, t_k, p_k) \to e_k^{\prime} \doteq (\mathbf{x}_k^{\prime}, t_{\mathrm{ref}}, p_k)$ . Provided that the time span of $\mathcal{E}$ is small, we can assume all pixels move with constant but different velocities on the image plane, that is, the motion model $\mathbf{W}$ is given by:
+
+$$
+\mathbf {x} _ {k} ^ {\prime} = \mathbf {x} _ {k} + \left(t _ {\text {r e f}} - t _ {k}\right) F (\mathbf {x} _ {k}), \tag {2}
+$$
+
+where $F(\mathbf{x}_k)$ is the optical flow at $\mathbf{x}_k$ [39].
+
+# 3.2. Event-based Photometric Error (PhE)
+
+We leverage the original EGM to derive the event-based PhE. Starting from (1), we warp an event $e_k \doteq (\mathbf{x}_k, t_k, p_k)$ and its predecessor (at the same pixel) $e_{k-1} \doteq (\mathbf{x}_k, t_k - \Delta t_k, p_{k-1})$ to a reference time $t_\mathrm{ref}$ . According to (2), their warped locations on the camera plane at $t_\mathrm{ref}$ are:
+
+$$
+\begin{array}{l} \mathbf {x} _ {k} ^ {\prime} = \mathbf {x} _ {k} + \left(t _ {\text {r e f}} - t _ {k}\right) F (\mathbf {x} _ {k}), \\ \mathbf {x} _ {k - 1} ^ {\prime} = \mathbf {x} _ {k} + \left(t _ {\text {r e f}} - \left(t _ {k} - \Delta t _ {k}\right)\right) F (\mathbf {x} _ {k}). \tag {3} \\ \end{array}
+$$
+
+Let the image intensity at $t_{\mathrm{ref}}$ be $L(\mathbf{x})$ , then we substitute (3) into (1) to obtain the PhE for the event $e_k$ :
+
+$$
+\epsilon_ {k} \doteq \left(L \left(\mathbf {x} _ {k} ^ {\prime}\right) - L \left(\mathbf {x} _ {k - 1} ^ {\prime}\right)\right) - p _ {k} C, \tag {4}
+$$
+
+
+Figure 2. The training pipeline of our proposed flow-intensity joint estimation method. In every training step, two consecutive event data samples are input to the network, respectively. The CMax and PhE losses for each sample are calculated with the output optical flow and image intensity. The TC loss is defined by the photometric error between the predicted $L_{i+1}$ and the one warped from $L_i$ through $F_{i\rightarrow i+1}$ .
+
+which is the difference between the predicted intensity increment and the measured one. In practice, $\mathbf{x}_k^{\prime}$ and $\mathbf{x}_{k - 1}^{\prime}$ have sub-pixel precision, so we use bilinear interpolation to compute $L(\mathbf{x}_k^{\prime})$ and $L(\mathbf{x}_{k - 1}^{\prime})$ . Therefore, every PhE term (4) provides constraints for the intensity values at up to eight pixels around $\mathbf{x}_k^\prime$ and $\mathbf{x}_{k - 1}^{\prime}$ , as well as the optical flow value at one pixel $\mathbf{x}_k$ . Finally, we sum the photometric error terms of all events in $\mathcal{E}$ , obtaining the PhE loss:
+
+$$
+\mathcal {L} _ {\mathrm {P h E}} (L, F) \doteq \frac {1}{N _ {e}} \sum_ {k = 1} ^ {N _ {e}} | \epsilon_ {k} |. \tag {5}
+$$
+
+It is an objective function of both intensity and flow, which opens the door to the joint estimation of both quantities. It is worth emphasizing that the PhE loss does not have the event collapse problem [36, 38] that CMax suffers from.
+
+# 3.3. Contrast Maximization (CMax)
+
+The CMax framework [7, 8] assumes events are triggered by moving edges, so that optical flow estimation can be determined by seeking the best motion compensation. Specifically, warped events $\mathcal{E}_{t_{\mathrm{ref}}}^{\prime}$ are aggregated on the image plane at $t_\mathrm{ref}$ , forming an image of warped events:
+
+$$
+\operatorname {I W E} (\mathbf {x}; \mathcal {E} _ {t _ {\text {r e f}}} ^ {\prime}, F) \doteq \sum_ {k = 1} ^ {N _ {e}} \mathcal {N} \left(\mathbf {x}; \mathbf {x} _ {k} ^ {\prime}, \sigma^ {2} = 1 \mathrm {p x}\right), \tag {6}
+$$
+
+where every pixel $\mathbf{x}$ counts its number of warped events.
+
+In this work, we adopt the inverse of the $L^1$ magnitude of the gradient to quantify the CMax loss:
+
+$$
+\mathcal {L} _ {\mathrm {C M a x}} (F) \doteq 1 / \left(\frac {1}{| \Omega |} \int_ {\Omega} \| \nabla \mathrm {I W E} (\mathbf {x}) \| _ {1} d \mathbf {x}\right). \tag {7}
+$$
+
+In contrast to PhD, the CMax loss recovers scene appearance in the form of a sharp edge map, which is the objective instead of the variable. The only estimizable variable is optical flow, which reflects that CMax loss focuses more on motion parameters, as mentioned in Sec. 1.
+
+# 3.4. Regularization
+
+Smoothness of Flow and Intensity. As stated in Sec. 3.2, the PhE loss only provides supervisory constraints on pixels that contain events (called valid pixels). To infer the values of the remaining pixels, regularization is needed; we use the total variation (TV) [33] to encourage smoothness of optical flow and intensity predictions: $\mathcal{L}_{\mathrm{FTV}}(F)\doteq \frac{1}{|\Omega|}\int_{\Omega}\| \nabla F(\mathbf{x})\| _1d\mathbf{x}$ , and $\mathcal{L}_{\mathrm{ITV}}(L)\doteq \frac{1}{|\Omega|}\int_{\Omega}\| \nabla L(\mathbf{x})\| _1d\mathbf{x}$ . Additionally, the smoothness of the flow mitigates the event collapse caused by the CMax loss.
+
+Temporal Consistency (TC). A key advantage of joint estimation (over a separate one) is being able to leverage the synergies between the quantities for better consistency. We achieve this by establishing associations between temporally consecutive predictions. As depicted in Fig. 2, in each training step, the network takes as input two consecutive data samples to predict the corresponding optical flow and image intensity. We leverage flow $F_{i\rightarrow i + 1}$ to transport $L_{i}$ to $t_{i + 1}$ , yielding $L_{i + 1}^{\prime}$ , whose photometric error with respect to $L_{i + 1}$ (predicted from the other data sample) is calculated to encourage temporal consistency (TC):
+
+$$
+\mathcal {L} _ {\mathrm {T C}} \doteq \frac {1}{| \Omega |} \int_ {\Omega} \left| L _ {i + 1} (\mathbf {x}) - \mathcal {W} (\mathbf {x}; L _ {i}, F _ {i \rightarrow i + 1}) \right| d \mathbf {x}, \tag {8}
+$$
+
+where $\mathcal{W}$ warps an image according to the optical flow. The introduction of the TC loss greatly improves the prediction quality, especially in image intensity (see Sec. 4.4).
+
+# 3.5. Training Pipeline
+
+An overview of the training pipeline is displayed in Fig. 2. During training, the loss terms (5), (7), etc. are evaluated with the predictions of each sample, while the TC loss (8), between consecutive samples. Consequently, the total loss is the weighted sum of all these terms:
+
+$$
+\mathcal {L} _ {\text {t o t a l}} = \lambda_ {1} \mathcal {L} _ {\text {P h E}} + \lambda_ {2} \mathcal {L} _ {\text {C M a x}} + \lambda_ {3} \mathcal {L} _ {\text {F T V}} + \lambda_ {4} \mathcal {L} _ {\text {I T V}} + \lambda_ {5} \mathcal {L} _ {\text {T C}},
+$$
+
+where the first four terms are the sum for the two data samples (Fig. 2). For every sample, the reference time of CMax is set to a random number within the time span of the event set [16], that is, keeping the IWE sharp at any time, which helps reduce the possibility of event collapse, while that of PhE is always set to the end time of the sample. For inference, users just need to input one event voxel grid $\mathcal{V}(t_{i-1}, t_i)$ to predict flow $F_{i-1 \to i}$ and intensity $L_i$ .
+
+# 4. Experiments
+
+We begin by describing the experimental setup (Sec. 4.1), then present the results of optical flow evaluation (Sec. 4.2) and of image intensity evaluation (Sec. 4.3), before finally introducing the ablation study (Sec. 4.4).
+
+# 4.1. Experimental setup
+
+Datasets. Table 2 summarizes the datasets used in our experiments. The ECD dataset [26] is collected with a handheld DAVIS240C camera in indoor scenarios, where the motion speed varies from slow to fast. The DSEC dataset [13] features urban and highway driving scenarios in daylight and night. It is recorded with an on-board Prophesee Gen3 camera, and the GT optical flow is computed from the LiDAR disparity data. The HDR dataset [31] contains event data captured in HDR illumination conditions, such as the Sun and a car driving out of a tunnel. It highlights the HDR property of event cameras. The BS-ERGB dataset [42] provides high-resolution event data recorded by a handheld co-capture system composed of a Prophesee Gen4 camera (1 megapixel) and a FLIR RGB camera, in complex outdoor scenes. The high quality of the GT frames makes them suitable for the evaluation of event-based intensity reconstruction. For intensity evaluation, we use the EVREAL tool [6], and adopt its sequence selection. The sole change made is the removal of the last seconds of the may29_rooftop sequences from the evaluation, where the camera does not move and event data consists of pure noise.
+
+Metrics. For optical flow, we adopt standard metrics: end-point error (EPE), angular error (AE) and $\% \mathrm{Out}$ (the percentage of flow estimates whose EPE $>3\mathrm{px}$ ). We also report the flow warp loss (FWL) proposed in [41]. For image intensity, we report full-reference metrics when GT images are available (e.g., BS-ERGB dataset): mean square error (MSE), structure similarity index (SSIM) [43]
+
+| Dataset | Camera | Pixels | Scenarios & Features |
| ECD [26] | DAVIS240C | 240 × 180 | Indoor handheld, varying speed |
| DSEC [12] | Prophesee Gen3 | 640 × 480 | Outdoor driving, daylight & night |
| HDR [31] | Samsung DVS Gen3 | 640 × 480 | Indoor & outdoor, handheld & driving, HDR |
| BS-ERGB [42] | PSEE Gen4 & FLIR | 970 × 625 | Outdoor handheld motion, HDR |
+
+Table 2. Configurations of the datasets used in the experiments. The BS-ERGB data is cropped; its resolution is a bit smaller than the event camera resolution.
+
+and perceptual similarity (LPIPS) [48]. Otherwise, we use no-reference metrics: BRISQUE [23], NIQE [24], MANIQA [46] (e.g., HDR dataset).
+
+Implementation Details. We train our model only on the DSEC training split for 130 epochs with an AdamW optimizer [20], whose learning rate is $10^{-3}$ for the first 100 epochs and then decays to $10^{-4}$ . The training is carried out on four NVIDIA RTX A6000 GPUs with a total batch size of 24. This trained model is used for the evaluation of optical flow on the test split of DSEC and those of image intensity on BS-ERGB and HDR datasets, without fine-tuning. The weights of the loss terms are: $\lambda_1 = 30$ , $\lambda_2 = 1$ , $\lambda_3 = 10$ , $\lambda_4 = 0.001$ , $\lambda_5 = 1$ . The contrast threshold $C$ is set to 0.2. We adopt the classical U-Net architecture [32], which has 15 input channels (number of time bins in the event voxel grid [52]) and three output channels (first two: optical flow, third one: intensity).
+
+During training and inference, we first apply average pooling with a kernel size of 16 to the raw output flow, and then perform bilinear interpolation to recover the original resolution for the output flow, to further guarantee flow smoothness. For inference, like [28], we convert the predicted logarithmic intensity into the linear scale through $I = \exp (L)$ , then perform the robust min/max normalization before evaluation and visualization: $\hat{I} = (I - m) / (M - m)$ , where $m$ and $M$ are the $1\%$ and $99\%$ percentiles of $I$ , respectively. The inference time reported in Tabs. 3 and 5 is measured on a single GPU of the same type (NVIDIA RTX A6000).
+
+# 4.2. Optical Flow Evaluation
+
+Accuracy. Table 3 presents a comprehensive comparison between our method and baseline approaches, where the methods that require GT optical flow (SL) and those that do not (MB/USL) are compared respectively in two categories. As mentioned in Sec. 2.1, SL methods achieve smaller errors because they are not only trained with GT, but also the GT of training and test sequences are from the same sensor (no distribution gap). In the MB/USL category, our method significantly outperforms all others in the summarized metrics ("All" columns) and the per-sequence values. The only exception is that our value of %Out on interlaken_00_b is slightly bigger than that of MotionPriorCM. Overall, our
+
+| Type | Method | \(t_{\text{inf}}[\text{ms}]\) | All | interlaken_00_b | interlaken_01_a | thun_01_a |
| EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ |
| SL | E-RAFT [13] | 46.33 | 0.79 | 10.56 | 2.68 | 1.29 | 1.39 | 6.22 | 6.19 | 1.32 | 0.90 | 6.88 | 3.91 | 1.42 | 0.65 | 9.75 | 1.87 | 1.20 |
| IDNet [45] | | 0.72 | 2.72 | 2.04 | - | 1.25 | 2.11 | 4.35 | - | 0.77 | 2.25 | 2.60 | - | 0.57 | 2.66 | 1.47 | - |
| MB/USL | RTEF [3] | | 4.88 | - | 41.95 | 2.51 | 8.59 | - | 59.84 | 2.89 | 5.94 | - | 47.33 | 2.92 | 3.01 | - | 29.70 | 2.39 |
| MultiCM [37] | \(9.9 \cdot 10^3\) | 3.47 | 13.98 | 30.86 | 1.37 | 5.74 | 9.19 | 38.93 | 1.50 | 3.74 | 9.77 | 31.37 | 1.51 | 2.12 | 11.06 | 17.68 | 1.24 |
| BTEB [28] | | 3.86 | - | 31.45 | 1.30 | 6.32 | - | 47.95 | 1.46 | 4.91 | - | 36.07 | 1.42 | 2.33 | - | 20.92 | 1.32 |
| Paredes et al. [29] | 40.1 | 2.33 | 10.56 | 17.77 | - | 3.34 | 6.22 | 25.72 | - | 2.49 | 6.88 | 19.15 | - | 1.73 | 9.75 | 10.39 | - |
| EV-FlowNet [52] | | 3.86 | - | 31.45 | 1.30 | 6.32 | - | 47.95 | 1.46 | 4.91 | - | 36.07 | 1.42 | 2.33 | - | 20.92 | 1.32 |
| MotionPriorCM [16] | 17.86 | 3.20 | 8.53 | 15.21 | 1.46 | 3.21 | 4.89 | 20.45 | 1.58 | 2.38 | 5.46 | 17.40 | 1.70 | 1.39 | 6.99 | 7.36 | 1.30 |
| VSA-SM [47] | | 2.22 | 8.86 | 16.83 | - | 3.20 | 6.23 | 24.61 | - | 2.46 | 7.00 | 20.23 | - | 1.55 | 6.63 | 10.67 | - |
| Ours | 15.12 | 1.78 | 6.44 | 11.24 | 1.79 | 3.08 | 3.87 | 20.76 | 1.92 | 1.90 | 4.11 | 12.62 | 2.06 | 1.26 | 5.69 | 6.61 | 1.56 |
+
+| Type | Method | thun_01_b | zurich_city_12_a | zurich_city_14_c | zurich_city_15_a |
| EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ |
| SL | E-RAFT [13] | 0.58 | 8.41 | 1.52 | 1.18 | 0.61 | 23.16 | 1.06 | 1.12 | 0.71 | 10.23 | 1.91 | 1.47 | 0.59 | 8.88 | 1.30 | 1.34 |
| IDNet [45] | 0.55 | 2.07 | 1.35 | - | 0.60 | 4.56 | 1.16 | - | 0.76 | 3.74 | 2.74 | - | 0.55 | 2.55 | 1.02 | - |
| MB/USL | RTEF [3] | 3.91 | - | 34.69 | 2.48 | 3.14 | - | 34.08 | 1.42 | 4.00 | - | 45.67 | 2.67 | 3.78 | - | 37.99 | 2.82 |
| MultiCM [37] | 2.48 | 12.05 | 23.56 | 1.24 | 3.86 | 28.61 | 43.96 | 1.14 | 2.72 | 12.62 | 30.53 | 1.50 | 2.35 | 11.82 | 20.99 | 1.41 |
| BTEB [28] | 3.04 | - | 25.41 | 1.33 | 2.62 | - | 25.80 | 1.03 | 3.36 | - | 36.34 | 1.24 | 2.97 | - | 25.53 | 1.33 |
| Paredes et al. [29] | 1.66 | 8.41 | 9.34 | - | 2.72 | 23.16 | 26.65 | - | 2.64 | 10.23 | 23.01 | - | 1.69 | 8.88 | 9.98 | - |
| EV-FlowNet [52] | 3.04 | - | 25.41 | 1.33 | 2.62 | - | 25.80 | 1.03 | 3.36 | - | 36.34 | 1.24 | 2.97 | - | 25.53 | 1.33 |
| MotionPriorCM [16] | 1.54 | 6.55 | 9.69 | 1.33 | 8.33 | 20.16 | 22.39 | 1.13 | 1.78 | 8.79 | 12.99 | 1.56 | 1.45 | 6.27 | 8.34 | 1.51 |
| VSA-SM [47] | 1.74 | 6.76 | 13.07 | - | 2.19 | 17.13 | 15.24 | - | 1.69 | 7.57 | 11.02 | - | 1.85 | 8.06 | 13.55 | - |
| Ours | 1.15 | 4.89 | 5.81 | 1.63 | 1.92 | 14.35 | 13.31 | 1.40 | 1.50 | 6.93 | 10.51 | 1.92 | 1.26 | 5.46 | 6.41 | 1.89 |
+
+Table 3. Optical flow evaluation. Results on the DSEC optical flow benchmark [13]. Bold is the best in each category, except the column of $t_{\mathrm{inf}}$ , where only the shortest $t_{\mathrm{inf}}$ is marked. Note that our model predicts both flow and intensity, while others only predicts the former.
+
+
+Figure 3. Qualitative comparisons on DSEC. From left to right: (a) input events; (b) image of warped events (IWE) with our predicted flow; (c) our predicted intensity; (d) our predicted flow; (e)-(f) two baseline methods that predict optical flow (USL and SL, respectively).
+
+method achieves great improvements of $20\%$ , $25\%$ and $26\%$ in terms of EPE, AE and $\% \text{Out}$ , respectively. Note that our method even outperforms E-RAFT (SL) in terms of AE, with a reduction of $39\%$ . RTEF directly adopts FWL as the objective function to optimize, so it has the highest FWL scores on all sequences, followed by our method in the second place. Note that a high FWL value may not always be good, as it can be indicative of event collapse [39]. In addition to the overall metrics, our method shows the best performance on all individual sequences that are recorded in various scenarios (urban and highway) and various illumination conditions (daylight and night). This demonstrates the robustness and versatility of the proposed approach.
+
+Figure 3 presents a qualitative comparison on the DSEC
+
+dataset. It is clear that the output flow maps (column d) of our method are more precise than those of the most recent USL method (MotionPriorCM, column e). Regarding scene appearance, our method not only generates sharp edge maps using the predicted flow (column b) –like flow-based methods–, but also simultaneously produces detailed intensity images (column c).
+
+Runtime. We also compare the inference time of some methods in Tab. 3 (" $t_{\mathrm{inf}}$ " column). Our method shows the best efficiency despite predicting two quantities (flow and intensity). Note that MotionPriorCM also uses a U-Net architecture, where the only difference from ours is the way of up-sampling features in the decoder (we use bilinear interpolation whereas [16] uses 2D transposed convolutions).
+
+
+Figure 4. Qualitative image-intensity comparisons on ECD, BS-ERGB, HDR and ECD-fast data. Best viewed when zoomed in.
+
+# 4.3. Evaluation of Image Intensity Reconstruction
+
+The results of the benchmarks with and without GT reference images on the BS-ERGB and HDR datasets are presented in Tab. 4. In addition, the inference times of all methods are reported in Tab. 5.
+
+Among supervised-learning (SL) approaches, ET-Net achieves the best image quality in five out of six metrics, but it is the slowest by a margin. Conversely, FireNet reports the shortest inference time, but its quality metrics are not as good as other methods.
+
+In the unsupervised-learning (USL) category, our method reports comparable results in full-reference metrics as those of BTEB [28]. However, our method significantly outperforms BTEB in all three metrics on the HDR dataset, with an improvement of around $50\%$ , where many SL methods are also surpassed. In particular, we achieve the best MANIQA value compared to all baselines. This implies that our method better unlocks the HDR properties of event cameras. In terms of inference time, our model stands in the middle of the ranking; however, our model outputs both flow and intensity, while the others only output intensity.
+
+An important remark to make is that the above metrics have limitations: as analyzed in [49], different metrics often lead to divergent conclusions, where discrepancies occur. For example, some methods achieve better MSE just by darkening the predictions (as GT images are dark). Our method reports better LPIPS, but worse MSE and SSIM values than BTEB; E2VID reports better BRISQUE than ET-Net, but it performs worse in terms of NIQE and MANIQA. The numbers do not seem to entirely reflect visual quality from a human perspective, as we present in the qualitative comparisons of Fig. 4. From the images, it is clear that
+
+| Type | Method | BS-ERGB | HDR |
| MSE↓ | SSIM↑ | LPIPS↓ | BRISQUE↓ | NIQE↓ | MANIQA↑ |
| SL | E2VID [31] | 0.14 | 0.33 | 0.56 | 12.63 | 4.27 | 0.30 |
| FireNet [35] | 0.10 | 0.34 | 0.53 | 18.57 | 3.85 | 0.30 |
| SPADE-E2VID [10] | 0.09 | 0.35 | 0.63 | 24.51 | 7.17 | 0.28 |
| ET-Net [44] | 0.07 | 0.37 | 0.44 | 19.20 | 3.45 | 0.32 |
| USL | BTEB [28] | 0.09 | 0.36 | 0.62 | 51.47 | 6.24 | 0.18 |
| Ours | 0.10 | 0.31 | 0.56 | 25.03 | 3.78 | 0.40 |
+
+Table 4. Image-intensity quality assessment. Full-reference evaluation results on the BS-ERGB [42] dataset (left), and nonreference evaluation results on the HDR [31] dataset (right). Bold is the best in each category. The between-frame event slicing is used for BS-ERGB while the fixed-duration slicing ( $\Delta t = 100\mathrm{ms}$ ) is used for HDR, where no frame is available.
+
+| Resolution | E2VID (2019) | FireNet (2020) | SPADE-E2VID (2021) | ET-Net (2021) | BTEB (2021) | Ours (2024) |
| 640 × 480 | 10.95 | 4.94 | 36.07 | 173.56 | 10.59 | 15.11 |
| 1280 × 720 | 31.04 | 14.67 | 105.87 | 1606.33 | 29.89 | 40.78 |
+
+Table 5. Runtime evaluation [ms] of event-based intensity estimation methods at VGA and HD resolutions. Note that our model infers both flow and intensity, while others only infer intensity.
+
+our approach is able to recover fine details (sharp image) of scene appearance despite the HDR illumination (selfie) and fast motion (poster fast). Figure 4 also illustrates the shortcomings of the above quantitative metrics. All images from SPADE-E2VID are visually blurred, but it reports better MSE and SSIM than FireNet and our method, whose images are markedly sharper and cleaner.
+
+# 4.4. Ablation Study
+
+We conduct an ablation study to illustrate the effects of some loss terms and the superiority of joint flow-intensity
+
+estimation over flow-only estimation. The quantitative and qualitative results are presented in Tab. 6 and Fig. 5. Please refer to the supplementary for the ablation studies on loss weights and camera contrast threshold $C$ .
+
+TC Loss. First, we disable the TC loss $(\lambda_5 = 0)$ . Although flow accuracy does not decrease dramatically (around $10\%$ ), intensity accuracy is reduced significantly (Tab. 6, 1st row). This is also revealed in Fig. 5 (column a), where texture at valid pixels is recovered, while invalid pixels are filled with markedly incorrect values due to the lack of constraints. This confirms our claim in Sec. 1, that better estimation for both visual quantities is achieved by leveraging their synergies.
+
+TV regularization. Next, we disable the TV regularization of both flow and intensity ( $\lambda_3 = \lambda_4 = 0$ ). Contrary to the previous test, intensity accuracy remains while flow accuracy drops considerably (Tab. 6, 2nd row). The same conclusion can be drawn from Fig. 5 (column b), where the estimated flow shows artifacts, mostly at invalid pixels. As a consequence, the output image intensity at such pixels is not as smooth as that of our main model (column c).
+
+Flow-only Estimation. Finally, we train the network to predict only optical flow ( $\lambda_{1} = \lambda_{4} = \lambda_{5} = 0$ , thus changing the number of output channels from three to two). In this case, the loss function basically reduces to the one used by recent purely CMax-based optical flow estimation methods [16, 37]. As reported in the third row of Tab. 6, the flow accuracy is slightly better than that of w/o TV reg., but still falls far behind our main model, with respective gaps of $43\%$ , $33\%$ , $53\%$ in terms of EPE, AE and %Out. This again confirms the advantages of our proposed joint estimation method over the separate ones.
+
+# 4.5. Single Network vs. Dual Network
+
+To illustrate the superiority of joint learning with a single network, we compare it to a dual network (two U-Nets, one for optical flow prediction and the other for intensity reconstruction), with configuration identical to ours (loss function, loss weights and training settings). Table 6 show that the estimation results of the dual network (4th row) are considerably worse than those of the single U-Net model (last row). Our joint learning scheme enables one single network to learn the motion and appearance, as well as their synergies, thus achieving better performance than separately.
+
+# 5. Limitations
+
+The event camera output depends on scene texture and camera motion. In regions where no events are produced, it is thus difficult to recover motion parameters and/or scene appearance. In this case, regularization is used to fill in those pixels by encouraging spatial smoothness. However, this may cause inaccuracies. This issue could be overcome by combining two visual modalities (events and frames),
+
+
+(a) w/o TC loss
+
+
+(b) w/o TV reg.
+
+
+(c) Ours
+Figure 5. Qualitative results of ablation study. The above are results from the thun_01_b sequence of DSEC. The reference optical flow is generated using E-RAFT [13].
+
+
+(d) References
+
+| Ablation | Flow | Intensity |
| EPE↓ | AE↓ | %Out↓ | MSE↓ | SSIM↑ | LPIPS↓ |
| w/o TC loss | 2.01 | 7.92 | 13.96 | 0.16 | 0.23 | 0.64 |
| w/o TV reg. | 3.30 | 14.93 | 24.95 | 0.10 | 0.30 | 0.55 |
| Flow-only | 3.13 | 9.61 | 23.56 | - | - | - |
| Dual network | 3.30 | 10.15 | 22.85 | 0.11 | 0.29 | 0.59 |
| Ours | 1.78 | 6.44 | 11.24 | 0.10 | 0.31 | 0.56 |
+
+Table 6. Quantitative results of an ablation study. Flow evaluation is performed on the DSEC dataset and intensity evaluation is done on the BS-ERGB dataset.
+
+not without considering data fusion challenges, and/or by adding recurrent connections (at the expense of increasing the initialization time and inertia of the system [31]).
+
+Events triggered by flickering lights or hot pixels do not satisfy the brightness constancy assumption, which is the basis of all involved MB/USL methods. As outliers, they can undermine estimation accuracy. Learning-based methods have some capacity to deal with such outliers. However outliers would be more sensibly treated in pre-processing by some denoising method, or more recently, jointly [40].
+
+# 6. Conclusion
+
+We have presented the first unsupervised joint learning framework for optical flow and image intensity estimation with event cameras. This enabled us to train a single and lightweight network for predicting both visual quantities simultaneously, exploiting their synergies. It is designed to match the natural sensing principle of event cameras, that is, that motion and appearance are intertwined and, therefore, shall be jointly estimated. A comprehensive and well-behaved loss function is proposed by combining the event generation model, photometric consistency, event alignment and regularization. The experiments demonstrate that our method is accurate and efficient: (i) it achieves the highest accuracy among MB/USL optical flow methods; (ii) it shows competitive intensity quality, especially in HDR conditions; and (iii) it reports very short inference time while predicting both flow and image intensity.
+
+# Acknowledgments
+
+Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC 2002/1 "Science of Intelligence" - project number 390523135.
+
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+[44] Wenming Weng, Yueyi Zhang, and Zhiwei Xiong. Event-based video reconstruction using transformer. In Int. Conf. Comput. Vis. (ICCV), pages 2543-2552, 2021.
+[45] Yilun Wu, Federico Paredes-Valles, and Guido C. H. E. de Croon. Lightweight event-based optical flow estimation via iterative deblurring. In IEEE Int. Conf. Robot. Autom. (ICRA), pages 14708-14715, 2024.
+[46] Sidi Yang, Tianhe Wu, Shuwei Shi, Shanshan Lao, Yuan Gong, Mingdeng Cao, Jiahao Wang, and Yujiu Yang. MANIQA: Multi-dimension attention network for no-reference image quality assessment. In IEEE Conf. Comput. Vis. Pattern Recog. Workshops (CVPRW), pages 1191-1200, 2022.
+[47] Hongzhi You, Yijun Cao, Wei Yuan, Fanjun Wang, Ning Qiao, and Yongjie Li. Vector-symbolic architecture for event-based optical flow. arXiv e-prints, 2024.
+[48] Richard Zhang, Phillip Isola, Alexei A. Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), 2018.
+[49] Zelin Zhang, Anthony Yezzi, and Guillermo Gallego. Formulating event-based image reconstruction as a linear inverse problem with deep regularization using optical flow. IEEE Trans. Pattern Anal. Mach. Intell., 45(7):8372-8389, 2023.
+[50] Xu Zheng, Yexin Liu, Yunfan Lu, Tongyan Hua, Tianbo Pan, Weiming Zhang, Dacheng Tao, and Lin Wang. Deep learning for event-based vision: A comprehensive survey and benchmarks. arXiv e-prints, 2023.
+[51] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. EV-FlowNet: Self-supervised optical flow estimation for event-based cameras. In Robotics: Science and Systems (RSS), pages 1–9, 2018.
+[52] Alex Zihao Zhu, Liangzhe Yuan, Kenneth Chaney, and Kostas Daniilidis. Unsupervised event-based learning of optical flow, depth, and egomotion. In IEEE Conf. Comput. Vis. Pattern Recog. (CVPR), pages 989-997, 2019.
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| IVM [5] | 2011 | MB | 3 | ✓ | “Consistency” of the data (Max. Likelihood) |
| SOFIE [1] | 2016 | MB | 6 | ✓ | Pixel-wise brightness change + TC |
| E-cGAN [25] | 2021 | SL | 6 | ✗ | Supervised: Error w.r.t. ground truth |
| BTEB [28] | 2021 | USL | 6 | ✗ | FlowNet: IWE sharpness; ReconNet: LEGM |
| Ours | 2025 | USL | 6 | ✓ | CMax + PhE of Flow and Intensity + TC |
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+ "content": " magnitude of the gradient to quantify the CMax loss:"
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+ "content": "\\mathcal {L} _ {\\mathrm {C M a x}} (F) \\doteq 1 / \\left(\\frac {1}{| \\Omega |} \\int_ {\\Omega} \\| \\nabla \\mathrm {I W E} (\\mathbf {x}) \\| _ {1} d \\mathbf {x}\\right). \\tag {7}",
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+ "content": "Datasets. Table 2 summarizes the datasets used in our experiments. The ECD dataset [26] is collected with a handheld DAVIS240C camera in indoor scenarios, where the motion speed varies from slow to fast. The DSEC dataset [13] features urban and highway driving scenarios in daylight and night. It is recorded with an on-board Prophesee Gen3 camera, and the GT optical flow is computed from the LiDAR disparity data. The HDR dataset [31] contains event data captured in HDR illumination conditions, such as the Sun and a car driving out of a tunnel. It highlights the HDR property of event cameras. The BS-ERGB dataset [42] provides high-resolution event data recorded by a handheld co-capture system composed of a Prophesee Gen4 camera (1 megapixel) and a FLIR RGB camera, in complex outdoor scenes. The high quality of the GT frames makes them suitable for the evaluation of event-based intensity reconstruction. For intensity evaluation, we use the EVREAL tool [6], and adopt its sequence selection. The sole change made is the removal of the last seconds of the may29_rooftop sequences from the evaluation, where the camera does not move and event data consists of pure noise."
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+ "content": " (the percentage of flow estimates whose EPE "
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+ "content": "). We also report the flow warp loss (FWL) proposed in [41]. For image intensity, we report full-reference metrics when GT images are available (e.g., BS-ERGB dataset): mean square error (MSE), structure similarity index (SSIM) [43]"
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+ "html": "| Dataset | Camera | Pixels | Scenarios & Features |
| ECD [26] | DAVIS240C | 240 × 180 | Indoor handheld, varying speed |
| DSEC [12] | Prophesee Gen3 | 640 × 480 | Outdoor driving, daylight & night |
| HDR [31] | Samsung DVS Gen3 | 640 × 480 | Indoor & outdoor, handheld & driving, HDR |
| BS-ERGB [42] | PSEE Gen4 & FLIR | 970 × 625 | Outdoor handheld motion, HDR |
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+ "content": "Table 2. Configurations of the datasets used in the experiments. The BS-ERGB data is cropped; its resolution is a bit smaller than the event camera resolution."
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+ "content": "and perceptual similarity (LPIPS) [48]. Otherwise, we use no-reference metrics: BRISQUE [23], NIQE [24], MANIQA [46] (e.g., HDR dataset)."
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+ "content": " is set to 0.2. We adopt the classical U-Net architecture [32], which has 15 input channels (number of time bins in the event voxel grid [52]) and three output channels (first two: optical flow, third one: intensity)."
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| EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ |
| SL | E-RAFT [13] | 46.33 | 0.79 | 10.56 | 2.68 | 1.29 | 1.39 | 6.22 | 6.19 | 1.32 | 0.90 | 6.88 | 3.91 | 1.42 | 0.65 | 9.75 | 1.87 | 1.20 |
| IDNet [45] | | 0.72 | 2.72 | 2.04 | - | 1.25 | 2.11 | 4.35 | - | 0.77 | 2.25 | 2.60 | - | 0.57 | 2.66 | 1.47 | - |
| MB/USL | RTEF [3] | | 4.88 | - | 41.95 | 2.51 | 8.59 | - | 59.84 | 2.89 | 5.94 | - | 47.33 | 2.92 | 3.01 | - | 29.70 | 2.39 |
| MultiCM [37] | \\(9.9 \\cdot 10^3\\) | 3.47 | 13.98 | 30.86 | 1.37 | 5.74 | 9.19 | 38.93 | 1.50 | 3.74 | 9.77 | 31.37 | 1.51 | 2.12 | 11.06 | 17.68 | 1.24 |
| BTEB [28] | | 3.86 | - | 31.45 | 1.30 | 6.32 | - | 47.95 | 1.46 | 4.91 | - | 36.07 | 1.42 | 2.33 | - | 20.92 | 1.32 |
| Paredes et al. [29] | 40.1 | 2.33 | 10.56 | 17.77 | - | 3.34 | 6.22 | 25.72 | - | 2.49 | 6.88 | 19.15 | - | 1.73 | 9.75 | 10.39 | - |
| EV-FlowNet [52] | | 3.86 | - | 31.45 | 1.30 | 6.32 | - | 47.95 | 1.46 | 4.91 | - | 36.07 | 1.42 | 2.33 | - | 20.92 | 1.32 |
| MotionPriorCM [16] | 17.86 | 3.20 | 8.53 | 15.21 | 1.46 | 3.21 | 4.89 | 20.45 | 1.58 | 2.38 | 5.46 | 17.40 | 1.70 | 1.39 | 6.99 | 7.36 | 1.30 |
| VSA-SM [47] | | 2.22 | 8.86 | 16.83 | - | 3.20 | 6.23 | 24.61 | - | 2.46 | 7.00 | 20.23 | - | 1.55 | 6.63 | 10.67 | - |
| Ours | 15.12 | 1.78 | 6.44 | 11.24 | 1.79 | 3.08 | 3.87 | 20.76 | 1.92 | 1.90 | 4.11 | 12.62 | 2.06 | 1.26 | 5.69 | 6.61 | 1.56 |
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| EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ | EPE ↓ | AE ↓ | %Out ↓ | FWL ↑ |
| SL | E-RAFT [13] | 0.58 | 8.41 | 1.52 | 1.18 | 0.61 | 23.16 | 1.06 | 1.12 | 0.71 | 10.23 | 1.91 | 1.47 | 0.59 | 8.88 | 1.30 | 1.34 |
| IDNet [45] | 0.55 | 2.07 | 1.35 | - | 0.60 | 4.56 | 1.16 | - | 0.76 | 3.74 | 2.74 | - | 0.55 | 2.55 | 1.02 | - |
| MB/USL | RTEF [3] | 3.91 | - | 34.69 | 2.48 | 3.14 | - | 34.08 | 1.42 | 4.00 | - | 45.67 | 2.67 | 3.78 | - | 37.99 | 2.82 |
| MultiCM [37] | 2.48 | 12.05 | 23.56 | 1.24 | 3.86 | 28.61 | 43.96 | 1.14 | 2.72 | 12.62 | 30.53 | 1.50 | 2.35 | 11.82 | 20.99 | 1.41 |
| BTEB [28] | 3.04 | - | 25.41 | 1.33 | 2.62 | - | 25.80 | 1.03 | 3.36 | - | 36.34 | 1.24 | 2.97 | - | 25.53 | 1.33 |
| Paredes et al. [29] | 1.66 | 8.41 | 9.34 | - | 2.72 | 23.16 | 26.65 | - | 2.64 | 10.23 | 23.01 | - | 1.69 | 8.88 | 9.98 | - |
| EV-FlowNet [52] | 3.04 | - | 25.41 | 1.33 | 2.62 | - | 25.80 | 1.03 | 3.36 | - | 36.34 | 1.24 | 2.97 | - | 25.53 | 1.33 |
| MotionPriorCM [16] | 1.54 | 6.55 | 9.69 | 1.33 | 8.33 | 20.16 | 22.39 | 1.13 | 1.78 | 8.79 | 12.99 | 1.56 | 1.45 | 6.27 | 8.34 | 1.51 |
| VSA-SM [47] | 1.74 | 6.76 | 13.07 | - | 2.19 | 17.13 | 15.24 | - | 1.69 | 7.57 | 11.02 | - | 1.85 | 8.06 | 13.55 | - |
| Ours | 1.15 | 4.89 | 5.81 | 1.63 | 1.92 | 14.35 | 13.31 | 1.40 | 1.50 | 6.93 | 10.51 | 1.92 | 1.26 | 5.46 | 6.41 | 1.89 |
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| SL | E2VID [31] | 0.14 | 0.33 | 0.56 | 12.63 | 4.27 | 0.30 |
| FireNet [35] | 0.10 | 0.34 | 0.53 | 18.57 | 3.85 | 0.30 |
| SPADE-E2VID [10] | 0.09 | 0.35 | 0.63 | 24.51 | 7.17 | 0.28 |
| ET-Net [44] | 0.07 | 0.37 | 0.44 | 19.20 | 3.45 | 0.32 |
| USL | BTEB [28] | 0.09 | 0.36 | 0.62 | 51.47 | 6.24 | 0.18 |
| Ours | 0.10 | 0.31 | 0.56 | 25.03 | 3.78 | 0.40 |
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| 640 × 480 | 10.95 | 4.94 | 36.07 | 173.56 | 10.59 | 15.11 |
| 1280 × 720 | 31.04 | 14.67 | 105.87 | 1606.33 | 29.89 | 40.78 |
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| EPE↓ | AE↓ | %Out↓ | MSE↓ | SSIM↑ | LPIPS↓ |
| w/o TC loss | 2.01 | 7.92 | 13.96 | 0.16 | 0.23 | 0.64 |
| w/o TV reg. | 3.30 | 14.93 | 24.95 | 0.10 | 0.30 | 0.55 |
| Flow-only | 3.13 | 9.61 | 23.56 | - | - | - |
| Dual network | 3.30 | 10.15 | 22.85 | 0.11 | 0.29 | 0.59 |
| Ours | 1.78 | 6.44 | 11.24 | 0.10 | 0.31 | 0.56 |
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+ "text": "Unsupervised Part Discovery via Descriptor-Based Masked Image Restoration with Optimized Constraints",
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+ "text": "Jiahao Xia $^{1}$ , Yike Wu $^{1}$ , Wenjian Huang $^{2}$ , Jianguo Zhang $^{2}$ , Jian Zhang $^{*,1}$",
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+ "text": "$^{1}$ Faculty of Engineering and IT, University of Technology Sydney",
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+ "text": "$^{2}$ Dept. of Comp. Sci. and Eng., Southern University of Science and Technology",
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+ "text": "Jiahao.Xia-1@uts.edu.au, Yike.Wu@student.uts.edu.au, {huangwj, zhangjg} $@$ sustech.edu.cn, Jian.Zhang@uts.edu.au",
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+ "type": "text",
+ "text": "Abstract",
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+ "text": "Part-level features are crucial for image understanding, but few studies focus on them because of the lack of fine-grained labels. Although unsupervised part discovery can eliminate the reliance on labels, most of them cannot maintain robustness across various categories and scenarios, which restricts their application range. To overcome this limitation, we present a more effective paradigm for unsupervised part discovery, named Masked Part Autoencoder (MPAE). It first learns part descriptors as well as a feature map from the inputs and produces patch features from a masked version of the original images. Then, the masked regions are filled with the learned part descriptors based on the similarity between the local features and descriptors. By restoring these masked patches using the part descriptors, they become better aligned with their part shapes, guided by appearance features from unmasked patches. Finally, MPAE robustly discovers meaningful parts that closely match the actual object shapes, even in complex scenarios. Moreover, several looser yet more effective constraints are proposed to enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner. This provides the foundation for addressing challenges posed by occlusion and for exploring part similarity across multiple categories. Extensive experiments demonstrate that our method robustly discovers meaningful parts across various categories and scenarios. The code is available at the project website1.",
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+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "Decomposing objects into meaningful parts drives models to gain better image understanding and further improves the performance of downstream tasks, such as person search [27], fine-grained classification [2, 35] and be",
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+ "img_path": "images/6280ebeb19be833a04d3589e8373f123da71938dceaf40250c9439d057653ec0.jpg",
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+ "Figure 1. MPAE uses similarity maps between local image features and part descriptors to assign these descriptors to fill masked regions in a randomly masked version of the inputs. The restoration implicitly clusters the features of the restored patches that share similar appearance, further aligning low-level appearance in unmasked patches and high-level semantics of part descriptors. This drives similarity maps to closely match the actual part shapes."
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+ "type": "text",
+ "text": "havior analysis [25]. But the high cost of part-level label results in a scarcity of training samples. Consequently, part-level feature learning has received much less attention compared to instance-level feature learning.",
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+ "text": "To eliminate the reliance on part-level labels, existing methods achieve part discovery mainly through two strategies: reconstruction [12, 19, 21, 23, 32, 40, 41, 43] and clustering [4, 6]. By directly reconstructing the input images using learned part descriptors, the descriptors are expected to align with the part shapes, allowing these part descriptors to further predict part masks. However, to discover meaningful parts, these descriptors are designed to learn high-level semantics rather than low-level appearance [1], which prevents such reconstruction and alignment, especially in complex scenarios. Clustering-based methods use foreground masks to remove irrelevant regions and directly cluster foreground features, regardless of their actual appearance similarity. Some near-outlier features are identified as separate parts, leading to the discovery of unreasonable parts.",
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+ "type": "text",
+ "text": "To address these limitations and extend unsupervised",
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+ "type": "header",
+ "text": "CVF",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "*Corresponding Author",
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+ "type": "page_footnote",
+ "text": "1https://github.com/Jiahao-UTS/MPAE",
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+ "type": "page_number",
+ "text": "8668",
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+ "text": "part discovery to more complex scenarios, we propose a novel paradigm, named Mask Part Autoencoder (MPAE). As shown in Fig. 1, instead of directly using part descriptors for image reconstruction, we first calculate the similarities between these descriptors and a feature map learned from the input. Based on the similarity maps, we assign these descriptors to fill the masked regions in a randomly masked version of inputs. By utilizing both filled part descriptors and unmasked patch features within the same part regions to generate image patches with similar appearances, these features are implicitly clustered together [42]. The appearance features of unmasked patches (e.g., boundaries and textures) further align the high-level semantics of the part descriptors with the part shapes. Guided by part appearance, the similarity maps closely match the shapes of corresponding parts even in complex scenarios. Thus, they can be viewed as pixel-level masks of the discovered parts.",
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+ "text": "Moreover, without using category labels, it is difficult for unsupervised methods to determine which object parts are present or absent in an image, because different categories consist of different types of parts. As a result, most existing methods [12, 19, 23, 41] are restricted to a single category and do not consider the absence of individual parts. However, it is still impossible for all parts to appear in every image, even within a single category, because objects can be occluded. Although [40] achieves part discovery on a dataset with multiple categories, it still relies on category labels to determine which parts appear before part discovery. Therefore, we propose a looser constraints to enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner. Additionally, a more effective constraint is proposed to ensure that the MPAE discovers part-level masks, as the model can easily degrade to predicting only a single instance-level mask when part absence is allowed. This provides a foundation for tackling challenges posed by occlusion. As a result, these optimized constraints allow MPAE to leverage similar parts across different categories to achieve more robust part discovery without relying on any labels.",
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+ "text": "To evaluate the effectiveness of MPAE and our optimized constraints, extensive experiments are conducted on four widely used benchmarks, including two with multiple categories and two with a single category. The experimental results clearly demonstrate that MPAE robustly discovers meaningful object parts across diverse categories and achieves more competitive performance on all datasets than other state-of-the-art methods.",
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+ "text": "The main contributions of this paper can be summarized as followings:",
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+ "type": "text",
+ "text": "- We present a novel paradigm named Masked Part Autoencoder (MPAE), which utilizes low-level appearance features of the unmasked patches to align the part descriptors with actual part shapes. Consequently, MPAE discovers",
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+ "text": "meaningful parts that closely match the object shapes.",
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+ "- Several looser yet effective constraints are proposed to enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner. As a result, MPAE can leverage similar parts across various categories to achieve more robust part discovery.",
+ "- Extensive experiments are carried out on four widely-used benchmarks. The results show that our method can robustly discover reasonable object parts in complex scenarios and achieve highly competitive performance."
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+ "type": "text",
+ "text": "2. Related works",
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+ "type": "text",
+ "text": "2.1. Unsupervised / Self-supervised Learning",
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+ "text": "Many works in natural language processing (NLP) [10, 28] show unsupervised / self-supervised learning learns more effective features for downstream tasks than supervised learning. Inspired by their success, recent works [4, 5, 8, 13, 14, 17, 18, 26, 30, 45] also adopt unsupervised / self-supervised learning to improve the effectiveness of visual features. In addition to performance improvements, some new properties also emerge in Vision Transformer (ViT) [11] with the use of unsupervised / self-supervised learning. Caron et al. [4] found using momentum encoder [16] and multi-crop augmentation [3] drives the ViT features from the same category to have high similarity. Based on this properties, Wang et al. [39] and Wang et al. [37, 38] achieve foreground segmentation, instance segmentation, and video instance segmentation, respectively, in an unsupervised manner by using normalized cut [31] to directly group self-similar regions. Although learned ViT features within the same part exhibit higher similarity [30, 45], discovering object parts from images is still much more challenging than discovering instances. The main reason is that features from different parts also have very high similarity, resulting in less consistent semantics and boundaries in the discovered parts. Unfortunately, there are relatively few works that focus on using unsupervised / self-supervised features to discover meaningful and consistent object parts.",
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+ "type": "text",
+ "text": "2.2. Part Discovery",
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+ "text": "Part discovery aims to identify meaningful object parts with consistent semantics and predict their pixel-level masks. Existing works mainly achieve part discovery through weakly-supervised or unsupervised learning. Weakly-supervised part discovery utilizes instance-level labels, such as category [2, 20, 35] and identity [27, 44], to discover relevant parts with pixel-level masks during training. Then, part-level features are extracted using these masks and further boost the performance of downstream tasks. Nevertheless, without aligning their the semantics from part embeddings with actual object appearances through reconstruction, their part masks do not follow the actual object bound",
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+ "type": "page_number",
+ "text": "8669",
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+ "type": "text",
+ "text": "aries well, making them insufficiently fine-grained.",
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+ "text": "Unsupervised part discovery is more challenging than weakly-supervised part discovery because no labels are provided during training. Early works discover meaningful object parts with rough part masks by factorizing deep features [7] or spatial embeddings [34]. Other methods [1, 6] directly cluster the foreground features across all images to discover meaningful parts. Nevertheless, the semantics and boundaries of the predicted part masks are not sufficiently stable due to appearance biases in each image. Most state-of-the-art methods [12, 21, 23, 32, 40, 41, 43] employ image reconstruction as a learning objective to align the part descriptors with the actual part shapes. Therefore, these part descriptors can further predict the part masks with consistent semantics. However, these descriptors are designed to capture high-level semantics rather than low-level appearance, which hinders reconstruction and alignment, ultimately degrading part discovery, especially in complex scenarios. Amir et al. [1] demonstrate that directly clustering self-supervised features in foreground regions can also discover meaningful parts. Nevertheless, they only consider feature similarity, disregarding actual appearance similarity. As a result, some near-outlier features are identified as independent parts, leading to unreasonably segmented parts. Therefore, robustly discovering meaningful parts in an unsupervised manner remains a significant challenge.",
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+ "type": "text",
+ "text": "3. Methodology",
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+ "text": "Unsupervised part discovery aims to learn a model that can parse all objects into a total of $K$ parts without any labels. Given an input image $\\pmb{I} \\in \\mathbb{R}^{H_{\\mathrm{I}} \\times W_{\\mathrm{I}} \\times 3}$ , the learned model predicts pixel-level mask $M_{\\mathrm{p}} \\in \\{0,1\\}^{H_{\\mathrm{I}} \\times W_{\\mathrm{I}} \\times (K + 1)}$ to assign each pixel into one of $K$ parts or background, where $(H_{\\mathrm{I}}, W_{\\mathrm{I}})$ is the size of the input image.",
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+ "text": "To achieve this goal, we present a novel paradigm, named Masked Part Autoencoder (MPAE), and further incorporate it with several optimized constraints. In what follows, we first detail the training and inference pipeline of MPAE, followed by an introduction to our optimized constraints and their corresponding functions.",
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+ "text": "3.1. Masked Part Autoencoder",
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+ "text": "3.1.1. Training pipeline",
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+ "text": "The overall training pipeline of MPAE is shown in Fig. 2. It consists of four blocks: (a) random masking block, (b) descriptor extraction block, (c) matching block, (d) image restoration block.",
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+ "text": "Random masking block first divides the input image $\\pmb{I}$ into patches of size $p$ . The patched image $\\pmb{I}^{\\mathrm{p}}$ is denoted as $\\pmb{I}^{\\mathrm{p}} \\in \\mathbb{R}^{\\frac{H_{\\mathrm{I}}}{p} \\times \\frac{W_{\\mathrm{I}}}{p} \\times 3p^{2}}$ . A binary mask $M = \\{0,1\\}^{\\frac{H_{\\mathrm{I}}}{p} \\times \\frac{W_{\\mathrm{I}}}{p}}$ is then generated to randomly mask out a specified proportion $r$ of the image patches. As MAE [18], these masked",
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+ "text": "patches will not be used in the following training. Only visible patches are finally fed into the MPAE encoder to learn unmasked patch features $\\pmb{F}^{\\mathrm{U}} \\in \\mathbb{R}^{\\frac{H_{\\mathrm{I}} \\times W_{\\mathrm{I}}}{p \\times p} (1 - r) \\times C}$ , where $C$ is the dimension of the unmasked patch feature.",
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+ "text": "Descriptor extraction block is designed to learn part-level descriptors from input images. Specifically, as [40], we replace the class embedding of a classical ViT with $K + 1$ embeddings to extract $K + 1$ descriptors. By incorporating MPAE with appropriate constraints, each embedding learns to specialize in one potential part, adaptively aggregating image features to produce the corresponding part descriptor. The $K + 1$ part descriptors $D \\in \\mathbb{R}^{(K + 1)\\times C}$ include $K$ descriptors for foreground parts and 1 for the background, where the descriptor dimension $C$ is the same as that of $F^{\\mathrm{U}}$ .",
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+ "text": "To determine how to assign the sparse part descriptors $D$ to fill the masked regions, we employ a frozen pre-trained ViT, followed by a trainable $1 \\times 1$ convolutional layer, to extract a dense feature map $F \\in \\mathbb{R}^{H_{\\mathrm{F}} \\times W_{\\mathrm{F}} \\times C}$ , where $(H_{\\mathrm{F}}, W_{\\mathrm{F}})$ is the size of the feature map. By matching $F$ with $D$ , we can obtain a similarity map for each part (as detailed in the following paragraphs). Based on the similarity maps, we can fill the masked patches using $D$ . Moreover, it enables PartFormer to leverage knowledge from the ViT, pre-trained through unsupervised or self-supervised learning, to discover more reasonable object parts.",
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+ "text": "Matching block calculates similarity maps $\\pmb{P}$ between $D$ and $F$ , which can be defined as:",
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+ "text": "\n$$\nP _ {i, j, k} = \\frac {\\exp \\left(\\boldsymbol {D} _ {k} \\cdot \\boldsymbol {F} _ {i , j}\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K + 1} \\exp \\left(\\boldsymbol {D} _ {k ^ {\\prime}} \\cdot \\boldsymbol {F} _ {i , j}\\right)}, \\tag {1}\n$$\n",
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+ "text": "where $\\pmb{F}_{i,j}$ indicates the pixel-level feature at $(i,j)$ of $\\pmb{F}$ , and $D_{k}$ is the part descriptor for the $k$ -th part, with $i \\in \\{1,\\dots ,W_{\\mathrm{F}}\\}$ , $j \\in \\{1,\\dots ,H_{\\mathrm{F}}\\}$ , and $k \\in \\{1,\\dots ,K + 1\\}$ . $P_{i,j,k}$ represents the normalized similarity between the $D_{k}$ and $F_{i,j}$ . Based on the similarity map, the part descriptors are assigned to fill the masked regions and reform a dense feature map $\\pmb{R}$ , which can be formulated as:",
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+ "text": "\n$$\n\\boldsymbol {R} _ {i, j} = \\left\\{ \\begin{array}{l l} \\boldsymbol {F} _ {i, j} ^ {\\mathrm {U}} & , M _ {i, j} = 0, \\\\ \\sum_ {k = 1} ^ {K + 1} \\left(P _ {i, j, k} \\boldsymbol {D} _ {k}\\right) & , M _ {i, j} = 1, \\end{array} \\right. \\tag {2}\n$$\n",
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+ "text": "where $\\pmb{R}_{i,j}$ is the feature vector of the filled feature map $\\pmb{R}$ at position $(i,j)$ . $M_{i,j}$ is the value of the binary mask $M$ , indicating that the position $(i,j)$ is masked or not in random masking block.",
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+ "text": "Image restoration block feeds $\\pmb{R}$ into the MPAE decoder to restore the masked patches, which can be written as:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r}} = \\frac {1}{2} \\| \\boldsymbol {I} - \\boldsymbol {I} ^ {\\prime} \\| _ {1} + \\frac {1}{2} \\| \\Phi (\\boldsymbol {I}) - \\Phi (\\boldsymbol {I} ^ {\\prime}) \\| _ {1}, \\tag {3}\n$$\n",
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+ "text": "where $\\pmb{I}^{\\prime}$ is the restored image and $\\Phi$ is a frozen VGG-19 [33]. Directly using the L1 loss constraint for image",
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+ "Figure 2. Training and inference pipelines of MPAE. The training pipeline consists of four blocks: (a) random masking block, (b) descriptor extraction block, (c) matching block, and (d) image restoration block. (a) randomly masks out a large proportion of patches and extracts patch features $\\pmb{F}^{\\mathrm{U}}$ from the unmasked patches using MPAE encoder. The input image $\\pmb{I}$ is also fed into (b), after being patchified, to extract part descriptors $\\pmb{D}$ and a feature map $\\pmb{F}$ . By matching $\\pmb{D}$ with $\\pmb{F}$ using Hadamard product and a Softmax function, we generate a similarity map for each descriptor in (c). Based on these similarity maps $\\pmb{P}$ , we use $\\pmb{D}$ to fill the masked regions and reconstruct a feature map $\\pmb{R}$ . In (d), $\\pmb{R}$ is further utilizes for image restoration, aligning the high-level semantics of the $\\pmb{D}$ with the corresponding part shapes. The inference pipeline directly employs $\\pmb{D}$ as mask prototypes to predict part-level masks from the Interpolated feature map $\\pmb{F}'$ ."
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+ "text": "restoration, as in [18], can lead to structure deviations between the raw and restored images [18], which in turn causes the features in different parts to be poorly clustered, regardless of their actual appearance similarity. Therefore, in addition to using the L1 loss, we employ VGG-19 to encourage greater structural similarity between the restored image and the input image as the perceptual loss [22].",
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+ "text": "The functions of this image restoration are threefold: 1) It retains low-level appearance features in MPAE through the unmasked patch features $F^{\\mathrm{U}}$ , thereby compensating for the lack of low-level appearance features in the part descriptors $D$ . 2) It implicitly clusters $F^{\\mathrm{U}}$ and $D$ within the same part region together in latent space by utilizing them to produce the image patches with similar appearance. Guided by low-level appearance features from $F^{\\mathrm{U}}$ , the high-level semantics from $D$ are aligned more accurately with the actual part shapes compared to directly using $D$ from image reconstruction. 3) This alignment further constrains the similarity maps $P$ , encouraging them to more closely match the actual shapes of their corresponding parts, even in highly complex scenarios. Consequently, $P$ can serve as pixel-level masks for the discovered parts.",
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+ "type": "text",
+ "text": "3.2. Learning Constraints",
+ "text_level": 1,
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+ "type": "text",
+ "text": "To ensure robust part discovery, we incorporate MPAE with three types of optimized constraints: the presence constraint $\\mathcal{L}_{\\mathrm{p}}$ , the semantic consistency constraint $\\mathcal{L}_{\\mathrm{s}}$ , and the distribution constraint $\\mathcal{L}_{\\mathrm{d}}$ .",
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+ "type": "text",
+ "text": "Presence constraint $\\mathcal{L}_{\\mathrm{p}} = \\mathcal{L}_{\\mathrm{f}} + \\mathcal{L}_{\\mathrm{b}}$ where $\\mathcal{L}_{\\mathrm{f}}$ and $\\mathcal{L}_{\\mathrm{b}}$",
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+ "type": "text",
+ "text": "represent the foreground and background presence losses respectively. $\\mathcal{L}_{\\mathrm{p}}$ is directly applied to $P$ to ensure the presence of $K$ foreground parts across the entire data and the presence of background in every image.",
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+ "type": "text",
+ "text": "$\\mathcal{L}_{\\mathrm{f}}$ divides each mini-batch into $N_{\\mathrm{g}}$ mini-groups with $G$ samples. Then, $\\mathcal{L}_{\\mathrm{f}}$ can be calculated as:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {f}} = \\frac {1}{N _ {\\mathrm {g}}} \\sum_ {n _ {\\mathrm {g}} = 1} ^ {N _ {\\mathrm {g}}} (2 - \\frac {1}{G} \\sum_ {g = 1} ^ {G} \\max _ {i, j, k} P _ {i, j, k} ^ {g, n _ {\\mathrm {g}}} - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\max _ {i, j, g} P _ {i, j, k} ^ {g, n _ {\\mathrm {g}}}), \\tag {4}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "where $P_{i,j,k}^{g,n_{\\mathrm{g}}}$ is the similarity $P_{i,j,k}$ of $g$ -th sample in $n_{\\mathrm{g}}$ -th mini-group. Instead of requiring all parts to appear in each image as previous unsupervised methods, $\\mathcal{L}_{\\mathrm{f}}$ only encourages them to appear at least once in each mini-group and each image to contain at least one part. This looser constraint provides the basis for MPAE to identify the presence of parts across various scenarios and categories. The influence of the mini-group will be discussed in the Appendix.",
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+ "type": "text",
+ "text": "$\\mathcal{L}_{\\mathrm{b}}$ encourages the background to appear near the boundaries of each image. Inspired by [2], we define $\\mathcal{L}_{\\mathrm{b}}$ as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {b}} = - \\frac {1}{N _ {\\mathrm {g}} G} \\sum_ {n _ {\\mathrm {g}} = 1} ^ {N _ {\\mathrm {g}}} \\sum_ {g = 1} ^ {G} \\log \\left(\\max _ {i, j} d _ {i, j} P _ {i, j, K + 1} ^ {g, n _ {\\mathrm {g}}}\\right), \\tag {5}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where $d_{i,j}$ is the distance from position $(i,j)$ to the image center. $d_{i,j}$ can be calculated as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nd _ {i, j} = 2 \\left(\\frac {i - 1}{W _ {\\mathrm {F}} - 1} - \\frac {1}{2}\\right) ^ {2} + 2 \\left(\\frac {j - 1}{H _ {\\mathrm {F}} - 1} - \\frac {1}{2}\\right) ^ {2}. \\tag {6}\n$$\n",
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+ "page_idx": 3
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+ {
+ "type": "page_number",
+ "text": "8671",
+ "bbox": [
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+ "type": "text",
+ "text": "Incorporated with $\\mathcal{L}_{\\mathrm{f}}$ and $\\mathcal{L}_{\\mathrm{b}}$ , our model also learns to distinguish the $K$ foreground parts and the background region.",
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+ {
+ "type": "text",
+ "text": "Semantic constraint $\\mathcal{L}_{\\mathrm{s}}$ : because $\\mathcal{L}_{\\mathrm{p}}$ only requires each image to contain at least one part, the model tends to simply segment out the entire foreground object, thereby degrading into an instance-discovery model. By encouraging each part descriptor to align only with the local features that exhibit very high similarity, $\\mathcal{L}_{\\mathrm{s}}$ ensures that the model decomposes the target into multiple object parts with consistent semantics. $\\mathcal{L}_{\\mathrm{s}}$ can be formulated as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s}} = - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\log \\frac {M ^ {k} e ^ {s \\left(\\cos \\left(\\theta_ {(k , k)} + m\\right)\\right)}}{M ^ {k} e ^ {s \\left(\\cos \\left(\\theta_ {(k , k)} + m\\right)\\right)} + \\sum_ {t = 1 , t \\neq k} ^ {K} M ^ {t} e ^ {s \\cos \\theta_ {(t , k)}}}, \\tag {7}\n$$\n",
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+ },
+ {
+ "type": "text",
+ "text": "where $M_{k}\\in \\{0,1\\}$ represents the presence of the $k$ -th part. When $\\sum_{i = 1}^{W_{\\mathrm{F}}}\\sum_{j = 1}^{H_{\\mathrm{F}}}P_{i,j,k} < = 0.001,M_{k} = 0$ , else, $M_{k} = 1$ . $m$ and $s$ are two hyperparameters. $\\theta_{(k,t)}$ is the angle between the $k$ -the part descriptor $D_{k}$ and the mean feature vector of $t$ -th part region $\\bar{F}_t$ in latent space. $\\bar{F}_t$ and $\\cos (\\theta_{(k,t)})$ are defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\bar {\\boldsymbol {F}} _ {t} = \\frac {\\sum_ {i = 1} ^ {W _ {1}} \\sum_ {j = 1} ^ {H _ {1}} P _ {i , j , t} \\boldsymbol {F} _ {i , j}}{\\sum_ {i = 1} ^ {W _ {1}} \\sum_ {j = 1} ^ {H _ {1}} P _ {i , j , t}}, \\tag {8}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\cos \\left(\\theta_ {(t, k)}\\right) = \\frac {\\boldsymbol {D} _ {k} \\cdot \\bar {\\boldsymbol {F}} _ {t}}{\\| \\boldsymbol {D} _ {k} \\| \\| \\bar {\\boldsymbol {F}} _ {t} \\|.} \\tag {9}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "As [9], $m$ enables $\\mathcal{L}_s$ to still have a certain gradient value for further maximizing $\\cos(\\theta_{(k,k)})$ when $\\theta_{(k,k)}$ is very small, and $s$ controls the smoothness of $\\mathcal{L}_s$ . By minimizing $\\theta_{(k,k)}$ and maximizing $\\theta_{(t,k)}$ , the discovered parts across different objects have more consistent semantics. Moreover, the use of $M^k$ enables $\\mathcal{L}_s$ to only consider the semantic consistency of those appeared parts, providing the basis to constrain the semantic consistency across multiple categories.",
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+ "type": "text",
+ "text": "Distribution constraint $\\mathcal{L}_{\\mathrm{d}} = \\mathcal{L}_{\\mathrm{v}} + \\mathcal{L}_{\\mathrm{e}}$ , where $\\mathcal{L}_{\\mathrm{v}}$ and $\\mathcal{L}_{\\mathrm{e}}$ are total variation loss [29] and entropy loss respectively. $\\mathcal{L}_{\\mathrm{d}}$ encourages the predicted probability map $P$ to better follow the shapes of object parts.",
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+ {
+ "type": "text",
+ "text": "$\\mathcal{L}_{\\mathrm{v}}$ minimizes the spatial gradient of the predicted $P$ which can be formulated as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {v}} = \\frac {1}{H _ {\\mathrm {F}} W _ {\\mathrm {F}}} \\sum_ {k = 1} ^ {K + 1} \\sum_ {i = 1} ^ {W _ {\\mathrm {F}}} \\sum_ {j = 1} ^ {H _ {\\mathrm {F}}} | \\nabla P _ {i, j, k} |, \\tag {10}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "where $\\nabla P_{i,j,k}$ represents the spatial image gradient at position $(i,j)$ on the probability map for the $k$ -th part. The function of $\\mathcal{L}_{\\mathrm{v}}$ is the same as that of the concentration loss [21], encouraging pixels with high confidence for the same part to form a connected region. However, the concentration loss penalizes pixels that are far from the part center much more heavily than those that are close. This imbalance further causes the discovered parts to take on an approximately",
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+ {
+ "type": "text",
+ "text": "square shape. $\\mathcal{L}_{\\mathrm{v}}$ successfully eliminates this imbalance by calculating the gradient of $P$ , enabling the discovered parts to more accurately follow the shapes of objects, even when they are very complex.",
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+ {
+ "type": "text",
+ "text": "$\\mathcal{L}_{\\mathrm{e}}$ ensures that the distribution at any position on $P$ has high similarity in only one part descriptor by penalizing its entropy:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {e}} = - \\frac {1}{K + 1} \\sum_ {k = 1} ^ {K + 1} \\sum_ {i = 1} ^ {W _ {\\mathrm {F}}} \\sum_ {j = 1} ^ {H _ {\\mathrm {F}}} P _ {i, j, k} \\log \\left(P _ {i, j, k}\\right). \\tag {11}\n$$\n",
+ "text_format": "latex",
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+ {
+ "type": "text",
+ "text": "This drives the similarity map $P$ to exhibit clear and stable boundaries, resulting in more precise part discovery.",
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+ {
+ "type": "text",
+ "text": "Overall training target: by minimizing $\\mathcal{L} = \\mathcal{L}_{\\mathrm{r}} + \\lambda_{\\mathrm{p}}\\mathcal{L}_{\\mathrm{p}} + \\lambda_{\\mathrm{s}}\\mathcal{L}_{\\mathrm{s}} + \\lambda_{\\mathrm{d}}\\mathcal{L}_{\\mathrm{d}}$ , MPAE learns to discover meaningful parts in complex scenarios, where $\\lambda_{\\mathrm{p}}, \\lambda_{\\mathrm{s}}$ , and $\\lambda_{\\mathrm{d}}$ are the weights of $\\mathcal{L}_{\\mathrm{p}}, \\mathcal{L}_{\\mathrm{s}}, \\mathcal{L}_{\\mathrm{d}}$ respectively.",
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+ {
+ "type": "text",
+ "text": "3.3. Inference pipeline",
+ "text_level": 1,
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+ "type": "text",
+ "text": "The overall inference pipeline is shown on the right in Fig. 2. In this phase, we retain only PartFormer and the pretrained ViT. However, the low-resolution of $\\pmb{F}$ is insufficient to produce high-resolution part masks. Therefore, we resize $\\pmb{F}$ to match the size of the input images using bilinear interpolation. By accurately aligning with part shapes with the guide of low-level appearance features, $D$ can still accurately respond to the corresponding part regions in the $F'$ with much higher resolution. Thus, the similarity maps calculated from $D$ and $F'$ can serve as high-resolution part masks for the parts discovered in an unsupervised manner.",
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+ "type": "text",
+ "text": "4. Experimental Setup",
+ "text_level": 1,
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+ "type": "text",
+ "text": "4.1. Datasets",
+ "text_level": 1,
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+ "type": "text",
+ "text": "To comprehensively validate the effectiveness of MPAE, we evaluate it on four widely-used benchmarks: two with multiple categories (PartImageNet OOD dataset [15] and PartImageNet Segmentation dataset [15]) and two with a single category (CUB dataset [36] and CelebA dataset [24]). More details about these four datasets and the implementation of our method are provided in Appendix A.1 and Appendix A.2 respectively.",
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+ "type": "text",
+ "text": "4.2. Evaluation Metrics",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Normalized Mutual information (NMI) and Adjusted Rand Index (ARI) are primarily used to measure the similarity between two clusters. In this task, the NMI and ARI scores between the annotated and discovered parts directly reflect how closely the semantics of the discovered parts align with human conception.",
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+ "type": "text",
+ "text": "Normalized Mean Error (NME): NME is calculated using the centroids of the predicted parts and the annotated keypoints, representing the semantic consistency of the discovered parts across the entire test set.",
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+ "text": "8672",
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+ {
+ "type": "table",
+ "img_path": "images/54248e557ddb2e9ee8da0115838fc0f516703c05bcff958da4523f8798900150.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Method | Label | K | PartImage_O (%) | PartImage_S (%) |
| NMI ↑ | ARI ↑ | NMI ↑ | ARI ↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Category label | 8 | 5.88 | 1.53 | - | - |
| 25 | 7.56 | 1.25 | - | - |
| 50 | 10.19 | 1.05 | - | - |
| PDisco-Net [35] | Category label | 8 | 27.13 | 8.76 | 10.68 | 32.43 |
| 25 | 32.41 | 10.69 | 18.44 | 40.70 |
| 50 | 41.49 | 14.17 | 21.98 | 39.40 |
| PDiscoNet + ViT-B/14 | Category label | 8 | 19.28 | 34.72 | 16.68 | 32.01 |
| 25 | 28.23 | 25.93 | 46.81 | 40.70 |
| 50 | 29.48 | 28.68 | 34.13 | 39.40 |
| PDiscoFormer [2]+ frozen ViT-B/14* | Category label | 8 | 28.84 | 55.66 | - | - |
| 25 | 43.36 | 62.82 | - | - |
| 50 | 44.48 | 57.91 | - | - |
| PDiscoFormer + ViT-B/14† | Category label | 8 | 29.00 | 52.40 | 20.29 | 38.90 |
| 25 | 44.71 | 59.27 | 43.18 | 64.61 |
| 50 | 46.29 | 62.21 | 44.06 | 60.10 |
| Unsupervised part discovery |
| DINO* [1] | N/A | 8 | 19.17 | 7.59 | - | - |
| 25 | 31.46 | 14.16 | - | - |
| 50 | 37.81 | 16.50 | - | - |
| Xia et al.* [40] | N/A | 4NC | 27.85 | 40.77 | 25.17 | 37.50 |
| MPAE* (ours) | N/A | 8 | 32.90 | 66.17 | 33.51 | 65.05 |
| 25 | 39.28 | 68.87 | 37.22 | 68.04 |
| 50 | 53.65 | 74.22 | 55.10 | 73.52 |
",
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+ "type": "text",
+ "text": "Table 1. Quantitative comparisons with state-of-the-art methods on PartImageNet OOD and Segmentation datasets. $N_{\\mathrm{c}}$ represents the number of categories, which is 109 and 158 for the OOD and Segmentation datasets respectively. $\\dagger =$ using a partially fine-tuned pretrained backbone, $\\star =$ using a frozen pretrained backbone.",
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+ "type": "text",
+ "text": "4.3. Comparisons with State-of-the-art Methods",
+ "text_level": 1,
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+ "type": "text",
+ "text": "PartImageNet OOD: the quantitative results of MPAE and other state-of-the-art methods on PartImageNet OOD dataset are reported in Table 1, and some randomly chosen qualitative results are shown in Fig. 3. MPAE achieves highly competitive performance among both unsupervised and weakly-supervised methods. In the second row of Fig. 3, we observe that some small, round areas are identified as separate parts by DINO. These unreasonable parts result from directly clustering foreground features, which identifies certain near-outlier features as separate parts. By considering part appearance into clustering through our paradigm, we observe significant improvements in NMI of $71.62\\%$ , $24.86\\%$ and $41.89\\%$ compared to DINO when $K = 8, 25, 50$ respectively. Due to the complex scenarios, it is difficult to align high-level semantics from part descriptors with object shapes through reconstruction. As a result, the parts discovered by Xia et al. are often incomplete. Although PDiscoFormer and PDiscoNet employ classification loss for part discovery in a weakly supervised manner, they do not further align high-level semantics with object shapes. Consequently, their predicted masks do not match objects as closely as those predicted by MPAE. With the same backbone (frozen ViT-B/14), MPAE still outperforms them.",
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+ "type": "text",
+ "text": "PartImageNet Segmentation increases category number $N_{\\mathrm{C}}$ from 109 to 158, which means larger variance in ob",
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+ "page_idx": 5
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+ {
+ "type": "image",
+ "img_path": "images/f7c65340dd250838a42c2e5b6cc7d71b1bb8ea80e42cf92928dba47d593823d2.jpg",
+ "image_caption": [
+ "Figure 3. Some qualitative results of MPAE (ours) and other state-of-the-art unsupervised and weakly-supervised methods on PartImageNet OOD dataset ( $K = 50$ )."
+ ],
+ "image_footnote": [],
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+ {
+ "type": "text",
+ "text": "ject appearance and shape. Therefore, as shown in Table 1, the metrics in both NMI and ARI of PDiscoFormer and Xia et al. degrade slightly. However, by using image restoration to constrain the learning and by exploring part similarities across different categories, MPAE successfully maintains strong robustness on this more challenging dataset. Compared to PDiscoFormer, MPAE still achieves an impressive improvement of $65.16\\%$ and $25.06\\%$ respectively in NMI when $K = 8$ and 50, even though PDiscoFormers employ both partially fine-tuned backbone and category labels.",
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+ "type": "text",
+ "text": "CUB: MPAE also achieves highly competitive performance on CUB (Table 2 and Fig. 4), demonstrating its effectiveness in part discovery within a single category. By implicitly clustering patch features with similar appearances and allowing for the absence of specific parts, MPAE can robustly discover meaningful bird parts in cases involving shadows, self-occlusion, and reflections (see first, second and fourth columns in Fig. 4). With the same frozen pretrained ViT-B/14, MPAE outperforms PDiscoFormer in all metrics, despite not using any labels for training. Compared to PDiscoFormer with a partially fine-tuned ViT-B/14, MPAE still outperforms it by $10.45\\%$ , $7.66\\%$ and $19.22\\%$ in NME, NMI and ARI respectively when $K = 16$ . CelebA: as shown in Fig. 4, the masks predicted by MPAE accurately follow the entire facial region, resulting in significantly better qualitative results. Despite less challenging scenarios, the masks predicted by Xia et al. remain incomplete and fail to cover the entire face region. Other methods",
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+ "type": "page_number",
+ "text": "8673",
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+ "type": "image",
+ "img_path": "images/afa318bcf449966b520e3760322402fd83098c94dde1f928b6fd09203a452d16.jpg",
+ "image_caption": [
+ "Figure 4. Some visualized part discovery results of MPAE (ours) and state-of-the-art methods on CUB dataset ( $K = 16$ ) and CelebA dataset ( $K = 8$ ). We use red boxes to highlight the regions with poor part discovery results."
+ ],
+ "image_footnote": [],
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+ {
+ "type": "image",
+ "img_path": "images/330c7d9c9235c6b5b3b6e5774bb21bb6add2daa02b8ae5d833a61b7e9df68d1a.jpg",
+ "image_caption": [],
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+ "type": "table",
+ "img_path": "images/9f87c3001631b7dea29a442d21fd869761a523fe8298d77c5428764cf9d92d9b.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Method | Label | K=4 (%) | K=8 (%) | K=16 (%) |
| NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Species label | 11.51 | 29.74 | 14.04 | 11.60 | 35.72 | 15.90 | 12.60 | 43.92 | 21.01 |
| PDiscoNet [35] | Species label | 9.12 | 37.82 | 15.26 | 8.52 | 50.08 | 26.96 | 7.64 | 56.87 | 38.05 |
| Choudhury et al. [6] | Foreground mask | 9.20 | 43.50 | 19.60 | - | 51.50 | 28.30 | - | - | - |
| PDiscoNet + ViT-B/14 | Species label | 7.70 | 52.59 | 26.66 | 6.34 | 65.01 | 37.90 | 5.95 | 68.63 | 43.41 |
| PDiscoFormer + ViT-B/14* [2] | Species label | 8.19 | 52.88 | 23.22 | 6.23 | 67.59 | 41.35 | 6.44 | 69.54 | 49.99 |
| PDiscoFormer + ViT-B/14† | Species label | 7.41 | 58.13 | 25.11 | 6.54 | 69.87 | 42.76 | 5.74 | 73.38 | 55.83 |
| Unsupervised part discovery |
| DINO* [1] | N/A | - | 31.18 | 11.21 | - | 47.21 | 19.76 | - | 50.57 | 26.14 |
| Xia et al.* [40] | N/A | 9.92 | 45.22 | 19.40 | 8.58 | 52.42 | 26.42 | 8.27 | 53.52 | 33.95 |
| MPAE* (ours) | N/A | 7.75 | 58.93 | 33.73 | 5.53 | 68.24 | 45.85 | 5.14 | 79.00 | 66.56 |
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+ "img_path": "images/3533795c07fe985296cd1d3878aa2b65e7b84af33e48e3ee2b79f1e858c351a0.jpg",
+ "table_caption": [
+ "Table 2. Quantitative comparisons with state-of-the-art methods on CUB. $\\dagger=$ using partially fine-tuned backbone, ${}^{*}=$ using a frozen pretrained backbone."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | Label | K=4 (%) | K=8 (%) | K=16 (%) |
| NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Attribute label | 8.75 | 56.69 | 34.74 | 7.96 | 54.80 | 34.74 | 7.62 | 62.22 | 41.01 |
| PDiscoNet [35] | Identity label | 11.11 | 75.97 | 69.53 | 9.82 | 62.61 | 51.89 | 9.46 | 77.43 | 70.58 |
| Unsupervised part discovery |
| DINO* [1] | N/A | 11.36 | 1.38 | 0.01 | 10.74 | 1.12 | 0.01 | - | 3.29 | 0.06 |
| GANseg‡ [19] | N/A | 12.26 | 41.71 | 28.06 | 6.18 | 67.28 | 56.23 | - | - | - |
| Xia et al.* [40] | N/A | 12.28 | 50.69 | 34.57 | 10.24 | 58.35 | 46.78 | - | - | - |
| MPAE* (ours) | N/A | 11.44 | 56.13 | 37.20 | 7.55 | 59.64 | 41.72 | 7.10 | 70.21 | 60.33 |
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+ {
+ "type": "text",
+ "text": "Table 3. Quantitative comparisons with state-of-the-art methods on CelebA. $\\star =$ using a frozen pretrained backbone, $\\ddagger =$ using a multi-stage self-training strategy.",
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+ "type": "text",
+ "text": "also misidentify some background regions as foreground parts. However, CelebA provides only five keypoints near the eyes, nose, and mouth for metric calculation, which is insufficient to reflect the improvements achieved by MPAE, as presented in Table 3.",
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+ "text": "4.4. Ablation Studies",
+ "text_level": 1,
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+ "text": "Influence of loss functions: to study the effectiveness of the loss functions used in MPAE, we conduct ablation stud",
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+ "type": "text",
+ "text": "ies on PartImageNet Segmentation dataset. The quantitative and qualitative results are shown in Table 4 and Fig. 5 respectively. Foreground loss $\\mathcal{L}_{\\mathrm{f}}$ and background loss $\\mathcal{L}_{\\mathrm{b}}$ are crucial for preventing the model from identifying all pixels as background or foreground. Otherwise, the learned model converges to a trivial solution. Without the prior knowledge provided by Total variation loss $\\mathcal{L}_{\\mathrm{v}}$ , the pixels identified as foreground regions cannot form connected and concentrated parts. Entropy loss $\\mathcal{L}_{\\mathrm{e}}$ leads to more sta",
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+ "img_path": "images/8cf0ebcd754aa67ffd1397e96bdb3ab5d93089c4c5edc38bfba87f775efda4bf.jpg",
+ "image_caption": [
+ "Raw Image Without $\\mathcal{L}_{\\mathrm{f}}$ Without $\\mathcal{L}_{\\mathrm{b}}$ Without $\\mathcal{L}_{\\mathrm{v}}$ Without $\\mathcal{L}_{\\mathrm{c}}$ Without $\\mathcal{L}_{\\mathrm{r}}$ Without $\\mathcal{L}_{\\mathrm{s}}$ Full Model",
+ "Figure 5. Qualitative results from the ablation studies of the loss functions on PartImageNet Segmentation dataset ( $K = 50$ ). From left to right: (1) raw images, models trained without (2) $\\mathcal{L}_{\\mathrm{f}}$ , (3) $\\mathcal{L}_{\\mathrm{b}}$ , (4) $\\mathcal{L}_{\\mathrm{v}}$ , (5) $\\mathcal{L}_{\\mathrm{e}}$ , (6) $\\mathcal{L}_{\\mathrm{r}}$ , (7) $\\mathcal{L}_{\\mathrm{s}}$ and (8) nothing (full model)."
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+ "img_path": "images/8f5b9f804bf7c912918fbd1efcb56478948bbfc8c356fb83c8e0ac9831cdca7d.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Method | K=8 (%) | K=25 (%) | K=50 (%) |
| NMI↑ | ARI↑ | NMI↑ | ARI↑ | NMI↑ | ARI↑ |
| Without Lf | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Without Lb | 30.91 | 73.20 | 33.67 | 67.85 | 39.36 | 55.24 |
| Without Lv | 18.30 | 20.62 | 13.52 | 4.54 | 14.37 | 4.08 |
| Without Le | 31.21 | 63.27 | 27.48 | 54.93 | 52.51 | 73.08 |
| Without LR | 25.60 | 57.39 | 31.53 | 63.39 | 22.32 | 49.73 |
| Without Ls | 55.69 | 76.54 | 57.70 | 76.97 | 56.42 | 74.03 |
| Full model | 33.51 | 65.05 | 37.22 | 68.04 | 55.10 | 73.52 |
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+ "img_path": "images/414cb50095b2dff48f217de606ce894334f920d7180f1ea290764e5e6a13fbff.jpg",
+ "table_caption": [
+ "Table 4. Performance comparisons of MPAE without different loss functions on the PartImageNet Segmentation dataset in the setting of $K = 8,25,50$ ."
+ ],
+ "table_footnote": [],
+ "table_body": "| Masking Ratio r | 50% | 75% | 80% | 85% | 90% | 95% | 100% |
| NMI (%) ↑ | 45.50 | 50.11 | 52.20 | 52.70 | 55.10 | 54.63 | 43.39 |
| ARI (%) ↑ | 70.25 | 70.89 | 70.90 | 71.85 | 73.52 | 73.23 | 41.29 |
",
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+ {
+ "type": "text",
+ "text": "ble and smooth part boundaries by enforcing that each pixel highly responds to a unique part descriptor. The absence of reconstruction loss $\\mathcal{L}_{\\mathrm{r}}$ results in a failure to align part descriptors with actual part shapes. Consequently, the predicted masks contain only rough regions without clear part boundaries. Without semantic constraint $\\mathcal{L}_{\\mathrm{s}}$ , the model identifies the regions with less semantic similarity as the same part. In some cases, the learned model even degrades into a foreground segmentation model. Although this degradation may improve the numerical metrics in NMI and ARI, the learned model cannot achieve the goal of part discovery. Therefore, all constraints used in MPAE are essential for learning a robust model for unsupervised part discovery.",
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+ "type": "text",
+ "text": "Influence of the masking ratio $r$ : the quantitative results of MPAE with different masking ratios $r$ are reported in Table 5. When $r < 90\\%$ , a higher $r$ results in more features in the filled feature map $R$ comes from part descriptors $D$ . Therefore, by aligning the part descriptors $D$",
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+ "img_path": "images/347e7d455520b579848fbeb74439a531c3a79dbc2bde0c244338f84ecf1955cc.jpg",
+ "table_caption": [
+ "Table 5. Performance comparisons of MPAE with different masking ratio $r$ on the PartImageNet Segmentation dataset in the setting of $K = {50}$ ."
+ ],
+ "table_footnote": [],
+ "table_body": "| Change from MPAE model: | NMI (%)↑ | ARI (%)↑ |
| Lf → Area loss in [40] | 1.90 | -0.14 |
| Lp → Presence loss in [2] | 42.45 | 60.24 |
| Ld → Concentration loss in [21] | 17.29 | 18.74 |
| Part number K → 4Nc | 47.59 | 70.71 |
| MPAE (our best model) | 55.10 | 73.52 |
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+ {
+ "type": "text",
+ "text": "Table 6. Comparisons of our optimized losses and designs with previous ones on the PartImageNet Segmentation dataset in the setting of $K = 50$ .",
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+ "type": "text",
+ "text": "with object part shapes, a stronger constraint can be applied to the similarity maps $P$ , requiring them to better match the actual part shapes. As a results, we observe an improvement in performance. When $r > 90\\%$ , a higher $r$ results in insufficient unmasked patches containing low-level appearance information to guide the alignment between descriptors and part shapes. Therefore, the optimal masking ratio $r$ is $90\\%$ .",
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+ "type": "text",
+ "text": "Improvements of our optimized constraints and designs: The area loss in [40] requires all parts to appear in each image. But, it is impossible for every object to contain all 50 parts. Consequently, $\\mathcal{L}_{\\mathrm{a}}$ leads to a collapse during training. The image classification loss in [2] ensures that each image to have at least one discovered part, as the embedding for classification cannot be a zero vector. Without any labels, presence loss in [2] cannot guarantee that unsupervised methods discover at least one part in each image. Therefore, some images may not have any discovered parts, which further leads to a degradation in metrics. The concentration loss in [21] penalizes pixels that are farther from the part center more heavily, which prevents the predicted parts from accurately following their actual shapes, whereas $\\mathcal{L}_{\\mathrm{d}}$ addresses this imbalance. As [40], we also implement a model that simply decomposes each category into four parts without exploring their semantic similarities ( $K \\to 4N_{\\mathrm{c}}$ ). Consequently, the number of training samples for each part significantly decreases, leading to reduced robustness.",
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+ "type": "text",
+ "text": "More ablation studies and visualized results are included in the Appendix.",
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+ {
+ "type": "text",
+ "text": "5. Conclusion",
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+ {
+ "type": "text",
+ "text": "In this paper, we present a novel paradigm (MPAE) with looser yet effective constraints for more robust unsupervised part discovery. By restoring masked image patches using the corresponding part descriptors, MPAE effectively aligns their high-level semantics with the part shapes under the guidance of low-level appearance features from un-masked patches. As a result, MPAE predicts masks that closely match the actual shapes of corresponding parts. The optimized constraints enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner, effectively addressing challenges posed by occlusion and diverse object categories.",
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+ "text": "References",
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+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "Unsupervised Part Discovery via Descriptor-Based Masked Image Restoration with Optimized Constraints"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Jiahao Xia\\(^{1}\\), Yike Wu\\(^{1}\\), Wenjian Huang\\(^{2}\\), Jianguo Zhang\\(^{2}\\), Jian Zhang\\(^{*,1}\\)"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\(^{1}\\)Faculty of Engineering and IT, University of Technology Sydney"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\(^{2}\\) Dept. of Comp. Sci. and Eng., Southern University of Science and Technology"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Jiahao.Xia-1@uts.edu.au, Yike.Wu@student.uts.edu.au, {huangwj, zhangjg} \\(@\\) sustech.edu.cn, Jian.Zhang@uts.edu.au"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "Abstract"
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "Part-level features are crucial for image understanding, but few studies focus on them because of the lack of fine-grained labels. Although unsupervised part discovery can eliminate the reliance on labels, most of them cannot maintain robustness across various categories and scenarios, which restricts their application range. To overcome this limitation, we present a more effective paradigm for unsupervised part discovery, named Masked Part Autoencoder (MPAE). It first learns part descriptors as well as a feature map from the inputs and produces patch features from a masked version of the original images. Then, the masked regions are filled with the learned part descriptors based on the similarity between the local features and descriptors. By restoring these masked patches using the part descriptors, they become better aligned with their part shapes, guided by appearance features from unmasked patches. Finally, MPAE robustly discovers meaningful parts that closely match the actual object shapes, even in complex scenarios. Moreover, several looser yet more effective constraints are proposed to enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner. This provides the foundation for addressing challenges posed by occlusion and for exploring part similarity across multiple categories. Extensive experiments demonstrate that our method robustly discovers meaningful parts across various categories and scenarios. The code is available at the project website1."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.804,
+ 0.485,
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+ "angle": 0,
+ "content": "Decomposing objects into meaningful parts drives models to gain better image understanding and further improves the performance of downstream tasks, such as person search [27], fine-grained classification [2, 35] and be"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.517,
+ 0.309,
+ 0.905,
+ 0.462
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.512,
+ 0.471,
+ 0.908,
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+ ],
+ "angle": 0,
+ "content": "Figure 1. MPAE uses similarity maps between local image features and part descriptors to assign these descriptors to fill masked regions in a randomly masked version of the inputs. The restoration implicitly clusters the features of the restored patches that share similar appearance, further aligning low-level appearance in unmasked patches and high-level semantics of part descriptors. This drives similarity maps to closely match the actual part shapes."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.597,
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+ 0.658
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+ "angle": 0,
+ "content": "havior analysis [25]. But the high cost of part-level label results in a scarcity of training samples. Consequently, part-level feature learning has received much less attention compared to instance-level feature learning."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.659,
+ 0.909,
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+ ],
+ "angle": 0,
+ "content": "To eliminate the reliance on part-level labels, existing methods achieve part discovery mainly through two strategies: reconstruction [12, 19, 21, 23, 32, 40, 41, 43] and clustering [4, 6]. By directly reconstructing the input images using learned part descriptors, the descriptors are expected to align with the part shapes, allowing these part descriptors to further predict part masks. However, to discover meaningful parts, these descriptors are designed to learn high-level semantics rather than low-level appearance [1], which prevents such reconstruction and alignment, especially in complex scenarios. Clustering-based methods use foreground masks to remove irrelevant regions and directly cluster foreground features, regardless of their actual appearance similarity. Some near-outlier features are identified as separate parts, leading to the discovery of unreasonable parts."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To address these limitations and extend unsupervised"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "*Corresponding Author"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "1https://github.com/Jiahao-UTS/MPAE"
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ 0.901
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "8668"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.482,
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+ ],
+ "angle": 0,
+ "content": "part discovery to more complex scenarios, we propose a novel paradigm, named Mask Part Autoencoder (MPAE). As shown in Fig. 1, instead of directly using part descriptors for image reconstruction, we first calculate the similarities between these descriptors and a feature map learned from the input. Based on the similarity maps, we assign these descriptors to fill the masked regions in a randomly masked version of inputs. By utilizing both filled part descriptors and unmasked patch features within the same part regions to generate image patches with similar appearances, these features are implicitly clustered together [42]. The appearance features of unmasked patches (e.g., boundaries and textures) further align the high-level semantics of the part descriptors with the part shapes. Guided by part appearance, the similarity maps closely match the shapes of corresponding parts even in complex scenarios. Thus, they can be viewed as pixel-level masks of the discovered parts."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Moreover, without using category labels, it is difficult for unsupervised methods to determine which object parts are present or absent in an image, because different categories consist of different types of parts. As a result, most existing methods [12, 19, 23, 41] are restricted to a single category and do not consider the absence of individual parts. However, it is still impossible for all parts to appear in every image, even within a single category, because objects can be occluded. Although [40] achieves part discovery on a dataset with multiple categories, it still relies on category labels to determine which parts appear before part discovery. Therefore, we propose a looser constraints to enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner. Additionally, a more effective constraint is proposed to ensure that the MPAE discovers part-level masks, as the model can easily degrade to predicting only a single instance-level mask when part absence is allowed. This provides a foundation for tackling challenges posed by occlusion. As a result, these optimized constraints allow MPAE to leverage similar parts across different categories to achieve more robust part discovery without relying on any labels."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.683,
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+ ],
+ "angle": 0,
+ "content": "To evaluate the effectiveness of MPAE and our optimized constraints, extensive experiments are conducted on four widely used benchmarks, including two with multiple categories and two with a single category. The experimental results clearly demonstrate that MPAE robustly discovers meaningful object parts across diverse categories and achieves more competitive performance on all datasets than other state-of-the-art methods."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The main contributions of this paper can be summarized as followings:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.092,
+ 0.84,
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+ ],
+ "angle": 0,
+ "content": "- We present a novel paradigm named Masked Part Autoencoder (MPAE), which utilizes low-level appearance features of the unmasked patches to align the part descriptors with actual part shapes. Consequently, MPAE discovers"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.527,
+ 0.092,
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+ 0.107
+ ],
+ "angle": 0,
+ "content": "meaningful parts that closely match the object shapes."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.514,
+ 0.108,
+ 0.905,
+ 0.182
+ ],
+ "angle": 0,
+ "content": "- Several looser yet effective constraints are proposed to enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner. As a result, MPAE can leverage similar parts across various categories to achieve more robust part discovery."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.183,
+ 0.905,
+ 0.243
+ ],
+ "angle": 0,
+ "content": "- Extensive experiments are carried out on four widely-used benchmarks. The results show that our method can robustly discover reasonable object parts in complex scenarios and achieve highly competitive performance."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
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+ "type": "title",
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+ "angle": 0,
+ "content": "2. Related works"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.1. Unsupervised / Self-supervised Learning"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.308,
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+ ],
+ "angle": 0,
+ "content": "Many works in natural language processing (NLP) [10, 28] show unsupervised / self-supervised learning learns more effective features for downstream tasks than supervised learning. Inspired by their success, recent works [4, 5, 8, 13, 14, 17, 18, 26, 30, 45] also adopt unsupervised / self-supervised learning to improve the effectiveness of visual features. In addition to performance improvements, some new properties also emerge in Vision Transformer (ViT) [11] with the use of unsupervised / self-supervised learning. Caron et al. [4] found using momentum encoder [16] and multi-crop augmentation [3] drives the ViT features from the same category to have high similarity. Based on this properties, Wang et al. [39] and Wang et al. [37, 38] achieve foreground segmentation, instance segmentation, and video instance segmentation, respectively, in an unsupervised manner by using normalized cut [31] to directly group self-similar regions. Although learned ViT features within the same part exhibit higher similarity [30, 45], discovering object parts from images is still much more challenging than discovering instances. The main reason is that features from different parts also have very high similarity, resulting in less consistent semantics and boundaries in the discovered parts. Unfortunately, there are relatively few works that focus on using unsupervised / self-supervised features to discover meaningful and consistent object parts."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.2. Part Discovery"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.72,
+ 0.905,
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+ ],
+ "angle": 0,
+ "content": "Part discovery aims to identify meaningful object parts with consistent semantics and predict their pixel-level masks. Existing works mainly achieve part discovery through weakly-supervised or unsupervised learning. Weakly-supervised part discovery utilizes instance-level labels, such as category [2, 20, 35] and identity [27, 44], to discover relevant parts with pixel-level masks during training. Then, part-level features are extracted using these masks and further boost the performance of downstream tasks. Nevertheless, without aligning their the semantics from part embeddings with actual object appearances through reconstruction, their part masks do not follow the actual object bound"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "8669"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
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+ ],
+ "angle": 0,
+ "content": "aries well, making them insufficiently fine-grained."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.093,
+ 0.109,
+ 0.485,
+ 0.486
+ ],
+ "angle": 0,
+ "content": "Unsupervised part discovery is more challenging than weakly-supervised part discovery because no labels are provided during training. Early works discover meaningful object parts with rough part masks by factorizing deep features [7] or spatial embeddings [34]. Other methods [1, 6] directly cluster the foreground features across all images to discover meaningful parts. Nevertheless, the semantics and boundaries of the predicted part masks are not sufficiently stable due to appearance biases in each image. Most state-of-the-art methods [12, 21, 23, 32, 40, 41, 43] employ image reconstruction as a learning objective to align the part descriptors with the actual part shapes. Therefore, these part descriptors can further predict the part masks with consistent semantics. However, these descriptors are designed to capture high-level semantics rather than low-level appearance, which hinders reconstruction and alignment, ultimately degrading part discovery, especially in complex scenarios. Amir et al. [1] demonstrate that directly clustering self-supervised features in foreground regions can also discover meaningful parts. Nevertheless, they only consider feature similarity, disregarding actual appearance similarity. As a result, some near-outlier features are identified as independent parts, leading to unreasonably segmented parts. Therefore, robustly discovering meaningful parts in an unsupervised manner remains a significant challenge."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3. Methodology"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Unsupervised part discovery aims to learn a model that can parse all objects into a total of \\(K\\) parts without any labels. Given an input image \\(\\pmb{I} \\in \\mathbb{R}^{H_{\\mathrm{I}} \\times W_{\\mathrm{I}} \\times 3}\\), the learned model predicts pixel-level mask \\(M_{\\mathrm{p}} \\in \\{0,1\\}^{H_{\\mathrm{I}} \\times W_{\\mathrm{I}} \\times (K + 1)}\\) to assign each pixel into one of \\(K\\) parts or background, where \\((H_{\\mathrm{I}}, W_{\\mathrm{I}})\\) is the size of the input image."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "To achieve this goal, we present a novel paradigm, named Masked Part Autoencoder (MPAE), and further incorporate it with several optimized constraints. In what follows, we first detail the training and inference pipeline of MPAE, followed by an introduction to our optimized constraints and their corresponding functions."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.1. Masked Part Autoencoder"
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "3.1.1. Training pipeline"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The overall training pipeline of MPAE is shown in Fig. 2. It consists of four blocks: (a) random masking block, (b) descriptor extraction block, (c) matching block, (d) image restoration block."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Random masking block first divides the input image \\( \\pmb{I} \\) into patches of size \\( p \\). The patched image \\( \\pmb{I}^{\\mathrm{p}} \\) is denoted as \\( \\pmb{I}^{\\mathrm{p}} \\in \\mathbb{R}^{\\frac{H_{\\mathrm{I}}}{p} \\times \\frac{W_{\\mathrm{I}}}{p} \\times 3p^{2}} \\). A binary mask \\( M = \\{0,1\\}^{\\frac{H_{\\mathrm{I}}}{p} \\times \\frac{W_{\\mathrm{I}}}{p}} \\) is then generated to randomly mask out a specified proportion \\( r \\) of the image patches. As MAE [18], these masked"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "patches will not be used in the following training. Only visible patches are finally fed into the MPAE encoder to learn unmasked patch features \\( \\pmb{F}^{\\mathrm{U}} \\in \\mathbb{R}^{\\frac{H_{\\mathrm{I}} \\times W_{\\mathrm{I}}}{p \\times p} (1 - r) \\times C} \\), where \\( C \\) is the dimension of the unmasked patch feature."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Descriptor extraction block is designed to learn part-level descriptors from input images. Specifically, as [40], we replace the class embedding of a classical ViT with \\( K + 1 \\) embeddings to extract \\( K + 1 \\) descriptors. By incorporating MPAE with appropriate constraints, each embedding learns to specialize in one potential part, adaptively aggregating image features to produce the corresponding part descriptor. The \\( K + 1 \\) part descriptors \\( D \\in \\mathbb{R}^{(K + 1)\\times C} \\) include \\( K \\) descriptors for foreground parts and 1 for the background, where the descriptor dimension \\( C \\) is the same as that of \\( F^{\\mathrm{U}} \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "To determine how to assign the sparse part descriptors \\(D\\) to fill the masked regions, we employ a frozen pre-trained ViT, followed by a trainable \\(1 \\times 1\\) convolutional layer, to extract a dense feature map \\(F \\in \\mathbb{R}^{H_{\\mathrm{F}} \\times W_{\\mathrm{F}} \\times C}\\), where \\((H_{\\mathrm{F}}, W_{\\mathrm{F}})\\) is the size of the feature map. By matching \\(F\\) with \\(D\\), we can obtain a similarity map for each part (as detailed in the following paragraphs). Based on the similarity maps, we can fill the masked patches using \\(D\\). Moreover, it enables PartFormer to leverage knowledge from the ViT, pre-trained through unsupervised or self-supervised learning, to discover more reasonable object parts."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Matching block calculates similarity maps \\( \\pmb{P} \\) between \\( D \\) and \\( F \\), which can be defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\nP _ {i, j, k} = \\frac {\\exp \\left(\\boldsymbol {D} _ {k} \\cdot \\boldsymbol {F} _ {i , j}\\right)}{\\sum_ {k ^ {\\prime} = 1} ^ {K + 1} \\exp \\left(\\boldsymbol {D} _ {k ^ {\\prime}} \\cdot \\boldsymbol {F} _ {i , j}\\right)}, \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\( \\pmb{F}_{i,j} \\) indicates the pixel-level feature at \\( (i,j) \\) of \\( \\pmb{F} \\), and \\( D_{k} \\) is the part descriptor for the \\( k \\)-th part, with \\( i \\in \\{1,\\dots ,W_{\\mathrm{F}}\\} \\), \\( j \\in \\{1,\\dots ,H_{\\mathrm{F}}\\} \\), and \\( k \\in \\{1,\\dots ,K + 1\\} \\). \\( P_{i,j,k} \\) represents the normalized similarity between the \\( D_{k} \\) and \\( F_{i,j} \\). Based on the similarity map, the part descriptors are assigned to fill the masked regions and reform a dense feature map \\( \\pmb{R} \\), which can be formulated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {R} _ {i, j} = \\left\\{ \\begin{array}{l l} \\boldsymbol {F} _ {i, j} ^ {\\mathrm {U}} & , M _ {i, j} = 0, \\\\ \\sum_ {k = 1} ^ {K + 1} \\left(P _ {i, j, k} \\boldsymbol {D} _ {k}\\right) & , M _ {i, j} = 1, \\end{array} \\right. \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\( \\pmb{R}_{i,j} \\) is the feature vector of the filled feature map \\( \\pmb{R} \\) at position \\( (i,j) \\). \\( M_{i,j} \\) is the value of the binary mask \\( M \\), indicating that the position \\( (i,j) \\) is masked or not in random masking block."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Image restoration block feeds \\(\\pmb{R}\\) into the MPAE decoder to restore the masked patches, which can be written as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {r}} = \\frac {1}{2} \\| \\boldsymbol {I} - \\boldsymbol {I} ^ {\\prime} \\| _ {1} + \\frac {1}{2} \\| \\Phi (\\boldsymbol {I}) - \\Phi (\\boldsymbol {I} ^ {\\prime}) \\| _ {1}, \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(\\pmb{I}^{\\prime}\\) is the restored image and \\(\\Phi\\) is a frozen VGG-19 [33]. Directly using the L1 loss constraint for image"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 2. Training and inference pipelines of MPAE. The training pipeline consists of four blocks: (a) random masking block, (b) descriptor extraction block, (c) matching block, and (d) image restoration block. (a) randomly masks out a large proportion of patches and extracts patch features \\( \\pmb{F}^{\\mathrm{U}} \\) from the unmasked patches using MPAE encoder. The input image \\( \\pmb{I} \\) is also fed into (b), after being patchified, to extract part descriptors \\( \\pmb{D} \\) and a feature map \\( \\pmb{F} \\). By matching \\( \\pmb{D} \\) with \\( \\pmb{F} \\) using Hadamard product and a Softmax function, we generate a similarity map for each descriptor in (c). Based on these similarity maps \\( \\pmb{P} \\), we use \\( \\pmb{D} \\) to fill the masked regions and reconstruct a feature map \\( \\pmb{R} \\). In (d), \\( \\pmb{R} \\) is further utilizes for image restoration, aligning the high-level semantics of the \\( \\pmb{D} \\) with the corresponding part shapes. The inference pipeline directly employs \\( \\pmb{D} \\) as mask prototypes to predict part-level masks from the Interpolated feature map \\( \\pmb{F}' \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.464,
+ 0.482,
+ 0.57
+ ],
+ "angle": 0,
+ "content": "restoration, as in [18], can lead to structure deviations between the raw and restored images [18], which in turn causes the features in different parts to be poorly clustered, regardless of their actual appearance similarity. Therefore, in addition to using the L1 loss, we employ VGG-19 to encourage greater structural similarity between the restored image and the input image as the perceptual loss [22]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.57,
+ 0.483,
+ 0.797
+ ],
+ "angle": 0,
+ "content": "The functions of this image restoration are threefold: 1) It retains low-level appearance features in MPAE through the unmasked patch features \\( F^{\\mathrm{U}} \\), thereby compensating for the lack of low-level appearance features in the part descriptors \\( D \\). 2) It implicitly clusters \\( F^{\\mathrm{U}} \\) and \\( D \\) within the same part region together in latent space by utilizing them to produce the image patches with similar appearance. Guided by low-level appearance features from \\( F^{\\mathrm{U}} \\), the high-level semantics from \\( D \\) are aligned more accurately with the actual part shapes compared to directly using \\( D \\) from image reconstruction. 3) This alignment further constrains the similarity maps \\( P \\), encouraging them to more closely match the actual shapes of their corresponding parts, even in highly complex scenarios. Consequently, \\( P \\) can serve as pixel-level masks for the discovered parts."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.804,
+ 0.294,
+ 0.82
+ ],
+ "angle": 0,
+ "content": "3.2. Learning Constraints"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.825,
+ 0.483,
+ 0.885
+ ],
+ "angle": 0,
+ "content": "To ensure robust part discovery, we incorporate MPAE with three types of optimized constraints: the presence constraint \\(\\mathcal{L}_{\\mathrm{p}}\\), the semantic consistency constraint \\(\\mathcal{L}_{\\mathrm{s}}\\), and the distribution constraint \\(\\mathcal{L}_{\\mathrm{d}}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.886,
+ 0.483,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Presence constraint \\(\\mathcal{L}_{\\mathrm{p}} = \\mathcal{L}_{\\mathrm{f}} + \\mathcal{L}_{\\mathrm{b}}\\) where \\(\\mathcal{L}_{\\mathrm{f}}\\) and \\(\\mathcal{L}_{\\mathrm{b}}\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.464,
+ 0.907,
+ 0.525
+ ],
+ "angle": 0,
+ "content": "represent the foreground and background presence losses respectively. \\(\\mathcal{L}_{\\mathrm{p}}\\) is directly applied to \\(P\\) to ensure the presence of \\(K\\) foreground parts across the entire data and the presence of background in every image."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.525,
+ 0.907,
+ 0.556
+ ],
+ "angle": 0,
+ "content": "\\(\\mathcal{L}_{\\mathrm{f}}\\) divides each mini-batch into \\(N_{\\mathrm{g}}\\) mini-groups with \\(G\\) samples. Then, \\(\\mathcal{L}_{\\mathrm{f}}\\) can be calculated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.513,
+ 0.562,
+ 0.907,
+ 0.62
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {f}} = \\frac {1}{N _ {\\mathrm {g}}} \\sum_ {n _ {\\mathrm {g}} = 1} ^ {N _ {\\mathrm {g}}} (2 - \\frac {1}{G} \\sum_ {g = 1} ^ {G} \\max _ {i, j, k} P _ {i, j, k} ^ {g, n _ {\\mathrm {g}}} - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\max _ {i, j, g} P _ {i, j, k} ^ {g, n _ {\\mathrm {g}}}), \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.62,
+ 0.906,
+ 0.741
+ ],
+ "angle": 0,
+ "content": "where \\(P_{i,j,k}^{g,n_{\\mathrm{g}}}\\) is the similarity \\(P_{i,j,k}\\) of \\(g\\) -th sample in \\(n_{\\mathrm{g}}\\) -th mini-group. Instead of requiring all parts to appear in each image as previous unsupervised methods, \\(\\mathcal{L}_{\\mathrm{f}}\\) only encourages them to appear at least once in each mini-group and each image to contain at least one part. This looser constraint provides the basis for MPAE to identify the presence of parts across various scenarios and categories. The influence of the mini-group will be discussed in the Appendix."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.741,
+ 0.905,
+ 0.772
+ ],
+ "angle": 0,
+ "content": "\\(\\mathcal{L}_{\\mathrm{b}}\\) encourages the background to appear near the boundaries of each image. Inspired by [2], we define \\(\\mathcal{L}_{\\mathrm{b}}\\) as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.553,
+ 0.778,
+ 0.907,
+ 0.823
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {b}} = - \\frac {1}{N _ {\\mathrm {g}} G} \\sum_ {n _ {\\mathrm {g}} = 1} ^ {N _ {\\mathrm {g}}} \\sum_ {g = 1} ^ {G} \\log \\left(\\max _ {i, j} d _ {i, j} P _ {i, j, K + 1} ^ {g, n _ {\\mathrm {g}}}\\right), \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.831,
+ 0.905,
+ 0.862
+ ],
+ "angle": 0,
+ "content": "where \\(d_{i,j}\\) is the distance from position \\((i,j)\\) to the image center. \\(d_{i,j}\\) can be calculated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.53,
+ 0.868,
+ 0.907,
+ 0.906
+ ],
+ "angle": 0,
+ "content": "\\[\nd _ {i, j} = 2 \\left(\\frac {i - 1}{W _ {\\mathrm {F}} - 1} - \\frac {1}{2}\\right) ^ {2} + 2 \\left(\\frac {j - 1}{H _ {\\mathrm {F}} - 1} - \\frac {1}{2}\\right) ^ {2}. \\tag {6}\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
+ 0.945,
+ 0.514,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "8671"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.483,
+ 0.121
+ ],
+ "angle": 0,
+ "content": "Incorporated with \\(\\mathcal{L}_{\\mathrm{f}}\\) and \\(\\mathcal{L}_{\\mathrm{b}}\\), our model also learns to distinguish the \\(K\\) foreground parts and the background region."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.122,
+ 0.484,
+ 0.243
+ ],
+ "angle": 0,
+ "content": "Semantic constraint \\(\\mathcal{L}_{\\mathrm{s}}\\): because \\(\\mathcal{L}_{\\mathrm{p}}\\) only requires each image to contain at least one part, the model tends to simply segment out the entire foreground object, thereby degrading into an instance-discovery model. By encouraging each part descriptor to align only with the local features that exhibit very high similarity, \\(\\mathcal{L}_{\\mathrm{s}}\\) ensures that the model decomposes the target into multiple object parts with consistent semantics. \\(\\mathcal{L}_{\\mathrm{s}}\\) can be formulated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.093,
+ 0.25,
+ 0.484,
+ 0.32
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {s}} = - \\frac {1}{K} \\sum_ {k = 1} ^ {K} \\log \\frac {M ^ {k} e ^ {s \\left(\\cos \\left(\\theta_ {(k , k)} + m\\right)\\right)}}{M ^ {k} e ^ {s \\left(\\cos \\left(\\theta_ {(k , k)} + m\\right)\\right)} + \\sum_ {t = 1 , t \\neq k} ^ {K} M ^ {t} e ^ {s \\cos \\theta_ {(t , k)}}}, \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.321,
+ 0.484,
+ 0.414
+ ],
+ "angle": 0,
+ "content": "where \\(M_{k}\\in \\{0,1\\}\\) represents the presence of the \\(k\\) -th part. When \\(\\sum_{i = 1}^{W_{\\mathrm{F}}}\\sum_{j = 1}^{H_{\\mathrm{F}}}P_{i,j,k} < = 0.001,M_{k} = 0\\) , else, \\(M_{k} = 1\\) . \\(m\\) and \\(s\\) are two hyperparameters. \\(\\theta_{(k,t)}\\) is the angle between the \\(k\\) -the part descriptor \\(D_{k}\\) and the mean feature vector of \\(t\\) -th part region \\(\\bar{F}_t\\) in latent space. \\(\\bar{F}_t\\) and \\(\\cos (\\theta_{(k,t)})\\) are defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.188,
+ 0.422,
+ 0.483,
+ 0.465
+ ],
+ "angle": 0,
+ "content": "\\[\n\\bar {\\boldsymbol {F}} _ {t} = \\frac {\\sum_ {i = 1} ^ {W _ {1}} \\sum_ {j = 1} ^ {H _ {1}} P _ {i , j , t} \\boldsymbol {F} _ {i , j}}{\\sum_ {i = 1} ^ {W _ {1}} \\sum_ {j = 1} ^ {H _ {1}} P _ {i , j , t}}, \\tag {8}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.198,
+ 0.475,
+ 0.482,
+ 0.509
+ ],
+ "angle": 0,
+ "content": "\\[\n\\cos \\left(\\theta_ {(t, k)}\\right) = \\frac {\\boldsymbol {D} _ {k} \\cdot \\bar {\\boldsymbol {F}} _ {t}}{\\| \\boldsymbol {D} _ {k} \\| \\| \\bar {\\boldsymbol {F}} _ {t} \\|.} \\tag {9}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.512,
+ 0.484,
+ 0.633
+ ],
+ "angle": 0,
+ "content": "As [9], \\( m \\) enables \\( \\mathcal{L}_s \\) to still have a certain gradient value for further maximizing \\( \\cos(\\theta_{(k,k)}) \\) when \\( \\theta_{(k,k)} \\) is very small, and \\( s \\) controls the smoothness of \\( \\mathcal{L}_s \\). By minimizing \\( \\theta_{(k,k)} \\) and maximizing \\( \\theta_{(t,k)} \\), the discovered parts across different objects have more consistent semantics. Moreover, the use of \\( M^k \\) enables \\( \\mathcal{L}_s \\) to only consider the semantic consistency of those appeared parts, providing the basis to constrain the semantic consistency across multiple categories."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.633,
+ 0.484,
+ 0.692
+ ],
+ "angle": 0,
+ "content": "Distribution constraint \\(\\mathcal{L}_{\\mathrm{d}} = \\mathcal{L}_{\\mathrm{v}} + \\mathcal{L}_{\\mathrm{e}}\\), where \\(\\mathcal{L}_{\\mathrm{v}}\\) and \\(\\mathcal{L}_{\\mathrm{e}}\\) are total variation loss [29] and entropy loss respectively. \\(\\mathcal{L}_{\\mathrm{d}}\\) encourages the predicted probability map \\(P\\) to better follow the shapes of object parts."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.693,
+ 0.484,
+ 0.723
+ ],
+ "angle": 0,
+ "content": "\\(\\mathcal{L}_{\\mathrm{v}}\\) minimizes the spatial gradient of the predicted \\(P\\) which can be formulated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.165,
+ 0.729,
+ 0.483,
+ 0.772
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {v}} = \\frac {1}{H _ {\\mathrm {F}} W _ {\\mathrm {F}}} \\sum_ {k = 1} ^ {K + 1} \\sum_ {i = 1} ^ {W _ {\\mathrm {F}}} \\sum_ {j = 1} ^ {H _ {\\mathrm {F}}} | \\nabla P _ {i, j, k} |, \\tag {10}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.781,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "where \\(\\nabla P_{i,j,k}\\) represents the spatial image gradient at position \\((i,j)\\) on the probability map for the \\(k\\)-th part. The function of \\(\\mathcal{L}_{\\mathrm{v}}\\) is the same as that of the concentration loss [21], encouraging pixels with high confidence for the same part to form a connected region. However, the concentration loss penalizes pixels that are far from the part center much more heavily than those that are close. This imbalance further causes the discovered parts to take on an approximately"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.906,
+ 0.152
+ ],
+ "angle": 0,
+ "content": "square shape. \\(\\mathcal{L}_{\\mathrm{v}}\\) successfully eliminates this imbalance by calculating the gradient of \\(P\\), enabling the discovered parts to more accurately follow the shapes of objects, even when they are very complex."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.152,
+ 0.907,
+ 0.198
+ ],
+ "angle": 0,
+ "content": "\\(\\mathcal{L}_{\\mathrm{e}}\\) ensures that the distribution at any position on \\(P\\) has high similarity in only one part descriptor by penalizing its entropy:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.541,
+ 0.205,
+ 0.906,
+ 0.248
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {e}} = - \\frac {1}{K + 1} \\sum_ {k = 1} ^ {K + 1} \\sum_ {i = 1} ^ {W _ {\\mathrm {F}}} \\sum_ {j = 1} ^ {H _ {\\mathrm {F}}} P _ {i, j, k} \\log \\left(P _ {i, j, k}\\right). \\tag {11}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.254,
+ 0.906,
+ 0.284
+ ],
+ "angle": 0,
+ "content": "This drives the similarity map \\( P \\) to exhibit clear and stable boundaries, resulting in more precise part discovery."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.285,
+ 0.907,
+ 0.346
+ ],
+ "angle": 0,
+ "content": "Overall training target: by minimizing \\(\\mathcal{L} = \\mathcal{L}_{\\mathrm{r}} + \\lambda_{\\mathrm{p}}\\mathcal{L}_{\\mathrm{p}} + \\lambda_{\\mathrm{s}}\\mathcal{L}_{\\mathrm{s}} + \\lambda_{\\mathrm{d}}\\mathcal{L}_{\\mathrm{d}}\\), MPAE learns to discover meaningful parts in complex scenarios, where \\(\\lambda_{\\mathrm{p}}, \\lambda_{\\mathrm{s}}\\), and \\(\\lambda_{\\mathrm{d}}\\) are the weights of \\(\\mathcal{L}_{\\mathrm{p}}, \\mathcal{L}_{\\mathrm{s}}, \\mathcal{L}_{\\mathrm{d}}\\) respectively."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.353,
+ 0.691,
+ 0.369
+ ],
+ "angle": 0,
+ "content": "3.3. Inference pipeline"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.375,
+ 0.907,
+ 0.542
+ ],
+ "angle": 0,
+ "content": "The overall inference pipeline is shown on the right in Fig. 2. In this phase, we retain only PartFormer and the pretrained ViT. However, the low-resolution of \\( \\pmb{F} \\) is insufficient to produce high-resolution part masks. Therefore, we resize \\( \\pmb{F} \\) to match the size of the input images using bilinear interpolation. By accurately aligning with part shapes with the guide of low-level appearance features, \\( D \\) can still accurately respond to the corresponding part regions in the \\( F' \\) with much higher resolution. Thus, the similarity maps calculated from \\( D \\) and \\( F' \\) can serve as high-resolution part masks for the parts discovered in an unsupervised manner."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.553,
+ 0.706,
+ 0.57
+ ],
+ "angle": 0,
+ "content": "4. Experimental Setup"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.578,
+ 0.617,
+ 0.592
+ ],
+ "angle": 0,
+ "content": "4.1. Datasets"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.6,
+ 0.907,
+ 0.721
+ ],
+ "angle": 0,
+ "content": "To comprehensively validate the effectiveness of MPAE, we evaluate it on four widely-used benchmarks: two with multiple categories (PartImageNet OOD dataset [15] and PartImageNet Segmentation dataset [15]) and two with a single category (CUB dataset [36] and CelebA dataset [24]). More details about these four datasets and the implementation of our method are provided in Appendix A.1 and Appendix A.2 respectively."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.728,
+ 0.698,
+ 0.743
+ ],
+ "angle": 0,
+ "content": "4.2. Evaluation Metrics"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.75,
+ 0.906,
+ 0.84
+ ],
+ "angle": 0,
+ "content": "Normalized Mutual information (NMI) and Adjusted Rand Index (ARI) are primarily used to measure the similarity between two clusters. In this task, the NMI and ARI scores between the annotated and discovered parts directly reflect how closely the semantics of the discovered parts align with human conception."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.84,
+ 0.906,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Normalized Mean Error (NME): NME is calculated using the centroids of the predicted parts and the annotated keypoints, representing the semantic consistency of the discovered parts across the entire test set."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
+ 0.945,
+ 0.516,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "8672"
+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
+ 0.095,
+ 0.089,
+ 0.48,
+ 0.38
+ ],
+ "angle": 0,
+ "content": "| Method | Label | K | PartImage_O (%) | PartImage_S (%) |
| NMI ↑ | ARI ↑ | NMI ↑ | ARI ↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Category label | 8 | 5.88 | 1.53 | - | - |
| 25 | 7.56 | 1.25 | - | - |
| 50 | 10.19 | 1.05 | - | - |
| PDisco-Net [35] | Category label | 8 | 27.13 | 8.76 | 10.68 | 32.43 |
| 25 | 32.41 | 10.69 | 18.44 | 40.70 |
| 50 | 41.49 | 14.17 | 21.98 | 39.40 |
| PDiscoNet + ViT-B/14 | Category label | 8 | 19.28 | 34.72 | 16.68 | 32.01 |
| 25 | 28.23 | 25.93 | 46.81 | 40.70 |
| 50 | 29.48 | 28.68 | 34.13 | 39.40 |
| PDiscoFormer [2]+ frozen ViT-B/14* | Category label | 8 | 28.84 | 55.66 | - | - |
| 25 | 43.36 | 62.82 | - | - |
| 50 | 44.48 | 57.91 | - | - |
| PDiscoFormer + ViT-B/14† | Category label | 8 | 29.00 | 52.40 | 20.29 | 38.90 |
| 25 | 44.71 | 59.27 | 43.18 | 64.61 |
| 50 | 46.29 | 62.21 | 44.06 | 60.10 |
| Unsupervised part discovery |
| DINO* [1] | N/A | 8 | 19.17 | 7.59 | - | - |
| 25 | 31.46 | 14.16 | - | - |
| 50 | 37.81 | 16.50 | - | - |
| Xia et al.* [40] | N/A | 4NC | 27.85 | 40.77 | 25.17 | 37.50 |
| MPAE* (ours) | N/A | 8 | 32.90 | 66.17 | 33.51 | 65.05 |
| 25 | 39.28 | 68.87 | 37.22 | 68.04 |
| 50 | 53.65 | 74.22 | 55.10 | 73.52 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
+ 0.391,
+ 0.483,
+ 0.462
+ ],
+ "angle": 0,
+ "content": "Table 1. Quantitative comparisons with state-of-the-art methods on PartImageNet OOD and Segmentation datasets. \\(N_{\\mathrm{c}}\\) represents the number of categories, which is 109 and 158 for the OOD and Segmentation datasets respectively. \\(\\dagger =\\) using a partially fine-tuned pretrained backbone, \\(\\star =\\) using a frozen pretrained backbone."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.494,
+ 0.462,
+ 0.51
+ ],
+ "angle": 0,
+ "content": "4.3. Comparisons with State-of-the-art Methods"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.52,
+ 0.483,
+ 0.867
+ ],
+ "angle": 0,
+ "content": "PartImageNet OOD: the quantitative results of MPAE and other state-of-the-art methods on PartImageNet OOD dataset are reported in Table 1, and some randomly chosen qualitative results are shown in Fig. 3. MPAE achieves highly competitive performance among both unsupervised and weakly-supervised methods. In the second row of Fig. 3, we observe that some small, round areas are identified as separate parts by DINO. These unreasonable parts result from directly clustering foreground features, which identifies certain near-outlier features as separate parts. By considering part appearance into clustering through our paradigm, we observe significant improvements in NMI of \\(71.62\\%\\), \\(24.86\\%\\) and \\(41.89\\%\\) compared to DINO when \\(K = 8, 25, 50\\) respectively. Due to the complex scenarios, it is difficult to align high-level semantics from part descriptors with object shapes through reconstruction. As a result, the parts discovered by Xia et al. are often incomplete. Although PDiscoFormer and PDiscoNet employ classification loss for part discovery in a weakly supervised manner, they do not further align high-level semantics with object shapes. Consequently, their predicted masks do not match objects as closely as those predicted by MPAE. With the same backbone (frozen ViT-B/14), MPAE still outperforms them."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.871,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "PartImageNet Segmentation increases category number \\(N_{\\mathrm{C}}\\) from 109 to 158, which means larger variance in ob"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.52,
+ 0.091,
+ 0.901,
+ 0.394
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.513,
+ 0.407,
+ 0.907,
+ 0.449
+ ],
+ "angle": 0,
+ "content": "Figure 3. Some qualitative results of MPAE (ours) and other state-of-the-art unsupervised and weakly-supervised methods on PartImageNet OOD dataset (\\(K = 50\\))."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.477,
+ 0.907,
+ 0.628
+ ],
+ "angle": 0,
+ "content": "ject appearance and shape. Therefore, as shown in Table 1, the metrics in both NMI and ARI of PDiscoFormer and Xia et al. degrade slightly. However, by using image restoration to constrain the learning and by exploring part similarities across different categories, MPAE successfully maintains strong robustness on this more challenging dataset. Compared to PDiscoFormer, MPAE still achieves an impressive improvement of \\(65.16\\%\\) and \\(25.06\\%\\) respectively in NMI when \\(K = 8\\) and 50, even though PDiscoFormers employ both partially fine-tuned backbone and category labels."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.629,
+ 0.909,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "CUB: MPAE also achieves highly competitive performance on CUB (Table 2 and Fig. 4), demonstrating its effectiveness in part discovery within a single category. By implicitly clustering patch features with similar appearances and allowing for the absence of specific parts, MPAE can robustly discover meaningful bird parts in cases involving shadows, self-occlusion, and reflections (see first, second and fourth columns in Fig. 4). With the same frozen pretrained ViT-B/14, MPAE outperforms PDiscoFormer in all metrics, despite not using any labels for training. Compared to PDiscoFormer with a partially fine-tuned ViT-B/14, MPAE still outperforms it by \\(10.45\\%\\), \\(7.66\\%\\) and \\(19.22\\%\\) in NME, NMI and ARI respectively when \\(K = 16\\). CelebA: as shown in Fig. 4, the masks predicted by MPAE accurately follow the entire facial region, resulting in significantly better qualitative results. Despite less challenging scenarios, the masks predicted by Xia et al. remain incomplete and fail to cover the entire face region. Other methods"
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+ [
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+ "content": "Figure 4. Some visualized part discovery results of MPAE (ours) and state-of-the-art methods on CUB dataset (\\(K = 16\\)) and CelebA dataset (\\(K = 8\\)). We use red boxes to highlight the regions with poor part discovery results."
+ },
+ {
+ "type": "table",
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+ "angle": 0,
+ "content": "| Method | Label | K=4 (%) | K=8 (%) | K=16 (%) |
| NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Species label | 11.51 | 29.74 | 14.04 | 11.60 | 35.72 | 15.90 | 12.60 | 43.92 | 21.01 |
| PDiscoNet [35] | Species label | 9.12 | 37.82 | 15.26 | 8.52 | 50.08 | 26.96 | 7.64 | 56.87 | 38.05 |
| Choudhury et al. [6] | Foreground mask | 9.20 | 43.50 | 19.60 | - | 51.50 | 28.30 | - | - | - |
| PDiscoNet + ViT-B/14 | Species label | 7.70 | 52.59 | 26.66 | 6.34 | 65.01 | 37.90 | 5.95 | 68.63 | 43.41 |
| PDiscoFormer + ViT-B/14* [2] | Species label | 8.19 | 52.88 | 23.22 | 6.23 | 67.59 | 41.35 | 6.44 | 69.54 | 49.99 |
| PDiscoFormer + ViT-B/14† | Species label | 7.41 | 58.13 | 25.11 | 6.54 | 69.87 | 42.76 | 5.74 | 73.38 | 55.83 |
| Unsupervised part discovery |
| DINO* [1] | N/A | - | 31.18 | 11.21 | - | 47.21 | 19.76 | - | 50.57 | 26.14 |
| Xia et al.* [40] | N/A | 9.92 | 45.22 | 19.40 | 8.58 | 52.42 | 26.42 | 8.27 | 53.52 | 33.95 |
| MPAE* (ours) | N/A | 7.75 | 58.93 | 33.73 | 5.53 | 68.24 | 45.85 | 5.14 | 79.00 | 66.56 |
"
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+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Quantitative comparisons with state-of-the-art methods on CUB. \\(\\dagger=\\) using partially fine-tuned backbone, \\({}^{*}=\\) using a frozen pretrained backbone."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Method | Label | K=4 (%) | K=8 (%) | K=16 (%) |
| NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Attribute label | 8.75 | 56.69 | 34.74 | 7.96 | 54.80 | 34.74 | 7.62 | 62.22 | 41.01 |
| PDiscoNet [35] | Identity label | 11.11 | 75.97 | 69.53 | 9.82 | 62.61 | 51.89 | 9.46 | 77.43 | 70.58 |
| Unsupervised part discovery |
| DINO* [1] | N/A | 11.36 | 1.38 | 0.01 | 10.74 | 1.12 | 0.01 | - | 3.29 | 0.06 |
| GANseg‡ [19] | N/A | 12.26 | 41.71 | 28.06 | 6.18 | 67.28 | 56.23 | - | - | - |
| Xia et al.* [40] | N/A | 12.28 | 50.69 | 34.57 | 10.24 | 58.35 | 46.78 | - | - | - |
| MPAE* (ours) | N/A | 11.44 | 56.13 | 37.20 | 7.55 | 59.64 | 41.72 | 7.10 | 70.21 | 60.33 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Quantitative comparisons with state-of-the-art methods on CelebA. \\(\\star =\\) using a frozen pretrained backbone, \\(\\ddagger =\\) using a multi-stage self-training strategy."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.764,
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+ "angle": 0,
+ "content": "also misidentify some background regions as foreground parts. However, CelebA provides only five keypoints near the eyes, nose, and mouth for metric calculation, which is insufficient to reflect the improvements achieved by MPAE, as presented in Table 3."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Ablation Studies"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Influence of loss functions: to study the effectiveness of the loss functions used in MPAE, we conduct ablation stud"
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "ies on PartImageNet Segmentation dataset. The quantitative and qualitative results are shown in Table 4 and Fig. 5 respectively. Foreground loss \\(\\mathcal{L}_{\\mathrm{f}}\\) and background loss \\(\\mathcal{L}_{\\mathrm{b}}\\) are crucial for preventing the model from identifying all pixels as background or foreground. Otherwise, the learned model converges to a trivial solution. Without the prior knowledge provided by Total variation loss \\(\\mathcal{L}_{\\mathrm{v}}\\), the pixels identified as foreground regions cannot form connected and concentrated parts. Entropy loss \\(\\mathcal{L}_{\\mathrm{e}}\\) leads to more sta"
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+ [
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.097,
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+ 0.098
+ ],
+ "angle": 0,
+ "content": "Raw Image Without \\(\\mathcal{L}_{\\mathrm{f}}\\) Without \\(\\mathcal{L}_{\\mathrm{b}}\\) Without \\(\\mathcal{L}_{\\mathrm{v}}\\) Without \\(\\mathcal{L}_{\\mathrm{c}}\\) Without \\(\\mathcal{L}_{\\mathrm{r}}\\) Without \\(\\mathcal{L}_{\\mathrm{s}}\\) Full Model"
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. Qualitative results from the ablation studies of the loss functions on PartImageNet Segmentation dataset (\\(K = 50\\)). From left to right: (1) raw images, models trained without (2) \\(\\mathcal{L}_{\\mathrm{f}}\\), (3) \\(\\mathcal{L}_{\\mathrm{b}}\\), (4) \\(\\mathcal{L}_{\\mathrm{v}}\\), (5) \\(\\mathcal{L}_{\\mathrm{e}}\\), (6) \\(\\mathcal{L}_{\\mathrm{r}}\\), (7) \\(\\mathcal{L}_{\\mathrm{s}}\\) and (8) nothing (full model)."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Method | K=8 (%) | K=25 (%) | K=50 (%) |
| NMI↑ | ARI↑ | NMI↑ | ARI↑ | NMI↑ | ARI↑ |
| Without Lf | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Without Lb | 30.91 | 73.20 | 33.67 | 67.85 | 39.36 | 55.24 |
| Without Lv | 18.30 | 20.62 | 13.52 | 4.54 | 14.37 | 4.08 |
| Without Le | 31.21 | 63.27 | 27.48 | 54.93 | 52.51 | 73.08 |
| Without LR | 25.60 | 57.39 | 31.53 | 63.39 | 22.32 | 49.73 |
| Without Ls | 55.69 | 76.54 | 57.70 | 76.97 | 56.42 | 74.03 |
| Full model | 33.51 | 65.05 | 37.22 | 68.04 | 55.10 | 73.52 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Performance comparisons of MPAE without different loss functions on the PartImageNet Segmentation dataset in the setting of \\( K = 8,25,50 \\)."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Masking Ratio r | 50% | 75% | 80% | 85% | 90% | 95% | 100% |
| NMI (%) ↑ | 45.50 | 50.11 | 52.20 | 52.70 | 55.10 | 54.63 | 43.39 |
| ARI (%) ↑ | 70.25 | 70.89 | 70.90 | 71.85 | 73.52 | 73.23 | 41.29 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Table 5. Performance comparisons of MPAE with different masking ratio \\( r \\) on the PartImageNet Segmentation dataset in the setting of \\( K = {50} \\) ."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.628,
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+ 0.825
+ ],
+ "angle": 0,
+ "content": "ble and smooth part boundaries by enforcing that each pixel highly responds to a unique part descriptor. The absence of reconstruction loss \\(\\mathcal{L}_{\\mathrm{r}}\\) results in a failure to align part descriptors with actual part shapes. Consequently, the predicted masks contain only rough regions without clear part boundaries. Without semantic constraint \\(\\mathcal{L}_{\\mathrm{s}}\\), the model identifies the regions with less semantic similarity as the same part. In some cases, the learned model even degrades into a foreground segmentation model. Although this degradation may improve the numerical metrics in NMI and ARI, the learned model cannot achieve the goal of part discovery. Therefore, all constraints used in MPAE are essential for learning a robust model for unsupervised part discovery."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Influence of the masking ratio \\( r \\): the quantitative results of MPAE with different masking ratios \\( r \\) are reported in Table 5. When \\( r < 90\\% \\), a higher \\( r \\) results in more features in the filled feature map \\( R \\) comes from part descriptors \\( D \\). Therefore, by aligning the part descriptors \\( D \\)"
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.52,
+ 0.089,
+ 0.903,
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+ "angle": 0,
+ "content": "| Change from MPAE model: | NMI (%)↑ | ARI (%)↑ |
| Lf → Area loss in [40] | 1.90 | -0.14 |
| Lp → Presence loss in [2] | 42.45 | 60.24 |
| Ld → Concentration loss in [21] | 17.29 | 18.74 |
| Part number K → 4Nc | 47.59 | 70.71 |
| MPAE (our best model) | 55.10 | 73.52 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "Table 6. Comparisons of our optimized losses and designs with previous ones on the PartImageNet Segmentation dataset in the setting of \\( K = 50 \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.256,
+ 0.907,
+ 0.361
+ ],
+ "angle": 0,
+ "content": "with object part shapes, a stronger constraint can be applied to the similarity maps \\( P \\), requiring them to better match the actual part shapes. As a results, we observe an improvement in performance. When \\( r > 90\\% \\), a higher \\( r \\) results in insufficient unmasked patches containing low-level appearance information to guide the alignment between descriptors and part shapes. Therefore, the optimal masking ratio \\( r \\) is \\( 90\\% \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.362,
+ 0.909,
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+ ],
+ "angle": 0,
+ "content": "Improvements of our optimized constraints and designs: The area loss in [40] requires all parts to appear in each image. But, it is impossible for every object to contain all 50 parts. Consequently, \\(\\mathcal{L}_{\\mathrm{a}}\\) leads to a collapse during training. The image classification loss in [2] ensures that each image to have at least one discovered part, as the embedding for classification cannot be a zero vector. Without any labels, presence loss in [2] cannot guarantee that unsupervised methods discover at least one part in each image. Therefore, some images may not have any discovered parts, which further leads to a degradation in metrics. The concentration loss in [21] penalizes pixels that are farther from the part center more heavily, which prevents the predicted parts from accurately following their actual shapes, whereas \\(\\mathcal{L}_{\\mathrm{d}}\\) addresses this imbalance. As [40], we also implement a model that simply decomposes each category into four parts without exploring their semantic similarities (\\(K \\to 4N_{\\mathrm{c}}\\)). Consequently, the number of training samples for each part significantly decreases, leading to reduced robustness."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "More ablation studies and visualized results are included in the Appendix."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.72,
+ 0.907,
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+ ],
+ "angle": 0,
+ "content": "In this paper, we present a novel paradigm (MPAE) with looser yet effective constraints for more robust unsupervised part discovery. By restoring masked image patches using the corresponding part descriptors, MPAE effectively aligns their high-level semantics with the part shapes under the guidance of low-level appearance features from un-masked patches. As a result, MPAE predicts masks that closely match the actual shapes of corresponding parts. The optimized constraints enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner, effectively addressing challenges posed by occlusion and diverse object categories."
+ },
+ {
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+ [
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+ "angle": 0,
+ "content": "References"
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+# Unsupervised Part Discovery via Descriptor-Based Masked Image Restoration with Optimized Constraints
+
+Jiahao Xia $^{1}$ , Yike Wu $^{1}$ , Wenjian Huang $^{2}$ , Jianguo Zhang $^{2}$ , Jian Zhang $^{*,1}$
+
+$^{1}$ Faculty of Engineering and IT, University of Technology Sydney
+
+$^{2}$ Dept. of Comp. Sci. and Eng., Southern University of Science and Technology
+
+Jiahao.Xia-1@uts.edu.au, Yike.Wu@student.uts.edu.au, {huangwj, zhangjg} $@$ sustech.edu.cn, Jian.Zhang@uts.edu.au
+
+# Abstract
+
+Part-level features are crucial for image understanding, but few studies focus on them because of the lack of fine-grained labels. Although unsupervised part discovery can eliminate the reliance on labels, most of them cannot maintain robustness across various categories and scenarios, which restricts their application range. To overcome this limitation, we present a more effective paradigm for unsupervised part discovery, named Masked Part Autoencoder (MPAE). It first learns part descriptors as well as a feature map from the inputs and produces patch features from a masked version of the original images. Then, the masked regions are filled with the learned part descriptors based on the similarity between the local features and descriptors. By restoring these masked patches using the part descriptors, they become better aligned with their part shapes, guided by appearance features from unmasked patches. Finally, MPAE robustly discovers meaningful parts that closely match the actual object shapes, even in complex scenarios. Moreover, several looser yet more effective constraints are proposed to enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner. This provides the foundation for addressing challenges posed by occlusion and for exploring part similarity across multiple categories. Extensive experiments demonstrate that our method robustly discovers meaningful parts across various categories and scenarios. The code is available at the project website1.
+
+# 1. Introduction
+
+Decomposing objects into meaningful parts drives models to gain better image understanding and further improves the performance of downstream tasks, such as person search [27], fine-grained classification [2, 35] and be
+
+
+Figure 1. MPAE uses similarity maps between local image features and part descriptors to assign these descriptors to fill masked regions in a randomly masked version of the inputs. The restoration implicitly clusters the features of the restored patches that share similar appearance, further aligning low-level appearance in unmasked patches and high-level semantics of part descriptors. This drives similarity maps to closely match the actual part shapes.
+
+havior analysis [25]. But the high cost of part-level label results in a scarcity of training samples. Consequently, part-level feature learning has received much less attention compared to instance-level feature learning.
+
+To eliminate the reliance on part-level labels, existing methods achieve part discovery mainly through two strategies: reconstruction [12, 19, 21, 23, 32, 40, 41, 43] and clustering [4, 6]. By directly reconstructing the input images using learned part descriptors, the descriptors are expected to align with the part shapes, allowing these part descriptors to further predict part masks. However, to discover meaningful parts, these descriptors are designed to learn high-level semantics rather than low-level appearance [1], which prevents such reconstruction and alignment, especially in complex scenarios. Clustering-based methods use foreground masks to remove irrelevant regions and directly cluster foreground features, regardless of their actual appearance similarity. Some near-outlier features are identified as separate parts, leading to the discovery of unreasonable parts.
+
+To address these limitations and extend unsupervised
+
+part discovery to more complex scenarios, we propose a novel paradigm, named Mask Part Autoencoder (MPAE). As shown in Fig. 1, instead of directly using part descriptors for image reconstruction, we first calculate the similarities between these descriptors and a feature map learned from the input. Based on the similarity maps, we assign these descriptors to fill the masked regions in a randomly masked version of inputs. By utilizing both filled part descriptors and unmasked patch features within the same part regions to generate image patches with similar appearances, these features are implicitly clustered together [42]. The appearance features of unmasked patches (e.g., boundaries and textures) further align the high-level semantics of the part descriptors with the part shapes. Guided by part appearance, the similarity maps closely match the shapes of corresponding parts even in complex scenarios. Thus, they can be viewed as pixel-level masks of the discovered parts.
+
+Moreover, without using category labels, it is difficult for unsupervised methods to determine which object parts are present or absent in an image, because different categories consist of different types of parts. As a result, most existing methods [12, 19, 23, 41] are restricted to a single category and do not consider the absence of individual parts. However, it is still impossible for all parts to appear in every image, even within a single category, because objects can be occluded. Although [40] achieves part discovery on a dataset with multiple categories, it still relies on category labels to determine which parts appear before part discovery. Therefore, we propose a looser constraints to enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner. Additionally, a more effective constraint is proposed to ensure that the MPAE discovers part-level masks, as the model can easily degrade to predicting only a single instance-level mask when part absence is allowed. This provides a foundation for tackling challenges posed by occlusion. As a result, these optimized constraints allow MPAE to leverage similar parts across different categories to achieve more robust part discovery without relying on any labels.
+
+To evaluate the effectiveness of MPAE and our optimized constraints, extensive experiments are conducted on four widely used benchmarks, including two with multiple categories and two with a single category. The experimental results clearly demonstrate that MPAE robustly discovers meaningful object parts across diverse categories and achieves more competitive performance on all datasets than other state-of-the-art methods.
+
+The main contributions of this paper can be summarized as followings:
+
+- We present a novel paradigm named Masked Part Autoencoder (MPAE), which utilizes low-level appearance features of the unmasked patches to align the part descriptors with actual part shapes. Consequently, MPAE discovers
+
+meaningful parts that closely match the object shapes.
+
+- Several looser yet effective constraints are proposed to enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner. As a result, MPAE can leverage similar parts across various categories to achieve more robust part discovery.
+- Extensive experiments are carried out on four widely-used benchmarks. The results show that our method can robustly discover reasonable object parts in complex scenarios and achieve highly competitive performance.
+
+# 2. Related works
+
+# 2.1. Unsupervised / Self-supervised Learning
+
+Many works in natural language processing (NLP) [10, 28] show unsupervised / self-supervised learning learns more effective features for downstream tasks than supervised learning. Inspired by their success, recent works [4, 5, 8, 13, 14, 17, 18, 26, 30, 45] also adopt unsupervised / self-supervised learning to improve the effectiveness of visual features. In addition to performance improvements, some new properties also emerge in Vision Transformer (ViT) [11] with the use of unsupervised / self-supervised learning. Caron et al. [4] found using momentum encoder [16] and multi-crop augmentation [3] drives the ViT features from the same category to have high similarity. Based on this properties, Wang et al. [39] and Wang et al. [37, 38] achieve foreground segmentation, instance segmentation, and video instance segmentation, respectively, in an unsupervised manner by using normalized cut [31] to directly group self-similar regions. Although learned ViT features within the same part exhibit higher similarity [30, 45], discovering object parts from images is still much more challenging than discovering instances. The main reason is that features from different parts also have very high similarity, resulting in less consistent semantics and boundaries in the discovered parts. Unfortunately, there are relatively few works that focus on using unsupervised / self-supervised features to discover meaningful and consistent object parts.
+
+# 2.2. Part Discovery
+
+Part discovery aims to identify meaningful object parts with consistent semantics and predict their pixel-level masks. Existing works mainly achieve part discovery through weakly-supervised or unsupervised learning. Weakly-supervised part discovery utilizes instance-level labels, such as category [2, 20, 35] and identity [27, 44], to discover relevant parts with pixel-level masks during training. Then, part-level features are extracted using these masks and further boost the performance of downstream tasks. Nevertheless, without aligning their the semantics from part embeddings with actual object appearances through reconstruction, their part masks do not follow the actual object bound
+
+aries well, making them insufficiently fine-grained.
+
+Unsupervised part discovery is more challenging than weakly-supervised part discovery because no labels are provided during training. Early works discover meaningful object parts with rough part masks by factorizing deep features [7] or spatial embeddings [34]. Other methods [1, 6] directly cluster the foreground features across all images to discover meaningful parts. Nevertheless, the semantics and boundaries of the predicted part masks are not sufficiently stable due to appearance biases in each image. Most state-of-the-art methods [12, 21, 23, 32, 40, 41, 43] employ image reconstruction as a learning objective to align the part descriptors with the actual part shapes. Therefore, these part descriptors can further predict the part masks with consistent semantics. However, these descriptors are designed to capture high-level semantics rather than low-level appearance, which hinders reconstruction and alignment, ultimately degrading part discovery, especially in complex scenarios. Amir et al. [1] demonstrate that directly clustering self-supervised features in foreground regions can also discover meaningful parts. Nevertheless, they only consider feature similarity, disregarding actual appearance similarity. As a result, some near-outlier features are identified as independent parts, leading to unreasonably segmented parts. Therefore, robustly discovering meaningful parts in an unsupervised manner remains a significant challenge.
+
+# 3. Methodology
+
+Unsupervised part discovery aims to learn a model that can parse all objects into a total of $K$ parts without any labels. Given an input image $\pmb{I} \in \mathbb{R}^{H_{\mathrm{I}} \times W_{\mathrm{I}} \times 3}$ , the learned model predicts pixel-level mask $M_{\mathrm{p}} \in \{0,1\}^{H_{\mathrm{I}} \times W_{\mathrm{I}} \times (K + 1)}$ to assign each pixel into one of $K$ parts or background, where $(H_{\mathrm{I}}, W_{\mathrm{I}})$ is the size of the input image.
+
+To achieve this goal, we present a novel paradigm, named Masked Part Autoencoder (MPAE), and further incorporate it with several optimized constraints. In what follows, we first detail the training and inference pipeline of MPAE, followed by an introduction to our optimized constraints and their corresponding functions.
+
+# 3.1. Masked Part Autoencoder
+
+# 3.1.1. Training pipeline
+
+The overall training pipeline of MPAE is shown in Fig. 2. It consists of four blocks: (a) random masking block, (b) descriptor extraction block, (c) matching block, (d) image restoration block.
+
+Random masking block first divides the input image $\pmb{I}$ into patches of size $p$ . The patched image $\pmb{I}^{\mathrm{p}}$ is denoted as $\pmb{I}^{\mathrm{p}} \in \mathbb{R}^{\frac{H_{\mathrm{I}}}{p} \times \frac{W_{\mathrm{I}}}{p} \times 3p^{2}}$ . A binary mask $M = \{0,1\}^{\frac{H_{\mathrm{I}}}{p} \times \frac{W_{\mathrm{I}}}{p}}$ is then generated to randomly mask out a specified proportion $r$ of the image patches. As MAE [18], these masked
+
+patches will not be used in the following training. Only visible patches are finally fed into the MPAE encoder to learn unmasked patch features $\pmb{F}^{\mathrm{U}} \in \mathbb{R}^{\frac{H_{\mathrm{I}} \times W_{\mathrm{I}}}{p \times p} (1 - r) \times C}$ , where $C$ is the dimension of the unmasked patch feature.
+
+Descriptor extraction block is designed to learn part-level descriptors from input images. Specifically, as [40], we replace the class embedding of a classical ViT with $K + 1$ embeddings to extract $K + 1$ descriptors. By incorporating MPAE with appropriate constraints, each embedding learns to specialize in one potential part, adaptively aggregating image features to produce the corresponding part descriptor. The $K + 1$ part descriptors $D \in \mathbb{R}^{(K + 1)\times C}$ include $K$ descriptors for foreground parts and 1 for the background, where the descriptor dimension $C$ is the same as that of $F^{\mathrm{U}}$ .
+
+To determine how to assign the sparse part descriptors $D$ to fill the masked regions, we employ a frozen pre-trained ViT, followed by a trainable $1 \times 1$ convolutional layer, to extract a dense feature map $F \in \mathbb{R}^{H_{\mathrm{F}} \times W_{\mathrm{F}} \times C}$ , where $(H_{\mathrm{F}}, W_{\mathrm{F}})$ is the size of the feature map. By matching $F$ with $D$ , we can obtain a similarity map for each part (as detailed in the following paragraphs). Based on the similarity maps, we can fill the masked patches using $D$ . Moreover, it enables PartFormer to leverage knowledge from the ViT, pre-trained through unsupervised or self-supervised learning, to discover more reasonable object parts.
+
+Matching block calculates similarity maps $\pmb{P}$ between $D$ and $F$ , which can be defined as:
+
+$$
+P _ {i, j, k} = \frac {\exp \left(\boldsymbol {D} _ {k} \cdot \boldsymbol {F} _ {i , j}\right)}{\sum_ {k ^ {\prime} = 1} ^ {K + 1} \exp \left(\boldsymbol {D} _ {k ^ {\prime}} \cdot \boldsymbol {F} _ {i , j}\right)}, \tag {1}
+$$
+
+where $\pmb{F}_{i,j}$ indicates the pixel-level feature at $(i,j)$ of $\pmb{F}$ , and $D_{k}$ is the part descriptor for the $k$ -th part, with $i \in \{1,\dots ,W_{\mathrm{F}}\}$ , $j \in \{1,\dots ,H_{\mathrm{F}}\}$ , and $k \in \{1,\dots ,K + 1\}$ . $P_{i,j,k}$ represents the normalized similarity between the $D_{k}$ and $F_{i,j}$ . Based on the similarity map, the part descriptors are assigned to fill the masked regions and reform a dense feature map $\pmb{R}$ , which can be formulated as:
+
+$$
+\boldsymbol {R} _ {i, j} = \left\{ \begin{array}{l l} \boldsymbol {F} _ {i, j} ^ {\mathrm {U}} & , M _ {i, j} = 0, \\ \sum_ {k = 1} ^ {K + 1} \left(P _ {i, j, k} \boldsymbol {D} _ {k}\right) & , M _ {i, j} = 1, \end{array} \right. \tag {2}
+$$
+
+where $\pmb{R}_{i,j}$ is the feature vector of the filled feature map $\pmb{R}$ at position $(i,j)$ . $M_{i,j}$ is the value of the binary mask $M$ , indicating that the position $(i,j)$ is masked or not in random masking block.
+
+Image restoration block feeds $\pmb{R}$ into the MPAE decoder to restore the masked patches, which can be written as:
+
+$$
+\mathcal {L} _ {\mathrm {r}} = \frac {1}{2} \| \boldsymbol {I} - \boldsymbol {I} ^ {\prime} \| _ {1} + \frac {1}{2} \| \Phi (\boldsymbol {I}) - \Phi (\boldsymbol {I} ^ {\prime}) \| _ {1}, \tag {3}
+$$
+
+where $\pmb{I}^{\prime}$ is the restored image and $\Phi$ is a frozen VGG-19 [33]. Directly using the L1 loss constraint for image
+
+
+Figure 2. Training and inference pipelines of MPAE. The training pipeline consists of four blocks: (a) random masking block, (b) descriptor extraction block, (c) matching block, and (d) image restoration block. (a) randomly masks out a large proportion of patches and extracts patch features $\pmb{F}^{\mathrm{U}}$ from the unmasked patches using MPAE encoder. The input image $\pmb{I}$ is also fed into (b), after being patchified, to extract part descriptors $\pmb{D}$ and a feature map $\pmb{F}$ . By matching $\pmb{D}$ with $\pmb{F}$ using Hadamard product and a Softmax function, we generate a similarity map for each descriptor in (c). Based on these similarity maps $\pmb{P}$ , we use $\pmb{D}$ to fill the masked regions and reconstruct a feature map $\pmb{R}$ . In (d), $\pmb{R}$ is further utilizes for image restoration, aligning the high-level semantics of the $\pmb{D}$ with the corresponding part shapes. The inference pipeline directly employs $\pmb{D}$ as mask prototypes to predict part-level masks from the Interpolated feature map $\pmb{F}'$ .
+
+restoration, as in [18], can lead to structure deviations between the raw and restored images [18], which in turn causes the features in different parts to be poorly clustered, regardless of their actual appearance similarity. Therefore, in addition to using the L1 loss, we employ VGG-19 to encourage greater structural similarity between the restored image and the input image as the perceptual loss [22].
+
+The functions of this image restoration are threefold: 1) It retains low-level appearance features in MPAE through the unmasked patch features $F^{\mathrm{U}}$ , thereby compensating for the lack of low-level appearance features in the part descriptors $D$ . 2) It implicitly clusters $F^{\mathrm{U}}$ and $D$ within the same part region together in latent space by utilizing them to produce the image patches with similar appearance. Guided by low-level appearance features from $F^{\mathrm{U}}$ , the high-level semantics from $D$ are aligned more accurately with the actual part shapes compared to directly using $D$ from image reconstruction. 3) This alignment further constrains the similarity maps $P$ , encouraging them to more closely match the actual shapes of their corresponding parts, even in highly complex scenarios. Consequently, $P$ can serve as pixel-level masks for the discovered parts.
+
+# 3.2. Learning Constraints
+
+To ensure robust part discovery, we incorporate MPAE with three types of optimized constraints: the presence constraint $\mathcal{L}_{\mathrm{p}}$ , the semantic consistency constraint $\mathcal{L}_{\mathrm{s}}$ , and the distribution constraint $\mathcal{L}_{\mathrm{d}}$ .
+
+Presence constraint $\mathcal{L}_{\mathrm{p}} = \mathcal{L}_{\mathrm{f}} + \mathcal{L}_{\mathrm{b}}$ where $\mathcal{L}_{\mathrm{f}}$ and $\mathcal{L}_{\mathrm{b}}$
+
+represent the foreground and background presence losses respectively. $\mathcal{L}_{\mathrm{p}}$ is directly applied to $P$ to ensure the presence of $K$ foreground parts across the entire data and the presence of background in every image.
+
+$\mathcal{L}_{\mathrm{f}}$ divides each mini-batch into $N_{\mathrm{g}}$ mini-groups with $G$ samples. Then, $\mathcal{L}_{\mathrm{f}}$ can be calculated as:
+
+$$
+\mathcal {L} _ {\mathrm {f}} = \frac {1}{N _ {\mathrm {g}}} \sum_ {n _ {\mathrm {g}} = 1} ^ {N _ {\mathrm {g}}} (2 - \frac {1}{G} \sum_ {g = 1} ^ {G} \max _ {i, j, k} P _ {i, j, k} ^ {g, n _ {\mathrm {g}}} - \frac {1}{K} \sum_ {k = 1} ^ {K} \max _ {i, j, g} P _ {i, j, k} ^ {g, n _ {\mathrm {g}}}), \tag {4}
+$$
+
+where $P_{i,j,k}^{g,n_{\mathrm{g}}}$ is the similarity $P_{i,j,k}$ of $g$ -th sample in $n_{\mathrm{g}}$ -th mini-group. Instead of requiring all parts to appear in each image as previous unsupervised methods, $\mathcal{L}_{\mathrm{f}}$ only encourages them to appear at least once in each mini-group and each image to contain at least one part. This looser constraint provides the basis for MPAE to identify the presence of parts across various scenarios and categories. The influence of the mini-group will be discussed in the Appendix.
+
+$\mathcal{L}_{\mathrm{b}}$ encourages the background to appear near the boundaries of each image. Inspired by [2], we define $\mathcal{L}_{\mathrm{b}}$ as:
+
+$$
+\mathcal {L} _ {\mathrm {b}} = - \frac {1}{N _ {\mathrm {g}} G} \sum_ {n _ {\mathrm {g}} = 1} ^ {N _ {\mathrm {g}}} \sum_ {g = 1} ^ {G} \log \left(\max _ {i, j} d _ {i, j} P _ {i, j, K + 1} ^ {g, n _ {\mathrm {g}}}\right), \tag {5}
+$$
+
+where $d_{i,j}$ is the distance from position $(i,j)$ to the image center. $d_{i,j}$ can be calculated as:
+
+$$
+d _ {i, j} = 2 \left(\frac {i - 1}{W _ {\mathrm {F}} - 1} - \frac {1}{2}\right) ^ {2} + 2 \left(\frac {j - 1}{H _ {\mathrm {F}} - 1} - \frac {1}{2}\right) ^ {2}. \tag {6}
+$$
+
+Incorporated with $\mathcal{L}_{\mathrm{f}}$ and $\mathcal{L}_{\mathrm{b}}$ , our model also learns to distinguish the $K$ foreground parts and the background region.
+
+Semantic constraint $\mathcal{L}_{\mathrm{s}}$ : because $\mathcal{L}_{\mathrm{p}}$ only requires each image to contain at least one part, the model tends to simply segment out the entire foreground object, thereby degrading into an instance-discovery model. By encouraging each part descriptor to align only with the local features that exhibit very high similarity, $\mathcal{L}_{\mathrm{s}}$ ensures that the model decomposes the target into multiple object parts with consistent semantics. $\mathcal{L}_{\mathrm{s}}$ can be formulated as:
+
+$$
+\mathcal {L} _ {\mathrm {s}} = - \frac {1}{K} \sum_ {k = 1} ^ {K} \log \frac {M ^ {k} e ^ {s \left(\cos \left(\theta_ {(k , k)} + m\right)\right)}}{M ^ {k} e ^ {s \left(\cos \left(\theta_ {(k , k)} + m\right)\right)} + \sum_ {t = 1 , t \neq k} ^ {K} M ^ {t} e ^ {s \cos \theta_ {(t , k)}}}, \tag {7}
+$$
+
+where $M_{k}\in \{0,1\}$ represents the presence of the $k$ -th part. When $\sum_{i = 1}^{W_{\mathrm{F}}}\sum_{j = 1}^{H_{\mathrm{F}}}P_{i,j,k} < = 0.001,M_{k} = 0$ , else, $M_{k} = 1$ . $m$ and $s$ are two hyperparameters. $\theta_{(k,t)}$ is the angle between the $k$ -the part descriptor $D_{k}$ and the mean feature vector of $t$ -th part region $\bar{F}_t$ in latent space. $\bar{F}_t$ and $\cos (\theta_{(k,t)})$ are defined as:
+
+$$
+\bar {\boldsymbol {F}} _ {t} = \frac {\sum_ {i = 1} ^ {W _ {1}} \sum_ {j = 1} ^ {H _ {1}} P _ {i , j , t} \boldsymbol {F} _ {i , j}}{\sum_ {i = 1} ^ {W _ {1}} \sum_ {j = 1} ^ {H _ {1}} P _ {i , j , t}}, \tag {8}
+$$
+
+$$
+\cos \left(\theta_ {(t, k)}\right) = \frac {\boldsymbol {D} _ {k} \cdot \bar {\boldsymbol {F}} _ {t}}{\| \boldsymbol {D} _ {k} \| \| \bar {\boldsymbol {F}} _ {t} \|.} \tag {9}
+$$
+
+As [9], $m$ enables $\mathcal{L}_s$ to still have a certain gradient value for further maximizing $\cos(\theta_{(k,k)})$ when $\theta_{(k,k)}$ is very small, and $s$ controls the smoothness of $\mathcal{L}_s$ . By minimizing $\theta_{(k,k)}$ and maximizing $\theta_{(t,k)}$ , the discovered parts across different objects have more consistent semantics. Moreover, the use of $M^k$ enables $\mathcal{L}_s$ to only consider the semantic consistency of those appeared parts, providing the basis to constrain the semantic consistency across multiple categories.
+
+Distribution constraint $\mathcal{L}_{\mathrm{d}} = \mathcal{L}_{\mathrm{v}} + \mathcal{L}_{\mathrm{e}}$ , where $\mathcal{L}_{\mathrm{v}}$ and $\mathcal{L}_{\mathrm{e}}$ are total variation loss [29] and entropy loss respectively. $\mathcal{L}_{\mathrm{d}}$ encourages the predicted probability map $P$ to better follow the shapes of object parts.
+
+$\mathcal{L}_{\mathrm{v}}$ minimizes the spatial gradient of the predicted $P$ which can be formulated as:
+
+$$
+\mathcal {L} _ {\mathrm {v}} = \frac {1}{H _ {\mathrm {F}} W _ {\mathrm {F}}} \sum_ {k = 1} ^ {K + 1} \sum_ {i = 1} ^ {W _ {\mathrm {F}}} \sum_ {j = 1} ^ {H _ {\mathrm {F}}} | \nabla P _ {i, j, k} |, \tag {10}
+$$
+
+where $\nabla P_{i,j,k}$ represents the spatial image gradient at position $(i,j)$ on the probability map for the $k$ -th part. The function of $\mathcal{L}_{\mathrm{v}}$ is the same as that of the concentration loss [21], encouraging pixels with high confidence for the same part to form a connected region. However, the concentration loss penalizes pixels that are far from the part center much more heavily than those that are close. This imbalance further causes the discovered parts to take on an approximately
+
+square shape. $\mathcal{L}_{\mathrm{v}}$ successfully eliminates this imbalance by calculating the gradient of $P$ , enabling the discovered parts to more accurately follow the shapes of objects, even when they are very complex.
+
+$\mathcal{L}_{\mathrm{e}}$ ensures that the distribution at any position on $P$ has high similarity in only one part descriptor by penalizing its entropy:
+
+$$
+\mathcal {L} _ {\mathrm {e}} = - \frac {1}{K + 1} \sum_ {k = 1} ^ {K + 1} \sum_ {i = 1} ^ {W _ {\mathrm {F}}} \sum_ {j = 1} ^ {H _ {\mathrm {F}}} P _ {i, j, k} \log \left(P _ {i, j, k}\right). \tag {11}
+$$
+
+This drives the similarity map $P$ to exhibit clear and stable boundaries, resulting in more precise part discovery.
+
+Overall training target: by minimizing $\mathcal{L} = \mathcal{L}_{\mathrm{r}} + \lambda_{\mathrm{p}}\mathcal{L}_{\mathrm{p}} + \lambda_{\mathrm{s}}\mathcal{L}_{\mathrm{s}} + \lambda_{\mathrm{d}}\mathcal{L}_{\mathrm{d}}$ , MPAE learns to discover meaningful parts in complex scenarios, where $\lambda_{\mathrm{p}}, \lambda_{\mathrm{s}}$ , and $\lambda_{\mathrm{d}}$ are the weights of $\mathcal{L}_{\mathrm{p}}, \mathcal{L}_{\mathrm{s}}, \mathcal{L}_{\mathrm{d}}$ respectively.
+
+# 3.3. Inference pipeline
+
+The overall inference pipeline is shown on the right in Fig. 2. In this phase, we retain only PartFormer and the pretrained ViT. However, the low-resolution of $\pmb{F}$ is insufficient to produce high-resolution part masks. Therefore, we resize $\pmb{F}$ to match the size of the input images using bilinear interpolation. By accurately aligning with part shapes with the guide of low-level appearance features, $D$ can still accurately respond to the corresponding part regions in the $F'$ with much higher resolution. Thus, the similarity maps calculated from $D$ and $F'$ can serve as high-resolution part masks for the parts discovered in an unsupervised manner.
+
+# 4. Experimental Setup
+
+# 4.1. Datasets
+
+To comprehensively validate the effectiveness of MPAE, we evaluate it on four widely-used benchmarks: two with multiple categories (PartImageNet OOD dataset [15] and PartImageNet Segmentation dataset [15]) and two with a single category (CUB dataset [36] and CelebA dataset [24]). More details about these four datasets and the implementation of our method are provided in Appendix A.1 and Appendix A.2 respectively.
+
+# 4.2. Evaluation Metrics
+
+Normalized Mutual information (NMI) and Adjusted Rand Index (ARI) are primarily used to measure the similarity between two clusters. In this task, the NMI and ARI scores between the annotated and discovered parts directly reflect how closely the semantics of the discovered parts align with human conception.
+
+Normalized Mean Error (NME): NME is calculated using the centroids of the predicted parts and the annotated keypoints, representing the semantic consistency of the discovered parts across the entire test set.
+
+| Method | Label | K | PartImage_O (%) | PartImage_S (%) |
| NMI ↑ | ARI ↑ | NMI ↑ | ARI ↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Category label | 8 | 5.88 | 1.53 | - | - |
| 25 | 7.56 | 1.25 | - | - |
| 50 | 10.19 | 1.05 | - | - |
| PDisco-Net [35] | Category label | 8 | 27.13 | 8.76 | 10.68 | 32.43 |
| 25 | 32.41 | 10.69 | 18.44 | 40.70 |
| 50 | 41.49 | 14.17 | 21.98 | 39.40 |
| PDiscoNet + ViT-B/14 | Category label | 8 | 19.28 | 34.72 | 16.68 | 32.01 |
| 25 | 28.23 | 25.93 | 46.81 | 40.70 |
| 50 | 29.48 | 28.68 | 34.13 | 39.40 |
| PDiscoFormer [2]+ frozen ViT-B/14* | Category label | 8 | 28.84 | 55.66 | - | - |
| 25 | 43.36 | 62.82 | - | - |
| 50 | 44.48 | 57.91 | - | - |
| PDiscoFormer + ViT-B/14† | Category label | 8 | 29.00 | 52.40 | 20.29 | 38.90 |
| 25 | 44.71 | 59.27 | 43.18 | 64.61 |
| 50 | 46.29 | 62.21 | 44.06 | 60.10 |
| Unsupervised part discovery |
| DINO* [1] | N/A | 8 | 19.17 | 7.59 | - | - |
| 25 | 31.46 | 14.16 | - | - |
| 50 | 37.81 | 16.50 | - | - |
| Xia et al.* [40] | N/A | 4NC | 27.85 | 40.77 | 25.17 | 37.50 |
| MPAE* (ours) | N/A | 8 | 32.90 | 66.17 | 33.51 | 65.05 |
| 25 | 39.28 | 68.87 | 37.22 | 68.04 |
| 50 | 53.65 | 74.22 | 55.10 | 73.52 |
+
+Table 1. Quantitative comparisons with state-of-the-art methods on PartImageNet OOD and Segmentation datasets. $N_{\mathrm{c}}$ represents the number of categories, which is 109 and 158 for the OOD and Segmentation datasets respectively. $\dagger =$ using a partially fine-tuned pretrained backbone, $\star =$ using a frozen pretrained backbone.
+
+# 4.3. Comparisons with State-of-the-art Methods
+
+PartImageNet OOD: the quantitative results of MPAE and other state-of-the-art methods on PartImageNet OOD dataset are reported in Table 1, and some randomly chosen qualitative results are shown in Fig. 3. MPAE achieves highly competitive performance among both unsupervised and weakly-supervised methods. In the second row of Fig. 3, we observe that some small, round areas are identified as separate parts by DINO. These unreasonable parts result from directly clustering foreground features, which identifies certain near-outlier features as separate parts. By considering part appearance into clustering through our paradigm, we observe significant improvements in NMI of $71.62\%$ , $24.86\%$ and $41.89\%$ compared to DINO when $K = 8, 25, 50$ respectively. Due to the complex scenarios, it is difficult to align high-level semantics from part descriptors with object shapes through reconstruction. As a result, the parts discovered by Xia et al. are often incomplete. Although PDiscoFormer and PDiscoNet employ classification loss for part discovery in a weakly supervised manner, they do not further align high-level semantics with object shapes. Consequently, their predicted masks do not match objects as closely as those predicted by MPAE. With the same backbone (frozen ViT-B/14), MPAE still outperforms them.
+
+PartImageNet Segmentation increases category number $N_{\mathrm{C}}$ from 109 to 158, which means larger variance in ob
+
+
+Figure 3. Some qualitative results of MPAE (ours) and other state-of-the-art unsupervised and weakly-supervised methods on PartImageNet OOD dataset ( $K = 50$ ).
+
+ject appearance and shape. Therefore, as shown in Table 1, the metrics in both NMI and ARI of PDiscoFormer and Xia et al. degrade slightly. However, by using image restoration to constrain the learning and by exploring part similarities across different categories, MPAE successfully maintains strong robustness on this more challenging dataset. Compared to PDiscoFormer, MPAE still achieves an impressive improvement of $65.16\%$ and $25.06\%$ respectively in NMI when $K = 8$ and 50, even though PDiscoFormers employ both partially fine-tuned backbone and category labels.
+
+CUB: MPAE also achieves highly competitive performance on CUB (Table 2 and Fig. 4), demonstrating its effectiveness in part discovery within a single category. By implicitly clustering patch features with similar appearances and allowing for the absence of specific parts, MPAE can robustly discover meaningful bird parts in cases involving shadows, self-occlusion, and reflections (see first, second and fourth columns in Fig. 4). With the same frozen pretrained ViT-B/14, MPAE outperforms PDiscoFormer in all metrics, despite not using any labels for training. Compared to PDiscoFormer with a partially fine-tuned ViT-B/14, MPAE still outperforms it by $10.45\%$ , $7.66\%$ and $19.22\%$ in NME, NMI and ARI respectively when $K = 16$ . CelebA: as shown in Fig. 4, the masks predicted by MPAE accurately follow the entire facial region, resulting in significantly better qualitative results. Despite less challenging scenarios, the masks predicted by Xia et al. remain incomplete and fail to cover the entire face region. Other methods
+
+
+Figure 4. Some visualized part discovery results of MPAE (ours) and state-of-the-art methods on CUB dataset ( $K = 16$ ) and CelebA dataset ( $K = 8$ ). We use red boxes to highlight the regions with poor part discovery results.
+
+
+
+| Method | Label | K=4 (%) | K=8 (%) | K=16 (%) |
| NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Species label | 11.51 | 29.74 | 14.04 | 11.60 | 35.72 | 15.90 | 12.60 | 43.92 | 21.01 |
| PDiscoNet [35] | Species label | 9.12 | 37.82 | 15.26 | 8.52 | 50.08 | 26.96 | 7.64 | 56.87 | 38.05 |
| Choudhury et al. [6] | Foreground mask | 9.20 | 43.50 | 19.60 | - | 51.50 | 28.30 | - | - | - |
| PDiscoNet + ViT-B/14 | Species label | 7.70 | 52.59 | 26.66 | 6.34 | 65.01 | 37.90 | 5.95 | 68.63 | 43.41 |
| PDiscoFormer + ViT-B/14* [2] | Species label | 8.19 | 52.88 | 23.22 | 6.23 | 67.59 | 41.35 | 6.44 | 69.54 | 49.99 |
| PDiscoFormer + ViT-B/14† | Species label | 7.41 | 58.13 | 25.11 | 6.54 | 69.87 | 42.76 | 5.74 | 73.38 | 55.83 |
| Unsupervised part discovery |
| DINO* [1] | N/A | - | 31.18 | 11.21 | - | 47.21 | 19.76 | - | 50.57 | 26.14 |
| Xia et al.* [40] | N/A | 9.92 | 45.22 | 19.40 | 8.58 | 52.42 | 26.42 | 8.27 | 53.52 | 33.95 |
| MPAE* (ours) | N/A | 7.75 | 58.93 | 33.73 | 5.53 | 68.24 | 45.85 | 5.14 | 79.00 | 66.56 |
+
+Table 2. Quantitative comparisons with state-of-the-art methods on CUB. $\dagger=$ using partially fine-tuned backbone, ${}^{*}=$ using a frozen pretrained backbone.
+
+| Method | Label | K=4 (%) | K=8 (%) | K=16 (%) |
| NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Attribute label | 8.75 | 56.69 | 34.74 | 7.96 | 54.80 | 34.74 | 7.62 | 62.22 | 41.01 |
| PDiscoNet [35] | Identity label | 11.11 | 75.97 | 69.53 | 9.82 | 62.61 | 51.89 | 9.46 | 77.43 | 70.58 |
| Unsupervised part discovery |
| DINO* [1] | N/A | 11.36 | 1.38 | 0.01 | 10.74 | 1.12 | 0.01 | - | 3.29 | 0.06 |
| GANseg‡ [19] | N/A | 12.26 | 41.71 | 28.06 | 6.18 | 67.28 | 56.23 | - | - | - |
| Xia et al.* [40] | N/A | 12.28 | 50.69 | 34.57 | 10.24 | 58.35 | 46.78 | - | - | - |
| MPAE* (ours) | N/A | 11.44 | 56.13 | 37.20 | 7.55 | 59.64 | 41.72 | 7.10 | 70.21 | 60.33 |
+
+Table 3. Quantitative comparisons with state-of-the-art methods on CelebA. $\star =$ using a frozen pretrained backbone, $\ddagger =$ using a multi-stage self-training strategy.
+
+also misidentify some background regions as foreground parts. However, CelebA provides only five keypoints near the eyes, nose, and mouth for metric calculation, which is insufficient to reflect the improvements achieved by MPAE, as presented in Table 3.
+
+# 4.4. Ablation Studies
+
+Influence of loss functions: to study the effectiveness of the loss functions used in MPAE, we conduct ablation stud
+
+ies on PartImageNet Segmentation dataset. The quantitative and qualitative results are shown in Table 4 and Fig. 5 respectively. Foreground loss $\mathcal{L}_{\mathrm{f}}$ and background loss $\mathcal{L}_{\mathrm{b}}$ are crucial for preventing the model from identifying all pixels as background or foreground. Otherwise, the learned model converges to a trivial solution. Without the prior knowledge provided by Total variation loss $\mathcal{L}_{\mathrm{v}}$ , the pixels identified as foreground regions cannot form connected and concentrated parts. Entropy loss $\mathcal{L}_{\mathrm{e}}$ leads to more sta
+
+
+Raw Image Without $\mathcal{L}_{\mathrm{f}}$ Without $\mathcal{L}_{\mathrm{b}}$ Without $\mathcal{L}_{\mathrm{v}}$ Without $\mathcal{L}_{\mathrm{c}}$ Without $\mathcal{L}_{\mathrm{r}}$ Without $\mathcal{L}_{\mathrm{s}}$ Full Model
+Figure 5. Qualitative results from the ablation studies of the loss functions on PartImageNet Segmentation dataset ( $K = 50$ ). From left to right: (1) raw images, models trained without (2) $\mathcal{L}_{\mathrm{f}}$ , (3) $\mathcal{L}_{\mathrm{b}}$ , (4) $\mathcal{L}_{\mathrm{v}}$ , (5) $\mathcal{L}_{\mathrm{e}}$ , (6) $\mathcal{L}_{\mathrm{r}}$ , (7) $\mathcal{L}_{\mathrm{s}}$ and (8) nothing (full model).
+
+| Method | K=8 (%) | K=25 (%) | K=50 (%) |
| NMI↑ | ARI↑ | NMI↑ | ARI↑ | NMI↑ | ARI↑ |
| Without Lf | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Without Lb | 30.91 | 73.20 | 33.67 | 67.85 | 39.36 | 55.24 |
| Without Lv | 18.30 | 20.62 | 13.52 | 4.54 | 14.37 | 4.08 |
| Without Le | 31.21 | 63.27 | 27.48 | 54.93 | 52.51 | 73.08 |
| Without LR | 25.60 | 57.39 | 31.53 | 63.39 | 22.32 | 49.73 |
| Without Ls | 55.69 | 76.54 | 57.70 | 76.97 | 56.42 | 74.03 |
| Full model | 33.51 | 65.05 | 37.22 | 68.04 | 55.10 | 73.52 |
+
+Table 4. Performance comparisons of MPAE without different loss functions on the PartImageNet Segmentation dataset in the setting of $K = 8,25,50$ .
+
+| Masking Ratio r | 50% | 75% | 80% | 85% | 90% | 95% | 100% |
| NMI (%) ↑ | 45.50 | 50.11 | 52.20 | 52.70 | 55.10 | 54.63 | 43.39 |
| ARI (%) ↑ | 70.25 | 70.89 | 70.90 | 71.85 | 73.52 | 73.23 | 41.29 |
+
+ble and smooth part boundaries by enforcing that each pixel highly responds to a unique part descriptor. The absence of reconstruction loss $\mathcal{L}_{\mathrm{r}}$ results in a failure to align part descriptors with actual part shapes. Consequently, the predicted masks contain only rough regions without clear part boundaries. Without semantic constraint $\mathcal{L}_{\mathrm{s}}$ , the model identifies the regions with less semantic similarity as the same part. In some cases, the learned model even degrades into a foreground segmentation model. Although this degradation may improve the numerical metrics in NMI and ARI, the learned model cannot achieve the goal of part discovery. Therefore, all constraints used in MPAE are essential for learning a robust model for unsupervised part discovery.
+
+Influence of the masking ratio $r$ : the quantitative results of MPAE with different masking ratios $r$ are reported in Table 5. When $r < 90\%$ , a higher $r$ results in more features in the filled feature map $R$ comes from part descriptors $D$ . Therefore, by aligning the part descriptors $D$
+
+Table 5. Performance comparisons of MPAE with different masking ratio $r$ on the PartImageNet Segmentation dataset in the setting of $K = {50}$ .
+
+| Change from MPAE model: | NMI (%)↑ | ARI (%)↑ |
| Lf → Area loss in [40] | 1.90 | -0.14 |
| Lp → Presence loss in [2] | 42.45 | 60.24 |
| Ld → Concentration loss in [21] | 17.29 | 18.74 |
| Part number K → 4Nc | 47.59 | 70.71 |
| MPAE (our best model) | 55.10 | 73.52 |
+
+Table 6. Comparisons of our optimized losses and designs with previous ones on the PartImageNet Segmentation dataset in the setting of $K = 50$ .
+
+with object part shapes, a stronger constraint can be applied to the similarity maps $P$ , requiring them to better match the actual part shapes. As a results, we observe an improvement in performance. When $r > 90\%$ , a higher $r$ results in insufficient unmasked patches containing low-level appearance information to guide the alignment between descriptors and part shapes. Therefore, the optimal masking ratio $r$ is $90\%$ .
+
+Improvements of our optimized constraints and designs: The area loss in [40] requires all parts to appear in each image. But, it is impossible for every object to contain all 50 parts. Consequently, $\mathcal{L}_{\mathrm{a}}$ leads to a collapse during training. The image classification loss in [2] ensures that each image to have at least one discovered part, as the embedding for classification cannot be a zero vector. Without any labels, presence loss in [2] cannot guarantee that unsupervised methods discover at least one part in each image. Therefore, some images may not have any discovered parts, which further leads to a degradation in metrics. The concentration loss in [21] penalizes pixels that are farther from the part center more heavily, which prevents the predicted parts from accurately following their actual shapes, whereas $\mathcal{L}_{\mathrm{d}}$ addresses this imbalance. As [40], we also implement a model that simply decomposes each category into four parts without exploring their semantic similarities ( $K \to 4N_{\mathrm{c}}$ ). Consequently, the number of training samples for each part significantly decreases, leading to reduced robustness.
+
+More ablation studies and visualized results are included in the Appendix.
+
+# 5. Conclusion
+
+In this paper, we present a novel paradigm (MPAE) with looser yet effective constraints for more robust unsupervised part discovery. By restoring masked image patches using the corresponding part descriptors, MPAE effectively aligns their high-level semantics with the part shapes under the guidance of low-level appearance features from un-masked patches. As a result, MPAE predicts masks that closely match the actual shapes of corresponding parts. The optimized constraints enable MPAE to identify the presence of parts across various scenarios and categories in an unsupervised manner, effectively addressing challenges posed by occlusion and diverse object categories.
+
+# References
+
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+[2] Ananthu Aniraj, Cassio F Dantas, Dino Ienco, and Diego Marcos. Pdiscoformer: Relaxing part discovery constraints with vision transformers. In ECCV, 2024. 1, 2, 4, 6, 7, 8
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+[4] Mathilde Caron, Hugo Touvron, Ishan Misra, Hervé Jegou, Julien Mairal, Piotr Bojanowski, and Armand Joulin. Emerging properties in self-supervised vision transformers. In ICCV, pages 9630-9640, 2021. 1, 2
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+ "content": " within the same part region together in latent space by utilizing them to produce the image patches with similar appearance. Guided by low-level appearance features from "
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+ }
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+ "html": "| Method | Label | K | PartImage_O (%) | PartImage_S (%) |
| NMI ↑ | ARI ↑ | NMI ↑ | ARI ↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Category label | 8 | 5.88 | 1.53 | - | - |
| 25 | 7.56 | 1.25 | - | - |
| 50 | 10.19 | 1.05 | - | - |
| PDisco-Net [35] | Category label | 8 | 27.13 | 8.76 | 10.68 | 32.43 |
| 25 | 32.41 | 10.69 | 18.44 | 40.70 |
| 50 | 41.49 | 14.17 | 21.98 | 39.40 |
| PDiscoNet + ViT-B/14 | Category label | 8 | 19.28 | 34.72 | 16.68 | 32.01 |
| 25 | 28.23 | 25.93 | 46.81 | 40.70 |
| 50 | 29.48 | 28.68 | 34.13 | 39.40 |
| PDiscoFormer [2]+ frozen ViT-B/14* | Category label | 8 | 28.84 | 55.66 | - | - |
| 25 | 43.36 | 62.82 | - | - |
| 50 | 44.48 | 57.91 | - | - |
| PDiscoFormer + ViT-B/14† | Category label | 8 | 29.00 | 52.40 | 20.29 | 38.90 |
| 25 | 44.71 | 59.27 | 43.18 | 64.61 |
| 50 | 46.29 | 62.21 | 44.06 | 60.10 |
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| DINO* [1] | N/A | 8 | 19.17 | 7.59 | - | - |
| 25 | 31.46 | 14.16 | - | - |
| 50 | 37.81 | 16.50 | - | - |
| Xia et al.* [40] | N/A | 4NC | 27.85 | 40.77 | 25.17 | 37.50 |
| MPAE* (ours) | N/A | 8 | 32.90 | 66.17 | 33.51 | 65.05 |
| 25 | 39.28 | 68.87 | 37.22 | 68.04 |
| 50 | 53.65 | 74.22 | 55.10 | 73.52 |
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| NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Species label | 11.51 | 29.74 | 14.04 | 11.60 | 35.72 | 15.90 | 12.60 | 43.92 | 21.01 |
| PDiscoNet [35] | Species label | 9.12 | 37.82 | 15.26 | 8.52 | 50.08 | 26.96 | 7.64 | 56.87 | 38.05 |
| Choudhury et al. [6] | Foreground mask | 9.20 | 43.50 | 19.60 | - | 51.50 | 28.30 | - | - | - |
| PDiscoNet + ViT-B/14 | Species label | 7.70 | 52.59 | 26.66 | 6.34 | 65.01 | 37.90 | 5.95 | 68.63 | 43.41 |
| PDiscoFormer + ViT-B/14* [2] | Species label | 8.19 | 52.88 | 23.22 | 6.23 | 67.59 | 41.35 | 6.44 | 69.54 | 49.99 |
| PDiscoFormer + ViT-B/14† | Species label | 7.41 | 58.13 | 25.11 | 6.54 | 69.87 | 42.76 | 5.74 | 73.38 | 55.83 |
| Unsupervised part discovery |
| DINO* [1] | N/A | - | 31.18 | 11.21 | - | 47.21 | 19.76 | - | 50.57 | 26.14 |
| Xia et al.* [40] | N/A | 9.92 | 45.22 | 19.40 | 8.58 | 52.42 | 26.42 | 8.27 | 53.52 | 33.95 |
| MPAE* (ours) | N/A | 7.75 | 58.93 | 33.73 | 5.53 | 68.24 | 45.85 | 5.14 | 79.00 | 66.56 |
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| NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ | NME↓ | NMI↑ | ARI↑ |
| Weakly-supervised part discovery |
| Huang et al. [20] | Attribute label | 8.75 | 56.69 | 34.74 | 7.96 | 54.80 | 34.74 | 7.62 | 62.22 | 41.01 |
| PDiscoNet [35] | Identity label | 11.11 | 75.97 | 69.53 | 9.82 | 62.61 | 51.89 | 9.46 | 77.43 | 70.58 |
| Unsupervised part discovery |
| DINO* [1] | N/A | 11.36 | 1.38 | 0.01 | 10.74 | 1.12 | 0.01 | - | 3.29 | 0.06 |
| GANseg‡ [19] | N/A | 12.26 | 41.71 | 28.06 | 6.18 | 67.28 | 56.23 | - | - | - |
| Xia et al.* [40] | N/A | 12.28 | 50.69 | 34.57 | 10.24 | 58.35 | 46.78 | - | - | - |
| MPAE* (ours) | N/A | 11.44 | 56.13 | 37.20 | 7.55 | 59.64 | 41.72 | 7.10 | 70.21 | 60.33 |
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| Without Lf | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 | 0.00 |
| Without Lb | 30.91 | 73.20 | 33.67 | 67.85 | 39.36 | 55.24 |
| Without Lv | 18.30 | 20.62 | 13.52 | 4.54 | 14.37 | 4.08 |
| Without Le | 31.21 | 63.27 | 27.48 | 54.93 | 52.51 | 73.08 |
| Without LR | 25.60 | 57.39 | 31.53 | 63.39 | 22.32 | 49.73 |
| Without Ls | 55.69 | 76.54 | 57.70 | 76.97 | 56.42 | 74.03 |
| Full model | 33.51 | 65.05 | 37.22 | 68.04 | 55.10 | 73.52 |
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| NMI (%) ↑ | 45.50 | 50.11 | 52.20 | 52.70 | 55.10 | 54.63 | 43.39 |
| ARI (%) ↑ | 70.25 | 70.89 | 70.90 | 71.85 | 73.52 | 73.23 | 41.29 |
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| Lf → Area loss in [40] | 1.90 | -0.14 |
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| Ld → Concentration loss in [21] | 17.29 | 18.74 |
| Part number K → 4Nc | 47.59 | 70.71 |
| MPAE (our best model) | 55.10 | 73.52 |
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diff --git a/2025/Unsupervised RGB-D Point Cloud Registration for Scenes with Low Overlap and Photometric Inconsistency/d34c24f1-e608-47c5-8100-5b5de8083fff_content_list.json b/2025/Unsupervised RGB-D Point Cloud Registration for Scenes with Low Overlap and Photometric Inconsistency/d34c24f1-e608-47c5-8100-5b5de8083fff_content_list.json
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+++ b/2025/Unsupervised RGB-D Point Cloud Registration for Scenes with Low Overlap and Photometric Inconsistency/d34c24f1-e608-47c5-8100-5b5de8083fff_content_list.json
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+ "type": "text",
+ "text": "Unsupervised RGB-D Point Cloud Registration for Scenes with Low Overlap and Photometric Inconsistency",
+ "text_level": 1,
+ "bbox": [
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+ "text": "Yejun Shou $^{1,2}$ , Haocheng Wang $^{1,2}$ , Lingfeng Shen $^{1,2}$ , Qian Zheng $^{3*}$ , Gang Pan $^{3}$ , Yanlong Cao $^{1,2*}$ $^{1}$ The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, China \n $^{2}$ The Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, China \n $^{3}$ College of Computer Science and Technology, Zhejiang University, China",
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+ {
+ "type": "text",
+ "text": "{syj12125092, 00whc, lfs, qianzheng, gpan, sdcaoyl}@zju.edu.cn",
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+ "type": "text",
+ "text": "Abstract",
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+ {
+ "type": "text",
+ "text": "Point cloud registration is a fundamental task in 3D vision, playing a crucial role in various fields. With the rapid advancement of RGB-D sensors, unsupervised point cloud registration methods based on RGB-D sequences have demonstrated excellent performance. However, existing methods struggle in scenes with low overlap and photometric inconsistency. Low overlap results in numerous correspondence outliers, while photometric inconsistency hinders the model's ability to extract discriminative features. To address these challenges, we first propose the Overlapping Constraint for Inliers Detection (OCID) module, which filters and optimizes the initial correspondence set using an overlapping constraint. This module robustly selects reliable correspondences within the overlapping region while maintaining a balance between accuracy and efficiency. Additionally, we introduce a novel scene representation, 3DGS, which integrates both geometric and texture information, making it particularly well-suited for RGB-D registration tasks. Building on this, we propose the Gaussian Rendering for Photometric Adaptation (GRPA) module, which refines the geometric transformation and enhances the model's adaptability to scenes with inconsistent photometric information. Extensive experiments on ScanNet and ScanNet1500 demonstrate that our method achieves state-of-the-art performance. The code will be released at OG-UPCR.",
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+ "text": "1. Introduction",
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+ {
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+ "text": "Point cloud registration is a critical task in 3D vision, with applications in navigation [30, 44, 56], pose estimation [10, 17], and 3D reconstruction [42, 43]. Typically, two frames of point clouds rely on feature extraction to estimate correspondences, followed by robust geometric fitting techniques to obtain the transformation.",
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+ "Figure 1. The objective of the proposed OG-UPCR is to effectively register scenes with low overlap and photometric inconsistency. The overlapping region constraint helps reduce correspondence outliers caused by low overlap, while photometric inconsistency is adaptively adjusted through the estimizable parameters contained in 3D Gaussians [24]. Compared to PointMBF [52], the proposed OG-UPCR produces more consistent results between input and rendered frames (highlighted in red boxes) and yields better registration outcomes."
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+ "text": "With the rapid development of RGB-D sensors, unsupervised registration methods [12-14, 27, 40, 45, 52] have demonstrated impressive performance. These methods rasterize 3D points into images using a differentiable renderer [32] and employ geometric and photometric consistency losses between the input and rendered frames to extract features, thereby estimating the geometric transformation between nearby frames without the need for ground truth. However, all these methods ignore that the geometric and photometric information between frames to be registered is not always consistent, particularly in scenes with low overlap and photometric inconsistency. Low overlap",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "type": "page_number",
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+ "type": "text",
+ "text": "complicates feature identification and correspondence estimation [20], while photometric inconsistency hinders the modeling of feature consistency between input and rendered frames, making it challenging for the model to obtain discriminative features, especially in scenes with reflections and rendering artifacts [52]. Despite the excellent registration performance of PointMBF [52], it still suffers from low overlap and photometric inconsistency, which result in a large number of correspondence outliers and erroneous rendered and registration results, as illustrated in Fig. 1.",
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+ "text": "We observe that inliers must be located within overlapping regions, whereas outliers can be filtered out early using overlapping constraint. Although identifying inliers and overlaps is a chicken-and-egg situation, it can be efficiently resolved through an iterative process. Meanwhile, recent advances in 3D Gaussian Splatting [24] have made significant strides in novel view synthesis [4, 54], 3D generation [6, 50], and SLAM [23, 26, 46]. This technique not only represents geometry in a smooth and continuously differentiable manner but also preserves view-varying texture information, which is adaptive to photometric changes. Additionally, 3D points convert easily into 3D Gaussians, making this approach highly suitable for RGB-D registration.",
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+ "text": "To this end, we propose OG-UPCR, an innovative unsupervised point cloud registration framework designed to address low overlap and photometric inconsistency, as shown in Fig. 1. Specifically, we propose the Overlapping Constraint for Inliers Detection module (OCID) based on the observation that inliers must lie within overlapping regions. This module leverages overlapping constraints to detect inliers, addressing issues arising from low overlap. Additionally, we design the Gaussian Rendering for Photometric Adaptation module (GRPA), which converts 3D points into 3D Gaussians and rasterizes them into image space, leveraging the rich geometric and texture information contained in the Gaussians. Based on this, nonlinear optimization is applied to each pixel to enhance photometric adaptation and enable the model to extract discriminative features. Moreover, this process refines the transformation and improves overall registration.",
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+ "text": "The OG-UPCR is thoroughly evaluated on the standard datasets, including 3DMatch [53], ScanNet [9], and the challenging ScanNet1500 [35], which contain paired views with low overlap and inconsistent photometric information, achieving state-of-the-art performance. Additionally, we conduct extensive ablation experiments on individual modules to demonstrate the effectiveness of each component.",
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+ "text": "In summary, our contributions are as follows:",
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+ "- We propose OG-UPCR, an unsupervised registration framework that combines overlapping constraint with gaussian splatting, enhancing the accuracy and robustness of the overall registration model.",
+ "- We propose a correspondence optimization strategy us"
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+ "text": "ing iterative random overlapping region prediction. This module selects faithful inliers of correspondences within the overlapping region, mitigating the impact of low overlap and enhancing the accuracy of geometric fitting.",
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+ "text": "- We propose a photometric adaptation module for paired views that employs Gaussian splatting to independently render the Gaussians of both views. This module models the photometric consistency of features across frames, and refines the final transformation.",
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+ "text": "Early point cloud registration methods [21, 33, 34, 39] rely on hand-crafted feature descriptors, which are sensitive to noise and not robust to changes in the number and density of point clouds. Recently, deep learning feature descriptors have demonstrated impressive performance and can achieve better registration results. Research based on deep learning can be divided into supervised [2, 20, 29, 37, 41, 51] and unsupervised [12, 13, 28, 36, 45, 52] methods. However, supervised methods require real poses as supervision signals, making them difficult to apply practically. When encountering new scenes with domain gaps, they can only rely on the trained weights to infer the registration results, which often affects their performance. Unsupervised methods can be further divided into geometric-based and RGB-D based methods according to the input data. Among geometric-based methods, RIENet [36] proposes a reliable inlier evaluation method based on neighborhood consensus. UDReg [28] operates by learning the posterior probability distribution of Gaussian Mixture Models from point clouds and then predicting distribution-level correspondences. Since the input contains only geometric information, these methods struggle with geometric weak regions (such as floors, ceilings, and walls) and repeated structures in real scenes. RGB-D based methods are able to handle real scenes, such as LLT [45] employing a linear attention module to fuse geometric and texture features. PointMBF [52] proposes a multi-scale bidirectional fusion network to fully utilize the complementary information of RGB-D. Nevertheless, these methods all employ a conventional differentiable renderer to render 3D points directly, making them susceptible to low overlap and photometric inconsistency. In contrast, we propose the OCID module based on overlapping constraint to help obtain more reliable correspondences. Additionally, we design the GRPA module to reduce the impact of photometric inconsistency, thereby enhancing registration accuracy.",
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+ "image_caption": [
+ "Figure 2. The overview of OG-UPCR. The backbone first extracts the features $F_{P}^{f}$ and $F_{Q}^{f}$ from the point clouds $P$ and $Q$ . The initial correspondences are estimated by calculating Lowe's ratio in the feature space, which is then optimized by the OCID module using the overlapping constraint. Subsequently, the rigid transformation is determined through geometric fitting. Finally, based on this transformation, the Gaussian cross-rendering results generated by the GRPA module form the paired views are used to calculate the loss. This process not only refines the final result but also aids the model in acquiring distinct features."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "recognized algorithms, their performance remains sensitive to outliers, often requiring numerous iterations to produce relatively accurate results. SC2PCR [5] and MAC [55] are also effective in managing correspondence outliers, but both rely on relative spatial constraint and fail to account for the fact that correct correspondences should be confined to the overlapping region from global spatial constraint. This oversight leads to inefficiency and inaccuracy, as excessive redundant point pairs are utilized. In contrast, we propose an overlapping constraint module based on global spatial to select reliable correspondences, thereby improving the efficiency and accuracy of the registration process.",
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+ "type": "text",
+ "text": "2.3. Gaussian Splatting",
+ "text_level": 1,
+ "bbox": [
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+ "text": "As a novel scene representation and efficient differentiable renderer, 3D Gaussian Splatting [24] has shown its significant advantages in novel view synthesis [4, 48, 54], 3D generation [6, 50] and SLAM [23, 26, 46]. SplaTAM [23] introduces an online tracking and mapping system based on the underlying 3D Gaussian representation, without requiring the real pose. However, it relies on dense RGB-D frame inputs, making it difficult to obtain accurate poses with sparse input. PixelSplat [6] proposes that the radiance field parameterized by 3D Gaussian primitives can be learned and reconstructed from sparse views. NoPoSplat [48] integrates PnP [18] and 3DGS [24] to estimate poses from sparse views, achieving superior novel",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "view synthesis. Nevertheless, these methods estimate poses from an image-based perspective, resulting in the loss of 3D information. In contrast, the proposed GRPA module derives a more precise geometric transformation from the point cloud perspective, producing rasterized outputs independent of true pose data. This approach exhibits robust generalization and achieves accurate registration even with sparse inputs.",
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+ "type": "text",
+ "text": "3. Method",
+ "text_level": 1,
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+ "type": "text",
+ "text": "3.1. Problem Statement and Overview",
+ "text_level": 1,
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+ "text": "Problem Statement. Given point clouds $P \\in \\mathbb{R}^{N \\times 3}$ and $Q \\in \\mathbb{R}^{N \\times 3}$ , the purpose of the registration task is to obtain a transformation matrix $\\mathbf{T} = \\{\\mathbf{R}, \\mathbf{t}\\}$ , that aligns $P$ and $Q$ in the same coordinate system. This transformation matrix consists of a rotation matrix $\\mathbf{R} \\in \\mathbf{SO}(3)$ and a translation vector $\\mathbf{t} \\in \\mathbb{R}^3$ . The correspondence set $C = \\{\\mathbf{p}_i, \\mathbf{q}_j | \\mathbf{p}_i \\in P, \\mathbf{q}_j \\in Q\\}$ is estimated by feature extraction and matching. The transformation can be determined by:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\underset {\\mathbf {R}, \\mathbf {t}} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {n} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {i} + \\mathbf {t} - \\mathbf {q} _ {j} \\| _ {2} ^ {2}, \\tag {1}\n$$\n",
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+ {
+ "type": "text",
+ "text": "where $\\| \\cdot \\| _2^2$ denotes the Euclidean norm, $n$ is the number of correspondences that can be found in paired point clouds.",
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+ "type": "page_number",
+ "text": "24870",
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+ "type": "text",
+ "text": "Overview. In this paper, we propose an OCID module and a GRPA module to address challenges associated with low overlap and photometric inconsistency. The OG-UPCR processes paired point clouds and their corresponding RGB-D frames as input, following the PointMBF [52] to extract feature descriptors. Using these descriptors, we compute an initial correspondence set by measuring distances in the feature space. The OCID module then filters this initial set based on an overlapping region constraint, selecting reliable seed points for geometric fitting, which produces a coarse transformation, denoted as $\\mathbf{T}_{gs}^{0}$ , as described in Section 3.2. This transformation serves as the initial pose for the GRPA module, where 3D points are first converted into 3D Gaussians and then projected onto an image using a Gaussian splatting renderer, which is subsequently refined to obtain the final result, $\\mathbf{T}_{gs}^{R}$ , as detailed in Section 3.3. Additionally, the entire registration framework is trained in an end-to-end unsupervised manner using geometric and photometric consistency losses between input and rendered frames, as discussed in UR&R [13]. An overview of OG-UPCR is provided in Fig. 2.",
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+ {
+ "type": "text",
+ "text": "Feature Extraction. Building upon prior research, we employ KPCov [38] and ResNet [19] to extract multi-scale information from the point clouds and images. Subsequently, a multi-scale bidirectional fusion method [52] generates distinctive fused feature descriptors $F_{P}^{f} \\in \\mathbb{R}^{N \\times C_{3D}}$ and $F_{Q}^{f} \\in \\mathbb{R}^{N \\times C_{3D}}$ for point clouds $P$ and $Q$ .",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "3.2. Correspondence Estimation",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "Initial Correspondence Set Acquisition. After obtaining the feature descriptors of the point clouds, we follow previous method [13, 45, 52] to obtain the initial correspondence set based on Lowe's ratio [25]. For a point $\\mathbf{p}_i$ , its Lowe's ratio can be computed as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nr _ {i} = \\frac {D \\left(\\mathbf {p} _ {i} , \\mathbf {q} _ {j} ^ {1 n n}\\right)}{D \\left(\\mathbf {p} _ {i} , \\mathbf {q} _ {j} ^ {2 n n}\\right)}, \\tag {2}\n$$\n",
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+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "where $D(\\cdot)$ represents the Euclidean distance in the feature space and $q_{j}^{knn}$ is the k-th similarity point in the point cloud $Q$ . We assign weights to each correspondence using the formula $w = 1 - r$ . Next, we apply the top-k algorithm to select the weighted correspondences, resulting in a correspondence set from $C_{P \\to Q}$ . We choose an equal number of correspondences from $C_{Q \\to P}$ in a similar manner to create the initial correspondence set:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nC _ {\\text {i n i t i a l}} = \\left\\{\\left(\\mathbf {p}, \\mathbf {q}, w\\right) _ {m}: 0 \\leq m < 2 k \\right\\}, \\tag {3}\n$$\n",
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+ "bbox": [
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+ "type": "text",
+ "text": "where $k$ denotes the top $k$ weights. The resulting correspondence $C_{\\mathrm{initial}}$ will be input into the OCID module for further optimization.",
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+ {
+ "type": "text",
+ "text": "Overlapping Constraint for Inliers Detection. This module is designed to detect inliers from the initial correspondence set, facilitating efficient registration in scenarios with",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "low overlap. Existing works [5, 55] directly remove outliers based on the consistency graph but neglect the importance of the overlapping region constraint, leading to significant computational expenses. As shown in Fig. 2, the module consists of two components, which are detailed below.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Random Overlapping Region Prediction. As is well known, Weighted SVD [8] produces an approximate geometric transformation by performing singular value decomposition on the weights of the correspondence set. The accuracy of this transformation will be affected by the inliers in the correspondence, meaning that the higher the weight of the inliers, the more accurate the transformation will be. Motivated by this and inspired by RANSAC [15], we first randomly select a partial subset from the initial correspondence:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nC _ {n} = \\left\\{\\left(\\mathbf {p}, \\mathbf {q}, w\\right) _ {n}: 0 \\leq n < 2 r k \\right\\} \\in C _ {\\text {i n i t i a l}}, \\tag {4}\n$$\n",
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+ "bbox": [
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+ {
+ "type": "text",
+ "text": "where $r$ denotes the proportion of the subset in the initial correspondence, which is set to 0.2. Next, we apply Weighted SVD to obtain the transformation $\\mathbf{T}_s$ of this subset. Unlike similar previous work [13, 45, 52], we do not directly leverage the common L2 distance to assess whether $\\mathbf{T}_s$ is correct, which is prone to fall into local optima. Instead, we propose a novel approach based on overlapping region prediction. Using $\\mathbf{T}_s$ , we predict the overlapping area of the point cloud and evaluate its success by the overlap ratio $O_p$ , which is defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nP ^ {\\prime} = \\mathbf {T} _ {s} \\odot P, \\tag {5}\n$$\n",
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+ "bbox": [
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+ "type": "equation",
+ "text": "\n$$\nO _ {p} = \\frac {1}{N} \\sum_ {n = 1} ^ {N _ {P ^ {\\prime}}} \\llbracket \\| \\mathbf {p} _ {n} ^ {\\prime} - \\mathbf {q} _ {n} \\| _ {2} < \\tau \\rrbracket , \\tag {6}\n$$\n",
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+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "where $\\llbracket \\cdot \\rrbracket$ is the Iverson bracket, $\\odot$ represents the rigid transformation, $N_{P^{\\prime}}$ is the number of points of the point cloud $P^{\\prime}$ and $\\tau$ is set to $5\\mathrm{cm}$ . If $O_p$ exceeds the threshold $O_{thr}$ , the prediction is considered successful. This implies that most of the correspondences within the selected subset are inliers, and the subset is classified as a positive subset, receiving a higher weight in the initial correspondence set. To meet these conditions, we multiply the weight of the points in the subset of successful predictions by a reward factor, thereby increasing their proportion in the initial correspondence. Conversely, if the prediction fails, it indicates that the selected subset contains a high percentage of outliers. In this case, the corresponding weights in those subsets are multiplied by a penalty factor, which is defined as follows:",
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+ "type": "equation",
+ "text": "\n$$\nw _ {n} = \\left\\{ \\begin{array}{l} w _ {n} \\cdot w _ {r}, O _ {p} \\geq O _ {t h r} \\\\ w _ {n} \\cdot w _ {p}, O _ {p} < O _ {t h r} \\end{array} , \\right. \\tag {7}\n$$\n",
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+ "type": "text",
+ "text": "where $w_{r}$ and $w_{p}$ denote the reward factor and penalty factor, and $w_{r} \\cdot w_{p} = 1$ to ensure the balance change of a correspondence when it is selected into the subset many times.",
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+ "type": "page_number",
+ "text": "24871",
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+ "type": "text",
+ "text": "The above prediction process is repeated $N$ times. After completing the random overlapping region prediction, the weights of the individual correspondences within the initial correspondence set are significantly optimized, with inliers receiving higher weights and the weights of outliers being reduced. To enhance the efficiency of the algorithm, we also use the top-k algorithm to select the appropriate correspondence. The optimized set of correspondences can be defined as follows:",
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+ "page_idx": 4
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\nC _ {f} = \\left\\{\\left(\\mathbf {p}, \\mathbf {q}, w\\right) _ {f}: 0 \\leq m < 2 k _ {f} \\right\\}, \\tag {8}\n$$\n",
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+ "bbox": [
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+ {
+ "type": "text",
+ "text": "where $k_{f}$ means that the top-k algorithm is used to select items with larger weights to speed up the algorithm. We also provide a pseudocode and simple flowchart in Supplementary Material. 2.",
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+ "type": "text",
+ "text": "Global-to-Local Inliers Detection. The optimized correspondence set $C_f$ already exhibits a high inlier ratio. However, one issue remains: the selected correspondences are concentrated in specific local regions rather than uniformly distributed. This concentration hinders the subsequent geometric fitting. To address this challenge, we propose a global-to-local inlier detection module based on spatial consistency, as shown in Fig. 2. First, we compute the second order spatial compatibility ( $SC^2$ ) [5] of the optimized correspondence set globally, which can be defined as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nS C _ {i j} ^ {2} = C _ {i j} \\cdot \\sum_ {k = 1} ^ {N} C _ {i k} \\cdot C _ {k j}, \\tag {9}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\nC _ {i j} = \\left\\{ \\begin{array}{l} 1, d _ {i j} \\leq d _ {t h r} \\\\ 0, d _ {i j} > d _ {t h r} \\end{array} , \\right. \\tag {10}\n$$\n",
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+ {
+ "type": "equation",
+ "text": "\n$$\nd _ {i j} = \\left| \\left\\| \\mathbf {p} _ {i} - \\mathbf {p} _ {j} \\right\\| _ {2} - \\left\\| \\mathbf {q} _ {i} - \\mathbf {q} _ {j} \\right\\| _ {2} \\right|, \\tag {11}\n$$\n",
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+ "bbox": [
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+ {
+ "type": "text",
+ "text": "where $\\mathbf{p}_i, \\mathbf{p}_j$ and $\\mathbf{q}_i, \\mathbf{q}_j$ denote two sets of correspondence points in $C_f$ , and $d_{thr}$ is set to $10\\mathrm{cm}$ . Subsequently, the optimized weights $w_f$ are employed to find the seed points with the maximum confidence score within their neighborhood, defined by a radius $R$ , ensuring that the correspondences are uniformly distributed. To ensure that the selected seed points are reliable inliers, we measure the correspondence of the seed point and its top- $K$ neighbors based on the constructed $SC^2$ metric to further prune potential outliers. Finally, these seed points and their neighboring points form multiple consensus sets.",
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+ "type": "text",
+ "text": "Geometric Fitting. To project images of the transformed point clouds $P$ and $Q$ using a Gaussian renderer, it is necessary to estimate their geometric transformation. This estimation is achieved through geometric fitting. Following [5], we estimate the geometric transformation according to each consensus set. Finally, we choose the transformation with the highest number of inliers as the result $\\mathbf{T}_{gs}^{0}$ .",
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+ {
+ "type": "text",
+ "text": "3.3. Gaussian Rendering",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "This module is designed to help the model adapt to inconsistent photometric information between the input and rendered frames. Previous approaches [13, 45, 52] rely on traditional differentiable renderer [32] to directly project 3D points into the image space, which makes their models susceptible to significant viewpoint changes and limits the ability to extract more discriminative features. To overcome these challenges, we draw inspiration from [22, 26] and introduce the 3D Gaussian splatting technique. Additionally, we propose a photometric adaptation mechanism for each pixel to resolve the inconsistencies caused by viewpoint changes, thereby enabling the model to learn more discriminative features for registration.",
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "Gaussian Rendering for Photometric Adaptation. Specifically, each point can be represented by a Gaussian [22] with eight parameter values: its point position $\\mu_{3D} \\in \\mathbb{R}^3$ , RGB color $\\mathbf{c} \\in \\mathbb{R}^3$ , radius $r$ , and opacity $o \\in [0,1]$ . Each Gaussian affects a point in 3D space $\\mathbf{x} \\in \\mathbb{R}^3$ as follows:",
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+ {
+ "type": "equation",
+ "text": "\n$$\ng (\\mathbf {x}) = o \\exp \\left(- \\frac {\\| \\mathbf {x} - \\mu_ {3 D} \\| ^ {2}}{2 r _ {3 D} ^ {2}}\\right), \\tag {12}\n$$\n",
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+ "type": "text",
+ "text": "each pixel $\\rho$ in the differentiable rendered RGB image can then be rendered as follows:",
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+ "type": "equation",
+ "text": "\n$$\nR _ {r g b} ^ {g s} (\\mathbb {G}, \\mathbf {T}) = \\sum_ {i = 1} ^ {n} c _ {i} g _ {i} (\\rho) \\prod_ {j = 1} ^ {i - 1} (1 - g _ {j} (\\rho)), \\tag {13}\n$$\n",
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+ "bbox": [
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+ {
+ "type": "text",
+ "text": "where $g(\\rho_a)$ can be obtained from Eq. (12) and (13), but with $\\mu_{3D}$ and $r_{3D}$ of the splatted 2D Gaussians in pixel space:",
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+ "type": "equation",
+ "text": "\n$$\n\\mu_ {2 D} = \\mathbf {K T} \\frac {\\mu_ {3 D}}{d}, r _ {2 D} = \\frac {f}{d}, \\tag {14}\n$$\n",
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+ "type": "text",
+ "text": "where $\\mathbf{K}$ is the camera intrinsic matrix, $\\mathbf{T}$ is the extrinsic matrix, $f$ is the focal length of the camera, and $d$ is the depth. To further enhance the adaptability to photometric changes, we optimize the nonlinear photometric adaptation of each pixel:",
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+ "type": "equation",
+ "text": "\n$$\nR _ {r g b} ^ {g s ^ {\\prime}} = \\exp (\\alpha) \\cdot R _ {r g b} ^ {g s} + \\beta , \\tag {15}\n$$\n",
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+ "type": "text",
+ "text": "where $\\alpha$ and $\\beta$ are both learnable parameters. A similar differentiable rendered depth image can be expressed as follows:",
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+ "type": "equation",
+ "text": "\n$$\nR _ {\\text {d e p t h}} ^ {g s} (\\mathbb {G}, \\mathbf {T}) = \\sum_ {i = 1} ^ {n} d _ {i} g _ {i} \\left(\\rho_ {a}\\right) \\prod_ {j = 1} ^ {i - 1} \\left(1 - g _ {j} \\left(\\rho_ {a}\\right)\\right). \\tag {16}\n$$\n",
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+ "type": "text",
+ "text": "This module refines transformations by rendering and comparing them to minimize the discrepancy between the rendered object and the actual observations in the query image. The loss function can be defined as:",
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+ "type": "equation",
+ "text": "\n$$\nL _ {g s} ^ {P} = L _ {r g b} ^ {P} + L _ {\\text {d e p t h}} ^ {P}, \\tag {17}\n$$\n",
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+ "type": "page_number",
+ "text": "24872",
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+ "type": "equation",
+ "text": "\n$$\nL _ {r g b} ^ {P} = \\left\\| R _ {r g b} ^ {g s ^ {\\prime}} \\left(\\mathbb {G} ^ {Q}, \\mathbf {T} _ {g s} ^ {0}\\right) - I ^ {P} \\right\\| _ {1}, \\tag {18}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\nL _ {\\text {d e p t h}} ^ {P} = \\left\\| R _ {\\text {d e p t h}} ^ {g s} \\left(\\mathbb {G} ^ {Q}, \\mathbf {T} _ {g s} ^ {0}\\right) - D ^ {P} \\right\\| _ {1}, \\tag {19}\n$$\n",
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+ "text": "where $\\mathbb{G}^Q$ denote Gaussians associated with the point cloud $Q$ , $I^P$ and $D^P$ correspond to RGB image and depth image. $L_{gs}^{Q}$ can be obtained in the same way. For the point cloud $Q$ , we set the extrinsic matrix corresponding to its Gaussian as $\\mathbf{T}_{gs}^{0}$ , the rendering viewpoint of the camera as $\\mathbf{T}_0$ ( $\\mathbf{T}_0$ is the identity matrix), and the opposite for the point cloud $P$ . The input initial transformation $\\mathbf{T}_{gs}^{0}$ can be refined into the final result $\\mathbf{T}_{gs}^{R}$ output after GRPA module.",
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+ "text": "3.4. Loss function",
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+ "text": "As in previous works [13, 45, 52], the loss function consists of photometric, depth, and correspondence consistency losses without the need for ground truth. It can be defined as follows:",
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+ "type": "equation",
+ "text": "\n$$\nL = \\lambda_ {g s} L _ {g s} + \\lambda_ {c o r r} L _ {c o r r}, \\tag {20}\n$$\n",
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+ "text": "where $L_{gs}$ represents the photometric and depth consistencies loss as defined in Eq. (17), Eq. (18) and Eq. (19), $\\lambda_{gs}$ and $\\lambda_{corr}$ control the magnitude of these losses ensuring they are within an appropriate order of magnitude. $L_{corr}$ represents the correspondence consistency loss of $C_f$ , which can be donated as:",
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+ "text": "\n$$\nL _ {c o r r} = \\sum_ {(p, q, w) _ {f} \\in C _ {f}} w _ {f} \\left(T _ {g s} ^ {R} \\odot p _ {f} - q _ {f}\\right) ^ {2} / 2 k _ {f}, \\tag {21}\n$$\n",
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+ "type": "text",
+ "text": "where $\\odot$ represents the rigid transformation.",
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+ "type": "text",
+ "text": "4. Experiments",
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+ "type": "text",
+ "text": "4.1. Experimental Settings",
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+ "text": "Dataset. Following [52], OG-UPCR has been evaluated on several indoor real-world scene datasets, including 3DMatch [53], ScanNet [9] and ScanNet1500 [35]. Among them, 3DMatch and ScanNet generate view pairs by sampling an interval of 20 frames, resulting in 3DMatch containing $122\\mathrm{k} / 1.5\\mathrm{k} / 1.5\\mathrm{k}$ view pairs and ScanNet containing $1594\\mathrm{k} / 12.6\\mathrm{k} / 26\\mathrm{k}$ view pairs for training/validation/test, respectively. ScanNet1500 contains 1500 view pairs with an average interval of 480.8 frames between views, which makes it more challenging for the registration task.",
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+ "type": "text",
+ "text": "Metrics. Following the convention [12, 13, 45, 52], we evaluate OG-UPCR by three evaluation metrics: rotation error, translation error, and chamfering error. In analysis, we report the mean and median values of these metrics and assess their accuracy across various thresholds.",
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+ "text": "Competitors. We compare OG-UPCR with other methods, which can be primarily divided into three categories: (1) Conventional methods, including SIFT [25], SuperPoint [11] and FCGF [7]. (2) Supervised methods, including 3DMVReg [16], REGTR [49], BUFFER [1], and",
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+ "type": "text",
+ "text": "PARENet [47]. (3) Unsupervised methods, including UR&R [13], BYOC [12], LLT [45], PointMBF [52], and CCAP [52]. For the supervised methods, we verify their generalization on ScanNet using the officially provided weights trained on 3DMatch.",
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+ "text": "4.2. Evaluation on ScanNet",
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+ "text": "We first evaluate our OG-UPCR on the widely used ScanNet, with training weights from 3DMatch and ScanNet, respectively. The former validates the generalization performance comparison with other methods, and the latter evaluates the conventional cases.",
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+ "text": "Trained on 3DMatch. As shown in Table 1, the generalization experimental results trained on 3DMatch demonstrate that our method achieves the state-of-the-art registration results compared with all other methods, both unsupervised and supervised. This indicates that our method has excellent adaptability to unseen scenes, balancing both registration accuracy and generalization.",
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+ "text": "Trained on ScanNet. When there is no domain gap between the training set and the test set, our method also achieves the best registration results, as shown in Table 1. Even when the baseline is almost saturated, our method still shows significant accuracy improvements across each evaluation metric, with average reductions in rotation/translation/chamfer distance errors of $40.0\\% /34.5\\% /41.3\\%$ , respectively. This demonstrates that our proposed method also delivers excellent registration performance in conventional cases.",
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+ "text": "4.3. Evaluation on ScanNet1500",
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+ "text": "Following previous work [52], we conduct experiments on the challenging ScanNet1500 dataset to further demonstrate the effectiveness of our method. As shown in Table 2, our method outperforms all other unsupervised and supervised methods on the most stringent accuracy metric, and performs only slightly worse than the supervised method with the best generalization performance on the most permissive accuracy metric. The ScanNet1500 includes view pairs with low overlap and significant viewpoint variations, which pose substantial challenges for existing unsupervised methods. These conditions hinder the performance of previous methods, as geometric and photometric consistency between view pairs is greatly affected. In contrast, our method maintains strong performance by identifying reliable correspondences through overlapping constraint and further optimizing the model using the Gaussian Splitting technique.",
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+ "text": "4.4. Ablation Studies",
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+ "text": "Analysis of Each Component. We conduct a comprehensive ablation study for each component. The OCID module comprises two key components: Random Overlapping region prediction (RO) and Global-to-Local inliers detection",
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+ "img_path": "images/e8114dc9e4f589f07b866178649aec16526e9a0ea1433451d7f3f97390ad8e65.jpg",
+ "table_caption": [
+ "Table 1. Pairwise Registration accuracies and errors on ScanNet. Pose Sup means training with ground truth. The best result is shown in bold and the second best is underlined."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | Train set | Pose Sup | Rotation(°) | Translation(cm) | Chamfer(mm) | Time(s) |
| Accuracy | Error | Accuracy | Error | Accuracy | Error |
| 5 | 10 | 45 | Mean | Med | 5 | 10 | 25 | Mean | Med | 1 | 5 | 10 | Mean | Med |
| SIFT | - | | 55.2 | 75.7 | 89.2 | 18.6 | 44.3 | 17.7 | 44.5 | 79.8 | 26.5 | 11.2 | 38.1 | 70.6 | 78.3 | 42.6 | 1.7 | - |
| SuperPoint | - | | 65.5 | 86.9 | 96.6 | 8.9 | 3.6 | 21.2 | 51.7 | 88.0 | 16.1 | 9.7 | 45.7 | 81.1 | 88.2 | 19.2 | 1.2 | - |
| FCGF | - | ✓ | 70.2 | 87.7 | 96.2 | 9.5 | 3.3 | 27.5 | 58.3 | 82.9 | 23.6 | 8.3 | 52.0 | 78.0 | 83.7 | 24.4 | 0.9 | 0.129 |
| 3DMVReg | 3DMatch | ✓ | 87.7 | 93.2 | 97.0 | 6.0 | 1.2 | 69.0 | 83.1 | 91.8 | 11.7 | 2.9 | 78.9 | 89.2 | 91.8 | 10.2 | 0.2 | - |
| REGTR | 3DMatch | ✓ | 86.0 | 93.9 | 98.6 | 4.4 | 1.6 | 61.4 | 80.3 | 91.4 | 14.4 | 3.8 | 80.9 | 90.9 | 93.6 | 13.5 | 0.2 | - |
| BUFFER | 3DMatch | ✓ | 95.9 | 98.4 | 99.2 | 2.4 | 0.9 | 79.6 | 92.3 | 96.9 | 5.7 | 2.4 | 93.6 | 97.3 | 98.6 | 4.2 | 0.2 | 0.177 |
| PARENet | 3DMatch | ✓ | 97.5 | 98.3 | 99.5 | 1.9 | 0.7 | 85.9 | 95.7 | 97.0 | 3.9 | 1.8 | 94.2 | 97.9 | 98.6 | 4.2 | 0.2 | 0.165 |
| UR&R | 3DMatch | ✓ | 92.3 | 95.3 | 98.2 | 3.8 | 0.8 | 77.6 | 89.4 | 95.5 | 7.8 | 2.3 | 86.1 | 94.0 | 95.6 | 6.7 | 0.1 | 0.070 |
| UR&R | 3DMatch | | 87.6 | 93.1 | 98.3 | 4.3 | 1.0 | 69.2 | 84.0 | 93.8 | 9.5 | 2.8 | 79.7 | 91.3 | 94.0 | 7.2 | 0.2 | 0.071 |
| BYOC | 3DMatch | | 66.5 | 85.2 | 97.8 | 7.4 | 3.3 | 30.7 | 57.6 | 88.9 | 16.0 | 8.2 | 54.1 | 82.8 | 89.5 | 9.5 | 0.9 | - |
| LLT | 3DMatch | | 93.4 | 96.5 | 98.8 | 2.5 | 0.8 | 76.9 | 90.2 | 96.7 | 5.5 | 2.2 | 86.4 | 95.1 | 96.8 | 4.6 | 0.1 | 0.125 |
| PointMBF | 3DMatch | | 94.6 | 97.0 | 98.7 | 3.0 | 0.8 | 81.0 | 92.0 | 97.1 | 6.2 | 2.1 | 91.3 | 96.6 | 97.4 | 4.9 | 0.1 | 0.079 |
| CCAP | 3DMatch | | 95.6 | 98.1 | - | 2.4 | 0.7 | 81.5 | 92.3 | - | 3.7 | 1.9 | - | - | - | - | - | - |
| Ours | 3DMatch | | 97.9 | 98.9 | 99.5 | 1.8 | 0.7 | 87.7 | 96.2 | 98.6 | 3.8 | 1.8 | 95.5 | 98.4 | 98.8 | 3.3 | 0.1 | 0.136 |
| UR&R | ScanNet | | 92.7 | 95.8 | 98.5 | 3.4 | 0.8 | 77.2 | 89.6 | 96.1 | 7.3 | 2.3 | 86.0 | 94.6 | 96.1 | 5.9 | 0.1 | 0.071 |
| BYOC | ScanNet | | 86.5 | 95.2 | 99.1 | 3.8 | 1.7 | 56.4 | 80.6 | 96.3 | 8.7 | 4.3 | 78.1 | 93.9 | 96.4 | 5.6 | 0.3 | - |
| LLT | ScanNet | | 95.5 | 97.6 | 99.1 | 2.5 | 0.8 | 80.4 | 92.2 | 97.6 | 5.5 | 2.2 | 88.9 | 96.4 | 97.6 | 4.6 | 0.1 | 0.125 |
| PointMBF | ScanNet | | 96.0 | 97.6 | 98.9 | 2.5 | 0.7 | 83.9 | 93.8 | 97.7 | 5.6 | 1.9 | 92.8 | 97.3 | 97.9 | 4.7 | 0.1 | 0.079 |
| CCAP | ScanNet | | 97.1 | 98.2 | - | 1.9 | 0.6 | 85.9 | 93.6 | - | 3.9 | 1.8 | - | - | - | - | - | - |
| Ours | ScanNet | | 98.3 | 99.2 | 99.7 | 1.5 | 0.7 | 88.8 | 96.7 | 99.0 | 3.3 | 1.7 | 96.1 | 98.8 | 99.1 | 2.8 | 0.1 | 0.136 |
",
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+ "Table 2. Pairwise Registration accuracies and errors on ScanNet1500. The performance of our method is comparable to the supervised BUFFER method and significantly surpasses other unsupervised methods."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | Train set | Pose Sup | Rotation(°) | Translation(cm) | Chamfer(mm) |
| Accuracy | Error | Accuracy | Error | Accuracy | Error |
| 5 | 10 | 45 | Med | 5 | 10 | 25 | Med | 1 | 5 | 10 | Med |
| LLT | 3DMatch | | 36.1 | 49.9 | 79.9 | 10.0 | 17.2 | 29.9 | 46.6 | 29.6 | 23.5 | 40.4 | 48.3 | 12.1 |
| PointMBF | 3DMatch | | 51.1 | 60.8 | 82.9 | 4.7 | 31.5 | 44.2 | 59.3 | 13.8 | 44.8 | 57.5 | 63.3 | 1.7 |
| BUFFER | 3DMatch | ✓ | 74.9 | 82.5 | 90.9 | 1.8 | 47.4 | 66.5 | 81.0 | 5.0 | 66.5 | 79.5 | 84.2 | 0.3 |
| PARENet | 3DMatch | ✓ | 65.6 | 71.9 | 88.6 | 3.1 | 50.1 | 71.7 | 83.3 | 4.7 | 61.7 | 77.9 | 82.7 | 0.3 |
| Ours | 3DMatch | | 76.9 | 83.4 | 89.3 | 1.6 | 49.5 | 68.4 | 80.9 | 5.1 | 67.9 | 80.2 | 83.4 | 0.3 |
| LLT | ScanNet | | 43.7 | 54.6 | 80.3 | 7.5 | 24.0 | 36.1 | 52.9 | 20.6 | 31.7 | 47.8 | 53.4 | 6.6 |
| PointMBF | ScanNet | | 55.9 | 65.9 | 84.9 | 3.4 | 37.1 | 49.9 | 63.1 | 10.0 | 48.5 | 62.1 | 67.2 | 1.2 |
| Ours | ScanNet | | 81.3 | 85.9 | 91.2 | 1.5 | 53.5 | 72.1 | 83.3 | 4.3 | 72.4 | 83.3 | 85.9 | 0.3 |
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+ "text": "(GL). For the GRPA module, we use a conventional differentiable renderer [32] instead. As shown in Table 3, the results reveal the following: 1) The baseline performs worst on both datasets when none of the proposed components are used. 2) Adding the GRPA module improves registration performance on both datasets, indicating that the GRPA refines transformation. 3) The complete OCID module significantly improves registration, with a notable increase in performance on ScanNet1500: $22.2\\%$ in rotation accuracy $(< 5^{\\circ})$ , $14.6\\%$ in translation accuracy $(< 5\\mathrm{cm})$ , and $20.4\\%$ in chamfering accuracy $(< 1\\mathrm{mm})$ . This shows the OCID module's effectiveness in low-overlap scenes. 4) Additionally, using RO and GL separately results in improved registration performance for the entire framework. While the performance improvements on ScanNet are similar for both methods, RO achieves greater performance gains on ScanNet1500, demonstrating that the inclusion of overlapping constraint is particularly effective in scenarios with low overlap. 5) Finally, the complete framework with all com",
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+ "text": "ponents shows the best performance on both ScanNet and ScanNet1500, highlighting its strong adaptability.",
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+ "Table 3. Ablation studies on OG-UPCR. The model is trained on ScanNet. The best result is shown in bold."
+ ],
+ "table_footnote": [],
+ "table_body": "| OCID | GRPA | Test set | Rotation(°) | Translation(cm) | Chamfer(mm) |
| RO | GL | Accuracy < 5 | Error Med | Accuracy < 5 | Error Med | Accuracy < 1 | Error Med |
| × | × | × | ScanNet | 96.0 | 0.8 | 83.9 | 1.9 | 92.8 | 0.1 |
| × | × | ✓ | 97.4 | 0.8 | 84.9 | 1.9 | 94.6 | 0.1 |
| ✓ | ✓ | × | 97.7 | 0.7 | 85.7 | 1.8 | 95.1 | 0.1 |
| × | ✓ | × | 97.5 | 0.8 | 85.5 | 1.9 | 95.0 | 0.1 |
| ✓ | × | × | 97.2 | 0.8 | 84.7 | 1.9 | 93.9 | 0.1 |
| ✓ | ✓ | ✓ | 98.3 | 0.7 | 88.8 | 1.7 | 96.1 | 0.1 |
| × | × | × | ScanNet1500 | 56.3 | 3.4 | 36.5 | 10.0 | 48.5 | 1.2 |
| × | × | ✓ | 65.1 | 2.1 | 42.3 | 6.8 | 57.1 | 0.5 |
| ✓ | ✓ | × | 78.5 | 1.6 | 51.1 | 4.9 | 68.9 | 0.3 |
| × | ✓ | × | 73.9 | 1.9 | 46.1 | 5.7 | 65.5 | 0.4 |
| ✓ | × | × | 74.7 | 1.6 | 46.7 | 4.8 | 66.4 | 0.3 |
| ✓ | ✓ | ✓ | 81.3 | 1.5 | 53.5 | 4.3 | 72.4 | 0.3 |
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+ "text": "Validation of the OCID for Inliers Detection. To evaluate the effect of the OCID module on the detection of inliers,",
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+ "Figure 3. The visualization of point cloud registration results for PointMBF and the proposed OG-UPCR is presented. The results in the first row depict registration case with low overlap, while the results in the second row illustrate registration case with inconsistent photometric information caused by significant viewpoint variation."
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+ "text": "we visually compared the results before and after incorporating it. As shown in Fig. 4, after integrating the OCID module, the proportion of inliers is significantly increased in scenarios with low overlap, which facilitates subsequent geometric fitting and enhances the overall performance of the registration model.",
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+ "text": "Validation of the GRPA for Photometric Adaptation. To explore the impact of the GRPA, we replaced it with a traditional differentiable renderer and compared the rendered results. As shown in Fig. 5, the results demonstrate that incorporating the GRPA significantly reduces artifacts and enhances inter-frame consistency. This improvement is essential for ensuring consistent feature descriptors, as further discussed in Supplementary Material 4.4.",
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+ "w/o GRPA",
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+ "Figure 5. Validation of the GRPA for Photometric Adaptation. Comparison of the rendered results reveals that after applying the GRPA module, the artifacts are significantly reduced, leading to improved consistency between the input and rendered frames."
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+ "text": "respondences, demonstrating enhanced adaptability to low overlap (first row). Additionally, our method performs better under inconsistent photometric conditions in the scene (second row), indicating greater robustness.",
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+ "text": "We introduce OG-UPCR, a framework for unsupervised point cloud registration. The method consists of two primary modules: OCID and GRVA. The OCID module enables the model to adapt to low-overlap scenes while maintaining a balance between accuracy and efficiency. The GRVA module refines the initial geometric transformation, enhancing the model's robustness to inconsistent photometric information. Extensive experiments on public datasets demonstrate the effectiveness of the proposed method.",
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+ "text": "Acknowledgement. This work is supported by the National Key R&D Program of China (No. 2023YFB3307202), Science and Technology Innovation Leading Talent Project of Special Support Plan for High-level Talents of Zhejiang Province (Grant No. 2022R52053).",
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+ "angle": 0,
+ "content": "Point cloud registration is a fundamental task in 3D vision, playing a crucial role in various fields. With the rapid advancement of RGB-D sensors, unsupervised point cloud registration methods based on RGB-D sequences have demonstrated excellent performance. However, existing methods struggle in scenes with low overlap and photometric inconsistency. Low overlap results in numerous correspondence outliers, while photometric inconsistency hinders the model's ability to extract discriminative features. To address these challenges, we first propose the Overlapping Constraint for Inliers Detection (OCID) module, which filters and optimizes the initial correspondence set using an overlapping constraint. This module robustly selects reliable correspondences within the overlapping region while maintaining a balance between accuracy and efficiency. Additionally, we introduce a novel scene representation, 3DGS, which integrates both geometric and texture information, making it particularly well-suited for RGB-D registration tasks. Building on this, we propose the Gaussian Rendering for Photometric Adaptation (GRPA) module, which refines the geometric transformation and enhances the model's adaptability to scenes with inconsistent photometric information. Extensive experiments on ScanNet and ScanNet1500 demonstrate that our method achieves state-of-the-art performance. The code will be released at OG-UPCR."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Point cloud registration is a critical task in 3D vision, with applications in navigation [30, 44, 56], pose estimation [10, 17], and 3D reconstruction [42, 43]. Typically, two frames of point clouds rely on feature extraction to estimate correspondences, followed by robust geometric fitting techniques to obtain the transformation."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 1. The objective of the proposed OG-UPCR is to effectively register scenes with low overlap and photometric inconsistency. The overlapping region constraint helps reduce correspondence outliers caused by low overlap, while photometric inconsistency is adaptively adjusted through the estimizable parameters contained in 3D Gaussians [24]. Compared to PointMBF [52], the proposed OG-UPCR produces more consistent results between input and rendered frames (highlighted in red boxes) and yields better registration outcomes."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.72,
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+ ],
+ "angle": 0,
+ "content": "With the rapid development of RGB-D sensors, unsupervised registration methods [12-14, 27, 40, 45, 52] have demonstrated impressive performance. These methods rasterize 3D points into images using a differentiable renderer [32] and employ geometric and photometric consistency losses between the input and rendered frames to extract features, thereby estimating the geometric transformation between nearby frames without the need for ground truth. However, all these methods ignore that the geometric and photometric information between frames to be registered is not always consistent, particularly in scenes with low overlap and photometric inconsistency. Low overlap"
+ },
+ {
+ "type": "page_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "*Corresponding author"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "24868"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.482,
+ 0.242
+ ],
+ "angle": 0,
+ "content": "complicates feature identification and correspondence estimation [20], while photometric inconsistency hinders the modeling of feature consistency between input and rendered frames, making it challenging for the model to obtain discriminative features, especially in scenes with reflections and rendering artifacts [52]. Despite the excellent registration performance of PointMBF [52], it still suffers from low overlap and photometric inconsistency, which result in a large number of correspondence outliers and erroneous rendered and registration results, as illustrated in Fig. 1."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.243,
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+ ],
+ "angle": 0,
+ "content": "We observe that inliers must be located within overlapping regions, whereas outliers can be filtered out early using overlapping constraint. Although identifying inliers and overlaps is a chicken-and-egg situation, it can be efficiently resolved through an iterative process. Meanwhile, recent advances in 3D Gaussian Splatting [24] have made significant strides in novel view synthesis [4, 54], 3D generation [6, 50], and SLAM [23, 26, 46]. This technique not only represents geometry in a smooth and continuously differentiable manner but also preserves view-varying texture information, which is adaptive to photometric changes. Additionally, 3D points convert easily into 3D Gaussians, making this approach highly suitable for RGB-D registration."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.439,
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+ 0.695
+ ],
+ "angle": 0,
+ "content": "To this end, we propose OG-UPCR, an innovative unsupervised point cloud registration framework designed to address low overlap and photometric inconsistency, as shown in Fig. 1. Specifically, we propose the Overlapping Constraint for Inliers Detection module (OCID) based on the observation that inliers must lie within overlapping regions. This module leverages overlapping constraints to detect inliers, addressing issues arising from low overlap. Additionally, we design the Gaussian Rendering for Photometric Adaptation module (GRPA), which converts 3D points into 3D Gaussians and rasterizes them into image space, leveraging the rich geometric and texture information contained in the Gaussians. Based on this, nonlinear optimization is applied to each pixel to enhance photometric adaptation and enable the model to extract discriminative features. Moreover, this process refines the transformation and improves overall registration."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "The OG-UPCR is thoroughly evaluated on the standard datasets, including 3DMatch [53], ScanNet [9], and the challenging ScanNet1500 [35], which contain paired views with low overlap and inconsistent photometric information, achieving state-of-the-art performance. Additionally, we conduct extensive ablation experiments on individual modules to demonstrate the effectiveness of each component."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In summary, our contributions are as follows:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.826,
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+ ],
+ "angle": 0,
+ "content": "- We propose OG-UPCR, an unsupervised registration framework that combines overlapping constraint with gaussian splatting, enhancing the accuracy and robustness of the overall registration model."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.887,
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+ 0.9
+ ],
+ "angle": 0,
+ "content": "- We propose a correspondence optimization strategy us"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.091,
+ 0.826,
+ 0.481,
+ 0.9
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.527,
+ 0.092,
+ 0.905,
+ 0.152
+ ],
+ "angle": 0,
+ "content": "ing iterative random overlapping region prediction. This module selects faithful inliers of correspondences within the overlapping region, mitigating the impact of low overlap and enhancing the accuracy of geometric fitting."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.514,
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+ ],
+ "angle": 0,
+ "content": "- We propose a photometric adaptation module for paired views that employs Gaussian splatting to independently render the Gaussians of both views. This module models the photometric consistency of features across frames, and refines the final transformation."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2. Related Work"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.1. Point Cloud Registration"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "Early point cloud registration methods [21, 33, 34, 39] rely on hand-crafted feature descriptors, which are sensitive to noise and not robust to changes in the number and density of point clouds. Recently, deep learning feature descriptors have demonstrated impressive performance and can achieve better registration results. Research based on deep learning can be divided into supervised [2, 20, 29, 37, 41, 51] and unsupervised [12, 13, 28, 36, 45, 52] methods. However, supervised methods require real poses as supervision signals, making them difficult to apply practically. When encountering new scenes with domain gaps, they can only rely on the trained weights to infer the registration results, which often affects their performance. Unsupervised methods can be further divided into geometric-based and RGB-D based methods according to the input data. Among geometric-based methods, RIENet [36] proposes a reliable inlier evaluation method based on neighborhood consensus. UDReg [28] operates by learning the posterior probability distribution of Gaussian Mixture Models from point clouds and then predicting distribution-level correspondences. Since the input contains only geometric information, these methods struggle with geometric weak regions (such as floors, ceilings, and walls) and repeated structures in real scenes. RGB-D based methods are able to handle real scenes, such as LLT [45] employing a linear attention module to fuse geometric and texture features. PointMBF [52] proposes a multi-scale bidirectional fusion network to fully utilize the complementary information of RGB-D. Nevertheless, these methods all employ a conventional differentiable renderer to render 3D points directly, making them susceptible to low overlap and photometric inconsistency. In contrast, we propose the OCID module based on overlapping constraint to help obtain more reliable correspondences. Additionally, we design the GRPA module to reduce the impact of photometric inconsistency, thereby enhancing registration accuracy."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "2.2. Correspondence Optimization Strategy"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The handling of correspondence outliers can be effectively addressed using methods such as RANSAC. Although RANSAC [15] and its variants [3, 31] are widely"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "24869"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.118,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
+ 0.392,
+ 0.908,
+ 0.465
+ ],
+ "angle": 0,
+ "content": "Figure 2. The overview of OG-UPCR. The backbone first extracts the features \\( F_{P}^{f} \\) and \\( F_{Q}^{f} \\) from the point clouds \\( P \\) and \\( Q \\). The initial correspondences are estimated by calculating Lowe's ratio in the feature space, which is then optimized by the OCID module using the overlapping constraint. Subsequently, the rigid transformation is determined through geometric fitting. Finally, based on this transformation, the Gaussian cross-rendering results generated by the GRPA module form the paired views are used to calculate the loss. This process not only refines the final result but also aids the model in acquiring distinct features."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
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+ ],
+ "angle": 0,
+ "content": "recognized algorithms, their performance remains sensitive to outliers, often requiring numerous iterations to produce relatively accurate results. SC2PCR [5] and MAC [55] are also effective in managing correspondence outliers, but both rely on relative spatial constraint and fail to account for the fact that correct correspondences should be confined to the overlapping region from global spatial constraint. This oversight leads to inefficiency and inaccuracy, as excessive redundant point pairs are utilized. In contrast, we propose an overlapping constraint module based on global spatial to select reliable correspondences, thereby improving the efficiency and accuracy of the registration process."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "2.3. Gaussian Splatting"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "As a novel scene representation and efficient differentiable renderer, 3D Gaussian Splatting [24] has shown its significant advantages in novel view synthesis [4, 48, 54], 3D generation [6, 50] and SLAM [23, 26, 46]. SplaTAM [23] introduces an online tracking and mapping system based on the underlying 3D Gaussian representation, without requiring the real pose. However, it relies on dense RGB-D frame inputs, making it difficult to obtain accurate poses with sparse input. PixelSplat [6] proposes that the radiance field parameterized by 3D Gaussian primitives can be learned and reconstructed from sparse views. NoPoSplat [48] integrates PnP [18] and 3DGS [24] to estimate poses from sparse views, achieving superior novel"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.489,
+ 0.909,
+ 0.612
+ ],
+ "angle": 0,
+ "content": "view synthesis. Nevertheless, these methods estimate poses from an image-based perspective, resulting in the loss of 3D information. In contrast, the proposed GRPA module derives a more precise geometric transformation from the point cloud perspective, producing rasterized outputs independent of true pose data. This approach exhibits robust generalization and achieves accurate registration even with sparse inputs."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3. Method"
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "3.1. Problem Statement and Overview"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "Problem Statement. Given point clouds \\( P \\in \\mathbb{R}^{N \\times 3} \\) and \\( Q \\in \\mathbb{R}^{N \\times 3} \\), the purpose of the registration task is to obtain a transformation matrix \\( \\mathbf{T} = \\{\\mathbf{R}, \\mathbf{t}\\} \\), that aligns \\( P \\) and \\( Q \\) in the same coordinate system. This transformation matrix consists of a rotation matrix \\( \\mathbf{R} \\in \\mathbf{SO}(3) \\) and a translation vector \\( \\mathbf{t} \\in \\mathbb{R}^3 \\). The correspondence set \\( C = \\{\\mathbf{p}_i, \\mathbf{q}_j | \\mathbf{p}_i \\in P, \\mathbf{q}_j \\in Q\\} \\) is estimated by feature extraction and matching. The transformation can be determined by:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.601,
+ 0.818,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\underset {\\mathbf {R}, \\mathbf {t}} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {n} \\| \\mathbf {R} \\cdot \\mathbf {p} _ {i} + \\mathbf {t} - \\mathbf {q} _ {j} \\| _ {2} ^ {2}, \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "where \\(\\| \\cdot \\| _2^2\\) denotes the Euclidean norm, \\(n\\) is the number of correspondences that can be found in paired point clouds."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "24870"
+ }
+ ],
+ [
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+ "type": "text",
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+ "angle": 0,
+ "content": "Overview. In this paper, we propose an OCID module and a GRPA module to address challenges associated with low overlap and photometric inconsistency. The OG-UPCR processes paired point clouds and their corresponding RGB-D frames as input, following the PointMBF [52] to extract feature descriptors. Using these descriptors, we compute an initial correspondence set by measuring distances in the feature space. The OCID module then filters this initial set based on an overlapping region constraint, selecting reliable seed points for geometric fitting, which produces a coarse transformation, denoted as \\(\\mathbf{T}_{gs}^{0}\\), as described in Section 3.2. This transformation serves as the initial pose for the GRPA module, where 3D points are first converted into 3D Gaussians and then projected onto an image using a Gaussian splatting renderer, which is subsequently refined to obtain the final result, \\(\\mathbf{T}_{gs}^{R}\\), as detailed in Section 3.3. Additionally, the entire registration framework is trained in an end-to-end unsupervised manner using geometric and photometric consistency losses between input and rendered frames, as discussed in UR&R [13]. An overview of OG-UPCR is provided in Fig. 2."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Feature Extraction. Building upon prior research, we employ KPCov [38] and ResNet [19] to extract multi-scale information from the point clouds and images. Subsequently, a multi-scale bidirectional fusion method [52] generates distinctive fused feature descriptors \\( F_{P}^{f} \\in \\mathbb{R}^{N \\times C_{3D}} \\) and \\( F_{Q}^{f} \\in \\mathbb{R}^{N \\times C_{3D}} \\) for point clouds \\( P \\) and \\( Q \\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3.2. Correspondence Estimation"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Initial Correspondence Set Acquisition. After obtaining the feature descriptors of the point clouds, we follow previous method [13, 45, 52] to obtain the initial correspondence set based on Lowe's ratio [25]. For a point \\(\\mathbf{p}_i\\), its Lowe's ratio can be computed as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\nr _ {i} = \\frac {D \\left(\\mathbf {p} _ {i} , \\mathbf {q} _ {j} ^ {1 n n}\\right)}{D \\left(\\mathbf {p} _ {i} , \\mathbf {q} _ {j} ^ {2 n n}\\right)}, \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\(D(\\cdot)\\) represents the Euclidean distance in the feature space and \\(q_{j}^{knn}\\) is the k-th similarity point in the point cloud \\(Q\\). We assign weights to each correspondence using the formula \\(w = 1 - r\\). Next, we apply the top-k algorithm to select the weighted correspondences, resulting in a correspondence set from \\(C_{P \\to Q}\\). We choose an equal number of correspondences from \\(C_{Q \\to P}\\) in a similar manner to create the initial correspondence set:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\nC _ {\\text {i n i t i a l}} = \\left\\{\\left(\\mathbf {p}, \\mathbf {q}, w\\right) _ {m}: 0 \\leq m < 2 k \\right\\}, \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "where \\( k \\) denotes the top \\( k \\) weights. The resulting correspondence \\( C_{\\mathrm{initial}} \\) will be input into the OCID module for further optimization."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Overlapping Constraint for Inliers Detection. This module is designed to detect inliers from the initial correspondence set, facilitating efficient registration in scenarios with"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "low overlap. Existing works [5, 55] directly remove outliers based on the consistency graph but neglect the importance of the overlapping region constraint, leading to significant computational expenses. As shown in Fig. 2, the module consists of two components, which are detailed below."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Random Overlapping Region Prediction. As is well known, Weighted SVD [8] produces an approximate geometric transformation by performing singular value decomposition on the weights of the correspondence set. The accuracy of this transformation will be affected by the inliers in the correspondence, meaning that the higher the weight of the inliers, the more accurate the transformation will be. Motivated by this and inspired by RANSAC [15], we first randomly select a partial subset from the initial correspondence:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.561,
+ 0.327,
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+ ],
+ "angle": 0,
+ "content": "\\[\nC _ {n} = \\left\\{\\left(\\mathbf {p}, \\mathbf {q}, w\\right) _ {n}: 0 \\leq n < 2 r k \\right\\} \\in C _ {\\text {i n i t i a l}}, \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "where \\( r \\) denotes the proportion of the subset in the initial correspondence, which is set to 0.2. Next, we apply Weighted SVD to obtain the transformation \\( \\mathbf{T}_s \\) of this subset. Unlike similar previous work [13, 45, 52], we do not directly leverage the common L2 distance to assess whether \\( \\mathbf{T}_s \\) is correct, which is prone to fall into local optima. Instead, we propose a novel approach based on overlapping region prediction. Using \\( \\mathbf{T}_s \\), we predict the overlapping area of the point cloud and evaluate its success by the overlap ratio \\( O_p \\), which is defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "\\[\nP ^ {\\prime} = \\mathbf {T} _ {s} \\odot P, \\tag {5}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.596,
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+ ],
+ "angle": 0,
+ "content": "\\[\nO _ {p} = \\frac {1}{N} \\sum_ {n = 1} ^ {N _ {P ^ {\\prime}}} \\llbracket \\| \\mathbf {p} _ {n} ^ {\\prime} - \\mathbf {q} _ {n} \\| _ {2} < \\tau \\rrbracket , \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "where \\(\\llbracket \\cdot \\rrbracket\\) is the Iverson bracket, \\(\\odot\\) represents the rigid transformation, \\(N_{P^{\\prime}}\\) is the number of points of the point cloud \\(P^{\\prime}\\) and \\(\\tau\\) is set to \\(5\\mathrm{cm}\\). If \\(O_p\\) exceeds the threshold \\(O_{thr}\\), the prediction is considered successful. This implies that most of the correspondences within the selected subset are inliers, and the subset is classified as a positive subset, receiving a higher weight in the initial correspondence set. To meet these conditions, we multiply the weight of the points in the subset of successful predictions by a reward factor, thereby increasing their proportion in the initial correspondence. Conversely, if the prediction fails, it indicates that the selected subset contains a high percentage of outliers. In this case, the corresponding weights in those subsets are multiplied by a penalty factor, which is defined as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.608,
+ 0.816,
+ 0.906,
+ 0.85
+ ],
+ "angle": 0,
+ "content": "\\[\nw _ {n} = \\left\\{ \\begin{array}{l} w _ {n} \\cdot w _ {r}, O _ {p} \\geq O _ {t h r} \\\\ w _ {n} \\cdot w _ {p}, O _ {p} < O _ {t h r} \\end{array} , \\right. \\tag {7}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.901
+ ],
+ "angle": 0,
+ "content": "where \\( w_{r} \\) and \\( w_{p} \\) denote the reward factor and penalty factor, and \\( w_{r} \\cdot w_{p} = 1 \\) to ensure the balance change of a correspondence when it is selected into the subset many times."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "24871"
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+ "angle": 0,
+ "content": "The above prediction process is repeated \\( N \\) times. After completing the random overlapping region prediction, the weights of the individual correspondences within the initial correspondence set are significantly optimized, with inliers receiving higher weights and the weights of outliers being reduced. To enhance the efficiency of the algorithm, we also use the top-k algorithm to select the appropriate correspondence. The optimized set of correspondences can be defined as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.162,
+ 0.237,
+ 0.483,
+ 0.263
+ ],
+ "angle": 0,
+ "content": "\\[\nC _ {f} = \\left\\{\\left(\\mathbf {p}, \\mathbf {q}, w\\right) _ {f}: 0 \\leq m < 2 k _ {f} \\right\\}, \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.275,
+ 0.484,
+ 0.334
+ ],
+ "angle": 0,
+ "content": "where \\( k_{f} \\) means that the top-k algorithm is used to select items with larger weights to speed up the algorithm. We also provide a pseudocode and simple flowchart in Supplementary Material. 2."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.336,
+ 0.484,
+ 0.486
+ ],
+ "angle": 0,
+ "content": "Global-to-Local Inliers Detection. The optimized correspondence set \\( C_f \\) already exhibits a high inlier ratio. However, one issue remains: the selected correspondences are concentrated in specific local regions rather than uniformly distributed. This concentration hinders the subsequent geometric fitting. To address this challenge, we propose a global-to-local inlier detection module based on spatial consistency, as shown in Fig. 2. First, we compute the second order spatial compatibility (\\( SC^2 \\)) [5] of the optimized correspondence set globally, which can be defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.192,
+ 0.5,
+ 0.483,
+ 0.542
+ ],
+ "angle": 0,
+ "content": "\\[\nS C _ {i j} ^ {2} = C _ {i j} \\cdot \\sum_ {k = 1} ^ {N} C _ {i k} \\cdot C _ {k j}, \\tag {9}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.208,
+ 0.558,
+ 0.482,
+ 0.591
+ ],
+ "angle": 0,
+ "content": "\\[\nC _ {i j} = \\left\\{ \\begin{array}{l} 1, d _ {i j} \\leq d _ {t h r} \\\\ 0, d _ {i j} > d _ {t h r} \\end{array} , \\right. \\tag {10}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.168,
+ 0.602,
+ 0.483,
+ 0.622
+ ],
+ "angle": 0,
+ "content": "\\[\nd _ {i j} = \\left| \\left\\| \\mathbf {p} _ {i} - \\mathbf {p} _ {j} \\right\\| _ {2} - \\left\\| \\mathbf {q} _ {i} - \\mathbf {q} _ {j} \\right\\| _ {2} \\right|, \\tag {11}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.63,
+ 0.484,
+ 0.794
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbf{p}_i, \\mathbf{p}_j\\) and \\(\\mathbf{q}_i, \\mathbf{q}_j\\) denote two sets of correspondence points in \\(C_f\\), and \\(d_{thr}\\) is set to \\(10\\mathrm{cm}\\). Subsequently, the optimized weights \\(w_f\\) are employed to find the seed points with the maximum confidence score within their neighborhood, defined by a radius \\(R\\), ensuring that the correspondences are uniformly distributed. To ensure that the selected seed points are reliable inliers, we measure the correspondence of the seed point and its top-\\(K\\) neighbors based on the constructed \\(SC^2\\) metric to further prune potential outliers. Finally, these seed points and their neighboring points form multiple consensus sets."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.796,
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+ ],
+ "angle": 0,
+ "content": "Geometric Fitting. To project images of the transformed point clouds \\( P \\) and \\( Q \\) using a Gaussian renderer, it is necessary to estimate their geometric transformation. This estimation is achieved through geometric fitting. Following [5], we estimate the geometric transformation according to each consensus set. Finally, we choose the transformation with the highest number of inliers as the result \\( \\mathbf{T}_{gs}^{0} \\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
+ 0.091,
+ 0.709,
+ 0.108
+ ],
+ "angle": 0,
+ "content": "3.3. Gaussian Rendering"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.113,
+ 0.907,
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+ ],
+ "angle": 0,
+ "content": "This module is designed to help the model adapt to inconsistent photometric information between the input and rendered frames. Previous approaches [13, 45, 52] rely on traditional differentiable renderer [32] to directly project 3D points into the image space, which makes their models susceptible to significant viewpoint changes and limits the ability to extract more discriminative features. To overcome these challenges, we draw inspiration from [22, 26] and introduce the 3D Gaussian splatting technique. Additionally, we propose a photometric adaptation mechanism for each pixel to resolve the inconsistencies caused by viewpoint changes, thereby enabling the model to learn more discriminative features for registration."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.31,
+ 0.907,
+ 0.399
+ ],
+ "angle": 0,
+ "content": "Gaussian Rendering for Photometric Adaptation. Specifically, each point can be represented by a Gaussian [22] with eight parameter values: its point position \\(\\mu_{3D} \\in \\mathbb{R}^3\\), RGB color \\(\\mathbf{c} \\in \\mathbb{R}^3\\), radius \\(r\\), and opacity \\(o \\in [0,1]\\). Each Gaussian affects a point in 3D space \\(\\mathbf{x} \\in \\mathbb{R}^3\\) as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.594,
+ 0.404,
+ 0.906,
+ 0.445
+ ],
+ "angle": 0,
+ "content": "\\[\ng (\\mathbf {x}) = o \\exp \\left(- \\frac {\\| \\mathbf {x} - \\mu_ {3 D} \\| ^ {2}}{2 r _ {3 D} ^ {2}}\\right), \\tag {12}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.451,
+ 0.906,
+ 0.479
+ ],
+ "angle": 0,
+ "content": "each pixel \\(\\rho\\) in the differentiable rendered RGB image can then be rendered as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.548,
+ 0.486,
+ 0.906,
+ 0.528
+ ],
+ "angle": 0,
+ "content": "\\[\nR _ {r g b} ^ {g s} (\\mathbb {G}, \\mathbf {T}) = \\sum_ {i = 1} ^ {n} c _ {i} g _ {i} (\\rho) \\prod_ {j = 1} ^ {i - 1} (1 - g _ {j} (\\rho)), \\tag {13}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.535,
+ 0.906,
+ 0.579
+ ],
+ "angle": 0,
+ "content": "where \\(g(\\rho_a)\\) can be obtained from Eq. (12) and (13), but with \\(\\mu_{3D}\\) and \\(r_{3D}\\) of the splatted 2D Gaussians in pixel space:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.615,
+ 0.579,
+ 0.905,
+ 0.608
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mu_ {2 D} = \\mathbf {K T} \\frac {\\mu_ {3 D}}{d}, r _ {2 D} = \\frac {f}{d}, \\tag {14}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.61,
+ 0.906,
+ 0.685
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbf{K}\\) is the camera intrinsic matrix, \\(\\mathbf{T}\\) is the extrinsic matrix, \\(f\\) is the focal length of the camera, and \\(d\\) is the depth. To further enhance the adaptability to photometric changes, we optimize the nonlinear photometric adaptation of each pixel:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.617,
+ 0.692,
+ 0.905,
+ 0.715
+ ],
+ "angle": 0,
+ "content": "\\[\nR _ {r g b} ^ {g s ^ {\\prime}} = \\exp (\\alpha) \\cdot R _ {r g b} ^ {g s} + \\beta , \\tag {15}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.719,
+ 0.906,
+ 0.763
+ ],
+ "angle": 0,
+ "content": "where \\(\\alpha\\) and \\(\\beta\\) are both learnable parameters. A similar differentiable rendered depth image can be expressed as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.536,
+ 0.769,
+ 0.905,
+ 0.811
+ ],
+ "angle": 0,
+ "content": "\\[\nR _ {\\text {d e p t h}} ^ {g s} (\\mathbb {G}, \\mathbf {T}) = \\sum_ {i = 1} ^ {n} d _ {i} g _ {i} \\left(\\rho_ {a}\\right) \\prod_ {j = 1} ^ {i - 1} \\left(1 - g _ {j} \\left(\\rho_ {a}\\right)\\right). \\tag {16}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.818,
+ 0.906,
+ 0.877
+ ],
+ "angle": 0,
+ "content": "This module refines transformations by rendering and comparing them to minimize the discrepancy between the rendered object and the actual observations in the query image. The loss function can be defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.638,
+ 0.884,
+ 0.905,
+ 0.904
+ ],
+ "angle": 0,
+ "content": "\\[\nL _ {g s} ^ {P} = L _ {r g b} ^ {P} + L _ {\\text {d e p t h}} ^ {P}, \\tag {17}\n\\]"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
+ 0.945,
+ 0.521,
+ 0.957
+ ],
+ "angle": 0,
+ "content": "24872"
+ }
+ ],
+ [
+ {
+ "type": "equation",
+ "bbox": [
+ 0.17,
+ 0.088,
+ 0.482,
+ 0.114
+ ],
+ "angle": 0,
+ "content": "\\[\nL _ {r g b} ^ {P} = \\left\\| R _ {r g b} ^ {g s ^ {\\prime}} \\left(\\mathbb {G} ^ {Q}, \\mathbf {T} _ {g s} ^ {0}\\right) - I ^ {P} \\right\\| _ {1}, \\tag {18}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.16,
+ 0.119,
+ 0.482,
+ 0.145
+ ],
+ "angle": 0,
+ "content": "\\[\nL _ {\\text {d e p t h}} ^ {P} = \\left\\| R _ {\\text {d e p t h}} ^ {g s} \\left(\\mathbb {G} ^ {Q}, \\mathbf {T} _ {g s} ^ {0}\\right) - D ^ {P} \\right\\| _ {1}, \\tag {19}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.149,
+ 0.483,
+ 0.273
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathbb{G}^Q\\) denote Gaussians associated with the point cloud \\(Q\\), \\(I^P\\) and \\(D^P\\) correspond to RGB image and depth image. \\(L_{gs}^{Q}\\) can be obtained in the same way. For the point cloud \\(Q\\), we set the extrinsic matrix corresponding to its Gaussian as \\(\\mathbf{T}_{gs}^{0}\\), the rendering viewpoint of the camera as \\(\\mathbf{T}_0\\) (\\(\\mathbf{T}_0\\) is the identity matrix), and the opposite for the point cloud \\(P\\). The input initial transformation \\(\\mathbf{T}_{gs}^{0}\\) can be refined into the final result \\(\\mathbf{T}_{gs}^{R}\\) output after GRPA module."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.28,
+ 0.232,
+ 0.294
+ ],
+ "angle": 0,
+ "content": "3.4. Loss function"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.302,
+ 0.484,
+ 0.36
+ ],
+ "angle": 0,
+ "content": "As in previous works [13, 45, 52], the loss function consists of photometric, depth, and correspondence consistency losses without the need for ground truth. It can be defined as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.196,
+ 0.362,
+ 0.482,
+ 0.379
+ ],
+ "angle": 0,
+ "content": "\\[\nL = \\lambda_ {g s} L _ {g s} + \\lambda_ {c o r r} L _ {c o r r}, \\tag {20}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.383,
+ 0.484,
+ 0.472
+ ],
+ "angle": 0,
+ "content": "where \\(L_{gs}\\) represents the photometric and depth consistencies loss as defined in Eq. (17), Eq. (18) and Eq. (19), \\(\\lambda_{gs}\\) and \\(\\lambda_{corr}\\) control the magnitude of these losses ensuring they are within an appropriate order of magnitude. \\(L_{corr}\\) represents the correspondence consistency loss of \\(C_f\\), which can be donated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.112,
+ 0.481,
+ 0.482,
+ 0.518
+ ],
+ "angle": 0,
+ "content": "\\[\nL _ {c o r r} = \\sum_ {(p, q, w) _ {f} \\in C _ {f}} w _ {f} \\left(T _ {g s} ^ {R} \\odot p _ {f} - q _ {f}\\right) ^ {2} / 2 k _ {f}, \\tag {21}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.525,
+ 0.385,
+ 0.54
+ ],
+ "angle": 0,
+ "content": "where \\(\\odot\\) represents the rigid transformation."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.552,
+ 0.224,
+ 0.569
+ ],
+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.577,
+ 0.299,
+ 0.594
+ ],
+ "angle": 0,
+ "content": "4.1. Experimental Settings"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.599,
+ 0.483,
+ 0.75
+ ],
+ "angle": 0,
+ "content": "Dataset. Following [52], OG-UPCR has been evaluated on several indoor real-world scene datasets, including 3DMatch [53], ScanNet [9] and ScanNet1500 [35]. Among them, 3DMatch and ScanNet generate view pairs by sampling an interval of 20 frames, resulting in 3DMatch containing \\(122\\mathrm{k} / 1.5\\mathrm{k} / 1.5\\mathrm{k}\\) view pairs and ScanNet containing \\(1594\\mathrm{k} / 12.6\\mathrm{k} / 26\\mathrm{k}\\) view pairs for training/validation/test, respectively. ScanNet1500 contains 1500 view pairs with an average interval of 480.8 frames between views, which makes it more challenging for the registration task."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.75,
+ 0.483,
+ 0.825
+ ],
+ "angle": 0,
+ "content": "Metrics. Following the convention [12, 13, 45, 52], we evaluate OG-UPCR by three evaluation metrics: rotation error, translation error, and chamfering error. In analysis, we report the mean and median values of these metrics and assess their accuracy across various thresholds."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.826,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Competitors. We compare OG-UPCR with other methods, which can be primarily divided into three categories: (1) Conventional methods, including SIFT [25], SuperPoint [11] and FCGF [7]. (2) Supervised methods, including 3DMVReg [16], REGTR [49], BUFFER [1], and"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.906,
+ 0.168
+ ],
+ "angle": 0,
+ "content": "PARENet [47]. (3) Unsupervised methods, including UR&R [13], BYOC [12], LLT [45], PointMBF [52], and CCAP [52]. For the supervised methods, we verify their generalization on ScanNet using the officially provided weights trained on 3DMatch."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.178,
+ 0.727,
+ 0.193
+ ],
+ "angle": 0,
+ "content": "4.2. Evaluation on ScanNet"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.2,
+ 0.906,
+ 0.275
+ ],
+ "angle": 0,
+ "content": "We first evaluate our OG-UPCR on the widely used ScanNet, with training weights from 3DMatch and ScanNet, respectively. The former validates the generalization performance comparison with other methods, and the latter evaluates the conventional cases."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.276,
+ 0.906,
+ 0.382
+ ],
+ "angle": 0,
+ "content": "Trained on 3DMatch. As shown in Table 1, the generalization experimental results trained on 3DMatch demonstrate that our method achieves the state-of-the-art registration results compared with all other methods, both unsupervised and supervised. This indicates that our method has excellent adaptability to unseen scenes, balancing both registration accuracy and generalization."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.382,
+ 0.907,
+ 0.533
+ ],
+ "angle": 0,
+ "content": "Trained on ScanNet. When there is no domain gap between the training set and the test set, our method also achieves the best registration results, as shown in Table 1. Even when the baseline is almost saturated, our method still shows significant accuracy improvements across each evaluation metric, with average reductions in rotation/translation/chamfer distance errors of \\(40.0\\% /34.5\\% /41.3\\%\\), respectively. This demonstrates that our proposed method also delivers excellent registration performance in conventional cases."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.543,
+ 0.762,
+ 0.558
+ ],
+ "angle": 0,
+ "content": "4.3. Evaluation on ScanNet1500"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.566,
+ 0.907,
+ 0.809
+ ],
+ "angle": 0,
+ "content": "Following previous work [52], we conduct experiments on the challenging ScanNet1500 dataset to further demonstrate the effectiveness of our method. As shown in Table 2, our method outperforms all other unsupervised and supervised methods on the most stringent accuracy metric, and performs only slightly worse than the supervised method with the best generalization performance on the most permissive accuracy metric. The ScanNet1500 includes view pairs with low overlap and significant viewpoint variations, which pose substantial challenges for existing unsupervised methods. These conditions hinder the performance of previous methods, as geometric and photometric consistency between view pairs is greatly affected. In contrast, our method maintains strong performance by identifying reliable correspondences through overlapping constraint and further optimizing the model using the Gaussian Splitting technique."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.818,
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+ ],
+ "angle": 0,
+ "content": "4.4. Ablation Studies"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.84,
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+ ],
+ "angle": 0,
+ "content": "Analysis of Each Component. We conduct a comprehensive ablation study for each component. The OCID module comprises two key components: Random Overlapping region prediction (RO) and Global-to-Local inliers detection"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "24873"
+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Table 1. Pairwise Registration accuracies and errors on ScanNet. Pose Sup means training with ground truth. The best result is shown in bold and the second best is underlined."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Method | Train set | Pose Sup | Rotation(°) | Translation(cm) | Chamfer(mm) | Time(s) |
| Accuracy | Error | Accuracy | Error | Accuracy | Error |
| 5 | 10 | 45 | Mean | Med | 5 | 10 | 25 | Mean | Med | 1 | 5 | 10 | Mean | Med |
| SIFT | - | | 55.2 | 75.7 | 89.2 | 18.6 | 44.3 | 17.7 | 44.5 | 79.8 | 26.5 | 11.2 | 38.1 | 70.6 | 78.3 | 42.6 | 1.7 | - |
| SuperPoint | - | | 65.5 | 86.9 | 96.6 | 8.9 | 3.6 | 21.2 | 51.7 | 88.0 | 16.1 | 9.7 | 45.7 | 81.1 | 88.2 | 19.2 | 1.2 | - |
| FCGF | - | ✓ | 70.2 | 87.7 | 96.2 | 9.5 | 3.3 | 27.5 | 58.3 | 82.9 | 23.6 | 8.3 | 52.0 | 78.0 | 83.7 | 24.4 | 0.9 | 0.129 |
| 3DMVReg | 3DMatch | ✓ | 87.7 | 93.2 | 97.0 | 6.0 | 1.2 | 69.0 | 83.1 | 91.8 | 11.7 | 2.9 | 78.9 | 89.2 | 91.8 | 10.2 | 0.2 | - |
| REGTR | 3DMatch | ✓ | 86.0 | 93.9 | 98.6 | 4.4 | 1.6 | 61.4 | 80.3 | 91.4 | 14.4 | 3.8 | 80.9 | 90.9 | 93.6 | 13.5 | 0.2 | - |
| BUFFER | 3DMatch | ✓ | 95.9 | 98.4 | 99.2 | 2.4 | 0.9 | 79.6 | 92.3 | 96.9 | 5.7 | 2.4 | 93.6 | 97.3 | 98.6 | 4.2 | 0.2 | 0.177 |
| PARENet | 3DMatch | ✓ | 97.5 | 98.3 | 99.5 | 1.9 | 0.7 | 85.9 | 95.7 | 97.0 | 3.9 | 1.8 | 94.2 | 97.9 | 98.6 | 4.2 | 0.2 | 0.165 |
| UR&R | 3DMatch | ✓ | 92.3 | 95.3 | 98.2 | 3.8 | 0.8 | 77.6 | 89.4 | 95.5 | 7.8 | 2.3 | 86.1 | 94.0 | 95.6 | 6.7 | 0.1 | 0.070 |
| UR&R | 3DMatch | | 87.6 | 93.1 | 98.3 | 4.3 | 1.0 | 69.2 | 84.0 | 93.8 | 9.5 | 2.8 | 79.7 | 91.3 | 94.0 | 7.2 | 0.2 | 0.071 |
| BYOC | 3DMatch | | 66.5 | 85.2 | 97.8 | 7.4 | 3.3 | 30.7 | 57.6 | 88.9 | 16.0 | 8.2 | 54.1 | 82.8 | 89.5 | 9.5 | 0.9 | - |
| LLT | 3DMatch | | 93.4 | 96.5 | 98.8 | 2.5 | 0.8 | 76.9 | 90.2 | 96.7 | 5.5 | 2.2 | 86.4 | 95.1 | 96.8 | 4.6 | 0.1 | 0.125 |
| PointMBF | 3DMatch | | 94.6 | 97.0 | 98.7 | 3.0 | 0.8 | 81.0 | 92.0 | 97.1 | 6.2 | 2.1 | 91.3 | 96.6 | 97.4 | 4.9 | 0.1 | 0.079 |
| CCAP | 3DMatch | | 95.6 | 98.1 | - | 2.4 | 0.7 | 81.5 | 92.3 | - | 3.7 | 1.9 | - | - | - | - | - | - |
| Ours | 3DMatch | | 97.9 | 98.9 | 99.5 | 1.8 | 0.7 | 87.7 | 96.2 | 98.6 | 3.8 | 1.8 | 95.5 | 98.4 | 98.8 | 3.3 | 0.1 | 0.136 |
| UR&R | ScanNet | | 92.7 | 95.8 | 98.5 | 3.4 | 0.8 | 77.2 | 89.6 | 96.1 | 7.3 | 2.3 | 86.0 | 94.6 | 96.1 | 5.9 | 0.1 | 0.071 |
| BYOC | ScanNet | | 86.5 | 95.2 | 99.1 | 3.8 | 1.7 | 56.4 | 80.6 | 96.3 | 8.7 | 4.3 | 78.1 | 93.9 | 96.4 | 5.6 | 0.3 | - |
| LLT | ScanNet | | 95.5 | 97.6 | 99.1 | 2.5 | 0.8 | 80.4 | 92.2 | 97.6 | 5.5 | 2.2 | 88.9 | 96.4 | 97.6 | 4.6 | 0.1 | 0.125 |
| PointMBF | ScanNet | | 96.0 | 97.6 | 98.9 | 2.5 | 0.7 | 83.9 | 93.8 | 97.7 | 5.6 | 1.9 | 92.8 | 97.3 | 97.9 | 4.7 | 0.1 | 0.079 |
| CCAP | ScanNet | | 97.1 | 98.2 | - | 1.9 | 0.6 | 85.9 | 93.6 | - | 3.9 | 1.8 | - | - | - | - | - | - |
| Ours | ScanNet | | 98.3 | 99.2 | 99.7 | 1.5 | 0.7 | 88.8 | 96.7 | 99.0 | 3.3 | 1.7 | 96.1 | 98.8 | 99.1 | 2.8 | 0.1 | 0.136 |
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+ "content": "| Method | Train set | Pose Sup | Rotation(°) | Translation(cm) | Chamfer(mm) |
| Accuracy | Error | Accuracy | Error | Accuracy | Error |
| 5 | 10 | 45 | Med | 5 | 10 | 25 | Med | 1 | 5 | 10 | Med |
| LLT | 3DMatch | | 36.1 | 49.9 | 79.9 | 10.0 | 17.2 | 29.9 | 46.6 | 29.6 | 23.5 | 40.4 | 48.3 | 12.1 |
| PointMBF | 3DMatch | | 51.1 | 60.8 | 82.9 | 4.7 | 31.5 | 44.2 | 59.3 | 13.8 | 44.8 | 57.5 | 63.3 | 1.7 |
| BUFFER | 3DMatch | ✓ | 74.9 | 82.5 | 90.9 | 1.8 | 47.4 | 66.5 | 81.0 | 5.0 | 66.5 | 79.5 | 84.2 | 0.3 |
| PARENet | 3DMatch | ✓ | 65.6 | 71.9 | 88.6 | 3.1 | 50.1 | 71.7 | 83.3 | 4.7 | 61.7 | 77.9 | 82.7 | 0.3 |
| Ours | 3DMatch | | 76.9 | 83.4 | 89.3 | 1.6 | 49.5 | 68.4 | 80.9 | 5.1 | 67.9 | 80.2 | 83.4 | 0.3 |
| LLT | ScanNet | | 43.7 | 54.6 | 80.3 | 7.5 | 24.0 | 36.1 | 52.9 | 20.6 | 31.7 | 47.8 | 53.4 | 6.6 |
| PointMBF | ScanNet | | 55.9 | 65.9 | 84.9 | 3.4 | 37.1 | 49.9 | 63.1 | 10.0 | 48.5 | 62.1 | 67.2 | 1.2 |
| Ours | ScanNet | | 81.3 | 85.9 | 91.2 | 1.5 | 53.5 | 72.1 | 83.3 | 4.3 | 72.4 | 83.3 | 85.9 | 0.3 |
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+ "content": "(GL). For the GRPA module, we use a conventional differentiable renderer [32] instead. As shown in Table 3, the results reveal the following: 1) The baseline performs worst on both datasets when none of the proposed components are used. 2) Adding the GRPA module improves registration performance on both datasets, indicating that the GRPA refines transformation. 3) The complete OCID module significantly improves registration, with a notable increase in performance on ScanNet1500: \\(22.2\\%\\) in rotation accuracy \\((< 5^{\\circ})\\), \\(14.6\\%\\) in translation accuracy \\((< 5\\mathrm{cm})\\), and \\(20.4\\%\\) in chamfering accuracy \\((< 1\\mathrm{mm})\\). This shows the OCID module's effectiveness in low-overlap scenes. 4) Additionally, using RO and GL separately results in improved registration performance for the entire framework. While the performance improvements on ScanNet are similar for both methods, RO achieves greater performance gains on ScanNet1500, demonstrating that the inclusion of overlapping constraint is particularly effective in scenarios with low overlap. 5) Finally, the complete framework with all com"
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+ "content": "Table 3. Ablation studies on OG-UPCR. The model is trained on ScanNet. The best result is shown in bold."
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+ "content": "| OCID | GRPA | Test set | Rotation(°) | Translation(cm) | Chamfer(mm) |
| RO | GL | Accuracy < 5 | Error Med | Accuracy < 5 | Error Med | Accuracy < 1 | Error Med |
| × | × | × | ScanNet | 96.0 | 0.8 | 83.9 | 1.9 | 92.8 | 0.1 |
| × | × | ✓ | 97.4 | 0.8 | 84.9 | 1.9 | 94.6 | 0.1 |
| ✓ | ✓ | × | 97.7 | 0.7 | 85.7 | 1.8 | 95.1 | 0.1 |
| × | ✓ | × | 97.5 | 0.8 | 85.5 | 1.9 | 95.0 | 0.1 |
| ✓ | × | × | 97.2 | 0.8 | 84.7 | 1.9 | 93.9 | 0.1 |
| ✓ | ✓ | ✓ | 98.3 | 0.7 | 88.8 | 1.7 | 96.1 | 0.1 |
| × | × | × | ScanNet1500 | 56.3 | 3.4 | 36.5 | 10.0 | 48.5 | 1.2 |
| × | × | ✓ | 65.1 | 2.1 | 42.3 | 6.8 | 57.1 | 0.5 |
| ✓ | ✓ | × | 78.5 | 1.6 | 51.1 | 4.9 | 68.9 | 0.3 |
| × | ✓ | × | 73.9 | 1.9 | 46.1 | 5.7 | 65.5 | 0.4 |
| ✓ | × | × | 74.7 | 1.6 | 46.7 | 4.8 | 66.4 | 0.3 |
| ✓ | ✓ | ✓ | 81.3 | 1.5 | 53.5 | 4.3 | 72.4 | 0.3 |
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+ "content": "Figure 3. The visualization of point cloud registration results for PointMBF and the proposed OG-UPCR is presented. The results in the first row depict registration case with low overlap, while the results in the second row illustrate registration case with inconsistent photometric information caused by significant viewpoint variation."
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+ "angle": 0,
+ "content": "Figure 4. Validation of the OCID for Inliers Detection. It is evident that after incorporating the OCID, the correspondences are constrained to the overlapping regions (highlighted in pink), which simplifies geometric fitting and improves registration accuracy."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "we visually compared the results before and after incorporating it. As shown in Fig. 4, after integrating the OCID module, the proportion of inliers is significantly increased in scenarios with low overlap, which facilitates subsequent geometric fitting and enhances the overall performance of the registration model."
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+ "type": "text",
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+ "content": "Validation of the GRPA for Photometric Adaptation. To explore the impact of the GRPA, we replaced it with a traditional differentiable renderer and compared the rendered results. As shown in Fig. 5, the results demonstrate that incorporating the GRPA significantly reduces artifacts and enhances inter-frame consistency. This improvement is essential for ensuring consistent feature descriptors, as further discussed in Supplementary Material 4.4."
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+ "content": "Qualitative Results. The qualitative results, compared with PointMBF, are shown in Fig. 3. OG-UPCR achieves superior registration results and identifies more accurate cor"
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+ "content": "w/o GRPA"
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+ "angle": 0,
+ "content": "Figure 5. Validation of the GRPA for Photometric Adaptation. Comparison of the rendered results reveals that after applying the GRPA module, the artifacts are significantly reduced, leading to improved consistency between the input and rendered frames."
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+ "bbox": [
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+ "angle": 0,
+ "content": "respondences, demonstrating enhanced adaptability to low overlap (first row). Additionally, our method performs better under inconsistent photometric conditions in the scene (second row), indicating greater robustness."
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+ "content": "5. Conclusion"
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+ "angle": 0,
+ "content": "We introduce OG-UPCR, a framework for unsupervised point cloud registration. The method consists of two primary modules: OCID and GRVA. The OCID module enables the model to adapt to low-overlap scenes while maintaining a balance between accuracy and efficiency. The GRVA module refines the initial geometric transformation, enhancing the model's robustness to inconsistent photometric information. Extensive experiments on public datasets demonstrate the effectiveness of the proposed method."
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+ "content": "Acknowledgement. This work is supported by the National Key R&D Program of China (No. 2023YFB3307202), Science and Technology Innovation Leading Talent Project of Special Support Plan for High-level Talents of Zhejiang Province (Grant No. 2022R52053)."
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+# Unsupervised RGB-D Point Cloud Registration for Scenes with Low Overlap and Photometric Inconsistency
+
+Yejun Shou $^{1,2}$ , Haocheng Wang $^{1,2}$ , Lingfeng Shen $^{1,2}$ , Qian Zheng $^{3*}$ , Gang Pan $^{3}$ , Yanlong Cao $^{1,2*}$ $^{1}$ The State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, China
+ $^{2}$ The Key Laboratory of Advanced Manufacturing Technology of Zhejiang Province, China
+ $^{3}$ College of Computer Science and Technology, Zhejiang University, China
+
+{syj12125092, 00whc, lfs, qianzheng, gpan, sdcaoyl}@zju.edu.cn
+
+# Abstract
+
+Point cloud registration is a fundamental task in 3D vision, playing a crucial role in various fields. With the rapid advancement of RGB-D sensors, unsupervised point cloud registration methods based on RGB-D sequences have demonstrated excellent performance. However, existing methods struggle in scenes with low overlap and photometric inconsistency. Low overlap results in numerous correspondence outliers, while photometric inconsistency hinders the model's ability to extract discriminative features. To address these challenges, we first propose the Overlapping Constraint for Inliers Detection (OCID) module, which filters and optimizes the initial correspondence set using an overlapping constraint. This module robustly selects reliable correspondences within the overlapping region while maintaining a balance between accuracy and efficiency. Additionally, we introduce a novel scene representation, 3DGS, which integrates both geometric and texture information, making it particularly well-suited for RGB-D registration tasks. Building on this, we propose the Gaussian Rendering for Photometric Adaptation (GRPA) module, which refines the geometric transformation and enhances the model's adaptability to scenes with inconsistent photometric information. Extensive experiments on ScanNet and ScanNet1500 demonstrate that our method achieves state-of-the-art performance. The code will be released at OG-UPCR.
+
+# 1. Introduction
+
+Point cloud registration is a critical task in 3D vision, with applications in navigation [30, 44, 56], pose estimation [10, 17], and 3D reconstruction [42, 43]. Typically, two frames of point clouds rely on feature extraction to estimate correspondences, followed by robust geometric fitting techniques to obtain the transformation.
+
+
+Figure 1. The objective of the proposed OG-UPCR is to effectively register scenes with low overlap and photometric inconsistency. The overlapping region constraint helps reduce correspondence outliers caused by low overlap, while photometric inconsistency is adaptively adjusted through the estimizable parameters contained in 3D Gaussians [24]. Compared to PointMBF [52], the proposed OG-UPCR produces more consistent results between input and rendered frames (highlighted in red boxes) and yields better registration outcomes.
+
+With the rapid development of RGB-D sensors, unsupervised registration methods [12-14, 27, 40, 45, 52] have demonstrated impressive performance. These methods rasterize 3D points into images using a differentiable renderer [32] and employ geometric and photometric consistency losses between the input and rendered frames to extract features, thereby estimating the geometric transformation between nearby frames without the need for ground truth. However, all these methods ignore that the geometric and photometric information between frames to be registered is not always consistent, particularly in scenes with low overlap and photometric inconsistency. Low overlap
+
+complicates feature identification and correspondence estimation [20], while photometric inconsistency hinders the modeling of feature consistency between input and rendered frames, making it challenging for the model to obtain discriminative features, especially in scenes with reflections and rendering artifacts [52]. Despite the excellent registration performance of PointMBF [52], it still suffers from low overlap and photometric inconsistency, which result in a large number of correspondence outliers and erroneous rendered and registration results, as illustrated in Fig. 1.
+
+We observe that inliers must be located within overlapping regions, whereas outliers can be filtered out early using overlapping constraint. Although identifying inliers and overlaps is a chicken-and-egg situation, it can be efficiently resolved through an iterative process. Meanwhile, recent advances in 3D Gaussian Splatting [24] have made significant strides in novel view synthesis [4, 54], 3D generation [6, 50], and SLAM [23, 26, 46]. This technique not only represents geometry in a smooth and continuously differentiable manner but also preserves view-varying texture information, which is adaptive to photometric changes. Additionally, 3D points convert easily into 3D Gaussians, making this approach highly suitable for RGB-D registration.
+
+To this end, we propose OG-UPCR, an innovative unsupervised point cloud registration framework designed to address low overlap and photometric inconsistency, as shown in Fig. 1. Specifically, we propose the Overlapping Constraint for Inliers Detection module (OCID) based on the observation that inliers must lie within overlapping regions. This module leverages overlapping constraints to detect inliers, addressing issues arising from low overlap. Additionally, we design the Gaussian Rendering for Photometric Adaptation module (GRPA), which converts 3D points into 3D Gaussians and rasterizes them into image space, leveraging the rich geometric and texture information contained in the Gaussians. Based on this, nonlinear optimization is applied to each pixel to enhance photometric adaptation and enable the model to extract discriminative features. Moreover, this process refines the transformation and improves overall registration.
+
+The OG-UPCR is thoroughly evaluated on the standard datasets, including 3DMatch [53], ScanNet [9], and the challenging ScanNet1500 [35], which contain paired views with low overlap and inconsistent photometric information, achieving state-of-the-art performance. Additionally, we conduct extensive ablation experiments on individual modules to demonstrate the effectiveness of each component.
+
+In summary, our contributions are as follows:
+
+- We propose OG-UPCR, an unsupervised registration framework that combines overlapping constraint with gaussian splatting, enhancing the accuracy and robustness of the overall registration model.
+- We propose a correspondence optimization strategy us
+
+ing iterative random overlapping region prediction. This module selects faithful inliers of correspondences within the overlapping region, mitigating the impact of low overlap and enhancing the accuracy of geometric fitting.
+
+- We propose a photometric adaptation module for paired views that employs Gaussian splatting to independently render the Gaussians of both views. This module models the photometric consistency of features across frames, and refines the final transformation.
+
+# 2. Related Work
+
+# 2.1. Point Cloud Registration
+
+Early point cloud registration methods [21, 33, 34, 39] rely on hand-crafted feature descriptors, which are sensitive to noise and not robust to changes in the number and density of point clouds. Recently, deep learning feature descriptors have demonstrated impressive performance and can achieve better registration results. Research based on deep learning can be divided into supervised [2, 20, 29, 37, 41, 51] and unsupervised [12, 13, 28, 36, 45, 52] methods. However, supervised methods require real poses as supervision signals, making them difficult to apply practically. When encountering new scenes with domain gaps, they can only rely on the trained weights to infer the registration results, which often affects their performance. Unsupervised methods can be further divided into geometric-based and RGB-D based methods according to the input data. Among geometric-based methods, RIENet [36] proposes a reliable inlier evaluation method based on neighborhood consensus. UDReg [28] operates by learning the posterior probability distribution of Gaussian Mixture Models from point clouds and then predicting distribution-level correspondences. Since the input contains only geometric information, these methods struggle with geometric weak regions (such as floors, ceilings, and walls) and repeated structures in real scenes. RGB-D based methods are able to handle real scenes, such as LLT [45] employing a linear attention module to fuse geometric and texture features. PointMBF [52] proposes a multi-scale bidirectional fusion network to fully utilize the complementary information of RGB-D. Nevertheless, these methods all employ a conventional differentiable renderer to render 3D points directly, making them susceptible to low overlap and photometric inconsistency. In contrast, we propose the OCID module based on overlapping constraint to help obtain more reliable correspondences. Additionally, we design the GRPA module to reduce the impact of photometric inconsistency, thereby enhancing registration accuracy.
+
+# 2.2. Correspondence Optimization Strategy
+
+The handling of correspondence outliers can be effectively addressed using methods such as RANSAC. Although RANSAC [15] and its variants [3, 31] are widely
+
+
+Figure 2. The overview of OG-UPCR. The backbone first extracts the features $F_{P}^{f}$ and $F_{Q}^{f}$ from the point clouds $P$ and $Q$ . The initial correspondences are estimated by calculating Lowe's ratio in the feature space, which is then optimized by the OCID module using the overlapping constraint. Subsequently, the rigid transformation is determined through geometric fitting. Finally, based on this transformation, the Gaussian cross-rendering results generated by the GRPA module form the paired views are used to calculate the loss. This process not only refines the final result but also aids the model in acquiring distinct features.
+
+recognized algorithms, their performance remains sensitive to outliers, often requiring numerous iterations to produce relatively accurate results. SC2PCR [5] and MAC [55] are also effective in managing correspondence outliers, but both rely on relative spatial constraint and fail to account for the fact that correct correspondences should be confined to the overlapping region from global spatial constraint. This oversight leads to inefficiency and inaccuracy, as excessive redundant point pairs are utilized. In contrast, we propose an overlapping constraint module based on global spatial to select reliable correspondences, thereby improving the efficiency and accuracy of the registration process.
+
+# 2.3. Gaussian Splatting
+
+As a novel scene representation and efficient differentiable renderer, 3D Gaussian Splatting [24] has shown its significant advantages in novel view synthesis [4, 48, 54], 3D generation [6, 50] and SLAM [23, 26, 46]. SplaTAM [23] introduces an online tracking and mapping system based on the underlying 3D Gaussian representation, without requiring the real pose. However, it relies on dense RGB-D frame inputs, making it difficult to obtain accurate poses with sparse input. PixelSplat [6] proposes that the radiance field parameterized by 3D Gaussian primitives can be learned and reconstructed from sparse views. NoPoSplat [48] integrates PnP [18] and 3DGS [24] to estimate poses from sparse views, achieving superior novel
+
+view synthesis. Nevertheless, these methods estimate poses from an image-based perspective, resulting in the loss of 3D information. In contrast, the proposed GRPA module derives a more precise geometric transformation from the point cloud perspective, producing rasterized outputs independent of true pose data. This approach exhibits robust generalization and achieves accurate registration even with sparse inputs.
+
+# 3. Method
+
+# 3.1. Problem Statement and Overview
+
+Problem Statement. Given point clouds $P \in \mathbb{R}^{N \times 3}$ and $Q \in \mathbb{R}^{N \times 3}$ , the purpose of the registration task is to obtain a transformation matrix $\mathbf{T} = \{\mathbf{R}, \mathbf{t}\}$ , that aligns $P$ and $Q$ in the same coordinate system. This transformation matrix consists of a rotation matrix $\mathbf{R} \in \mathbf{SO}(3)$ and a translation vector $\mathbf{t} \in \mathbb{R}^3$ . The correspondence set $C = \{\mathbf{p}_i, \mathbf{q}_j | \mathbf{p}_i \in P, \mathbf{q}_j \in Q\}$ is estimated by feature extraction and matching. The transformation can be determined by:
+
+$$
+\underset {\mathbf {R}, \mathbf {t}} {\operatorname {a r g m i n}} \sum_ {i = 1} ^ {n} \| \mathbf {R} \cdot \mathbf {p} _ {i} + \mathbf {t} - \mathbf {q} _ {j} \| _ {2} ^ {2}, \tag {1}
+$$
+
+where $\| \cdot \| _2^2$ denotes the Euclidean norm, $n$ is the number of correspondences that can be found in paired point clouds.
+
+Overview. In this paper, we propose an OCID module and a GRPA module to address challenges associated with low overlap and photometric inconsistency. The OG-UPCR processes paired point clouds and their corresponding RGB-D frames as input, following the PointMBF [52] to extract feature descriptors. Using these descriptors, we compute an initial correspondence set by measuring distances in the feature space. The OCID module then filters this initial set based on an overlapping region constraint, selecting reliable seed points for geometric fitting, which produces a coarse transformation, denoted as $\mathbf{T}_{gs}^{0}$ , as described in Section 3.2. This transformation serves as the initial pose for the GRPA module, where 3D points are first converted into 3D Gaussians and then projected onto an image using a Gaussian splatting renderer, which is subsequently refined to obtain the final result, $\mathbf{T}_{gs}^{R}$ , as detailed in Section 3.3. Additionally, the entire registration framework is trained in an end-to-end unsupervised manner using geometric and photometric consistency losses between input and rendered frames, as discussed in UR&R [13]. An overview of OG-UPCR is provided in Fig. 2.
+
+Feature Extraction. Building upon prior research, we employ KPCov [38] and ResNet [19] to extract multi-scale information from the point clouds and images. Subsequently, a multi-scale bidirectional fusion method [52] generates distinctive fused feature descriptors $F_{P}^{f} \in \mathbb{R}^{N \times C_{3D}}$ and $F_{Q}^{f} \in \mathbb{R}^{N \times C_{3D}}$ for point clouds $P$ and $Q$ .
+
+# 3.2. Correspondence Estimation
+
+Initial Correspondence Set Acquisition. After obtaining the feature descriptors of the point clouds, we follow previous method [13, 45, 52] to obtain the initial correspondence set based on Lowe's ratio [25]. For a point $\mathbf{p}_i$ , its Lowe's ratio can be computed as:
+
+$$
+r _ {i} = \frac {D \left(\mathbf {p} _ {i} , \mathbf {q} _ {j} ^ {1 n n}\right)}{D \left(\mathbf {p} _ {i} , \mathbf {q} _ {j} ^ {2 n n}\right)}, \tag {2}
+$$
+
+where $D(\cdot)$ represents the Euclidean distance in the feature space and $q_{j}^{knn}$ is the k-th similarity point in the point cloud $Q$ . We assign weights to each correspondence using the formula $w = 1 - r$ . Next, we apply the top-k algorithm to select the weighted correspondences, resulting in a correspondence set from $C_{P \to Q}$ . We choose an equal number of correspondences from $C_{Q \to P}$ in a similar manner to create the initial correspondence set:
+
+$$
+C _ {\text {i n i t i a l}} = \left\{\left(\mathbf {p}, \mathbf {q}, w\right) _ {m}: 0 \leq m < 2 k \right\}, \tag {3}
+$$
+
+where $k$ denotes the top $k$ weights. The resulting correspondence $C_{\mathrm{initial}}$ will be input into the OCID module for further optimization.
+
+Overlapping Constraint for Inliers Detection. This module is designed to detect inliers from the initial correspondence set, facilitating efficient registration in scenarios with
+
+low overlap. Existing works [5, 55] directly remove outliers based on the consistency graph but neglect the importance of the overlapping region constraint, leading to significant computational expenses. As shown in Fig. 2, the module consists of two components, which are detailed below.
+
+Random Overlapping Region Prediction. As is well known, Weighted SVD [8] produces an approximate geometric transformation by performing singular value decomposition on the weights of the correspondence set. The accuracy of this transformation will be affected by the inliers in the correspondence, meaning that the higher the weight of the inliers, the more accurate the transformation will be. Motivated by this and inspired by RANSAC [15], we first randomly select a partial subset from the initial correspondence:
+
+$$
+C _ {n} = \left\{\left(\mathbf {p}, \mathbf {q}, w\right) _ {n}: 0 \leq n < 2 r k \right\} \in C _ {\text {i n i t i a l}}, \tag {4}
+$$
+
+where $r$ denotes the proportion of the subset in the initial correspondence, which is set to 0.2. Next, we apply Weighted SVD to obtain the transformation $\mathbf{T}_s$ of this subset. Unlike similar previous work [13, 45, 52], we do not directly leverage the common L2 distance to assess whether $\mathbf{T}_s$ is correct, which is prone to fall into local optima. Instead, we propose a novel approach based on overlapping region prediction. Using $\mathbf{T}_s$ , we predict the overlapping area of the point cloud and evaluate its success by the overlap ratio $O_p$ , which is defined as:
+
+$$
+P ^ {\prime} = \mathbf {T} _ {s} \odot P, \tag {5}
+$$
+
+$$
+O _ {p} = \frac {1}{N} \sum_ {n = 1} ^ {N _ {P ^ {\prime}}} \llbracket \| \mathbf {p} _ {n} ^ {\prime} - \mathbf {q} _ {n} \| _ {2} < \tau \rrbracket , \tag {6}
+$$
+
+where $\llbracket \cdot \rrbracket$ is the Iverson bracket, $\odot$ represents the rigid transformation, $N_{P^{\prime}}$ is the number of points of the point cloud $P^{\prime}$ and $\tau$ is set to $5\mathrm{cm}$ . If $O_p$ exceeds the threshold $O_{thr}$ , the prediction is considered successful. This implies that most of the correspondences within the selected subset are inliers, and the subset is classified as a positive subset, receiving a higher weight in the initial correspondence set. To meet these conditions, we multiply the weight of the points in the subset of successful predictions by a reward factor, thereby increasing their proportion in the initial correspondence. Conversely, if the prediction fails, it indicates that the selected subset contains a high percentage of outliers. In this case, the corresponding weights in those subsets are multiplied by a penalty factor, which is defined as follows:
+
+$$
+w _ {n} = \left\{ \begin{array}{l} w _ {n} \cdot w _ {r}, O _ {p} \geq O _ {t h r} \\ w _ {n} \cdot w _ {p}, O _ {p} < O _ {t h r} \end{array} , \right. \tag {7}
+$$
+
+where $w_{r}$ and $w_{p}$ denote the reward factor and penalty factor, and $w_{r} \cdot w_{p} = 1$ to ensure the balance change of a correspondence when it is selected into the subset many times.
+
+The above prediction process is repeated $N$ times. After completing the random overlapping region prediction, the weights of the individual correspondences within the initial correspondence set are significantly optimized, with inliers receiving higher weights and the weights of outliers being reduced. To enhance the efficiency of the algorithm, we also use the top-k algorithm to select the appropriate correspondence. The optimized set of correspondences can be defined as follows:
+
+$$
+C _ {f} = \left\{\left(\mathbf {p}, \mathbf {q}, w\right) _ {f}: 0 \leq m < 2 k _ {f} \right\}, \tag {8}
+$$
+
+where $k_{f}$ means that the top-k algorithm is used to select items with larger weights to speed up the algorithm. We also provide a pseudocode and simple flowchart in Supplementary Material. 2.
+
+Global-to-Local Inliers Detection. The optimized correspondence set $C_f$ already exhibits a high inlier ratio. However, one issue remains: the selected correspondences are concentrated in specific local regions rather than uniformly distributed. This concentration hinders the subsequent geometric fitting. To address this challenge, we propose a global-to-local inlier detection module based on spatial consistency, as shown in Fig. 2. First, we compute the second order spatial compatibility ( $SC^2$ ) [5] of the optimized correspondence set globally, which can be defined as:
+
+$$
+S C _ {i j} ^ {2} = C _ {i j} \cdot \sum_ {k = 1} ^ {N} C _ {i k} \cdot C _ {k j}, \tag {9}
+$$
+
+$$
+C _ {i j} = \left\{ \begin{array}{l} 1, d _ {i j} \leq d _ {t h r} \\ 0, d _ {i j} > d _ {t h r} \end{array} , \right. \tag {10}
+$$
+
+$$
+d _ {i j} = \left| \left\| \mathbf {p} _ {i} - \mathbf {p} _ {j} \right\| _ {2} - \left\| \mathbf {q} _ {i} - \mathbf {q} _ {j} \right\| _ {2} \right|, \tag {11}
+$$
+
+where $\mathbf{p}_i, \mathbf{p}_j$ and $\mathbf{q}_i, \mathbf{q}_j$ denote two sets of correspondence points in $C_f$ , and $d_{thr}$ is set to $10\mathrm{cm}$ . Subsequently, the optimized weights $w_f$ are employed to find the seed points with the maximum confidence score within their neighborhood, defined by a radius $R$ , ensuring that the correspondences are uniformly distributed. To ensure that the selected seed points are reliable inliers, we measure the correspondence of the seed point and its top- $K$ neighbors based on the constructed $SC^2$ metric to further prune potential outliers. Finally, these seed points and their neighboring points form multiple consensus sets.
+
+Geometric Fitting. To project images of the transformed point clouds $P$ and $Q$ using a Gaussian renderer, it is necessary to estimate their geometric transformation. This estimation is achieved through geometric fitting. Following [5], we estimate the geometric transformation according to each consensus set. Finally, we choose the transformation with the highest number of inliers as the result $\mathbf{T}_{gs}^{0}$ .
+
+# 3.3. Gaussian Rendering
+
+This module is designed to help the model adapt to inconsistent photometric information between the input and rendered frames. Previous approaches [13, 45, 52] rely on traditional differentiable renderer [32] to directly project 3D points into the image space, which makes their models susceptible to significant viewpoint changes and limits the ability to extract more discriminative features. To overcome these challenges, we draw inspiration from [22, 26] and introduce the 3D Gaussian splatting technique. Additionally, we propose a photometric adaptation mechanism for each pixel to resolve the inconsistencies caused by viewpoint changes, thereby enabling the model to learn more discriminative features for registration.
+
+Gaussian Rendering for Photometric Adaptation. Specifically, each point can be represented by a Gaussian [22] with eight parameter values: its point position $\mu_{3D} \in \mathbb{R}^3$ , RGB color $\mathbf{c} \in \mathbb{R}^3$ , radius $r$ , and opacity $o \in [0,1]$ . Each Gaussian affects a point in 3D space $\mathbf{x} \in \mathbb{R}^3$ as follows:
+
+$$
+g (\mathbf {x}) = o \exp \left(- \frac {\| \mathbf {x} - \mu_ {3 D} \| ^ {2}}{2 r _ {3 D} ^ {2}}\right), \tag {12}
+$$
+
+each pixel $\rho$ in the differentiable rendered RGB image can then be rendered as follows:
+
+$$
+R _ {r g b} ^ {g s} (\mathbb {G}, \mathbf {T}) = \sum_ {i = 1} ^ {n} c _ {i} g _ {i} (\rho) \prod_ {j = 1} ^ {i - 1} (1 - g _ {j} (\rho)), \tag {13}
+$$
+
+where $g(\rho_a)$ can be obtained from Eq. (12) and (13), but with $\mu_{3D}$ and $r_{3D}$ of the splatted 2D Gaussians in pixel space:
+
+$$
+\mu_ {2 D} = \mathbf {K T} \frac {\mu_ {3 D}}{d}, r _ {2 D} = \frac {f}{d}, \tag {14}
+$$
+
+where $\mathbf{K}$ is the camera intrinsic matrix, $\mathbf{T}$ is the extrinsic matrix, $f$ is the focal length of the camera, and $d$ is the depth. To further enhance the adaptability to photometric changes, we optimize the nonlinear photometric adaptation of each pixel:
+
+$$
+R _ {r g b} ^ {g s ^ {\prime}} = \exp (\alpha) \cdot R _ {r g b} ^ {g s} + \beta , \tag {15}
+$$
+
+where $\alpha$ and $\beta$ are both learnable parameters. A similar differentiable rendered depth image can be expressed as follows:
+
+$$
+R _ {\text {d e p t h}} ^ {g s} (\mathbb {G}, \mathbf {T}) = \sum_ {i = 1} ^ {n} d _ {i} g _ {i} \left(\rho_ {a}\right) \prod_ {j = 1} ^ {i - 1} \left(1 - g _ {j} \left(\rho_ {a}\right)\right). \tag {16}
+$$
+
+This module refines transformations by rendering and comparing them to minimize the discrepancy between the rendered object and the actual observations in the query image. The loss function can be defined as:
+
+$$
+L _ {g s} ^ {P} = L _ {r g b} ^ {P} + L _ {\text {d e p t h}} ^ {P}, \tag {17}
+$$
+
+$$
+L _ {r g b} ^ {P} = \left\| R _ {r g b} ^ {g s ^ {\prime}} \left(\mathbb {G} ^ {Q}, \mathbf {T} _ {g s} ^ {0}\right) - I ^ {P} \right\| _ {1}, \tag {18}
+$$
+
+$$
+L _ {\text {d e p t h}} ^ {P} = \left\| R _ {\text {d e p t h}} ^ {g s} \left(\mathbb {G} ^ {Q}, \mathbf {T} _ {g s} ^ {0}\right) - D ^ {P} \right\| _ {1}, \tag {19}
+$$
+
+where $\mathbb{G}^Q$ denote Gaussians associated with the point cloud $Q$ , $I^P$ and $D^P$ correspond to RGB image and depth image. $L_{gs}^{Q}$ can be obtained in the same way. For the point cloud $Q$ , we set the extrinsic matrix corresponding to its Gaussian as $\mathbf{T}_{gs}^{0}$ , the rendering viewpoint of the camera as $\mathbf{T}_0$ ( $\mathbf{T}_0$ is the identity matrix), and the opposite for the point cloud $P$ . The input initial transformation $\mathbf{T}_{gs}^{0}$ can be refined into the final result $\mathbf{T}_{gs}^{R}$ output after GRPA module.
+
+# 3.4. Loss function
+
+As in previous works [13, 45, 52], the loss function consists of photometric, depth, and correspondence consistency losses without the need for ground truth. It can be defined as follows:
+
+$$
+L = \lambda_ {g s} L _ {g s} + \lambda_ {c o r r} L _ {c o r r}, \tag {20}
+$$
+
+where $L_{gs}$ represents the photometric and depth consistencies loss as defined in Eq. (17), Eq. (18) and Eq. (19), $\lambda_{gs}$ and $\lambda_{corr}$ control the magnitude of these losses ensuring they are within an appropriate order of magnitude. $L_{corr}$ represents the correspondence consistency loss of $C_f$ , which can be donated as:
+
+$$
+L _ {c o r r} = \sum_ {(p, q, w) _ {f} \in C _ {f}} w _ {f} \left(T _ {g s} ^ {R} \odot p _ {f} - q _ {f}\right) ^ {2} / 2 k _ {f}, \tag {21}
+$$
+
+where $\odot$ represents the rigid transformation.
+
+# 4. Experiments
+
+# 4.1. Experimental Settings
+
+Dataset. Following [52], OG-UPCR has been evaluated on several indoor real-world scene datasets, including 3DMatch [53], ScanNet [9] and ScanNet1500 [35]. Among them, 3DMatch and ScanNet generate view pairs by sampling an interval of 20 frames, resulting in 3DMatch containing $122\mathrm{k} / 1.5\mathrm{k} / 1.5\mathrm{k}$ view pairs and ScanNet containing $1594\mathrm{k} / 12.6\mathrm{k} / 26\mathrm{k}$ view pairs for training/validation/test, respectively. ScanNet1500 contains 1500 view pairs with an average interval of 480.8 frames between views, which makes it more challenging for the registration task.
+
+Metrics. Following the convention [12, 13, 45, 52], we evaluate OG-UPCR by three evaluation metrics: rotation error, translation error, and chamfering error. In analysis, we report the mean and median values of these metrics and assess their accuracy across various thresholds.
+
+Competitors. We compare OG-UPCR with other methods, which can be primarily divided into three categories: (1) Conventional methods, including SIFT [25], SuperPoint [11] and FCGF [7]. (2) Supervised methods, including 3DMVReg [16], REGTR [49], BUFFER [1], and
+
+PARENet [47]. (3) Unsupervised methods, including UR&R [13], BYOC [12], LLT [45], PointMBF [52], and CCAP [52]. For the supervised methods, we verify their generalization on ScanNet using the officially provided weights trained on 3DMatch.
+
+# 4.2. Evaluation on ScanNet
+
+We first evaluate our OG-UPCR on the widely used ScanNet, with training weights from 3DMatch and ScanNet, respectively. The former validates the generalization performance comparison with other methods, and the latter evaluates the conventional cases.
+
+Trained on 3DMatch. As shown in Table 1, the generalization experimental results trained on 3DMatch demonstrate that our method achieves the state-of-the-art registration results compared with all other methods, both unsupervised and supervised. This indicates that our method has excellent adaptability to unseen scenes, balancing both registration accuracy and generalization.
+
+Trained on ScanNet. When there is no domain gap between the training set and the test set, our method also achieves the best registration results, as shown in Table 1. Even when the baseline is almost saturated, our method still shows significant accuracy improvements across each evaluation metric, with average reductions in rotation/translation/chamfer distance errors of $40.0\% /34.5\% /41.3\%$ , respectively. This demonstrates that our proposed method also delivers excellent registration performance in conventional cases.
+
+# 4.3. Evaluation on ScanNet1500
+
+Following previous work [52], we conduct experiments on the challenging ScanNet1500 dataset to further demonstrate the effectiveness of our method. As shown in Table 2, our method outperforms all other unsupervised and supervised methods on the most stringent accuracy metric, and performs only slightly worse than the supervised method with the best generalization performance on the most permissive accuracy metric. The ScanNet1500 includes view pairs with low overlap and significant viewpoint variations, which pose substantial challenges for existing unsupervised methods. These conditions hinder the performance of previous methods, as geometric and photometric consistency between view pairs is greatly affected. In contrast, our method maintains strong performance by identifying reliable correspondences through overlapping constraint and further optimizing the model using the Gaussian Splitting technique.
+
+# 4.4. Ablation Studies
+
+Analysis of Each Component. We conduct a comprehensive ablation study for each component. The OCID module comprises two key components: Random Overlapping region prediction (RO) and Global-to-Local inliers detection
+
+Table 1. Pairwise Registration accuracies and errors on ScanNet. Pose Sup means training with ground truth. The best result is shown in bold and the second best is underlined.
+
+| Method | Train set | Pose Sup | Rotation(°) | Translation(cm) | Chamfer(mm) | Time(s) |
| Accuracy | Error | Accuracy | Error | Accuracy | Error |
| 5 | 10 | 45 | Mean | Med | 5 | 10 | 25 | Mean | Med | 1 | 5 | 10 | Mean | Med |
| SIFT | - | | 55.2 | 75.7 | 89.2 | 18.6 | 44.3 | 17.7 | 44.5 | 79.8 | 26.5 | 11.2 | 38.1 | 70.6 | 78.3 | 42.6 | 1.7 | - |
| SuperPoint | - | | 65.5 | 86.9 | 96.6 | 8.9 | 3.6 | 21.2 | 51.7 | 88.0 | 16.1 | 9.7 | 45.7 | 81.1 | 88.2 | 19.2 | 1.2 | - |
| FCGF | - | ✓ | 70.2 | 87.7 | 96.2 | 9.5 | 3.3 | 27.5 | 58.3 | 82.9 | 23.6 | 8.3 | 52.0 | 78.0 | 83.7 | 24.4 | 0.9 | 0.129 |
| 3DMVReg | 3DMatch | ✓ | 87.7 | 93.2 | 97.0 | 6.0 | 1.2 | 69.0 | 83.1 | 91.8 | 11.7 | 2.9 | 78.9 | 89.2 | 91.8 | 10.2 | 0.2 | - |
| REGTR | 3DMatch | ✓ | 86.0 | 93.9 | 98.6 | 4.4 | 1.6 | 61.4 | 80.3 | 91.4 | 14.4 | 3.8 | 80.9 | 90.9 | 93.6 | 13.5 | 0.2 | - |
| BUFFER | 3DMatch | ✓ | 95.9 | 98.4 | 99.2 | 2.4 | 0.9 | 79.6 | 92.3 | 96.9 | 5.7 | 2.4 | 93.6 | 97.3 | 98.6 | 4.2 | 0.2 | 0.177 |
| PARENet | 3DMatch | ✓ | 97.5 | 98.3 | 99.5 | 1.9 | 0.7 | 85.9 | 95.7 | 97.0 | 3.9 | 1.8 | 94.2 | 97.9 | 98.6 | 4.2 | 0.2 | 0.165 |
| UR&R | 3DMatch | ✓ | 92.3 | 95.3 | 98.2 | 3.8 | 0.8 | 77.6 | 89.4 | 95.5 | 7.8 | 2.3 | 86.1 | 94.0 | 95.6 | 6.7 | 0.1 | 0.070 |
| UR&R | 3DMatch | | 87.6 | 93.1 | 98.3 | 4.3 | 1.0 | 69.2 | 84.0 | 93.8 | 9.5 | 2.8 | 79.7 | 91.3 | 94.0 | 7.2 | 0.2 | 0.071 |
| BYOC | 3DMatch | | 66.5 | 85.2 | 97.8 | 7.4 | 3.3 | 30.7 | 57.6 | 88.9 | 16.0 | 8.2 | 54.1 | 82.8 | 89.5 | 9.5 | 0.9 | - |
| LLT | 3DMatch | | 93.4 | 96.5 | 98.8 | 2.5 | 0.8 | 76.9 | 90.2 | 96.7 | 5.5 | 2.2 | 86.4 | 95.1 | 96.8 | 4.6 | 0.1 | 0.125 |
| PointMBF | 3DMatch | | 94.6 | 97.0 | 98.7 | 3.0 | 0.8 | 81.0 | 92.0 | 97.1 | 6.2 | 2.1 | 91.3 | 96.6 | 97.4 | 4.9 | 0.1 | 0.079 |
| CCAP | 3DMatch | | 95.6 | 98.1 | - | 2.4 | 0.7 | 81.5 | 92.3 | - | 3.7 | 1.9 | - | - | - | - | - | - |
| Ours | 3DMatch | | 97.9 | 98.9 | 99.5 | 1.8 | 0.7 | 87.7 | 96.2 | 98.6 | 3.8 | 1.8 | 95.5 | 98.4 | 98.8 | 3.3 | 0.1 | 0.136 |
| UR&R | ScanNet | | 92.7 | 95.8 | 98.5 | 3.4 | 0.8 | 77.2 | 89.6 | 96.1 | 7.3 | 2.3 | 86.0 | 94.6 | 96.1 | 5.9 | 0.1 | 0.071 |
| BYOC | ScanNet | | 86.5 | 95.2 | 99.1 | 3.8 | 1.7 | 56.4 | 80.6 | 96.3 | 8.7 | 4.3 | 78.1 | 93.9 | 96.4 | 5.6 | 0.3 | - |
| LLT | ScanNet | | 95.5 | 97.6 | 99.1 | 2.5 | 0.8 | 80.4 | 92.2 | 97.6 | 5.5 | 2.2 | 88.9 | 96.4 | 97.6 | 4.6 | 0.1 | 0.125 |
| PointMBF | ScanNet | | 96.0 | 97.6 | 98.9 | 2.5 | 0.7 | 83.9 | 93.8 | 97.7 | 5.6 | 1.9 | 92.8 | 97.3 | 97.9 | 4.7 | 0.1 | 0.079 |
| CCAP | ScanNet | | 97.1 | 98.2 | - | 1.9 | 0.6 | 85.9 | 93.6 | - | 3.9 | 1.8 | - | - | - | - | - | - |
| Ours | ScanNet | | 98.3 | 99.2 | 99.7 | 1.5 | 0.7 | 88.8 | 96.7 | 99.0 | 3.3 | 1.7 | 96.1 | 98.8 | 99.1 | 2.8 | 0.1 | 0.136 |
+
+Table 2. Pairwise Registration accuracies and errors on ScanNet1500. The performance of our method is comparable to the supervised BUFFER method and significantly surpasses other unsupervised methods.
+
+| Method | Train set | Pose Sup | Rotation(°) | Translation(cm) | Chamfer(mm) |
| Accuracy | Error | Accuracy | Error | Accuracy | Error |
| 5 | 10 | 45 | Med | 5 | 10 | 25 | Med | 1 | 5 | 10 | Med |
| LLT | 3DMatch | | 36.1 | 49.9 | 79.9 | 10.0 | 17.2 | 29.9 | 46.6 | 29.6 | 23.5 | 40.4 | 48.3 | 12.1 |
| PointMBF | 3DMatch | | 51.1 | 60.8 | 82.9 | 4.7 | 31.5 | 44.2 | 59.3 | 13.8 | 44.8 | 57.5 | 63.3 | 1.7 |
| BUFFER | 3DMatch | ✓ | 74.9 | 82.5 | 90.9 | 1.8 | 47.4 | 66.5 | 81.0 | 5.0 | 66.5 | 79.5 | 84.2 | 0.3 |
| PARENet | 3DMatch | ✓ | 65.6 | 71.9 | 88.6 | 3.1 | 50.1 | 71.7 | 83.3 | 4.7 | 61.7 | 77.9 | 82.7 | 0.3 |
| Ours | 3DMatch | | 76.9 | 83.4 | 89.3 | 1.6 | 49.5 | 68.4 | 80.9 | 5.1 | 67.9 | 80.2 | 83.4 | 0.3 |
| LLT | ScanNet | | 43.7 | 54.6 | 80.3 | 7.5 | 24.0 | 36.1 | 52.9 | 20.6 | 31.7 | 47.8 | 53.4 | 6.6 |
| PointMBF | ScanNet | | 55.9 | 65.9 | 84.9 | 3.4 | 37.1 | 49.9 | 63.1 | 10.0 | 48.5 | 62.1 | 67.2 | 1.2 |
| Ours | ScanNet | | 81.3 | 85.9 | 91.2 | 1.5 | 53.5 | 72.1 | 83.3 | 4.3 | 72.4 | 83.3 | 85.9 | 0.3 |
+
+(GL). For the GRPA module, we use a conventional differentiable renderer [32] instead. As shown in Table 3, the results reveal the following: 1) The baseline performs worst on both datasets when none of the proposed components are used. 2) Adding the GRPA module improves registration performance on both datasets, indicating that the GRPA refines transformation. 3) The complete OCID module significantly improves registration, with a notable increase in performance on ScanNet1500: $22.2\%$ in rotation accuracy $(< 5^{\circ})$ , $14.6\%$ in translation accuracy $(< 5\mathrm{cm})$ , and $20.4\%$ in chamfering accuracy $(< 1\mathrm{mm})$ . This shows the OCID module's effectiveness in low-overlap scenes. 4) Additionally, using RO and GL separately results in improved registration performance for the entire framework. While the performance improvements on ScanNet are similar for both methods, RO achieves greater performance gains on ScanNet1500, demonstrating that the inclusion of overlapping constraint is particularly effective in scenarios with low overlap. 5) Finally, the complete framework with all com
+
+ponents shows the best performance on both ScanNet and ScanNet1500, highlighting its strong adaptability.
+
+Table 3. Ablation studies on OG-UPCR. The model is trained on ScanNet. The best result is shown in bold.
+
+| OCID | GRPA | Test set | Rotation(°) | Translation(cm) | Chamfer(mm) |
| RO | GL | Accuracy < 5 | Error Med | Accuracy < 5 | Error Med | Accuracy < 1 | Error Med |
| × | × | × | ScanNet | 96.0 | 0.8 | 83.9 | 1.9 | 92.8 | 0.1 |
| × | × | ✓ | 97.4 | 0.8 | 84.9 | 1.9 | 94.6 | 0.1 |
| ✓ | ✓ | × | 97.7 | 0.7 | 85.7 | 1.8 | 95.1 | 0.1 |
| × | ✓ | × | 97.5 | 0.8 | 85.5 | 1.9 | 95.0 | 0.1 |
| ✓ | × | × | 97.2 | 0.8 | 84.7 | 1.9 | 93.9 | 0.1 |
| ✓ | ✓ | ✓ | 98.3 | 0.7 | 88.8 | 1.7 | 96.1 | 0.1 |
| × | × | × | ScanNet1500 | 56.3 | 3.4 | 36.5 | 10.0 | 48.5 | 1.2 |
| × | × | ✓ | 65.1 | 2.1 | 42.3 | 6.8 | 57.1 | 0.5 |
| ✓ | ✓ | × | 78.5 | 1.6 | 51.1 | 4.9 | 68.9 | 0.3 |
| × | ✓ | × | 73.9 | 1.9 | 46.1 | 5.7 | 65.5 | 0.4 |
| ✓ | × | × | 74.7 | 1.6 | 46.7 | 4.8 | 66.4 | 0.3 |
| ✓ | ✓ | ✓ | 81.3 | 1.5 | 53.5 | 4.3 | 72.4 | 0.3 |
+
+Validation of the OCID for Inliers Detection. To evaluate the effect of the OCID module on the detection of inliers,
+
+
+RGB Input
+
+
+Point Cloud Input
+
+
+Overlap: $28.1\%$
+GT
+
+
+RRE:0.95
+RTE:2.25
+Ours
+
+
+Point corr: 40%
+Inlier ratio: 92.8
+Ours
+
+
+RRE:104.25
+RTE:392.32
+PointMBF
+
+
+Point corr: 400 Inlier ratio: $18.0\%$
+PointMBF
+
+
+
+
+RGB Input
+
+
+Point Cloud Input
+
+
+Overlap: $67.5\%$
+GT
+Figure 3. The visualization of point cloud registration results for PointMBF and the proposed OG-UPCR is presented. The results in the first row depict registration case with low overlap, while the results in the second row illustrate registration case with inconsistent photometric information caused by significant viewpoint variation.
+
+
+RRE: 1.741
+RTE: 4.208
+Ours
+
+
+Point corr: 400
+Inlier ratio: $65.1\%$
+Ours
+
+
+RRE: 30.54
+RTE: 113.62
+PointMBF
+
+
+Point corr: 400
+Inlier ratio: $13.5\%$
+PointMBF
+
+
+Overlap Ratio: $30.7\%$
+Inlier Ratio: $51.5\%$
+Overlap Ratio: $33.1\%$
+
+
+Inlier Ratio: $48.5\%$
+w/o OCID
+Figure 4. Validation of the OCID for Inliers Detection. It is evident that after incorporating the OCID, the correspondences are constrained to the overlapping regions (highlighted in pink), which simplifies geometric fitting and improves registration accuracy.
+
+
+
+
+Inlier Ratio: 86.5%
+
+
+Inlier Ratio: $78.5\%$
+Ours
+
+we visually compared the results before and after incorporating it. As shown in Fig. 4, after integrating the OCID module, the proportion of inliers is significantly increased in scenarios with low overlap, which facilitates subsequent geometric fitting and enhances the overall performance of the registration model.
+
+Validation of the GRPA for Photometric Adaptation. To explore the impact of the GRPA, we replaced it with a traditional differentiable renderer and compared the rendered results. As shown in Fig. 5, the results demonstrate that incorporating the GRPA significantly reduces artifacts and enhances inter-frame consistency. This improvement is essential for ensuring consistent feature descriptors, as further discussed in Supplementary Material 4.4.
+
+Qualitative Results. The qualitative results, compared with PointMBF, are shown in Fig. 3. OG-UPCR achieves superior registration results and identifies more accurate cor
+
+
+
+
+
+
+
+
+w/o GRPA
+Ours
+GT
+Figure 5. Validation of the GRPA for Photometric Adaptation. Comparison of the rendered results reveals that after applying the GRPA module, the artifacts are significantly reduced, leading to improved consistency between the input and rendered frames.
+
+respondences, demonstrating enhanced adaptability to low overlap (first row). Additionally, our method performs better under inconsistent photometric conditions in the scene (second row), indicating greater robustness.
+
+# 5. Conclusion
+
+We introduce OG-UPCR, a framework for unsupervised point cloud registration. The method consists of two primary modules: OCID and GRVA. The OCID module enables the model to adapt to low-overlap scenes while maintaining a balance between accuracy and efficiency. The GRVA module refines the initial geometric transformation, enhancing the model's robustness to inconsistent photometric information. Extensive experiments on public datasets demonstrate the effectiveness of the proposed method.
+
+Acknowledgement. This work is supported by the National Key R&D Program of China (No. 2023YFB3307202), Science and Technology Innovation Leading Talent Project of Special Support Plan for High-level Talents of Zhejiang Province (Grant No. 2022R52053).
+
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+ "content": "To this end, we propose OG-UPCR, an innovative unsupervised point cloud registration framework designed to address low overlap and photometric inconsistency, as shown in Fig. 1. Specifically, we propose the Overlapping Constraint for Inliers Detection module (OCID) based on the observation that inliers must lie within overlapping regions. This module leverages overlapping constraints to detect inliers, addressing issues arising from low overlap. Additionally, we design the Gaussian Rendering for Photometric Adaptation module (GRPA), which converts 3D points into 3D Gaussians and rasterizes them into image space, leveraging the rich geometric and texture information contained in the Gaussians. Based on this, nonlinear optimization is applied to each pixel to enhance photometric adaptation and enable the model to extract discriminative features. Moreover, this process refines the transformation and improves overall registration."
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+ "content": ", ensuring that the correspondences are uniformly distributed. To ensure that the selected seed points are reliable inliers, we measure the correspondence of the seed point and its top-"
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+ "content": " using a Gaussian renderer, it is necessary to estimate their geometric transformation. This estimation is achieved through geometric fitting. Following [5], we estimate the geometric transformation according to each consensus set. Finally, we choose the transformation with the highest number of inliers as the result "
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+ "content": "Following previous work [52], we conduct experiments on the challenging ScanNet1500 dataset to further demonstrate the effectiveness of our method. As shown in Table 2, our method outperforms all other unsupervised and supervised methods on the most stringent accuracy metric, and performs only slightly worse than the supervised method with the best generalization performance on the most permissive accuracy metric. The ScanNet1500 includes view pairs with low overlap and significant viewpoint variations, which pose substantial challenges for existing unsupervised methods. These conditions hinder the performance of previous methods, as geometric and photometric consistency between view pairs is greatly affected. In contrast, our method maintains strong performance by identifying reliable correspondences through overlapping constraint and further optimizing the model using the Gaussian Splitting technique."
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| SuperPoint | - | | 65.5 | 86.9 | 96.6 | 8.9 | 3.6 | 21.2 | 51.7 | 88.0 | 16.1 | 9.7 | 45.7 | 81.1 | 88.2 | 19.2 | 1.2 | - |
| FCGF | - | ✓ | 70.2 | 87.7 | 96.2 | 9.5 | 3.3 | 27.5 | 58.3 | 82.9 | 23.6 | 8.3 | 52.0 | 78.0 | 83.7 | 24.4 | 0.9 | 0.129 |
| 3DMVReg | 3DMatch | ✓ | 87.7 | 93.2 | 97.0 | 6.0 | 1.2 | 69.0 | 83.1 | 91.8 | 11.7 | 2.9 | 78.9 | 89.2 | 91.8 | 10.2 | 0.2 | - |
| REGTR | 3DMatch | ✓ | 86.0 | 93.9 | 98.6 | 4.4 | 1.6 | 61.4 | 80.3 | 91.4 | 14.4 | 3.8 | 80.9 | 90.9 | 93.6 | 13.5 | 0.2 | - |
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| PARENet | 3DMatch | ✓ | 97.5 | 98.3 | 99.5 | 1.9 | 0.7 | 85.9 | 95.7 | 97.0 | 3.9 | 1.8 | 94.2 | 97.9 | 98.6 | 4.2 | 0.2 | 0.165 |
| UR&R | 3DMatch | ✓ | 92.3 | 95.3 | 98.2 | 3.8 | 0.8 | 77.6 | 89.4 | 95.5 | 7.8 | 2.3 | 86.1 | 94.0 | 95.6 | 6.7 | 0.1 | 0.070 |
| UR&R | 3DMatch | | 87.6 | 93.1 | 98.3 | 4.3 | 1.0 | 69.2 | 84.0 | 93.8 | 9.5 | 2.8 | 79.7 | 91.3 | 94.0 | 7.2 | 0.2 | 0.071 |
| BYOC | 3DMatch | | 66.5 | 85.2 | 97.8 | 7.4 | 3.3 | 30.7 | 57.6 | 88.9 | 16.0 | 8.2 | 54.1 | 82.8 | 89.5 | 9.5 | 0.9 | - |
| LLT | 3DMatch | | 93.4 | 96.5 | 98.8 | 2.5 | 0.8 | 76.9 | 90.2 | 96.7 | 5.5 | 2.2 | 86.4 | 95.1 | 96.8 | 4.6 | 0.1 | 0.125 |
| PointMBF | 3DMatch | | 94.6 | 97.0 | 98.7 | 3.0 | 0.8 | 81.0 | 92.0 | 97.1 | 6.2 | 2.1 | 91.3 | 96.6 | 97.4 | 4.9 | 0.1 | 0.079 |
| CCAP | 3DMatch | | 95.6 | 98.1 | - | 2.4 | 0.7 | 81.5 | 92.3 | - | 3.7 | 1.9 | - | - | - | - | - | - |
| Ours | 3DMatch | | 97.9 | 98.9 | 99.5 | 1.8 | 0.7 | 87.7 | 96.2 | 98.6 | 3.8 | 1.8 | 95.5 | 98.4 | 98.8 | 3.3 | 0.1 | 0.136 |
| UR&R | ScanNet | | 92.7 | 95.8 | 98.5 | 3.4 | 0.8 | 77.2 | 89.6 | 96.1 | 7.3 | 2.3 | 86.0 | 94.6 | 96.1 | 5.9 | 0.1 | 0.071 |
| BYOC | ScanNet | | 86.5 | 95.2 | 99.1 | 3.8 | 1.7 | 56.4 | 80.6 | 96.3 | 8.7 | 4.3 | 78.1 | 93.9 | 96.4 | 5.6 | 0.3 | - |
| LLT | ScanNet | | 95.5 | 97.6 | 99.1 | 2.5 | 0.8 | 80.4 | 92.2 | 97.6 | 5.5 | 2.2 | 88.9 | 96.4 | 97.6 | 4.6 | 0.1 | 0.125 |
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| CCAP | ScanNet | | 97.1 | 98.2 | - | 1.9 | 0.6 | 85.9 | 93.6 | - | 3.9 | 1.8 | - | - | - | - | - | - |
| Ours | ScanNet | | 98.3 | 99.2 | 99.7 | 1.5 | 0.7 | 88.8 | 96.7 | 99.0 | 3.3 | 1.7 | 96.1 | 98.8 | 99.1 | 2.8 | 0.1 | 0.136 |
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| PointMBF | ScanNet | | 55.9 | 65.9 | 84.9 | 3.4 | 37.1 | 49.9 | 63.1 | 10.0 | 48.5 | 62.1 | 67.2 | 1.2 |
| Ours | ScanNet | | 81.3 | 85.9 | 91.2 | 1.5 | 53.5 | 72.1 | 83.3 | 4.3 | 72.4 | 83.3 | 85.9 | 0.3 |
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| × | × | × | ScanNet | 96.0 | 0.8 | 83.9 | 1.9 | 92.8 | 0.1 |
| × | × | ✓ | 97.4 | 0.8 | 84.9 | 1.9 | 94.6 | 0.1 |
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| × | ✓ | × | 97.5 | 0.8 | 85.5 | 1.9 | 95.0 | 0.1 |
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| ✓ | ✓ | ✓ | 98.3 | 0.7 | 88.8 | 1.7 | 96.1 | 0.1 |
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| × | × | ✓ | 65.1 | 2.1 | 42.3 | 6.8 | 57.1 | 0.5 |
| ✓ | ✓ | × | 78.5 | 1.6 | 51.1 | 4.9 | 68.9 | 0.3 |
| × | ✓ | × | 73.9 | 1.9 | 46.1 | 5.7 | 65.5 | 0.4 |
| ✓ | × | × | 74.7 | 1.6 | 46.7 | 4.8 | 66.4 | 0.3 |
| ✓ | ✓ | ✓ | 81.3 | 1.5 | 53.5 | 4.3 | 72.4 | 0.3 |
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+ }
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+ "content": "[3] Daniel Barath, Jiri Matas, and Jana Noskova. Magsac: marginalizing sample consensus. In CVPR, pages 10197-10205, 2019. 2"
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diff --git a/2025/Unsupervised Visible-Infrared Person Re-identification under Unpaired Settings/8bad0627-426a-4c79-849d-e7d54bb417e5_content_list.json b/2025/Unsupervised Visible-Infrared Person Re-identification under Unpaired Settings/8bad0627-426a-4c79-849d-e7d54bb417e5_content_list.json
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+ "text": "Unsupervised Visible-Infrared Person Re-identification under Unpaired Settings",
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+ "text": "Haoyu Yao $^{1,2,3,4*}$ Bin Yang $^{1,2,3*}$ Wenke Huang $^{1,2,3}$ Bo Du $^{1,2,3}$ Mang Ye $^{1,2,3\\dagger}$",
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+ "text": "$^{2}$ National Engineering Research Center for Multimedia Software, Wuhan University, China \n $^{3}$ Hubei Key Laboratory of Multimedia and Network Communication Engineering, Wuhan University, China \n $^{4}$ School of Remote Sensing and Information Engineering, Wuhan University, China",
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+ "text": "Unsupervised visible-infrared person re-identification (USL-VI-ReID) aims to train a cross-modality retrieval model without labels, reducing the reliance on expensive cross-modality manual annotation. However, existing USL-VI-ReID methods rely on artificially cross-modality paired data as implicit supervision, which is also expensive for human annotation and contrary to the setting of unsupervised tasks. In addition, this full alignment of identity across modalities is inconsistent with real-world scenarios, where unpaired settings are prevalent. To this end, we study the USL-VI-ReID task under unpaired settings, which uses cross-modality unpaired and unlabeled data for training a VI-ReID model. We propose a novel Mapping and Collaborative Learning (MCL) framework. Specifically, we first design a simple yet effective Cross-modality Feature Mapping (CFM) module to map and generate fake cross-modality positive feature pairs, constructing a cross-modal pseudo-identity space for feature alignment. Then, a Static-Dynamic Collaborative (SDC) learning strategy is proposed to align cross-modality correspondences through a collaborative approach, eliminating inter-modality discrepancies across different aspects i.e., cluster-level and instance-level, in scenarios with cross-modal identity mismatches. Extensive experiments on the conducted SYSU-MM01 and RegDB benchmarks under paired and unpaired settings demonstrate that our proposed MCL significantly outperforms existing unsupervised methods, facilitating USL-VI-ReID to real-world deployment.",
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+ "Figure 1. Illustration of the motivation. Previous advanced works for USL-VI-ReID mainly focus on paired settings, which leads to the leakage of supervised information and is inconsistent with the real-world scenarios. Under the underexplored unpaired settings, the cross-modality correspondences are hard to align with unpaired and unlabeled data, which poses a great challenge of how to establish the relation of unpaired samples among different modalities for learning modality-invariant knowledge."
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+ "text": "Traditional ReID methods primarily rely on daytime visible-light images, which struggle to extract discriminative features in low-light environments, limiting single-modality ReID deployment in real-world surveillance [13, 26]. To address this problem, the cross-modality visible-infrared person re-identification (VI-ReID) is proposed to identify the same person across a set of visible and infrared images [42]. While supervised VI-ReID methods use plenty of costly cross-modality (visible-infrared) identity labels to learn modality-invariant feature representations [15, 19, 30, 38, 41], the unsupervised VI-ReID (USL-VI-ReID) methods eliminate the need for annotation by generating pseudo-labels [20, 31, 32], which reduce the cost of",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "However, existing USL-VI-ReID methods [2-4, 16, 31, 33, 37] operate under the unrealistic assumption of precisely paired cross-modality data, which contradicts real-world scenarios where unpaired settings are more common, as shown in Fig. 1. For instance, a commuter captured by daytime visible cameras may never appear in nighttime infrared surveillance due to social behaviors or hidden activity patterns [14]. More critically, this unrealistic assumption introduces supervised information leakage, violating the unsupervised paradigm and necessitating extensive, costly annotations. To bridge this gap, we introduce a new task: unsupervised visible-infrared person re-identification under unpaired settings, which seeks to train a cross-modality ReID model using unpaired and unlabeled data. When applied to unpaired scenarios, existing USL-VI-ReID methods face two fundamental challenges, as shown in Fig. 1. First, pseudo-label generation depends on cross-modality correspondences, which are absent in unpaired settings, leading to erroneous label assignments. Second, the lack of identity pairs across modalities amplifies the modality gap, hindering effective feature alignment and obstructing the learning of modality-invariant representations.",
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+ "text": "To overcome these challenges, we construct the first public visible-infrared pedestrian benchmarks under unpaired settings. Based on these benchmarks, we propose a novel Mapping and Collaborative Learning (MCL) framework that establishes cross-modality associations without paired supervision. To handle the absence of paired data, the Cross-modality Feature Mapping (CFM) module is designed to supplement the missing cross-modality paired data while preserving identity consistency. Then, a Static-Dynamic Collaborative (SDC) learning strategy is proposed to achieve unprecedented capability in bridging modality gaps through dual-level alignment. The static learning could establish holistic identity prototypes that capture comprehensive identity characteristics at cluster level, ensuring robust alignment under severe modality mismatches and improving the reliability of cross-modality correspondence. For the dynamic learning strategy, it can reduce the discrepancy between the two modalities by pulling fake samples towards their corresponding actual ones, thereby narrowing the modality gap through instance-level intermodality alignment. Joint learning of the static and dynamic method forms a collaborative learning strategy, achieving better learning of discriminative and modality-invariant representations for cross-modality retrieval.",
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+ "type": "text",
+ "text": "The main contributions can be summarized as follows:",
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+ "text": "- We formally characterize the prevalent unpaired settings encountered in real-world scenarios and introduce the first public visible-infrared pedestrian benchmarks under such conditions. To our knowledge, this work marks the inaugural exploration of unsupervised scenarios featuring",
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+ "type": "text",
+ "text": "cross-modal identity mismatches.",
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+ "- We propose a novel Mapping and Collaborative Learning (MCL) framework to address the problem of lacking cross-modality paired and labeled data under unpaired settings, establishing a kind of implicit cross-modality associations without paired supervision for learning modality-invariant representations.",
+ "- We introduce a straightforward yet effective Cross-modality Feature Mapping (CFM) module that synthesizes positive feature pairs across modalities to achieve robust alignment. Building upon these synthesized pairs, a novel Static-Dynamic Collaborative (SDC) learning strategy is designed to mitigate cross-modality discrepancies at both the cluster and instance levels by leveraging complementary static and dynamic optimization.",
+ "- Extensive experiments on two benchmark datasets demonstrate that the proposed framework surpasses existing state-of-the-art USL-VI-ReID methods in unpaired settings, while maintaining competitive performance under paired scenarios."
+ ],
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+ {
+ "type": "text",
+ "text": "2. RELATED WORK",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "2.1. Supervised Visible-Infrared Person ReID",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "Supervised visible-infrared person re-identification (VI-ReID) has received considerable attention for its applicability in 24-hour surveillance systems. A key challenge is to mitigate the significant intra-class discrepancies between the visible and infrared modalities [29]. Current approaches bridging this cross-modality gap can fall into two categories: image-level and feature-level matching. Image-level methods [25, 36] focus on the generation of cross-modal images to extract modality-invariant features. In contrast, feature-level alignment approaches [9, 17, 18, 28, 35, 40] impose constraints to embed heterogeneous images into a shared feature space. However, these methods rely heavily on extensive cross-modality annotation, which is expensive and time-consuming, making supervised VI-ReID less scalable in real-world deployments.",
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+ {
+ "type": "text",
+ "text": "2.2. Unsupervised Visible-Infrared Person ReID",
+ "text_level": 1,
+ "bbox": [
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+ "text": "Unsupervised visible-infrared person re-identification (USL-VI-ReID) faces two key challenges. First, the significant modality gap between visible and infrared data amplifies intra-class variation, making it difficult to consistently generate cross-modality pseudo-labels. Second, the lack of annotated cross-modality identities prevents the learning of modality-invariant representations. Previous work [16, 23, 24, 32, 34, 43, 51] are mainly based on pseudo labels, which establish a bridge with the supervised method. H2H [16] first pioneers a two-stage learning framework, and OTLA [24] introduces an optimal transport strategy for further pseudo-label assignment.",
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+ {
+ "type": "page_number",
+ "text": "11917",
+ "bbox": [
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+ "text": "However, both methods rely on external RGB datasets for pre-training, while OTLA also assumes uniform infrared-to-visible label distributions, which is an impractical constraint for real-world scalability. Yang et al. [32] explore cluster-level relationships through cross-modality memory aggregation, but fail to address identity mismatch scenarios. Critically, existing approaches require full cross-modality identity alignment during training, rendering them inapplicable to unpaired data settings.",
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "3. Methodology",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "3.1. Preliminary",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "We propose a Mapping and Collaborative Learnin (MCL) framework for USL-VI-ReID under unpaired settings, as shown in Fig. 2. Our MCL has two components including Cross-modality Feature Mapping (CFM) module and Static-Dynamic Collaborative (SDC) learning strategy. In this paper, we follow Augmented Dual-Contrastive Aggregation (ADCA) [32] to establish our baseline, where a dualpath contrastive learning framework with two modality-specific memories to learn intra-modality representations.",
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+ {
+ "type": "text",
+ "text": "To facilitate the description of our method, we first introduce the notations used in this paper. Let $\\mathbf{X}_m = \\{\\pmb{x}_m^1, \\pmb{x}_m^2, \\dots, \\pmb{x}_m^{N_m}\\}$ denote the unlabeled infrared/visible images with $N_m$ instances, where $m \\in \\{i, v\\}$ denotes the infrared and visible modality, respectively. $\\mathbf{U}_m = \\{\\pmb{u}_m^1, \\pmb{u}_m^2, \\dots, \\pmb{u}_m^{N_m}\\}$ represents the corresponding features extracted by the modality-specific feature extractor $f_m^\\theta \\cdot \\pmb{q}_m$ is the query instance feature extracted by $f_m^\\theta \\cdot \\{\\overline{y}_m^k\\}_{k=1}^{N_m}$ represents the ground-truth labels of different modalities. In this work, we study the under-explored unpaired settings of USL-VI-ReID, where there are unpaired cross-modality data in the training set, i.e., there exist $k, l$ that satisfy $\\overline{y}_i^k \\neq \\overline{y}_v^l$ . In comparison, existing USL-VI-ReID methods are under the traditional label settings where a large number of cross-modality positive pairs are captured in the training data, i.e., $\\overline{y}_i^k = \\overline{y}_v^l$ for all $k, l$ .",
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+ "type": "text",
+ "text": "3.2. Cross-modality Feature Mapping",
+ "text_level": 1,
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+ "type": "text",
+ "text": "In USL-VI-ReID, the feature extractor $f_{m}^{\\theta}$ is designed to extract discriminative representation $\\pmb{u}_{m}^{k} = f_{m}^{\\theta}(\\pmb{x}_{m}^{k})$ for image $\\pmb{x}_{m}^{k}$ to match, as described by:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nD \\left(\\boldsymbol {u} _ {m _ {a}} ^ {a}, \\boldsymbol {u} _ {m _ {p}} ^ {p}\\right) < D \\left(\\boldsymbol {u} _ {m _ {a}} ^ {a}, \\boldsymbol {u} _ {m _ {n}} ^ {n}\\right), \\tag {1}\n$$\n",
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+ "type": "text",
+ "text": "where $D$ denotes a distance function, and $\\pmb{u}_{m_a}^a$ , $\\pmb{u}_{m_p}^p$ , and $\\pmb{u}_{m_n}^n$ represent the anchor, positive, and negative features extracted from modalities $m_{a}$ , $m_{p}$ , and $m_{n}$ , respectively. The goal is to ensure that the anchor is closer to the positive than to the negative in the feature space. By reducing the distance between cross-modality positive pairs (i.e., $\\pmb{u}_{m_a}^a$ and $\\pmb{u}_{m_p}^p$ with $m_{a} \\neq m_{p}$ ), the discrepancy can be eliminated across modalities, which facilitates the learning of discriminative features.",
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+ "text": "However, in unpaired settings, the lack of cross-modality positive pairs in the training data poses a significant challenge. Given an anchor feature $\\mathbf{u}_{m_a}^a$ , it is difficult to find a corresponding positive sample $\\mathbf{u}_{m_p}^p$ from a different modality, which hinders the ability to model intra-class variations across modalities. Therefore, establishing the relation between unpaired cross-modal data is paramount.",
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+ "type": "text",
+ "text": "To handle this situation, we substitute the unavailable actual cross-modality positive pair $(\\pmb{u}_{m_a}^a,\\pmb{u}_{m_p}^p)$ with a synthetic or fake positive pair $(\\pmb{u}_{m_a}^a,\\hat{\\pmb{u}}_{m_p}^p)$ . The fake feature $\\hat{\\pmb{u}}_{m_p}^p$ is generated through a modality-aware transformation:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\hat {\\boldsymbol {u}} _ {m _ {p}} ^ {p} = \\operatorname {M a p p i n g} \\left(\\boldsymbol {u} _ {m _ {a}} ^ {a}, m _ {p}\\right), \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "where Mapping denotes a function that projects the feature $\\mathbf{u}_{m_a}^a$ from its source modality $m_{a}$ into the feature space of the target modality $m_p$ .",
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+ "type": "text",
+ "text": "To achieve the transformation, we introduce a cross-modality feature mapping module comprising two modality-specific mappers, each of which estimates the modality-dependent moment statistics $\\{\\pmb{\\mu}_m,\\pmb{\\sigma}_m^2\\}$ of feature distributions. For a given set of features from modality $m$ , the associated mapper derives its mean and variance by:",
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+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {\\mu} _ {m} = \\frac {1}{N _ {m}} \\sum_ {k = 1} ^ {N _ {m}} \\boldsymbol {u} _ {m} ^ {k}, \\quad \\sigma_ {m} ^ {2} = \\frac {1}{N _ {m}} \\sum_ {k = 1} ^ {N _ {m}} \\left(\\boldsymbol {u} _ {m} ^ {k} - \\boldsymbol {\\mu} _ {m}\\right) ^ {2}, \\tag {3}\n$$\n",
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+ "type": "text",
+ "text": "where $\\pmb{\\mu}_{m}$ and $\\sigma_{m}$ are the modality-specific mean and variance, respectively.",
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+ "type": "text",
+ "text": "In the cross-modality feature mapping process, a feature $\\pmb{u}_m^k$ of modality $m$ is transformed to a fake feature in the modality-specific distribution of a different modality $m'$ by:",
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+ "type": "equation",
+ "text": "\n$$\n\\hat {\\boldsymbol {u}} _ {m ^ {\\prime}} ^ {k} = \\operatorname {M a p p i n g} \\left(\\boldsymbol {u} _ {m} ^ {k}, m ^ {\\prime}\\right) = \\gamma \\frac {\\boldsymbol {u} _ {m} ^ {k} - \\boldsymbol {\\mu} _ {m ^ {\\prime}}}{\\sqrt {\\boldsymbol {\\sigma} _ {m ^ {\\prime}} ^ {2} + \\epsilon}} - \\zeta , \\tag {4}\n$$\n",
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+ "type": "text",
+ "text": "where $\\gamma$ and $\\zeta$ are scaling and shifting parameters of $m^{\\prime}$ -specific mapper, which are learned during training. $\\epsilon$ is a small constant to ensure stability.",
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+ "text": "The CFM module applies a cross-modality affine transformation to align source features with the target distribution by matching mean and variance. We precisely estimate the distributions of both modalities and use the transformation to map features. Since the actual feature $\\pmb{u}_{m}^{k}$ and mapped feature $\\hat{\\pmb{u}}_{m'}^{k}$ are encoded from the same image $\\pmb{x}_{m}^{k}$ , we regard they share the same identity $(\\hat{y}_{m'}^{k} = y_{m}^{k})$ and respectively construct an original modality-specific space and a cross-modal pseudo-identity space for further alignment.",
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+ "type": "text",
+ "text": "3.3. Static-Dynamic Collaborative Learning",
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+ "type": "text",
+ "text": "The CFM module complements the missing cross-modality unpaired data by estimating modality-specific feature distributions and transforming them into different modalities.",
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+ {
+ "type": "page_number",
+ "text": "11918",
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+ {
+ "type": "image",
+ "img_path": "images/eabac5f06e4bf8fe56466ef3400bba02fa937284e23158ae81432d8e8ee42449.jpg",
+ "image_caption": [
+ "Figure 2. Illustration of mapping and collaborative learning framework. The framework integrates two core components: a Cross-Modality Feature Mapping (CFM) module and a Static-Dynamic Collaborative (SDC) learning strategy. The CFM synthesizes cross-modality positive feature pairs by estimating modality-specific distributions. Concurrently, the SDC strategy addresses inter-modality discrepancies through a twofold alignment: (1) Static Learning employs multi-memory banks to derive reliable cross-modality correspondences by learning holistic representations, establishing robust cluster-level associations. (2) Dynamic Learning utilizes a cross-modality label-preserving loss (CLP) to bridge substantial modality gaps, achieving fine-grained instance-level alignment."
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+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "However, it does not use any features prior to and after the mapping process to align cross-modal correspondences. To associate fake cross-modality positive feature pairs and effectively eliminate inter-modality discrepancies, we propose a static-dynamic collaborative learning framework to bridge the gap between the visible and infrared modalities both at cluster-level and instance-level.",
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+ "type": "text",
+ "text": "Static Learning. We note that the existing methods typically rely on a single memory to represent individual characteristics and establish cross-modality correspondences. However, a single memory may not capture all individual nuances in scenarios with cross-modal identity mismatches, which naturally leads to poor cross-modality correspondences. Therefore, we design a static learning method to obtain reliable cross-modality correspondences by clustering actual samples and fake cross-modality samples as multi-memory banks, jointly conducting the contrastive learning in the original modality-specific space and the cross-modal pseudo-identity space.",
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+ "type": "text",
+ "text": "At the beginning of each training epoch, all infrared",
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+ "type": "text",
+ "text": "and visible features $\\mathbf{U}_i$ and $\\mathbf{U}_v$ are firstly clustered to generate pseudo labels, where each cluster's representations $\\{\\phi_i^1,\\dots,\\phi_i^K\\}$ and $\\{\\phi_v^1,\\dots,\\phi_v^L\\}$ of infrared and visible features are stored in infrared and visible memory dictionaries. This process can be written as:",
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+ "type": "equation",
+ "text": "\n$$\n\\phi_ {i} ^ {k} = \\frac {1}{\\left| \\mathcal {H} _ {i} ^ {k} \\right|} \\sum_ {\\boldsymbol {u} _ {i} ^ {n} \\in \\mathcal {H} _ {i} ^ {k}} \\boldsymbol {u} _ {i} ^ {n}, \\phi_ {v} ^ {l} = \\frac {1}{\\left| \\mathcal {H} _ {v} ^ {l} \\right|} \\sum_ {\\boldsymbol {u} _ {v} ^ {m} \\in \\mathcal {H} _ {v} ^ {l}} \\boldsymbol {u} _ {v} ^ {m}, \\tag {5}\n$$\n",
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+ "type": "text",
+ "text": "where $\\mathcal{H}_{i(v)}^k$ is the $k$ -th cluster set in infrared or visible modality, and $|\\cdot|$ is the number of instances per cluster.",
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+ "type": "text",
+ "text": "Then, these actual features $\\pmb{U}_i$ and $\\pmb{U}_v$ are transformed into corresponding fake cross-modality features $\\hat{\\pmb{U}}_v$ and $\\hat{\\pmb{U}}_i$ through CFM. While this mapping process alters the feature distributions, it preserves the original identity information. To maintain consistency in the number of clusters, DBSCAN is applied solely to the actual features for generating pseudo identity labels. Consequently, the cluster representations of the fake cross-modality features are denoted as $\\{\\hat{\\phi}_v^1,\\dots ,\\hat{\\phi}_v^K\\}$ and $\\{\\hat{\\phi}_i^1,\\dots ,\\hat{\\phi}_i^L\\}$ , which constitute two additional memory banks in the cross-modal pseudo-",
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+ "type": "page_number",
+ "text": "11919",
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+ {
+ "type": "text",
+ "text": "identity space. This process is formally defined as:",
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+ "page_idx": 4
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\hat {\\phi} _ {v} ^ {k} = \\frac {1}{\\left| \\hat {\\mathcal {H}} _ {v} ^ {k} \\right|} \\sum_ {\\hat {\\boldsymbol {u}} _ {v} ^ {n} \\in \\hat {\\mathcal {H}} _ {v} ^ {k}} \\hat {\\boldsymbol {u}} _ {v} ^ {n}, \\hat {\\phi} _ {i} ^ {l} = \\frac {1}{\\left| \\hat {\\mathcal {H}} _ {i} ^ {l} \\right|} \\sum_ {\\hat {\\boldsymbol {u}} _ {i} ^ {m} \\in \\hat {\\mathcal {H}} _ {i} ^ {l}} \\hat {\\boldsymbol {u}} _ {i} ^ {m}, \\tag {6}\n$$\n",
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+ "type": "text",
+ "text": "where $\\hat{\\mathcal{H}}_{i(v)}^k$ denotes the $k$ -th cluster set in the mapped infrared or visible modality, and $|\\cdot|$ indicates the number of instances per cluster.",
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+ "type": "text",
+ "text": "During training, we sample $P$ person identities and $Z$ instances for each identity from each modality training set. Then, we use a batch of infrared and visible queries to update the actual memories by a momentum updating strategy:",
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+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {\\phi} _ {i} ^ {k (\\delta)} \\leftarrow \\beta \\boldsymbol {\\phi} _ {i} ^ {k (\\delta - 1)} + (1 - \\beta) \\boldsymbol {q} _ {i}, \\tag {7}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\boldsymbol {\\phi} _ {v} ^ {l (\\delta)} \\leftarrow \\beta \\boldsymbol {\\phi} _ {v} ^ {l (\\delta - 1)} + (1 - \\beta) \\boldsymbol {q} _ {v}, \\tag {8}\n$$\n",
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+ "type": "text",
+ "text": "The memories of fake cross-modality features are updated by a similar momentum strategy:",
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+ "type": "equation",
+ "text": "\n$$\n\\hat {\\phi} _ {v} ^ {k (\\delta)} \\leftarrow \\beta \\hat {\\phi} _ {v} ^ {k (\\delta - 1)} + (1 - \\beta) \\boldsymbol {q} _ {i}, \\tag {9}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\hat {\\phi} _ {i} ^ {l (\\delta)} \\leftarrow \\beta \\hat {\\phi} _ {i} ^ {l (\\delta - 1)} + (1 - \\beta) \\boldsymbol {q} _ {v}, \\tag {10}\n$$\n",
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+ "type": "text",
+ "text": "where $\\beta$ is the momentum factor and $\\delta$ is the iteration step.",
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+ "type": "text",
+ "text": "In each iteration, the feature extractors are jointly updated by a multi ClusterNCE [7] loss, including the actual infrared loss $\\mathcal{L}_i$ , actual visible loss $\\mathcal{L}_v$ , fake infrared loss $\\hat{\\mathcal{L}}_i$ , and fake visible loss $\\hat{\\mathcal{L}}_v$ by the following equations:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {i} = - \\log \\frac {\\exp \\left(\\boldsymbol {q} _ {i} \\cdot \\phi_ {i} ^ {+} / \\tau\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(\\boldsymbol {q} _ {i} \\cdot \\phi_ {i} ^ {k} / \\tau\\right)}, \\tag {11}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {v} = - \\log \\frac {\\exp \\left(\\boldsymbol {q} _ {v} \\cdot \\phi_ {v} ^ {+} / \\tau\\right)}{\\sum_ {l = 1} ^ {L} \\exp \\left(\\boldsymbol {q} _ {v} \\cdot \\phi_ {v} ^ {l} / \\tau\\right)}, \\tag {12}\n$$\n",
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+ "text": "\n$$\n\\hat {\\mathcal {L}} _ {i} = - \\log \\frac {\\exp \\left(\\boldsymbol {q} _ {v} \\cdot \\hat {\\phi} _ {i} ^ {+} / \\tau\\right)}{\\sum_ {l = 1} ^ {L} \\exp \\left(\\boldsymbol {q} _ {v} \\cdot \\hat {\\phi} _ {i} ^ {l} / \\tau\\right)}, \\tag {13}\n$$\n",
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+ "text": "\n$$\n\\hat {\\mathcal {L}} _ {v} = - \\log \\frac {\\exp \\left(\\boldsymbol {q} _ {i} \\cdot \\hat {\\phi} _ {v} ^ {+} / \\tau\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(\\boldsymbol {q} _ {i} \\cdot \\hat {\\phi} _ {v} ^ {k} / \\tau\\right)}, \\tag {14}\n$$\n",
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+ "text": "where $\\phi_i^+$ and $\\phi_v^+$ are the positive representation vector of the actual infrared and visible cluster, respectively, corresponding to the pseudo label of the query. $\\hat{\\phi}_i^+$ and $\\hat{\\phi}_v^+$ are the positive feature vector of the fake infrared and visible cluster. The $\\tau$ is a temperature hyper-parameter.",
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+ "type": "text",
+ "text": "Certainly, four types of ClusterNCE [5] loss are designed to learn discriminative representation:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {S L}} = \\mathcal {L} _ {i} + \\mathcal {L} _ {v} + \\hat {\\mathcal {L}} _ {i} + \\hat {\\mathcal {L}} _ {v}. \\tag {15}\n$$\n",
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+ "text": "Dynamic Learning. The generated cross-modality samples are useful in bridging significant inter-modality discrepancies by including the abundant information of missing identities. However, it is expected that these samples will not change significantly, as they share the same identity with the original samples, which should be aligned during the learning. Inspired by ISE [45], we further propose a Cross-modality Label Preserving (CLP) loss to enforce the fake cross-modality features to be close to their corresponding actual features, which facilitates the learning of cross-modality representations at the instance level. During training, the CLP loss enforces identity consistency between the actual and mapped features, allowing CFM to transfer cross-modal knowledge and capture the complex, non-linear modality discrepancies.",
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+ "text": "Certainly, two types of CLP loss function are introduced in the dynamic learning method:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C L P}} ^ {i} = - \\log \\frac {\\exp \\left(\\operatorname {s i m} \\left(\\boldsymbol {u} _ {i} \\cdot \\hat {\\boldsymbol {u}} _ {v} ^ {+}\\right) / \\tau^ {\\prime}\\right)}{\\sum_ {c = 1} ^ {C _ {i}} \\exp \\left(\\operatorname {s i m} \\left(\\boldsymbol {u} _ {i} \\cdot \\hat {\\boldsymbol {u}} _ {v} ^ {c -}\\right) / \\tau^ {\\prime}\\right)}, \\tag {16}\n$$\n",
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+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {C L P}} ^ {v} = - \\log \\frac {\\exp \\left(\\operatorname {s i m} \\left(\\boldsymbol {u} _ {v} \\cdot \\hat {\\boldsymbol {u}} _ {i} ^ {+}\\right) / \\tau^ {\\prime}\\right)}{\\sum_ {c = 1} ^ {C _ {v}} \\exp \\left(\\operatorname {s i m} \\left(\\boldsymbol {u} _ {v} \\cdot \\hat {\\boldsymbol {u}} _ {i} ^ {c -}\\right) / \\tau^ {\\prime}\\right)}, \\tag {17}\n$$\n",
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+ "type": "text",
+ "text": "where $C_i$ and $C_v$ are the cluster number of a mini-batch in infrared and visible modality, respectively. $\\sin(\\cdot)$ denotes the cosine similarity. $\\hat{\\pmb{u}}_v^+$ is the hardest positive fake visible sample for a given infrared feature $\\pmb{u}_i$ , and $\\hat{\\pmb{u}}_v^{c-}$ is the hardest negative one in the $c$ -th fake visible cluster of a minibatch. $\\hat{\\pmb{u}}_i^+$ and $\\hat{\\pmb{u}}_i^{c-}$ are defined similarly to above. $\\tau'$ is a temperature hyper-parameter.",
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+ "type": "text",
+ "text": "Consequently, the two cross-modality label preserving loss functions are combined in the dynamic learning method to learn distinctive representations:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {D L}} = \\mathcal {L} _ {\\mathrm {C L P}} ^ {i} + \\mathcal {L} _ {\\mathrm {C L P}} ^ {v}. \\tag {18}\n$$\n",
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+ "type": "text",
+ "text": "Collaborative Learning. The cluster-level static learning method and instance-level dynamic learning method jointly forms the static-dynamic collaborative learning strategy, which aims to achieve better learning of discriminative and modality-invariant representations in the absence of cross-modality identity pairs.",
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+ "type": "text",
+ "text": "The overall loss for training the model is defined by the following equation:",
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+ "text": "\n$$\n\\mathcal {L} _ {\\text {o v e r a l l}} = \\mathcal {L} _ {\\mathrm {S L}} + \\eta \\mathcal {L} _ {\\mathrm {D L}}, \\tag {19}\n$$\n",
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+ "text": "where $\\eta$ is the loss weight, balancing two loss functions.",
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+ "type": "text",
+ "text": "4. EXPERIMENTS",
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+ "text": "4.1. Datasets and Evaluation Protocol",
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+ "text": "Paired Datasets. To validate the proposed framework under paired settings, we conduct comprehensive evaluations",
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+ "text": "11920",
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+ "type": "table",
+ "img_path": "images/21774599724493c3968966088d13a52e812989b28e3f019edfcad942e3ff174b.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": " | | | SYSU-MM01 (unpaired settings) | RegDB (unpaired settings) |
| All Search | Indoor Search | Visible to Infrared | Infrared to Visible |
| α value | Methods | Venue | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| 0.25 | ADCA [32] | MM-22 | 41.80 | 37.54 | 22.04 | 47.00 | 56.24 | 51.79 | 50.82 | 43.72 | 42.63 | 64.22 | 55.90 | 44.29 |
| OTPA [47] | arXiv-24 | 49.15 | 44.75 | 30.62 | 51.70 | 60.82 | 57.23 | 51.37 | 50.30 | 44.60 | 66.27 | 65.82 | 64.97 |
| MMM [20] | ECCV-24 | 54.68 | 47.35 | 35.42 | 55.19 | 63.76 | 61.21 | 62.27 | 55.09 | 44.34 | 76.69 | 69.93 | 66.44 |
| PCAL[37] | TIFS-25 | 48.84 | 41.30 | 26.05 | 50.48 | 62.63 | 59.72 | 59.33 | 56.26 | 45.73 | 77.18 | 75.24 | 63.83 |
| N-ULC [21] | AAAI-25 | 53.70 | 49.69 | 33.56 | 57.39 | 65.00 | 60.64 | 60.76 | 56.82 | 42.91 | 79.35 | 76.06 | 60.40 |
| MCL (Ours) | - | 58.57 | 57.74 | 45.45 | 65.72 | 71.84 | 68.30 | 65.97 | 63.53 | 55.84 | 84.31 | 78.67 | 67.28 |
| 0.5 | ADCA [32] | MM-22 | 34.34 | 32.21 | 18.76 | 36.59 | 47.07 | 43.23 | 40.28 | 32.60 | 34.93 | 52.94 | 47.48 | 37.05 |
| OTPA [47] | arXiv-24 | 48.80 | 45.64 | 31.01 | 49.19 | 58.74 | 54.83 | 40.58 | 41.52 | 32.44 | 59.26 | 58.68 | 57.13 |
| MMM [20] | ECCV-24 | 44.14 | 42.94 | 30.71 | 54.25 | 60.17 | 52.49 | 52.90 | 43.91 | 36.51 | 63.91 | 58.17 | 58.47 |
| PCAL[37] | TIFS-25 | 46.24 | 37.62 | 22.03 | 45.39 | 52.73 | 46.42 | 46.48 | 47.88 | 36.05 | 64.21 | 66.30 | 50.41 |
| N-ULC [21] | AAAI-25 | 49.36 | 45.12 | 29.17 | 51.59 | 60.24 | 55.89 | 50.24 | 45.96 | 34.61 | 70.31 | 62.84 | 54.74 |
| MCL (Ours) | - | 54.29 | 53.98 | 42.64 | 61.71 | 68.45 | 64.40 | 60.78 | 59.69 | 52.91 | 80.36 | 73.02 | 64.25 |
| 0.75 | ADCA [32] | MM-22 | 32.66 | 30.61 | 17.98 | 37.02 | 47.59 | 43.79 | 35.80 | 28.71 | 27.96 | 47.28 | 43.92 | 34.70 |
| OTPA [47] | arXiv-24 | 33.65 | 30.50 | 16.94 | 45.3 | 53.32 | 50.17 | 31.48 | 35.60 | 29.52 | 51.98 | 49.25 | 47.62 |
| MMM [20] | ECCV-24 | 36.19 | 34.60 | 23.56 | 43.91 | 50.60 | 45.20 | 41.73 | 38.64 | 32.75 | 54.79 | 47.90 | 46.16 |
| PCAL[37] | TIFS-25 | 30.74 | 29.83 | 20.54 | 40.60 | 47.42 | 39.34 | 38.10 | 37.09 | 33.54 | 59.80 | 59.61 | 47.20 |
| N-ULC [21] | AAAI-25 | 42.56 | 39.44 | 27.06 | 55.03 | 63.11 | 58.80 | 43.38 | 39.27 | 30.06 | 66.72 | 57.51 | 44.38 |
| MCL (Ours) | - | 52.16 | 51.57 | 39.57 | 59.63 | 66.46 | 62.24 | 55.30 | 52.79 | 48.26 | 74.19 | 69.37 | 60.58 |
| 1.0 | ADCA [32] | MM-22 | 23.48 | 23.23 | 12.53 | 28.39 | 37.40 | 32.80 | 26.18 | 15.93 | 14.72 | 33.10 | 28.43 | 24.95 |
| OTPA [47] | arXiv-24 | 20.53 | 19.46 | 10.32 | 36.18 | 43.54 | 40.02 | 19.20 | 18.03 | 19.70 | 39.74 | 38.42 | 35.11 |
| MMM [20] | ECCV-24 | 30.81 | 27.53 | 17.92 | 36.19 | 40.60 | 38.38 | 30.98 | 27.10 | 20.03 | 40.26 | 33.54 | 30.12 |
| PCAL[37] | TIFS-25 | 28.95 | 25.31 | 18.54 | 32.10 | 38.48 | 36.20 | 28.74 | 25.90 | 18.68 | 37.56 | 29.69 | 27.24 |
| N-ULC [21] | AAAI-25 | 34.40 | 31.83 | 25.77 | 40.36 | 43.70 | 43.86 | 34.71 | 28.06 | 25.48 | 42.83 | 32.40 | 28.92 |
| MCL (Ours) | - | 45.98 | 44.95 | 32.85 | 51.53 | 59.06 | 54.54 | 43.18 | 39.29 | 36.95 | 58.37 | 49.40 | 47.21 |
",
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+ {
+ "type": "text",
+ "text": "Table 1. The comparison with the state-of-the-art methods on SYSU-MM01 and RegDB under unpaired settings. It contains four settings, i.e., the unpaired ratio $\\alpha$ ranges from 0.25 to 1.0 in increments of 0.25. Rank-1 accuracy(%) , mAP (%) and mINP (%) are reported.",
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+ {
+ "type": "text",
+ "text": "on two benchmark visible-infrared person re-identification datasets: SYSU-MM01 [29] and RegDB [41]. The SYSUMM01 dataset is a large-scale cross-modality collection of 22,257 visible images and 11,909 near-infrared images captured in indoor and outdoor environments by 4 visible cameras and 2 infrared cameras. In contrast, the RegDB dataset is a smaller and less demanding dataset with 412 different person identities, where each identity contains 10 visible and 10 infrared image pairs. This thermal-infrared dataset is collected using an aligned pair of cameras (one visible and one infrared), which has a comparatively lower environmental complexity than SYSU-MM01.",
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+ {
+ "type": "text",
+ "text": "Unpaired Datasets. To evaluate the effectiveness of our model in unpaired settings, experiments are conducted on the modified SYSU-MM01 and RegDB datasets. It is noted that existing datasets lack cross-modality unpaired training data, thus necessitating adjustments to the existing benchmarks. In order to systematically analyse the impact of unpaired settings, we introduce a hyper-parameter $\\alpha$ that controls the proportion of unpaired identities between the visible and infrared modalities. Unlike OTPA [47], which reduces training data by dropping identities, our setup preserves the overall dataset size. Instead of adjusting the overlap ratio by selecting modality-specific subsets, we randomly replace a portion of the visible identities with external images. Specifically, the visible images of selected identities are replaced with images from three visible ReID",
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+ {
+ "type": "text",
+ "text": "datasets(i.e., Market-1501 [49], MSMT17 [27] and LLCM [46]), while maintaining a roughly consistent number of images per identity before and after replacement. Details of the replacement process are provided in the supplementary materials. This design mitigates the potential effects of data reduction. The test sets and evaluation protocols remain unchanged throughout the experiments.",
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+ "type": "text",
+ "text": "Evaluation Protocol. On the two benchmark datasets and their original counterpart, we follow the popular protocols [39] for evaluation, where cumulative match characteristic (CMC), mean average precision (mAP), and mean inverse negative penalty (mINP) [41] are adopted. For SYSU-MM01 under paired and unpaired settings, we adopt all-search and indoor-search evaluation modes. For RegDB in paired and unpaired settings, we evaluate our method in the two test modes, including thermal to visible and visible to thermal, and we strictly follow existing methods to perform ten trials of the gallery set selection [40], and calculate the average performance.",
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+ "type": "text",
+ "text": "4.2. Implementation Details",
+ "text_level": 1,
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+ "text": "MCL is implemented in the PyTorch platform. Our work is based on the Augmented Dual-Contrastive Aggregation [32] and incorporates the feature extractor from TransReID [10] as the backbone network. In each mini-batch, 16 identities are selected per modality, with each identity comprising 16 instances. We resize input images to $288 \\times 144$ pixels for training. Standard data augmentation techniques,",
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+ "img_path": "images/50a249f586130d8cc661ffc1053f42b82e86b2d66bd8f02cb33d8d44686dc0db.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": " | | | SYSU-MM01 | RegDB |
| All Search | Indoor Search | Visible to Infrared | Infrared to Visible |
| Methods | Venue | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| Supervised | AGW [41] | TPAMI-21 | 47.50 | 47.65 | 35.30 | 54.17 | 62.97 | 59.23 | 70.05 | 66.37 | 50.19 | 70.49 | 65.90 | 51.24 |
| DFLN-ViT [48] | TMM-22 | 59.84 | 57.70 | - | 62.13 | 69.03 | - | 92.10 | 82.11 | - | 91.21 | 81.62 | - |
| PartMix [12] | CVPR-23 | 77.78 | 74.62 | - | 81.52 | 84.38 | - | 85.66 | 82.27 | - | 84.93 | 82.52 | - |
| MUN [44] | ICCV-23 | 76.24 | 73.81 | - | 79.42 | 82.06 | - | 95.19 | 87.15 | - | 91.86 | 85.01 | - |
| SAAI [8] | ICCV-23 | 75.90 | 77.03 | - | 83.20 | 88.01 | - | 91.07 | 91.45 | - | 92.09 | 92.01 | - |
| YYDS [6] | arXiv-24 | 85.54 | 81.64 | - | 89.13 | 91.00 | - | - | - | - | 90.20 | 83.50 | - |
| TVI-LFM [11] | NIPS-24 | 84.90 | 81.47 | 70.85 | 89.06 | 90.78 | 88.39 | - | - | - | 91.38 | 85.92 | 72.73 |
| Unsupervised | H2H* [16] | TIP-21 | 30.15 | 29.40 | - | - | - | - | 23.81 | 18.87 | - | - | - | - |
| OTLA* [24] | ECCV-22 | 29.90 | 27.10 | - | 29.80 | 38.80 | - | 32.90 | 29.70 | - | 32.10 | 28.60 | - |
| ADCA [32] | MM-22 | 45.51 | 42.73 | 28.29 | 50.60 | 59.11 | 55.17 | 67.20 | 64.05 | 52.67 | 68.48 | 63.81 | 49.62 |
| PGM [31] | CVPR-23 | 57.27 | 51.78 | 34.96 | 56.23 | 62.74 | 58.13 | 69.48 | 65.41 | - | 69.85 | 65.17 | - |
| DOTLA* [4] | MM-23 | 50.36 | 47.36 | 32.40 | 53.47 | 61.73 | 57.35 | 85.63 | 76.71 | 61.58 | 82.91 | 74.97 | 58.60 |
| MBCCM [3] | MM-23 | 53.14 | 48.16 | 32.41 | 55.21 | 61.98 | 57.13 | 83.79 | 77.87 | 65.04 | 82.82 | 76.74 | 61.73 |
| CCLNet [2] | MM-23 | 54.03 | 50.19 | - | 56.68 | 65.12 | - | 69.94 | 65.53 | - | 70.17 | 66.66 | - |
| GUR†[33] | ICCV-23 | 60.95 | 56.99 | 41.85 | 64.22 | 69.49 | 64.81 | 73.91 | 70.23 | 8.88 | 75.00 | 69.94 | 56.21 |
| SCA-RCP [15] | TKDE-24 | 51.41 | 48.52 | 33.56 | 56.77 | 64.19 | 59.25 | 85.59 | 79.12 | - | 82.41 | 75.73 | - |
| MMM [20] | ECCV-24 | 61.60 | 57.90 | - | 64.40 | 70.40 | - | 89.70 | 80.50 | - | 85.80 | 77.00 | - |
| PCAL [37] | TIFS-25 | 54.39 | 51.95 | 38.09 | 59.69 | 66.72 | 62.44 | 86.43 | 82.51 | 72.33 | 86.21 | 81.23 | 68.71 |
| N-ULC [21] | AAAI-25 | 61.81 | 58.92 | 45.01 | 67.04 | 73.08 | 69.42 | 88.75 | 82.14 | 68.75 | 88.17 | 81.11 | 66.05 |
| MCL (Ours) | - | 62.95 | 62.71 | 50.63 | 67.81 | 74.19 | 70.82 | 89.83 | 83.12 | 72.86 | 88.64 | 82.04 | 69.12 |
",
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+ "Table 2. The comparison with the state-of-the-art methods on SYSU-MM01 and RegDB under paired settings. It contains two groups, i.e., unsupervised VI-ReID methods and supervised VI-ReID methods. * means the model is pre-trained on an extra labeled visible dataset. GUR† denotes the results without camera information. Rank-1 accuracy(%) , mAP (%) and mINP (%) are reported."
+ ],
+ "table_footnote": [],
+ "table_body": " | Components | SYSU-MM01* (All Search) | SYSU-MM01* (Indoor Search) | RegDB* (Visible to Infrared) |
| Index | Baseline | CFM | SL | DL | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| 1 | ✓ | | | | 47.14 | 47.29 | 34.63 | 55.39 | 63.10 | 59.43 | 49.28 | 48.6 | 43.93 |
| 2 | ✓ | ✓ | ✓ | | 51.65 | 52.48 | 40.08 | 58.38 | 66.87 | 63.66 | 56.39 | 54.52 | 49.70 |
| 3 | ✓ | ✓ | | ✓ | 49.46 | 50.67 | 39.24 | 57.00 | 65.53 | 62.92 | 52.73 | 50.84 | 47.92 |
| 4 | ✓ | ✓ | ✓ | ✓ | 54.29 | 53.98 | 42.64 | 61.71 | 68.45 | 64.40 | 60.78 | 59.69 | 52.91 |
",
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+ "type": "text",
+ "text": "Table 3. Ablation studies conducted on the SYSU-MM01 and RegDB datasets under unpaired settings. * refers to $\\alpha = 0.5$ in both unpaired datasets. \"CFM\" denotes the cross-modality feature mapping module, while \"SL\" and \"DL\" mean the static learning method and the dynamic learning method in 3.3, respectively. Rank-1 accuracy (\\%), mAP (\\%), and mINP (\\%) are reported.",
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+ "text": "including random cropping, random flipping and random erasing, are applied. At the beginning of each epoch, we perform the DBSCAN [7] clustering to generate pseudo labels in each modality independently. The learnable scaling and shifting parameters, $\\gamma$ and $\\zeta$ , are initialized to 1 and 0, respectively, and the constant $\\epsilon$ is set to $10^{-5}$ . The temperature factors $\\tau$ and $\\tau'$ are 0.05 and 0.6, respectively. We train the model in total of 50 epochs, in which the previous 30 epochs are used for pre-training, and CFM and SDC are executed in the last 20 epochs. All other experimental settings follow the previous work [32]. For consistency, we use the same MCL framework in paired settings to demonstrate its general applicability.",
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+ "text": "To validate the efficacy of our method, we comprehensively compare it with state-of-the-art approaches under both unpaired and paired settings, as shown in Tab. 1 and Tab. 2.",
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+ "text": "Comparison with unsupervised methods under unpaired settings. The experiments demonstrate that our MCL significantly outperforms existing unsupervised methods under unpaired settings at various ratios. These con",
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+ "text": "siderable gains benefit from the insightful design of our method for USL-VI-ReID. There are two major advantages of our method: 1) We use a mapping-based solution to effectively address the lack of cross-modality correlations in unpaired scenarios by synthesizing fake paired data while preserving discriminative identity. 2) Our collaborative learning strategy achieves a dual-level alignment paradigm for cluster- and instance-level optimization.",
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+ "text": "Comparison with supervised methods under paired settings. We compare our method with several recent supervised visible-infrared ReID approaches under paired settings. Notably, although supervised methods rely on accurate manual annotations, our method achieves competitive performance of certain baselines (e.g. DFLN-ViT [48]).",
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+ "text": "Comparison with unsupervised methods under paired settings. We also evaluate our method against advanced USL-VI-ReID approaches under paired settings. Among these, H2H [16], OTLA [24] and DOTLA [4] need an extra annotated visible dataset. In Tab. 2, our method is significantly better than all existing USL-VI-ReID methods, demonstrating the effectiveness under paired settings.",
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+ "text": "4.4. Ablation Study",
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+ "text": "The performance boost of the MCL framework in the task of USL-VI-ReID under unpaired settings mainly comes from the proposed CFM module and the collaborative learning strategy with Static Learning (SL) and Dynamic Learning (DL). We validate the effectiveness of each component by conducting ablation studies on the SYSU-MM01 and RegDB under unpaired settings where $\\alpha$ is representatively set to 0.5, which incorporate a balance of paired and unpaired scenarios. Results are shown in Tab. 3.",
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+ "text": "Baseline in index 1 denotes that we directly train the model on the unpaired SYSU-MM01 and RegDB tasks with ADCA [32] method, using the feature extractor from TransReID [10] as the backbone. Although ADCA has a promising performance under unpaired settings, it is observed that the baseline only achieves $47.29\\%$ mAP on SYSU-MM01 (all search) and $48.6\\%$ mAP on RegDB (visible to infrared). Therefore, directly using ADCA method can hardly tackle the problem of unpaired settings for the USL-VI-ReID task. Effectiveness of SL. Index 2 means the static learning strategy with CFM module. Compared with baseline, SL improves the performance of $5.19\\%$ and $5.92\\%$ mAP on the unpaired SYSU-MM01 (all search) and RegDB (visible to infrared). The main gain is achieved by the design of the multi-memory banks in both the original and pseudoidentity space, which additionally cluster all mapped features for contrastive learning, allowing the model to capture certain modality-invariant features in scenarios with cross-modal identity mismatches.",
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+ "text": "Effectiveness of DL. Index 3 represents the dynamic learning strategy with CFM module. Compared with baseline, the significant improvements demonstrate the effectiveness of DL. The improvements are $3.38\\%$ and $2.24\\%$ mAP on the unpaired SYSU-MM01 (all search) and RegDB (visible to infrared). DL can further use fake cross-modality features and pull them towards their corresponding actual samples, facilitating instance-level cross-modality learning.",
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+ "text": "Effectiveness of Collaborative Learning. Index 4 denotes the collaborative learning strategy with SL and DL. In comparison, the collaborative learning brings consistent improvement in all settings, which shows the effectiveness of static-dynamic collaborative learning in mitigating intra-modality discrepancies while enhancing cross-modality correspondence alignment.",
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+ "text": "Hyper-parameter Analysis for $\\eta$ . We explore the influence of hyper-parameter $\\eta$ in Eq. 19, as presented in the supplementary materials. When $\\eta = 1.0$ , the method achieves a balance in static and dynamic learning.",
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+ "text": "Visualization. In Fig. 3, it shows the t-SNE [22] visualization of 20 randomly selected identities from the unpaired SYSU-MM01 dataset with $\\alpha = 0.5$ . Compared to the",
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+ "Figure 3. The t-SNE (top) and similarity distribution (bottom) visualizations for randomly sampled identities. Colors represent identities; circles and triangles denote visible and infrared samples, respectively. The similarity distribution represents similarity scores of cross-modality positive and negative pairs, where larger separation indicates better identity discrimination."
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+ "text": "baseline, MCL brings infrared and visible positive samples closer together and effectively increases the separation from negative pairs, thus improving performance under unpaired settings. However, some same-identity samples remain dispersed, indicating challenges for unpaired USL-VI-ReID.",
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+ "text": "5. CONCLUSION",
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+ "text": "This paper addresses unsupervised visible-infrared person re-identification (USL-VI-ReID) under unpaired settings, which is a prevalent yet underexplored challenge in real-world surveillance systems. While existing USL-VI-ReID methods often overlook the critical issue of aligning cross-modality relations without paired data, we propose the Mapping and Collaborative Learning (MCL) framework to bridge this gap. We integrates a cross-modality feature mapping module to establish inter-modal correlations and a static-dynamic collaborative learning strategy to refine discriminative representations in unpaired scenarios. Extensive experiments on SYSU-MM01 and RegDB demonstrate that MCL not only outperforms state-of-the-art unsupervised methods under unpaired settings but also achieves competitive performance in paired scenarios, pushing USL-VI-ReID to real-world deployment.",
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+ "text": "Limitations and Future Work. While effective, MCL still faces challenges in extremely unpaired settings and requires relatively high training cost. Future work will focus on improving robustness in such scenarios and designing lightweight variants for efficient deployment.",
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+ "text": "This work is partially supported by National Natural Science Foundation of China under Grants (62176188, 62225113, 623B2080), the Innovative Research Group Project of Hubei Province under Grants (2024AFA017), the Major Project of Science and Technology Innovation of Hubei Province (2024BCA003), Postdoctoral Fellowship Program of China Postdoctoral Science Foundation (GZC20241268, 2024M762479), Hubei Postdoctoral Talent Introduction Program (2024HBBHJD070) and Hubei Provincial Natural Science Foundation of China (2025AFB219). The numerical calculations in this paper had been supported by the super-computing system in the Supercomputing Center of Wuhan University.",
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+++ b/2025/Unsupervised Visible-Infrared Person Re-identification under Unpaired Settings/8bad0627-426a-4c79-849d-e7d54bb417e5_model.json
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+ "type": "header",
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+ "content": "CVF"
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+ "type": "header",
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+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "content": "Unsupervised Visible-Infrared Person Re-identification under Unpaired Settings"
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+ "type": "text",
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+ "content": "Haoyu Yao\\(^{1,2,3,4*}\\) Bin Yang\\(^{1,2,3*}\\) Wenke Huang\\(^{1,2,3}\\) Bo Du\\(^{1,2,3}\\) Mang Ye\\(^{1,2,3\\dagger}\\)"
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+ "content": "\\(^{1}\\) School of Computer Science, Wuhan University, China"
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+ "type": "text",
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+ "content": "\\(^{2}\\) National Engineering Research Center for Multimedia Software, Wuhan University, China \n\\(^{3}\\) Hubei Key Laboratory of Multimedia and Network Communication Engineering, Wuhan University, China \n\\(^{4}\\) School of Remote Sensing and Information Engineering, Wuhan University, China"
+ },
+ {
+ "type": "text",
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+ "content": "https://github.com/USL-VI-ReID/MCL"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "Abstract"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Unsupervised visible-infrared person re-identification (USL-VI-ReID) aims to train a cross-modality retrieval model without labels, reducing the reliance on expensive cross-modality manual annotation. However, existing USL-VI-ReID methods rely on artificially cross-modality paired data as implicit supervision, which is also expensive for human annotation and contrary to the setting of unsupervised tasks. In addition, this full alignment of identity across modalities is inconsistent with real-world scenarios, where unpaired settings are prevalent. To this end, we study the USL-VI-ReID task under unpaired settings, which uses cross-modality unpaired and unlabeled data for training a VI-ReID model. We propose a novel Mapping and Collaborative Learning (MCL) framework. Specifically, we first design a simple yet effective Cross-modality Feature Mapping (CFM) module to map and generate fake cross-modality positive feature pairs, constructing a cross-modal pseudo-identity space for feature alignment. Then, a Static-Dynamic Collaborative (SDC) learning strategy is proposed to align cross-modality correspondences through a collaborative approach, eliminating inter-modality discrepancies across different aspects i.e., cluster-level and instance-level, in scenarios with cross-modal identity mismatches. Extensive experiments on the conducted SYSU-MM01 and RegDB benchmarks under paired and unpaired settings demonstrate that our proposed MCL significantly outperforms existing unsupervised methods, facilitating USL-VI-ReID to real-world deployment."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "1. Introduction"
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+ "type": "text",
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+ "angle": 0,
+ "content": "Person re-identification (ReID) focuses on retrieving specific individuals across non-overlapping cameras [1, 50]."
+ },
+ {
+ "type": "image",
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+ "type": "image_caption",
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+ "content": "Figure 1. Illustration of the motivation. Previous advanced works for USL-VI-ReID mainly focus on paired settings, which leads to the leakage of supervised information and is inconsistent with the real-world scenarios. Under the underexplored unpaired settings, the cross-modality correspondences are hard to align with unpaired and unlabeled data, which poses a great challenge of how to establish the relation of unpaired samples among different modalities for learning modality-invariant knowledge."
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+ {
+ "type": "text",
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+ "content": "Traditional ReID methods primarily rely on daytime visible-light images, which struggle to extract discriminative features in low-light environments, limiting single-modality ReID deployment in real-world surveillance [13, 26]. To address this problem, the cross-modality visible-infrared person re-identification (VI-ReID) is proposed to identify the same person across a set of visible and infrared images [42]. While supervised VI-ReID methods use plenty of costly cross-modality (visible-infrared) identity labels to learn modality-invariant feature representations [15, 19, 30, 38, 41], the unsupervised VI-ReID (USL-VI-ReID) methods eliminate the need for annotation by generating pseudo-labels [20, 31, 32], which reduce the cost of"
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+ "type": "page_footnote",
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+ "angle": 0,
+ "content": "*Equal contribution."
+ },
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+ "content": "† Corresponding author."
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+ "angle": 0,
+ "content": "11916"
+ }
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+ [
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "expensive cross-modality annotations."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "However, existing USL-VI-ReID methods [2-4, 16, 31, 33, 37] operate under the unrealistic assumption of precisely paired cross-modality data, which contradicts real-world scenarios where unpaired settings are more common, as shown in Fig. 1. For instance, a commuter captured by daytime visible cameras may never appear in nighttime infrared surveillance due to social behaviors or hidden activity patterns [14]. More critically, this unrealistic assumption introduces supervised information leakage, violating the unsupervised paradigm and necessitating extensive, costly annotations. To bridge this gap, we introduce a new task: unsupervised visible-infrared person re-identification under unpaired settings, which seeks to train a cross-modality ReID model using unpaired and unlabeled data. When applied to unpaired scenarios, existing USL-VI-ReID methods face two fundamental challenges, as shown in Fig. 1. First, pseudo-label generation depends on cross-modality correspondences, which are absent in unpaired settings, leading to erroneous label assignments. Second, the lack of identity pairs across modalities amplifies the modality gap, hindering effective feature alignment and obstructing the learning of modality-invariant representations."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To overcome these challenges, we construct the first public visible-infrared pedestrian benchmarks under unpaired settings. Based on these benchmarks, we propose a novel Mapping and Collaborative Learning (MCL) framework that establishes cross-modality associations without paired supervision. To handle the absence of paired data, the Cross-modality Feature Mapping (CFM) module is designed to supplement the missing cross-modality paired data while preserving identity consistency. Then, a Static-Dynamic Collaborative (SDC) learning strategy is proposed to achieve unprecedented capability in bridging modality gaps through dual-level alignment. The static learning could establish holistic identity prototypes that capture comprehensive identity characteristics at cluster level, ensuring robust alignment under severe modality mismatches and improving the reliability of cross-modality correspondence. For the dynamic learning strategy, it can reduce the discrepancy between the two modalities by pulling fake samples towards their corresponding actual ones, thereby narrowing the modality gap through instance-level intermodality alignment. Joint learning of the static and dynamic method forms a collaborative learning strategy, achieving better learning of discriminative and modality-invariant representations for cross-modality retrieval."
+ },
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+ "type": "text",
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+ "content": "The main contributions can be summarized as follows:"
+ },
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+ "type": "text",
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+ "content": "- We formally characterize the prevalent unpaired settings encountered in real-world scenarios and introduce the first public visible-infrared pedestrian benchmarks under such conditions. To our knowledge, this work marks the inaugural exploration of unsupervised scenarios featuring"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "cross-modal identity mismatches."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "- We propose a novel Mapping and Collaborative Learning (MCL) framework to address the problem of lacking cross-modality paired and labeled data under unpaired settings, establishing a kind of implicit cross-modality associations without paired supervision for learning modality-invariant representations."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We introduce a straightforward yet effective Cross-modality Feature Mapping (CFM) module that synthesizes positive feature pairs across modalities to achieve robust alignment. Building upon these synthesized pairs, a novel Static-Dynamic Collaborative (SDC) learning strategy is designed to mitigate cross-modality discrepancies at both the cluster and instance levels by leveraging complementary static and dynamic optimization."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- Extensive experiments on two benchmark datasets demonstrate that the proposed framework surpasses existing state-of-the-art USL-VI-ReID methods in unpaired settings, while maintaining competitive performance under paired scenarios."
+ },
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+ "type": "title",
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+ "content": "2. RELATED WORK"
+ },
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+ "type": "title",
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+ "angle": 0,
+ "content": "2.1. Supervised Visible-Infrared Person ReID"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Supervised visible-infrared person re-identification (VI-ReID) has received considerable attention for its applicability in 24-hour surveillance systems. A key challenge is to mitigate the significant intra-class discrepancies between the visible and infrared modalities [29]. Current approaches bridging this cross-modality gap can fall into two categories: image-level and feature-level matching. Image-level methods [25, 36] focus on the generation of cross-modal images to extract modality-invariant features. In contrast, feature-level alignment approaches [9, 17, 18, 28, 35, 40] impose constraints to embed heterogeneous images into a shared feature space. However, these methods rely heavily on extensive cross-modality annotation, which is expensive and time-consuming, making supervised VI-ReID less scalable in real-world deployments."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "2.2. Unsupervised Visible-Infrared Person ReID"
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "Unsupervised visible-infrared person re-identification (USL-VI-ReID) faces two key challenges. First, the significant modality gap between visible and infrared data amplifies intra-class variation, making it difficult to consistently generate cross-modality pseudo-labels. Second, the lack of annotated cross-modality identities prevents the learning of modality-invariant representations. Previous work [16, 23, 24, 32, 34, 43, 51] are mainly based on pseudo labels, which establish a bridge with the supervised method. H2H [16] first pioneers a two-stage learning framework, and OTLA [24] introduces an optimal transport strategy for further pseudo-label assignment."
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+ "type": "page_number",
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+ "content": "11917"
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+ "content": "However, both methods rely on external RGB datasets for pre-training, while OTLA also assumes uniform infrared-to-visible label distributions, which is an impractical constraint for real-world scalability. Yang et al. [32] explore cluster-level relationships through cross-modality memory aggregation, but fail to address identity mismatch scenarios. Critically, existing approaches require full cross-modality identity alignment during training, rendering them inapplicable to unpaired data settings."
+ },
+ {
+ "type": "title",
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+ "content": "3. Methodology"
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+ "angle": 0,
+ "content": "3.1. Preliminary"
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+ "type": "text",
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+ "content": "We propose a Mapping and Collaborative Learnin (MCL) framework for USL-VI-ReID under unpaired settings, as shown in Fig. 2. Our MCL has two components including Cross-modality Feature Mapping (CFM) module and Static-Dynamic Collaborative (SDC) learning strategy. In this paper, we follow Augmented Dual-Contrastive Aggregation (ADCA) [32] to establish our baseline, where a dualpath contrastive learning framework with two modality-specific memories to learn intra-modality representations."
+ },
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+ "content": "To facilitate the description of our method, we first introduce the notations used in this paper. Let \\( \\mathbf{X}_m = \\{\\pmb{x}_m^1, \\pmb{x}_m^2, \\dots, \\pmb{x}_m^{N_m}\\} \\) denote the unlabeled infrared/visible images with \\( N_m \\) instances, where \\( m \\in \\{i, v\\} \\) denotes the infrared and visible modality, respectively. \\( \\mathbf{U}_m = \\{\\pmb{u}_m^1, \\pmb{u}_m^2, \\dots, \\pmb{u}_m^{N_m}\\} \\) represents the corresponding features extracted by the modality-specific feature extractor \\( f_m^\\theta \\cdot \\pmb{q}_m \\) is the query instance feature extracted by \\( f_m^\\theta \\cdot \\{\\overline{y}_m^k\\}_{k=1}^{N_m} \\) represents the ground-truth labels of different modalities. In this work, we study the under-explored unpaired settings of USL-VI-ReID, where there are unpaired cross-modality data in the training set, i.e., there exist \\( k, l \\) that satisfy \\( \\overline{y}_i^k \\neq \\overline{y}_v^l \\). In comparison, existing USL-VI-ReID methods are under the traditional label settings where a large number of cross-modality positive pairs are captured in the training data, i.e., \\( \\overline{y}_i^k = \\overline{y}_v^l \\) for all \\( k, l \\)."
+ },
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+ "content": "3.2. Cross-modality Feature Mapping"
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+ "content": "In USL-VI-ReID, the feature extractor \\( f_{m}^{\\theta} \\) is designed to extract discriminative representation \\( \\pmb{u}_{m}^{k} = f_{m}^{\\theta}(\\pmb{x}_{m}^{k}) \\) for image \\( \\pmb{x}_{m}^{k} \\) to match, as described by:"
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+ {
+ "type": "equation",
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+ "angle": 0,
+ "content": "\\[\nD \\left(\\boldsymbol {u} _ {m _ {a}} ^ {a}, \\boldsymbol {u} _ {m _ {p}} ^ {p}\\right) < D \\left(\\boldsymbol {u} _ {m _ {a}} ^ {a}, \\boldsymbol {u} _ {m _ {n}} ^ {n}\\right), \\tag {1}\n\\]"
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+ "content": "where \\(D\\) denotes a distance function, and \\(\\pmb{u}_{m_a}^a\\), \\(\\pmb{u}_{m_p}^p\\), and \\(\\pmb{u}_{m_n}^n\\) represent the anchor, positive, and negative features extracted from modalities \\(m_{a}\\), \\(m_{p}\\), and \\(m_{n}\\), respectively. The goal is to ensure that the anchor is closer to the positive than to the negative in the feature space. By reducing the distance between cross-modality positive pairs (i.e., \\(\\pmb{u}_{m_a}^a\\) and \\(\\pmb{u}_{m_p}^p\\) with \\(m_{a} \\neq m_{p}\\)), the discrepancy can be eliminated across modalities, which facilitates the learning of discriminative features."
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+ "content": "However, in unpaired settings, the lack of cross-modality positive pairs in the training data poses a significant challenge. Given an anchor feature \\(\\mathbf{u}_{m_a}^a\\), it is difficult to find a corresponding positive sample \\(\\mathbf{u}_{m_p}^p\\) from a different modality, which hinders the ability to model intra-class variations across modalities. Therefore, establishing the relation between unpaired cross-modal data is paramount."
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+ "content": "To handle this situation, we substitute the unavailable actual cross-modality positive pair \\((\\pmb{u}_{m_a}^a,\\pmb{u}_{m_p}^p)\\) with a synthetic or fake positive pair \\((\\pmb{u}_{m_a}^a,\\hat{\\pmb{u}}_{m_p}^p)\\). The fake feature \\(\\hat{\\pmb{u}}_{m_p}^p\\) is generated through a modality-aware transformation:"
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+ "content": "\\[\n\\hat {\\boldsymbol {u}} _ {m _ {p}} ^ {p} = \\operatorname {M a p p i n g} \\left(\\boldsymbol {u} _ {m _ {a}} ^ {a}, m _ {p}\\right), \\tag {2}\n\\]"
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+ "type": "text",
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+ "angle": 0,
+ "content": "where Mapping denotes a function that projects the feature \\( \\mathbf{u}_{m_a}^a \\) from its source modality \\( m_{a} \\) into the feature space of the target modality \\( m_p \\)."
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+ "type": "text",
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+ "content": "To achieve the transformation, we introduce a cross-modality feature mapping module comprising two modality-specific mappers, each of which estimates the modality-dependent moment statistics \\(\\{\\pmb{\\mu}_m,\\pmb{\\sigma}_m^2\\}\\) of feature distributions. For a given set of features from modality \\(m\\), the associated mapper derives its mean and variance by:"
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+ "content": "\\[\n\\boldsymbol {\\mu} _ {m} = \\frac {1}{N _ {m}} \\sum_ {k = 1} ^ {N _ {m}} \\boldsymbol {u} _ {m} ^ {k}, \\quad \\sigma_ {m} ^ {2} = \\frac {1}{N _ {m}} \\sum_ {k = 1} ^ {N _ {m}} \\left(\\boldsymbol {u} _ {m} ^ {k} - \\boldsymbol {\\mu} _ {m}\\right) ^ {2}, \\tag {3}\n\\]"
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+ "content": "where \\(\\pmb{\\mu}_{m}\\) and \\(\\sigma_{m}\\) are the modality-specific mean and variance, respectively."
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+ "content": "In the cross-modality feature mapping process, a feature \\( \\pmb{u}_m^k \\) of modality \\( m \\) is transformed to a fake feature in the modality-specific distribution of a different modality \\( m' \\) by:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "content": "\\[\n\\hat {\\boldsymbol {u}} _ {m ^ {\\prime}} ^ {k} = \\operatorname {M a p p i n g} \\left(\\boldsymbol {u} _ {m} ^ {k}, m ^ {\\prime}\\right) = \\gamma \\frac {\\boldsymbol {u} _ {m} ^ {k} - \\boldsymbol {\\mu} _ {m ^ {\\prime}}}{\\sqrt {\\boldsymbol {\\sigma} _ {m ^ {\\prime}} ^ {2} + \\epsilon}} - \\zeta , \\tag {4}\n\\]"
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+ "angle": 0,
+ "content": "where \\(\\gamma\\) and \\(\\zeta\\) are scaling and shifting parameters of \\(m^{\\prime}\\)-specific mapper, which are learned during training. \\(\\epsilon\\) is a small constant to ensure stability."
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+ "type": "text",
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+ "content": "The CFM module applies a cross-modality affine transformation to align source features with the target distribution by matching mean and variance. We precisely estimate the distributions of both modalities and use the transformation to map features. Since the actual feature \\( \\pmb{u}_{m}^{k} \\) and mapped feature \\( \\hat{\\pmb{u}}_{m'}^{k} \\) are encoded from the same image \\( \\pmb{x}_{m}^{k} \\), we regard they share the same identity \\( (\\hat{y}_{m'}^{k} = y_{m}^{k}) \\) and respectively construct an original modality-specific space and a cross-modal pseudo-identity space for further alignment."
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+ "content": "3.3. Static-Dynamic Collaborative Learning"
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+ "content": "The CFM module complements the missing cross-modality unpaired data by estimating modality-specific feature distributions and transforming them into different modalities."
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+ "type": "image",
+ "bbox": [
+ 0.152,
+ 0.088,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
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+ ],
+ "angle": 0,
+ "content": "Figure 2. Illustration of mapping and collaborative learning framework. The framework integrates two core components: a Cross-Modality Feature Mapping (CFM) module and a Static-Dynamic Collaborative (SDC) learning strategy. The CFM synthesizes cross-modality positive feature pairs by estimating modality-specific distributions. Concurrently, the SDC strategy addresses inter-modality discrepancies through a twofold alignment: (1) Static Learning employs multi-memory banks to derive reliable cross-modality correspondences by learning holistic representations, establishing robust cluster-level associations. (2) Dynamic Learning utilizes a cross-modality label-preserving loss (CLP) to bridge substantial modality gaps, achieving fine-grained instance-level alignment."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.587,
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+ ],
+ "angle": 0,
+ "content": "However, it does not use any features prior to and after the mapping process to align cross-modal correspondences. To associate fake cross-modality positive feature pairs and effectively eliminate inter-modality discrepancies, we propose a static-dynamic collaborative learning framework to bridge the gap between the visible and infrared modalities both at cluster-level and instance-level."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.698,
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+ ],
+ "angle": 0,
+ "content": "Static Learning. We note that the existing methods typically rely on a single memory to represent individual characteristics and establish cross-modality correspondences. However, a single memory may not capture all individual nuances in scenarios with cross-modal identity mismatches, which naturally leads to poor cross-modality correspondences. Therefore, we design a static learning method to obtain reliable cross-modality correspondences by clustering actual samples and fake cross-modality samples as multi-memory banks, jointly conducting the contrastive learning in the original modality-specific space and the cross-modal pseudo-identity space."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.11,
+ 0.886,
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+ ],
+ "angle": 0,
+ "content": "At the beginning of each training epoch, all infrared"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "and visible features \\( \\mathbf{U}_i \\) and \\( \\mathbf{U}_v \\) are firstly clustered to generate pseudo labels, where each cluster's representations \\( \\{\\phi_i^1,\\dots,\\phi_i^K\\} \\) and \\( \\{\\phi_v^1,\\dots,\\phi_v^L\\} \\) of infrared and visible features are stored in infrared and visible memory dictionaries. This process can be written as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.542,
+ 0.669,
+ 0.907,
+ 0.709
+ ],
+ "angle": 0,
+ "content": "\\[\n\\phi_ {i} ^ {k} = \\frac {1}{\\left| \\mathcal {H} _ {i} ^ {k} \\right|} \\sum_ {\\boldsymbol {u} _ {i} ^ {n} \\in \\mathcal {H} _ {i} ^ {k}} \\boldsymbol {u} _ {i} ^ {n}, \\phi_ {v} ^ {l} = \\frac {1}{\\left| \\mathcal {H} _ {v} ^ {l} \\right|} \\sum_ {\\boldsymbol {u} _ {v} ^ {m} \\in \\mathcal {H} _ {v} ^ {l}} \\boldsymbol {u} _ {v} ^ {m}, \\tag {5}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.718,
+ 0.905,
+ 0.75
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathcal{H}_{i(v)}^k\\) is the \\(k\\)-th cluster set in infrared or visible modality, and \\(|\\cdot|\\) is the number of instances per cluster."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Then, these actual features \\( \\pmb{U}_i \\) and \\( \\pmb{U}_v \\) are transformed into corresponding fake cross-modality features \\( \\hat{\\pmb{U}}_v \\) and \\( \\hat{\\pmb{U}}_i \\) through CFM. While this mapping process alters the feature distributions, it preserves the original identity information. To maintain consistency in the number of clusters, DBSCAN is applied solely to the actual features for generating pseudo identity labels. Consequently, the cluster representations of the fake cross-modality features are denoted as \\( \\{\\hat{\\phi}_v^1,\\dots ,\\hat{\\phi}_v^K\\} \\) and \\( \\{\\hat{\\phi}_i^1,\\dots ,\\hat{\\phi}_i^L\\} \\), which constitute two additional memory banks in the cross-modal pseudo-"
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+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "11919"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
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+ ],
+ "angle": 0,
+ "content": "identity space. This process is formally defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.131,
+ 0.117,
+ 0.483,
+ 0.161
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\phi} _ {v} ^ {k} = \\frac {1}{\\left| \\hat {\\mathcal {H}} _ {v} ^ {k} \\right|} \\sum_ {\\hat {\\boldsymbol {u}} _ {v} ^ {n} \\in \\hat {\\mathcal {H}} _ {v} ^ {k}} \\hat {\\boldsymbol {u}} _ {v} ^ {n}, \\hat {\\phi} _ {i} ^ {l} = \\frac {1}{\\left| \\hat {\\mathcal {H}} _ {i} ^ {l} \\right|} \\sum_ {\\hat {\\boldsymbol {u}} _ {i} ^ {m} \\in \\hat {\\mathcal {H}} _ {i} ^ {l}} \\hat {\\boldsymbol {u}} _ {i} ^ {m}, \\tag {6}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.171,
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+ ],
+ "angle": 0,
+ "content": "where \\(\\hat{\\mathcal{H}}_{i(v)}^k\\) denotes the \\(k\\)-th cluster set in the mapped infrared or visible modality, and \\(|\\cdot|\\) indicates the number of instances per cluster."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "During training, we sample \\( P \\) person identities and \\( Z \\) instances for each identity from each modality training set. Then, we use a batch of infrared and visible queries to update the actual memories by a momentum updating strategy:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.177,
+ 0.292,
+ 0.483,
+ 0.314
+ ],
+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {\\phi} _ {i} ^ {k (\\delta)} \\leftarrow \\beta \\boldsymbol {\\phi} _ {i} ^ {k (\\delta - 1)} + (1 - \\beta) \\boldsymbol {q} _ {i}, \\tag {7}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.18,
+ 0.332,
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+ "angle": 0,
+ "content": "\\[\n\\boldsymbol {\\phi} _ {v} ^ {l (\\delta)} \\leftarrow \\beta \\boldsymbol {\\phi} _ {v} ^ {l (\\delta - 1)} + (1 - \\beta) \\boldsymbol {q} _ {v}, \\tag {8}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "The memories of fake cross-modality features are updated by a similar momentum strategy:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ 0.399,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\phi} _ {v} ^ {k (\\delta)} \\leftarrow \\beta \\hat {\\phi} _ {v} ^ {k (\\delta - 1)} + (1 - \\beta) \\boldsymbol {q} _ {i}, \\tag {9}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.18,
+ 0.442,
+ 0.482,
+ 0.463
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\phi} _ {i} ^ {l (\\delta)} \\leftarrow \\beta \\hat {\\phi} _ {i} ^ {l (\\delta - 1)} + (1 - \\beta) \\boldsymbol {q} _ {v}, \\tag {10}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "where \\(\\beta\\) is the momentum factor and \\(\\delta\\) is the iteration step."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.485,
+ 0.484,
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+ ],
+ "angle": 0,
+ "content": "In each iteration, the feature extractors are jointly updated by a multi ClusterNCE [7] loss, including the actual infrared loss \\(\\mathcal{L}_i\\), actual visible loss \\(\\mathcal{L}_v\\), fake infrared loss \\(\\hat{\\mathcal{L}}_i\\), and fake visible loss \\(\\hat{\\mathcal{L}}_v\\) by the following equations:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.166,
+ 0.556,
+ 0.483,
+ 0.597
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {i} = - \\log \\frac {\\exp \\left(\\boldsymbol {q} _ {i} \\cdot \\phi_ {i} ^ {+} / \\tau\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(\\boldsymbol {q} _ {i} \\cdot \\phi_ {i} ^ {k} / \\tau\\right)}, \\tag {11}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.166,
+ 0.604,
+ 0.483,
+ 0.642
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {v} = - \\log \\frac {\\exp \\left(\\boldsymbol {q} _ {v} \\cdot \\phi_ {v} ^ {+} / \\tau\\right)}{\\sum_ {l = 1} ^ {L} \\exp \\left(\\boldsymbol {q} _ {v} \\cdot \\phi_ {v} ^ {l} / \\tau\\right)}, \\tag {12}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.166,
+ 0.647,
+ 0.483,
+ 0.7
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\mathcal {L}} _ {i} = - \\log \\frac {\\exp \\left(\\boldsymbol {q} _ {v} \\cdot \\hat {\\phi} _ {i} ^ {+} / \\tau\\right)}{\\sum_ {l = 1} ^ {L} \\exp \\left(\\boldsymbol {q} _ {v} \\cdot \\hat {\\phi} _ {i} ^ {l} / \\tau\\right)}, \\tag {13}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.163,
+ 0.708,
+ 0.483,
+ 0.761
+ ],
+ "angle": 0,
+ "content": "\\[\n\\hat {\\mathcal {L}} _ {v} = - \\log \\frac {\\exp \\left(\\boldsymbol {q} _ {i} \\cdot \\hat {\\phi} _ {v} ^ {+} / \\tau\\right)}{\\sum_ {k = 1} ^ {K} \\exp \\left(\\boldsymbol {q} _ {i} \\cdot \\hat {\\phi} _ {v} ^ {k} / \\tau\\right)}, \\tag {14}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.767,
+ 0.484,
+ 0.843
+ ],
+ "angle": 0,
+ "content": "where \\(\\phi_i^+\\) and \\(\\phi_v^+\\) are the positive representation vector of the actual infrared and visible cluster, respectively, corresponding to the pseudo label of the query. \\(\\hat{\\phi}_i^+\\) and \\(\\hat{\\phi}_v^+\\) are the positive feature vector of the fake infrared and visible cluster. The \\(\\tau\\) is a temperature hyper-parameter."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.843,
+ 0.484,
+ 0.873
+ ],
+ "angle": 0,
+ "content": "Certainly, four types of ClusterNCE [5] loss are designed to learn discriminative representation:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.192,
+ 0.884,
+ 0.483,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {S L}} = \\mathcal {L} _ {i} + \\mathcal {L} _ {v} + \\hat {\\mathcal {L}} _ {i} + \\hat {\\mathcal {L}} _ {v}. \\tag {15}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.318
+ ],
+ "angle": 0,
+ "content": "Dynamic Learning. The generated cross-modality samples are useful in bridging significant inter-modality discrepancies by including the abundant information of missing identities. However, it is expected that these samples will not change significantly, as they share the same identity with the original samples, which should be aligned during the learning. Inspired by ISE [45], we further propose a Cross-modality Label Preserving (CLP) loss to enforce the fake cross-modality features to be close to their corresponding actual features, which facilitates the learning of cross-modality representations at the instance level. During training, the CLP loss enforces identity consistency between the actual and mapped features, allowing CFM to transfer cross-modal knowledge and capture the complex, non-linear modality discrepancies."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.318,
+ 0.905,
+ 0.349
+ ],
+ "angle": 0,
+ "content": "Certainly, two types of CLP loss function are introduced in the dynamic learning method:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.536,
+ 0.367,
+ 0.905,
+ 0.406
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {C L P}} ^ {i} = - \\log \\frac {\\exp \\left(\\operatorname {s i m} \\left(\\boldsymbol {u} _ {i} \\cdot \\hat {\\boldsymbol {u}} _ {v} ^ {+}\\right) / \\tau^ {\\prime}\\right)}{\\sum_ {c = 1} ^ {C _ {i}} \\exp \\left(\\operatorname {s i m} \\left(\\boldsymbol {u} _ {i} \\cdot \\hat {\\boldsymbol {u}} _ {v} ^ {c -}\\right) / \\tau^ {\\prime}\\right)}, \\tag {16}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.535,
+ 0.42,
+ 0.905,
+ 0.458
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {C L P}} ^ {v} = - \\log \\frac {\\exp \\left(\\operatorname {s i m} \\left(\\boldsymbol {u} _ {v} \\cdot \\hat {\\boldsymbol {u}} _ {i} ^ {+}\\right) / \\tau^ {\\prime}\\right)}{\\sum_ {c = 1} ^ {C _ {v}} \\exp \\left(\\operatorname {s i m} \\left(\\boldsymbol {u} _ {v} \\cdot \\hat {\\boldsymbol {u}} _ {i} ^ {c -}\\right) / \\tau^ {\\prime}\\right)}, \\tag {17}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.462,
+ 0.906,
+ 0.568
+ ],
+ "angle": 0,
+ "content": "where \\( C_i \\) and \\( C_v \\) are the cluster number of a mini-batch in infrared and visible modality, respectively. \\( \\sin(\\cdot) \\) denotes the cosine similarity. \\( \\hat{\\pmb{u}}_v^+ \\) is the hardest positive fake visible sample for a given infrared feature \\( \\pmb{u}_i \\), and \\( \\hat{\\pmb{u}}_v^{c-} \\) is the hardest negative one in the \\( c \\)-th fake visible cluster of a minibatch. \\( \\hat{\\pmb{u}}_i^+ \\) and \\( \\hat{\\pmb{u}}_i^{c-} \\) are defined similarly to above. \\( \\tau' \\) is a temperature hyper-parameter."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.568,
+ 0.906,
+ 0.613
+ ],
+ "angle": 0,
+ "content": "Consequently, the two cross-modality label preserving loss functions are combined in the dynamic learning method to learn distinctive representations:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.631,
+ 0.621,
+ 0.905,
+ 0.639
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {D L}} = \\mathcal {L} _ {\\mathrm {C L P}} ^ {i} + \\mathcal {L} _ {\\mathrm {C L P}} ^ {v}. \\tag {18}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.645,
+ 0.906,
+ 0.736
+ ],
+ "angle": 0,
+ "content": "Collaborative Learning. The cluster-level static learning method and instance-level dynamic learning method jointly forms the static-dynamic collaborative learning strategy, which aims to achieve better learning of discriminative and modality-invariant representations in the absence of cross-modality identity pairs."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.735,
+ 0.905,
+ 0.766
+ ],
+ "angle": 0,
+ "content": "The overall loss for training the model is defined by the following equation:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.625,
+ 0.774,
+ 0.905,
+ 0.79
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {o v e r a l l}} = \\mathcal {L} _ {\\mathrm {S L}} + \\eta \\mathcal {L} _ {\\mathrm {D L}}, \\tag {19}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
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+ 0.812
+ ],
+ "angle": 0,
+ "content": "where \\(\\eta\\) is the loss weight, balancing two loss functions."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4. EXPERIMENTS"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.1. Datasets and Evaluation Protocol"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Paired Datasets. To validate the proposed framework under paired settings, we conduct comprehensive evaluations"
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+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "11920"
+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
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+ 0.889,
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+ "angle": 0,
+ "content": " | | | SYSU-MM01 (unpaired settings) | RegDB (unpaired settings) |
| All Search | Indoor Search | Visible to Infrared | Infrared to Visible |
| α value | Methods | Venue | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| 0.25 | ADCA [32] | MM-22 | 41.80 | 37.54 | 22.04 | 47.00 | 56.24 | 51.79 | 50.82 | 43.72 | 42.63 | 64.22 | 55.90 | 44.29 |
| OTPA [47] | arXiv-24 | 49.15 | 44.75 | 30.62 | 51.70 | 60.82 | 57.23 | 51.37 | 50.30 | 44.60 | 66.27 | 65.82 | 64.97 |
| MMM [20] | ECCV-24 | 54.68 | 47.35 | 35.42 | 55.19 | 63.76 | 61.21 | 62.27 | 55.09 | 44.34 | 76.69 | 69.93 | 66.44 |
| PCAL[37] | TIFS-25 | 48.84 | 41.30 | 26.05 | 50.48 | 62.63 | 59.72 | 59.33 | 56.26 | 45.73 | 77.18 | 75.24 | 63.83 |
| N-ULC [21] | AAAI-25 | 53.70 | 49.69 | 33.56 | 57.39 | 65.00 | 60.64 | 60.76 | 56.82 | 42.91 | 79.35 | 76.06 | 60.40 |
| MCL (Ours) | - | 58.57 | 57.74 | 45.45 | 65.72 | 71.84 | 68.30 | 65.97 | 63.53 | 55.84 | 84.31 | 78.67 | 67.28 |
| 0.5 | ADCA [32] | MM-22 | 34.34 | 32.21 | 18.76 | 36.59 | 47.07 | 43.23 | 40.28 | 32.60 | 34.93 | 52.94 | 47.48 | 37.05 |
| OTPA [47] | arXiv-24 | 48.80 | 45.64 | 31.01 | 49.19 | 58.74 | 54.83 | 40.58 | 41.52 | 32.44 | 59.26 | 58.68 | 57.13 |
| MMM [20] | ECCV-24 | 44.14 | 42.94 | 30.71 | 54.25 | 60.17 | 52.49 | 52.90 | 43.91 | 36.51 | 63.91 | 58.17 | 58.47 |
| PCAL[37] | TIFS-25 | 46.24 | 37.62 | 22.03 | 45.39 | 52.73 | 46.42 | 46.48 | 47.88 | 36.05 | 64.21 | 66.30 | 50.41 |
| N-ULC [21] | AAAI-25 | 49.36 | 45.12 | 29.17 | 51.59 | 60.24 | 55.89 | 50.24 | 45.96 | 34.61 | 70.31 | 62.84 | 54.74 |
| MCL (Ours) | - | 54.29 | 53.98 | 42.64 | 61.71 | 68.45 | 64.40 | 60.78 | 59.69 | 52.91 | 80.36 | 73.02 | 64.25 |
| 0.75 | ADCA [32] | MM-22 | 32.66 | 30.61 | 17.98 | 37.02 | 47.59 | 43.79 | 35.80 | 28.71 | 27.96 | 47.28 | 43.92 | 34.70 |
| OTPA [47] | arXiv-24 | 33.65 | 30.50 | 16.94 | 45.3 | 53.32 | 50.17 | 31.48 | 35.60 | 29.52 | 51.98 | 49.25 | 47.62 |
| MMM [20] | ECCV-24 | 36.19 | 34.60 | 23.56 | 43.91 | 50.60 | 45.20 | 41.73 | 38.64 | 32.75 | 54.79 | 47.90 | 46.16 |
| PCAL[37] | TIFS-25 | 30.74 | 29.83 | 20.54 | 40.60 | 47.42 | 39.34 | 38.10 | 37.09 | 33.54 | 59.80 | 59.61 | 47.20 |
| N-ULC [21] | AAAI-25 | 42.56 | 39.44 | 27.06 | 55.03 | 63.11 | 58.80 | 43.38 | 39.27 | 30.06 | 66.72 | 57.51 | 44.38 |
| MCL (Ours) | - | 52.16 | 51.57 | 39.57 | 59.63 | 66.46 | 62.24 | 55.30 | 52.79 | 48.26 | 74.19 | 69.37 | 60.58 |
| 1.0 | ADCA [32] | MM-22 | 23.48 | 23.23 | 12.53 | 28.39 | 37.40 | 32.80 | 26.18 | 15.93 | 14.72 | 33.10 | 28.43 | 24.95 |
| OTPA [47] | arXiv-24 | 20.53 | 19.46 | 10.32 | 36.18 | 43.54 | 40.02 | 19.20 | 18.03 | 19.70 | 39.74 | 38.42 | 35.11 |
| MMM [20] | ECCV-24 | 30.81 | 27.53 | 17.92 | 36.19 | 40.60 | 38.38 | 30.98 | 27.10 | 20.03 | 40.26 | 33.54 | 30.12 |
| PCAL[37] | TIFS-25 | 28.95 | 25.31 | 18.54 | 32.10 | 38.48 | 36.20 | 28.74 | 25.90 | 18.68 | 37.56 | 29.69 | 27.24 |
| N-ULC [21] | AAAI-25 | 34.40 | 31.83 | 25.77 | 40.36 | 43.70 | 43.86 | 34.71 | 28.06 | 25.48 | 42.83 | 32.40 | 28.92 |
| MCL (Ours) | - | 45.98 | 44.95 | 32.85 | 51.53 | 59.06 | 54.54 | 43.18 | 39.29 | 36.95 | 58.37 | 49.40 | 47.21 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. The comparison with the state-of-the-art methods on SYSU-MM01 and RegDB under unpaired settings. It contains four settings, i.e., the unpaired ratio \\(\\alpha\\) ranges from 0.25 to 1.0 in increments of 0.25. Rank-1 accuracy(%) , mAP (%) and mINP (%) are reported."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "on two benchmark visible-infrared person re-identification datasets: SYSU-MM01 [29] and RegDB [41]. The SYSUMM01 dataset is a large-scale cross-modality collection of 22,257 visible images and 11,909 near-infrared images captured in indoor and outdoor environments by 4 visible cameras and 2 infrared cameras. In contrast, the RegDB dataset is a smaller and less demanding dataset with 412 different person identities, where each identity contains 10 visible and 10 infrared image pairs. This thermal-infrared dataset is collected using an aligned pair of cameras (one visible and one infrared), which has a comparatively lower environmental complexity than SYSU-MM01."
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+ "content": "Unpaired Datasets. To evaluate the effectiveness of our model in unpaired settings, experiments are conducted on the modified SYSU-MM01 and RegDB datasets. It is noted that existing datasets lack cross-modality unpaired training data, thus necessitating adjustments to the existing benchmarks. In order to systematically analyse the impact of unpaired settings, we introduce a hyper-parameter \\(\\alpha\\) that controls the proportion of unpaired identities between the visible and infrared modalities. Unlike OTPA [47], which reduces training data by dropping identities, our setup preserves the overall dataset size. Instead of adjusting the overlap ratio by selecting modality-specific subsets, we randomly replace a portion of the visible identities with external images. Specifically, the visible images of selected identities are replaced with images from three visible ReID"
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+ "content": "datasets(i.e., Market-1501 [49], MSMT17 [27] and LLCM [46]), while maintaining a roughly consistent number of images per identity before and after replacement. Details of the replacement process are provided in the supplementary materials. This design mitigates the potential effects of data reduction. The test sets and evaluation protocols remain unchanged throughout the experiments."
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+ "content": "Evaluation Protocol. On the two benchmark datasets and their original counterpart, we follow the popular protocols [39] for evaluation, where cumulative match characteristic (CMC), mean average precision (mAP), and mean inverse negative penalty (mINP) [41] are adopted. For SYSU-MM01 under paired and unpaired settings, we adopt all-search and indoor-search evaluation modes. For RegDB in paired and unpaired settings, we evaluate our method in the two test modes, including thermal to visible and visible to thermal, and we strictly follow existing methods to perform ten trials of the gallery set selection [40], and calculate the average performance."
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+ "content": "4.2. Implementation Details"
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+ "content": "MCL is implemented in the PyTorch platform. Our work is based on the Augmented Dual-Contrastive Aggregation [32] and incorporates the feature extractor from TransReID [10] as the backbone network. In each mini-batch, 16 identities are selected per modality, with each identity comprising 16 instances. We resize input images to \\(288 \\times 144\\) pixels for training. Standard data augmentation techniques,"
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+ "content": " | | | SYSU-MM01 | RegDB |
| All Search | Indoor Search | Visible to Infrared | Infrared to Visible |
| Methods | Venue | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| Supervised | AGW [41] | TPAMI-21 | 47.50 | 47.65 | 35.30 | 54.17 | 62.97 | 59.23 | 70.05 | 66.37 | 50.19 | 70.49 | 65.90 | 51.24 |
| DFLN-ViT [48] | TMM-22 | 59.84 | 57.70 | - | 62.13 | 69.03 | - | 92.10 | 82.11 | - | 91.21 | 81.62 | - |
| PartMix [12] | CVPR-23 | 77.78 | 74.62 | - | 81.52 | 84.38 | - | 85.66 | 82.27 | - | 84.93 | 82.52 | - |
| MUN [44] | ICCV-23 | 76.24 | 73.81 | - | 79.42 | 82.06 | - | 95.19 | 87.15 | - | 91.86 | 85.01 | - |
| SAAI [8] | ICCV-23 | 75.90 | 77.03 | - | 83.20 | 88.01 | - | 91.07 | 91.45 | - | 92.09 | 92.01 | - |
| YYDS [6] | arXiv-24 | 85.54 | 81.64 | - | 89.13 | 91.00 | - | - | - | - | 90.20 | 83.50 | - |
| TVI-LFM [11] | NIPS-24 | 84.90 | 81.47 | 70.85 | 89.06 | 90.78 | 88.39 | - | - | - | 91.38 | 85.92 | 72.73 |
| Unsupervised | H2H* [16] | TIP-21 | 30.15 | 29.40 | - | - | - | - | 23.81 | 18.87 | - | - | - | - |
| OTLA* [24] | ECCV-22 | 29.90 | 27.10 | - | 29.80 | 38.80 | - | 32.90 | 29.70 | - | 32.10 | 28.60 | - |
| ADCA [32] | MM-22 | 45.51 | 42.73 | 28.29 | 50.60 | 59.11 | 55.17 | 67.20 | 64.05 | 52.67 | 68.48 | 63.81 | 49.62 |
| PGM [31] | CVPR-23 | 57.27 | 51.78 | 34.96 | 56.23 | 62.74 | 58.13 | 69.48 | 65.41 | - | 69.85 | 65.17 | - |
| DOTLA* [4] | MM-23 | 50.36 | 47.36 | 32.40 | 53.47 | 61.73 | 57.35 | 85.63 | 76.71 | 61.58 | 82.91 | 74.97 | 58.60 |
| MBCCM [3] | MM-23 | 53.14 | 48.16 | 32.41 | 55.21 | 61.98 | 57.13 | 83.79 | 77.87 | 65.04 | 82.82 | 76.74 | 61.73 |
| CCLNet [2] | MM-23 | 54.03 | 50.19 | - | 56.68 | 65.12 | - | 69.94 | 65.53 | - | 70.17 | 66.66 | - |
| GUR†[33] | ICCV-23 | 60.95 | 56.99 | 41.85 | 64.22 | 69.49 | 64.81 | 73.91 | 70.23 | 8.88 | 75.00 | 69.94 | 56.21 |
| SCA-RCP [15] | TKDE-24 | 51.41 | 48.52 | 33.56 | 56.77 | 64.19 | 59.25 | 85.59 | 79.12 | - | 82.41 | 75.73 | - |
| MMM [20] | ECCV-24 | 61.60 | 57.90 | - | 64.40 | 70.40 | - | 89.70 | 80.50 | - | 85.80 | 77.00 | - |
| PCAL [37] | TIFS-25 | 54.39 | 51.95 | 38.09 | 59.69 | 66.72 | 62.44 | 86.43 | 82.51 | 72.33 | 86.21 | 81.23 | 68.71 |
| N-ULC [21] | AAAI-25 | 61.81 | 58.92 | 45.01 | 67.04 | 73.08 | 69.42 | 88.75 | 82.14 | 68.75 | 88.17 | 81.11 | 66.05 |
| MCL (Ours) | - | 62.95 | 62.71 | 50.63 | 67.81 | 74.19 | 70.82 | 89.83 | 83.12 | 72.86 | 88.64 | 82.04 | 69.12 |
"
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+ "content": "Table 2. The comparison with the state-of-the-art methods on SYSU-MM01 and RegDB under paired settings. It contains two groups, i.e., unsupervised VI-ReID methods and supervised VI-ReID methods. * means the model is pre-trained on an extra labeled visible dataset. GUR† denotes the results without camera information. Rank-1 accuracy(%) , mAP (%) and mINP (%) are reported."
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+ "content": " | Components | SYSU-MM01* (All Search) | SYSU-MM01* (Indoor Search) | RegDB* (Visible to Infrared) |
| Index | Baseline | CFM | SL | DL | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| 1 | ✓ | | | | 47.14 | 47.29 | 34.63 | 55.39 | 63.10 | 59.43 | 49.28 | 48.6 | 43.93 |
| 2 | ✓ | ✓ | ✓ | | 51.65 | 52.48 | 40.08 | 58.38 | 66.87 | 63.66 | 56.39 | 54.52 | 49.70 |
| 3 | ✓ | ✓ | | ✓ | 49.46 | 50.67 | 39.24 | 57.00 | 65.53 | 62.92 | 52.73 | 50.84 | 47.92 |
| 4 | ✓ | ✓ | ✓ | ✓ | 54.29 | 53.98 | 42.64 | 61.71 | 68.45 | 64.40 | 60.78 | 59.69 | 52.91 |
"
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+ "content": "Table 3. Ablation studies conducted on the SYSU-MM01 and RegDB datasets under unpaired settings. * refers to \\(\\alpha = 0.5\\) in both unpaired datasets. \"CFM\" denotes the cross-modality feature mapping module, while \"SL\" and \"DL\" mean the static learning method and the dynamic learning method in 3.3, respectively. Rank-1 accuracy (\\%), mAP (\\%), and mINP (\\%) are reported."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "including random cropping, random flipping and random erasing, are applied. At the beginning of each epoch, we perform the DBSCAN [7] clustering to generate pseudo labels in each modality independently. The learnable scaling and shifting parameters, \\(\\gamma\\) and \\(\\zeta\\), are initialized to 1 and 0, respectively, and the constant \\(\\epsilon\\) is set to \\(10^{-5}\\). The temperature factors \\(\\tau\\) and \\(\\tau'\\) are 0.05 and 0.6, respectively. We train the model in total of 50 epochs, in which the previous 30 epochs are used for pre-training, and CFM and SDC are executed in the last 20 epochs. All other experimental settings follow the previous work [32]. For consistency, we use the same MCL framework in paired settings to demonstrate its general applicability."
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+ "content": "4.3. Comparison with State-of-the-Arts"
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+ "content": "To validate the efficacy of our method, we comprehensively compare it with state-of-the-art approaches under both unpaired and paired settings, as shown in Tab. 1 and Tab. 2."
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+ "content": "Comparison with unsupervised methods under unpaired settings. The experiments demonstrate that our MCL significantly outperforms existing unsupervised methods under unpaired settings at various ratios. These con"
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+ "content": "siderable gains benefit from the insightful design of our method for USL-VI-ReID. There are two major advantages of our method: 1) We use a mapping-based solution to effectively address the lack of cross-modality correlations in unpaired scenarios by synthesizing fake paired data while preserving discriminative identity. 2) Our collaborative learning strategy achieves a dual-level alignment paradigm for cluster- and instance-level optimization."
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+ "angle": 0,
+ "content": "Comparison with supervised methods under paired settings. We compare our method with several recent supervised visible-infrared ReID approaches under paired settings. Notably, although supervised methods rely on accurate manual annotations, our method achieves competitive performance of certain baselines (e.g. DFLN-ViT [48])."
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+ "content": "Comparison with unsupervised methods under paired settings. We also evaluate our method against advanced USL-VI-ReID approaches under paired settings. Among these, H2H [16], OTLA [24] and DOTLA [4] need an extra annotated visible dataset. In Tab. 2, our method is significantly better than all existing USL-VI-ReID methods, demonstrating the effectiveness under paired settings."
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+ [
+ {
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+ "content": "4.4. Ablation Study"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The performance boost of the MCL framework in the task of USL-VI-ReID under unpaired settings mainly comes from the proposed CFM module and the collaborative learning strategy with Static Learning (SL) and Dynamic Learning (DL). We validate the effectiveness of each component by conducting ablation studies on the SYSU-MM01 and RegDB under unpaired settings where \\(\\alpha\\) is representatively set to 0.5, which incorporate a balance of paired and unpaired scenarios. Results are shown in Tab. 3."
+ },
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+ "content": "Baseline in index 1 denotes that we directly train the model on the unpaired SYSU-MM01 and RegDB tasks with ADCA [32] method, using the feature extractor from TransReID [10] as the backbone. Although ADCA has a promising performance under unpaired settings, it is observed that the baseline only achieves \\(47.29\\%\\) mAP on SYSU-MM01 (all search) and \\(48.6\\%\\) mAP on RegDB (visible to infrared). Therefore, directly using ADCA method can hardly tackle the problem of unpaired settings for the USL-VI-ReID task. Effectiveness of SL. Index 2 means the static learning strategy with CFM module. Compared with baseline, SL improves the performance of \\(5.19\\%\\) and \\(5.92\\%\\) mAP on the unpaired SYSU-MM01 (all search) and RegDB (visible to infrared). The main gain is achieved by the design of the multi-memory banks in both the original and pseudoidentity space, which additionally cluster all mapped features for contrastive learning, allowing the model to capture certain modality-invariant features in scenarios with cross-modal identity mismatches."
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+ "content": "Effectiveness of DL. Index 3 represents the dynamic learning strategy with CFM module. Compared with baseline, the significant improvements demonstrate the effectiveness of DL. The improvements are \\(3.38\\%\\) and \\(2.24\\%\\) mAP on the unpaired SYSU-MM01 (all search) and RegDB (visible to infrared). DL can further use fake cross-modality features and pull them towards their corresponding actual samples, facilitating instance-level cross-modality learning."
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+ "angle": 0,
+ "content": "Effectiveness of Collaborative Learning. Index 4 denotes the collaborative learning strategy with SL and DL. In comparison, the collaborative learning brings consistent improvement in all settings, which shows the effectiveness of static-dynamic collaborative learning in mitigating intra-modality discrepancies while enhancing cross-modality correspondence alignment."
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+ "content": "4.5. Further Analysis"
+ },
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+ "angle": 0,
+ "content": "Hyper-parameter Analysis for \\(\\eta\\). We explore the influence of hyper-parameter \\(\\eta\\) in Eq. 19, as presented in the supplementary materials. When \\(\\eta = 1.0\\), the method achieves a balance in static and dynamic learning."
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+ "angle": 0,
+ "content": "Visualization. In Fig. 3, it shows the t-SNE [22] visualization of 20 randomly selected identities from the unpaired SYSU-MM01 dataset with \\(\\alpha = 0.5\\). Compared to the"
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+ "angle": 0,
+ "content": "Figure 3. The t-SNE (top) and similarity distribution (bottom) visualizations for randomly sampled identities. Colors represent identities; circles and triangles denote visible and infrared samples, respectively. The similarity distribution represents similarity scores of cross-modality positive and negative pairs, where larger separation indicates better identity discrimination."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "baseline, MCL brings infrared and visible positive samples closer together and effectively increases the separation from negative pairs, thus improving performance under unpaired settings. However, some same-identity samples remain dispersed, indicating challenges for unpaired USL-VI-ReID."
+ },
+ {
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+ "content": "5. CONCLUSION"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "This paper addresses unsupervised visible-infrared person re-identification (USL-VI-ReID) under unpaired settings, which is a prevalent yet underexplored challenge in real-world surveillance systems. While existing USL-VI-ReID methods often overlook the critical issue of aligning cross-modality relations without paired data, we propose the Mapping and Collaborative Learning (MCL) framework to bridge this gap. We integrates a cross-modality feature mapping module to establish inter-modal correlations and a static-dynamic collaborative learning strategy to refine discriminative representations in unpaired scenarios. Extensive experiments on SYSU-MM01 and RegDB demonstrate that MCL not only outperforms state-of-the-art unsupervised methods under unpaired settings but also achieves competitive performance in paired scenarios, pushing USL-VI-ReID to real-world deployment."
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+ "content": "Limitations and Future Work. While effective, MCL still faces challenges in extremely unpaired settings and requires relatively high training cost. Future work will focus on improving robustness in such scenarios and designing lightweight variants for efficient deployment."
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+ "angle": 0,
+ "content": "Acknowledgments"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "This work is partially supported by National Natural Science Foundation of China under Grants (62176188, 62225113, 623B2080), the Innovative Research Group Project of Hubei Province under Grants (2024AFA017), the Major Project of Science and Technology Innovation of Hubei Province (2024BCA003), Postdoctoral Fellowship Program of China Postdoctoral Science Foundation (GZC20241268, 2024M762479), Hubei Postdoctoral Talent Introduction Program (2024HBBHJD070) and Hubei Provincial Natural Science Foundation of China (2025AFB219). The numerical calculations in this paper had been supported by the super-computing system in the Supercomputing Center of Wuhan University."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "References"
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+ {
+ "type": "ref_text",
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+ 0.1,
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+ ],
+ "angle": 0,
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+# Unsupervised Visible-Infrared Person Re-identification under Unpaired Settings
+
+Haoyu Yao $^{1,2,3,4*}$ Bin Yang $^{1,2,3*}$ Wenke Huang $^{1,2,3}$ Bo Du $^{1,2,3}$ Mang Ye $^{1,2,3\dagger}$
+
+$^{1}$ School of Computer Science, Wuhan University, China
+
+$^{2}$ National Engineering Research Center for Multimedia Software, Wuhan University, China
+ $^{3}$ Hubei Key Laboratory of Multimedia and Network Communication Engineering, Wuhan University, China
+ $^{4}$ School of Remote Sensing and Information Engineering, Wuhan University, China
+
+https://github.com/USL-VI-ReID/MCL
+
+# Abstract
+
+Unsupervised visible-infrared person re-identification (USL-VI-ReID) aims to train a cross-modality retrieval model without labels, reducing the reliance on expensive cross-modality manual annotation. However, existing USL-VI-ReID methods rely on artificially cross-modality paired data as implicit supervision, which is also expensive for human annotation and contrary to the setting of unsupervised tasks. In addition, this full alignment of identity across modalities is inconsistent with real-world scenarios, where unpaired settings are prevalent. To this end, we study the USL-VI-ReID task under unpaired settings, which uses cross-modality unpaired and unlabeled data for training a VI-ReID model. We propose a novel Mapping and Collaborative Learning (MCL) framework. Specifically, we first design a simple yet effective Cross-modality Feature Mapping (CFM) module to map and generate fake cross-modality positive feature pairs, constructing a cross-modal pseudo-identity space for feature alignment. Then, a Static-Dynamic Collaborative (SDC) learning strategy is proposed to align cross-modality correspondences through a collaborative approach, eliminating inter-modality discrepancies across different aspects i.e., cluster-level and instance-level, in scenarios with cross-modal identity mismatches. Extensive experiments on the conducted SYSU-MM01 and RegDB benchmarks under paired and unpaired settings demonstrate that our proposed MCL significantly outperforms existing unsupervised methods, facilitating USL-VI-ReID to real-world deployment.
+
+# 1. Introduction
+
+Person re-identification (ReID) focuses on retrieving specific individuals across non-overlapping cameras [1, 50].
+
+
+
+
+Figure 1. Illustration of the motivation. Previous advanced works for USL-VI-ReID mainly focus on paired settings, which leads to the leakage of supervised information and is inconsistent with the real-world scenarios. Under the underexplored unpaired settings, the cross-modality correspondences are hard to align with unpaired and unlabeled data, which poses a great challenge of how to establish the relation of unpaired samples among different modalities for learning modality-invariant knowledge.
+
+Traditional ReID methods primarily rely on daytime visible-light images, which struggle to extract discriminative features in low-light environments, limiting single-modality ReID deployment in real-world surveillance [13, 26]. To address this problem, the cross-modality visible-infrared person re-identification (VI-ReID) is proposed to identify the same person across a set of visible and infrared images [42]. While supervised VI-ReID methods use plenty of costly cross-modality (visible-infrared) identity labels to learn modality-invariant feature representations [15, 19, 30, 38, 41], the unsupervised VI-ReID (USL-VI-ReID) methods eliminate the need for annotation by generating pseudo-labels [20, 31, 32], which reduce the cost of
+
+expensive cross-modality annotations.
+
+However, existing USL-VI-ReID methods [2-4, 16, 31, 33, 37] operate under the unrealistic assumption of precisely paired cross-modality data, which contradicts real-world scenarios where unpaired settings are more common, as shown in Fig. 1. For instance, a commuter captured by daytime visible cameras may never appear in nighttime infrared surveillance due to social behaviors or hidden activity patterns [14]. More critically, this unrealistic assumption introduces supervised information leakage, violating the unsupervised paradigm and necessitating extensive, costly annotations. To bridge this gap, we introduce a new task: unsupervised visible-infrared person re-identification under unpaired settings, which seeks to train a cross-modality ReID model using unpaired and unlabeled data. When applied to unpaired scenarios, existing USL-VI-ReID methods face two fundamental challenges, as shown in Fig. 1. First, pseudo-label generation depends on cross-modality correspondences, which are absent in unpaired settings, leading to erroneous label assignments. Second, the lack of identity pairs across modalities amplifies the modality gap, hindering effective feature alignment and obstructing the learning of modality-invariant representations.
+
+To overcome these challenges, we construct the first public visible-infrared pedestrian benchmarks under unpaired settings. Based on these benchmarks, we propose a novel Mapping and Collaborative Learning (MCL) framework that establishes cross-modality associations without paired supervision. To handle the absence of paired data, the Cross-modality Feature Mapping (CFM) module is designed to supplement the missing cross-modality paired data while preserving identity consistency. Then, a Static-Dynamic Collaborative (SDC) learning strategy is proposed to achieve unprecedented capability in bridging modality gaps through dual-level alignment. The static learning could establish holistic identity prototypes that capture comprehensive identity characteristics at cluster level, ensuring robust alignment under severe modality mismatches and improving the reliability of cross-modality correspondence. For the dynamic learning strategy, it can reduce the discrepancy between the two modalities by pulling fake samples towards their corresponding actual ones, thereby narrowing the modality gap through instance-level intermodality alignment. Joint learning of the static and dynamic method forms a collaborative learning strategy, achieving better learning of discriminative and modality-invariant representations for cross-modality retrieval.
+
+The main contributions can be summarized as follows:
+
+- We formally characterize the prevalent unpaired settings encountered in real-world scenarios and introduce the first public visible-infrared pedestrian benchmarks under such conditions. To our knowledge, this work marks the inaugural exploration of unsupervised scenarios featuring
+
+cross-modal identity mismatches.
+
+- We propose a novel Mapping and Collaborative Learning (MCL) framework to address the problem of lacking cross-modality paired and labeled data under unpaired settings, establishing a kind of implicit cross-modality associations without paired supervision for learning modality-invariant representations.
+- We introduce a straightforward yet effective Cross-modality Feature Mapping (CFM) module that synthesizes positive feature pairs across modalities to achieve robust alignment. Building upon these synthesized pairs, a novel Static-Dynamic Collaborative (SDC) learning strategy is designed to mitigate cross-modality discrepancies at both the cluster and instance levels by leveraging complementary static and dynamic optimization.
+- Extensive experiments on two benchmark datasets demonstrate that the proposed framework surpasses existing state-of-the-art USL-VI-ReID methods in unpaired settings, while maintaining competitive performance under paired scenarios.
+
+# 2. RELATED WORK
+
+# 2.1. Supervised Visible-Infrared Person ReID
+
+Supervised visible-infrared person re-identification (VI-ReID) has received considerable attention for its applicability in 24-hour surveillance systems. A key challenge is to mitigate the significant intra-class discrepancies between the visible and infrared modalities [29]. Current approaches bridging this cross-modality gap can fall into two categories: image-level and feature-level matching. Image-level methods [25, 36] focus on the generation of cross-modal images to extract modality-invariant features. In contrast, feature-level alignment approaches [9, 17, 18, 28, 35, 40] impose constraints to embed heterogeneous images into a shared feature space. However, these methods rely heavily on extensive cross-modality annotation, which is expensive and time-consuming, making supervised VI-ReID less scalable in real-world deployments.
+
+# 2.2. Unsupervised Visible-Infrared Person ReID
+
+Unsupervised visible-infrared person re-identification (USL-VI-ReID) faces two key challenges. First, the significant modality gap between visible and infrared data amplifies intra-class variation, making it difficult to consistently generate cross-modality pseudo-labels. Second, the lack of annotated cross-modality identities prevents the learning of modality-invariant representations. Previous work [16, 23, 24, 32, 34, 43, 51] are mainly based on pseudo labels, which establish a bridge with the supervised method. H2H [16] first pioneers a two-stage learning framework, and OTLA [24] introduces an optimal transport strategy for further pseudo-label assignment.
+
+However, both methods rely on external RGB datasets for pre-training, while OTLA also assumes uniform infrared-to-visible label distributions, which is an impractical constraint for real-world scalability. Yang et al. [32] explore cluster-level relationships through cross-modality memory aggregation, but fail to address identity mismatch scenarios. Critically, existing approaches require full cross-modality identity alignment during training, rendering them inapplicable to unpaired data settings.
+
+# 3. Methodology
+
+# 3.1. Preliminary
+
+We propose a Mapping and Collaborative Learnin (MCL) framework for USL-VI-ReID under unpaired settings, as shown in Fig. 2. Our MCL has two components including Cross-modality Feature Mapping (CFM) module and Static-Dynamic Collaborative (SDC) learning strategy. In this paper, we follow Augmented Dual-Contrastive Aggregation (ADCA) [32] to establish our baseline, where a dualpath contrastive learning framework with two modality-specific memories to learn intra-modality representations.
+
+To facilitate the description of our method, we first introduce the notations used in this paper. Let $\mathbf{X}_m = \{\pmb{x}_m^1, \pmb{x}_m^2, \dots, \pmb{x}_m^{N_m}\}$ denote the unlabeled infrared/visible images with $N_m$ instances, where $m \in \{i, v\}$ denotes the infrared and visible modality, respectively. $\mathbf{U}_m = \{\pmb{u}_m^1, \pmb{u}_m^2, \dots, \pmb{u}_m^{N_m}\}$ represents the corresponding features extracted by the modality-specific feature extractor $f_m^\theta \cdot \pmb{q}_m$ is the query instance feature extracted by $f_m^\theta \cdot \{\overline{y}_m^k\}_{k=1}^{N_m}$ represents the ground-truth labels of different modalities. In this work, we study the under-explored unpaired settings of USL-VI-ReID, where there are unpaired cross-modality data in the training set, i.e., there exist $k, l$ that satisfy $\overline{y}_i^k \neq \overline{y}_v^l$ . In comparison, existing USL-VI-ReID methods are under the traditional label settings where a large number of cross-modality positive pairs are captured in the training data, i.e., $\overline{y}_i^k = \overline{y}_v^l$ for all $k, l$ .
+
+# 3.2. Cross-modality Feature Mapping
+
+In USL-VI-ReID, the feature extractor $f_{m}^{\theta}$ is designed to extract discriminative representation $\pmb{u}_{m}^{k} = f_{m}^{\theta}(\pmb{x}_{m}^{k})$ for image $\pmb{x}_{m}^{k}$ to match, as described by:
+
+$$
+D \left(\boldsymbol {u} _ {m _ {a}} ^ {a}, \boldsymbol {u} _ {m _ {p}} ^ {p}\right) < D \left(\boldsymbol {u} _ {m _ {a}} ^ {a}, \boldsymbol {u} _ {m _ {n}} ^ {n}\right), \tag {1}
+$$
+
+where $D$ denotes a distance function, and $\pmb{u}_{m_a}^a$ , $\pmb{u}_{m_p}^p$ , and $\pmb{u}_{m_n}^n$ represent the anchor, positive, and negative features extracted from modalities $m_{a}$ , $m_{p}$ , and $m_{n}$ , respectively. The goal is to ensure that the anchor is closer to the positive than to the negative in the feature space. By reducing the distance between cross-modality positive pairs (i.e., $\pmb{u}_{m_a}^a$ and $\pmb{u}_{m_p}^p$ with $m_{a} \neq m_{p}$ ), the discrepancy can be eliminated across modalities, which facilitates the learning of discriminative features.
+
+However, in unpaired settings, the lack of cross-modality positive pairs in the training data poses a significant challenge. Given an anchor feature $\mathbf{u}_{m_a}^a$ , it is difficult to find a corresponding positive sample $\mathbf{u}_{m_p}^p$ from a different modality, which hinders the ability to model intra-class variations across modalities. Therefore, establishing the relation between unpaired cross-modal data is paramount.
+
+To handle this situation, we substitute the unavailable actual cross-modality positive pair $(\pmb{u}_{m_a}^a,\pmb{u}_{m_p}^p)$ with a synthetic or fake positive pair $(\pmb{u}_{m_a}^a,\hat{\pmb{u}}_{m_p}^p)$ . The fake feature $\hat{\pmb{u}}_{m_p}^p$ is generated through a modality-aware transformation:
+
+$$
+\hat {\boldsymbol {u}} _ {m _ {p}} ^ {p} = \operatorname {M a p p i n g} \left(\boldsymbol {u} _ {m _ {a}} ^ {a}, m _ {p}\right), \tag {2}
+$$
+
+where Mapping denotes a function that projects the feature $\mathbf{u}_{m_a}^a$ from its source modality $m_{a}$ into the feature space of the target modality $m_p$ .
+
+To achieve the transformation, we introduce a cross-modality feature mapping module comprising two modality-specific mappers, each of which estimates the modality-dependent moment statistics $\{\pmb{\mu}_m,\pmb{\sigma}_m^2\}$ of feature distributions. For a given set of features from modality $m$ , the associated mapper derives its mean and variance by:
+
+$$
+\boldsymbol {\mu} _ {m} = \frac {1}{N _ {m}} \sum_ {k = 1} ^ {N _ {m}} \boldsymbol {u} _ {m} ^ {k}, \quad \sigma_ {m} ^ {2} = \frac {1}{N _ {m}} \sum_ {k = 1} ^ {N _ {m}} \left(\boldsymbol {u} _ {m} ^ {k} - \boldsymbol {\mu} _ {m}\right) ^ {2}, \tag {3}
+$$
+
+where $\pmb{\mu}_{m}$ and $\sigma_{m}$ are the modality-specific mean and variance, respectively.
+
+In the cross-modality feature mapping process, a feature $\pmb{u}_m^k$ of modality $m$ is transformed to a fake feature in the modality-specific distribution of a different modality $m'$ by:
+
+$$
+\hat {\boldsymbol {u}} _ {m ^ {\prime}} ^ {k} = \operatorname {M a p p i n g} \left(\boldsymbol {u} _ {m} ^ {k}, m ^ {\prime}\right) = \gamma \frac {\boldsymbol {u} _ {m} ^ {k} - \boldsymbol {\mu} _ {m ^ {\prime}}}{\sqrt {\boldsymbol {\sigma} _ {m ^ {\prime}} ^ {2} + \epsilon}} - \zeta , \tag {4}
+$$
+
+where $\gamma$ and $\zeta$ are scaling and shifting parameters of $m^{\prime}$ -specific mapper, which are learned during training. $\epsilon$ is a small constant to ensure stability.
+
+The CFM module applies a cross-modality affine transformation to align source features with the target distribution by matching mean and variance. We precisely estimate the distributions of both modalities and use the transformation to map features. Since the actual feature $\pmb{u}_{m}^{k}$ and mapped feature $\hat{\pmb{u}}_{m'}^{k}$ are encoded from the same image $\pmb{x}_{m}^{k}$ , we regard they share the same identity $(\hat{y}_{m'}^{k} = y_{m}^{k})$ and respectively construct an original modality-specific space and a cross-modal pseudo-identity space for further alignment.
+
+# 3.3. Static-Dynamic Collaborative Learning
+
+The CFM module complements the missing cross-modality unpaired data by estimating modality-specific feature distributions and transforming them into different modalities.
+
+
+Figure 2. Illustration of mapping and collaborative learning framework. The framework integrates two core components: a Cross-Modality Feature Mapping (CFM) module and a Static-Dynamic Collaborative (SDC) learning strategy. The CFM synthesizes cross-modality positive feature pairs by estimating modality-specific distributions. Concurrently, the SDC strategy addresses inter-modality discrepancies through a twofold alignment: (1) Static Learning employs multi-memory banks to derive reliable cross-modality correspondences by learning holistic representations, establishing robust cluster-level associations. (2) Dynamic Learning utilizes a cross-modality label-preserving loss (CLP) to bridge substantial modality gaps, achieving fine-grained instance-level alignment.
+
+However, it does not use any features prior to and after the mapping process to align cross-modal correspondences. To associate fake cross-modality positive feature pairs and effectively eliminate inter-modality discrepancies, we propose a static-dynamic collaborative learning framework to bridge the gap between the visible and infrared modalities both at cluster-level and instance-level.
+
+Static Learning. We note that the existing methods typically rely on a single memory to represent individual characteristics and establish cross-modality correspondences. However, a single memory may not capture all individual nuances in scenarios with cross-modal identity mismatches, which naturally leads to poor cross-modality correspondences. Therefore, we design a static learning method to obtain reliable cross-modality correspondences by clustering actual samples and fake cross-modality samples as multi-memory banks, jointly conducting the contrastive learning in the original modality-specific space and the cross-modal pseudo-identity space.
+
+At the beginning of each training epoch, all infrared
+
+and visible features $\mathbf{U}_i$ and $\mathbf{U}_v$ are firstly clustered to generate pseudo labels, where each cluster's representations $\{\phi_i^1,\dots,\phi_i^K\}$ and $\{\phi_v^1,\dots,\phi_v^L\}$ of infrared and visible features are stored in infrared and visible memory dictionaries. This process can be written as:
+
+$$
+\phi_ {i} ^ {k} = \frac {1}{\left| \mathcal {H} _ {i} ^ {k} \right|} \sum_ {\boldsymbol {u} _ {i} ^ {n} \in \mathcal {H} _ {i} ^ {k}} \boldsymbol {u} _ {i} ^ {n}, \phi_ {v} ^ {l} = \frac {1}{\left| \mathcal {H} _ {v} ^ {l} \right|} \sum_ {\boldsymbol {u} _ {v} ^ {m} \in \mathcal {H} _ {v} ^ {l}} \boldsymbol {u} _ {v} ^ {m}, \tag {5}
+$$
+
+where $\mathcal{H}_{i(v)}^k$ is the $k$ -th cluster set in infrared or visible modality, and $|\cdot|$ is the number of instances per cluster.
+
+Then, these actual features $\pmb{U}_i$ and $\pmb{U}_v$ are transformed into corresponding fake cross-modality features $\hat{\pmb{U}}_v$ and $\hat{\pmb{U}}_i$ through CFM. While this mapping process alters the feature distributions, it preserves the original identity information. To maintain consistency in the number of clusters, DBSCAN is applied solely to the actual features for generating pseudo identity labels. Consequently, the cluster representations of the fake cross-modality features are denoted as $\{\hat{\phi}_v^1,\dots ,\hat{\phi}_v^K\}$ and $\{\hat{\phi}_i^1,\dots ,\hat{\phi}_i^L\}$ , which constitute two additional memory banks in the cross-modal pseudo-
+
+identity space. This process is formally defined as:
+
+$$
+\hat {\phi} _ {v} ^ {k} = \frac {1}{\left| \hat {\mathcal {H}} _ {v} ^ {k} \right|} \sum_ {\hat {\boldsymbol {u}} _ {v} ^ {n} \in \hat {\mathcal {H}} _ {v} ^ {k}} \hat {\boldsymbol {u}} _ {v} ^ {n}, \hat {\phi} _ {i} ^ {l} = \frac {1}{\left| \hat {\mathcal {H}} _ {i} ^ {l} \right|} \sum_ {\hat {\boldsymbol {u}} _ {i} ^ {m} \in \hat {\mathcal {H}} _ {i} ^ {l}} \hat {\boldsymbol {u}} _ {i} ^ {m}, \tag {6}
+$$
+
+where $\hat{\mathcal{H}}_{i(v)}^k$ denotes the $k$ -th cluster set in the mapped infrared or visible modality, and $|\cdot|$ indicates the number of instances per cluster.
+
+During training, we sample $P$ person identities and $Z$ instances for each identity from each modality training set. Then, we use a batch of infrared and visible queries to update the actual memories by a momentum updating strategy:
+
+$$
+\boldsymbol {\phi} _ {i} ^ {k (\delta)} \leftarrow \beta \boldsymbol {\phi} _ {i} ^ {k (\delta - 1)} + (1 - \beta) \boldsymbol {q} _ {i}, \tag {7}
+$$
+
+$$
+\boldsymbol {\phi} _ {v} ^ {l (\delta)} \leftarrow \beta \boldsymbol {\phi} _ {v} ^ {l (\delta - 1)} + (1 - \beta) \boldsymbol {q} _ {v}, \tag {8}
+$$
+
+The memories of fake cross-modality features are updated by a similar momentum strategy:
+
+$$
+\hat {\phi} _ {v} ^ {k (\delta)} \leftarrow \beta \hat {\phi} _ {v} ^ {k (\delta - 1)} + (1 - \beta) \boldsymbol {q} _ {i}, \tag {9}
+$$
+
+$$
+\hat {\phi} _ {i} ^ {l (\delta)} \leftarrow \beta \hat {\phi} _ {i} ^ {l (\delta - 1)} + (1 - \beta) \boldsymbol {q} _ {v}, \tag {10}
+$$
+
+where $\beta$ is the momentum factor and $\delta$ is the iteration step.
+
+In each iteration, the feature extractors are jointly updated by a multi ClusterNCE [7] loss, including the actual infrared loss $\mathcal{L}_i$ , actual visible loss $\mathcal{L}_v$ , fake infrared loss $\hat{\mathcal{L}}_i$ , and fake visible loss $\hat{\mathcal{L}}_v$ by the following equations:
+
+$$
+\mathcal {L} _ {i} = - \log \frac {\exp \left(\boldsymbol {q} _ {i} \cdot \phi_ {i} ^ {+} / \tau\right)}{\sum_ {k = 1} ^ {K} \exp \left(\boldsymbol {q} _ {i} \cdot \phi_ {i} ^ {k} / \tau\right)}, \tag {11}
+$$
+
+$$
+\mathcal {L} _ {v} = - \log \frac {\exp \left(\boldsymbol {q} _ {v} \cdot \phi_ {v} ^ {+} / \tau\right)}{\sum_ {l = 1} ^ {L} \exp \left(\boldsymbol {q} _ {v} \cdot \phi_ {v} ^ {l} / \tau\right)}, \tag {12}
+$$
+
+$$
+\hat {\mathcal {L}} _ {i} = - \log \frac {\exp \left(\boldsymbol {q} _ {v} \cdot \hat {\phi} _ {i} ^ {+} / \tau\right)}{\sum_ {l = 1} ^ {L} \exp \left(\boldsymbol {q} _ {v} \cdot \hat {\phi} _ {i} ^ {l} / \tau\right)}, \tag {13}
+$$
+
+$$
+\hat {\mathcal {L}} _ {v} = - \log \frac {\exp \left(\boldsymbol {q} _ {i} \cdot \hat {\phi} _ {v} ^ {+} / \tau\right)}{\sum_ {k = 1} ^ {K} \exp \left(\boldsymbol {q} _ {i} \cdot \hat {\phi} _ {v} ^ {k} / \tau\right)}, \tag {14}
+$$
+
+where $\phi_i^+$ and $\phi_v^+$ are the positive representation vector of the actual infrared and visible cluster, respectively, corresponding to the pseudo label of the query. $\hat{\phi}_i^+$ and $\hat{\phi}_v^+$ are the positive feature vector of the fake infrared and visible cluster. The $\tau$ is a temperature hyper-parameter.
+
+Certainly, four types of ClusterNCE [5] loss are designed to learn discriminative representation:
+
+$$
+\mathcal {L} _ {\mathrm {S L}} = \mathcal {L} _ {i} + \mathcal {L} _ {v} + \hat {\mathcal {L}} _ {i} + \hat {\mathcal {L}} _ {v}. \tag {15}
+$$
+
+Dynamic Learning. The generated cross-modality samples are useful in bridging significant inter-modality discrepancies by including the abundant information of missing identities. However, it is expected that these samples will not change significantly, as they share the same identity with the original samples, which should be aligned during the learning. Inspired by ISE [45], we further propose a Cross-modality Label Preserving (CLP) loss to enforce the fake cross-modality features to be close to their corresponding actual features, which facilitates the learning of cross-modality representations at the instance level. During training, the CLP loss enforces identity consistency between the actual and mapped features, allowing CFM to transfer cross-modal knowledge and capture the complex, non-linear modality discrepancies.
+
+Certainly, two types of CLP loss function are introduced in the dynamic learning method:
+
+$$
+\mathcal {L} _ {\mathrm {C L P}} ^ {i} = - \log \frac {\exp \left(\operatorname {s i m} \left(\boldsymbol {u} _ {i} \cdot \hat {\boldsymbol {u}} _ {v} ^ {+}\right) / \tau^ {\prime}\right)}{\sum_ {c = 1} ^ {C _ {i}} \exp \left(\operatorname {s i m} \left(\boldsymbol {u} _ {i} \cdot \hat {\boldsymbol {u}} _ {v} ^ {c -}\right) / \tau^ {\prime}\right)}, \tag {16}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {C L P}} ^ {v} = - \log \frac {\exp \left(\operatorname {s i m} \left(\boldsymbol {u} _ {v} \cdot \hat {\boldsymbol {u}} _ {i} ^ {+}\right) / \tau^ {\prime}\right)}{\sum_ {c = 1} ^ {C _ {v}} \exp \left(\operatorname {s i m} \left(\boldsymbol {u} _ {v} \cdot \hat {\boldsymbol {u}} _ {i} ^ {c -}\right) / \tau^ {\prime}\right)}, \tag {17}
+$$
+
+where $C_i$ and $C_v$ are the cluster number of a mini-batch in infrared and visible modality, respectively. $\sin(\cdot)$ denotes the cosine similarity. $\hat{\pmb{u}}_v^+$ is the hardest positive fake visible sample for a given infrared feature $\pmb{u}_i$ , and $\hat{\pmb{u}}_v^{c-}$ is the hardest negative one in the $c$ -th fake visible cluster of a minibatch. $\hat{\pmb{u}}_i^+$ and $\hat{\pmb{u}}_i^{c-}$ are defined similarly to above. $\tau'$ is a temperature hyper-parameter.
+
+Consequently, the two cross-modality label preserving loss functions are combined in the dynamic learning method to learn distinctive representations:
+
+$$
+\mathcal {L} _ {\mathrm {D L}} = \mathcal {L} _ {\mathrm {C L P}} ^ {i} + \mathcal {L} _ {\mathrm {C L P}} ^ {v}. \tag {18}
+$$
+
+Collaborative Learning. The cluster-level static learning method and instance-level dynamic learning method jointly forms the static-dynamic collaborative learning strategy, which aims to achieve better learning of discriminative and modality-invariant representations in the absence of cross-modality identity pairs.
+
+The overall loss for training the model is defined by the following equation:
+
+$$
+\mathcal {L} _ {\text {o v e r a l l}} = \mathcal {L} _ {\mathrm {S L}} + \eta \mathcal {L} _ {\mathrm {D L}}, \tag {19}
+$$
+
+where $\eta$ is the loss weight, balancing two loss functions.
+
+# 4. EXPERIMENTS
+
+# 4.1. Datasets and Evaluation Protocol
+
+Paired Datasets. To validate the proposed framework under paired settings, we conduct comprehensive evaluations
+
+ | | | SYSU-MM01 (unpaired settings) | RegDB (unpaired settings) |
| All Search | Indoor Search | Visible to Infrared | Infrared to Visible |
| α value | Methods | Venue | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| 0.25 | ADCA [32] | MM-22 | 41.80 | 37.54 | 22.04 | 47.00 | 56.24 | 51.79 | 50.82 | 43.72 | 42.63 | 64.22 | 55.90 | 44.29 |
| OTPA [47] | arXiv-24 | 49.15 | 44.75 | 30.62 | 51.70 | 60.82 | 57.23 | 51.37 | 50.30 | 44.60 | 66.27 | 65.82 | 64.97 |
| MMM [20] | ECCV-24 | 54.68 | 47.35 | 35.42 | 55.19 | 63.76 | 61.21 | 62.27 | 55.09 | 44.34 | 76.69 | 69.93 | 66.44 |
| PCAL[37] | TIFS-25 | 48.84 | 41.30 | 26.05 | 50.48 | 62.63 | 59.72 | 59.33 | 56.26 | 45.73 | 77.18 | 75.24 | 63.83 |
| N-ULC [21] | AAAI-25 | 53.70 | 49.69 | 33.56 | 57.39 | 65.00 | 60.64 | 60.76 | 56.82 | 42.91 | 79.35 | 76.06 | 60.40 |
| MCL (Ours) | - | 58.57 | 57.74 | 45.45 | 65.72 | 71.84 | 68.30 | 65.97 | 63.53 | 55.84 | 84.31 | 78.67 | 67.28 |
| 0.5 | ADCA [32] | MM-22 | 34.34 | 32.21 | 18.76 | 36.59 | 47.07 | 43.23 | 40.28 | 32.60 | 34.93 | 52.94 | 47.48 | 37.05 |
| OTPA [47] | arXiv-24 | 48.80 | 45.64 | 31.01 | 49.19 | 58.74 | 54.83 | 40.58 | 41.52 | 32.44 | 59.26 | 58.68 | 57.13 |
| MMM [20] | ECCV-24 | 44.14 | 42.94 | 30.71 | 54.25 | 60.17 | 52.49 | 52.90 | 43.91 | 36.51 | 63.91 | 58.17 | 58.47 |
| PCAL[37] | TIFS-25 | 46.24 | 37.62 | 22.03 | 45.39 | 52.73 | 46.42 | 46.48 | 47.88 | 36.05 | 64.21 | 66.30 | 50.41 |
| N-ULC [21] | AAAI-25 | 49.36 | 45.12 | 29.17 | 51.59 | 60.24 | 55.89 | 50.24 | 45.96 | 34.61 | 70.31 | 62.84 | 54.74 |
| MCL (Ours) | - | 54.29 | 53.98 | 42.64 | 61.71 | 68.45 | 64.40 | 60.78 | 59.69 | 52.91 | 80.36 | 73.02 | 64.25 |
| 0.75 | ADCA [32] | MM-22 | 32.66 | 30.61 | 17.98 | 37.02 | 47.59 | 43.79 | 35.80 | 28.71 | 27.96 | 47.28 | 43.92 | 34.70 |
| OTPA [47] | arXiv-24 | 33.65 | 30.50 | 16.94 | 45.3 | 53.32 | 50.17 | 31.48 | 35.60 | 29.52 | 51.98 | 49.25 | 47.62 |
| MMM [20] | ECCV-24 | 36.19 | 34.60 | 23.56 | 43.91 | 50.60 | 45.20 | 41.73 | 38.64 | 32.75 | 54.79 | 47.90 | 46.16 |
| PCAL[37] | TIFS-25 | 30.74 | 29.83 | 20.54 | 40.60 | 47.42 | 39.34 | 38.10 | 37.09 | 33.54 | 59.80 | 59.61 | 47.20 |
| N-ULC [21] | AAAI-25 | 42.56 | 39.44 | 27.06 | 55.03 | 63.11 | 58.80 | 43.38 | 39.27 | 30.06 | 66.72 | 57.51 | 44.38 |
| MCL (Ours) | - | 52.16 | 51.57 | 39.57 | 59.63 | 66.46 | 62.24 | 55.30 | 52.79 | 48.26 | 74.19 | 69.37 | 60.58 |
| 1.0 | ADCA [32] | MM-22 | 23.48 | 23.23 | 12.53 | 28.39 | 37.40 | 32.80 | 26.18 | 15.93 | 14.72 | 33.10 | 28.43 | 24.95 |
| OTPA [47] | arXiv-24 | 20.53 | 19.46 | 10.32 | 36.18 | 43.54 | 40.02 | 19.20 | 18.03 | 19.70 | 39.74 | 38.42 | 35.11 |
| MMM [20] | ECCV-24 | 30.81 | 27.53 | 17.92 | 36.19 | 40.60 | 38.38 | 30.98 | 27.10 | 20.03 | 40.26 | 33.54 | 30.12 |
| PCAL[37] | TIFS-25 | 28.95 | 25.31 | 18.54 | 32.10 | 38.48 | 36.20 | 28.74 | 25.90 | 18.68 | 37.56 | 29.69 | 27.24 |
| N-ULC [21] | AAAI-25 | 34.40 | 31.83 | 25.77 | 40.36 | 43.70 | 43.86 | 34.71 | 28.06 | 25.48 | 42.83 | 32.40 | 28.92 |
| MCL (Ours) | - | 45.98 | 44.95 | 32.85 | 51.53 | 59.06 | 54.54 | 43.18 | 39.29 | 36.95 | 58.37 | 49.40 | 47.21 |
+
+Table 1. The comparison with the state-of-the-art methods on SYSU-MM01 and RegDB under unpaired settings. It contains four settings, i.e., the unpaired ratio $\alpha$ ranges from 0.25 to 1.0 in increments of 0.25. Rank-1 accuracy(%) , mAP (%) and mINP (%) are reported.
+
+on two benchmark visible-infrared person re-identification datasets: SYSU-MM01 [29] and RegDB [41]. The SYSUMM01 dataset is a large-scale cross-modality collection of 22,257 visible images and 11,909 near-infrared images captured in indoor and outdoor environments by 4 visible cameras and 2 infrared cameras. In contrast, the RegDB dataset is a smaller and less demanding dataset with 412 different person identities, where each identity contains 10 visible and 10 infrared image pairs. This thermal-infrared dataset is collected using an aligned pair of cameras (one visible and one infrared), which has a comparatively lower environmental complexity than SYSU-MM01.
+
+Unpaired Datasets. To evaluate the effectiveness of our model in unpaired settings, experiments are conducted on the modified SYSU-MM01 and RegDB datasets. It is noted that existing datasets lack cross-modality unpaired training data, thus necessitating adjustments to the existing benchmarks. In order to systematically analyse the impact of unpaired settings, we introduce a hyper-parameter $\alpha$ that controls the proportion of unpaired identities between the visible and infrared modalities. Unlike OTPA [47], which reduces training data by dropping identities, our setup preserves the overall dataset size. Instead of adjusting the overlap ratio by selecting modality-specific subsets, we randomly replace a portion of the visible identities with external images. Specifically, the visible images of selected identities are replaced with images from three visible ReID
+
+datasets(i.e., Market-1501 [49], MSMT17 [27] and LLCM [46]), while maintaining a roughly consistent number of images per identity before and after replacement. Details of the replacement process are provided in the supplementary materials. This design mitigates the potential effects of data reduction. The test sets and evaluation protocols remain unchanged throughout the experiments.
+
+Evaluation Protocol. On the two benchmark datasets and their original counterpart, we follow the popular protocols [39] for evaluation, where cumulative match characteristic (CMC), mean average precision (mAP), and mean inverse negative penalty (mINP) [41] are adopted. For SYSU-MM01 under paired and unpaired settings, we adopt all-search and indoor-search evaluation modes. For RegDB in paired and unpaired settings, we evaluate our method in the two test modes, including thermal to visible and visible to thermal, and we strictly follow existing methods to perform ten trials of the gallery set selection [40], and calculate the average performance.
+
+# 4.2. Implementation Details
+
+MCL is implemented in the PyTorch platform. Our work is based on the Augmented Dual-Contrastive Aggregation [32] and incorporates the feature extractor from TransReID [10] as the backbone network. In each mini-batch, 16 identities are selected per modality, with each identity comprising 16 instances. We resize input images to $288 \times 144$ pixels for training. Standard data augmentation techniques,
+
+ | | | SYSU-MM01 | RegDB |
| All Search | Indoor Search | Visible to Infrared | Infrared to Visible |
| Methods | Venue | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| Supervised | AGW [41] | TPAMI-21 | 47.50 | 47.65 | 35.30 | 54.17 | 62.97 | 59.23 | 70.05 | 66.37 | 50.19 | 70.49 | 65.90 | 51.24 |
| DFLN-ViT [48] | TMM-22 | 59.84 | 57.70 | - | 62.13 | 69.03 | - | 92.10 | 82.11 | - | 91.21 | 81.62 | - |
| PartMix [12] | CVPR-23 | 77.78 | 74.62 | - | 81.52 | 84.38 | - | 85.66 | 82.27 | - | 84.93 | 82.52 | - |
| MUN [44] | ICCV-23 | 76.24 | 73.81 | - | 79.42 | 82.06 | - | 95.19 | 87.15 | - | 91.86 | 85.01 | - |
| SAAI [8] | ICCV-23 | 75.90 | 77.03 | - | 83.20 | 88.01 | - | 91.07 | 91.45 | - | 92.09 | 92.01 | - |
| YYDS [6] | arXiv-24 | 85.54 | 81.64 | - | 89.13 | 91.00 | - | - | - | - | 90.20 | 83.50 | - |
| TVI-LFM [11] | NIPS-24 | 84.90 | 81.47 | 70.85 | 89.06 | 90.78 | 88.39 | - | - | - | 91.38 | 85.92 | 72.73 |
| Unsupervised | H2H* [16] | TIP-21 | 30.15 | 29.40 | - | - | - | - | 23.81 | 18.87 | - | - | - | - |
| OTLA* [24] | ECCV-22 | 29.90 | 27.10 | - | 29.80 | 38.80 | - | 32.90 | 29.70 | - | 32.10 | 28.60 | - |
| ADCA [32] | MM-22 | 45.51 | 42.73 | 28.29 | 50.60 | 59.11 | 55.17 | 67.20 | 64.05 | 52.67 | 68.48 | 63.81 | 49.62 |
| PGM [31] | CVPR-23 | 57.27 | 51.78 | 34.96 | 56.23 | 62.74 | 58.13 | 69.48 | 65.41 | - | 69.85 | 65.17 | - |
| DOTLA* [4] | MM-23 | 50.36 | 47.36 | 32.40 | 53.47 | 61.73 | 57.35 | 85.63 | 76.71 | 61.58 | 82.91 | 74.97 | 58.60 |
| MBCCM [3] | MM-23 | 53.14 | 48.16 | 32.41 | 55.21 | 61.98 | 57.13 | 83.79 | 77.87 | 65.04 | 82.82 | 76.74 | 61.73 |
| CCLNet [2] | MM-23 | 54.03 | 50.19 | - | 56.68 | 65.12 | - | 69.94 | 65.53 | - | 70.17 | 66.66 | - |
| GUR†[33] | ICCV-23 | 60.95 | 56.99 | 41.85 | 64.22 | 69.49 | 64.81 | 73.91 | 70.23 | 8.88 | 75.00 | 69.94 | 56.21 |
| SCA-RCP [15] | TKDE-24 | 51.41 | 48.52 | 33.56 | 56.77 | 64.19 | 59.25 | 85.59 | 79.12 | - | 82.41 | 75.73 | - |
| MMM [20] | ECCV-24 | 61.60 | 57.90 | - | 64.40 | 70.40 | - | 89.70 | 80.50 | - | 85.80 | 77.00 | - |
| PCAL [37] | TIFS-25 | 54.39 | 51.95 | 38.09 | 59.69 | 66.72 | 62.44 | 86.43 | 82.51 | 72.33 | 86.21 | 81.23 | 68.71 |
| N-ULC [21] | AAAI-25 | 61.81 | 58.92 | 45.01 | 67.04 | 73.08 | 69.42 | 88.75 | 82.14 | 68.75 | 88.17 | 81.11 | 66.05 |
| MCL (Ours) | - | 62.95 | 62.71 | 50.63 | 67.81 | 74.19 | 70.82 | 89.83 | 83.12 | 72.86 | 88.64 | 82.04 | 69.12 |
+
+Table 2. The comparison with the state-of-the-art methods on SYSU-MM01 and RegDB under paired settings. It contains two groups, i.e., unsupervised VI-ReID methods and supervised VI-ReID methods. * means the model is pre-trained on an extra labeled visible dataset. GUR† denotes the results without camera information. Rank-1 accuracy(%) , mAP (%) and mINP (%) are reported.
+
+ | Components | SYSU-MM01* (All Search) | SYSU-MM01* (Indoor Search) | RegDB* (Visible to Infrared) |
| Index | Baseline | CFM | SL | DL | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| 1 | ✓ | | | | 47.14 | 47.29 | 34.63 | 55.39 | 63.10 | 59.43 | 49.28 | 48.6 | 43.93 |
| 2 | ✓ | ✓ | ✓ | | 51.65 | 52.48 | 40.08 | 58.38 | 66.87 | 63.66 | 56.39 | 54.52 | 49.70 |
| 3 | ✓ | ✓ | | ✓ | 49.46 | 50.67 | 39.24 | 57.00 | 65.53 | 62.92 | 52.73 | 50.84 | 47.92 |
| 4 | ✓ | ✓ | ✓ | ✓ | 54.29 | 53.98 | 42.64 | 61.71 | 68.45 | 64.40 | 60.78 | 59.69 | 52.91 |
+
+Table 3. Ablation studies conducted on the SYSU-MM01 and RegDB datasets under unpaired settings. * refers to $\alpha = 0.5$ in both unpaired datasets. "CFM" denotes the cross-modality feature mapping module, while "SL" and "DL" mean the static learning method and the dynamic learning method in 3.3, respectively. Rank-1 accuracy (\%), mAP (\%), and mINP (\%) are reported.
+
+including random cropping, random flipping and random erasing, are applied. At the beginning of each epoch, we perform the DBSCAN [7] clustering to generate pseudo labels in each modality independently. The learnable scaling and shifting parameters, $\gamma$ and $\zeta$ , are initialized to 1 and 0, respectively, and the constant $\epsilon$ is set to $10^{-5}$ . The temperature factors $\tau$ and $\tau'$ are 0.05 and 0.6, respectively. We train the model in total of 50 epochs, in which the previous 30 epochs are used for pre-training, and CFM and SDC are executed in the last 20 epochs. All other experimental settings follow the previous work [32]. For consistency, we use the same MCL framework in paired settings to demonstrate its general applicability.
+
+# 4.3. Comparison with State-of-the-Arts
+
+To validate the efficacy of our method, we comprehensively compare it with state-of-the-art approaches under both unpaired and paired settings, as shown in Tab. 1 and Tab. 2.
+
+Comparison with unsupervised methods under unpaired settings. The experiments demonstrate that our MCL significantly outperforms existing unsupervised methods under unpaired settings at various ratios. These con
+
+siderable gains benefit from the insightful design of our method for USL-VI-ReID. There are two major advantages of our method: 1) We use a mapping-based solution to effectively address the lack of cross-modality correlations in unpaired scenarios by synthesizing fake paired data while preserving discriminative identity. 2) Our collaborative learning strategy achieves a dual-level alignment paradigm for cluster- and instance-level optimization.
+
+Comparison with supervised methods under paired settings. We compare our method with several recent supervised visible-infrared ReID approaches under paired settings. Notably, although supervised methods rely on accurate manual annotations, our method achieves competitive performance of certain baselines (e.g. DFLN-ViT [48]).
+
+Comparison with unsupervised methods under paired settings. We also evaluate our method against advanced USL-VI-ReID approaches under paired settings. Among these, H2H [16], OTLA [24] and DOTLA [4] need an extra annotated visible dataset. In Tab. 2, our method is significantly better than all existing USL-VI-ReID methods, demonstrating the effectiveness under paired settings.
+
+# 4.4. Ablation Study
+
+The performance boost of the MCL framework in the task of USL-VI-ReID under unpaired settings mainly comes from the proposed CFM module and the collaborative learning strategy with Static Learning (SL) and Dynamic Learning (DL). We validate the effectiveness of each component by conducting ablation studies on the SYSU-MM01 and RegDB under unpaired settings where $\alpha$ is representatively set to 0.5, which incorporate a balance of paired and unpaired scenarios. Results are shown in Tab. 3.
+
+Baseline in index 1 denotes that we directly train the model on the unpaired SYSU-MM01 and RegDB tasks with ADCA [32] method, using the feature extractor from TransReID [10] as the backbone. Although ADCA has a promising performance under unpaired settings, it is observed that the baseline only achieves $47.29\%$ mAP on SYSU-MM01 (all search) and $48.6\%$ mAP on RegDB (visible to infrared). Therefore, directly using ADCA method can hardly tackle the problem of unpaired settings for the USL-VI-ReID task. Effectiveness of SL. Index 2 means the static learning strategy with CFM module. Compared with baseline, SL improves the performance of $5.19\%$ and $5.92\%$ mAP on the unpaired SYSU-MM01 (all search) and RegDB (visible to infrared). The main gain is achieved by the design of the multi-memory banks in both the original and pseudoidentity space, which additionally cluster all mapped features for contrastive learning, allowing the model to capture certain modality-invariant features in scenarios with cross-modal identity mismatches.
+
+Effectiveness of DL. Index 3 represents the dynamic learning strategy with CFM module. Compared with baseline, the significant improvements demonstrate the effectiveness of DL. The improvements are $3.38\%$ and $2.24\%$ mAP on the unpaired SYSU-MM01 (all search) and RegDB (visible to infrared). DL can further use fake cross-modality features and pull them towards their corresponding actual samples, facilitating instance-level cross-modality learning.
+
+Effectiveness of Collaborative Learning. Index 4 denotes the collaborative learning strategy with SL and DL. In comparison, the collaborative learning brings consistent improvement in all settings, which shows the effectiveness of static-dynamic collaborative learning in mitigating intra-modality discrepancies while enhancing cross-modality correspondence alignment.
+
+# 4.5. Further Analysis
+
+Hyper-parameter Analysis for $\eta$ . We explore the influence of hyper-parameter $\eta$ in Eq. 19, as presented in the supplementary materials. When $\eta = 1.0$ , the method achieves a balance in static and dynamic learning.
+
+Visualization. In Fig. 3, it shows the t-SNE [22] visualization of 20 randomly selected identities from the unpaired SYSU-MM01 dataset with $\alpha = 0.5$ . Compared to the
+
+
+
+
+
+
+Figure 3. The t-SNE (top) and similarity distribution (bottom) visualizations for randomly sampled identities. Colors represent identities; circles and triangles denote visible and infrared samples, respectively. The similarity distribution represents similarity scores of cross-modality positive and negative pairs, where larger separation indicates better identity discrimination.
+
+
+
+baseline, MCL brings infrared and visible positive samples closer together and effectively increases the separation from negative pairs, thus improving performance under unpaired settings. However, some same-identity samples remain dispersed, indicating challenges for unpaired USL-VI-ReID.
+
+# 5. CONCLUSION
+
+This paper addresses unsupervised visible-infrared person re-identification (USL-VI-ReID) under unpaired settings, which is a prevalent yet underexplored challenge in real-world surveillance systems. While existing USL-VI-ReID methods often overlook the critical issue of aligning cross-modality relations without paired data, we propose the Mapping and Collaborative Learning (MCL) framework to bridge this gap. We integrates a cross-modality feature mapping module to establish inter-modal correlations and a static-dynamic collaborative learning strategy to refine discriminative representations in unpaired scenarios. Extensive experiments on SYSU-MM01 and RegDB demonstrate that MCL not only outperforms state-of-the-art unsupervised methods under unpaired settings but also achieves competitive performance in paired scenarios, pushing USL-VI-ReID to real-world deployment.
+
+Limitations and Future Work. While effective, MCL still faces challenges in extremely unpaired settings and requires relatively high training cost. Future work will focus on improving robustness in such scenarios and designing lightweight variants for efficient deployment.
+
+# Acknowledgments
+
+This work is partially supported by National Natural Science Foundation of China under Grants (62176188, 62225113, 623B2080), the Innovative Research Group Project of Hubei Province under Grants (2024AFA017), the Major Project of Science and Technology Innovation of Hubei Province (2024BCA003), Postdoctoral Fellowship Program of China Postdoctoral Science Foundation (GZC20241268, 2024M762479), Hubei Postdoctoral Talent Introduction Program (2024HBBHJD070) and Hubei Provincial Natural Science Foundation of China (2025AFB219). The numerical calculations in this paper had been supported by the super-computing system in the Supercomputing Center of Wuhan University.
+
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+ "content": "Unsupervised visible-infrared person re-identification (USL-VI-ReID) aims to train a cross-modality retrieval model without labels, reducing the reliance on expensive cross-modality manual annotation. However, existing USL-VI-ReID methods rely on artificially cross-modality paired data as implicit supervision, which is also expensive for human annotation and contrary to the setting of unsupervised tasks. In addition, this full alignment of identity across modalities is inconsistent with real-world scenarios, where unpaired settings are prevalent. To this end, we study the USL-VI-ReID task under unpaired settings, which uses cross-modality unpaired and unlabeled data for training a VI-ReID model. We propose a novel Mapping and Collaborative Learning (MCL) framework. Specifically, we first design a simple yet effective Cross-modality Feature Mapping (CFM) module to map and generate fake cross-modality positive feature pairs, constructing a cross-modal pseudo-identity space for feature alignment. Then, a Static-Dynamic Collaborative (SDC) learning strategy is proposed to align cross-modality correspondences through a collaborative approach, eliminating inter-modality discrepancies across different aspects i.e., cluster-level and instance-level, in scenarios with cross-modal identity mismatches. Extensive experiments on the conducted SYSU-MM01 and RegDB benchmarks under paired and unpaired settings demonstrate that our proposed MCL significantly outperforms existing unsupervised methods, facilitating USL-VI-ReID to real-world deployment."
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+ "content": "Traditional ReID methods primarily rely on daytime visible-light images, which struggle to extract discriminative features in low-light environments, limiting single-modality ReID deployment in real-world surveillance [13, 26]. To address this problem, the cross-modality visible-infrared person re-identification (VI-ReID) is proposed to identify the same person across a set of visible and infrared images [42]. While supervised VI-ReID methods use plenty of costly cross-modality (visible-infrared) identity labels to learn modality-invariant feature representations [15, 19, 30, 38, 41], the unsupervised VI-ReID (USL-VI-ReID) methods eliminate the need for annotation by generating pseudo-labels [20, 31, 32], which reduce the cost of"
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+ "content": "Supervised visible-infrared person re-identification (VI-ReID) has received considerable attention for its applicability in 24-hour surveillance systems. A key challenge is to mitigate the significant intra-class discrepancies between the visible and infrared modalities [29]. Current approaches bridging this cross-modality gap can fall into two categories: image-level and feature-level matching. Image-level methods [25, 36] focus on the generation of cross-modal images to extract modality-invariant features. In contrast, feature-level alignment approaches [9, 17, 18, 28, 35, 40] impose constraints to embed heterogeneous images into a shared feature space. However, these methods rely heavily on extensive cross-modality annotation, which is expensive and time-consuming, making supervised VI-ReID less scalable in real-world deployments."
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+ "content": "We propose a Mapping and Collaborative Learnin (MCL) framework for USL-VI-ReID under unpaired settings, as shown in Fig. 2. Our MCL has two components including Cross-modality Feature Mapping (CFM) module and Static-Dynamic Collaborative (SDC) learning strategy. In this paper, we follow Augmented Dual-Contrastive Aggregation (ADCA) [32] to establish our baseline, where a dualpath contrastive learning framework with two modality-specific memories to learn intra-modality representations."
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+ "content": "f_m^\\theta \\cdot \\{\\overline{y}_m^k\\}_{k=1}^{N_m}"
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+ "content": " represents the ground-truth labels of different modalities. In this work, we study the under-explored unpaired settings of USL-VI-ReID, where there are unpaired cross-modality data in the training set, i.e., there exist "
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+ "content": "\\mathcal {L} _ {\\mathrm {S L}} = \\mathcal {L} _ {i} + \\mathcal {L} _ {v} + \\hat {\\mathcal {L}} _ {i} + \\hat {\\mathcal {L}} _ {v}. \\tag {15}",
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| All Search | Indoor Search | Visible to Infrared | Infrared to Visible |
| α value | Methods | Venue | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| 0.25 | ADCA [32] | MM-22 | 41.80 | 37.54 | 22.04 | 47.00 | 56.24 | 51.79 | 50.82 | 43.72 | 42.63 | 64.22 | 55.90 | 44.29 |
| OTPA [47] | arXiv-24 | 49.15 | 44.75 | 30.62 | 51.70 | 60.82 | 57.23 | 51.37 | 50.30 | 44.60 | 66.27 | 65.82 | 64.97 |
| MMM [20] | ECCV-24 | 54.68 | 47.35 | 35.42 | 55.19 | 63.76 | 61.21 | 62.27 | 55.09 | 44.34 | 76.69 | 69.93 | 66.44 |
| PCAL[37] | TIFS-25 | 48.84 | 41.30 | 26.05 | 50.48 | 62.63 | 59.72 | 59.33 | 56.26 | 45.73 | 77.18 | 75.24 | 63.83 |
| N-ULC [21] | AAAI-25 | 53.70 | 49.69 | 33.56 | 57.39 | 65.00 | 60.64 | 60.76 | 56.82 | 42.91 | 79.35 | 76.06 | 60.40 |
| MCL (Ours) | - | 58.57 | 57.74 | 45.45 | 65.72 | 71.84 | 68.30 | 65.97 | 63.53 | 55.84 | 84.31 | 78.67 | 67.28 |
| 0.5 | ADCA [32] | MM-22 | 34.34 | 32.21 | 18.76 | 36.59 | 47.07 | 43.23 | 40.28 | 32.60 | 34.93 | 52.94 | 47.48 | 37.05 |
| OTPA [47] | arXiv-24 | 48.80 | 45.64 | 31.01 | 49.19 | 58.74 | 54.83 | 40.58 | 41.52 | 32.44 | 59.26 | 58.68 | 57.13 |
| MMM [20] | ECCV-24 | 44.14 | 42.94 | 30.71 | 54.25 | 60.17 | 52.49 | 52.90 | 43.91 | 36.51 | 63.91 | 58.17 | 58.47 |
| PCAL[37] | TIFS-25 | 46.24 | 37.62 | 22.03 | 45.39 | 52.73 | 46.42 | 46.48 | 47.88 | 36.05 | 64.21 | 66.30 | 50.41 |
| N-ULC [21] | AAAI-25 | 49.36 | 45.12 | 29.17 | 51.59 | 60.24 | 55.89 | 50.24 | 45.96 | 34.61 | 70.31 | 62.84 | 54.74 |
| MCL (Ours) | - | 54.29 | 53.98 | 42.64 | 61.71 | 68.45 | 64.40 | 60.78 | 59.69 | 52.91 | 80.36 | 73.02 | 64.25 |
| 0.75 | ADCA [32] | MM-22 | 32.66 | 30.61 | 17.98 | 37.02 | 47.59 | 43.79 | 35.80 | 28.71 | 27.96 | 47.28 | 43.92 | 34.70 |
| OTPA [47] | arXiv-24 | 33.65 | 30.50 | 16.94 | 45.3 | 53.32 | 50.17 | 31.48 | 35.60 | 29.52 | 51.98 | 49.25 | 47.62 |
| MMM [20] | ECCV-24 | 36.19 | 34.60 | 23.56 | 43.91 | 50.60 | 45.20 | 41.73 | 38.64 | 32.75 | 54.79 | 47.90 | 46.16 |
| PCAL[37] | TIFS-25 | 30.74 | 29.83 | 20.54 | 40.60 | 47.42 | 39.34 | 38.10 | 37.09 | 33.54 | 59.80 | 59.61 | 47.20 |
| N-ULC [21] | AAAI-25 | 42.56 | 39.44 | 27.06 | 55.03 | 63.11 | 58.80 | 43.38 | 39.27 | 30.06 | 66.72 | 57.51 | 44.38 |
| MCL (Ours) | - | 52.16 | 51.57 | 39.57 | 59.63 | 66.46 | 62.24 | 55.30 | 52.79 | 48.26 | 74.19 | 69.37 | 60.58 |
| 1.0 | ADCA [32] | MM-22 | 23.48 | 23.23 | 12.53 | 28.39 | 37.40 | 32.80 | 26.18 | 15.93 | 14.72 | 33.10 | 28.43 | 24.95 |
| OTPA [47] | arXiv-24 | 20.53 | 19.46 | 10.32 | 36.18 | 43.54 | 40.02 | 19.20 | 18.03 | 19.70 | 39.74 | 38.42 | 35.11 |
| MMM [20] | ECCV-24 | 30.81 | 27.53 | 17.92 | 36.19 | 40.60 | 38.38 | 30.98 | 27.10 | 20.03 | 40.26 | 33.54 | 30.12 |
| PCAL[37] | TIFS-25 | 28.95 | 25.31 | 18.54 | 32.10 | 38.48 | 36.20 | 28.74 | 25.90 | 18.68 | 37.56 | 29.69 | 27.24 |
| N-ULC [21] | AAAI-25 | 34.40 | 31.83 | 25.77 | 40.36 | 43.70 | 43.86 | 34.71 | 28.06 | 25.48 | 42.83 | 32.40 | 28.92 |
| MCL (Ours) | - | 45.98 | 44.95 | 32.85 | 51.53 | 59.06 | 54.54 | 43.18 | 39.29 | 36.95 | 58.37 | 49.40 | 47.21 |
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| All Search | Indoor Search | Visible to Infrared | Infrared to Visible |
| Methods | Venue | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| Supervised | AGW [41] | TPAMI-21 | 47.50 | 47.65 | 35.30 | 54.17 | 62.97 | 59.23 | 70.05 | 66.37 | 50.19 | 70.49 | 65.90 | 51.24 |
| DFLN-ViT [48] | TMM-22 | 59.84 | 57.70 | - | 62.13 | 69.03 | - | 92.10 | 82.11 | - | 91.21 | 81.62 | - |
| PartMix [12] | CVPR-23 | 77.78 | 74.62 | - | 81.52 | 84.38 | - | 85.66 | 82.27 | - | 84.93 | 82.52 | - |
| MUN [44] | ICCV-23 | 76.24 | 73.81 | - | 79.42 | 82.06 | - | 95.19 | 87.15 | - | 91.86 | 85.01 | - |
| SAAI [8] | ICCV-23 | 75.90 | 77.03 | - | 83.20 | 88.01 | - | 91.07 | 91.45 | - | 92.09 | 92.01 | - |
| YYDS [6] | arXiv-24 | 85.54 | 81.64 | - | 89.13 | 91.00 | - | - | - | - | 90.20 | 83.50 | - |
| TVI-LFM [11] | NIPS-24 | 84.90 | 81.47 | 70.85 | 89.06 | 90.78 | 88.39 | - | - | - | 91.38 | 85.92 | 72.73 |
| Unsupervised | H2H* [16] | TIP-21 | 30.15 | 29.40 | - | - | - | - | 23.81 | 18.87 | - | - | - | - |
| OTLA* [24] | ECCV-22 | 29.90 | 27.10 | - | 29.80 | 38.80 | - | 32.90 | 29.70 | - | 32.10 | 28.60 | - |
| ADCA [32] | MM-22 | 45.51 | 42.73 | 28.29 | 50.60 | 59.11 | 55.17 | 67.20 | 64.05 | 52.67 | 68.48 | 63.81 | 49.62 |
| PGM [31] | CVPR-23 | 57.27 | 51.78 | 34.96 | 56.23 | 62.74 | 58.13 | 69.48 | 65.41 | - | 69.85 | 65.17 | - |
| DOTLA* [4] | MM-23 | 50.36 | 47.36 | 32.40 | 53.47 | 61.73 | 57.35 | 85.63 | 76.71 | 61.58 | 82.91 | 74.97 | 58.60 |
| MBCCM [3] | MM-23 | 53.14 | 48.16 | 32.41 | 55.21 | 61.98 | 57.13 | 83.79 | 77.87 | 65.04 | 82.82 | 76.74 | 61.73 |
| CCLNet [2] | MM-23 | 54.03 | 50.19 | - | 56.68 | 65.12 | - | 69.94 | 65.53 | - | 70.17 | 66.66 | - |
| GUR†[33] | ICCV-23 | 60.95 | 56.99 | 41.85 | 64.22 | 69.49 | 64.81 | 73.91 | 70.23 | 8.88 | 75.00 | 69.94 | 56.21 |
| SCA-RCP [15] | TKDE-24 | 51.41 | 48.52 | 33.56 | 56.77 | 64.19 | 59.25 | 85.59 | 79.12 | - | 82.41 | 75.73 | - |
| MMM [20] | ECCV-24 | 61.60 | 57.90 | - | 64.40 | 70.40 | - | 89.70 | 80.50 | - | 85.80 | 77.00 | - |
| PCAL [37] | TIFS-25 | 54.39 | 51.95 | 38.09 | 59.69 | 66.72 | 62.44 | 86.43 | 82.51 | 72.33 | 86.21 | 81.23 | 68.71 |
| N-ULC [21] | AAAI-25 | 61.81 | 58.92 | 45.01 | 67.04 | 73.08 | 69.42 | 88.75 | 82.14 | 68.75 | 88.17 | 81.11 | 66.05 |
| MCL (Ours) | - | 62.95 | 62.71 | 50.63 | 67.81 | 74.19 | 70.82 | 89.83 | 83.12 | 72.86 | 88.64 | 82.04 | 69.12 |
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| Index | Baseline | CFM | SL | DL | r1 | mAP | mINP | r1 | mAP | mINP | r1 | mAP | mINP |
| 1 | ✓ | | | | 47.14 | 47.29 | 34.63 | 55.39 | 63.10 | 59.43 | 49.28 | 48.6 | 43.93 |
| 2 | ✓ | ✓ | ✓ | | 51.65 | 52.48 | 40.08 | 58.38 | 66.87 | 63.66 | 56.39 | 54.52 | 49.70 |
| 3 | ✓ | ✓ | | ✓ | 49.46 | 50.67 | 39.24 | 57.00 | 65.53 | 62.92 | 52.73 | 50.84 | 47.92 |
| 4 | ✓ | ✓ | ✓ | ✓ | 54.29 | 53.98 | 42.64 | 61.71 | 68.45 | 64.40 | 60.78 | 59.69 | 52.91 |
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+ "content": " are 0.05 and 0.6, respectively. We train the model in total of 50 epochs, in which the previous 30 epochs are used for pre-training, and CFM and SDC are executed in the last 20 epochs. All other experimental settings follow the previous work [32]. For consistency, we use the same MCL framework in paired settings to demonstrate its general applicability."
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diff --git a/2025/Unsupervised Visual Chain-of-Thought Reasoning via Preference Optimization/2dfcc225-7530-4e71-9b57-14637900f483_content_list.json b/2025/Unsupervised Visual Chain-of-Thought Reasoning via Preference Optimization/2dfcc225-7530-4e71-9b57-14637900f483_content_list.json
new file mode 100644
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+++ b/2025/Unsupervised Visual Chain-of-Thought Reasoning via Preference Optimization/2dfcc225-7530-4e71-9b57-14637900f483_content_list.json
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+ {
+ "type": "text",
+ "text": "Unsupervised Visual Chain-of-Thought Reasoning via Preference Optimization",
+ "text_level": 1,
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+ "page_idx": 0
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+ "type": "text",
+ "text": "Kesen Zhao $^{1}$ Beier Zhu $^{1*}$ Qianru Sun $^{2}$ Hanwang Zhang $^{1}$",
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+ "page_idx": 0
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+ {
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+ "text": "$^{1}$ Nanyang Technological University, $^{2}$ Singapore Management University",
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "kesen002@e.ntu.edu.sg, qianrusun@smu.edu.sg",
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+ "page_idx": 0
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+ "text": "{beier.zhu,hanwangzhang}@ntu.edu.sg",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Abstract",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "Chain-of-thought (CoT) reasoning greatly improves the interpretability and problem-solving abilities of multimodal large language models (MLLMs). However, existing approaches focus on text CoT, limiting their ability to leverage visual cues. Visual CoT remains underexplored, and the only work [35] is based on supervised fine-tuning that relies on extensive labeled bounding-box data and is hard to generalize to unseen cases. In this paper, we introduce Unsupervised Visual CoT (UV-Cot), a novel framework for image-level CoT reasoning via preference optimization. UV-Cot performs preference comparisons between model-generated bounding boxes (one is preferred and the other is dis-preferred), eliminating the need for bounding-box annotations. We get such preference data by introducing an automatic data generation pipeline. Given an image, our target MLLM (e.g., LLaVA-1.5-7B) generates seed bounding boxes using a template prompt and then answers the question using each bounded region as input. An evaluator MLLM (e.g., OmniLLM-12B) ranks the responses, and these rankings serve as supervision to train the target MLLM with UV-Cot by minimizing negative log-likelihood losses. By emulating human perception-identifying key regions and reasoning based on them-UV-Cot can improve visual comprehension, particularly in spatial reasoning tasks where textual descriptions alone fall short. Our experiments on six datasets demonstrate the superiority of UV-Cot, compared to the state-of-the-art textual and visual CoT methods. Our zero-shot testing on four unseen datasets shows the strong generalization of UV-Cot.",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "With the recent advancements in multimodal large language models (MLLMs) [3, 21, 22, 45], many efforts have been made to incorporate text CoT reasoning [9, 17, 40, 49] to",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "handle complex vision-language tasks [42, 43, 50]. However, the visual understanding ability of MLLM is limited by fixed-granularity image processing, i.e., the MLLM cannot dynamically adjust focus across different spatial regions of the input image, even when guided by text CoT prompts [11]. This underscores the critical need to explicitly integrate visual cues into the CoT process.",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "A very recent work, Visual-CoT [35], has made an initial attempt towards this goal. The model is trained using supervised fine-tuning (SFT) with human-labeled bounding boxes that indicate the key image regions relevant to the question. It performs the multimodal CoT approach with human-annotated reasoning steps by associating textual inputs with the detected regions. An overview of Visual-CoT is presented in Fig. 1. However, it has two key drawbacks: (1) it relies on large-scale, high-quality labeled data, making it costly and hard to scale; and (2) SFT learns only from positive examples (i.e., the labeled data), limiting its ability to generalize to unseen or ambiguous scenarios where intermediate reasoning or dynamic interpretation is needed.",
+ "bbox": [
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+ "type": "text",
+ "text": "To address these issues, we introduce an Unsupervised approach to Visual CoT dubbed as UV-CoT. It has two key parts: data collection and model training. The data collection does not need human annotation, as it leverages the data generation and evaluation capabilities of pre-trained MLLMs. The model training is inspired by the idea of direct preference optimization (DPO). It is implemented with an adapted version of DPO to address specific limitations in capturing the degree of preference and fine-grained region-based reasoning when conducting visual CoT on MLLMs.",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "Our method UV-CoT, as shown in Fig. 1, differs from Visual-CoT [35] by adopting an unsupervised approach with contrastive preference data. We design an automatic two-step pipeline to generate this data: 1) Region Generation: Given an image, the target model generates multiple seed bounding boxes using a template prompt. Then it answers the question by processing each bounded region together with the question as input. 2) Quality Assessment: An evaluator MLLM scores the responses, using these scores as proxies to measure the quality of the regions.",
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+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
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+ {
+ "type": "page_footnote",
+ "text": "*Corresponding author. The code is available in https://github.com/kesenzhao/UV-CoT.",
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+ "page_idx": 0
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+ "text": "2303",
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+ {
+ "type": "image",
+ "img_path": "images/cece163b4bafccc0138bd475d4c40b1d2628f2006a000c706b6d66fe1f432a99.jpg",
+ "image_caption": [
+ "Figure 1. Comparison of Visual-CoT [35] and our UV-CoT. Left: Visual-CoT relies on human-annotated bounding boxes to identify key regions. The model is trained via supervised fine-tuning to maximize the likelihood of the labeled data. Right: UV-CoT eliminates the need for human annotation. Given an image, the target model generates seed bounding boxes and answers questions based on these regions, respectively. An evaluator MLLM then scores the responses as a proxy for assessing region quality. Lastly, the target model is optimized via preference optimization by maximizing the likelihood of preferred regions over dis-preferred ones."
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+ "image_footnote": [],
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+ {
+ "type": "image",
+ "img_path": "images/db461ee0fe0e05f3abffdc4e2b0da94fca5fbc3b9b1a632f257ac83baf32bdc0.jpg",
+ "image_caption": [],
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+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Unlike traditional DPO, we propose Score-DPO (sDPO), which not only ranks preference data (i.e., preferred and dis-preferred responses shown in Fig. 1) but also assigns preference scores. This scoring enables more precise optimization based on score differences. During UV-CoT training, the rankings of the preference data act as supervision by minimizing negative log-likelihood loss, while the scores define the decision margin. By mimicking human perception—first identifying key regions, then reasoning over them—UV-CoT significantly improves visual comprehension, especially in spatial reasoning tasks where text-based methods fall short. By leveraging unsupervised data in a contrastive way, UV-CoT also shows strong generalization ability when tested on unseen datasets.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Our contributions in this paper include: 1) an automatic pipeline for generating high-quality preference data, enabling robust and scalable preference learning of UV-CoT; 2) an improved version of DPO by integrating the degree of preference for visual regions, allowing the model to distinguish key regions more precisely; and 3) extensive experiments on multiple challenging datasets, demonstrating state-of-the-art performance of UV-CoT on four benchmarks and strong generalization to four unseen test datasets.",
+ "bbox": [
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+ "text": "2. Related Works",
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+ {
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+ "text": "Chain-of-thought in LLMs and MLLMs. LLMs [3, 10, 14, 24, 29, 38] with CoT [5, 8, 40] show strong inferential abilities by introducing intermediate reasoning steps. Both manually designed [40] and self-generated [17, 49] reason-",
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "ing approaches have proven effective. In contrast, MLLMs rely on image encoders [15, 32, 52-54] to extract visual features but often struggle with reasoning due to inherent differences in how textual and visual data are processed [23, 48, 51]. Multimodal CoT methods [42, 43, 50] attempt to address this by transforming multimodal inputs into a unified textual format, enabling LLMs to perform CoT at the text level. However, this transformation introduces significant information loss and prevents the models from capturing key visual details [50]. For example, LLaVA-CoT [42] leverages GPT-4o to summarize questions and image captions but suffers from weak optical character recognition and sometimes hallucinations.",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "A very recent work, Visual-CoT [35], improves the MLLM reasoning by introducing CoT methods at the image level. This approach involves scanning the entire image, identifying key references, and then focusing the model on specific regions for reasoning. Despite its improvements, Visual-CoT is heavily based on costly human-annotated data. In contrast, our UV-CoT framework utilizes unsupervised preference optimization with auto-generated preference data, eliminating the need for manual annotations.",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "Preference learning in LLMs and MLLMs. RLHF [56] aligns LLMs with human preferences by training a reward model via contrastive response evaluations. To reduce reliance on human annotations, RLAIF [19] leverages pretrained LLMs for preference label generation. However, RL-based fine-tuning faces stability and efficiency challenges. Direct Preference Optimization (DPO) [33] ad",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "header",
+ "text": "$f_{tar}$ Target Model",
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+ "text": "$f_{eval}$ Evaluator Model",
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+ {
+ "type": "header",
+ "text": "D",
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+ "type": "header",
+ "text": "Preference Data",
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+ {
+ "type": "page_number",
+ "text": "2304",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "image",
+ "img_path": "images/9b9ff29162e631ac3d3671cfe43fb009176c0298cc271976596163b874e24560.jpg",
+ "image_caption": [
+ "Figure 2. Illustration of UV-CoT reasoning."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "dresses this by directly linking reward functions to optimal policies, eliminating reward model fine-tuning. Further improvements include IPO [2], which mitigates overfitting with a bounded preference function, and KTO [7], which removes the need for paired preference data, relying instead on single examples labeled as either 'good' or 'bad'.",
+ "bbox": [
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "These preference learning techniques are applied to MLLMs, with RLHF-V and RLAIF-V [46, 47] refining behavior alignments using human and LLM-generated labels. To mitigate reward hacking, Sun et al. [37] enhance reward models with additional factual details, such as image captions and verified choices, further improving the performance of MLLM. Some works have attempted to apply DPO in the CoT process [18, 30]. However, these methods are designed for only text-level CoT and do not effectively handle visual features or cues. In contrast, in this paper, we propose UV-CoT, a specialized framework for image-level CoT reasoning inspired by the idea of DPO. Unlike traditional DPO, UV-CoT not only ranks preference data (i.e., preferred and dis-preferred data) but also assigns preference scores. This scoring enables more precise optimization of the MLLMs based on score differences.",
+ "bbox": [
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+ "page_idx": 2
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+ "type": "text",
+ "text": "3. Method",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 2
+ },
+ {
+ "type": "text",
+ "text": "Fig. 2 illustrates the pipeline of UV-CoT reasoning. Given the original image and the question, we append a CoT prompt to guide the target MLLM in identifying the most informative image region and specifying its location via bounding box coordinates. A visual sampler then extracts the bounded region from the image. The MLLM subsequently integrates visual tokens from original and cropped images to generate more precise and comprehensive answers. In Sec. 3.1, we detail the automatic preference data generation pipeline. In Sec. 3.2, we describe our Score-",
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "Algorithm 1 Preference data generation for a query $x$",
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+ "page_idx": 2
+ },
+ {
+ "type": "list",
+ "sub_type": "text",
+ "list_items": [
+ "1: Input: Target model $f_{\\mathrm{tar}}$ , evaluator $f_{\\mathrm{eval}}$ , an image-question query $x$ , number of seeds $n$ , and number of preference pairs $k$ .",
+ "2: Output: Preference data $\\mathcal{D}$",
+ "3: Initialize $y_0 = x$",
+ "4: for $t = 1$ to $T$ do",
+ "5: $\\{y_t^i\\}_{i = 1}^n\\gets \\text{Generate}(f_{\\text{tar}},y_{0:t - 1},n)$",
+ "6: $\\{s^i\\}_{i = 1}^n\\gets \\text{Evaluate}(f_{\\text{eval}},y_{0:t - 1},\\{y_{t}^i\\}_{i = 1}^n)$",
+ "7: $\\mathcal{D}_t\\gets \\mathrm{ConstructPairs}(y_{0:t - 1},\\{y_t^i\\}_{i = 1}^n,\\{s^i\\}_{i = 1}^n,k)$",
+ "8: $y_{t}\\gets \\mathsf{Select}(y_{0:t - 1},\\{y_{t}^{i}\\}_{i = 1}^{n},\\{s^{i}\\}_{i = 1}^{n})$",
+ "9: end for",
+ "10: return $\\mathcal{D} = \\{\\mathcal{D}_1, \\dots, \\mathcal{D}_T\\}$"
+ ],
+ "bbox": [
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "DPO (sDPO) for image-level CoT reasoning.",
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+ "type": "text",
+ "text": "3.1. Preference Data Generation",
+ "text_level": 1,
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+ "text": "Given a target model $f_{\\mathrm{tar}}$ , an evaluator model $f_{\\mathrm{eval}}$ (the target MLLM can also serve as the evaluator, validated in Tab. 5), and an image-question pair $x$ , we illustrate how to construct $n$ preference data points. Assuming there are $T$ steps in CoT reasoning process, we generate preference data for $T$ times on the way, as described in Algorithm 1. At each timestep $t$ (i.e., a reasoning step $t$ ), the process includes four stages: Response Generation, Response Evaluation, Pair Construction, and Response Selection.",
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+ "text": "Response generation. The goal of this stage is to generate seed bounding boxes and produce intermediate responses to the question using the target model. Here, a 'response' refers to any model output at an intermediate step, not necessarily the final answer to the question. We denote the model's response at timestep $t$ as $y_{t}$ , with the initial input $x$ represented as $y_{0}$ . To encourage diversity in the bounding boxes and subsequent responses, we apply stochastic decoding to the target model $f_{\\mathrm{tar}}$ with $n$ different random seeds, resulting in a set of responses $\\{y_t^i\\}_{i = 1}^n$ .",
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+ "text": "Response evaluation. This stage evaluates the quality of all generated responses. The evaluator model not only scores each individual response but also counts how this response influences the quality of its next response in the chain. This cumulative evaluation approach helps quantify the impact of each bounded region on the overall reasoning process. Below, we elaborate on the formulation. At timestep $t$ , the evaluator assigns scores for $y_{t}^{i}$ as follows:",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} s _ {\\text {c u r}} ^ {i} = f _ {\\text {e v a l}} \\left(y _ {t} ^ {i} \\mid y _ {0: t - 1}\\right), \\\\ s _ {n x t} ^ {i} = \\mathbb {E} \\left[ f _ {\\text {e v a l}} \\left(y _ {t + 1} ^ {i} \\mid y _ {0: t - 1}, y _ {t} ^ {i}\\right) \\right], \\tag {1} \\\\ s ^ {i} = s _ {\\text {c u r}} ^ {i} + \\gamma s _ {\\text {n x t}} ^ {i}, \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "where $s_{\\mathrm{nxt}}^i$ reflects the impact on the next response and $\\gamma > 0$ is a hyperparameter to combine the current and next",
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+ "type": "page_number",
+ "text": "2305",
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+ "type": "text",
+ "text": "response scores, with $\\gamma = 0$ at the last step. We estimate the expectation $\\mathbb{E}[\\cdot ]$ by randomly sampling next responses.",
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+ "text": "Pair construction. At each timestep $t$ , we randomly select $k$ (preferred and dis-preferred) pairs from $\\{y_t^i\\}_{i=1}^n$ . For a single pair, we concatenate the preferred response with the past response chain $y_{0:t-1}$ (preserved after $t-1$ timesteps) and get a \"preferred chain\" denoted as $y_t^w$ , and then we concatenate the dis-preferred response in the same way to get a \"dis-preferred chain\" denoted as $y_t^l$ . The pair of chains also includes their respective scores, and they are represented as $\\{y_w, s_w, y_l, s_l\\}$ . The overall $k$ pairs of chains compose the preference dataset $\\mathcal{D}_t$ .",
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+ "text": "Response selection. The abovementioned 'past response chain $y_{0:t-1}$ ' is unique and is concatenated by the highest-scoring response at timestep $t-1$ and the preserved chain at timestep $t=2$ , i.e., $y_{0:t-2}$ . In other words, when finishing each timestep process, we preserve only the best chain and use it for the next step.",
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+ "type": "text",
+ "text": "3.2. Unsupervised Learning of UV-CoT",
+ "text_level": 1,
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+ "text": "Assume the preference dataset $\\mathcal{D}$ has been generated across $t$ timesteps, we then optimize the target model with our UV-CoT via preference optimization on $\\mathcal{D}$ . DPO [1] is widely used in preference learning, and it ranks responses without quantifying preference intensity. In our case of image-level reasoning, key regions vary in influence, necessitating finer differentiation between responses. Therefore, we refine DPO by adjusting the margin to capture the key region's influence. We name our loss Score-DPO, abbreviated as sDPO, as it incorporates the preference score into the optimization. The loss is formulated as:",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {s D P O}} (\\theta) = - \\underset {(x, y _ {w}, y _ {l}) \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\log \\sigma \\left(\\beta \\log \\frac {\\pi_ {\\theta} (y _ {w} \\mid x)}{\\pi_ {\\mathrm {r e f}} (y _ {w} \\mid x)} \\right. \\right. \\\\ \\left. \\left. - \\beta \\log \\frac {\\pi_ {\\theta} \\left(y _ {l} \\mid x\\right)}{\\pi_ {\\mathrm {r e f}} \\left(y _ {l} \\mid x\\right)} - \\left(g \\left(s _ {w}\\right) - g \\left(s _ {l}\\right)\\right)\\right) \\right], \\tag {2} \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "where $\\pi_{\\theta}$ is the target model, and $\\pi_{\\mathrm{ref}}$ is its frozen initialization, serving as a reference to constrain deviation from the original model. $g(\\cdot):\\mathbb{R}\\to \\mathbb{R}$ is a monotonically increasing function that maps preference scores into the logit space of the DPO objective.",
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+ "type": "text",
+ "text": "To provide a deeper understanding of our sDPO loss, we establish its connection to the standard DPO loss. DPO reformulates reward model training as policy optimization by reparameterizing the reward function in PPO [34]:",
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+ "type": "equation",
+ "text": "\n$$\nr (x, y) = \\beta \\log \\frac {\\pi_ {\\theta} (y \\mid x)}{\\pi_ {\\text {r e f}} (y \\mid x)} + \\beta \\log Z (x) \\tag {3}\n$$\n",
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+ "type": "text",
+ "text": "Using the Bradley-Terry [4] model, the standard DPO aims to minimize the negative log-likelihood of the difference of",
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+ {
+ "type": "text",
+ "text": "Algorithm 2 Iterative learning of UV-CoT",
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+ "type": "text",
+ "text": "1: Input: Initial target model $f_{\\mathrm{tar}}^{1}$ , evaluator model $f_{\\mathrm{eval}}$ , $\\mathcal{X} = \\{\\mathcal{X}_1, \\dots, \\mathcal{X}_m\\}$ , each $\\mathcal{X}_i$ is a subset of image-question query",
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+ "2: Output: $f_{\\mathrm{tar}}^{m}$",
+ "3: for $i = 1$ to $m$ do",
+ "4: $\\mathcal{D}_i\\gets$ GenerateData $(f_{\\mathrm{tar}}^i,f_{\\mathrm{eval}},\\mathcal{X}_i)$ $\\triangleright$ Algorithm 1",
+ "5: $f_{\\mathrm{tar}}^{i + 1}\\gets \\mathrm{Train}(f_{\\mathrm{tar}}^i,\\mathcal{D}_i)$ $\\triangleright$ Eq. (2)",
+ "6: end for",
+ "7: return $f_{\\mathrm{tar}}^{m}$"
+ ],
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+ "type": "text",
+ "text": "rewards between paired responses:",
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+ "type": "equation",
+ "text": "\n$$\nP \\left(y _ {w} - y _ {l} > 0\\right) = \\sigma \\left(r \\left(x, y _ {w}\\right) - r \\left(x, y _ {l}\\right)\\right) \\tag {4}\n$$\n",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\mathrm {D P O}} = - \\mathbb {E} _ {(x, y _ {w}, y _ {l}) \\sim \\mathcal {D}} [ \\log P (y _ {w} - y _ {l} > 0) ],\n$$\n",
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+ {
+ "type": "text",
+ "text": "where $\\sigma (x) = \\frac{1}{1 + \\exp(-x)}$ is the sigmoid function.",
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+ {
+ "type": "text",
+ "text": "Let $\\Delta_r = g(s_w) - g(s_l)$ and define the Gumbeldistributed random variables $R_{w}\\sim \\mathrm{Gumbel}(r(x,y_{w}),1)$ and $R_{l}\\sim \\mathrm{Gumbel}(r(x,y_{l}),1)$ . Then, we derive:",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} P \\left(R _ {w} - R _ {l} > \\Delta_ {r}\\right) = \\sigma \\left(r \\left(x, y _ {w}\\right) - r \\left(x, y _ {l}\\right) - \\Delta r\\right) \\\\ = \\sigma \\left(\\beta \\log \\frac {\\pi^ {*} (y _ {w} \\mid x)}{\\pi_ {\\text {r e f}} (y _ {w} \\mid x)} - \\beta \\log \\frac {\\pi^ {*} (y _ {l} \\mid x)}{\\pi_ {\\text {r e f}} (y _ {l} \\mid x)} - \\Delta r\\right) \\tag {5} \\\\ \\end{array}\n$$\n",
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+ "text": "This result follows from the definition of Gumbel random variables [1] and the Gumbel-max trick [25]. We provide a detailed proof in Appendix B. By maximizing the log-likelihood, we obtain our proposed loss function. The Gumbel distribution models the extreme values of a variable, while $\\Delta_{\\tau}$ quantifies the degree of difference between preference pairs. Thus, our loss function explicitly optimizes preference learning by distinguishing not only the order but also the magnitude of preference differences.",
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+ "type": "text",
+ "text": "Iterative learning. Standard DPO relies on static preference data during training, which can lead to distributional mismatch between training data and the model's generated outputs. To mitigate this issue, we adopt an iterative learning approach inspired by [47]. Algorithm 2 outlines the iterative learning process of UV-CoT, which incrementally refines a target model through preference learning. The iteration repeats $m$ times, and the total image-question query set $\\mathcal{X}$ is evenly divided into $m$ subsets, $\\mathcal{X} = \\{\\mathcal{X}_1, \\dots, \\mathcal{X}_m\\}$ , each assigned to one iteration. The process starts with an initial target model $f_{\\mathrm{tar}}$ , an evaluator model $f_{\\mathrm{eval}}$ , and $\\mathcal{X}$ . In each iteration $i$ , the algorithm first generates preference data $\\mathcal{D}_i$ using the current target model $f_{\\mathrm{tar}}^i$ and the subset $\\mathcal{X}_i$ , using the procedure in Algorithm 1. This newly generated preference data is then used to train the next iteration of the target model $f_{\\mathrm{tar}}^{i+1}$ using our UV-CoT loss of Eq. (2). The process continues until the final model $f_{\\mathrm{tar}}^m$ is obtained. By dynamically updating the preference data, our approach",
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+ "type": "page_number",
+ "text": "2306",
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+ {
+ "type": "table",
+ "img_path": "images/1ffb09f7e4094269f1bc19baa8a03ca43278d4cca023753242d185c31c5f4b01.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| MLLM | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| LLaVA-1.5-7B | 0.198 | 0.507 | 0.131 | 0.539 | 0.480 | 0.504 | 0.393 |
| LLaVA-1.5-13B | 0.225 | 0.543 | 0.169 | 0.607 | 0.506 | 0.512 | 0.427 |
| MiniCPM-o-8B | 0.232 | 0.529 | 0.175 | 0.618 | 0.495 | 0.521 | 0.428 |
| OmniLMM-12B | 0.254 | 0.578 | 0.172 | 0.621 | 0.509 | 0.523 | 0.443 |
| Visual-CoT-7B (100% label) | 0.294 | 0.673 | 0.194 | 0.652 | 0.546 | 0.532 | 0.482 |
| UV-CoT (0% label) | 0.265 | 0.686 | 0.173 | 0.632 | 0.536 | 0.548 | 0.473 |
| UV-CoT (10% label) | 0.283 | 0.711 | 0.198 | 0.649 | 0.568 | 0.553 | 0.494 |
",
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+ "type": "table",
+ "img_path": "images/4125b69619efd602dbca817c26be7a63f9da09885f48e4c4df2bc67f53a69017.jpg",
+ "table_caption": [
+ "Table 1. Overall comparison of different models on six evaluation benchmarks. The best result is bold, the second-best is underlined. %' indicates the percentage of supervised data used in Visual-CoT. By default, our UV-CoT uses only unsupervised data."
+ ],
+ "table_footnote": [],
+ "table_body": "| MLLM | DUDE | SROIE | Visual7w | Average |
| LLaVA-1.5-7B | 0.165 | 0.147 | 0.340 | 0.217 |
| LLaVA-1.5-13B | 0.174 | 0.159 | 0.352 | 0.228 |
| MiniCPM-o-8B | 0.182 | 0.165 | 0.341 | 0.229 |
| OmniLMM-12B | 0.194 | 0.166 | 0.357 | 0.239 |
| Visual-CoT-7B | 0.206 | 0.181 | 0.397 | 0.261 |
| UV-Cot | 0.241 | 0.184 | 0.432 | 0.286 |
| UV-Cot* | 0.253 | 0.227 | 0.455 | 0.312 |
",
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+ {
+ "type": "text",
+ "text": "ensures that the learned model adapts to its evolving distribution, enhancing training robustness.",
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+ },
+ {
+ "type": "text",
+ "text": "4. Experiments",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "4.1. Setup",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "Datasets. For a comprehensive evaluation, we adopt ten datasets spanning five domains: (1) Text/Document: DocVQA [26], TextVQA [36], DUDE [39], and SROIE [12]. (2) Chart: InfographicsVQA [27]. (3) General VQA: Flickr30k [31] and Visual7W [55]. (4) Relation Reasoning: VSR [20] and GQA [13]. (5) High-Resolution Image Reasoning: $\\mathrm{V}^{*}$ Bench [41]. Notably, we also provide a model trained on data excluding DUDE, SROIE, Visual7W, and $\\mathrm{V}^{*}$ Bench, which is used to evaluate zero-shot performance. See Appendix C.1 for details.",
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+ "type": "text",
+ "text": "Evaluation. Following prior work [22], we prompt GPT-4o [28] to assign a score between 0 and 1, with higher scores indicating better prediction. See details in Appendix C.2.",
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+ "type": "text",
+ "text": "Baselines. We compare UV-CoT with five baselines. LLaVA-1.5-{7B, 13B} [21] and OmniLMM-12B are strong general baselines. MiniCPM-o-8B [44] adopts adaptive visual encoding for fine-grained understanding and Visual-CoT-7B [35] learns image-level CoT via SFT.",
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+ "type": "text",
+ "text": "Implementation details. We use LLaVA-1.5-7B as the tar",
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+ "img_path": "images/052d27b4a94f92b8c61be0d7e450befc876c8604dfe90f528f23d50040dc98b4.jpg",
+ "table_caption": [
+ "Table 2. Zero-shot experiments on DUDE, SROIE and Visual7w. 'UV-CoT' denotes our model trained with additional unlabeled preference data from the three zero-shot datasets."
+ ],
+ "table_footnote": [],
+ "table_body": "| MLLM | Attributes | GPT4V-hard | OCR | Average |
| LLaVA-1.5-7B | 0.317 | 0 | 0.1 | 0.139 |
| LLaVA-1.5-13B | 0.326 | 0.118 | 0.133 | 0.192 |
| MiniCPM-o-8B | 0.322 | 0.118 | 0.1 | 0.180 |
| OmniLMM-12B | 0.326 | 0.118 | 0.167 | 0.204 |
| Visual-CoT-7B | 0.330 | 0.118 | 0.593 | 0.347 |
| UV-CoT | 0.352 | 0.176 | 0.677 | 0.402 |
",
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+ "type": "text",
+ "text": "Table 3. Zero-shot experiments on $\\mathrm{V}^*$ Bench (high-resolution image reasoning task, average resolution $2246 \\times 1582$ ).",
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+ {
+ "type": "text",
+ "text": "get model and OmniLMM-12B as the evaluator. To ensure scalability, we avoid using GPT-4 as the evaluator, preventing constraints imposed by high API costs. We implement iterative learning of UV-CoT over four iterations, utilizing a total of 249K preference data pairs. Notably, UV-CoT achieves higher data efficiency than Visual-CoT, which uses 376K data pairs. For each iteration, we train the model with AdamW optimizer for 4 epochs with a learning rate of $5 \\times 10^{-7}$ , $\\beta = 0.1$ , and a batch size of 8. In total, data generation takes 80 hours and training requires 60 hours, both conducted on an $8 \\times A100$ 40GB machine. Additionally, we provide a variant UV-CoT trained with extra SFT on $10\\%$ of the labeled Visual-CoT data, denoted as UV-CoT (10%).",
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+ "type": "text",
+ "text": "4.2. Comparison with State-of-the-Art Methods",
+ "text_level": 1,
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+ "type": "text",
+ "text": "The overall performance comparisons are reported in Tab. 1, leading to the following key observations:",
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+ "type": "text",
+ "text": "Explicitly incorporating visual cues proves beneficial for multimodal reasoning. For instance, MiniCPM-o-8B, which uses rule-based cropping to focus on salient regions, outperforms LLaVA-1.5-7B by an average of $3.5\\%$ . However, its reliance on heuristics limits adaptability. In contrast, image-level CoT models like Visual-CoT and our UV-CoT achieve greater performance gains, even surpassing the larger LLaVA-1.5-13B, by leveraging MLLMs to adaptively generate key visual regions. This highlights the superior effectiveness of image-level CoT reasoning.",
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+ "text": "2307",
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+ "type": "table",
+ "img_path": "images/f25f9c5d0ce33c940dc0cc582ebaf8f532ed48c41852c459466b448ab211e081.jpg",
+ "table_caption": [],
+ "table_footnote": [
+ "Table 4. Ablation study on key components of UV-CoT (10% labeled data). 'w/o UV-CoT' denotes standard inference without CoT reasoning. 'UV-CoT w/ G.T. BBox' uses annotated ground truth bounding boxes. 'w/ naive DPO' applies the standard DPO loss. 'w/o iterative learning' generates preference pairs for the entire set of question queries $\\mathcal{X}$ in a single pass and trains once. 'w/o $\\gamma$ evaluates responses with $\\gamma = 0$ . IF, Tr, and Ge indicate ablations on the inference process, training loss, and data generation, respectively."
+ ],
+ "table_body": "| Model | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| UV-CoT (10% labels) | 0.283 | 0.711 | 0.198 | 0.649 | 0.568 | 0.553 | 0.494 |
| IF: w/o UV-CoT | 0.149 | 0.574 | 0.160 | 0.585 | 0.509 | 0.522 | 0.417 |
| IF: UV-CoT w/ G.T. BBox | 0.528 | 0.769 | 0.504 | 0.655 | 0.664 | 0.585 | 0.618 |
| Tr: w/ naive DPO | 0.258 | 0.695 | 0.189 | 0.623 | 0.552 | 0.534 | 0.475 |
| Tr: w/o iterative learning | 0.256 | 0.671 | 0.162 | 0.609 | 0.523 | 0.531 | 0.459 |
| Ge: w/o γ | 0.247 | 0.539 | 0.152 | 0.551 | 0.484 | 0.460 | 0.406 |
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+ "text": "UV-CoT fundamentally differs from distillation/pseudolabeling. Unlike distillation, where student performance is typically bounded by the teacher, UV-CoT outperforms its evaluator OmniLMM-12B by $5.1\\%$ on average. This suggests that UV-CoT goes beyond simply mimicking a larger model. Direct generation of accurate bounding boxes remains a challenge for MLLMs due to the need for precise spatial localization. Instead, UV-CoT reformulates the task as ranking—an inherently simpler and more tractable problem—which leads to better performance.",
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+ "text": "UV-CoT outperforms the supervised Visual-CoT. Despite using significantly less data (249K unlabeled vs. 376K labeled), UV-CoT outperforms Visual-CoT-7B on TextVQA $(+1.3\\%)$ and VSR $(+1.6\\%)$ . Moreover, UV-CoT $(10\\%)$ surpasses Visual-CoT-7B by $2.1\\%$ on average, with notable gains on TextVQA $(+2.5\\%)$ , GQA $(+2.2\\%)$ , and VSR $(+2.1\\%)$ and achieves comparable or better performance on the remaining datasets. This validates the effectiveness of our high-quality preference data generation and enhanced preference optimization method.",
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+ "text": "4.3. Zero-Shot Generalization",
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+ "text": "We evaluate the zero-shot performance of UV-CoT on the test sets of SROIE, DUDE, Visual7W, and V* Bench [41], without any training exposure to these datasets. V* Bench is a high-resolution benchmark (avg. size: $2246 \\times 1582$ ) covering diverse tasks; we focus on three representative ones: Attributes (object attribute recognition), GPT4V-Hard (complex visual reasoning), and OCR. Additionally, we train a variant of our model, UV-CoT*, using preference data generated from the training splits of SROIE, DUDE, and Visual7W. The results are reported in Tab. 2 and Tab. 3, leading to the following observations:",
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+ "text": "UV-CoT exhibits stronger zero-shot performance. Supervised CoT learning relies on labeled data and often overfits to specific annotation distributions, limiting its generalization to unseen tasks. In contrast, UV-CoT uses preference optimization based on relative comparisons, avoiding reliance on absolute labels and enhancing general",
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+ "text": "ization. As a result, UV-CoT outperforms all baselines across zero-shot datasets $(+2.5\\%$ on average), with notable gains on DUDE and Visual7W (both $+3.5\\%$ ). Furthermore, UV-CoT* achieves greater gains $(5.1\\%$ on average), showing that our model can effectively learn the image-level CoT process without the need for costly human annotation.",
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+ "text": "UV-CoT excels in high-resolution image reasoning. Image-level CoT methods—UV-CoT (+19.8%) and Visual-CoT-7B (+14.3%)—significantly outperform non-CoT baselines, with over 50% gains on OCR tasks. UV-CoT further surpasses Visual-CoT-7B by 5.5% on average, achieving the best performance across all tasks. This large performance gap underscores the advantage of unsupervised image-level CoT for high-resolution visual reasoning.",
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+ "text": "4.4. Ablation Studies",
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+ "text": "In Tab. 4, we present the ablations on key components.",
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+ "text": "Image-level CoT: We design two variants to evaluate the impact of image-level CoT: (1) 'w/o UV-Cot' removes intermediate reasoning and directly outputs answers; (2) 'UV-Cot w/ G.T. BBox' replaces predicted regions with ground truth bounding boxes to assess localization quality. Results show that removing CoT leads to a significant drop $(-7.7\\%)$ on average), confirming its necessity. On Flickr30k, UV-Cot matches the G.T. variant, suggesting accurate region selection. However, in DocVQA and InfographicsVQA, using G.T. boxes yields better performance, revealing the difficulty of precise localization. This highlights the potential of our method and suggests future work for improving region accuracy for complex tasks.",
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+ "text": "Score-DPO (sDPO): 'w/ naive DPO' applies standard DPO loss and shows degraded performance across all datasets (1.9% on average), especially on DocVQA (2.5%) and Flickr30k (2.6%), revealing its limitations for CoT learning. In contrast, our sDPO incorporates preference scores to better differentiate choices, yielding consistent gains.",
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+ "text": "Iterative learning: 'w/o iterative learning' generates all preference pairs in a single pass and trains only once, leading to a significant performance drop (3.5% on average).",
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+ "Figure 3. (a&b) Bounding box evaluation on (a) training datasets and (b) zero-shot datasets. Our UV-CoT performs better than Visual-CoT. (c) Model performance under varying visual token sizes. Our UV-CoT demonstrates better token efficiency."
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+ "table_body": "| Model | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| OmniLMM-12B | 0.254 | 0.578 | 0.172 | 0.621 | 0.509 | 0.523 | 0.443 |
| IF: OmniLMM-12B + CoT | 0.305 | 0.722 | 0.217 | 0.675 | 0.580 | 0.595 | 0.516 |
| LLaVA-1.5-7B | 0.198 | 0.507 | 0.131 | 0.539 | 0.480 | 0.504 | 0.393 |
| IF: LLaVA-1.5-7B + CoT | 0.245 | 0.577 | 0.149 | 0.606 | 0.530 | 0.533 | 0.440 |
| Tr: UV-CoT (Evaluator: self-evaluated) | 0.242 | 0.609 | 0.153 | 0.598 | 0.517 | 0.526 | 0.441 |
| Tr: UV-CoT (Evaluator: OmniLMM-12B) | 0.265 | 0.686 | 0.173 | 0.632 | 0.536 | 0.548 | 0.473 |
",
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+ "text": "Table 5. Analysis of evaluator model. $^+$ CoT' refers to inference assisted by bounding boxes generated by UV-CoT. Self-evaluated denotes using target model as the evaluator during training. IF and Tr indicate experiments conducted on the inference and training process.",
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+ "text": "This underscores the importance of iterative learning in continuously aligning the preference data distribution with the model's evolving policy throughout the training process.",
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+ "text": "Response evaluation: 'w/o $\\gamma$ model' sets $\\gamma = 0$ during response evaluation stage, ignoring the next response when generating preference scores. We observe a significant performance drop (8.8% on average), particularly on TextVQA (17.2%), highlighting the difficulty MLLMs face in directly evaluating bounding boxes. This underscores the necessity of incorporating next response in our evaluation method.",
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+ "text": "4.5. Bounding Box Evaluation",
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+ "text": "We compare the quality of bounding boxes learned from supervised and unsupervised strategies using GPT-4o as a scorer, on both training datasets (Fig. 3 (a)) and zero-shot datasets (Fig. 3 (b)). Our main observations are:",
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+ "(1) Our UV-CoT outperforms Visual-CoT-7B, achieving higher scores in five of six datasets, supporting its superior performance in generating helpful bounding box.",
+ "(2) The bounding box quality is closely related to the final performance. Our model exhibits lower scores (below 0.210) for bounding box generation in DocVQA and InfographicsVQA, correlating with its reduced final scores in these datasets (below 0.290 in Tab. 1). It underscores the validity of evaluating bounding box quality through its impact on subsequent answers.",
+ "(3) Both UV-CoT and UV-CoT* outperform Visual-CoT"
+ ],
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+ "text": "7B across all zero-shot datasets, which illustrates the strong generalization of our method in bounding box generation.",
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+ "text": "4.6. Insight of Evaluator Model",
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+ "text": "We further perform studies to better understand the role of evaluator model. Key findings from Tab. 5 are:",
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+ "(1) We compare UV-CoT with its self-evaluated variant, where the evaluator model is the same as the target model (initiated with LLaVA-1.5-7B). Although the self-evaluated version exhibits a performance decrease of $3.2\\%$ compared to the original UV-CoT, it still outperforms LLaVA-1.5-7B $(+4.8\\%)$ on average) across all evaluated datasets and achieves performance comparable to the larger OmniLMM-12B model $(-0.2\\%)$ on average). This demonstrates that UV-CoT maintains robust performance even under self-evaluation, highlighting its efficiency without requiring larger model scales.",
+ "(2) For OmniLMM-12B and LLaVA-1.5-7B, we incorporate a CoT process using bounding boxes generated by UV-CoT. The CoT-enhanced versions significantly outperform their original counterparts, achieving average performance gains of $4.7\\%$ for LLaVA-1.5-7B and $7.4\\%$ for OmniLMM-12B. Remarkably, these models were not finetuned for the CoT process, indicating that the bounding box information alone substantially improves performance. This finding underscores that our evaluating process simplifies the task of generating complex spatial annotations,"
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+ "text": "2309",
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+ "img_path": "images/2849c61fce4e3680abb99c2bf83da03a592f41f0593cb7dfadbaf5f0a6d376db.jpg",
+ "image_caption": [
+ "Figure 4. Visualization of preference data generated by Algorithm 1. Preferred BBoxes are in red. Dis-preferred BBoxes are in blue."
+ ],
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+ {
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+ "img_path": "images/15b6f7061c76a18c23ecb5991d590da4618b1c6ebe2f0bb396a64c33da75b233.jpg",
+ "image_caption": [
+ "Figure 5. Visualization of our UV-Cot inference. Model-generated bounding boxes are shown in red."
+ ],
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+ "img_path": "images/ee6f102e9730aa1eb4546a37ba425e068889545546691b8a74fd8c15b45fb4d4.jpg",
+ "image_caption": [],
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+ {
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+ "img_path": "images/3beb198ce3baaf11a3ecab1d6d97f5fd0d93c1cd8fa9b601b76ff272bd4797b4.jpg",
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+ {
+ "type": "text",
+ "text": "enabling MLLMs to focus on evaluating final answers.",
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+ "type": "text",
+ "text": "4.7. Other Detailed Analyses",
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+ "sub_type": "text",
+ "list_items": [
+ "Visual token efficiency. Compared to standard MLLM generation, image-level CoT doubles the number of visual tokens by processing additional local image regions. To evaluate token efficiency, i.e., performance under the same visual token budget, we resize the input image to different resolutions $(224^{2}, 336^{2}$ and $448^{2}$ ) and report the average score of different models in Fig. 3(c). Our key findings are: (1) MLLMs with image-level reasoning (Visual-CoT-7B and our UV-CoT) demonstrate better token efficiency than the standard answer generation pipeline. E.g., they achieve higher performance with 512 visual tokens than the standard pipeline does with 1024 tokens.",
+ "(2) Our UV-CoT consistently outperforms Visual-CoT-7B across all scales, achieving higher average scores. This highlights the token efficiency of our method."
+ ],
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+ {
+ "type": "text",
+ "text": "Visualization. Fig. 4 visualizes some preference data from our UV-CoS inference process. Given different local regions and their corresponding answers, the evaluator MLLM assigns reasonable scores, validating the effective",
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+ {
+ "type": "text",
+ "text": "ness of our automatic generation and labeling process. In Fig. 5, we present reasoning cases with model-generated bounding boxes overlaid. The precision of bounding box detection and the depth of understanding play a crucial role in determining the quality of generated answers.",
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+ "type": "text",
+ "text": "5. Conclusion",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "In this work, we propose UV-CoT, a framework that enables image-level CoT reasoning in MLLMs via preference optimization. Unlike previous methods that rely on SFT needing large amounts of labeled data, our approach leverages unsupervised learning to refine the model's ability with image-level CoT using model-generated preference data (which are rough but useful). We address key challenges in preference data generation and effective optimization, ensuring a more adaptive and interpretable reasoning process. Extensive experiments demonstrate that UV-CoT achieves state-of-the-art performance, significantly improving visual comprehension in MLLMs on ten reasoning datasets. Our findings highlight the potential of preference learning as a scalable alternative to traditional SFT, enabling more robust and data-efficient multimodal reasoning.",
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+ "type": "page_number",
+ "text": "2310",
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+ "type": "text",
+ "text": "Acknowledgements",
+ "text_level": 1,
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+ "text": "This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-030). Thanks to Zichen Tian for his assistance with figure visualization throughout this work. The authors also thank the reviewers for their valuable comments and suggestions.",
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+ "text": "References",
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+ "bbox": [
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+ {
+ "type": "list",
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+ ],
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diff --git a/2025/Unsupervised Visual Chain-of-Thought Reasoning via Preference Optimization/2dfcc225-7530-4e71-9b57-14637900f483_model.json b/2025/Unsupervised Visual Chain-of-Thought Reasoning via Preference Optimization/2dfcc225-7530-4e71-9b57-14637900f483_model.json
new file mode 100644
index 0000000000000000000000000000000000000000..7a13af41ddd5c09f41dafc6e4e1bf6159aecc953
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+++ b/2025/Unsupervised Visual Chain-of-Thought Reasoning via Preference Optimization/2dfcc225-7530-4e71-9b57-14637900f483_model.json
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+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+ "content": "Abstract"
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+ "content": "Chain-of-thought (CoT) reasoning greatly improves the interpretability and problem-solving abilities of multimodal large language models (MLLMs). However, existing approaches focus on text CoT, limiting their ability to leverage visual cues. Visual CoT remains underexplored, and the only work [35] is based on supervised fine-tuning that relies on extensive labeled bounding-box data and is hard to generalize to unseen cases. In this paper, we introduce Unsupervised Visual CoT (UV-Cot), a novel framework for image-level CoT reasoning via preference optimization. UV-Cot performs preference comparisons between model-generated bounding boxes (one is preferred and the other is dis-preferred), eliminating the need for bounding-box annotations. We get such preference data by introducing an automatic data generation pipeline. Given an image, our target MLLM (e.g., LLaVA-1.5-7B) generates seed bounding boxes using a template prompt and then answers the question using each bounded region as input. An evaluator MLLM (e.g., OmniLLM-12B) ranks the responses, and these rankings serve as supervision to train the target MLLM with UV-Cot by minimizing negative log-likelihood losses. By emulating human perception-identifying key regions and reasoning based on them-UV-Cot can improve visual comprehension, particularly in spatial reasoning tasks where textual descriptions alone fall short. Our experiments on six datasets demonstrate the superiority of UV-Cot, compared to the state-of-the-art textual and visual CoT methods. Our zero-shot testing on four unseen datasets shows the strong generalization of UV-Cot."
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+ "content": "With the recent advancements in multimodal large language models (MLLMs) [3, 21, 22, 45], many efforts have been made to incorporate text CoT reasoning [9, 17, 40, 49] to"
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+ "content": "handle complex vision-language tasks [42, 43, 50]. However, the visual understanding ability of MLLM is limited by fixed-granularity image processing, i.e., the MLLM cannot dynamically adjust focus across different spatial regions of the input image, even when guided by text CoT prompts [11]. This underscores the critical need to explicitly integrate visual cues into the CoT process."
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+ "content": "A very recent work, Visual-CoT [35], has made an initial attempt towards this goal. The model is trained using supervised fine-tuning (SFT) with human-labeled bounding boxes that indicate the key image regions relevant to the question. It performs the multimodal CoT approach with human-annotated reasoning steps by associating textual inputs with the detected regions. An overview of Visual-CoT is presented in Fig. 1. However, it has two key drawbacks: (1) it relies on large-scale, high-quality labeled data, making it costly and hard to scale; and (2) SFT learns only from positive examples (i.e., the labeled data), limiting its ability to generalize to unseen or ambiguous scenarios where intermediate reasoning or dynamic interpretation is needed."
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+ "content": "To address these issues, we introduce an Unsupervised approach to Visual CoT dubbed as UV-CoT. It has two key parts: data collection and model training. The data collection does not need human annotation, as it leverages the data generation and evaluation capabilities of pre-trained MLLMs. The model training is inspired by the idea of direct preference optimization (DPO). It is implemented with an adapted version of DPO to address specific limitations in capturing the degree of preference and fine-grained region-based reasoning when conducting visual CoT on MLLMs."
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+ "content": "Our method UV-CoT, as shown in Fig. 1, differs from Visual-CoT [35] by adopting an unsupervised approach with contrastive preference data. We design an automatic two-step pipeline to generate this data: 1) Region Generation: Given an image, the target model generates multiple seed bounding boxes using a template prompt. Then it answers the question by processing each bounded region together with the question as input. 2) Quality Assessment: An evaluator MLLM scores the responses, using these scores as proxies to measure the quality of the regions."
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+ "content": "*Corresponding author. The code is available in https://github.com/kesenzhao/UV-CoT."
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+ "content": "\\(f_{tar}\\) Target Model"
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+ "content": "Preference Data"
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+ "content": "Figure 1. Comparison of Visual-CoT [35] and our UV-CoT. Left: Visual-CoT relies on human-annotated bounding boxes to identify key regions. The model is trained via supervised fine-tuning to maximize the likelihood of the labeled data. Right: UV-CoT eliminates the need for human annotation. Given an image, the target model generates seed bounding boxes and answers questions based on these regions, respectively. An evaluator MLLM then scores the responses as a proxy for assessing region quality. Lastly, the target model is optimized via preference optimization by maximizing the likelihood of preferred regions over dis-preferred ones."
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+ "content": "Unlike traditional DPO, we propose Score-DPO (sDPO), which not only ranks preference data (i.e., preferred and dis-preferred responses shown in Fig. 1) but also assigns preference scores. This scoring enables more precise optimization based on score differences. During UV-CoT training, the rankings of the preference data act as supervision by minimizing negative log-likelihood loss, while the scores define the decision margin. By mimicking human perception—first identifying key regions, then reasoning over them—UV-CoT significantly improves visual comprehension, especially in spatial reasoning tasks where text-based methods fall short. By leveraging unsupervised data in a contrastive way, UV-CoT also shows strong generalization ability when tested on unseen datasets."
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+ "content": "Our contributions in this paper include: 1) an automatic pipeline for generating high-quality preference data, enabling robust and scalable preference learning of UV-CoT; 2) an improved version of DPO by integrating the degree of preference for visual regions, allowing the model to distinguish key regions more precisely; and 3) extensive experiments on multiple challenging datasets, demonstrating state-of-the-art performance of UV-CoT on four benchmarks and strong generalization to four unseen test datasets."
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+ "content": "2. Related Works"
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+ "content": "Chain-of-thought in LLMs and MLLMs. LLMs [3, 10, 14, 24, 29, 38] with CoT [5, 8, 40] show strong inferential abilities by introducing intermediate reasoning steps. Both manually designed [40] and self-generated [17, 49] reason-"
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+ "content": "ing approaches have proven effective. In contrast, MLLMs rely on image encoders [15, 32, 52-54] to extract visual features but often struggle with reasoning due to inherent differences in how textual and visual data are processed [23, 48, 51]. Multimodal CoT methods [42, 43, 50] attempt to address this by transforming multimodal inputs into a unified textual format, enabling LLMs to perform CoT at the text level. However, this transformation introduces significant information loss and prevents the models from capturing key visual details [50]. For example, LLaVA-CoT [42] leverages GPT-4o to summarize questions and image captions but suffers from weak optical character recognition and sometimes hallucinations."
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+ "angle": 0,
+ "content": "A very recent work, Visual-CoT [35], improves the MLLM reasoning by introducing CoT methods at the image level. This approach involves scanning the entire image, identifying key references, and then focusing the model on specific regions for reasoning. Despite its improvements, Visual-CoT is heavily based on costly human-annotated data. In contrast, our UV-CoT framework utilizes unsupervised preference optimization with auto-generated preference data, eliminating the need for manual annotations."
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+ "type": "text",
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+ "angle": 0,
+ "content": "Preference learning in LLMs and MLLMs. RLHF [56] aligns LLMs with human preferences by training a reward model via contrastive response evaluations. To reduce reliance on human annotations, RLAIF [19] leverages pretrained LLMs for preference label generation. However, RL-based fine-tuning faces stability and efficiency challenges. Direct Preference Optimization (DPO) [33] ad"
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+ [
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+ "bbox": [
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+ "angle": 0,
+ "content": null
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+ {
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+ "angle": 0,
+ "content": "Figure 2. Illustration of UV-CoT reasoning."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "dresses this by directly linking reward functions to optimal policies, eliminating reward model fine-tuning. Further improvements include IPO [2], which mitigates overfitting with a bounded preference function, and KTO [7], which removes the need for paired preference data, relying instead on single examples labeled as either 'good' or 'bad'."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "These preference learning techniques are applied to MLLMs, with RLHF-V and RLAIF-V [46, 47] refining behavior alignments using human and LLM-generated labels. To mitigate reward hacking, Sun et al. [37] enhance reward models with additional factual details, such as image captions and verified choices, further improving the performance of MLLM. Some works have attempted to apply DPO in the CoT process [18, 30]. However, these methods are designed for only text-level CoT and do not effectively handle visual features or cues. In contrast, in this paper, we propose UV-CoT, a specialized framework for image-level CoT reasoning inspired by the idea of DPO. Unlike traditional DPO, UV-CoT not only ranks preference data (i.e., preferred and dis-preferred data) but also assigns preference scores. This scoring enables more precise optimization of the MLLMs based on score differences."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "content": "3. Method"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Fig. 2 illustrates the pipeline of UV-CoT reasoning. Given the original image and the question, we append a CoT prompt to guide the target MLLM in identifying the most informative image region and specifying its location via bounding box coordinates. A visual sampler then extracts the bounded region from the image. The MLLM subsequently integrates visual tokens from original and cropped images to generate more precise and comprehensive answers. In Sec. 3.1, we detail the automatic preference data generation pipeline. In Sec. 3.2, we describe our Score-"
+ },
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+ "content": "Algorithm 1 Preference data generation for a query \\( x \\)"
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+ "content": "1: Input: Target model \\( f_{\\mathrm{tar}} \\), evaluator \\( f_{\\mathrm{eval}} \\), an image-question query \\( x \\), number of seeds \\( n \\), and number of preference pairs \\( k \\)."
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+ "type": "text",
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+ "angle": 0,
+ "content": "2: Output: Preference data \\(\\mathcal{D}\\)"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "3: Initialize \\( y_0 = x \\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.523,
+ 0.187,
+ 0.661,
+ 0.2
+ ],
+ "angle": 0,
+ "content": "4: for \\( t = 1 \\) to \\( T \\) do"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.523,
+ 0.201,
+ 0.809,
+ 0.217
+ ],
+ "angle": 0,
+ "content": "5: \\(\\{y_t^i\\}_{i = 1}^n\\gets \\text{Generate}(f_{\\text{tar}},y_{0:t - 1},n)\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.523,
+ 0.217,
+ 0.854,
+ 0.233
+ ],
+ "angle": 0,
+ "content": "6: \\(\\{s^i\\}_{i = 1}^n\\gets \\text{Evaluate}(f_{\\text{eval}},y_{0:t - 1},\\{y_{t}^i\\}_{i = 1}^n)\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.523,
+ 0.233,
+ 0.901,
+ 0.248
+ ],
+ "angle": 0,
+ "content": "7: \\(\\mathcal{D}_t\\gets \\mathrm{ConstructPairs}(y_{0:t - 1},\\{y_t^i\\}_{i = 1}^n,\\{s^i\\}_{i = 1}^n,k)\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.523,
+ 0.248,
+ 0.821,
+ 0.264
+ ],
+ "angle": 0,
+ "content": "8: \\(y_{t}\\gets \\mathsf{Select}(y_{0:t - 1},\\{y_{t}^{i}\\}_{i = 1}^{n},\\{s^{i}\\}_{i = 1}^{n})\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.523,
+ 0.264,
+ 0.597,
+ 0.275
+ ],
+ "angle": 0,
+ "content": "9: end for"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.522,
+ 0.277,
+ 0.724,
+ 0.293
+ ],
+ "angle": 0,
+ "content": "10: return \\(\\mathcal{D} = \\{\\mathcal{D}_1, \\dots, \\mathcal{D}_T\\}\\)"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.522,
+ 0.111,
+ 0.907,
+ 0.293
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.514,
+ 0.325,
+ 0.813,
+ 0.34
+ ],
+ "angle": 0,
+ "content": "DPO (sDPO) for image-level CoT reasoning."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.514,
+ 0.352,
+ 0.766,
+ 0.367
+ ],
+ "angle": 0,
+ "content": "3.1. Preference Data Generation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.375,
+ 0.907,
+ 0.511
+ ],
+ "angle": 0,
+ "content": "Given a target model \\( f_{\\mathrm{tar}} \\), an evaluator model \\( f_{\\mathrm{eval}} \\) (the target MLLM can also serve as the evaluator, validated in Tab. 5), and an image-question pair \\( x \\), we illustrate how to construct \\( n \\) preference data points. Assuming there are \\( T \\) steps in CoT reasoning process, we generate preference data for \\( T \\) times on the way, as described in Algorithm 1. At each timestep \\( t \\) (i.e., a reasoning step \\( t \\)), the process includes four stages: Response Generation, Response Evaluation, Pair Construction, and Response Selection."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.512,
+ 0.906,
+ 0.664
+ ],
+ "angle": 0,
+ "content": "Response generation. The goal of this stage is to generate seed bounding boxes and produce intermediate responses to the question using the target model. Here, a 'response' refers to any model output at an intermediate step, not necessarily the final answer to the question. We denote the model's response at timestep \\( t \\) as \\( y_{t} \\), with the initial input \\( x \\) represented as \\( y_{0} \\). To encourage diversity in the bounding boxes and subsequent responses, we apply stochastic decoding to the target model \\( f_{\\mathrm{tar}} \\) with \\( n \\) different random seeds, resulting in a set of responses \\( \\{y_t^i\\}_{i = 1}^n \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.664,
+ 0.906,
+ 0.785
+ ],
+ "angle": 0,
+ "content": "Response evaluation. This stage evaluates the quality of all generated responses. The evaluator model not only scores each individual response but also counts how this response influences the quality of its next response in the chain. This cumulative evaluation approach helps quantify the impact of each bounded region on the overall reasoning process. Below, we elaborate on the formulation. At timestep \\( t \\), the evaluator assigns scores for \\( y_{t}^{i} \\) as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.598,
+ 0.798,
+ 0.905,
+ 0.856
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} s _ {\\text {c u r}} ^ {i} = f _ {\\text {e v a l}} \\left(y _ {t} ^ {i} \\mid y _ {0: t - 1}\\right), \\\\ s _ {n x t} ^ {i} = \\mathbb {E} \\left[ f _ {\\text {e v a l}} \\left(y _ {t + 1} ^ {i} \\mid y _ {0: t - 1}, y _ {t} ^ {i}\\right) \\right], \\tag {1} \\\\ s ^ {i} = s _ {\\text {c u r}} ^ {i} + \\gamma s _ {\\text {n x t}} ^ {i}, \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.871,
+ 0.907,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "where \\( s_{\\mathrm{nxt}}^i \\) reflects the impact on the next response and \\( \\gamma > 0 \\) is a hyperparameter to combine the current and next"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
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+ ],
+ "angle": 0,
+ "content": "2305"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.092,
+ 0.482,
+ 0.122
+ ],
+ "angle": 0,
+ "content": "response scores, with \\(\\gamma = 0\\) at the last step. We estimate the expectation \\(\\mathbb{E}[\\cdot ]\\) by randomly sampling next responses."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.123,
+ 0.484,
+ 0.273
+ ],
+ "angle": 0,
+ "content": "Pair construction. At each timestep \\( t \\), we randomly select \\( k \\) (preferred and dis-preferred) pairs from \\( \\{y_t^i\\}_{i=1}^n \\). For a single pair, we concatenate the preferred response with the past response chain \\( y_{0:t-1} \\) (preserved after \\( t-1 \\) timesteps) and get a \"preferred chain\" denoted as \\( y_t^w \\), and then we concatenate the dis-preferred response in the same way to get a \"dis-preferred chain\" denoted as \\( y_t^l \\). The pair of chains also includes their respective scores, and they are represented as \\( \\{y_w, s_w, y_l, s_l\\} \\). The overall \\( k \\) pairs of chains compose the preference dataset \\( \\mathcal{D}_t \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.275,
+ 0.484,
+ 0.366
+ ],
+ "angle": 0,
+ "content": "Response selection. The abovementioned 'past response chain \\( y_{0:t-1} \\)' is unique and is concatenated by the highest-scoring response at timestep \\( t-1 \\) and the preserved chain at timestep \\( t=2 \\), i.e., \\( y_{0:t-2} \\). In other words, when finishing each timestep process, we preserve only the best chain and use it for the next step."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.379,
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+ 0.394
+ ],
+ "angle": 0,
+ "content": "3.2. Unsupervised Learning of UV-CoT"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.402,
+ 0.484,
+ 0.568
+ ],
+ "angle": 0,
+ "content": "Assume the preference dataset \\(\\mathcal{D}\\) has been generated across \\(t\\) timesteps, we then optimize the target model with our UV-CoT via preference optimization on \\(\\mathcal{D}\\). DPO [1] is widely used in preference learning, and it ranks responses without quantifying preference intensity. In our case of image-level reasoning, key regions vary in influence, necessitating finer differentiation between responses. Therefore, we refine DPO by adjusting the margin to capture the key region's influence. We name our loss Score-DPO, abbreviated as sDPO, as it incorporates the preference score into the optimization. The loss is formulated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.113,
+ 0.596,
+ 0.482,
+ 0.675
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {s D P O}} (\\theta) = - \\underset {(x, y _ {w}, y _ {l}) \\sim \\mathcal {D}} {\\mathbb {E}} \\left[ \\log \\sigma \\left(\\beta \\log \\frac {\\pi_ {\\theta} (y _ {w} \\mid x)}{\\pi_ {\\mathrm {r e f}} (y _ {w} \\mid x)} \\right. \\right. \\\\ \\left. \\left. - \\beta \\log \\frac {\\pi_ {\\theta} \\left(y _ {l} \\mid x\\right)}{\\pi_ {\\mathrm {r e f}} \\left(y _ {l} \\mid x\\right)} - \\left(g \\left(s _ {w}\\right) - g \\left(s _ {l}\\right)\\right)\\right) \\right], \\tag {2} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.676,
+ 0.484,
+ 0.751
+ ],
+ "angle": 0,
+ "content": "where \\(\\pi_{\\theta}\\) is the target model, and \\(\\pi_{\\mathrm{ref}}\\) is its frozen initialization, serving as a reference to constrain deviation from the original model. \\(g(\\cdot):\\mathbb{R}\\to \\mathbb{R}\\) is a monotonically increasing function that maps preference scores into the logit space of the DPO objective."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.752,
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+ ],
+ "angle": 0,
+ "content": "To provide a deeper understanding of our sDPO loss, we establish its connection to the standard DPO loss. DPO reformulates reward model training as policy optimization by reparameterizing the reward function in PPO [34]:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.153,
+ 0.827,
+ 0.482,
+ 0.859
+ ],
+ "angle": 0,
+ "content": "\\[\nr (x, y) = \\beta \\log \\frac {\\pi_ {\\theta} (y \\mid x)}{\\pi_ {\\text {r e f}} (y \\mid x)} + \\beta \\log Z (x) \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.871,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Using the Bradley-Terry [4] model, the standard DPO aims to minimize the negative log-likelihood of the difference of"
+ },
+ {
+ "type": "code_caption",
+ "bbox": [
+ 0.516,
+ 0.092,
+ 0.804,
+ 0.107
+ ],
+ "angle": 0,
+ "content": "Algorithm 2 Iterative learning of UV-CoT"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.522,
+ 0.112,
+ 0.905,
+ 0.158
+ ],
+ "angle": 0,
+ "content": "1: Input: Initial target model \\( f_{\\mathrm{tar}}^{1} \\), evaluator model \\( f_{\\mathrm{eval}} \\), \\( \\mathcal{X} = \\{\\mathcal{X}_1, \\dots, \\mathcal{X}_m\\} \\), each \\( \\mathcal{X}_i \\) is a subset of image-question query"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.526,
+ 0.159,
+ 0.631,
+ 0.173
+ ],
+ "angle": 0,
+ "content": "2: Output: \\( f_{\\mathrm{tar}}^{m} \\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.526,
+ 0.174,
+ 0.663,
+ 0.186
+ ],
+ "angle": 0,
+ "content": "3: for \\( i = 1 \\) to \\( m \\) do"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.526,
+ 0.188,
+ 0.904,
+ 0.203
+ ],
+ "angle": 0,
+ "content": "4: \\(\\mathcal{D}_i\\gets\\) GenerateData \\((f_{\\mathrm{tar}}^i,f_{\\mathrm{eval}},\\mathcal{X}_i)\\) \\(\\triangleright\\) Algorithm 1"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.526,
+ 0.204,
+ 0.905,
+ 0.218
+ ],
+ "angle": 0,
+ "content": "5: \\(f_{\\mathrm{tar}}^{i + 1}\\gets \\mathrm{Train}(f_{\\mathrm{tar}}^i,\\mathcal{D}_i)\\) \\(\\triangleright\\) Eq. (2)"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.526,
+ 0.22,
+ 0.596,
+ 0.232
+ ],
+ "angle": 0,
+ "content": "6: end for"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.526,
+ 0.234,
+ 0.617,
+ 0.249
+ ],
+ "angle": 0,
+ "content": "7: return \\( f_{\\mathrm{tar}}^{m} \\)"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.526,
+ 0.159,
+ 0.905,
+ 0.249
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.28,
+ 0.745,
+ 0.294
+ ],
+ "angle": 0,
+ "content": "rewards between paired responses:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.558,
+ 0.308,
+ 0.904,
+ 0.329
+ ],
+ "angle": 0,
+ "content": "\\[\nP \\left(y _ {w} - y _ {l} > 0\\right) = \\sigma \\left(r \\left(x, y _ {w}\\right) - r \\left(x, y _ {l}\\right)\\right) \\tag {4}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.558,
+ 0.328,
+ 0.864,
+ 0.342
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\mathrm {D P O}} = - \\mathbb {E} _ {(x, y _ {w}, y _ {l}) \\sim \\mathcal {D}} [ \\log P (y _ {w} - y _ {l} > 0) ],\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.353,
+ 0.842,
+ 0.372
+ ],
+ "angle": 0,
+ "content": "where \\(\\sigma (x) = \\frac{1}{1 + \\exp(-x)}\\) is the sigmoid function."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.372,
+ 0.905,
+ 0.417
+ ],
+ "angle": 0,
+ "content": "Let \\(\\Delta_r = g(s_w) - g(s_l)\\) and define the Gumbeldistributed random variables \\(R_{w}\\sim \\mathrm{Gumbel}(r(x,y_{w}),1)\\) and \\(R_{l}\\sim \\mathrm{Gumbel}(r(x,y_{l}),1)\\). Then, we derive:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.532,
+ 0.43,
+ 0.904,
+ 0.492
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} P \\left(R _ {w} - R _ {l} > \\Delta_ {r}\\right) = \\sigma \\left(r \\left(x, y _ {w}\\right) - r \\left(x, y _ {l}\\right) - \\Delta r\\right) \\\\ = \\sigma \\left(\\beta \\log \\frac {\\pi^ {*} (y _ {w} \\mid x)}{\\pi_ {\\text {r e f}} (y _ {w} \\mid x)} - \\beta \\log \\frac {\\pi^ {*} (y _ {l} \\mid x)}{\\pi_ {\\text {r e f}} (y _ {l} \\mid x)} - \\Delta r\\right) \\tag {5} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.494,
+ 0.906,
+ 0.629
+ ],
+ "angle": 0,
+ "content": "This result follows from the definition of Gumbel random variables [1] and the Gumbel-max trick [25]. We provide a detailed proof in Appendix B. By maximizing the log-likelihood, we obtain our proposed loss function. The Gumbel distribution models the extreme values of a variable, while \\(\\Delta_{\\tau}\\) quantifies the degree of difference between preference pairs. Thus, our loss function explicitly optimizes preference learning by distinguishing not only the order but also the magnitude of preference differences."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.63,
+ 0.907,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Iterative learning. Standard DPO relies on static preference data during training, which can lead to distributional mismatch between training data and the model's generated outputs. To mitigate this issue, we adopt an iterative learning approach inspired by [47]. Algorithm 2 outlines the iterative learning process of UV-CoT, which incrementally refines a target model through preference learning. The iteration repeats \\( m \\) times, and the total image-question query set \\( \\mathcal{X} \\) is evenly divided into \\( m \\) subsets, \\( \\mathcal{X} = \\{\\mathcal{X}_1, \\dots, \\mathcal{X}_m\\} \\), each assigned to one iteration. The process starts with an initial target model \\( f_{\\mathrm{tar}} \\), an evaluator model \\( f_{\\mathrm{eval}} \\), and \\( \\mathcal{X} \\). In each iteration \\( i \\), the algorithm first generates preference data \\( \\mathcal{D}_i \\) using the current target model \\( f_{\\mathrm{tar}}^i \\) and the subset \\( \\mathcal{X}_i \\), using the procedure in Algorithm 1. This newly generated preference data is then used to train the next iteration of the target model \\( f_{\\mathrm{tar}}^{i+1} \\) using our UV-CoT loss of Eq. (2). The process continues until the final model \\( f_{\\mathrm{tar}}^m \\) is obtained. By dynamically updating the preference data, our approach"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
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+ ],
+ "angle": 0,
+ "content": "2306"
+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
+ 0.1,
+ 0.089,
+ 0.9,
+ 0.235
+ ],
+ "angle": 0,
+ "content": "| MLLM | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| LLaVA-1.5-7B | 0.198 | 0.507 | 0.131 | 0.539 | 0.480 | 0.504 | 0.393 |
| LLaVA-1.5-13B | 0.225 | 0.543 | 0.169 | 0.607 | 0.506 | 0.512 | 0.427 |
| MiniCPM-o-8B | 0.232 | 0.529 | 0.175 | 0.618 | 0.495 | 0.521 | 0.428 |
| OmniLMM-12B | 0.254 | 0.578 | 0.172 | 0.621 | 0.509 | 0.523 | 0.443 |
| Visual-CoT-7B (100% label) | 0.294 | 0.673 | 0.194 | 0.652 | 0.546 | 0.532 | 0.482 |
| UV-CoT (0% label) | 0.265 | 0.686 | 0.173 | 0.632 | 0.536 | 0.548 | 0.473 |
| UV-CoT (10% label) | 0.283 | 0.711 | 0.198 | 0.649 | 0.568 | 0.553 | 0.494 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.091,
+ 0.246,
+ 0.905,
+ 0.276
+ ],
+ "angle": 0,
+ "content": "Table 1. Overall comparison of different models on six evaluation benchmarks. The best result is bold, the second-best is underlined. %' indicates the percentage of supervised data used in Visual-CoT. By default, our UV-CoT uses only unsupervised data."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.103,
+ 0.298,
+ 0.475,
+ 0.433
+ ],
+ "angle": 0,
+ "content": "| MLLM | DUDE | SROIE | Visual7w | Average |
| LLaVA-1.5-7B | 0.165 | 0.147 | 0.340 | 0.217 |
| LLaVA-1.5-13B | 0.174 | 0.159 | 0.352 | 0.228 |
| MiniCPM-o-8B | 0.182 | 0.165 | 0.341 | 0.229 |
| OmniLMM-12B | 0.194 | 0.166 | 0.357 | 0.239 |
| Visual-CoT-7B | 0.206 | 0.181 | 0.397 | 0.261 |
| UV-Cot | 0.241 | 0.184 | 0.432 | 0.286 |
| UV-Cot* | 0.253 | 0.227 | 0.455 | 0.312 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.091,
+ 0.443,
+ 0.483,
+ 0.486
+ ],
+ "angle": 0,
+ "content": "Table 2. Zero-shot experiments on DUDE, SROIE and Visual7w. 'UV-CoT' denotes our model trained with additional unlabeled preference data from the three zero-shot datasets."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.515,
+ 0.483,
+ 0.545
+ ],
+ "angle": 0,
+ "content": "ensures that the learned model adapts to its evolving distribution, enhancing training robustness."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.562,
+ 0.224,
+ 0.579
+ ],
+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.588,
+ 0.173,
+ 0.604
+ ],
+ "angle": 0,
+ "content": "4.1. Setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.611,
+ 0.483,
+ 0.761
+ ],
+ "angle": 0,
+ "content": "Datasets. For a comprehensive evaluation, we adopt ten datasets spanning five domains: (1) Text/Document: DocVQA [26], TextVQA [36], DUDE [39], and SROIE [12]. (2) Chart: InfographicsVQA [27]. (3) General VQA: Flickr30k [31] and Visual7W [55]. (4) Relation Reasoning: VSR [20] and GQA [13]. (5) High-Resolution Image Reasoning: \\(\\mathrm{V}^{*}\\) Bench [41]. Notably, we also provide a model trained on data excluding DUDE, SROIE, Visual7W, and \\(\\mathrm{V}^{*}\\) Bench, which is used to evaluate zero-shot performance. See Appendix C.1 for details."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.763,
+ 0.483,
+ 0.809
+ ],
+ "angle": 0,
+ "content": "Evaluation. Following prior work [22], we prompt GPT-4o [28] to assign a score between 0 and 1, with higher scores indicating better prediction. See details in Appendix C.2."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.81,
+ 0.483,
+ 0.884
+ ],
+ "angle": 0,
+ "content": "Baselines. We compare UV-CoT with five baselines. LLaVA-1.5-{7B, 13B} [21] and OmniLMM-12B are strong general baselines. MiniCPM-o-8B [44] adopts adaptive visual encoding for fine-grained understanding and Visual-CoT-7B [35] learns image-level CoT via SFT."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.886,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Implementation details. We use LLaVA-1.5-7B as the tar"
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.518,
+ 0.298,
+ 0.905,
+ 0.42
+ ],
+ "angle": 0,
+ "content": "| MLLM | Attributes | GPT4V-hard | OCR | Average |
| LLaVA-1.5-7B | 0.317 | 0 | 0.1 | 0.139 |
| LLaVA-1.5-13B | 0.326 | 0.118 | 0.133 | 0.192 |
| MiniCPM-o-8B | 0.322 | 0.118 | 0.1 | 0.180 |
| OmniLMM-12B | 0.326 | 0.118 | 0.167 | 0.204 |
| Visual-CoT-7B | 0.330 | 0.118 | 0.593 | 0.347 |
| UV-CoT | 0.352 | 0.176 | 0.677 | 0.402 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "Table 3. Zero-shot experiments on \\( \\mathrm{V}^* \\) Bench (high-resolution image reasoning task, average resolution \\( 2246 \\times 1582 \\))."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "get model and OmniLMM-12B as the evaluator. To ensure scalability, we avoid using GPT-4 as the evaluator, preventing constraints imposed by high API costs. We implement iterative learning of UV-CoT over four iterations, utilizing a total of 249K preference data pairs. Notably, UV-CoT achieves higher data efficiency than Visual-CoT, which uses 376K data pairs. For each iteration, we train the model with AdamW optimizer for 4 epochs with a learning rate of \\(5 \\times 10^{-7}\\), \\(\\beta = 0.1\\), and a batch size of 8. In total, data generation takes 80 hours and training requires 60 hours, both conducted on an \\(8 \\times A100\\) 40GB machine. Additionally, we provide a variant UV-CoT trained with extra SFT on \\(10\\%\\) of the labeled Visual-CoT data, denoted as UV-CoT (10%)."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Comparison with State-of-the-Art Methods"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The overall performance comparisons are reported in Tab. 1, leading to the following key observations:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Explicitly incorporating visual cues proves beneficial for multimodal reasoning. For instance, MiniCPM-o-8B, which uses rule-based cropping to focus on salient regions, outperforms LLaVA-1.5-7B by an average of \\(3.5\\%\\). However, its reliance on heuristics limits adaptability. In contrast, image-level CoT models like Visual-CoT and our UV-CoT achieve greater performance gains, even surpassing the larger LLaVA-1.5-13B, by leveraging MLLMs to adaptively generate key visual regions. This highlights the superior effectiveness of image-level CoT reasoning."
+ },
+ {
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+ {
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+ "angle": 0,
+ "content": "| Model | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| UV-CoT (10% labels) | 0.283 | 0.711 | 0.198 | 0.649 | 0.568 | 0.553 | 0.494 |
| IF: w/o UV-CoT | 0.149 | 0.574 | 0.160 | 0.585 | 0.509 | 0.522 | 0.417 |
| IF: UV-CoT w/ G.T. BBox | 0.528 | 0.769 | 0.504 | 0.655 | 0.664 | 0.585 | 0.618 |
| Tr: w/ naive DPO | 0.258 | 0.695 | 0.189 | 0.623 | 0.552 | 0.534 | 0.475 |
| Tr: w/o iterative learning | 0.256 | 0.671 | 0.162 | 0.609 | 0.523 | 0.531 | 0.459 |
| Ge: w/o γ | 0.247 | 0.539 | 0.152 | 0.551 | 0.484 | 0.460 | 0.406 |
"
+ },
+ {
+ "type": "table_footnote",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Ablation study on key components of UV-CoT (10% labeled data). 'w/o UV-CoT' denotes standard inference without CoT reasoning. 'UV-CoT w/ G.T. BBox' uses annotated ground truth bounding boxes. 'w/ naive DPO' applies the standard DPO loss. 'w/o iterative learning' generates preference pairs for the entire set of question queries \\(\\mathcal{X}\\) in a single pass and trains once. 'w/o \\(\\gamma\\) evaluates responses with \\(\\gamma = 0\\). IF, Tr, and Ge indicate ablations on the inference process, training loss, and data generation, respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "UV-CoT fundamentally differs from distillation/pseudolabeling. Unlike distillation, where student performance is typically bounded by the teacher, UV-CoT outperforms its evaluator OmniLMM-12B by \\(5.1\\%\\) on average. This suggests that UV-CoT goes beyond simply mimicking a larger model. Direct generation of accurate bounding boxes remains a challenge for MLLMs due to the need for precise spatial localization. Instead, UV-CoT reformulates the task as ranking—an inherently simpler and more tractable problem—which leads to better performance."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "UV-CoT outperforms the supervised Visual-CoT. Despite using significantly less data (249K unlabeled vs. 376K labeled), UV-CoT outperforms Visual-CoT-7B on TextVQA \\((+1.3\\%)\\) and VSR \\((+1.6\\%)\\). Moreover, UV-CoT \\((10\\%)\\) surpasses Visual-CoT-7B by \\(2.1\\%\\) on average, with notable gains on TextVQA \\((+2.5\\%)\\), GQA \\((+2.2\\%)\\), and VSR \\((+2.1\\%)\\) and achieves comparable or better performance on the remaining datasets. This validates the effectiveness of our high-quality preference data generation and enhanced preference optimization method."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "content": "4.3. Zero-Shot Generalization"
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+ "content": "We evaluate the zero-shot performance of UV-CoT on the test sets of SROIE, DUDE, Visual7W, and V* Bench [41], without any training exposure to these datasets. V* Bench is a high-resolution benchmark (avg. size: \\(2246 \\times 1582\\)) covering diverse tasks; we focus on three representative ones: Attributes (object attribute recognition), GPT4V-Hard (complex visual reasoning), and OCR. Additionally, we train a variant of our model, UV-CoT*, using preference data generated from the training splits of SROIE, DUDE, and Visual7W. The results are reported in Tab. 2 and Tab. 3, leading to the following observations:"
+ },
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+ "type": "text",
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+ "angle": 0,
+ "content": "UV-CoT exhibits stronger zero-shot performance. Supervised CoT learning relies on labeled data and often overfits to specific annotation distributions, limiting its generalization to unseen tasks. In contrast, UV-CoT uses preference optimization based on relative comparisons, avoiding reliance on absolute labels and enhancing general"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "ization. As a result, UV-CoT outperforms all baselines across zero-shot datasets \\((+2.5\\%\\) on average), with notable gains on DUDE and Visual7W (both \\(+3.5\\%\\)). Furthermore, UV-CoT* achieves greater gains \\((5.1\\%\\) on average), showing that our model can effectively learn the image-level CoT process without the need for costly human annotation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "UV-CoT excels in high-resolution image reasoning. Image-level CoT methods—UV-CoT (+19.8%) and Visual-CoT-7B (+14.3%)—significantly outperform non-CoT baselines, with over 50% gains on OCR tasks. UV-CoT further surpasses Visual-CoT-7B by 5.5% on average, achieving the best performance across all tasks. This large performance gap underscores the advantage of unsupervised image-level CoT for high-resolution visual reasoning."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Ablation Studies"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In Tab. 4, we present the ablations on key components."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ "angle": 0,
+ "content": "Image-level CoT: We design two variants to evaluate the impact of image-level CoT: (1) 'w/o UV-Cot' removes intermediate reasoning and directly outputs answers; (2) 'UV-Cot w/ G.T. BBox' replaces predicted regions with ground truth bounding boxes to assess localization quality. Results show that removing CoT leads to a significant drop \\((-7.7\\%)\\) on average), confirming its necessity. On Flickr30k, UV-Cot matches the G.T. variant, suggesting accurate region selection. However, in DocVQA and InfographicsVQA, using G.T. boxes yields better performance, revealing the difficulty of precise localization. This highlights the potential of our method and suggests future work for improving region accuracy for complex tasks."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Score-DPO (sDPO): 'w/ naive DPO' applies standard DPO loss and shows degraded performance across all datasets (1.9% on average), especially on DocVQA (2.5%) and Flickr30k (2.6%), revealing its limitations for CoT learning. In contrast, our sDPO incorporates preference scores to better differentiate choices, yielding consistent gains."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Iterative learning: 'w/o iterative learning' generates all preference pairs in a single pass and trains only once, leading to a significant performance drop (3.5% on average)."
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+ "content": "2308"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
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+ 0.627,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Figure 3. (a&b) Bounding box evaluation on (a) training datasets and (b) zero-shot datasets. Our UV-CoT performs better than Visual-CoT. (c) Model performance under varying visual token sizes. Our UV-CoT demonstrates better token efficiency."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Model | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| OmniLMM-12B | 0.254 | 0.578 | 0.172 | 0.621 | 0.509 | 0.523 | 0.443 |
| IF: OmniLMM-12B + CoT | 0.305 | 0.722 | 0.217 | 0.675 | 0.580 | 0.595 | 0.516 |
| LLaVA-1.5-7B | 0.198 | 0.507 | 0.131 | 0.539 | 0.480 | 0.504 | 0.393 |
| IF: LLaVA-1.5-7B + CoT | 0.245 | 0.577 | 0.149 | 0.606 | 0.530 | 0.533 | 0.440 |
| Tr: UV-CoT (Evaluator: self-evaluated) | 0.242 | 0.609 | 0.153 | 0.598 | 0.517 | 0.526 | 0.441 |
| Tr: UV-CoT (Evaluator: OmniLMM-12B) | 0.265 | 0.686 | 0.173 | 0.632 | 0.536 | 0.548 | 0.473 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
+ 0.441,
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+ 0.471
+ ],
+ "angle": 0,
+ "content": "Table 5. Analysis of evaluator model. \\(^+\\) CoT' refers to inference assisted by bounding boxes generated by UV-CoT. Self-evaluated denotes using target model as the evaluator during training. IF and Tr indicate experiments conducted on the inference and training process."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This underscores the importance of iterative learning in continuously aligning the preference data distribution with the model's evolving policy throughout the training process."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "Response evaluation: 'w/o \\(\\gamma\\) model' sets \\(\\gamma = 0\\) during response evaluation stage, ignoring the next response when generating preference scores. We observe a significant performance drop (8.8% on average), particularly on TextVQA (17.2%), highlighting the difficulty MLLMs face in directly evaluating bounding boxes. This underscores the necessity of incorporating next response in our evaluation method."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.65,
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+ 0.667
+ ],
+ "angle": 0,
+ "content": "4.5. Bounding Box Evaluation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.672,
+ 0.483,
+ 0.732
+ ],
+ "angle": 0,
+ "content": "We compare the quality of bounding boxes learned from supervised and unsupervised strategies using GPT-4o as a scorer, on both training datasets (Fig. 3 (a)) and zero-shot datasets (Fig. 3 (b)). Our main observations are:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "(1) Our UV-CoT outperforms Visual-CoT-7B, achieving higher scores in five of six datasets, supporting its superior performance in generating helpful bounding box."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.884
+ ],
+ "angle": 0,
+ "content": "(2) The bounding box quality is closely related to the final performance. Our model exhibits lower scores (below 0.210) for bounding box generation in DocVQA and InfographicsVQA, correlating with its reduced final scores in these datasets (below 0.290 in Tab. 1). It underscores the validity of evaluating bounding box quality through its impact on subsequent answers."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.901
+ ],
+ "angle": 0,
+ "content": "(3) Both UV-CoT and UV-CoT* outperform Visual-CoT"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.09,
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+ 0.901
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "7B across all zero-shot datasets, which illustrates the strong generalization of our method in bounding box generation."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
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+ 0.544
+ ],
+ "angle": 0,
+ "content": "4.6. Insight of Evaluator Model"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ 0.581
+ ],
+ "angle": 0,
+ "content": "We further perform studies to better understand the role of evaluator model. Key findings from Tab. 5 are:"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.583,
+ 0.906,
+ 0.748
+ ],
+ "angle": 0,
+ "content": "(1) We compare UV-CoT with its self-evaluated variant, where the evaluator model is the same as the target model (initiated with LLaVA-1.5-7B). Although the self-evaluated version exhibits a performance decrease of \\(3.2\\%\\) compared to the original UV-CoT, it still outperforms LLaVA-1.5-7B \\((+4.8\\%)\\) on average) across all evaluated datasets and achieves performance comparable to the larger OmniLMM-12B model \\((-0.2\\%)\\) on average). This demonstrates that UV-CoT maintains robust performance even under self-evaluation, highlighting its efficiency without requiring larger model scales."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.75,
+ 0.906,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "(2) For OmniLMM-12B and LLaVA-1.5-7B, we incorporate a CoT process using bounding boxes generated by UV-CoT. The CoT-enhanced versions significantly outperform their original counterparts, achieving average performance gains of \\(4.7\\%\\) for LLaVA-1.5-7B and \\(7.4\\%\\) for OmniLMM-12B. Remarkably, these models were not finetuned for the CoT process, indicating that the bounding box information alone substantially improves performance. This finding underscores that our evaluating process simplifies the task of generating complex spatial annotations,"
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.512,
+ 0.583,
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+ "angle": 0,
+ "content": null
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+ "angle": 0,
+ "content": "2309"
+ }
+ ],
+ [
+ {
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+ "bbox": [
+ 0.139,
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.105,
+ 0.311,
+ 0.89,
+ 0.325
+ ],
+ "angle": 0,
+ "content": "Figure 4. Visualization of preference data generated by Algorithm 1. Preferred BBoxes are in red. Dis-preferred BBoxes are in blue."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.143,
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+ "angle": 0,
+ "content": null
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+ {
+ "type": "image",
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+ "content": null
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+ {
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.195,
+ 0.53,
+ 0.8,
+ 0.545
+ ],
+ "angle": 0,
+ "content": "Figure 5. Visualization of our UV-Cot inference. Model-generated bounding boxes are shown in red."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.561,
+ 0.454,
+ 0.576
+ ],
+ "angle": 0,
+ "content": "enabling MLLMs to focus on evaluating final answers."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.09,
+ 0.588,
+ 0.315,
+ 0.604
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+ "angle": 0,
+ "content": "4.7. Other Detailed Analyses"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.611,
+ 0.484,
+ 0.793
+ ],
+ "angle": 0,
+ "content": "Visual token efficiency. Compared to standard MLLM generation, image-level CoT doubles the number of visual tokens by processing additional local image regions. To evaluate token efficiency, i.e., performance under the same visual token budget, we resize the input image to different resolutions \\((224^{2}, 336^{2}\\) and \\(448^{2}\\)) and report the average score of different models in Fig. 3(c). Our key findings are: (1) MLLMs with image-level reasoning (Visual-CoT-7B and our UV-CoT) demonstrate better token efficiency than the standard answer generation pipeline. E.g., they achieve higher performance with 512 visual tokens than the standard pipeline does with 1024 tokens."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.794,
+ 0.484,
+ 0.84
+ ],
+ "angle": 0,
+ "content": "(2) Our UV-CoT consistently outperforms Visual-CoT-7B across all scales, achieving higher average scores. This highlights the token efficiency of our method."
+ },
+ {
+ "type": "list",
+ "bbox": [
+ 0.09,
+ 0.611,
+ 0.484,
+ 0.84
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.841,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Visualization. Fig. 4 visualizes some preference data from our UV-CoS inference process. Given different local regions and their corresponding answers, the evaluator MLLM assigns reasonable scores, validating the effective"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.561,
+ 0.907,
+ 0.637
+ ],
+ "angle": 0,
+ "content": "ness of our automatic generation and labeling process. In Fig. 5, we present reasoning cases with model-generated bounding boxes overlaid. The precision of bounding box detection and the depth of understanding play a crucial role in determining the quality of generated answers."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.649,
+ 0.634,
+ 0.665
+ ],
+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.675,
+ 0.907,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "In this work, we propose UV-CoT, a framework that enables image-level CoT reasoning in MLLMs via preference optimization. Unlike previous methods that rely on SFT needing large amounts of labeled data, our approach leverages unsupervised learning to refine the model's ability with image-level CoT using model-generated preference data (which are rough but useful). We address key challenges in preference data generation and effective optimization, ensuring a more adaptive and interpretable reasoning process. Extensive experiments demonstrate that UV-CoT achieves state-of-the-art performance, significantly improving visual comprehension in MLLMs on ten reasoning datasets. Our findings highlight the potential of preference learning as a scalable alternative to traditional SFT, enabling more robust and data-efficient multimodal reasoning."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.483,
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+ ],
+ "angle": 0,
+ "content": "2310"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.092,
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+ ],
+ "angle": 0,
+ "content": "Acknowledgements"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.116,
+ 0.484,
+ 0.207
+ ],
+ "angle": 0,
+ "content": "This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-030). Thanks to Zichen Tian for his assistance with figure visualization throughout this work. The authors also thank the reviewers for their valuable comments and suggestions."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.093,
+ 0.221,
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+# Unsupervised Visual Chain-of-Thought Reasoning via Preference Optimization
+
+Kesen Zhao $^{1}$ Beier Zhu $^{1*}$ Qianru Sun $^{2}$ Hanwang Zhang $^{1}$
+
+$^{1}$ Nanyang Technological University, $^{2}$ Singapore Management University
+
+kesen002@e.ntu.edu.sg, qianrusun@smu.edu.sg
+
+{beier.zhu,hanwangzhang}@ntu.edu.sg
+
+# Abstract
+
+Chain-of-thought (CoT) reasoning greatly improves the interpretability and problem-solving abilities of multimodal large language models (MLLMs). However, existing approaches focus on text CoT, limiting their ability to leverage visual cues. Visual CoT remains underexplored, and the only work [35] is based on supervised fine-tuning that relies on extensive labeled bounding-box data and is hard to generalize to unseen cases. In this paper, we introduce Unsupervised Visual CoT (UV-Cot), a novel framework for image-level CoT reasoning via preference optimization. UV-Cot performs preference comparisons between model-generated bounding boxes (one is preferred and the other is dis-preferred), eliminating the need for bounding-box annotations. We get such preference data by introducing an automatic data generation pipeline. Given an image, our target MLLM (e.g., LLaVA-1.5-7B) generates seed bounding boxes using a template prompt and then answers the question using each bounded region as input. An evaluator MLLM (e.g., OmniLLM-12B) ranks the responses, and these rankings serve as supervision to train the target MLLM with UV-Cot by minimizing negative log-likelihood losses. By emulating human perception-identifying key regions and reasoning based on them-UV-Cot can improve visual comprehension, particularly in spatial reasoning tasks where textual descriptions alone fall short. Our experiments on six datasets demonstrate the superiority of UV-Cot, compared to the state-of-the-art textual and visual CoT methods. Our zero-shot testing on four unseen datasets shows the strong generalization of UV-Cot.
+
+# 1. Introduction
+
+With the recent advancements in multimodal large language models (MLLMs) [3, 21, 22, 45], many efforts have been made to incorporate text CoT reasoning [9, 17, 40, 49] to
+
+handle complex vision-language tasks [42, 43, 50]. However, the visual understanding ability of MLLM is limited by fixed-granularity image processing, i.e., the MLLM cannot dynamically adjust focus across different spatial regions of the input image, even when guided by text CoT prompts [11]. This underscores the critical need to explicitly integrate visual cues into the CoT process.
+
+A very recent work, Visual-CoT [35], has made an initial attempt towards this goal. The model is trained using supervised fine-tuning (SFT) with human-labeled bounding boxes that indicate the key image regions relevant to the question. It performs the multimodal CoT approach with human-annotated reasoning steps by associating textual inputs with the detected regions. An overview of Visual-CoT is presented in Fig. 1. However, it has two key drawbacks: (1) it relies on large-scale, high-quality labeled data, making it costly and hard to scale; and (2) SFT learns only from positive examples (i.e., the labeled data), limiting its ability to generalize to unseen or ambiguous scenarios where intermediate reasoning or dynamic interpretation is needed.
+
+To address these issues, we introduce an Unsupervised approach to Visual CoT dubbed as UV-CoT. It has two key parts: data collection and model training. The data collection does not need human annotation, as it leverages the data generation and evaluation capabilities of pre-trained MLLMs. The model training is inspired by the idea of direct preference optimization (DPO). It is implemented with an adapted version of DPO to address specific limitations in capturing the degree of preference and fine-grained region-based reasoning when conducting visual CoT on MLLMs.
+
+Our method UV-CoT, as shown in Fig. 1, differs from Visual-CoT [35] by adopting an unsupervised approach with contrastive preference data. We design an automatic two-step pipeline to generate this data: 1) Region Generation: Given an image, the target model generates multiple seed bounding boxes using a template prompt. Then it answers the question by processing each bounded region together with the question as input. 2) Quality Assessment: An evaluator MLLM scores the responses, using these scores as proxies to measure the quality of the regions.
+
+
+Figure 1. Comparison of Visual-CoT [35] and our UV-CoT. Left: Visual-CoT relies on human-annotated bounding boxes to identify key regions. The model is trained via supervised fine-tuning to maximize the likelihood of the labeled data. Right: UV-CoT eliminates the need for human annotation. Given an image, the target model generates seed bounding boxes and answers questions based on these regions, respectively. An evaluator MLLM then scores the responses as a proxy for assessing region quality. Lastly, the target model is optimized via preference optimization by maximizing the likelihood of preferred regions over dis-preferred ones.
+
+
+
+Unlike traditional DPO, we propose Score-DPO (sDPO), which not only ranks preference data (i.e., preferred and dis-preferred responses shown in Fig. 1) but also assigns preference scores. This scoring enables more precise optimization based on score differences. During UV-CoT training, the rankings of the preference data act as supervision by minimizing negative log-likelihood loss, while the scores define the decision margin. By mimicking human perception—first identifying key regions, then reasoning over them—UV-CoT significantly improves visual comprehension, especially in spatial reasoning tasks where text-based methods fall short. By leveraging unsupervised data in a contrastive way, UV-CoT also shows strong generalization ability when tested on unseen datasets.
+
+Our contributions in this paper include: 1) an automatic pipeline for generating high-quality preference data, enabling robust and scalable preference learning of UV-CoT; 2) an improved version of DPO by integrating the degree of preference for visual regions, allowing the model to distinguish key regions more precisely; and 3) extensive experiments on multiple challenging datasets, demonstrating state-of-the-art performance of UV-CoT on four benchmarks and strong generalization to four unseen test datasets.
+
+# 2. Related Works
+
+Chain-of-thought in LLMs and MLLMs. LLMs [3, 10, 14, 24, 29, 38] with CoT [5, 8, 40] show strong inferential abilities by introducing intermediate reasoning steps. Both manually designed [40] and self-generated [17, 49] reason-
+
+ing approaches have proven effective. In contrast, MLLMs rely on image encoders [15, 32, 52-54] to extract visual features but often struggle with reasoning due to inherent differences in how textual and visual data are processed [23, 48, 51]. Multimodal CoT methods [42, 43, 50] attempt to address this by transforming multimodal inputs into a unified textual format, enabling LLMs to perform CoT at the text level. However, this transformation introduces significant information loss and prevents the models from capturing key visual details [50]. For example, LLaVA-CoT [42] leverages GPT-4o to summarize questions and image captions but suffers from weak optical character recognition and sometimes hallucinations.
+
+A very recent work, Visual-CoT [35], improves the MLLM reasoning by introducing CoT methods at the image level. This approach involves scanning the entire image, identifying key references, and then focusing the model on specific regions for reasoning. Despite its improvements, Visual-CoT is heavily based on costly human-annotated data. In contrast, our UV-CoT framework utilizes unsupervised preference optimization with auto-generated preference data, eliminating the need for manual annotations.
+
+Preference learning in LLMs and MLLMs. RLHF [56] aligns LLMs with human preferences by training a reward model via contrastive response evaluations. To reduce reliance on human annotations, RLAIF [19] leverages pretrained LLMs for preference label generation. However, RL-based fine-tuning faces stability and efficiency challenges. Direct Preference Optimization (DPO) [33] ad
+
+
+Figure 2. Illustration of UV-CoT reasoning.
+
+dresses this by directly linking reward functions to optimal policies, eliminating reward model fine-tuning. Further improvements include IPO [2], which mitigates overfitting with a bounded preference function, and KTO [7], which removes the need for paired preference data, relying instead on single examples labeled as either 'good' or 'bad'.
+
+These preference learning techniques are applied to MLLMs, with RLHF-V and RLAIF-V [46, 47] refining behavior alignments using human and LLM-generated labels. To mitigate reward hacking, Sun et al. [37] enhance reward models with additional factual details, such as image captions and verified choices, further improving the performance of MLLM. Some works have attempted to apply DPO in the CoT process [18, 30]. However, these methods are designed for only text-level CoT and do not effectively handle visual features or cues. In contrast, in this paper, we propose UV-CoT, a specialized framework for image-level CoT reasoning inspired by the idea of DPO. Unlike traditional DPO, UV-CoT not only ranks preference data (i.e., preferred and dis-preferred data) but also assigns preference scores. This scoring enables more precise optimization of the MLLMs based on score differences.
+
+# 3. Method
+
+Fig. 2 illustrates the pipeline of UV-CoT reasoning. Given the original image and the question, we append a CoT prompt to guide the target MLLM in identifying the most informative image region and specifying its location via bounding box coordinates. A visual sampler then extracts the bounded region from the image. The MLLM subsequently integrates visual tokens from original and cropped images to generate more precise and comprehensive answers. In Sec. 3.1, we detail the automatic preference data generation pipeline. In Sec. 3.2, we describe our Score-
+
+Algorithm 1 Preference data generation for a query $x$
+
+1: Input: Target model $f_{\mathrm{tar}}$ , evaluator $f_{\mathrm{eval}}$ , an image-question query $x$ , number of seeds $n$ , and number of preference pairs $k$ .
+2: Output: Preference data $\mathcal{D}$
+3: Initialize $y_0 = x$
+4: for $t = 1$ to $T$ do
+5: $\{y_t^i\}_{i = 1}^n\gets \text{Generate}(f_{\text{tar}},y_{0:t - 1},n)$
+6: $\{s^i\}_{i = 1}^n\gets \text{Evaluate}(f_{\text{eval}},y_{0:t - 1},\{y_{t}^i\}_{i = 1}^n)$
+7: $\mathcal{D}_t\gets \mathrm{ConstructPairs}(y_{0:t - 1},\{y_t^i\}_{i = 1}^n,\{s^i\}_{i = 1}^n,k)$
+8: $y_{t}\gets \mathsf{Select}(y_{0:t - 1},\{y_{t}^{i}\}_{i = 1}^{n},\{s^{i}\}_{i = 1}^{n})$
+9: end for
+10: return $\mathcal{D} = \{\mathcal{D}_1, \dots, \mathcal{D}_T\}$
+
+DPO (sDPO) for image-level CoT reasoning.
+
+# 3.1. Preference Data Generation
+
+Given a target model $f_{\mathrm{tar}}$ , an evaluator model $f_{\mathrm{eval}}$ (the target MLLM can also serve as the evaluator, validated in Tab. 5), and an image-question pair $x$ , we illustrate how to construct $n$ preference data points. Assuming there are $T$ steps in CoT reasoning process, we generate preference data for $T$ times on the way, as described in Algorithm 1. At each timestep $t$ (i.e., a reasoning step $t$ ), the process includes four stages: Response Generation, Response Evaluation, Pair Construction, and Response Selection.
+
+Response generation. The goal of this stage is to generate seed bounding boxes and produce intermediate responses to the question using the target model. Here, a 'response' refers to any model output at an intermediate step, not necessarily the final answer to the question. We denote the model's response at timestep $t$ as $y_{t}$ , with the initial input $x$ represented as $y_{0}$ . To encourage diversity in the bounding boxes and subsequent responses, we apply stochastic decoding to the target model $f_{\mathrm{tar}}$ with $n$ different random seeds, resulting in a set of responses $\{y_t^i\}_{i = 1}^n$ .
+
+Response evaluation. This stage evaluates the quality of all generated responses. The evaluator model not only scores each individual response but also counts how this response influences the quality of its next response in the chain. This cumulative evaluation approach helps quantify the impact of each bounded region on the overall reasoning process. Below, we elaborate on the formulation. At timestep $t$ , the evaluator assigns scores for $y_{t}^{i}$ as follows:
+
+$$
+\begin{array}{l} s _ {\text {c u r}} ^ {i} = f _ {\text {e v a l}} \left(y _ {t} ^ {i} \mid y _ {0: t - 1}\right), \\ s _ {n x t} ^ {i} = \mathbb {E} \left[ f _ {\text {e v a l}} \left(y _ {t + 1} ^ {i} \mid y _ {0: t - 1}, y _ {t} ^ {i}\right) \right], \tag {1} \\ s ^ {i} = s _ {\text {c u r}} ^ {i} + \gamma s _ {\text {n x t}} ^ {i}, \\ \end{array}
+$$
+
+where $s_{\mathrm{nxt}}^i$ reflects the impact on the next response and $\gamma > 0$ is a hyperparameter to combine the current and next
+
+response scores, with $\gamma = 0$ at the last step. We estimate the expectation $\mathbb{E}[\cdot ]$ by randomly sampling next responses.
+
+Pair construction. At each timestep $t$ , we randomly select $k$ (preferred and dis-preferred) pairs from $\{y_t^i\}_{i=1}^n$ . For a single pair, we concatenate the preferred response with the past response chain $y_{0:t-1}$ (preserved after $t-1$ timesteps) and get a "preferred chain" denoted as $y_t^w$ , and then we concatenate the dis-preferred response in the same way to get a "dis-preferred chain" denoted as $y_t^l$ . The pair of chains also includes their respective scores, and they are represented as $\{y_w, s_w, y_l, s_l\}$ . The overall $k$ pairs of chains compose the preference dataset $\mathcal{D}_t$ .
+
+Response selection. The abovementioned 'past response chain $y_{0:t-1}$ ' is unique and is concatenated by the highest-scoring response at timestep $t-1$ and the preserved chain at timestep $t=2$ , i.e., $y_{0:t-2}$ . In other words, when finishing each timestep process, we preserve only the best chain and use it for the next step.
+
+# 3.2. Unsupervised Learning of UV-CoT
+
+Assume the preference dataset $\mathcal{D}$ has been generated across $t$ timesteps, we then optimize the target model with our UV-CoT via preference optimization on $\mathcal{D}$ . DPO [1] is widely used in preference learning, and it ranks responses without quantifying preference intensity. In our case of image-level reasoning, key regions vary in influence, necessitating finer differentiation between responses. Therefore, we refine DPO by adjusting the margin to capture the key region's influence. We name our loss Score-DPO, abbreviated as sDPO, as it incorporates the preference score into the optimization. The loss is formulated as:
+
+$$
+\begin{array}{l} \mathcal {L} _ {\mathrm {s D P O}} (\theta) = - \underset {(x, y _ {w}, y _ {l}) \sim \mathcal {D}} {\mathbb {E}} \left[ \log \sigma \left(\beta \log \frac {\pi_ {\theta} (y _ {w} \mid x)}{\pi_ {\mathrm {r e f}} (y _ {w} \mid x)} \right. \right. \\ \left. \left. - \beta \log \frac {\pi_ {\theta} \left(y _ {l} \mid x\right)}{\pi_ {\mathrm {r e f}} \left(y _ {l} \mid x\right)} - \left(g \left(s _ {w}\right) - g \left(s _ {l}\right)\right)\right) \right], \tag {2} \\ \end{array}
+$$
+
+where $\pi_{\theta}$ is the target model, and $\pi_{\mathrm{ref}}$ is its frozen initialization, serving as a reference to constrain deviation from the original model. $g(\cdot):\mathbb{R}\to \mathbb{R}$ is a monotonically increasing function that maps preference scores into the logit space of the DPO objective.
+
+To provide a deeper understanding of our sDPO loss, we establish its connection to the standard DPO loss. DPO reformulates reward model training as policy optimization by reparameterizing the reward function in PPO [34]:
+
+$$
+r (x, y) = \beta \log \frac {\pi_ {\theta} (y \mid x)}{\pi_ {\text {r e f}} (y \mid x)} + \beta \log Z (x) \tag {3}
+$$
+
+Using the Bradley-Terry [4] model, the standard DPO aims to minimize the negative log-likelihood of the difference of
+
+Algorithm 2 Iterative learning of UV-CoT
+
+1: Input: Initial target model $f_{\mathrm{tar}}^{1}$ , evaluator model $f_{\mathrm{eval}}$ , $\mathcal{X} = \{\mathcal{X}_1, \dots, \mathcal{X}_m\}$ , each $\mathcal{X}_i$ is a subset of image-question query
+
+2: Output: $f_{\mathrm{tar}}^{m}$
+3: for $i = 1$ to $m$ do
+4: $\mathcal{D}_i\gets$ GenerateData $(f_{\mathrm{tar}}^i,f_{\mathrm{eval}},\mathcal{X}_i)$ $\triangleright$ Algorithm 1
+5: $f_{\mathrm{tar}}^{i + 1}\gets \mathrm{Train}(f_{\mathrm{tar}}^i,\mathcal{D}_i)$ $\triangleright$ Eq. (2)
+6: end for
+7: return $f_{\mathrm{tar}}^{m}$
+
+rewards between paired responses:
+
+$$
+P \left(y _ {w} - y _ {l} > 0\right) = \sigma \left(r \left(x, y _ {w}\right) - r \left(x, y _ {l}\right)\right) \tag {4}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {D P O}} = - \mathbb {E} _ {(x, y _ {w}, y _ {l}) \sim \mathcal {D}} [ \log P (y _ {w} - y _ {l} > 0) ],
+$$
+
+where $\sigma (x) = \frac{1}{1 + \exp(-x)}$ is the sigmoid function.
+
+Let $\Delta_r = g(s_w) - g(s_l)$ and define the Gumbeldistributed random variables $R_{w}\sim \mathrm{Gumbel}(r(x,y_{w}),1)$ and $R_{l}\sim \mathrm{Gumbel}(r(x,y_{l}),1)$ . Then, we derive:
+
+$$
+\begin{array}{l} P \left(R _ {w} - R _ {l} > \Delta_ {r}\right) = \sigma \left(r \left(x, y _ {w}\right) - r \left(x, y _ {l}\right) - \Delta r\right) \\ = \sigma \left(\beta \log \frac {\pi^ {*} (y _ {w} \mid x)}{\pi_ {\text {r e f}} (y _ {w} \mid x)} - \beta \log \frac {\pi^ {*} (y _ {l} \mid x)}{\pi_ {\text {r e f}} (y _ {l} \mid x)} - \Delta r\right) \tag {5} \\ \end{array}
+$$
+
+This result follows from the definition of Gumbel random variables [1] and the Gumbel-max trick [25]. We provide a detailed proof in Appendix B. By maximizing the log-likelihood, we obtain our proposed loss function. The Gumbel distribution models the extreme values of a variable, while $\Delta_{\tau}$ quantifies the degree of difference between preference pairs. Thus, our loss function explicitly optimizes preference learning by distinguishing not only the order but also the magnitude of preference differences.
+
+Iterative learning. Standard DPO relies on static preference data during training, which can lead to distributional mismatch between training data and the model's generated outputs. To mitigate this issue, we adopt an iterative learning approach inspired by [47]. Algorithm 2 outlines the iterative learning process of UV-CoT, which incrementally refines a target model through preference learning. The iteration repeats $m$ times, and the total image-question query set $\mathcal{X}$ is evenly divided into $m$ subsets, $\mathcal{X} = \{\mathcal{X}_1, \dots, \mathcal{X}_m\}$ , each assigned to one iteration. The process starts with an initial target model $f_{\mathrm{tar}}$ , an evaluator model $f_{\mathrm{eval}}$ , and $\mathcal{X}$ . In each iteration $i$ , the algorithm first generates preference data $\mathcal{D}_i$ using the current target model $f_{\mathrm{tar}}^i$ and the subset $\mathcal{X}_i$ , using the procedure in Algorithm 1. This newly generated preference data is then used to train the next iteration of the target model $f_{\mathrm{tar}}^{i+1}$ using our UV-CoT loss of Eq. (2). The process continues until the final model $f_{\mathrm{tar}}^m$ is obtained. By dynamically updating the preference data, our approach
+
+| MLLM | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| LLaVA-1.5-7B | 0.198 | 0.507 | 0.131 | 0.539 | 0.480 | 0.504 | 0.393 |
| LLaVA-1.5-13B | 0.225 | 0.543 | 0.169 | 0.607 | 0.506 | 0.512 | 0.427 |
| MiniCPM-o-8B | 0.232 | 0.529 | 0.175 | 0.618 | 0.495 | 0.521 | 0.428 |
| OmniLMM-12B | 0.254 | 0.578 | 0.172 | 0.621 | 0.509 | 0.523 | 0.443 |
| Visual-CoT-7B (100% label) | 0.294 | 0.673 | 0.194 | 0.652 | 0.546 | 0.532 | 0.482 |
| UV-CoT (0% label) | 0.265 | 0.686 | 0.173 | 0.632 | 0.536 | 0.548 | 0.473 |
| UV-CoT (10% label) | 0.283 | 0.711 | 0.198 | 0.649 | 0.568 | 0.553 | 0.494 |
+
+Table 1. Overall comparison of different models on six evaluation benchmarks. The best result is bold, the second-best is underlined. %' indicates the percentage of supervised data used in Visual-CoT. By default, our UV-CoT uses only unsupervised data.
+
+| MLLM | DUDE | SROIE | Visual7w | Average |
| LLaVA-1.5-7B | 0.165 | 0.147 | 0.340 | 0.217 |
| LLaVA-1.5-13B | 0.174 | 0.159 | 0.352 | 0.228 |
| MiniCPM-o-8B | 0.182 | 0.165 | 0.341 | 0.229 |
| OmniLMM-12B | 0.194 | 0.166 | 0.357 | 0.239 |
| Visual-CoT-7B | 0.206 | 0.181 | 0.397 | 0.261 |
| UV-Cot | 0.241 | 0.184 | 0.432 | 0.286 |
| UV-Cot* | 0.253 | 0.227 | 0.455 | 0.312 |
+
+ensures that the learned model adapts to its evolving distribution, enhancing training robustness.
+
+# 4. Experiments
+
+# 4.1. Setup
+
+Datasets. For a comprehensive evaluation, we adopt ten datasets spanning five domains: (1) Text/Document: DocVQA [26], TextVQA [36], DUDE [39], and SROIE [12]. (2) Chart: InfographicsVQA [27]. (3) General VQA: Flickr30k [31] and Visual7W [55]. (4) Relation Reasoning: VSR [20] and GQA [13]. (5) High-Resolution Image Reasoning: $\mathrm{V}^{*}$ Bench [41]. Notably, we also provide a model trained on data excluding DUDE, SROIE, Visual7W, and $\mathrm{V}^{*}$ Bench, which is used to evaluate zero-shot performance. See Appendix C.1 for details.
+
+Evaluation. Following prior work [22], we prompt GPT-4o [28] to assign a score between 0 and 1, with higher scores indicating better prediction. See details in Appendix C.2.
+
+Baselines. We compare UV-CoT with five baselines. LLaVA-1.5-{7B, 13B} [21] and OmniLMM-12B are strong general baselines. MiniCPM-o-8B [44] adopts adaptive visual encoding for fine-grained understanding and Visual-CoT-7B [35] learns image-level CoT via SFT.
+
+Implementation details. We use LLaVA-1.5-7B as the tar
+
+Table 2. Zero-shot experiments on DUDE, SROIE and Visual7w. 'UV-CoT' denotes our model trained with additional unlabeled preference data from the three zero-shot datasets.
+
+| MLLM | Attributes | GPT4V-hard | OCR | Average |
| LLaVA-1.5-7B | 0.317 | 0 | 0.1 | 0.139 |
| LLaVA-1.5-13B | 0.326 | 0.118 | 0.133 | 0.192 |
| MiniCPM-o-8B | 0.322 | 0.118 | 0.1 | 0.180 |
| OmniLMM-12B | 0.326 | 0.118 | 0.167 | 0.204 |
| Visual-CoT-7B | 0.330 | 0.118 | 0.593 | 0.347 |
| UV-CoT | 0.352 | 0.176 | 0.677 | 0.402 |
+
+Table 3. Zero-shot experiments on $\mathrm{V}^*$ Bench (high-resolution image reasoning task, average resolution $2246 \times 1582$ ).
+
+get model and OmniLMM-12B as the evaluator. To ensure scalability, we avoid using GPT-4 as the evaluator, preventing constraints imposed by high API costs. We implement iterative learning of UV-CoT over four iterations, utilizing a total of 249K preference data pairs. Notably, UV-CoT achieves higher data efficiency than Visual-CoT, which uses 376K data pairs. For each iteration, we train the model with AdamW optimizer for 4 epochs with a learning rate of $5 \times 10^{-7}$ , $\beta = 0.1$ , and a batch size of 8. In total, data generation takes 80 hours and training requires 60 hours, both conducted on an $8 \times A100$ 40GB machine. Additionally, we provide a variant UV-CoT trained with extra SFT on $10\%$ of the labeled Visual-CoT data, denoted as UV-CoT (10%).
+
+# 4.2. Comparison with State-of-the-Art Methods
+
+The overall performance comparisons are reported in Tab. 1, leading to the following key observations:
+
+Explicitly incorporating visual cues proves beneficial for multimodal reasoning. For instance, MiniCPM-o-8B, which uses rule-based cropping to focus on salient regions, outperforms LLaVA-1.5-7B by an average of $3.5\%$ . However, its reliance on heuristics limits adaptability. In contrast, image-level CoT models like Visual-CoT and our UV-CoT achieve greater performance gains, even surpassing the larger LLaVA-1.5-13B, by leveraging MLLMs to adaptively generate key visual regions. This highlights the superior effectiveness of image-level CoT reasoning.
+
+| Model | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| UV-CoT (10% labels) | 0.283 | 0.711 | 0.198 | 0.649 | 0.568 | 0.553 | 0.494 |
| IF: w/o UV-CoT | 0.149 | 0.574 | 0.160 | 0.585 | 0.509 | 0.522 | 0.417 |
| IF: UV-CoT w/ G.T. BBox | 0.528 | 0.769 | 0.504 | 0.655 | 0.664 | 0.585 | 0.618 |
| Tr: w/ naive DPO | 0.258 | 0.695 | 0.189 | 0.623 | 0.552 | 0.534 | 0.475 |
| Tr: w/o iterative learning | 0.256 | 0.671 | 0.162 | 0.609 | 0.523 | 0.531 | 0.459 |
| Ge: w/o γ | 0.247 | 0.539 | 0.152 | 0.551 | 0.484 | 0.460 | 0.406 |
+
+Table 4. Ablation study on key components of UV-CoT (10% labeled data). 'w/o UV-CoT' denotes standard inference without CoT reasoning. 'UV-CoT w/ G.T. BBox' uses annotated ground truth bounding boxes. 'w/ naive DPO' applies the standard DPO loss. 'w/o iterative learning' generates preference pairs for the entire set of question queries $\mathcal{X}$ in a single pass and trains once. 'w/o $\gamma$ evaluates responses with $\gamma = 0$ . IF, Tr, and Ge indicate ablations on the inference process, training loss, and data generation, respectively.
+
+UV-CoT fundamentally differs from distillation/pseudolabeling. Unlike distillation, where student performance is typically bounded by the teacher, UV-CoT outperforms its evaluator OmniLMM-12B by $5.1\%$ on average. This suggests that UV-CoT goes beyond simply mimicking a larger model. Direct generation of accurate bounding boxes remains a challenge for MLLMs due to the need for precise spatial localization. Instead, UV-CoT reformulates the task as ranking—an inherently simpler and more tractable problem—which leads to better performance.
+
+UV-CoT outperforms the supervised Visual-CoT. Despite using significantly less data (249K unlabeled vs. 376K labeled), UV-CoT outperforms Visual-CoT-7B on TextVQA $(+1.3\%)$ and VSR $(+1.6\%)$ . Moreover, UV-CoT $(10\%)$ surpasses Visual-CoT-7B by $2.1\%$ on average, with notable gains on TextVQA $(+2.5\%)$ , GQA $(+2.2\%)$ , and VSR $(+2.1\%)$ and achieves comparable or better performance on the remaining datasets. This validates the effectiveness of our high-quality preference data generation and enhanced preference optimization method.
+
+# 4.3. Zero-Shot Generalization
+
+We evaluate the zero-shot performance of UV-CoT on the test sets of SROIE, DUDE, Visual7W, and V* Bench [41], without any training exposure to these datasets. V* Bench is a high-resolution benchmark (avg. size: $2246 \times 1582$ ) covering diverse tasks; we focus on three representative ones: Attributes (object attribute recognition), GPT4V-Hard (complex visual reasoning), and OCR. Additionally, we train a variant of our model, UV-CoT*, using preference data generated from the training splits of SROIE, DUDE, and Visual7W. The results are reported in Tab. 2 and Tab. 3, leading to the following observations:
+
+UV-CoT exhibits stronger zero-shot performance. Supervised CoT learning relies on labeled data and often overfits to specific annotation distributions, limiting its generalization to unseen tasks. In contrast, UV-CoT uses preference optimization based on relative comparisons, avoiding reliance on absolute labels and enhancing general
+
+ization. As a result, UV-CoT outperforms all baselines across zero-shot datasets $(+2.5\%$ on average), with notable gains on DUDE and Visual7W (both $+3.5\%$ ). Furthermore, UV-CoT* achieves greater gains $(5.1\%$ on average), showing that our model can effectively learn the image-level CoT process without the need for costly human annotation.
+
+UV-CoT excels in high-resolution image reasoning. Image-level CoT methods—UV-CoT (+19.8%) and Visual-CoT-7B (+14.3%)—significantly outperform non-CoT baselines, with over 50% gains on OCR tasks. UV-CoT further surpasses Visual-CoT-7B by 5.5% on average, achieving the best performance across all tasks. This large performance gap underscores the advantage of unsupervised image-level CoT for high-resolution visual reasoning.
+
+# 4.4. Ablation Studies
+
+In Tab. 4, we present the ablations on key components.
+
+Image-level CoT: We design two variants to evaluate the impact of image-level CoT: (1) 'w/o UV-Cot' removes intermediate reasoning and directly outputs answers; (2) 'UV-Cot w/ G.T. BBox' replaces predicted regions with ground truth bounding boxes to assess localization quality. Results show that removing CoT leads to a significant drop $(-7.7\%)$ on average), confirming its necessity. On Flickr30k, UV-Cot matches the G.T. variant, suggesting accurate region selection. However, in DocVQA and InfographicsVQA, using G.T. boxes yields better performance, revealing the difficulty of precise localization. This highlights the potential of our method and suggests future work for improving region accuracy for complex tasks.
+
+Score-DPO (sDPO): 'w/ naive DPO' applies standard DPO loss and shows degraded performance across all datasets (1.9% on average), especially on DocVQA (2.5%) and Flickr30k (2.6%), revealing its limitations for CoT learning. In contrast, our sDPO incorporates preference scores to better differentiate choices, yielding consistent gains.
+
+Iterative learning: 'w/o iterative learning' generates all preference pairs in a single pass and trains only once, leading to a significant performance drop (3.5% on average).
+
+
+Figure 3. (a&b) Bounding box evaluation on (a) training datasets and (b) zero-shot datasets. Our UV-CoT performs better than Visual-CoT. (c) Model performance under varying visual token sizes. Our UV-CoT demonstrates better token efficiency.
+
+
+
+| Model | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| OmniLMM-12B | 0.254 | 0.578 | 0.172 | 0.621 | 0.509 | 0.523 | 0.443 |
| IF: OmniLMM-12B + CoT | 0.305 | 0.722 | 0.217 | 0.675 | 0.580 | 0.595 | 0.516 |
| LLaVA-1.5-7B | 0.198 | 0.507 | 0.131 | 0.539 | 0.480 | 0.504 | 0.393 |
| IF: LLaVA-1.5-7B + CoT | 0.245 | 0.577 | 0.149 | 0.606 | 0.530 | 0.533 | 0.440 |
| Tr: UV-CoT (Evaluator: self-evaluated) | 0.242 | 0.609 | 0.153 | 0.598 | 0.517 | 0.526 | 0.441 |
| Tr: UV-CoT (Evaluator: OmniLMM-12B) | 0.265 | 0.686 | 0.173 | 0.632 | 0.536 | 0.548 | 0.473 |
+
+Table 5. Analysis of evaluator model. $^+$ CoT' refers to inference assisted by bounding boxes generated by UV-CoT. Self-evaluated denotes using target model as the evaluator during training. IF and Tr indicate experiments conducted on the inference and training process.
+
+This underscores the importance of iterative learning in continuously aligning the preference data distribution with the model's evolving policy throughout the training process.
+
+Response evaluation: 'w/o $\gamma$ model' sets $\gamma = 0$ during response evaluation stage, ignoring the next response when generating preference scores. We observe a significant performance drop (8.8% on average), particularly on TextVQA (17.2%), highlighting the difficulty MLLMs face in directly evaluating bounding boxes. This underscores the necessity of incorporating next response in our evaluation method.
+
+# 4.5. Bounding Box Evaluation
+
+We compare the quality of bounding boxes learned from supervised and unsupervised strategies using GPT-4o as a scorer, on both training datasets (Fig. 3 (a)) and zero-shot datasets (Fig. 3 (b)). Our main observations are:
+
+(1) Our UV-CoT outperforms Visual-CoT-7B, achieving higher scores in five of six datasets, supporting its superior performance in generating helpful bounding box.
+(2) The bounding box quality is closely related to the final performance. Our model exhibits lower scores (below 0.210) for bounding box generation in DocVQA and InfographicsVQA, correlating with its reduced final scores in these datasets (below 0.290 in Tab. 1). It underscores the validity of evaluating bounding box quality through its impact on subsequent answers.
+(3) Both UV-CoT and UV-CoT* outperform Visual-CoT
+
+7B across all zero-shot datasets, which illustrates the strong generalization of our method in bounding box generation.
+
+# 4.6. Insight of Evaluator Model
+
+We further perform studies to better understand the role of evaluator model. Key findings from Tab. 5 are:
+
+(1) We compare UV-CoT with its self-evaluated variant, where the evaluator model is the same as the target model (initiated with LLaVA-1.5-7B). Although the self-evaluated version exhibits a performance decrease of $3.2\%$ compared to the original UV-CoT, it still outperforms LLaVA-1.5-7B $(+4.8\%)$ on average) across all evaluated datasets and achieves performance comparable to the larger OmniLMM-12B model $(-0.2\%)$ on average). This demonstrates that UV-CoT maintains robust performance even under self-evaluation, highlighting its efficiency without requiring larger model scales.
+(2) For OmniLMM-12B and LLaVA-1.5-7B, we incorporate a CoT process using bounding boxes generated by UV-CoT. The CoT-enhanced versions significantly outperform their original counterparts, achieving average performance gains of $4.7\%$ for LLaVA-1.5-7B and $7.4\%$ for OmniLMM-12B. Remarkably, these models were not finetuned for the CoT process, indicating that the bounding box information alone substantially improves performance. This finding underscores that our evaluating process simplifies the task of generating complex spatial annotations,
+
+
+Figure 4. Visualization of preference data generated by Algorithm 1. Preferred BBoxes are in red. Dis-preferred BBoxes are in blue.
+
+
+
+
+
+
+Figure 5. Visualization of our UV-Cot inference. Model-generated bounding boxes are shown in red.
+
+
+
+
+
+enabling MLLMs to focus on evaluating final answers.
+
+# 4.7. Other Detailed Analyses
+
+Visual token efficiency. Compared to standard MLLM generation, image-level CoT doubles the number of visual tokens by processing additional local image regions. To evaluate token efficiency, i.e., performance under the same visual token budget, we resize the input image to different resolutions $(224^{2}, 336^{2}$ and $448^{2}$ ) and report the average score of different models in Fig. 3(c). Our key findings are: (1) MLLMs with image-level reasoning (Visual-CoT-7B and our UV-CoT) demonstrate better token efficiency than the standard answer generation pipeline. E.g., they achieve higher performance with 512 visual tokens than the standard pipeline does with 1024 tokens.
+(2) Our UV-CoT consistently outperforms Visual-CoT-7B across all scales, achieving higher average scores. This highlights the token efficiency of our method.
+
+Visualization. Fig. 4 visualizes some preference data from our UV-CoS inference process. Given different local regions and their corresponding answers, the evaluator MLLM assigns reasonable scores, validating the effective
+
+ness of our automatic generation and labeling process. In Fig. 5, we present reasoning cases with model-generated bounding boxes overlaid. The precision of bounding box detection and the depth of understanding play a crucial role in determining the quality of generated answers.
+
+# 5. Conclusion
+
+In this work, we propose UV-CoT, a framework that enables image-level CoT reasoning in MLLMs via preference optimization. Unlike previous methods that rely on SFT needing large amounts of labeled data, our approach leverages unsupervised learning to refine the model's ability with image-level CoT using model-generated preference data (which are rough but useful). We address key challenges in preference data generation and effective optimization, ensuring a more adaptive and interpretable reasoning process. Extensive experiments demonstrate that UV-CoT achieves state-of-the-art performance, significantly improving visual comprehension in MLLMs on ten reasoning datasets. Our findings highlight the potential of preference learning as a scalable alternative to traditional SFT, enabling more robust and data-efficient multimodal reasoning.
+
+# Acknowledgements
+
+This research is supported by the National Research Foundation, Singapore under its AI Singapore Programme (AISG Award No: AISG3-RP-2022-030). Thanks to Zichen Tian for his assistance with figure visualization throughout this work. The authors also thank the reviewers for their valuable comments and suggestions.
+
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+ "content": "Chain-of-thought (CoT) reasoning greatly improves the interpretability and problem-solving abilities of multimodal large language models (MLLMs). However, existing approaches focus on text CoT, limiting their ability to leverage visual cues. Visual CoT remains underexplored, and the only work [35] is based on supervised fine-tuning that relies on extensive labeled bounding-box data and is hard to generalize to unseen cases. In this paper, we introduce Unsupervised Visual CoT (UV-Cot), a novel framework for image-level CoT reasoning via preference optimization. UV-Cot performs preference comparisons between model-generated bounding boxes (one is preferred and the other is dis-preferred), eliminating the need for bounding-box annotations. We get such preference data by introducing an automatic data generation pipeline. Given an image, our target MLLM (e.g., LLaVA-1.5-7B) generates seed bounding boxes using a template prompt and then answers the question using each bounded region as input. An evaluator MLLM (e.g., OmniLLM-12B) ranks the responses, and these rankings serve as supervision to train the target MLLM with UV-Cot by minimizing negative log-likelihood losses. By emulating human perception-identifying key regions and reasoning based on them-UV-Cot can improve visual comprehension, particularly in spatial reasoning tasks where textual descriptions alone fall short. Our experiments on six datasets demonstrate the superiority of UV-Cot, compared to the state-of-the-art textual and visual CoT methods. Our zero-shot testing on four unseen datasets shows the strong generalization of UV-Cot."
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+ "type": "text",
+ "content": "dresses this by directly linking reward functions to optimal policies, eliminating reward model fine-tuning. Further improvements include IPO [2], which mitigates overfitting with a bounded preference function, and KTO [7], which removes the need for paired preference data, relying instead on single examples labeled as either 'good' or 'bad'."
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+ "content": "These preference learning techniques are applied to MLLMs, with RLHF-V and RLAIF-V [46, 47] refining behavior alignments using human and LLM-generated labels. To mitigate reward hacking, Sun et al. [37] enhance reward models with additional factual details, such as image captions and verified choices, further improving the performance of MLLM. Some works have attempted to apply DPO in the CoT process [18, 30]. However, these methods are designed for only text-level CoT and do not effectively handle visual features or cues. In contrast, in this paper, we propose UV-CoT, a specialized framework for image-level CoT reasoning inspired by the idea of DPO. Unlike traditional DPO, UV-CoT not only ranks preference data (i.e., preferred and dis-preferred data) but also assigns preference scores. This scoring enables more precise optimization of the MLLMs based on score differences."
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+ "content": "Fig. 2 illustrates the pipeline of UV-CoT reasoning. Given the original image and the question, we append a CoT prompt to guide the target MLLM in identifying the most informative image region and specifying its location via bounding box coordinates. A visual sampler then extracts the bounded region from the image. The MLLM subsequently integrates visual tokens from original and cropped images to generate more precise and comprehensive answers. In Sec. 3.1, we detail the automatic preference data generation pipeline. In Sec. 3.2, we describe our Score-"
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+ "content": "Algorithm 1 Preference data generation for a query "
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+ "content": " timesteps, we then optimize the target model with our UV-CoT via preference optimization on "
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+ "content": ". DPO [1] is widely used in preference learning, and it ranks responses without quantifying preference intensity. In our case of image-level reasoning, key regions vary in influence, necessitating finer differentiation between responses. Therefore, we refine DPO by adjusting the margin to capture the key region's influence. We name our loss Score-DPO, abbreviated as sDPO, as it incorporates the preference score into the optimization. The loss is formulated as:"
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+ "type": "text",
+ "content": " is a monotonically increasing function that maps preference scores into the logit space of the DPO objective."
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+ "content": "To provide a deeper understanding of our sDPO loss, we establish its connection to the standard DPO loss. DPO reformulates reward model training as policy optimization by reparameterizing the reward function in PPO [34]:"
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+ "type": "interline_equation",
+ "content": "r (x, y) = \\beta \\log \\frac {\\pi_ {\\theta} (y \\mid x)}{\\pi_ {\\text {r e f}} (y \\mid x)} + \\beta \\log Z (x) \\tag {3}",
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+ "content": "Using the Bradley-Terry [4] model, the standard DPO aims to minimize the negative log-likelihood of the difference of"
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+ "content": "Algorithm 2 Iterative learning of UV-CoT"
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| LLaVA-1.5-7B | 0.198 | 0.507 | 0.131 | 0.539 | 0.480 | 0.504 | 0.393 |
| LLaVA-1.5-13B | 0.225 | 0.543 | 0.169 | 0.607 | 0.506 | 0.512 | 0.427 |
| MiniCPM-o-8B | 0.232 | 0.529 | 0.175 | 0.618 | 0.495 | 0.521 | 0.428 |
| OmniLMM-12B | 0.254 | 0.578 | 0.172 | 0.621 | 0.509 | 0.523 | 0.443 |
| Visual-CoT-7B (100% label) | 0.294 | 0.673 | 0.194 | 0.652 | 0.546 | 0.532 | 0.482 |
| UV-CoT (0% label) | 0.265 | 0.686 | 0.173 | 0.632 | 0.536 | 0.548 | 0.473 |
| UV-CoT (10% label) | 0.283 | 0.711 | 0.198 | 0.649 | 0.568 | 0.553 | 0.494 |
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| LLaVA-1.5-7B | 0.165 | 0.147 | 0.340 | 0.217 |
| LLaVA-1.5-13B | 0.174 | 0.159 | 0.352 | 0.228 |
| MiniCPM-o-8B | 0.182 | 0.165 | 0.341 | 0.229 |
| OmniLMM-12B | 0.194 | 0.166 | 0.357 | 0.239 |
| Visual-CoT-7B | 0.206 | 0.181 | 0.397 | 0.261 |
| UV-Cot | 0.241 | 0.184 | 0.432 | 0.286 |
| UV-Cot* | 0.253 | 0.227 | 0.455 | 0.312 |
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| LLaVA-1.5-13B | 0.326 | 0.118 | 0.133 | 0.192 |
| MiniCPM-o-8B | 0.322 | 0.118 | 0.1 | 0.180 |
| OmniLMM-12B | 0.326 | 0.118 | 0.167 | 0.204 |
| Visual-CoT-7B | 0.330 | 0.118 | 0.593 | 0.347 |
| UV-CoT | 0.352 | 0.176 | 0.677 | 0.402 |
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| UV-CoT (10% labels) | 0.283 | 0.711 | 0.198 | 0.649 | 0.568 | 0.553 | 0.494 |
| IF: w/o UV-CoT | 0.149 | 0.574 | 0.160 | 0.585 | 0.509 | 0.522 | 0.417 |
| IF: UV-CoT w/ G.T. BBox | 0.528 | 0.769 | 0.504 | 0.655 | 0.664 | 0.585 | 0.618 |
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| Tr: w/o iterative learning | 0.256 | 0.671 | 0.162 | 0.609 | 0.523 | 0.531 | 0.459 |
| Ge: w/o γ | 0.247 | 0.539 | 0.152 | 0.551 | 0.484 | 0.460 | 0.406 |
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+ "html": "| Model | DocVQA | TextVQA | InfographicsVQA | Flickr30k | GQA | VSR | Average |
| OmniLMM-12B | 0.254 | 0.578 | 0.172 | 0.621 | 0.509 | 0.523 | 0.443 |
| IF: OmniLMM-12B + CoT | 0.305 | 0.722 | 0.217 | 0.675 | 0.580 | 0.595 | 0.516 |
| LLaVA-1.5-7B | 0.198 | 0.507 | 0.131 | 0.539 | 0.480 | 0.504 | 0.393 |
| IF: LLaVA-1.5-7B + CoT | 0.245 | 0.577 | 0.149 | 0.606 | 0.530 | 0.533 | 0.440 |
| Tr: UV-CoT (Evaluator: self-evaluated) | 0.242 | 0.609 | 0.153 | 0.598 | 0.517 | 0.526 | 0.441 |
| Tr: UV-CoT (Evaluator: OmniLMM-12B) | 0.265 | 0.686 | 0.173 | 0.632 | 0.536 | 0.548 | 0.473 |
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+ "content": " during response evaluation stage, ignoring the next response when generating preference scores. We observe a significant performance drop (8.8% on average), particularly on TextVQA (17.2%), highlighting the difficulty MLLMs face in directly evaluating bounding boxes. This underscores the necessity of incorporating next response in our evaluation method."
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+ "content": "(1) Our UV-CoT outperforms Visual-CoT-7B, achieving higher scores in five of six datasets, supporting its superior performance in generating helpful bounding box."
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diff --git a/2025/Unveiling the Invisible_ Reasoning Complex Occlusions Amodally with AURA/5862fa00-d00b-4bf4-b924-a02792140ae7_content_list.json b/2025/Unveiling the Invisible_ Reasoning Complex Occlusions Amodally with AURA/5862fa00-d00b-4bf4-b924-a02792140ae7_content_list.json
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+ {
+ "type": "text",
+ "text": "Unveiling the Invisible: Reasoning Complex Occlusions Amodally with AURA",
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+ "bbox": [
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+ "type": "text",
+ "text": "Zhixuan Li $^{1}$ Hyunse Yoon $^{2}$ Sanghoon Lee $^{2}$ Weisi Lin $^{1*}$",
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+ "type": "text",
+ "text": "$^{1}$ College of Computing and Data Science, Nanyang Technological University, Singapore $^{2}$ Department of Electrical and Electronic Engineering, Yonsei University, Korea",
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+ {
+ "type": "text",
+ "text": "zhixuanli520@gmail.com, hsyoon97, slee@yonsei.ac.kr, wslin@ntu.edu.sg",
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+ "img_path": "images/fe8c712667be32f0fe429f28865cdb46f2db1181bcc11d48621aae7b46d153e5.jpg",
+ "image_caption": [
+ "Figure 1. We introduce AURA, a multi-modal approach designed for reasoning the amodal segmentation mask including both visible and occlusion regions based on the user's question. AURA can deduce the implicit purpose underneath the question and respond with the textual answer along with predicted amodal masks for various objects. Best viewed in color."
+ ],
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+ "text": "Abstract",
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+ {
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+ "text": "Amodal segmentation aims to infer the complete shape of occluded objects, even when the occluded region's appearance is unavailable. However, current amodal segmentation methods lack the capability to interact with users through text input and struggle to understand or reason about implicit and complex purposes. While methods like LISA integrate multi-modal large language models (LLMs) with segmentation for reasoning tasks, they are limited to predicting only visible object regions and face challenges in handling complex occlusion scenarios. To address these limitations, we propose a novel task named amodal reasoning segmentation, aiming to predict the complete amodal shape of occluded objects while providing answers with elaborations based on user text input. We develop a generalizable dataset generation pipeline and introduce a new dataset focusing",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "on daily life scenarios, encompassing diverse real-world occlusions. Furthermore, we present AURA (Amodal Understanding and Reasoning Assistant), a novel model with advanced global and spatial-level designs specifically tailored to handle complex occlusions. Extensive experiments validate AURA's effectiveness on the proposed dataset. The code, model, and dataset are released in this page.",
+ "bbox": [
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+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "With the development of the Segment Anything Model (SAM) series methods [24, 25, 58], predicting the segmentation mask of visible regions has been largely solved. Amodal segmentation aims to predict the entire shape of an object, including both visible and occluded regions, which is naturally challenging since visual cues for the occluded regions are unavailable. Predicting the intact shape of occluded objects is crucial for various real-world applications,",
+ "bbox": [
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+ "page_idx": 0
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+ {
+ "type": "header",
+ "text": "CVF",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
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+ {
+ "type": "page_footnote",
+ "text": "* Corresponding author.",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "page_number",
+ "text": "21927",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "such as autonomous driving [12, 45, 50], robotics [2, 5, 22], and image editing [59, 63].",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "Existing amodal segmentation approaches have covered the fields including semantic [3, 49], instance [28, 37, 71], and panoptic [42] segmentation. Although existing amodal segmentation methods [10, 14, 45, 57] can address the problem of inferring occluded object shapes to some extent, they lack the ability to integrate with large language models (LLMs) [53, 54, 65], especially in performing reasoning and segmentation based on scene context, limiting their ability in interacting with users and understanding the implicit purpose underneath users questions. Meanwhile, although existing reasoning segmentation methods [26, 55] can work well on predicting the visible segmentation, they cannot predict the complete amodal segmentation mask, limiting their ability to reason in scenarios with complex occlusions. As a matter of fact, there is currently a significant gap in the availability of datasets designed for amodal reasoning segmentation, as well as in the development of algorithms specifically tailored to this task.",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "To address this gap, we propose a novel task named Amodal Reasoning Segmentation (ARS). As shown in Figure 1, the ARS task aims to interact with the user through textual questions, reasoning in the complex scene, and predicting accurate segmentation masks with textual answers. For this task, we present a highly generalizable data collection pipeline and construct a new dataset, AmodalReasonSeg, which covers daily life scenes (encompassing both indoor and outdoor environments) derived from the challenging COCOA-cls dataset [10, 71]. The AmodalReasonSeg dataset facilitates object reasoning and segmentation for visible and amodal masks across diverse scenes.",
+ "bbox": [
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+ "page_idx": 1
+ },
+ {
+ "type": "text",
+ "text": "Along with the new task and dataset, we introduce a novel model named AURA (Amodal Understanding and Reasoning Assistant). AURA can understand the user's input questions, reason about the scene in the image, and predict both visible and amodal segmentation masks simultaneously. Given the challenge of predicting the shape of occluded parts, which are invisible in the image, we propose two key designs to enhance occlusion prediction capabilities. Specifically, we introduce the Occlusion Condition Encoder, which can distinguish whether objects are occluded and assess the occlusion degree comprehensively. Besides, the Spatial Occlusion Encoder can provide spatial guidance on whether each region is occluded, ensuring consistency between visible and amodal mask predictions. It is worth noticing that the proposed AmodalReasonSeg dataset and the designed AURA method support reasoning and mask prediction for various objects within a single-turn conversation, enhancing applicability to real-world scenarios. Furthermore, AURA supports multi-round conversations, increasing its versatility.",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "Extensive experiments on the proposed AmodalReason",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "Seg dataset show that AURA outperforms existing methods in prediction accuracy, reasoning capability, and generalizability for complex occlusion scenarios.",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "text",
+ "text": "The contributions of this paper can be summarized as follows: (1) We propose a novel task: amodal reasoning segmentation, along with a generalizable dataset collection pipeline. We construct a new dataset, AmodalReasonSeg, covering a variety of complex scenes from daily life. (2) We introduce AURA, a multi-modal method integrating vision and language for complex reasoning, capable of predicting both visible and amodal segmentation masks accurately. To the best of our knowledge, AURA is the first method explicitly designed for reasoning segmentation of amodal regions. (3) Extensive experiments demonstrate the effectiveness of AURA through both quantitative and qualitative evaluations.",
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+ "type": "text",
+ "text": "2. Related Work",
+ "text_level": 1,
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+ "text": "Amodal segmentation [28] aims to predict the complete shape of an occluded object, encompassing both visible and occluded parts. Several methods [10, 28, 30, 32, 37, 38, 45] are developed by extending the methods designed for visible segmentation or object detection [4, 18-20, 23, 64], while the relative occlusion order information is leveraged by many methods [43, 63, 66, 68]. Since shape prior knowledge is an essential approach for inferring the shape of the occluded region, several methods [6, 9, 11, 29, 31, 34, 52, 57] are designed to learn and utilize it. For instance, VRSP [57] designs a codebook to store and retrieve shape priors for amodal masks. A3D [29] learns to reconstruct 3D shape priors to guide amodal segmentation. C2F-Seg [11] works in a coarse-to-fine manner equipped with a Vector-Quantized codebook [9]. Moreover, various datasets have been proposed for diverse scenarios, including daily life [10, 71], indoor [7, 8, 62, 70], autonomous driving [42, 45, 47], industrial [10], shopping [32], and gaming [14]. However, existing amodal segmentation methods and datasets are limited to using images or videos as input, focusing solely on predicting amodal masks without user interaction or reasoning about implicit user purposes. In this paper, we present the first high-quality dataset for the newly proposed amodal reasoning segmentation task and introduce a Vision-Language Model-based approach specifically designed for this task.",
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+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 1
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+ {
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+ "text": "With the rapid advancement of Large Language Models (LLMs) [53, 54, 65] such as GPT-4 [1] and LLaMA [53], language-based approaches have demonstrated impressive zero-shot generalization abilities across diverse real-world applications. Additionally, Vision Language Models",
+ "bbox": [
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+ "page_idx": 1
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+ {
+ "type": "page_number",
+ "text": "21928",
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+ "img_path": "images/88c3eeded22d3045e8557a2621c691f8df1e22f3960e2e0ff14be302c7b04076.jpg",
+ "image_caption": [
+ "Figure 2. Overall architecture of the proposed AURA. (a) Given an input image and the input question from the user, the Vision Backbone extracts the visual features of the input image, and the Multi-Modal LLM equipped with LoRA is utilized for understanding the input image and textual questions simultaneously and responding with textual answers that include the [SEG] tokens indicating the segmentation masks. (b) For each [SEG], the Prompt Encoder takes its embedding of the Multi-Modal LLM and outputs the refined embeddings corresponding to the [SEG]. (c) Finally, the Visible Mask Decoder predicts the visible mask using each [SEG]'s refined embeddings. The Amodal Decoder predicts the amodal mask using the occlusion-aware embedding predicted by the Occlusion Condition Encoder. A Spatial Occlusion Encoder is designed to constrain the spatial occlusion information of the predicted visible and amodal segmentation masks to be accurate. Best viewed in color."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 2
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+ {
+ "type": "text",
+ "text": "(VLMs) [21, 35, 36] like BLIP-2 [27] and LLaVA [36] have achieved state-of-the-art performance in comprehensively understanding both visual and textual information. To leverage the reasoning capabilities of VLMs, LISA [26] introduces the task of reasoning segmentation, which predicts visible segmentation masks by reasoning based on user input questions. Building upon LISA, several recent methods, such as Pixel-LM [48], VISA [60], and LLM-Seg [55], have been proposed to enhance different aspects of the reasoning segmentation task, such as multi-object segmentation, video segmentation, and training efficiency, respectively. Despite these advancements, all existing methods are limited to segmenting only the visible region of target objects, leaving segmenting and analyzing the occluded region untouched. Our work aims to bridge this gap by enabling reasoning and segmenting in an amodal manner, specifically designed to handle complex occlusions in real-world scenarios.",
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+ "type": "text",
+ "text": "In this section, we first introduce the definition of the proposed amodal reasoning segmentation task in 3.1. Then the overall architecture of the designed method is presented in 3.2. Next, the special designs for learning and handling occlusion are introduced in 3.3. Finally, the loss functions that organize the training objectives are shown in 3.4.",
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+ "text": "For the proposed amodal reasoning segmentation (ARS) task, each image $x_{img}$ of the dataset is associated with various questions $x_{text}$ , answers $y_{text}$ , and segmentations $y_{seg}$ .",
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+ "text": "For each pair, $x_{text}$ is a question from the user input that does not directly point to objects in the image. $y_{text}$ is the ground-truth textual answer that responds to the question and includes the description of one or more objects alongside the [SEG] token representing the position of the segmentation mask. $y_{seg}$ represents the ground-truth visible and amodal segmentation masks $(M_v$ and $M_a)$ , corresponding to the [SEG] in the answer $y_{text}$ .",
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+ "type": "text",
+ "text": "3.2. Overall Architecture",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "As shown in Figure 2, the overall architecture of the proposed AURA includes three stages. Specifically, (1) the Vision Backbone takes the input image $I$ as input for extracting its visual feature $F_{I}$ , and the Multi-Modal LLM $\\mathcal{E}_{MLLM}$ equipped with LoRA is employed to understand the input image $I$ and the user's input question $x_{text}$ , and predict the textual answer $\\hat{y}_{text}$ to respond the question. (2) The Prompt Encoder $\\mathcal{E}_P$ takes the embedding $e_{mllm}$ of each [SEG] from the hidden states of the Multi-Modal LLM and predicts the refined embedding $e_r$ for each [SEG]. (3) Finally the $e_r$ and $F_{I}$ are fed into the Visible Mask Decoder $\\mathcal{D}_V$ for predicting the visible segmentation mask $\\hat{M}_v$ of each [SEG]. Besides, the $e_r$ is used by the Occlusion Condition Encoder $\\mathcal{E}_{OC}$ , which learns to predict the occlusion-aware embedding $e_{oa}$ that is contained within the occlusion condition information. Then the Amodal Mask Decoder $\\mathcal{D}_A$ uses the $F_{I}$ and $e_{oa}$ for predicting the amodal segmentation mask $\\hat{M}_a$ of each [SEG]. The Spatial Occlusion Encoder $\\mathcal{E}_{SO}$ is designed to constrain the predicted $\\hat{M}_v$ and $\\hat{M}_a$ to conform to the spatial occlusion relationship, which implic",
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+ "type": "page_number",
+ "text": "21929",
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+ "page_idx": 2
+ },
+ {
+ "type": "image",
+ "img_path": "images/df72bda979b1f5323805392ea8cfccb4f6cf159423b14b1611cce4bde426fbea.jpg",
+ "image_caption": [
+ "(a)",
+ "Figure 3. The designed occlusion encoders. (a) The Occlusion Condition Encoder learns to embed the occlusion condition of each mask and output the occlusion-aware embedding. (b) The Spatial Occlusion Encoder takes the predicted visible and amodal masks as input and predicts the occlusion-aware spatial map to constrain the spatial relationship between the two predicted masks."
+ ],
+ "image_footnote": [],
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+ "page_idx": 3
+ },
+ {
+ "type": "image",
+ "img_path": "images/45f17ea8f151e9036cd0926c285cd0ff4348e0f8ca8d72611b62cc4184221ce6.jpg",
+ "image_caption": [
+ "(b)"
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "itly improves the accuracy of the two predicted masks.",
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+ },
+ {
+ "type": "text",
+ "text": "The textual prediction of the Multi-Modal LLM is supervised using the $\\mathcal{L}_{text}$ , which can be denoted as:",
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {t e x t}} = \\mathcal {L} _ {C E} \\left(\\hat {y} _ {\\text {t e x t}}, y _ {\\text {t e x t}}\\right), \\tag {1}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "where $\\mathcal{L}_{CE}$ is the Cross-Entropy loss [61]. Moreover, for supervising the visible and amodal mask predictions, the $\\mathcal{L}_{mask}$ is used as shown in the following:",
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+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {\\text {m a s k}} = \\mathcal {L} _ {C E} (\\hat {M} _ {v}, M _ {v}) + \\mathcal {L} _ {C E} (\\hat {M} _ {a}, M _ {a}) + \\tag {2}\n$$\n",
+ "text_format": "latex",
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+ "page_idx": 3
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {D i c e} \\left(\\tilde {M} _ {v}, M _ {v}\\right) + \\mathcal {L} _ {D i c e} \\left(\\tilde {M} _ {a}, M _ {a}\\right),\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "where $\\mathcal{L}_{Dice}$ is the Dice loss [51].",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "3.3. Occlusion Learning",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "Figure 3 illustrates the designed occlusion encoders for handling occlusion learning in AURA. Detailed network structures, inputs and outputs, and losses are presented.",
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+ },
+ {
+ "type": "text",
+ "text": "Occlusion Condition Encoder is designed to improve the ability of the refined embedding $e_r$ predicted by the Prompt Encoder to be aware of the occlusion condition of the object(s) corresponding to the [SEG]. Specifically, the $e_r$ is fed into the Occlusion Condition Encoder $\\mathcal{E}_{OC}$ and predicts the occlusion-aware embedding $e_{oa}$ that is distinguishable by the degree of occlusion. The Occlusion Condition Encoder $\\mathcal{E}_{OC}$ additionally predicts the occlusion rate $\\hat{r}$ of the object, which reflects the occlusion condition comprehensively and is supervised by $\\mathcal{L}_{occ - oc}$ with the ground-truth occlusion rate $r$ . Moreover, a Linear layer and a Sigmoid layer are employed to predict the occlusion rate $\\hat{r}$ based on the refined embedding $e_r$ .",
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+ {
+ "type": "text",
+ "text": "Spatial Occlusion Encoder is proposed to constrain the spatial occlusion conditions between the predicted visible masks $\\hat{M}_v$ and amodal masks $\\hat{M}_a$ , enhancing the accuracy of visible and amodal segmentation prediction. Specifically, the Spatial Occlusion Encoder $\\mathcal{E}_{SO}$ takes both $\\hat{M}_v$ and $\\hat{M}_a$ as input and predicts the occlusion-aware spatial map $\\hat{M}_{sp}$ , which is supervised by $\\mathcal{L}_{occ-sp}$ with the ground-truth occlusion-aware spatial map $M_{sp}$ . The ground truth $M_{sp}$ is defined by setting regions belonging to the ground-truth visible mask $M_v$ as 1 and setting regions belonging to the ground-truth amodal mask $M_a$ but not $M_v$ as 2, and setting other background regions as 0. In this approach, the constraint between predicted masks $\\hat{M}_v$ and $\\hat{M}_a$ is constructed and contributes to accurate segmentation.",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "For supervising the predictions of the occlusion condition and the spatial occlusion map, the $\\mathcal{L}_{occ}$ is used as shown below:",
+ "bbox": [
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+ ],
+ "page_idx": 3
+ },
+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} _ {o c c} = \\mathcal {L} _ {M S E} (\\hat {r}, r) + \\mathcal {L} _ {C E} (\\hat {M} _ {s p}, M _ {s p}), \\tag {3}\n$$\n",
+ "text_format": "latex",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "where $\\mathcal{L}_{MSE}$ is the Mean Squared Error loss.",
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "3.4. Loss Functions",
+ "text_level": 1,
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "The overall loss function $\\mathcal{L}$ consists of four parts, supervising the textual answers $\\hat{y}_{text}$ predicted by the MultiModal LLM, the predicted visible and amodal masks $(\\hat{M}_v$ and $\\hat{M}_a)$ , and the predictions of two designed occlusion encoders including the occlusion rate $\\hat{r}$ and the occlusion-aware spatial map $\\hat{M}_{sp}$ . The overall loss function can be formulated as:",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {t e x t}} + \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\text {o c c}}. \\tag {4}\n$$\n",
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+ {
+ "type": "text",
+ "text": "4. AmodalReasonSeg Dataset",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "Existing amodal segmentation datasets [10, 45, 62] only contain images/videos and ground-truth masks without language annotations, which cannot fulfill the requirement of the amodal reasoning segmentation task. To this end, it is essential to construct a large-scale dataset with high-quality language annotations, including implicit user questions and the corresponding answers.",
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+ {
+ "type": "text",
+ "text": "In this section, we first introduce the basic information of the newly constructed dataset in 4.1. Next, we demonstrate a general dataset generation pipeline that is generable for diverse scenarios and can be applied to generate new datasets efficiently in 4.2.",
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+ "type": "text",
+ "text": "4.1. Overview of the Dataset",
+ "text_level": 1,
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+ "type": "text",
+ "text": "To construct the new dataset for the amodal reasoning segmentation task, the challenging amodal segmentation dataset COCOA-cls [10, 71] is utilized. The COCOA-cls dataset is built upon the famous COCO [33] dataset, which includes daily scenarios with indoor and outdoor scenes.",
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+ "text": "21930",
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+ {
+ "type": "image",
+ "img_path": "images/f8e51f1a9f0236d16e306b65e467e273168aa58b7f8fd710efa3445d26c8fc99.jpg",
+ "image_caption": [
+ "Figure 4. The designed generalizable pipeline for dataset generation. (a) Each image and the information of objects in it are gathered and fed into the GPT to generate questions and answers. (b) Then human annotators will check the generated data and improve it manually. Cross-check ensures the quality of the generated data."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "For benchmarking the proposed amodal reasoning segmentation (ARS) task, we present the AmodalReasonSeg dataset, which is built upon the COCOA-cls dataset. The AmodalReasonSeg dataset includes 3,143 images and 35,494 high-quality question-and-answer pairs corresponding to the visible and amodal segmentation masks. The visible and amodal bounding boxes and the category information are included in our dataset. For each image, there are 11.3 pairs of questions and answers on average annotated to cover diverse potential conversations. Overall, there are 2,018 images and 22,856 pairs of questions and answers in the train set and 1,125 images and 12,638 question-and-answer pairs in the test set.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Compared with existing amodal segmentation datasets, the AmodalReasonSeg dataset supports interacting with users by using textual questions as input, and the answers respond to the implicit purpose underneath the questions and alongside the visible and amodal segmentation predictions. Moreover, it is worth noticing that the answer corresponding to each image could refer to various objects, meaning the proposed dataset supports reasoning and predicting different targets in a single conversation, which is essential in real-world applications.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "4.2. Dataset Generation",
+ "text_level": 1,
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "A generalizable pipeline is designed to generate the new dataset, as shown in Figure 4. Since manually annotating the question-and-answer pairs and the visible and amodal segmentation masks is labor-intensive and time-consuming, we present a semi-automatic pipeline inspired by [48] to keep the efficiency of the annotating process and high-quality annotations. Specifically, the images and annotations, including category information and visible and amodal masks, are reserved from the original dataset.",
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+ "type": "text",
+ "text": "For generating the question-and-answer pairs, each image alongside the annotations is organized by a designed prompt template to be understood by a powerful and versatile large Vision-Language model, which is the ChatGPT-4o in our work that could take both image and text as input and output text response.",
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+ "type": "text",
+ "text": "The prompt template is carefully designed to require ChatGPT-4o to generate question-and-answer pairs that satisfy the requirements to ensure the generation of high-quality data. The annotation information of objects for this image is collected and fed to ChatGPT-4o. For each image, ten question-and-answer pairs are required to be generated. Different objects are required to be organized and contained in one answer. Besides, the relative occlusion information between different objects is required to be considered when generating the question-and-answer pairs, which makes the text description in the answer helpful for discriminating the occlusion relationship between objects. The existing annotations from the original dataset of all objects in the image are organized and taken as input for the ChatGPT-4o. Finally, three human annotators check the generated questions and verify if they are qualified. During human verification, qualified samples are retained, while flawed ones are revised with appropriate questions and answers instead of being discarded. Common issues include incorrect object references, implausible functions, or inaccurate quantities. For the ones that need to be improved, human annotators will manually design appropriate questions and answers for these images. Cross-check is utilized between different human annotators to ensure the quality of the generated data.",
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+ {
+ "type": "text",
+ "text": "5. Experiments",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "5.1. Experimental Settings",
+ "text_level": 1,
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+ },
+ {
+ "type": "text",
+ "text": "Dataset. All experiments, including our proposed method and compared methods, are trained on the training set of the proposed AmodalReasonSeg dataset, and evaluated on the validation set of this dataset for fairness. No extra dataset besides the AmodalReasonSeg dataset is used.",
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+ "type": "text",
+ "text": "Model Structure. We employ the LLaVA-7B-v1-1 [36] as the multi-modal LLM, which is equipped with LoRA for efficient fine-tuning. For the Vision Backbone and the Prompt Encoder, the SAM [25] method with the ViT-H version is utilized. The mask decoder of SAM is employed for the Visible Mask Decoder and Amodal Mask Decoder. Unless specifically specified, all experiments of the proposed AURA method are based on the model structure of using the LLaVA-7B-v1-1 [36] as the multi-modal LLM and the ViT-H version of SAM [25].",
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+ },
+ {
+ "type": "text",
+ "text": "Implementation Details. We implement our proposed AURA based on Pytorch [44]. The AdamW [39] optimizer is used with the learning rate set to 1e-3. The WarmupDecayLR learning rate adjustment policy is used with 100 iter",
+ "bbox": [
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+ {
+ "type": "page_number",
+ "text": "21931",
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+ {
+ "type": "table",
+ "img_path": "images/f9c2b310204631387bfa456bc5847a4ed270f59a39b7803bb8f2a0dac7c258b9.jpg",
+ "table_caption": [],
+ "table_footnote": [
+ "Table 1. Comparison of the amodal reasoning segmentation performance on the AmodalReasonSeg dataset. † denotes that this method is trained twice with ground-truth visible and amodal masks of the proposed AmodalReasonSeg dataset, respectively. Best in bold, second underlined."
+ ],
+ "table_body": "| Method | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| Amodal Segmentation Methods |
| VRSP† [57] AAAI'21 | 15.18 | 16.55 | 17.41 | 19.75 |
| C2F-Seg† [11] ICCV'23 | 18.62 | 18.25 | 19.12 | 20.31 |
| SD-Amodal† [62] CVPR'24 | 20.87 | 20.09 | 21.52 | 23.10 |
| MLLM-based Methods |
| LISA† [26] CVPR'24 | 23.05 | 22.87 | 24.39 | 26.81 |
| LLM-Seg† [55] CVPR'24 | 24.62 | 23.06 | 25.19 | 27.94 |
| GSVA† [56] CVPR'24 | 42.30 | 42.87 | 47.01 | 48.22 |
| OMG-LLaVA† [67] NeurIPS'24 | 43.92 | 44.21 | 49.41 | 49.38 |
| GLaMM† [46] CVPR'24 | 45.75 | 46.82 | 49.93 | 54.14 |
| PSALM† [69] ECCV'24 | 46.81 | 47.03 | 50.64 | 55.19 |
| Baseline | 43.55 | 43.92 | 48.96 | 48.63 |
| AURA | 47.76 | 47.32 | 51.31 | 55.38 |
",
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+ {
+ "type": "text",
+ "text": "ations for warmup and then linearly decreases the learning rate to 0. Apart from the ablation studies using 13B models as Multi-Modal LLM Backbone that use two NVIDIA A100 GPUs (80GB Memory) for experiments, all of our experiments are conducted on two NVIDIA V100 GPUs (32GB Memory). The batch size for each GPU card is set to 1. The entire training iterations are 5000, and the gradient accumulation technique is used by setting the accumulation step to 4. The entire training time is about 10 hours.",
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+ "type": "text",
+ "text": "Evaluation Metrics. The gIoU and cIoU metrics are used for evaluating the segmentation performance of amodal and visible masks. The gIoU is calculated by averaging the Intersection-over-Unions (IoUs) of all images, while the cIoU is calculated by dividing the cumulative intersection by the cumulative union of all masks.",
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+ "type": "text",
+ "text": "5.2. Amodal Reasoning Segmentation",
+ "text_level": 1,
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+ "page_idx": 5
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+ "type": "text",
+ "text": "Compared Methods. To benchmark the performance of amodal reasoning segmentation on the proposed Amodal-ReasonSeg dataset, state-of-the-art amodal segmentation methods [11, 57, 62] and multimodal large language model (MLLM)-based methods [26, 46, 55, 56, 67, 69] for reasoning segmentation of visible region are used for comparison. All methods are trained and evaluated on the train set and the val set of our proposed AmodalReasonSeg dataset, ensuring fairness. LLaVA-7B-v1-1 is employed for all MLLM-based methods.",
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "The amodal segmentation methods [11, 57, 62] are designed for taking an image as input and predicting amodal segmentation masks for all objects, but cannot understand the user's question, reasoning, and response with textual answers and segmentations. Besides, MLLM-based meth",
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "ods [26, 46, 55, 56, 67, 69] are designed to segment the visible regions of each object by taking the image and the user's question as input.",
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+ "type": "text",
+ "text": "However, these aforementioned methods can only predict either visible or amodal masks by training twice with ground-truth visible or amodal masks, while the proposed AURA can reason and predict the visible and amodal masks simultaneously. Moreover, MLLM-based methods like LISA can only reason for one object to each question, while the proposed AURA could reason and respond with various objects with textual answers describing them and corresponding segmentation predictions. The baseline method is the proposed AURA without using the designed two occlusion learning modules, including the Occlusion Condition Encoder $\\mathcal{E}_{OC}$ and the Spatial Occlusion Encoder $\\mathcal{E}_{SO}$ .",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Quantitative Results. Table 1 shows the performance of all compared methods on the proposed AmodalReasonSeg dataset. $\\dagger$ means this method is trained twice on ground-truth visible and amodal masks, respectively, due to a lack of the ability to predict both masks at the same time. AURA achieves the best performance among all metrics regarding amodal and visible segmentations. To be more specific: (1) Firstly, since amodal segmentation methods [11, 57, 62] are designed for amodal segmentation and cannot take a textual question as input and understand it, they cannot be certain of which objects to segment, and the predicted masks could not be for the target objects. Therefore, these methods are evaluated by computing metrics between all predicted objects and target objects. In contrast, the proposed AURA can understand the purpose underneath the user's question and predict the amodal and visible masks for the targeted objects mentioned in the generated textual answer. (2) Secondly, since these MLLM-based methods are designed for segmenting visible regions of objects, their performance is not as well as AURA, which is specifically designed for the amodal reasoning segmentation task with task-specific designs for handling occlusions. Moreover, methods like LISA are designed to only segment one object for each question with other objects missed. However, AURA can support multi-object segmentation in a single conversation, responding with textual answers describing various objects with detailed elaborations.",
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+ "page_idx": 5
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+ {
+ "type": "text",
+ "text": "Qualitative Results. Figure 5 presents the visualization results of AURA in three cases, showing that AURA can accurately understand the occlusion relation between objects in the image, reason the purpose underneath the question, and predict segmentation masks for various objects. In the first case, although part of the orange is completely occluded by the ice cream on top, and the plate below has a messy pattern, which may cause confusion, AURA still can correctly understand the question and predict an intact amodal segmentation mask for the occluded orange. In the second case, the black cat and the person's black clothing are easily con",
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+ "text": "21932",
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+ "table_body": "| Index | \\( \\mathcal{E}_{OC} \\) | \\( \\mathcal{E}_{SO} \\) | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| 1 | | | 43.55 | 43.92 | 48.96 | 48.63 |
| 2 | ✓ | | 44.86 | 44.07 | 49.57 | 49.10 |
| 3 | | ✓ | 46.95 | 45.60 | 50.68 | 53.72 |
| 4 | ✓ | ✓ | 47.76 | 47.32 | 51.31 | 55.38 |
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+ "Table 2. Ablation study of designs for occlusion learning. Best in bold, second underlined."
+ ],
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+ "table_body": "| Method | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| AURA w/o LoRA | 20.84 | 21.03 | 25.43 | 27.95 |
| AURA w/ LoRA | 47.76 | 47.32 | 51.31 | 55.38 |
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+ "text": "fused, especially in a dark environment. However, AURA can precisely distinguish between the cat and the person's black clothing and accurately predict the complete amodal mask of the person, even though a large region of the person is occluded by the cat. In the third case, the front side of the toilet is occluded by the cat to a large extent, while AURA can reason the purpose of the question and predict a high-quality amodal segmentation mask for the occluded toilet and an accurate segmentation mask for the cat.",
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+ "text": "5.3. Ablation Study",
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+ "text": "We conduct ablation studies for the proposed AURA from various aspects, including the design of occlusion learning modules, the effectiveness of LoRA, the scale of the MultiModal LLM Backbone, and the scale of the Vision Backbone.",
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+ "text": "Occlusion Learning. As shown in Table 2, when the two designed Occlusion Condition Encoder $\\mathcal{E}_{OC}$ and Spatial Occlusion Encoder $\\mathcal{E}_{SO}$ are not used, the performance of AURA drops in a certain degree. When only using $\\mathcal{E}_{OC}$ , the occlusion conditions of all objects are learned and can help with our model for comprehensively distinguishing whether objects are occluded and the degree of occlusion for these objects. Besides, when only using $\\mathcal{E}_{SO}$ , the spatial occlusion distribution can be learned and guide our model to be aware of whether each region is occluded or visible, and constrain the consistency between the predicted visible and amodal masks regarding the spatial occlusion condition. Finally, when both $\\mathcal{E}_{OC}$ and $\\mathcal{E}_{SO}$ are utilized, the best performance is achieved with the learning of global and spatial occlusion conditions simultaneously.",
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+ "text": "Effectiveness of LoRA. We conduct experiments to evaluate the effectiveness of LoRA, as shown in Table 3. The LoRA [13] technique is utilized to be equipped with",
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+ "Table 3. Ablation study of the effectiveness of using LoRA in the Multi-Modal LLM for efficient fine-tuning. w/o and w/ denote without and with the LoRA technique, respectively. Best in bold."
+ ],
+ "table_footnote": [],
+ "table_body": "| Multi-Modal LLM Backbone | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| AURA-7B | 47.76 | 47.32 | 51.31 | 55.38 |
| AURA-13B | 49.41 | 49.74 | 54.13 | 57.97 |
| AURA-Llama2-13B | 52.34 | 52.95 | 58.42 | 60.21 |
",
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+ "img_path": "images/9af46d254ca61f3a58f0fe8aa746a9130f6206ec0ed9483343805afc62e6f683.jpg",
+ "table_caption": [
+ "Table 4. Ablation study of the scale of the backbone for the MultiModal LLM. Best in bold, second underlined."
+ ],
+ "table_footnote": [],
+ "table_body": "| Vision Backbone | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| SAM-ViT-B | 42.85 | 42.76 | 46.92 | 50.12 |
| SAM-ViT-L | 45.23 | 45.31 | 49.18 | 53.71 |
| SAM-ViT-H | 47.76 | 47.32 | 51.31 | 55.38 |
",
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+ "type": "text",
+ "text": "Table 5. Ablation study of the scale of the Vision Backbone. B, L, and H denote Base, Large, and Huge, respectively. Best in bold, second underlined.",
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+ "type": "text",
+ "text": "the Multi-Modal LLM for efficiently fine-tuning new data while keeping the pre-trained weight of LLM frozen. As shown in Table 3, when not using the LoRA technique, the performance of AURA drops to a certain extent. This is because the Multi-Modal LLM is not pre-trained on the AmodalReasonSeg dataset and has no specific knowledge learned to understand the purpose underneath the user's question and reason for various occluded objects. Therefore, the Multi-Modal LLM cannot predict textual answers correctly to respond to the user's question, leading to the performance of visible and amodal segmentation not well.",
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+ "text": "Scale of Multi-Modal LLM Backbone. The effect of the scale of the Multi-Modal LLM backbone is evaluated as shown in Table 4. The AURA-7B, AURA-13B, and AURA-Llama2-13B denote the AURA method with different Multi-Modal LLM backbones corresponding to LLaVA-7B, LLaVA-13B, and LLaVA-Llama2-13B models. These models are different variants of the LLaVA model with different scales of parameters (7 billion and 13 billion) and different generations of Llama. All experiments, apart from this ablation study, are based on the AURA-7B model. We can observe from Table 4 that the AURA-7B model does not perform as well as the other two models since the smaller number of parameters limits its learning ability for fine-tuning on the proposed AmodalReasonSeg dataset. Moreover, using larger models with 13 billion parameters can bring better performance since the learning capabilities of these models are better. Finally, upgrading the Llama large language model from the first to the second generation further enhances segmentation performance by generating higher-quality answers and refined embeddings used for segmentation.",
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+ "text": "Scale of the Vision Backbone. To evaluate the effect of the scale of the Vision Backbone, which is utilized to ex",
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+ "text": "21933",
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+ "type": "image",
+ "img_path": "images/7363457d998800e48e611089fbb9abebd70ed4515f1f8dea828e946891e711bb.jpg",
+ "image_caption": [
+ "Figure 5. Visualization results of AURA. Three cases are shown from top to bottom with questions and ground-truth (GT) answers. The first two cases show the images, ground-truth amodal and visible masks, and the predicted masks of AURA. In the last case, the predicted amodal mask by AURA for the occludee, which is the occluded toilet, is shown replacing the ground-truth visible mask."
+ ],
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+ {
+ "type": "text",
+ "text": "tract vision features of the input image and plays an essential role in providing informative features to the segmentation decoders, experiments are conducted, and the results are shown in Table 5. Three scales of the Vision Backbone are compared, including the Base, Large, and Huge versions of SAM, corresponding to 93.7M, 312M, and 641M parameters, respectively. We can observe that the model with a larger number of parameters can achieve better segmentation performance and greater learning ability.",
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+ "type": "text",
+ "text": "6. Conclusion",
+ "text_level": 1,
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+ "text": "In this work, we propose a new task named Amodal Reasoning Segmentation, aiming to predict textual answers alongside visible and amodal segmentation masks in response to the user's input question that requires understanding and complex reasoning in the image. A generalizable dataset generation pipeline is proposed, which can generate anno",
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+ {
+ "type": "text",
+ "text": "tations with high quality efficiently. A new dataset named AmodalReasonSeg is presented for daily scenarios where occlusions are challenging for amodal segmentation. Extensive textual question-and-answer pairs are generated, and various objects are referred to in the answers. Moreover, we propose AURA to understand the user's implicit purpose and reason for the answer, which organizes various objects coherently with accurately predicted visible and amodal segmentation masks. Extensive experiments demonstrate the effectiveness of our proposed AURA on reasoning and segmenting the amodal masks in diverse complex scenarios. To enhance the applicability in real-world scenarios, we plan to further optimize the efficiency of our LLM-based model and enrich our dataset's diversity and granularity. Moreover, feature compression approaches [15-17, 40, 41] can be considered to improve the inference speed of the proposed approach.",
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+ "text": "21934",
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+ {
+ "type": "text",
+ "text": "Acknowledgments",
+ "text_level": 1,
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+ {
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+ "text": "This research was supported by the Ministry of Education of Singapore Tier3 grant MOET32022-0006. This research was also supported by Culture, Sports and Tourism R&D Program through the Korea Creative Content Agency grant funded by the Ministry of Culture, Sports and Tourism in 2024 (Project Name: Global Talent for Generative AI Copyright Infringement and Copyright Theft, Project Number: RS-2024-00398413, Contribution Rate: $10\\%$ ).",
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+ "type": "text",
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+ "[58] Yunyang Xiong, Bala Varadarajan, Lemeng Wu, Xiaoyu Xiang, Fanyi Xiao, Chenchen Zhu, Xiaoliang Dai, Dilin Wang, Fei Sun, Forrest Iandola, et al. EfficientSAM: Leveraged masked image pretraining for efficient segment anything. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 16111-16121, 2024.",
+ "[59] Katherine Xu, Lingzhi Zhang, and Jianbo Shi. Amodal completion via progressive mixed context diffusion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 9099-9109, 2024.",
+ "[60] Cilin Yan, Haochen Wang, Shilin Yan, Xiaolong Jiang, Yao Hu, Guoliang Kang, Weidi Xie, and Efstratios Gavves. VISA: Reasoning video object segmentation via large language models. Proceedings of the IEEE/CVF European Conference on Computer Vision, 2024."
+ ],
+ "bbox": [
+ 91,
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+ 900
+ ],
+ "page_idx": 10
+ },
+ {
+ "type": "list",
+ "sub_type": "ref_text",
+ "list_items": [
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+ "[62] Guanqi Zhan, Chuanxia Zheng, Weidi Xie, and Andrew Zisserman. Amodal ground truth and completion in the wild. Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, 2024.",
+ "[63] Xiaohang Zhan, Xingang Pan, Bo Dai, Ziwei Liu, Dahua Lin, and Chen Change Loy. Self-supervised scene deocclusion. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3784-3792, 2020.",
+ "[64] Jingyi Zhang, Jiaxing Huang, Xueying Jiang, and Shijian Lu. Black-box unsupervised domain adaptation with bidirectional atkinson-shiffrin memory. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 11771-11782, 2023.",
+ "[65] Renrui Zhang, Jiaming Han, Chris Liu, Peng Gao, Aojun Zhou, Xiangfei Hu, Shilin Yan, Pan Lu, Hongsheng Li, and Yu Qiao. LLaMA-Adapter: Efficient fine-tuning of language models with zero-init attention. International Conference on Learning Representations, 2024.",
+ "[66] Shihui Zhang, Ziteng Xue, Yuhong Jiang, and Houlin Wang. Opnet: Deep occlusion perception network with boundary awareness for amodal instance segmentation. In International Conference on Acoustics, Speech, and Signal Processing, pages 2595-2599. IEEE, 2024.",
+ "[67] Tao Zhang, Xiangtai Li, Hao Fei, Haobo Yuan, Shengqiong Wu, Shunping Ji, Chen Change Loy, and Shuicheng Yan. Omg-llava: Bridging image-level, object-level, pixel-level reasoning and understanding. Advances in Neural Information Processing Systems, 37:71737-71767, 2024.",
+ "[68] Ziheng Zhang, Anpei Chen, Ling Xie, Jingyi Yu, and Shenghua Gao. Learning semantics-aware distance map with semantics layering network for amodal instance segmentation. In ACM International Conference on Multimedia, pages 2124-2132, 2019.",
+ "[69] Zheng Zhang, Yeyao Ma, Enming Zhang, and Xiang Bai. Psalm: Pixelwise segmentation with large multi-modal model. In Proceedings of the IEEE/CVF European Conference on Computer Vision, pages 74-91. Springer, 2024.",
+ "[70] Chuanxia Zheng, Duy-Son Dao, Guoxian Song, Tat-Jen Cham, and Jianfei Cai. Visiting the invisible: Layer-by-layer completed scene decomposition. International Journal of Computer Vision, 129:3195-3215, 2021.",
+ "[71] Yan Zhu, Yuandong Tian, Dimitris Metaxas, and Piotr Dóllár. Semantic amodal segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1464-1472, 2017."
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diff --git a/2025/Unveiling the Invisible_ Reasoning Complex Occlusions Amodally with AURA/5862fa00-d00b-4bf4-b924-a02792140ae7_model.json b/2025/Unveiling the Invisible_ Reasoning Complex Occlusions Amodally with AURA/5862fa00-d00b-4bf4-b924-a02792140ae7_model.json
new file mode 100644
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+ "content": "CVF"
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+ "angle": 0,
+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
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+ "type": "title",
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+ "content": "Unveiling the Invisible: Reasoning Complex Occlusions Amodally with AURA"
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+ "content": "Zhixuan Li\\(^{1}\\) Hyunse Yoon\\(^{2}\\) Sanghoon Lee\\(^{2}\\) Weisi Lin\\(^{1*}\\)"
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+ "content": "\\(^{1}\\)College of Computing and Data Science, Nanyang Technological University, Singapore \\(^{2}\\)Department of Electrical and Electronic Engineering, Yonsei University, Korea"
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+ "content": "zhixuanli520@gmail.com, hsyoon97, slee@yonsei.ac.kr, wslin@ntu.edu.sg"
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+ "angle": 0,
+ "content": "Figure 1. We introduce AURA, a multi-modal approach designed for reasoning the amodal segmentation mask including both visible and occlusion regions based on the user's question. AURA can deduce the implicit purpose underneath the question and respond with the textual answer along with predicted amodal masks for various objects. Best viewed in color."
+ },
+ {
+ "type": "title",
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+ "content": "Abstract"
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+ "content": "Amodal segmentation aims to infer the complete shape of occluded objects, even when the occluded region's appearance is unavailable. However, current amodal segmentation methods lack the capability to interact with users through text input and struggle to understand or reason about implicit and complex purposes. While methods like LISA integrate multi-modal large language models (LLMs) with segmentation for reasoning tasks, they are limited to predicting only visible object regions and face challenges in handling complex occlusion scenarios. To address these limitations, we propose a novel task named amodal reasoning segmentation, aiming to predict the complete amodal shape of occluded objects while providing answers with elaborations based on user text input. We develop a generalizable dataset generation pipeline and introduce a new dataset focusing"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "on daily life scenarios, encompassing diverse real-world occlusions. Furthermore, we present AURA (Amodal Understanding and Reasoning Assistant), a novel model with advanced global and spatial-level designs specifically tailored to handle complex occlusions. Extensive experiments validate AURA's effectiveness on the proposed dataset. The code, model, and dataset are released in this page."
+ },
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+ "type": "title",
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+ "content": "1. Introduction"
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+ "content": "With the development of the Segment Anything Model (SAM) series methods [24, 25, 58], predicting the segmentation mask of visible regions has been largely solved. Amodal segmentation aims to predict the entire shape of an object, including both visible and occluded regions, which is naturally challenging since visual cues for the occluded regions are unavailable. Predicting the intact shape of occluded objects is crucial for various real-world applications,"
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+ "angle": 0,
+ "content": "* Corresponding author."
+ },
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+ "type": "page_number",
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+ [
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "such as autonomous driving [12, 45, 50], robotics [2, 5, 22], and image editing [59, 63]."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "Existing amodal segmentation approaches have covered the fields including semantic [3, 49], instance [28, 37, 71], and panoptic [42] segmentation. Although existing amodal segmentation methods [10, 14, 45, 57] can address the problem of inferring occluded object shapes to some extent, they lack the ability to integrate with large language models (LLMs) [53, 54, 65], especially in performing reasoning and segmentation based on scene context, limiting their ability in interacting with users and understanding the implicit purpose underneath users questions. Meanwhile, although existing reasoning segmentation methods [26, 55] can work well on predicting the visible segmentation, they cannot predict the complete amodal segmentation mask, limiting their ability to reason in scenarios with complex occlusions. As a matter of fact, there is currently a significant gap in the availability of datasets designed for amodal reasoning segmentation, as well as in the development of algorithms specifically tailored to this task."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To address this gap, we propose a novel task named Amodal Reasoning Segmentation (ARS). As shown in Figure 1, the ARS task aims to interact with the user through textual questions, reasoning in the complex scene, and predicting accurate segmentation masks with textual answers. For this task, we present a highly generalizable data collection pipeline and construct a new dataset, AmodalReasonSeg, which covers daily life scenes (encompassing both indoor and outdoor environments) derived from the challenging COCOA-cls dataset [10, 71]. The AmodalReasonSeg dataset facilitates object reasoning and segmentation for visible and amodal masks across diverse scenes."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Along with the new task and dataset, we introduce a novel model named AURA (Amodal Understanding and Reasoning Assistant). AURA can understand the user's input questions, reason about the scene in the image, and predict both visible and amodal segmentation masks simultaneously. Given the challenge of predicting the shape of occluded parts, which are invisible in the image, we propose two key designs to enhance occlusion prediction capabilities. Specifically, we introduce the Occlusion Condition Encoder, which can distinguish whether objects are occluded and assess the occlusion degree comprehensively. Besides, the Spatial Occlusion Encoder can provide spatial guidance on whether each region is occluded, ensuring consistency between visible and amodal mask predictions. It is worth noticing that the proposed AmodalReasonSeg dataset and the designed AURA method support reasoning and mask prediction for various objects within a single-turn conversation, enhancing applicability to real-world scenarios. Furthermore, AURA supports multi-round conversations, increasing its versatility."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Extensive experiments on the proposed AmodalReason"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Seg dataset show that AURA outperforms existing methods in prediction accuracy, reasoning capability, and generalizability for complex occlusion scenarios."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The contributions of this paper can be summarized as follows: (1) We propose a novel task: amodal reasoning segmentation, along with a generalizable dataset collection pipeline. We construct a new dataset, AmodalReasonSeg, covering a variety of complex scenes from daily life. (2) We introduce AURA, a multi-modal method integrating vision and language for complex reasoning, capable of predicting both visible and amodal segmentation masks accurately. To the best of our knowledge, AURA is the first method explicitly designed for reasoning segmentation of amodal regions. (3) Extensive experiments demonstrate the effectiveness of AURA through both quantitative and qualitative evaluations."
+ },
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+ "type": "title",
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+ "angle": 0,
+ "content": "2. Related Work"
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+ "angle": 0,
+ "content": "2.1. Amodal Segmentation"
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+ "angle": 0,
+ "content": "Amodal segmentation [28] aims to predict the complete shape of an occluded object, encompassing both visible and occluded parts. Several methods [10, 28, 30, 32, 37, 38, 45] are developed by extending the methods designed for visible segmentation or object detection [4, 18-20, 23, 64], while the relative occlusion order information is leveraged by many methods [43, 63, 66, 68]. Since shape prior knowledge is an essential approach for inferring the shape of the occluded region, several methods [6, 9, 11, 29, 31, 34, 52, 57] are designed to learn and utilize it. For instance, VRSP [57] designs a codebook to store and retrieve shape priors for amodal masks. A3D [29] learns to reconstruct 3D shape priors to guide amodal segmentation. C2F-Seg [11] works in a coarse-to-fine manner equipped with a Vector-Quantized codebook [9]. Moreover, various datasets have been proposed for diverse scenarios, including daily life [10, 71], indoor [7, 8, 62, 70], autonomous driving [42, 45, 47], industrial [10], shopping [32], and gaming [14]. However, existing amodal segmentation methods and datasets are limited to using images or videos as input, focusing solely on predicting amodal masks without user interaction or reasoning about implicit user purposes. In this paper, we present the first high-quality dataset for the newly proposed amodal reasoning segmentation task and introduce a Vision-Language Model-based approach specifically designed for this task."
+ },
+ {
+ "type": "title",
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+ "content": "2.2. Large Models for Reasoning Segmentation"
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+ "angle": 0,
+ "content": "With the rapid advancement of Large Language Models (LLMs) [53, 54, 65] such as GPT-4 [1] and LLaMA [53], language-based approaches have demonstrated impressive zero-shot generalization abilities across diverse real-world applications. Additionally, Vision Language Models"
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+ "content": "Figure 2. Overall architecture of the proposed AURA. (a) Given an input image and the input question from the user, the Vision Backbone extracts the visual features of the input image, and the Multi-Modal LLM equipped with LoRA is utilized for understanding the input image and textual questions simultaneously and responding with textual answers that include the [SEG] tokens indicating the segmentation masks. (b) For each [SEG], the Prompt Encoder takes its embedding of the Multi-Modal LLM and outputs the refined embeddings corresponding to the [SEG]. (c) Finally, the Visible Mask Decoder predicts the visible mask using each [SEG]'s refined embeddings. The Amodal Decoder predicts the amodal mask using the occlusion-aware embedding predicted by the Occlusion Condition Encoder. A Spatial Occlusion Encoder is designed to constrain the spatial occlusion information of the predicted visible and amodal segmentation masks to be accurate. Best viewed in color."
+ },
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+ "content": "(VLMs) [21, 35, 36] like BLIP-2 [27] and LLaVA [36] have achieved state-of-the-art performance in comprehensively understanding both visual and textual information. To leverage the reasoning capabilities of VLMs, LISA [26] introduces the task of reasoning segmentation, which predicts visible segmentation masks by reasoning based on user input questions. Building upon LISA, several recent methods, such as Pixel-LM [48], VISA [60], and LLM-Seg [55], have been proposed to enhance different aspects of the reasoning segmentation task, such as multi-object segmentation, video segmentation, and training efficiency, respectively. Despite these advancements, all existing methods are limited to segmenting only the visible region of target objects, leaving segmenting and analyzing the occluded region untouched. Our work aims to bridge this gap by enabling reasoning and segmenting in an amodal manner, specifically designed to handle complex occlusions in real-world scenarios."
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+ "content": "In this section, we first introduce the definition of the proposed amodal reasoning segmentation task in 3.1. Then the overall architecture of the designed method is presented in 3.2. Next, the special designs for learning and handling occlusion are introduced in 3.3. Finally, the loss functions that organize the training objectives are shown in 3.4."
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+ "content": "For the proposed amodal reasoning segmentation (ARS) task, each image \\( x_{img} \\) of the dataset is associated with various questions \\( x_{text} \\), answers \\( y_{text} \\), and segmentations \\( y_{seg} \\)."
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+ "content": "For each pair, \\( x_{text} \\) is a question from the user input that does not directly point to objects in the image. \\( y_{text} \\) is the ground-truth textual answer that responds to the question and includes the description of one or more objects alongside the [SEG] token representing the position of the segmentation mask. \\( y_{seg} \\) represents the ground-truth visible and amodal segmentation masks \\( (M_v \\) and \\( M_a) \\), corresponding to the [SEG] in the answer \\( y_{text} \\)."
+ },
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+ "content": "As shown in Figure 2, the overall architecture of the proposed AURA includes three stages. Specifically, (1) the Vision Backbone takes the input image \\(I\\) as input for extracting its visual feature \\(F_{I}\\), and the Multi-Modal LLM \\(\\mathcal{E}_{MLLM}\\) equipped with LoRA is employed to understand the input image \\(I\\) and the user's input question \\(x_{text}\\), and predict the textual answer \\(\\hat{y}_{text}\\) to respond the question. (2) The Prompt Encoder \\(\\mathcal{E}_P\\) takes the embedding \\(e_{mllm}\\) of each [SEG] from the hidden states of the Multi-Modal LLM and predicts the refined embedding \\(e_r\\) for each [SEG]. (3) Finally the \\(e_r\\) and \\(F_{I}\\) are fed into the Visible Mask Decoder \\(\\mathcal{D}_V\\) for predicting the visible segmentation mask \\(\\hat{M}_v\\) of each [SEG]. Besides, the \\(e_r\\) is used by the Occlusion Condition Encoder \\(\\mathcal{E}_{OC}\\), which learns to predict the occlusion-aware embedding \\(e_{oa}\\) that is contained within the occlusion condition information. Then the Amodal Mask Decoder \\(\\mathcal{D}_A\\) uses the \\(F_{I}\\) and \\(e_{oa}\\) for predicting the amodal segmentation mask \\(\\hat{M}_a\\) of each [SEG]. The Spatial Occlusion Encoder \\(\\mathcal{E}_{SO}\\) is designed to constrain the predicted \\(\\hat{M}_v\\) and \\(\\hat{M}_a\\) to conform to the spatial occlusion relationship, which implic"
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+ "content": "Figure 3. The designed occlusion encoders. (a) The Occlusion Condition Encoder learns to embed the occlusion condition of each mask and output the occlusion-aware embedding. (b) The Spatial Occlusion Encoder takes the predicted visible and amodal masks as input and predicts the occlusion-aware spatial map to constrain the spatial relationship between the two predicted masks."
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+ "content": "itly improves the accuracy of the two predicted masks."
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+ "content": "The textual prediction of the Multi-Modal LLM is supervised using the \\(\\mathcal{L}_{text}\\), which can be denoted as:"
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+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {t e x t}} = \\mathcal {L} _ {C E} \\left(\\hat {y} _ {\\text {t e x t}}, y _ {\\text {t e x t}}\\right), \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.489,
+ 0.484,
+ 0.535
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathcal{L}_{CE}\\) is the Cross-Entropy loss [61]. Moreover, for supervising the visible and amodal mask predictions, the \\(\\mathcal{L}_{mask}\\) is used as shown in the following:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.135,
+ 0.559,
+ 0.483,
+ 0.586
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {\\text {m a s k}} = \\mathcal {L} _ {C E} (\\hat {M} _ {v}, M _ {v}) + \\mathcal {L} _ {C E} (\\hat {M} _ {a}, M _ {a}) + \\tag {2}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.198,
+ 0.583,
+ 0.437,
+ 0.599
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {D i c e} \\left(\\tilde {M} _ {v}, M _ {v}\\right) + \\mathcal {L} _ {D i c e} \\left(\\tilde {M} _ {a}, M _ {a}\\right),\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.611,
+ 0.318,
+ 0.627
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathcal{L}_{Dice}\\) is the Dice loss [51]."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.637,
+ 0.281,
+ 0.654
+ ],
+ "angle": 0,
+ "content": "3.3. Occlusion Learning"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.659,
+ 0.483,
+ 0.704
+ ],
+ "angle": 0,
+ "content": "Figure 3 illustrates the designed occlusion encoders for handling occlusion learning in AURA. Detailed network structures, inputs and outputs, and losses are presented."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.705,
+ 0.484,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Occlusion Condition Encoder is designed to improve the ability of the refined embedding \\( e_r \\) predicted by the Prompt Encoder to be aware of the occlusion condition of the object(s) corresponding to the [SEG]. Specifically, the \\( e_r \\) is fed into the Occlusion Condition Encoder \\( \\mathcal{E}_{OC} \\) and predicts the occlusion-aware embedding \\( e_{oa} \\) that is distinguishable by the degree of occlusion. The Occlusion Condition Encoder \\( \\mathcal{E}_{OC} \\) additionally predicts the occlusion rate \\( \\hat{r} \\) of the object, which reflects the occlusion condition comprehensively and is supervised by \\( \\mathcal{L}_{occ - oc} \\) with the ground-truth occlusion rate \\( r \\). Moreover, a Linear layer and a Sigmoid layer are employed to predict the occlusion rate \\( \\hat{r} \\) based on the refined embedding \\( e_r \\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.302
+ ],
+ "angle": 0,
+ "content": "Spatial Occlusion Encoder is proposed to constrain the spatial occlusion conditions between the predicted visible masks \\(\\hat{M}_v\\) and amodal masks \\(\\hat{M}_a\\), enhancing the accuracy of visible and amodal segmentation prediction. Specifically, the Spatial Occlusion Encoder \\(\\mathcal{E}_{SO}\\) takes both \\(\\hat{M}_v\\) and \\(\\hat{M}_a\\) as input and predicts the occlusion-aware spatial map \\(\\hat{M}_{sp}\\), which is supervised by \\(\\mathcal{L}_{occ-sp}\\) with the ground-truth occlusion-aware spatial map \\(M_{sp}\\). The ground truth \\(M_{sp}\\) is defined by setting regions belonging to the ground-truth visible mask \\(M_v\\) as 1 and setting regions belonging to the ground-truth amodal mask \\(M_a\\) but not \\(M_v\\) as 2, and setting other background regions as 0. In this approach, the constraint between predicted masks \\(\\hat{M}_v\\) and \\(\\hat{M}_a\\) is constructed and contributes to accurate segmentation."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.303,
+ 0.905,
+ 0.348
+ ],
+ "angle": 0,
+ "content": "For supervising the predictions of the occlusion condition and the spatial occlusion map, the \\(\\mathcal{L}_{occ}\\) is used as shown below:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.573,
+ 0.363,
+ 0.905,
+ 0.381
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} _ {o c c} = \\mathcal {L} _ {M S E} (\\hat {r}, r) + \\mathcal {L} _ {C E} (\\hat {M} _ {s p}, M _ {s p}), \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.388,
+ 0.816,
+ 0.403
+ ],
+ "angle": 0,
+ "content": "where \\(\\mathcal{L}_{MSE}\\) is the Mean Squared Error loss."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.413,
+ 0.667,
+ 0.428
+ ],
+ "angle": 0,
+ "content": "3.4. Loss Functions"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.435,
+ 0.906,
+ 0.54
+ ],
+ "angle": 0,
+ "content": "The overall loss function \\(\\mathcal{L}\\) consists of four parts, supervising the textual answers \\(\\hat{y}_{text}\\) predicted by the MultiModal LLM, the predicted visible and amodal masks \\((\\hat{M}_v\\) and \\(\\hat{M}_a)\\), and the predictions of two designed occlusion encoders including the occlusion rate \\(\\hat{r}\\) and the occlusion-aware spatial map \\(\\hat{M}_{sp}\\). The overall loss function can be formulated as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.614,
+ 0.557,
+ 0.905,
+ 0.573
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {t e x t}} + \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\text {o c c}}. \\tag {4}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.587,
+ 0.764,
+ 0.604
+ ],
+ "angle": 0,
+ "content": "4. AmodalReasonSeg Dataset"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.612,
+ 0.906,
+ 0.717
+ ],
+ "angle": 0,
+ "content": "Existing amodal segmentation datasets [10, 45, 62] only contain images/videos and ground-truth masks without language annotations, which cannot fulfill the requirement of the amodal reasoning segmentation task. To this end, it is essential to construct a large-scale dataset with high-quality language annotations, including implicit user questions and the corresponding answers."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.718,
+ 0.905,
+ 0.793
+ ],
+ "angle": 0,
+ "content": "In this section, we first introduce the basic information of the newly constructed dataset in 4.1. Next, we demonstrate a general dataset generation pipeline that is generable for diverse scenarios and can be applied to generate new datasets efficiently in 4.2."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.804,
+ 0.734,
+ 0.818
+ ],
+ "angle": 0,
+ "content": "4.1. Overview of the Dataset"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.826,
+ 0.906,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "To construct the new dataset for the amodal reasoning segmentation task, the challenging amodal segmentation dataset COCOA-cls [10, 71] is utilized. The COCOA-cls dataset is built upon the famous COCO [33] dataset, which includes daily scenarios with indoor and outdoor scenes."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "21930"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.114,
+ 0.088,
+ 0.468,
+ 0.277
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.289,
+ 0.487,
+ 0.361
+ ],
+ "angle": 0,
+ "content": "Figure 4. The designed generalizable pipeline for dataset generation. (a) Each image and the information of objects in it are gathered and fed into the GPT to generate questions and answers. (b) Then human annotators will check the generated data and improve it manually. Cross-check ensures the quality of the generated data."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.386,
+ 0.484,
+ 0.581
+ ],
+ "angle": 0,
+ "content": "For benchmarking the proposed amodal reasoning segmentation (ARS) task, we present the AmodalReasonSeg dataset, which is built upon the COCOA-cls dataset. The AmodalReasonSeg dataset includes 3,143 images and 35,494 high-quality question-and-answer pairs corresponding to the visible and amodal segmentation masks. The visible and amodal bounding boxes and the category information are included in our dataset. For each image, there are 11.3 pairs of questions and answers on average annotated to cover diverse potential conversations. Overall, there are 2,018 images and 22,856 pairs of questions and answers in the train set and 1,125 images and 12,638 question-and-answer pairs in the test set."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.582,
+ 0.484,
+ 0.734
+ ],
+ "angle": 0,
+ "content": "Compared with existing amodal segmentation datasets, the AmodalReasonSeg dataset supports interacting with users by using textual questions as input, and the answers respond to the implicit purpose underneath the questions and alongside the visible and amodal segmentation predictions. Moreover, it is worth noticing that the answer corresponding to each image could refer to various objects, meaning the proposed dataset supports reasoning and predicting different targets in a single conversation, which is essential in real-world applications."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.743,
+ 0.279,
+ 0.758
+ ],
+ "angle": 0,
+ "content": "4.2. Dataset Generation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.765,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "A generalizable pipeline is designed to generate the new dataset, as shown in Figure 4. Since manually annotating the question-and-answer pairs and the visible and amodal segmentation masks is labor-intensive and time-consuming, we present a semi-automatic pipeline inspired by [48] to keep the efficiency of the annotating process and high-quality annotations. Specifically, the images and annotations, including category information and visible and amodal masks, are reserved from the original dataset."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.182
+ ],
+ "angle": 0,
+ "content": "For generating the question-and-answer pairs, each image alongside the annotations is organized by a designed prompt template to be understood by a powerful and versatile large Vision-Language model, which is the ChatGPT-4o in our work that could take both image and text as input and output text response."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.184,
+ 0.907,
+ 0.546
+ ],
+ "angle": 0,
+ "content": "The prompt template is carefully designed to require ChatGPT-4o to generate question-and-answer pairs that satisfy the requirements to ensure the generation of high-quality data. The annotation information of objects for this image is collected and fed to ChatGPT-4o. For each image, ten question-and-answer pairs are required to be generated. Different objects are required to be organized and contained in one answer. Besides, the relative occlusion information between different objects is required to be considered when generating the question-and-answer pairs, which makes the text description in the answer helpful for discriminating the occlusion relationship between objects. The existing annotations from the original dataset of all objects in the image are organized and taken as input for the ChatGPT-4o. Finally, three human annotators check the generated questions and verify if they are qualified. During human verification, qualified samples are retained, while flawed ones are revised with appropriate questions and answers instead of being discarded. Common issues include incorrect object references, implausible functions, or inaccurate quantities. For the ones that need to be improved, human annotators will manually design appropriate questions and answers for these images. Cross-check is utilized between different human annotators to ensure the quality of the generated data."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.563,
+ 0.649,
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+ ],
+ "angle": 0,
+ "content": "5. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.589,
+ 0.722,
+ 0.605
+ ],
+ "angle": 0,
+ "content": "5.1. Experimental Settings"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.612,
+ 0.906,
+ 0.687
+ ],
+ "angle": 0,
+ "content": "Dataset. All experiments, including our proposed method and compared methods, are trained on the training set of the proposed AmodalReasonSeg dataset, and evaluated on the validation set of this dataset for fairness. No extra dataset besides the AmodalReasonSeg dataset is used."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.688,
+ 0.906,
+ 0.839
+ ],
+ "angle": 0,
+ "content": "Model Structure. We employ the LLaVA-7B-v1-1 [36] as the multi-modal LLM, which is equipped with LoRA for efficient fine-tuning. For the Vision Backbone and the Prompt Encoder, the SAM [25] method with the ViT-H version is utilized. The mask decoder of SAM is employed for the Visible Mask Decoder and Amodal Mask Decoder. Unless specifically specified, all experiments of the proposed AURA method are based on the model structure of using the LLaVA-7B-v1-1 [36] as the multi-modal LLM and the ViT-H version of SAM [25]."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.84,
+ 0.909,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "Implementation Details. We implement our proposed AURA based on Pytorch [44]. The AdamW [39] optimizer is used with the learning rate set to 1e-3. The WarmupDecayLR learning rate adjustment policy is used with 100 iter"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.479,
+ 0.945,
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+ ],
+ "angle": 0,
+ "content": "21931"
+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
+ 0.097,
+ 0.089,
+ 0.48,
+ 0.311
+ ],
+ "angle": 0,
+ "content": "| Method | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| Amodal Segmentation Methods |
| VRSP† [57] AAAI'21 | 15.18 | 16.55 | 17.41 | 19.75 |
| C2F-Seg† [11] ICCV'23 | 18.62 | 18.25 | 19.12 | 20.31 |
| SD-Amodal† [62] CVPR'24 | 20.87 | 20.09 | 21.52 | 23.10 |
| MLLM-based Methods |
| LISA† [26] CVPR'24 | 23.05 | 22.87 | 24.39 | 26.81 |
| LLM-Seg† [55] CVPR'24 | 24.62 | 23.06 | 25.19 | 27.94 |
| GSVA† [56] CVPR'24 | 42.30 | 42.87 | 47.01 | 48.22 |
| OMG-LLaVA† [67] NeurIPS'24 | 43.92 | 44.21 | 49.41 | 49.38 |
| GLaMM† [46] CVPR'24 | 45.75 | 46.82 | 49.93 | 54.14 |
| PSALM† [69] ECCV'24 | 46.81 | 47.03 | 50.64 | 55.19 |
| Baseline | 43.55 | 43.92 | 48.96 | 48.63 |
| AURA | 47.76 | 47.32 | 51.31 | 55.38 |
"
+ },
+ {
+ "type": "table_footnote",
+ "bbox": [
+ 0.09,
+ 0.322,
+ 0.483,
+ 0.391
+ ],
+ "angle": 0,
+ "content": "Table 1. Comparison of the amodal reasoning segmentation performance on the AmodalReasonSeg dataset. † denotes that this method is trained twice with ground-truth visible and amodal masks of the proposed AmodalReasonSeg dataset, respectively. Best in bold, second underlined."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.417,
+ 0.483,
+ 0.552
+ ],
+ "angle": 0,
+ "content": "ations for warmup and then linearly decreases the learning rate to 0. Apart from the ablation studies using 13B models as Multi-Modal LLM Backbone that use two NVIDIA A100 GPUs (80GB Memory) for experiments, all of our experiments are conducted on two NVIDIA V100 GPUs (32GB Memory). The batch size for each GPU card is set to 1. The entire training iterations are 5000, and the gradient accumulation technique is used by setting the accumulation step to 4. The entire training time is about 10 hours."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.553,
+ 0.483,
+ 0.645
+ ],
+ "angle": 0,
+ "content": "Evaluation Metrics. The gIoU and cIoU metrics are used for evaluating the segmentation performance of amodal and visible masks. The gIoU is calculated by averaging the Intersection-over-Unions (IoUs) of all images, while the cIoU is calculated by dividing the cumulative intersection by the cumulative union of all masks."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.653,
+ 0.383,
+ 0.669
+ ],
+ "angle": 0,
+ "content": "5.2. Amodal Reasoning Segmentation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.674,
+ 0.483,
+ 0.824
+ ],
+ "angle": 0,
+ "content": "Compared Methods. To benchmark the performance of amodal reasoning segmentation on the proposed Amodal-ReasonSeg dataset, state-of-the-art amodal segmentation methods [11, 57, 62] and multimodal large language model (MLLM)-based methods [26, 46, 55, 56, 67, 69] for reasoning segmentation of visible region are used for comparison. All methods are trained and evaluated on the train set and the val set of our proposed AmodalReasonSeg dataset, ensuring fairness. LLaVA-7B-v1-1 is employed for all MLLM-based methods."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.825,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "The amodal segmentation methods [11, 57, 62] are designed for taking an image as input and predicting amodal segmentation masks for all objects, but cannot understand the user's question, reasoning, and response with textual answers and segmentations. Besides, MLLM-based meth"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.137
+ ],
+ "angle": 0,
+ "content": "ods [26, 46, 55, 56, 67, 69] are designed to segment the visible regions of each object by taking the image and the user's question as input."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.14,
+ 0.907,
+ 0.321
+ ],
+ "angle": 0,
+ "content": "However, these aforementioned methods can only predict either visible or amodal masks by training twice with ground-truth visible or amodal masks, while the proposed AURA can reason and predict the visible and amodal masks simultaneously. Moreover, MLLM-based methods like LISA can only reason for one object to each question, while the proposed AURA could reason and respond with various objects with textual answers describing them and corresponding segmentation predictions. The baseline method is the proposed AURA without using the designed two occlusion learning modules, including the Occlusion Condition Encoder \\(\\mathcal{E}_{OC}\\) and the Spatial Occlusion Encoder \\(\\mathcal{E}_{SO}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.324,
+ 0.908,
+ 0.732
+ ],
+ "angle": 0,
+ "content": "Quantitative Results. Table 1 shows the performance of all compared methods on the proposed AmodalReasonSeg dataset. \\(\\dagger\\) means this method is trained twice on ground-truth visible and amodal masks, respectively, due to a lack of the ability to predict both masks at the same time. AURA achieves the best performance among all metrics regarding amodal and visible segmentations. To be more specific: (1) Firstly, since amodal segmentation methods [11, 57, 62] are designed for amodal segmentation and cannot take a textual question as input and understand it, they cannot be certain of which objects to segment, and the predicted masks could not be for the target objects. Therefore, these methods are evaluated by computing metrics between all predicted objects and target objects. In contrast, the proposed AURA can understand the purpose underneath the user's question and predict the amodal and visible masks for the targeted objects mentioned in the generated textual answer. (2) Secondly, since these MLLM-based methods are designed for segmenting visible regions of objects, their performance is not as well as AURA, which is specifically designed for the amodal reasoning segmentation task with task-specific designs for handling occlusions. Moreover, methods like LISA are designed to only segment one object for each question with other objects missed. However, AURA can support multi-object segmentation in a single conversation, responding with textual answers describing various objects with detailed elaborations."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.735,
+ 0.909,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Qualitative Results. Figure 5 presents the visualization results of AURA in three cases, showing that AURA can accurately understand the occlusion relation between objects in the image, reason the purpose underneath the question, and predict segmentation masks for various objects. In the first case, although part of the orange is completely occluded by the ice cream on top, and the plate below has a messy pattern, which may cause confusion, AURA still can correctly understand the question and predict an intact amodal segmentation mask for the occluded orange. In the second case, the black cat and the person's black clothing are easily con"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "21932"
+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
+ 0.127,
+ 0.089,
+ 0.454,
+ 0.182
+ ],
+ "angle": 0,
+ "content": "| Index | \\( \\mathcal{E}_{OC} \\) | \\( \\mathcal{E}_{SO} \\) | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| 1 | | | 43.55 | 43.92 | 48.96 | 48.63 |
| 2 | ✓ | | 44.86 | 44.07 | 49.57 | 49.10 |
| 3 | | ✓ | 46.95 | 45.60 | 50.68 | 53.72 |
| 4 | ✓ | ✓ | 47.76 | 47.32 | 51.31 | 55.38 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
+ 0.191,
+ 0.483,
+ 0.22
+ ],
+ "angle": 0,
+ "content": "Table 2. Ablation study of designs for occlusion learning. Best in bold, second underlined."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.126,
+ 0.235,
+ 0.456,
+ 0.302
+ ],
+ "angle": 0,
+ "content": "| Method | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| AURA w/o LoRA | 20.84 | 21.03 | 25.43 | 27.95 |
| AURA w/ LoRA | 47.76 | 47.32 | 51.31 | 55.38 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
+ 0.312,
+ 0.483,
+ 0.355
+ ],
+ "angle": 0,
+ "content": "Table 3. Ablation study of the effectiveness of using LoRA in the Multi-Modal LLM for efficient fine-tuning. w/o and w/ denote without and with the LoRA technique, respectively. Best in bold."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.381,
+ 0.483,
+ 0.518
+ ],
+ "angle": 0,
+ "content": "fused, especially in a dark environment. However, AURA can precisely distinguish between the cat and the person's black clothing and accurately predict the complete amodal mask of the person, even though a large region of the person is occluded by the cat. In the third case, the front side of the toilet is occluded by the cat to a large extent, while AURA can reason the purpose of the question and predict a high-quality amodal segmentation mask for the occluded toilet and an accurate segmentation mask for the cat."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.09,
+ 0.529,
+ 0.245,
+ 0.545
+ ],
+ "angle": 0,
+ "content": "5.3. Ablation Study"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.552,
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+ ],
+ "angle": 0,
+ "content": "We conduct ablation studies for the proposed AURA from various aspects, including the design of occlusion learning modules, the effectiveness of LoRA, the scale of the MultiModal LLM Backbone, and the scale of the Vision Backbone."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.855
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+ "angle": 0,
+ "content": "Occlusion Learning. As shown in Table 2, when the two designed Occlusion Condition Encoder \\(\\mathcal{E}_{OC}\\) and Spatial Occlusion Encoder \\(\\mathcal{E}_{SO}\\) are not used, the performance of AURA drops in a certain degree. When only using \\(\\mathcal{E}_{OC}\\), the occlusion conditions of all objects are learned and can help with our model for comprehensively distinguishing whether objects are occluded and the degree of occlusion for these objects. Besides, when only using \\(\\mathcal{E}_{SO}\\), the spatial occlusion distribution can be learned and guide our model to be aware of whether each region is occluded or visible, and constrain the consistency between the predicted visible and amodal masks regarding the spatial occlusion condition. Finally, when both \\(\\mathcal{E}_{OC}\\) and \\(\\mathcal{E}_{SO}\\) are utilized, the best performance is achieved with the learning of global and spatial occlusion conditions simultaneously."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Effectiveness of LoRA. We conduct experiments to evaluate the effectiveness of LoRA, as shown in Table 3. The LoRA [13] technique is utilized to be equipped with"
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+ "type": "table",
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+ "content": "| Multi-Modal LLM Backbone | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| AURA-7B | 47.76 | 47.32 | 51.31 | 55.38 |
| AURA-13B | 49.41 | 49.74 | 54.13 | 57.97 |
| AURA-Llama2-13B | 52.34 | 52.95 | 58.42 | 60.21 |
"
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Ablation study of the scale of the backbone for the MultiModal LLM. Best in bold, second underlined."
+ },
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+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Vision Backbone | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| SAM-ViT-B | 42.85 | 42.76 | 46.92 | 50.12 |
| SAM-ViT-L | 45.23 | 45.31 | 49.18 | 53.71 |
| SAM-ViT-H | 47.76 | 47.32 | 51.31 | 55.38 |
"
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+ "type": "table_caption",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "Table 5. Ablation study of the scale of the Vision Backbone. B, L, and H denote Base, Large, and Huge, respectively. Best in bold, second underlined."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "the Multi-Modal LLM for efficiently fine-tuning new data while keeping the pre-trained weight of LLM frozen. As shown in Table 3, when not using the LoRA technique, the performance of AURA drops to a certain extent. This is because the Multi-Modal LLM is not pre-trained on the AmodalReasonSeg dataset and has no specific knowledge learned to understand the purpose underneath the user's question and reason for various occluded objects. Therefore, the Multi-Modal LLM cannot predict textual answers correctly to respond to the user's question, leading to the performance of visible and amodal segmentation not well."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Scale of Multi-Modal LLM Backbone. The effect of the scale of the Multi-Modal LLM backbone is evaluated as shown in Table 4. The AURA-7B, AURA-13B, and AURA-Llama2-13B denote the AURA method with different Multi-Modal LLM backbones corresponding to LLaVA-7B, LLaVA-13B, and LLaVA-Llama2-13B models. These models are different variants of the LLaVA model with different scales of parameters (7 billion and 13 billion) and different generations of Llama. All experiments, apart from this ablation study, are based on the AURA-7B model. We can observe from Table 4 that the AURA-7B model does not perform as well as the other two models since the smaller number of parameters limits its learning ability for fine-tuning on the proposed AmodalReasonSeg dataset. Moreover, using larger models with 13 billion parameters can bring better performance since the learning capabilities of these models are better. Finally, upgrading the Llama large language model from the first to the second generation further enhances segmentation performance by generating higher-quality answers and refined embeddings used for segmentation."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Scale of the Vision Backbone. To evaluate the effect of the scale of the Vision Backbone, which is utilized to ex"
+ },
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+ "type": "page_number",
+ "bbox": [
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+ "content": "21933"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 5. Visualization results of AURA. Three cases are shown from top to bottom with questions and ground-truth (GT) answers. The first two cases show the images, ground-truth amodal and visible masks, and the predicted masks of AURA. In the last case, the predicted amodal mask by AURA for the occludee, which is the occluded toilet, is shown replacing the ground-truth visible mask."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "tract vision features of the input image and plays an essential role in providing informative features to the segmentation decoders, experiments are conducted, and the results are shown in Table 5. Three scales of the Vision Backbone are compared, including the Base, Large, and Huge versions of SAM, corresponding to 93.7M, 312M, and 641M parameters, respectively. We can observe that the model with a larger number of parameters can achieve better segmentation performance and greater learning ability."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "6. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "In this work, we propose a new task named Amodal Reasoning Segmentation, aiming to predict textual answers alongside visible and amodal segmentation masks in response to the user's input question that requires understanding and complex reasoning in the image. A generalizable dataset generation pipeline is proposed, which can generate anno"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.638,
+ 0.909,
+ 0.897
+ ],
+ "angle": 0,
+ "content": "tations with high quality efficiently. A new dataset named AmodalReasonSeg is presented for daily scenarios where occlusions are challenging for amodal segmentation. Extensive textual question-and-answer pairs are generated, and various objects are referred to in the answers. Moreover, we propose AURA to understand the user's implicit purpose and reason for the answer, which organizes various objects coherently with accurately predicted visible and amodal segmentation masks. Extensive experiments demonstrate the effectiveness of our proposed AURA on reasoning and segmenting the amodal masks in diverse complex scenarios. To enhance the applicability in real-world scenarios, we plan to further optimize the efficiency of our LLM-based model and enrich our dataset's diversity and granularity. Moreover, feature compression approaches [15-17, 40, 41] can be considered to improve the inference speed of the proposed approach."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
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+ }
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+ [
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "Acknowledgments"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This research was supported by the Ministry of Education of Singapore Tier3 grant MOET32022-0006. This research was also supported by Culture, Sports and Tourism R&D Program through the Korea Creative Content Agency grant funded by the Ministry of Culture, Sports and Tourism in 2024 (Project Name: Global Talent for Generative AI Copyright Infringement and Copyright Theft, Project Number: RS-2024-00398413, Contribution Rate: \\(10\\%\\))."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "References"
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+# Unveiling the Invisible: Reasoning Complex Occlusions Amodally with AURA
+
+Zhixuan Li $^{1}$ Hyunse Yoon $^{2}$ Sanghoon Lee $^{2}$ Weisi Lin $^{1*}$
+
+$^{1}$ College of Computing and Data Science, Nanyang Technological University, Singapore $^{2}$ Department of Electrical and Electronic Engineering, Yonsei University, Korea
+
+zhixuanli520@gmail.com, hsyoon97, slee@yonsei.ac.kr, wslin@ntu.edu.sg
+
+
+Figure 1. We introduce AURA, a multi-modal approach designed for reasoning the amodal segmentation mask including both visible and occlusion regions based on the user's question. AURA can deduce the implicit purpose underneath the question and respond with the textual answer along with predicted amodal masks for various objects. Best viewed in color.
+
+# Abstract
+
+Amodal segmentation aims to infer the complete shape of occluded objects, even when the occluded region's appearance is unavailable. However, current amodal segmentation methods lack the capability to interact with users through text input and struggle to understand or reason about implicit and complex purposes. While methods like LISA integrate multi-modal large language models (LLMs) with segmentation for reasoning tasks, they are limited to predicting only visible object regions and face challenges in handling complex occlusion scenarios. To address these limitations, we propose a novel task named amodal reasoning segmentation, aiming to predict the complete amodal shape of occluded objects while providing answers with elaborations based on user text input. We develop a generalizable dataset generation pipeline and introduce a new dataset focusing
+
+on daily life scenarios, encompassing diverse real-world occlusions. Furthermore, we present AURA (Amodal Understanding and Reasoning Assistant), a novel model with advanced global and spatial-level designs specifically tailored to handle complex occlusions. Extensive experiments validate AURA's effectiveness on the proposed dataset. The code, model, and dataset are released in this page.
+
+# 1. Introduction
+
+With the development of the Segment Anything Model (SAM) series methods [24, 25, 58], predicting the segmentation mask of visible regions has been largely solved. Amodal segmentation aims to predict the entire shape of an object, including both visible and occluded regions, which is naturally challenging since visual cues for the occluded regions are unavailable. Predicting the intact shape of occluded objects is crucial for various real-world applications,
+
+such as autonomous driving [12, 45, 50], robotics [2, 5, 22], and image editing [59, 63].
+
+Existing amodal segmentation approaches have covered the fields including semantic [3, 49], instance [28, 37, 71], and panoptic [42] segmentation. Although existing amodal segmentation methods [10, 14, 45, 57] can address the problem of inferring occluded object shapes to some extent, they lack the ability to integrate with large language models (LLMs) [53, 54, 65], especially in performing reasoning and segmentation based on scene context, limiting their ability in interacting with users and understanding the implicit purpose underneath users questions. Meanwhile, although existing reasoning segmentation methods [26, 55] can work well on predicting the visible segmentation, they cannot predict the complete amodal segmentation mask, limiting their ability to reason in scenarios with complex occlusions. As a matter of fact, there is currently a significant gap in the availability of datasets designed for amodal reasoning segmentation, as well as in the development of algorithms specifically tailored to this task.
+
+To address this gap, we propose a novel task named Amodal Reasoning Segmentation (ARS). As shown in Figure 1, the ARS task aims to interact with the user through textual questions, reasoning in the complex scene, and predicting accurate segmentation masks with textual answers. For this task, we present a highly generalizable data collection pipeline and construct a new dataset, AmodalReasonSeg, which covers daily life scenes (encompassing both indoor and outdoor environments) derived from the challenging COCOA-cls dataset [10, 71]. The AmodalReasonSeg dataset facilitates object reasoning and segmentation for visible and amodal masks across diverse scenes.
+
+Along with the new task and dataset, we introduce a novel model named AURA (Amodal Understanding and Reasoning Assistant). AURA can understand the user's input questions, reason about the scene in the image, and predict both visible and amodal segmentation masks simultaneously. Given the challenge of predicting the shape of occluded parts, which are invisible in the image, we propose two key designs to enhance occlusion prediction capabilities. Specifically, we introduce the Occlusion Condition Encoder, which can distinguish whether objects are occluded and assess the occlusion degree comprehensively. Besides, the Spatial Occlusion Encoder can provide spatial guidance on whether each region is occluded, ensuring consistency between visible and amodal mask predictions. It is worth noticing that the proposed AmodalReasonSeg dataset and the designed AURA method support reasoning and mask prediction for various objects within a single-turn conversation, enhancing applicability to real-world scenarios. Furthermore, AURA supports multi-round conversations, increasing its versatility.
+
+Extensive experiments on the proposed AmodalReason
+
+Seg dataset show that AURA outperforms existing methods in prediction accuracy, reasoning capability, and generalizability for complex occlusion scenarios.
+
+The contributions of this paper can be summarized as follows: (1) We propose a novel task: amodal reasoning segmentation, along with a generalizable dataset collection pipeline. We construct a new dataset, AmodalReasonSeg, covering a variety of complex scenes from daily life. (2) We introduce AURA, a multi-modal method integrating vision and language for complex reasoning, capable of predicting both visible and amodal segmentation masks accurately. To the best of our knowledge, AURA is the first method explicitly designed for reasoning segmentation of amodal regions. (3) Extensive experiments demonstrate the effectiveness of AURA through both quantitative and qualitative evaluations.
+
+# 2. Related Work
+
+# 2.1. Amodal Segmentation
+
+Amodal segmentation [28] aims to predict the complete shape of an occluded object, encompassing both visible and occluded parts. Several methods [10, 28, 30, 32, 37, 38, 45] are developed by extending the methods designed for visible segmentation or object detection [4, 18-20, 23, 64], while the relative occlusion order information is leveraged by many methods [43, 63, 66, 68]. Since shape prior knowledge is an essential approach for inferring the shape of the occluded region, several methods [6, 9, 11, 29, 31, 34, 52, 57] are designed to learn and utilize it. For instance, VRSP [57] designs a codebook to store and retrieve shape priors for amodal masks. A3D [29] learns to reconstruct 3D shape priors to guide amodal segmentation. C2F-Seg [11] works in a coarse-to-fine manner equipped with a Vector-Quantized codebook [9]. Moreover, various datasets have been proposed for diverse scenarios, including daily life [10, 71], indoor [7, 8, 62, 70], autonomous driving [42, 45, 47], industrial [10], shopping [32], and gaming [14]. However, existing amodal segmentation methods and datasets are limited to using images or videos as input, focusing solely on predicting amodal masks without user interaction or reasoning about implicit user purposes. In this paper, we present the first high-quality dataset for the newly proposed amodal reasoning segmentation task and introduce a Vision-Language Model-based approach specifically designed for this task.
+
+# 2.2. Large Models for Reasoning Segmentation
+
+With the rapid advancement of Large Language Models (LLMs) [53, 54, 65] such as GPT-4 [1] and LLaMA [53], language-based approaches have demonstrated impressive zero-shot generalization abilities across diverse real-world applications. Additionally, Vision Language Models
+
+
+Figure 2. Overall architecture of the proposed AURA. (a) Given an input image and the input question from the user, the Vision Backbone extracts the visual features of the input image, and the Multi-Modal LLM equipped with LoRA is utilized for understanding the input image and textual questions simultaneously and responding with textual answers that include the [SEG] tokens indicating the segmentation masks. (b) For each [SEG], the Prompt Encoder takes its embedding of the Multi-Modal LLM and outputs the refined embeddings corresponding to the [SEG]. (c) Finally, the Visible Mask Decoder predicts the visible mask using each [SEG]'s refined embeddings. The Amodal Decoder predicts the amodal mask using the occlusion-aware embedding predicted by the Occlusion Condition Encoder. A Spatial Occlusion Encoder is designed to constrain the spatial occlusion information of the predicted visible and amodal segmentation masks to be accurate. Best viewed in color.
+
+(VLMs) [21, 35, 36] like BLIP-2 [27] and LLaVA [36] have achieved state-of-the-art performance in comprehensively understanding both visual and textual information. To leverage the reasoning capabilities of VLMs, LISA [26] introduces the task of reasoning segmentation, which predicts visible segmentation masks by reasoning based on user input questions. Building upon LISA, several recent methods, such as Pixel-LM [48], VISA [60], and LLM-Seg [55], have been proposed to enhance different aspects of the reasoning segmentation task, such as multi-object segmentation, video segmentation, and training efficiency, respectively. Despite these advancements, all existing methods are limited to segmenting only the visible region of target objects, leaving segmenting and analyzing the occluded region untouched. Our work aims to bridge this gap by enabling reasoning and segmenting in an amodal manner, specifically designed to handle complex occlusions in real-world scenarios.
+
+# 3. Methodology
+
+In this section, we first introduce the definition of the proposed amodal reasoning segmentation task in 3.1. Then the overall architecture of the designed method is presented in 3.2. Next, the special designs for learning and handling occlusion are introduced in 3.3. Finally, the loss functions that organize the training objectives are shown in 3.4.
+
+# 3.1. Task Definition
+
+For the proposed amodal reasoning segmentation (ARS) task, each image $x_{img}$ of the dataset is associated with various questions $x_{text}$ , answers $y_{text}$ , and segmentations $y_{seg}$ .
+
+For each pair, $x_{text}$ is a question from the user input that does not directly point to objects in the image. $y_{text}$ is the ground-truth textual answer that responds to the question and includes the description of one or more objects alongside the [SEG] token representing the position of the segmentation mask. $y_{seg}$ represents the ground-truth visible and amodal segmentation masks $(M_v$ and $M_a)$ , corresponding to the [SEG] in the answer $y_{text}$ .
+
+# 3.2. Overall Architecture
+
+As shown in Figure 2, the overall architecture of the proposed AURA includes three stages. Specifically, (1) the Vision Backbone takes the input image $I$ as input for extracting its visual feature $F_{I}$ , and the Multi-Modal LLM $\mathcal{E}_{MLLM}$ equipped with LoRA is employed to understand the input image $I$ and the user's input question $x_{text}$ , and predict the textual answer $\hat{y}_{text}$ to respond the question. (2) The Prompt Encoder $\mathcal{E}_P$ takes the embedding $e_{mllm}$ of each [SEG] from the hidden states of the Multi-Modal LLM and predicts the refined embedding $e_r$ for each [SEG]. (3) Finally the $e_r$ and $F_{I}$ are fed into the Visible Mask Decoder $\mathcal{D}_V$ for predicting the visible segmentation mask $\hat{M}_v$ of each [SEG]. Besides, the $e_r$ is used by the Occlusion Condition Encoder $\mathcal{E}_{OC}$ , which learns to predict the occlusion-aware embedding $e_{oa}$ that is contained within the occlusion condition information. Then the Amodal Mask Decoder $\mathcal{D}_A$ uses the $F_{I}$ and $e_{oa}$ for predicting the amodal segmentation mask $\hat{M}_a$ of each [SEG]. The Spatial Occlusion Encoder $\mathcal{E}_{SO}$ is designed to constrain the predicted $\hat{M}_v$ and $\hat{M}_a$ to conform to the spatial occlusion relationship, which implic
+
+
+(a)
+Figure 3. The designed occlusion encoders. (a) The Occlusion Condition Encoder learns to embed the occlusion condition of each mask and output the occlusion-aware embedding. (b) The Spatial Occlusion Encoder takes the predicted visible and amodal masks as input and predicts the occlusion-aware spatial map to constrain the spatial relationship between the two predicted masks.
+
+
+(b)
+
+itly improves the accuracy of the two predicted masks.
+
+The textual prediction of the Multi-Modal LLM is supervised using the $\mathcal{L}_{text}$ , which can be denoted as:
+
+$$
+\mathcal {L} _ {\text {t e x t}} = \mathcal {L} _ {C E} \left(\hat {y} _ {\text {t e x t}}, y _ {\text {t e x t}}\right), \tag {1}
+$$
+
+where $\mathcal{L}_{CE}$ is the Cross-Entropy loss [61]. Moreover, for supervising the visible and amodal mask predictions, the $\mathcal{L}_{mask}$ is used as shown in the following:
+
+$$
+\mathcal {L} _ {\text {m a s k}} = \mathcal {L} _ {C E} (\hat {M} _ {v}, M _ {v}) + \mathcal {L} _ {C E} (\hat {M} _ {a}, M _ {a}) + \tag {2}
+$$
+
+$$
+\mathcal {L} _ {D i c e} \left(\tilde {M} _ {v}, M _ {v}\right) + \mathcal {L} _ {D i c e} \left(\tilde {M} _ {a}, M _ {a}\right),
+$$
+
+where $\mathcal{L}_{Dice}$ is the Dice loss [51].
+
+# 3.3. Occlusion Learning
+
+Figure 3 illustrates the designed occlusion encoders for handling occlusion learning in AURA. Detailed network structures, inputs and outputs, and losses are presented.
+
+Occlusion Condition Encoder is designed to improve the ability of the refined embedding $e_r$ predicted by the Prompt Encoder to be aware of the occlusion condition of the object(s) corresponding to the [SEG]. Specifically, the $e_r$ is fed into the Occlusion Condition Encoder $\mathcal{E}_{OC}$ and predicts the occlusion-aware embedding $e_{oa}$ that is distinguishable by the degree of occlusion. The Occlusion Condition Encoder $\mathcal{E}_{OC}$ additionally predicts the occlusion rate $\hat{r}$ of the object, which reflects the occlusion condition comprehensively and is supervised by $\mathcal{L}_{occ - oc}$ with the ground-truth occlusion rate $r$ . Moreover, a Linear layer and a Sigmoid layer are employed to predict the occlusion rate $\hat{r}$ based on the refined embedding $e_r$ .
+
+Spatial Occlusion Encoder is proposed to constrain the spatial occlusion conditions between the predicted visible masks $\hat{M}_v$ and amodal masks $\hat{M}_a$ , enhancing the accuracy of visible and amodal segmentation prediction. Specifically, the Spatial Occlusion Encoder $\mathcal{E}_{SO}$ takes both $\hat{M}_v$ and $\hat{M}_a$ as input and predicts the occlusion-aware spatial map $\hat{M}_{sp}$ , which is supervised by $\mathcal{L}_{occ-sp}$ with the ground-truth occlusion-aware spatial map $M_{sp}$ . The ground truth $M_{sp}$ is defined by setting regions belonging to the ground-truth visible mask $M_v$ as 1 and setting regions belonging to the ground-truth amodal mask $M_a$ but not $M_v$ as 2, and setting other background regions as 0. In this approach, the constraint between predicted masks $\hat{M}_v$ and $\hat{M}_a$ is constructed and contributes to accurate segmentation.
+
+For supervising the predictions of the occlusion condition and the spatial occlusion map, the $\mathcal{L}_{occ}$ is used as shown below:
+
+$$
+\mathcal {L} _ {o c c} = \mathcal {L} _ {M S E} (\hat {r}, r) + \mathcal {L} _ {C E} (\hat {M} _ {s p}, M _ {s p}), \tag {3}
+$$
+
+where $\mathcal{L}_{MSE}$ is the Mean Squared Error loss.
+
+# 3.4. Loss Functions
+
+The overall loss function $\mathcal{L}$ consists of four parts, supervising the textual answers $\hat{y}_{text}$ predicted by the MultiModal LLM, the predicted visible and amodal masks $(\hat{M}_v$ and $\hat{M}_a)$ , and the predictions of two designed occlusion encoders including the occlusion rate $\hat{r}$ and the occlusion-aware spatial map $\hat{M}_{sp}$ . The overall loss function can be formulated as:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {t e x t}} + \mathcal {L} _ {\text {m a s k}} + \mathcal {L} _ {\text {o c c}}. \tag {4}
+$$
+
+# 4. AmodalReasonSeg Dataset
+
+Existing amodal segmentation datasets [10, 45, 62] only contain images/videos and ground-truth masks without language annotations, which cannot fulfill the requirement of the amodal reasoning segmentation task. To this end, it is essential to construct a large-scale dataset with high-quality language annotations, including implicit user questions and the corresponding answers.
+
+In this section, we first introduce the basic information of the newly constructed dataset in 4.1. Next, we demonstrate a general dataset generation pipeline that is generable for diverse scenarios and can be applied to generate new datasets efficiently in 4.2.
+
+# 4.1. Overview of the Dataset
+
+To construct the new dataset for the amodal reasoning segmentation task, the challenging amodal segmentation dataset COCOA-cls [10, 71] is utilized. The COCOA-cls dataset is built upon the famous COCO [33] dataset, which includes daily scenarios with indoor and outdoor scenes.
+
+
+Figure 4. The designed generalizable pipeline for dataset generation. (a) Each image and the information of objects in it are gathered and fed into the GPT to generate questions and answers. (b) Then human annotators will check the generated data and improve it manually. Cross-check ensures the quality of the generated data.
+
+For benchmarking the proposed amodal reasoning segmentation (ARS) task, we present the AmodalReasonSeg dataset, which is built upon the COCOA-cls dataset. The AmodalReasonSeg dataset includes 3,143 images and 35,494 high-quality question-and-answer pairs corresponding to the visible and amodal segmentation masks. The visible and amodal bounding boxes and the category information are included in our dataset. For each image, there are 11.3 pairs of questions and answers on average annotated to cover diverse potential conversations. Overall, there are 2,018 images and 22,856 pairs of questions and answers in the train set and 1,125 images and 12,638 question-and-answer pairs in the test set.
+
+Compared with existing amodal segmentation datasets, the AmodalReasonSeg dataset supports interacting with users by using textual questions as input, and the answers respond to the implicit purpose underneath the questions and alongside the visible and amodal segmentation predictions. Moreover, it is worth noticing that the answer corresponding to each image could refer to various objects, meaning the proposed dataset supports reasoning and predicting different targets in a single conversation, which is essential in real-world applications.
+
+# 4.2. Dataset Generation
+
+A generalizable pipeline is designed to generate the new dataset, as shown in Figure 4. Since manually annotating the question-and-answer pairs and the visible and amodal segmentation masks is labor-intensive and time-consuming, we present a semi-automatic pipeline inspired by [48] to keep the efficiency of the annotating process and high-quality annotations. Specifically, the images and annotations, including category information and visible and amodal masks, are reserved from the original dataset.
+
+For generating the question-and-answer pairs, each image alongside the annotations is organized by a designed prompt template to be understood by a powerful and versatile large Vision-Language model, which is the ChatGPT-4o in our work that could take both image and text as input and output text response.
+
+The prompt template is carefully designed to require ChatGPT-4o to generate question-and-answer pairs that satisfy the requirements to ensure the generation of high-quality data. The annotation information of objects for this image is collected and fed to ChatGPT-4o. For each image, ten question-and-answer pairs are required to be generated. Different objects are required to be organized and contained in one answer. Besides, the relative occlusion information between different objects is required to be considered when generating the question-and-answer pairs, which makes the text description in the answer helpful for discriminating the occlusion relationship between objects. The existing annotations from the original dataset of all objects in the image are organized and taken as input for the ChatGPT-4o. Finally, three human annotators check the generated questions and verify if they are qualified. During human verification, qualified samples are retained, while flawed ones are revised with appropriate questions and answers instead of being discarded. Common issues include incorrect object references, implausible functions, or inaccurate quantities. For the ones that need to be improved, human annotators will manually design appropriate questions and answers for these images. Cross-check is utilized between different human annotators to ensure the quality of the generated data.
+
+# 5. Experiments
+
+# 5.1. Experimental Settings
+
+Dataset. All experiments, including our proposed method and compared methods, are trained on the training set of the proposed AmodalReasonSeg dataset, and evaluated on the validation set of this dataset for fairness. No extra dataset besides the AmodalReasonSeg dataset is used.
+
+Model Structure. We employ the LLaVA-7B-v1-1 [36] as the multi-modal LLM, which is equipped with LoRA for efficient fine-tuning. For the Vision Backbone and the Prompt Encoder, the SAM [25] method with the ViT-H version is utilized. The mask decoder of SAM is employed for the Visible Mask Decoder and Amodal Mask Decoder. Unless specifically specified, all experiments of the proposed AURA method are based on the model structure of using the LLaVA-7B-v1-1 [36] as the multi-modal LLM and the ViT-H version of SAM [25].
+
+Implementation Details. We implement our proposed AURA based on Pytorch [44]. The AdamW [39] optimizer is used with the learning rate set to 1e-3. The WarmupDecayLR learning rate adjustment policy is used with 100 iter
+
+| Method | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| Amodal Segmentation Methods |
| VRSP† [57] AAAI'21 | 15.18 | 16.55 | 17.41 | 19.75 |
| C2F-Seg† [11] ICCV'23 | 18.62 | 18.25 | 19.12 | 20.31 |
| SD-Amodal† [62] CVPR'24 | 20.87 | 20.09 | 21.52 | 23.10 |
| MLLM-based Methods |
| LISA† [26] CVPR'24 | 23.05 | 22.87 | 24.39 | 26.81 |
| LLM-Seg† [55] CVPR'24 | 24.62 | 23.06 | 25.19 | 27.94 |
| GSVA† [56] CVPR'24 | 42.30 | 42.87 | 47.01 | 48.22 |
| OMG-LLaVA† [67] NeurIPS'24 | 43.92 | 44.21 | 49.41 | 49.38 |
| GLaMM† [46] CVPR'24 | 45.75 | 46.82 | 49.93 | 54.14 |
| PSALM† [69] ECCV'24 | 46.81 | 47.03 | 50.64 | 55.19 |
| Baseline | 43.55 | 43.92 | 48.96 | 48.63 |
| AURA | 47.76 | 47.32 | 51.31 | 55.38 |
+
+Table 1. Comparison of the amodal reasoning segmentation performance on the AmodalReasonSeg dataset. † denotes that this method is trained twice with ground-truth visible and amodal masks of the proposed AmodalReasonSeg dataset, respectively. Best in bold, second underlined.
+
+ations for warmup and then linearly decreases the learning rate to 0. Apart from the ablation studies using 13B models as Multi-Modal LLM Backbone that use two NVIDIA A100 GPUs (80GB Memory) for experiments, all of our experiments are conducted on two NVIDIA V100 GPUs (32GB Memory). The batch size for each GPU card is set to 1. The entire training iterations are 5000, and the gradient accumulation technique is used by setting the accumulation step to 4. The entire training time is about 10 hours.
+
+Evaluation Metrics. The gIoU and cIoU metrics are used for evaluating the segmentation performance of amodal and visible masks. The gIoU is calculated by averaging the Intersection-over-Unions (IoUs) of all images, while the cIoU is calculated by dividing the cumulative intersection by the cumulative union of all masks.
+
+# 5.2. Amodal Reasoning Segmentation
+
+Compared Methods. To benchmark the performance of amodal reasoning segmentation on the proposed Amodal-ReasonSeg dataset, state-of-the-art amodal segmentation methods [11, 57, 62] and multimodal large language model (MLLM)-based methods [26, 46, 55, 56, 67, 69] for reasoning segmentation of visible region are used for comparison. All methods are trained and evaluated on the train set and the val set of our proposed AmodalReasonSeg dataset, ensuring fairness. LLaVA-7B-v1-1 is employed for all MLLM-based methods.
+
+The amodal segmentation methods [11, 57, 62] are designed for taking an image as input and predicting amodal segmentation masks for all objects, but cannot understand the user's question, reasoning, and response with textual answers and segmentations. Besides, MLLM-based meth
+
+ods [26, 46, 55, 56, 67, 69] are designed to segment the visible regions of each object by taking the image and the user's question as input.
+
+However, these aforementioned methods can only predict either visible or amodal masks by training twice with ground-truth visible or amodal masks, while the proposed AURA can reason and predict the visible and amodal masks simultaneously. Moreover, MLLM-based methods like LISA can only reason for one object to each question, while the proposed AURA could reason and respond with various objects with textual answers describing them and corresponding segmentation predictions. The baseline method is the proposed AURA without using the designed two occlusion learning modules, including the Occlusion Condition Encoder $\mathcal{E}_{OC}$ and the Spatial Occlusion Encoder $\mathcal{E}_{SO}$ .
+
+Quantitative Results. Table 1 shows the performance of all compared methods on the proposed AmodalReasonSeg dataset. $\dagger$ means this method is trained twice on ground-truth visible and amodal masks, respectively, due to a lack of the ability to predict both masks at the same time. AURA achieves the best performance among all metrics regarding amodal and visible segmentations. To be more specific: (1) Firstly, since amodal segmentation methods [11, 57, 62] are designed for amodal segmentation and cannot take a textual question as input and understand it, they cannot be certain of which objects to segment, and the predicted masks could not be for the target objects. Therefore, these methods are evaluated by computing metrics between all predicted objects and target objects. In contrast, the proposed AURA can understand the purpose underneath the user's question and predict the amodal and visible masks for the targeted objects mentioned in the generated textual answer. (2) Secondly, since these MLLM-based methods are designed for segmenting visible regions of objects, their performance is not as well as AURA, which is specifically designed for the amodal reasoning segmentation task with task-specific designs for handling occlusions. Moreover, methods like LISA are designed to only segment one object for each question with other objects missed. However, AURA can support multi-object segmentation in a single conversation, responding with textual answers describing various objects with detailed elaborations.
+
+Qualitative Results. Figure 5 presents the visualization results of AURA in three cases, showing that AURA can accurately understand the occlusion relation between objects in the image, reason the purpose underneath the question, and predict segmentation masks for various objects. In the first case, although part of the orange is completely occluded by the ice cream on top, and the plate below has a messy pattern, which may cause confusion, AURA still can correctly understand the question and predict an intact amodal segmentation mask for the occluded orange. In the second case, the black cat and the person's black clothing are easily con
+
+| Index | \( \mathcal{E}_{OC} \) | \( \mathcal{E}_{SO} \) | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| 1 | | | 43.55 | 43.92 | 48.96 | 48.63 |
| 2 | ✓ | | 44.86 | 44.07 | 49.57 | 49.10 |
| 3 | | ✓ | 46.95 | 45.60 | 50.68 | 53.72 |
| 4 | ✓ | ✓ | 47.76 | 47.32 | 51.31 | 55.38 |
+
+Table 2. Ablation study of designs for occlusion learning. Best in bold, second underlined.
+
+| Method | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| AURA w/o LoRA | 20.84 | 21.03 | 25.43 | 27.95 |
| AURA w/ LoRA | 47.76 | 47.32 | 51.31 | 55.38 |
+
+fused, especially in a dark environment. However, AURA can precisely distinguish between the cat and the person's black clothing and accurately predict the complete amodal mask of the person, even though a large region of the person is occluded by the cat. In the third case, the front side of the toilet is occluded by the cat to a large extent, while AURA can reason the purpose of the question and predict a high-quality amodal segmentation mask for the occluded toilet and an accurate segmentation mask for the cat.
+
+# 5.3. Ablation Study
+
+We conduct ablation studies for the proposed AURA from various aspects, including the design of occlusion learning modules, the effectiveness of LoRA, the scale of the MultiModal LLM Backbone, and the scale of the Vision Backbone.
+
+Occlusion Learning. As shown in Table 2, when the two designed Occlusion Condition Encoder $\mathcal{E}_{OC}$ and Spatial Occlusion Encoder $\mathcal{E}_{SO}$ are not used, the performance of AURA drops in a certain degree. When only using $\mathcal{E}_{OC}$ , the occlusion conditions of all objects are learned and can help with our model for comprehensively distinguishing whether objects are occluded and the degree of occlusion for these objects. Besides, when only using $\mathcal{E}_{SO}$ , the spatial occlusion distribution can be learned and guide our model to be aware of whether each region is occluded or visible, and constrain the consistency between the predicted visible and amodal masks regarding the spatial occlusion condition. Finally, when both $\mathcal{E}_{OC}$ and $\mathcal{E}_{SO}$ are utilized, the best performance is achieved with the learning of global and spatial occlusion conditions simultaneously.
+
+Effectiveness of LoRA. We conduct experiments to evaluate the effectiveness of LoRA, as shown in Table 3. The LoRA [13] technique is utilized to be equipped with
+
+Table 3. Ablation study of the effectiveness of using LoRA in the Multi-Modal LLM for efficient fine-tuning. w/o and w/ denote without and with the LoRA technique, respectively. Best in bold.
+
+| Multi-Modal LLM Backbone | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| AURA-7B | 47.76 | 47.32 | 51.31 | 55.38 |
| AURA-13B | 49.41 | 49.74 | 54.13 | 57.97 |
| AURA-Llama2-13B | 52.34 | 52.95 | 58.42 | 60.21 |
+
+Table 4. Ablation study of the scale of the backbone for the MultiModal LLM. Best in bold, second underlined.
+
+| Vision Backbone | Amodal | Visible |
| gIoU | cIoU | gIoU | cIoU |
| SAM-ViT-B | 42.85 | 42.76 | 46.92 | 50.12 |
| SAM-ViT-L | 45.23 | 45.31 | 49.18 | 53.71 |
| SAM-ViT-H | 47.76 | 47.32 | 51.31 | 55.38 |
+
+Table 5. Ablation study of the scale of the Vision Backbone. B, L, and H denote Base, Large, and Huge, respectively. Best in bold, second underlined.
+
+the Multi-Modal LLM for efficiently fine-tuning new data while keeping the pre-trained weight of LLM frozen. As shown in Table 3, when not using the LoRA technique, the performance of AURA drops to a certain extent. This is because the Multi-Modal LLM is not pre-trained on the AmodalReasonSeg dataset and has no specific knowledge learned to understand the purpose underneath the user's question and reason for various occluded objects. Therefore, the Multi-Modal LLM cannot predict textual answers correctly to respond to the user's question, leading to the performance of visible and amodal segmentation not well.
+
+Scale of Multi-Modal LLM Backbone. The effect of the scale of the Multi-Modal LLM backbone is evaluated as shown in Table 4. The AURA-7B, AURA-13B, and AURA-Llama2-13B denote the AURA method with different Multi-Modal LLM backbones corresponding to LLaVA-7B, LLaVA-13B, and LLaVA-Llama2-13B models. These models are different variants of the LLaVA model with different scales of parameters (7 billion and 13 billion) and different generations of Llama. All experiments, apart from this ablation study, are based on the AURA-7B model. We can observe from Table 4 that the AURA-7B model does not perform as well as the other two models since the smaller number of parameters limits its learning ability for fine-tuning on the proposed AmodalReasonSeg dataset. Moreover, using larger models with 13 billion parameters can bring better performance since the learning capabilities of these models are better. Finally, upgrading the Llama large language model from the first to the second generation further enhances segmentation performance by generating higher-quality answers and refined embeddings used for segmentation.
+
+Scale of the Vision Backbone. To evaluate the effect of the scale of the Vision Backbone, which is utilized to ex
+
+
+Figure 5. Visualization results of AURA. Three cases are shown from top to bottom with questions and ground-truth (GT) answers. The first two cases show the images, ground-truth amodal and visible masks, and the predicted masks of AURA. In the last case, the predicted amodal mask by AURA for the occludee, which is the occluded toilet, is shown replacing the ground-truth visible mask.
+
+tract vision features of the input image and plays an essential role in providing informative features to the segmentation decoders, experiments are conducted, and the results are shown in Table 5. Three scales of the Vision Backbone are compared, including the Base, Large, and Huge versions of SAM, corresponding to 93.7M, 312M, and 641M parameters, respectively. We can observe that the model with a larger number of parameters can achieve better segmentation performance and greater learning ability.
+
+# 6. Conclusion
+
+In this work, we propose a new task named Amodal Reasoning Segmentation, aiming to predict textual answers alongside visible and amodal segmentation masks in response to the user's input question that requires understanding and complex reasoning in the image. A generalizable dataset generation pipeline is proposed, which can generate anno
+
+tations with high quality efficiently. A new dataset named AmodalReasonSeg is presented for daily scenarios where occlusions are challenging for amodal segmentation. Extensive textual question-and-answer pairs are generated, and various objects are referred to in the answers. Moreover, we propose AURA to understand the user's implicit purpose and reason for the answer, which organizes various objects coherently with accurately predicted visible and amodal segmentation masks. Extensive experiments demonstrate the effectiveness of our proposed AURA on reasoning and segmenting the amodal masks in diverse complex scenarios. To enhance the applicability in real-world scenarios, we plan to further optimize the efficiency of our LLM-based model and enrich our dataset's diversity and granularity. Moreover, feature compression approaches [15-17, 40, 41] can be considered to improve the inference speed of the proposed approach.
+
+# Acknowledgments
+
+This research was supported by the Ministry of Education of Singapore Tier3 grant MOET32022-0006. This research was also supported by Culture, Sports and Tourism R&D Program through the Korea Creative Content Agency grant funded by the Ministry of Culture, Sports and Tourism in 2024 (Project Name: Global Talent for Generative AI Copyright Infringement and Copyright Theft, Project Number: RS-2024-00398413, Contribution Rate: $10\%$ ).
+
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| gIoU | cIoU | gIoU | cIoU |
| Amodal Segmentation Methods |
| VRSP† [57] AAAI'21 | 15.18 | 16.55 | 17.41 | 19.75 |
| C2F-Seg† [11] ICCV'23 | 18.62 | 18.25 | 19.12 | 20.31 |
| SD-Amodal† [62] CVPR'24 | 20.87 | 20.09 | 21.52 | 23.10 |
| MLLM-based Methods |
| LISA† [26] CVPR'24 | 23.05 | 22.87 | 24.39 | 26.81 |
| LLM-Seg† [55] CVPR'24 | 24.62 | 23.06 | 25.19 | 27.94 |
| GSVA† [56] CVPR'24 | 42.30 | 42.87 | 47.01 | 48.22 |
| OMG-LLaVA† [67] NeurIPS'24 | 43.92 | 44.21 | 49.41 | 49.38 |
| GLaMM† [46] CVPR'24 | 45.75 | 46.82 | 49.93 | 54.14 |
| PSALM† [69] ECCV'24 | 46.81 | 47.03 | 50.64 | 55.19 |
| Baseline | 43.55 | 43.92 | 48.96 | 48.63 |
| AURA | 47.76 | 47.32 | 51.31 | 55.38 |
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+ "content": "ations for warmup and then linearly decreases the learning rate to 0. Apart from the ablation studies using 13B models as Multi-Modal LLM Backbone that use two NVIDIA A100 GPUs (80GB Memory) for experiments, all of our experiments are conducted on two NVIDIA V100 GPUs (32GB Memory). The batch size for each GPU card is set to 1. The entire training iterations are 5000, and the gradient accumulation technique is used by setting the accumulation step to 4. The entire training time is about 10 hours."
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| 1 | | | 43.55 | 43.92 | 48.96 | 48.63 |
| 2 | ✓ | | 44.86 | 44.07 | 49.57 | 49.10 |
| 3 | | ✓ | 46.95 | 45.60 | 50.68 | 53.72 |
| 4 | ✓ | ✓ | 47.76 | 47.32 | 51.31 | 55.38 |
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| AURA-Llama2-13B | 52.34 | 52.95 | 58.42 | 60.21 |
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| SAM-ViT-L | 45.23 | 45.31 | 49.18 | 53.71 |
| SAM-ViT-H | 47.76 | 47.32 | 51.31 | 55.38 |
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+ "content": "the Multi-Modal LLM for efficiently fine-tuning new data while keeping the pre-trained weight of LLM frozen. As shown in Table 3, when not using the LoRA technique, the performance of AURA drops to a certain extent. This is because the Multi-Modal LLM is not pre-trained on the AmodalReasonSeg dataset and has no specific knowledge learned to understand the purpose underneath the user's question and reason for various occluded objects. Therefore, the Multi-Modal LLM cannot predict textual answers correctly to respond to the user's question, leading to the performance of visible and amodal segmentation not well."
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+ "content": "tations with high quality efficiently. A new dataset named AmodalReasonSeg is presented for daily scenarios where occlusions are challenging for amodal segmentation. Extensive textual question-and-answer pairs are generated, and various objects are referred to in the answers. Moreover, we propose AURA to understand the user's implicit purpose and reason for the answer, which organizes various objects coherently with accurately predicted visible and amodal segmentation masks. Extensive experiments demonstrate the effectiveness of our proposed AURA on reasoning and segmenting the amodal masks in diverse complex scenarios. To enhance the applicability in real-world scenarios, we plan to further optimize the efficiency of our LLM-based model and enrich our dataset's diversity and granularity. Moreover, feature compression approaches [15-17, 40, 41] can be considered to improve the inference speed of the proposed approach."
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+ {
+ "type": "text",
+ "text": "UrbanLLaVA: A Multi-modal Large Language Model for Urban Intelligence",
+ "text_level": 1,
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+ "text": "Jie Feng†, Shengyuan Wang‡, Tianhui Liu§, Yanxin Xi¶, Yong Li†",
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+ "text": "$^{\\dagger}$ Department of Electronic Engineering, BNRist, Tsinghua University, Beijing, China \n $^{\\ddagger}$ Department of Computer Science and Technology, Tsinghua University, Beijing, China \n $^{\\S}$ School of Electronic and Information Engineering, Beijing Jiaotong University, China \n $^{\\text{¶}}$ University of Helsinki, Finland \n{fengjie, liyong07}@tsinghua.edu.cn",
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+ {
+ "type": "text",
+ "text": "Abstract",
+ "text_level": 1,
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+ "text": "Urban research involves a wide range of scenarios and tasks that require the understanding of multi-modal data. Current methods often focus on specific data types and lack a unified framework in urban field for processing them comprehensively. The recent success of multi-modal large language models (MLLMs) presents a promising opportunity to overcome this limitation. In this paper, we introduce UrbanLLaVA, a multi-modal large language model designed to process these four types of data simultaneously and achieve strong performance across diverse urban tasks compared with general MLLMs. In UrbanLLaVA, we first curate a diverse urban instruction dataset encompassing both single-modal and cross-modal urban data, spanning from location view to global view of urban environment. Additionally, we propose a multi-stage training framework that decouples spatial reasoning enhancement from domain knowledge learning, thereby improving the compatibility and downstream performance of UrbanLLaVA across diverse urban tasks. Finally, we also extend existing benchmark for urban research to assess the performance of MLLMs across a wide range of urban tasks. Experimental results from three cities demonstrate that UrbanLLaVA outperforms open-source and proprietary MLLMs in both single-modal tasks and complex cross-modal tasks and shows robust generalization abilities across cities. Source codes and data are openly accessible to the research community via https://github.com/tsinghua-fiblab/UrbanLLaVA.",
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+ {
+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
+ "bbox": [
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+ },
+ {
+ "type": "text",
+ "text": "Urban science [53, 57] and geographic science research[35] highlight that urban data spans multiple modalities, including urban visual data [14], geo-text [45], structured geospatial data [1, 2], and spatiotemporal series data [20, 28]. To",
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+ {
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+ "img_path": "images/0df9f2f59a36d9f1adc4f194ae28cf7868b788ec2bfb8f2cad458d0292e39d50.jpg",
+ "image_caption": [
+ "Figure 1. Existing works vs. our UrbanLLaVA in urban research."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ "type": "text",
+ "text": "gather, these data types capture the multi-faceted nature of urban environments, representing a wide range of spatial information and urban knowledge [35, 46, 57]. Integrating these multi-modal data into a cohesive framework is essential for developing a systematic understanding of urban spaces and advancing complex modeling architectures in urban research. However, the inherent heterogeneity of these diverse urban data presents substantial challenges for the integration. While numerous deep learning based methods have been proposed to fuse various cross-domain urban data [57], they are often designed for specific urban tasks, limiting their ability to achieve a comprehensive understanding of urban environment and advanced reasoning for real-world urban applications [46, 53].",
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+ "text": "Recently, multi-modal large language models (MLLMs) [49] have made notable advancements by leveraging large language models (LLMs) [38] with build-in common sense and reasoning abilities as a central component for unifying the processing data across various modalities, such as images [31], speech [19], and",
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+ "text": "CVF",
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+ {
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "img_path": "images/42a34b51edc2463e8e259a0c3ce39024af647b54632c324eb5d4cc7717a8fe4c.jpg",
+ "image_caption": [
+ "Figure 2. The framework of UrbanLLaVA, including UData, UTrain and UBench."
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+ "text": "time series [25]. For example, Ma et al. [34] develop a vision-language model as a conversational assistant for autonomous driving, Brohan et al. [4] introduce RT-2, a vision language model based end-to-end model for flexible robotics control, Li et al. [27] train LLaVA-Med for answering open-ended questions related to biomedicine images. Building on this trend, researchers have begun to explore the potential of MLLMs in urban studies [53]. As shown in the left part of Figure 1, notable examples include GeoChat [26], an early effort in creating MLLMs for remote sensing tasks; Mobility-LLM [20], which extends LLM with capabilities for trajectory modeling; and CityGPT [16], designed to process structured geospatial data with LLMs. In contrast to earlier urban data fusion methods developing in the deep learning era [53, 57], these recent studies incorporate various unimodal urban data into LLMs to create obtain MLLMs that maintain the powerful reasoning abilities and address diverse urban tasks within a single modality.",
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+ "type": "text",
+ "text": "However, these recent works focus solely on processing unimodal urban data and fall short of achieving a comprehensive understanding and modeling of urban system across diverse tasks involving multi-modal urban data. Unified modeling of multi-modal urban data poses significant challenges. The first challenge is the scarcity of high-quality data for cross-modality alignment. While previous works [16, 26] propose various methods for constructing",
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+ {
+ "type": "text",
+ "text": "instruction tuning dataset for different types of unimodal urban data integrated with language, these efforts are insufficient for unified modeling across multiple modalities. A second challenge lies in the potential conflicts among diverse urban tasks across different modalities, which can lead to unstable training and inconsistent performance.",
+ "bbox": [
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+ "text": "In this paper, we introduce UrbanLLaVA, a multi-modal large language model designed to build comprehensive urban cognition and addressing a wide range of urban tasks, which is shown in the right part of Figure 1. In UrbanLLaVA, we first design UData, a systematic urban instruction data pipeline that enables the generation of high-quality synthetic data. In UData, data generation is meticulously structured to span multiple perspectives—from a localized view for single modality data to trajectory and global view for cross-modality data—capturing the inherently multi-faceted nature of urban system. To improve the training stability and model performance, we conduct extensive experiments to identify key factors impacting the training process and develop an effective three-stage training pipeline UTrain, based on these insights. In fact, the proposed multi-stage training framework can be viewed as a promising practice that explicitly decouples the learning of reasoning capabilities from domain-specific knowledge in MLLMs. Finally, we extend existing urban benchmarks to build a systematic urban benchmark UBench for evaluating the capabilities of MLLMs in tackling diverse urban",
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+ "text": "6210",
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+ "img_path": "images/1528406d5dcb708f09105acc90980fa7b32ef4239081b853c793b2856a81a0bc.jpg",
+ "image_caption": [
+ "Figure 3. The thorough composition of UData in Beijing."
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+ "image_footnote": [],
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+ "type": "text",
+ "text": "tasks. In summary, our contributions are as follows,",
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+ "- UrbanLLaVA is the first MLLM designed for the unified modeling of four major types of urban data, with the goal of fostering comprehensive understanding and effective task-solving for urban environments, to the best of our knowledge.",
+ "- We conduct extensive experiments to identify the key factors influencing training and propose a three-stage training pipeline that ensures stable performance of UrbanLLaVA across a wide range of urban tasks involving multiple data modalities.",
+ "- UrbanLLaVA demonstrates effective integration of multi-modal data, establishing comprehensive spatial cognition and outperforming general MLLMs across various urban tasks based on results from an enhanced urban task benchmark."
+ ],
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+ "type": "text",
+ "text": "2. Methods",
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+ {
+ "type": "text",
+ "text": "As illustrated in Figure 2, UrbanLLaVA comprises three key components: 1) the data pipeline, UData, designed for generating diverse and high-quality urban instruction data across various urban scenarios; 2) the training pipeline, UTrain, which facilitates efficient and stable training across a wide range of urban tasks; 3) the evaluation benchmark, UBench, for evaluating the capabilities of MLLMs in multimodal urban tasks.",
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+ "type": "text",
+ "text": "2.1. UData: Constructing Urban Instruction Data from a Multi-View Perspective of Urban Space",
+ "text_level": 1,
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+ "text": "Over the past decade, effectively integrating multi-modal urban data has emerged as a key research question in urban studies [57]. Building on the successes of MLLMs in various fields [49, 53], we extend the modelling of four types of urban data into a unified model, UrbanLLaVA, by constructing a diverse urban instruction data from a systematic view on the urban environment. Specifically, we organize the urban instruction data in a sequence that move from location view to a trajectory view, and finally to a global view. This approach ensures both broad spatial coverage and the integrity of relationships between different modalities in the final data. UData builds upon four kinds of original urban data: 1) the structured geospatial data from OpenStreetMap $^{1}$ ; 2) public trajectory data, e.g., Foursquare-checkins [48] and OpenStreetMap traces $^{2}$ ; 3) satellite images from GoogleEarth $^{3}$ ; 4) street view images from GoogleMap $^{4}$ and BaiduMap $^{5}$ . Before experiments, we collect original data from above platforms and using the following data pipeline to build instruction data. We follow the license of these platforms and ensure that the data is used only for academic research.",
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+ "type": "text",
+ "text": "2.1.1. Location View Data",
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+ "text": "In the location view data construction stage, we focus on structured geospatial data and single street view images. Following the recent practices [1, 16] for structured geospatial knowledge learning, we create geospatial instruction data by designing question templates that transform basic geospatial data into natural language question and answers. For single street view image, we synthesize three types of questions: 1) two types based on predefined templates populated with information from structured geospatial data, such as, location addresses and landmark details; 2) one general MLLM generated detailed description of the image content, following the common practice for image captioning [6]. Throughout the data construction, we maintain a core principle of integrating street view image content with structured geographical knowledge, such as consistency in location addresses and landmark descriptions.",
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+ "text": "2.1.2. Trajectory View Data",
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+ "text": "Here, we construct the trajectory view data, which includes the geospatial data, trajectory data, and street view images. We start by creating two types of text-based trajectory data. The first type is generated by randomly sampling origin and destination points for routing, while the second type uses the real-world trajectory data collected from the public web",
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+ "type": "page_footnote",
+ "text": "1https://www.openstreetmap.org",
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+ "text": "$^{2}$ https://www.openstreetmap.org/traces",
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+ "text": "3https://earth.google.com/",
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+ "type": "page_footnote",
+ "text": "4https://www.google.com/maps",
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+ "type": "page_number",
+ "text": "6211",
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+ "type": "text",
+ "text": "source, including Foursquare-checkins and OpenStreetMap traces. To enhance geospatial context of trajectory data, we align the GPS coordinates from these original data sources with the structured geospatial data, using the textual addresses to represent locations within the trajectory. Additionally, we integrate street view images to enrich trajectory data, resulting two types of vision-augmented trajectory data. The first data extends the text-based trajectory data by incorporating street view images captured along the route (excluding intersections). We organize this data with the similar interleaved image-text format in VILA [29]. The second data builds on the navigation instruction format akin to the classic vision-language navigation task [5]. In this data, multiple street view images are presented at intersection during the trajectory, and the correct image is selected to guide the continuation of the journey.",
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+ "text": "2.1.3. Global View Data",
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+ "text": "Here, we present the construction of global view data designed to capture relationships among diverse data types over long distances, with street view images and satellite images as primary components and geospatial data serving as auxiliary support. Initially, we create a basic form of global view data by generating captions for single satellite image data enriched with structured geospatial data. Specifically, we define three types of data: 1) prompting general MLLM to produce detailed content description for individual satellite image; 2) sampling location address within satellite image and using a general LLM to summarize the spatial coverage of it based on these location address; 3) prompting general MLLM with land use ground-truth label to generate land use inference results with reason.",
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+ "text": "Furthermore, we introduce the multiple satellite images for more complex instruction data. The first task is to compare the building densities across multiple satellite images. The second task focuses on identifying functional point of interest within these images. For these tasks, we provide manually crafted reasoning steps in a chain-of-thoughts format, supported by structured geospatial data, to improve the alignment between satellite images and geospatial data. Finally, we design two tasks to strengthen the alignment between the street view images and satellite images. The first task is to select the correct satellite image from a set when given a street view image, requiring the model to understand and match content or address across both image types. The second, more challenging task involves pinpointing the location of the street view image within a specific satellite image, such as identifying it as located in the top-left region of satellite image.",
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+ "type": "text",
+ "text": "Based on the data generation steps described before, we perform data quality checks and filtering on the synthesized data to ensure its quality.",
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+ "text": "2.2. UTrain: A Multi-Stage Training Pipeline for Decoupling Reasoning and Knowledge Learning",
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+ {
+ "type": "image",
+ "img_path": "images/31b99f5284a9556b2db2a4da263a4d626af243193ccc6008180ede935dcf0910.jpg",
+ "image_caption": [
+ "Figure 4. UTrain: three-stage training pipeline."
+ ],
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+ "text": "Training UrbanLLaVA presents significant challenges due to the heterogeneity of multi-modal urban instruction data and the diversity of urban tasks. Achieving stable training and balancing performance across various tasks is notably difficult. We chose VILA[29] as the base model for our experiments and conduct extensive studies to identify key factors affecting training. We examine the impact of the training order of multi-modal data and trained components, observing minimal effects. However, we find that learning rate has significant effects on training stability and performance. Detailed results of them are provided in the section 3.3. Additionally, inspired by Dong et al. [12], we explore and propose an effective multi-stage training pipeline which is shown in the Figure 4.",
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+ "text": "We first introduce three kinds of learning procedures: knowledge learning, task alignment and mixture learning. The knowledge learning procedure refers to the training process which UrbanLLaVA acquires foundational urban knowledge from various urban data, such as the information of geospatial data, pure textual trajectory, and detailed description of street view and satellite images. The task alignment learning focuses on equipping UrbanLLaVA with task-specific skills for urban applications, including vision-language navigation, trajectory prediction, chain-of-thoughts reasoning across multiple satellite and street view images. Finally, mixture learning represents the standard training method used by most MLLMs, which training by directly mixing all types of instruction data.",
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+ "type": "text",
+ "text": "During our experiments, we observe that different combination of various learning procedures significantly impact the training. Based on the observations, we propose a three-stage tuning pipeline to improve the training stability and performance on diverse urban tasks. This pipeline consists of three sequential stages: task alignment, knowledge learning, and finally mixture learning. Starting with a well-trained general MLLM as our base model, we first introduce the task alignment learning procedure, fine-tuning the model with diverse urban task related instructions to prepare it for various urban tasks. Through this phase, the model become familiar with a variety of urban tasks, lever",
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+ "type": "page_number",
+ "text": "6212",
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+ "type": "text",
+ "text": "aging its pre-existing general knowledge to complete them. However, familiarity with general knowledge alone is insufficient for effectively addressing diverse urban tasks, so we incorporate the second stage, knowledge learning procedure. This stage imparts specialized urban knowledge from multi-modal urban data that is essential for task resolution. Finally, we introduce the mixture learning stage to enhance the model's awareness of combining knowledge and skills for solving diverse urban tasks. Here, we resample 1/3 domain specific data from the first two stages and 1/3 general textual instruction data, e.g. ShareGPT $^{6}$ and UltralChat [11], for final tuning.",
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+ "type": "text",
+ "text": "2.3. UBench: An Enhanced Multimodal Benchmark for Urban Intelligence Tasks",
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+ "text": "To assess the potential of MLLMs in urban studies, City-Bench [18] and Urbench [56] have been recently introduced. Drawing from the diverse evaluation tasks in these two benchmarks, we reorganize and expand them to create the urban evaluation benchmark UBench, which includes 12 tasks for our experiments. All the evaluation tasks are presented in Table1. We select 6 of these tasks based on the utility of the evaluation data and their relevance to urban scenarios involving UrbanLLaVA's urban data. For structured geospatial data and trajectory modelling, we incorporate the GeoQA, trajectory prediction and navigation task from CityBench. For cross-view urban tasks involving both street view and satellite images, we adopt the image retrieval, camera localization, and scene comparison task from UrBench. In addition, we introduce 6 new tasks in UBench. Four of these tasks are designed for single street view and satellite images, including address inference for both image types, landmark recognition for street view images, and land use inference for satellite images. These single-image tasks are aligned with the urban instruction data, and we partition the original dataset into training and validation sets to prevent potential data leakage. Moreover, we build 2 additional tasks involving multiple images: 1) STV-Outlier, is a spatial consistency task for street view image, where multiple images from a single trajectory are compared to identify an outlier image not part of the trajectory; 2) SceneFunc, extends the scene comparison task from UrBench, challenging model to select the correct satellite image that fulfills specific functional requirements.",
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+ "type": "text",
+ "text": "3. Experiments",
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+ "type": "text",
+ "text": "3.1. Settings",
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+ "text": "We select Beijing, London and New York to conduct experiments. Due to the large volume of data, we select a region",
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+ "type": "table",
+ "img_path": "images/bb733a189992563f3e5961c1277829fa776ed9dd5edd292765fa5c60dec067bc.jpg",
+ "table_caption": [
+ "Table 1. Detailed information about UBench for Beijing, 'STV' refers to street view image, and 'SAT' refers to satellite image."
+ ],
+ "table_footnote": [],
+ "table_body": "| Tasks | Data | Category | Metrics | Samples | Source |
| GeoQA | Geospatial Data | GeoQA | Avg. Accuracy | 1450 | CityBench |
| TrajPredict | Trajectory Data | Geo+Traj | Top-1 | 500 | CityBench |
| Navigation | Single STV | Geo+Traj | Success Rate | 50 | CityBench |
| SceneComp | Multi SAT | Geo+SAT | Accuracy | 200 | UrBench |
| ImgRetrieval | Multi STV & SAT | Geo+SS | Accuracy | 200 | UrBench |
| CameraLoc | Multi STV & SAT | Geo+SS | Accuracy | 200 | UrBench |
| STV-Address | Single STV | Geo+STV | Accuracy | 200 | UBench |
| STV-Landmark | Single STV | Geo+STV | Accuracy | 200 | UBench |
| SAT-Address | Single SAT | Geo+SAT | Accuracy | 200 | UBench |
| SAT-Landuse | Single SAT | Geo+SAT | Accuracy | 200 | UBench |
| STV-Outlier | Multi STV | Geo+STV | Accuracy | 200 | UBench |
| SceneFunc | Multi SAT | Geo+SAT | Accuracy | 200 | UBench |
",
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+ {
+ "type": "text",
+ "text": "from each city to conduct experiments. The spatial coverage of each region is shown in supplementary material.",
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+ "text": "MLLMs We consider the following MLLMs as baselines: Qwen2VL-7B/72B [41], InternVL2-8B/26B [7, 8], VILA1.5-3B/8B/13B [29], LLama3.2-11B/90B [36], and GPT4o and GPT4o-mini [40]. For open source MLLMs, we deploy them through VLMEvalKit [13]. The max output tokens are set to 1000, and the temperature is set as 0.",
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+ "text": "Metrics Table 1 contains all the metrics for UBench. For general evaluation tasks including LLaVA-Bench(In-the-Wild) [30], RealWorldQA [44], and MM-Vet [50], RealWorldQA uses accuracy as the metric, while LLaVA-Bench(In-the-Wild) and MM-Vet use rating score form GPT4o as the judgement.",
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+ "text": "Implementation We use codes from official repository 7 of VILA [29] for fine-tuning on a single 8xA100 node. The training parameters are set as follows: a learning rate of 1e-5, a maximum sequence length of 2048, a batch size of 8 per GPU, and one training epoch. Training UrbanLLaVA for Beijing on 4xA100 took a total of 10.7 hours.",
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+ "text": "3.2. Main Results",
+ "text_level": 1,
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+ "text": "The main results of UrbanLLaVA on three cities are presented in Table 2. We use VILA1.5-8B as the default base model in most experiments and use UData with UTrain methods to fine-tune it to obtain the final model UrbanLLaVA.",
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+ "text": "We analyze the results in Beijing first. One point to note is that, since LLama3.2 series models currently do not support multi-image input, the results for evaluation tasks involving multiple images in the UBench are left blank. For models within the same series, the general trend is that larger parameter models tend to perform better, e.g., VILA1.5-13b significantly outperforms VILA1.5-3b on 5 out of 6 tasks, including both single modal and cross modal tasks. Additionally, we observe that the latest released Qwen2VL series models outperform the GPT4o se",
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+ "text": "$^{6}$ https://huggingface.co/datasets/shareAI/ShareGPT-Chinese-English-90k",
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+ "text": "7https://github.com/NVlabs/VILA",
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+ "text": "6213",
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+ "img_path": "images/f890ea738ad0fdda7e5de5f9e3235c1c45400832bee645bd154cd0d16adea0f4.jpg",
+ "table_caption": [
+ "Table 2. Results on UBench at Beijing, London, and New York. UrbanLLaVA significantly outperforms other baselines in most task across cities. Here, 'STV' denotes street view images related tasks, 'Geo' denotes geospatial data, 'Traj' denotes trajectory related task, 'SAT' denotes satellite images related tasks, and 'SS' denotes street view + satellite images. Detailed subtask and metrics can refer to Table 1."
+ ],
+ "table_footnote": [],
+ "table_body": "| City Task Group | Beijing | London | New York |
| GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS | GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS | GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS |
| VILA1.5-3B | 0.3873 | 0.0200 | 0.3967 | 0.3200 | 0.2575 | 0.4362 | 0.0400 | 0.2557 | 0.2850 | 0.2725 | 0.3954 | 0.0400 | 0.4400 | 0.2713 | 0.2425 |
| VILA1.5-8B | 0.4322 | 0.0589 | 0.4300 | 0.3488 | 0.2425 | 0.4841 | 0.0884 | 0.4495 | 0.4575 | 0.2575 | 0.4575 | 0.1200 | 0.4983 | 0.3763 | 0.2525 |
| VILA1.5-13B | 0.4410 | 0.1156 | 0.5167 | 0.3638 | 0.2400 | 0.4592 | 0.1298 | 0.4991 | 0.4538 | 0.2625 | 0.4501 | 0.2350 | 0.5583 | 0.4025 | 0.2825 |
| InternVL2-8B | 0.4709 | 0.1578 | 0.4667 | 0.3313 | 0.2325 | 0.4973 | 0.1347 | 0.4477 | 0.4763 | 0.2400 | 0.4632 | 0.1830 | 0.4917 | 0.4175 | 0.2400 |
| InternVL2-26B | 0.4877 | 0.1478 | 0.4550 | 0.3825 | 0.2275 | 0.5168 | 0.1288 | 0.4923 | 0.5138 | 0.2425 | 0.4766 | 0.2240 | 0.5217 | 0.4738 | 0.2375 |
| Qwen2VL-7B | 0.4950 | 0.1389 | 0.4383 | 0.3638 | 0.2675 | 0.4991 | 0.1560 | 0.4381 | 0.4863 | 0.2775 | 0.4567 | 0.1700 | 0.5117 | 0.5100 | 0.2950 |
| Qwen2VL-72B | 0.5491 | 0.1611 | 0.5817 | 0.3588 | 0.2975 | 0.5802 | 0.2322 | 0.6375 | 0.4375 | 0.3250 | 0.5273 | 0.2540 | 0.6333 | 0.3788 | 0.3275 |
| LLaMA3.2-11B | 0.4229 | 0.0756 | 0.4375 | 0.3075 | / | 0.4804 | 0.1180 | 0.4000 | 0.3800 | / | 0.4127 | 0.1100 | 0.5200 | 0.2225 | / |
| LLaMA3.2-90B | 0.4502 | 0.1056 | 0.5325 | 0.2925 | / | 0.5659 | 0.2010 | 0.5450 | 0.4700 | / | 0.5234 | 0.1570 | 0.6825 | 0.3400 | / |
| GPT4o-mini | 0.4542 | 0.1622 | 0.4350 | 0.3800 | 0.2475 | 0.5357 | 0.1278 | 0.4752 | 0.5388 | 0.2675 | 0.5075 | 0.2320 | 0.5633 | 0.4775 | 0.2350 |
| GPT4o | 0.5479 | 0.1522 | 0.4300 | 0.4125 | 0.3025 | 0.6446 | 0.1300 | 0.5469 | 0.6050 | 0.2850 | 0.6232 | 0.2340 | 0.5767 | 0.5400 | 0.2900 |
| UrbanLLaVA-VILA1.5-8B | 0.5682 | 0.2800 | 0.8650 | 0.6663 | 0.7025 | 0.6399 | 0.2680 | 0.7500 | 0.7100 | 0.4325 | 0.5773 | 0.3060 | 0.8500 | 0.7725 | 0.5825 |
| vs. VILA1.5-8B | +31.47% | +375.38% | +101.16% | +91.03% | +189.69% | +32.18% | +203.17% | +66.85% | +55.19% | +67.96% | +26.19% | +155.00% | +70.57% | +105.32% | +130.69% |
| vs. Best Baseline | +3.48% | +72.63% | +48.70% | +61.53% | +132.23% | -0.73% | +15.42% | +17.65% | +17.36% | +33.08% | -7.37% | +20.47% | +24.54% | +43.06% | +77.86% |
",
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+ {
+ "type": "text",
+ "text": "ries models on 2 tasks. These results demonstrate the validity and usability of our UBench. Our UrbanLLaVA shows marked improvements over all baselines across all tasks in UBench. Against the best baselines, UrbanLLaVA achieves performance gains ranging from $3.48\\%$ to $132.23\\%$ for each task. When compared to the base model VILA1.5-8B, the minimum increase is $31.47\\%$ on the GeoQA task, while the maximum reaches an impressive $375.38\\%$ on the Geo+Traj task. These results highlight the effectiveness of the proposed multi modal dataset, UData, which successfully equips smaller MLLMs with a variety of capabilities within urban space, achieving superior performance over all advanced general MLLMs.",
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+ "text": "The results in New York and London are similar to those in Beijing. Out of 5 tasks, UrbanLLaVA@London and UrbanLLaVA@NewYork both perform best in 4 tasks. However, in GeoQA task, their performance is slightly inferior to GPT4o, with reductions of $-0.73\\%$ and $-7.37\\%$ , respectively. For UrbanLLaVA's performance falling short of expectations on certain task, we speculate two possible reasons: first, the quality of relevant data in the two cities may be lower than that in Beijing, preventing the model from acquiring urban capabilities through learning in the training stage; second, the base model VILA1.5-8B may have comparatively weaker capabilities than commercial API GPT4o, e.g., for the GeoQA task, UrbanLLaVA@London outperforms VILA1.5-8B by $32.18\\%$ but falls short of GPT4o by $0.73\\%$ .",
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+ "type": "text",
+ "text": "Overall, the proposed UrbanLLaVA successfully enhance the performance of small MLLMs on diverse urban tasks.",
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+ "text": "3.3. Effects of Training Strategies",
+ "text_level": 1,
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+ "text": "Since UrbanLLaVA is trained with multi-modal urban instruction data, we conduct various experiments to explore a",
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+ "text": "stable and well-performing training strategies. Due to the limitation of space, we only report the multi-stage results here, more results on learning rate, modality and trained components can refer the supplementary material.",
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+ "text": "We divide the training dataset into two categories: basic knowledge data and task format aligned data, aiming to develop a training pipeline that enables the model to perform stably and effectively on diverse urban tasks. As Figure 5a shows, 'Three stage: $\\mathrm{TA} \\rightarrow \\mathrm{K} \\rightarrow \\mathrm{Mix}$ ' performs best in most tasks and maintains reliable performance, surpassing the default tuning method for MLLMs. We also probe the effects of the order between knowledge learning and task alignment in Figure 5b and Figure 5c. We find that in two-stage training, $\\mathrm{K} \\rightarrow \\mathrm{TA}$ slightly outperforms $\\mathrm{TA} \\rightarrow \\mathrm{K}$ . However, when the third mixture learning is added in a two-stage training model, having task alignment first achieves better results, surpassing the models in two-stage training. We hypothesize that this is because in the two-stage training, the model first learns the foundational knowledge and then learns how to solve specific tasks. In the three-stage training, the two-stage model that knowledge learning first and then task alignment already possesses considerable capabilities, so the impact of mixture training is not significant. However, for two-stage model that completes task alignment before knowledge learning, mixture learning can enhance its abilities, allowing it to recall how to solve urban tasks learned previously.",
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+ "text": "On the whole, the proposed three-stage training pipeline UTrain integrates cross-modal data to achieve stable training and balanced performance across various urban tasks.",
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+ "text": "3.4. Model Generalization Study",
+ "text_level": 1,
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+ "text": "Here, we show that UrbanLLaVA can be generalized to different data distributions and tasks, which are crucial for",
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+ "text": "6214",
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+ "img_path": "images/5b1c8274439c5a14d42c22f45ede2e932ba46aafb721bf106fc24b528a542009.jpg",
+ "image_caption": [
+ "(a) The performance of three-stage tuning, gray part is the default tuning method for MLLMs."
+ ],
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+ {
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+ "img_path": "images/a66cf03c7359d5afa8af5e850e7dfab838fd4c6e94bc61da369bf61b12f45ebc.jpg",
+ "image_caption": [
+ "Figure 5. Performance of different training strategies. 'K' refers to knowledge learning, 'TA' refers to task alignment, and 'Mix' refers to mixture learning. 'One stage: K + TA' means knowledge learning and task alignment are merged in the same stage. 'Two stage: TA → K' means task alignment first then knowledge learning in the second stage. 'Three stage: TA → K → Mix' adds a step in the third stage: mixture learning. The tasks detailed in the table are those with significant differences across different training strategies, while 'Others' refers to other tasks in UBench with smaller differences."
+ ],
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+ {
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+ "img_path": "images/6085b08929119c8fee6d45becf422a7c2a5bcde9df6f5c0729772dc57c523e77.jpg",
+ "image_caption": [
+ "(b) The effects of the order between knowledge learning and task alignment in two-stage tuning.",
+ "(c) The effects of the order between knowledge learning and task alignment in three-stage tuning."
+ ],
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+ "text": "general urban intelligence. As Table 3 shows, while our UrbanLLaVA performs well in diverse urban tasks, it also maintains the original stability in general scenarios, including LLaVA-Bench [30], RealWorldQA [44], and MMVet [50]. The results demonstrate that UrbanLLaVA is competitive in the dimension of various daily-life visual tasks, real-world spatial understanding and integrated capabilities which is the base for general urban intelligence.",
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+ "img_path": "images/a868d947da452e0dfaed62ccb22f7cf23e5f6ad9f0491264bba36e326ed57acb.jpg",
+ "table_caption": [
+ "Table 3. General benchmark results. Rating Score refers to result from the LLM-as-a-judge method with GPT4o. For LLaVA-Bench, scores range from 0 to 100, for MM-Vet, scores range from 0.0 to 1.0. Higher scores indicate better performance."
+ ],
+ "table_footnote": [],
+ "table_body": "| Test@General | LLaVA-Bench (In-the-Wild) | RealWorldQA | MM-Vet |
| Metric | Rating Score | ACC | Rating Score |
| VILA1.5-8B | 60.75 | 0.3765 | 0.3518 |
| Ours-8B | 58.95 | 0.4052 | 0.3239 |
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+ "text": "Different cities exhibit various natural and artificial features. Thus, the transferability of urban model is important for its application. As Figure 6 shows, apart from in-domain capabilities empowering and performance improvement after learning, UrbanLLaVA can generalize to out-of-domain tasks in various cities. Here, we examined our model trained in the Beijing training set and it exhibits competitive capabilities when tested on London and New York benchmarks. We can see from Figure 6, performance improvements are observed across all tasks in London and New York. Notably, for challenging aspects such as trajectory and regional tasks, the enhancements are significant, indicating the presence of similarity structures across cities that go beyond simple, naive differences.",
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+ "text": "3.5. Data Ablation Study",
+ "text_level": 1,
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+ "text": "Here, we investigate the influences of different data compositions, with results shown in Table 4. As outlined in Sec-",
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+ "text": "tion 2.1, the urban instruction data is divided into three different subsets: local view, trajectory view, and global view. We remove each subset individually and observe the resulting performance differences. Local view: It consists of textual urban geography denoted as CityQA and street view related data denoted as STV. Local view data is important for different tasks requiring intelligence about a local part of cities. Noticeable deterioration is observed in both single-modal and multi-modal tasks, indicating the importance of locality knowledge for overall urban understanding. Trajectory view: It describes the knowledge about continuous spaces in urban areas. It contains text-trajectory (random walk routing and real-world trajectories) and visual-trajectory (visual-language navigation instructions and random walk with visual input). Both text and multi-modal trajectory view datasets are essential for navigation task. It is also shown that trajectory view data is helpful for different tasks like SceneFunc and GeoQA. Global view: It includes a subset of single satellite images that focus on urban knowledge from a specific area, as well as a subset of multiple satellite images that highlight the correlations between different regions and cross alignment between satellite and street view images. Results show that they are essential to empower MLLM to handle urban tasks from a global view, e.g., ImgRetrieval and CameraLoc, while local capabilities are already competitive.",
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+ "type": "text",
+ "text": "4. Related Work",
+ "text_level": 1,
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+ {
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+ "text": "4.1. Multi-modal Large Language Model",
+ "text_level": 1,
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+ "text": "Since the success of GPT4-V [39], MLLM [49] have become a major area of focus in research community, exemplified by the development of models like the LLaVA [30, 31], VILA [29], QwenVL [41] and InternVL [7, 8]. One of the most promising solution to develop advanced MLLM is constructing diverse and high-quality instruction dataset. For example, LLaVA [31] use GPT4-V to create visual in-",
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+ "img_path": "images/42520df309eb121a40bbcf92fcf3074b123fe1b3db411fd5177356fd1bc784db.jpg",
+ "image_caption": [
+ "Figure 6. Learning from one city (Beijing) can be directly generalized to other cities (London and New York). In this figure, Baseline is VILA1.5-8b, and our UrbanLLaVA is only trained with the urban instruction data from Beijing."
+ ],
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+ "img_path": "images/5b3cbfe04deb9a63068fe51ec762b8b803fb05716a6ee867e2bbbde5247bf2e5.jpg",
+ "table_caption": [
+ "Table 4. Ablation results on different urban instruction data compositions. The arrows indicate corresponding comparison with ours. Only significant differences are denoted. For TrajPredict task, the threshold is $1\\%$ , for other tasks, the threshold is $5\\%$ . All models are trained using the one-stage strategy to optimize experimental efficiency."
+ ],
+ "table_footnote": [],
+ "table_body": "| Task | Data View | GeoQA | TrajPredict | Address | Landmark | Address | LandUse | Navigation | STV-Outlier | SceneComp | SceneFunc | ImgRetrieval | CameraLoc |
| Metric | | Avg. Acc | Acc@1 | Acc | Acc | Acc | Acc | Success Rate | Acc | Acc | Acc | Acc | Acc |
| Ours | - | 0.5741 | 0.0711 | 0.8550 | 0.8750 | 0.7450 | 0.7850 | 0.3600 | 0.7800 | 0.5500 | 0.5050 | 0.7300 | 0.5100 |
| w/o CityQA | Local | 0.5409 | 0.0822↑ | 0.8700 | 0.8900 | 0.7150 | 0.6950↓ | 0.4000 | 0.8050 | 0.5400 | 0.5200 | 0.7750 | 0.5200 |
| w/o STV | Local | 0.5192↓ | 0.0622 | 0.4300↓ | 0.7300↓ | 0.4700↓ | 0.7200↓ | 0.4200↑ | 0.6700↓ | 0.4900↓ | 0.4550↓ | 0.6250↓ | 0.4250↓ |
| w/o Traj-Text&Nav | Trajectory | 0.4769↓ | 0.0644 | 0.8100 | 0.8800 | 0.6350↓ | 0.7050↓ | 0.0000↓ | 0.7600 | 0.4950↓ | 0.4300↓ | 0.6800↓ | 0.4600↓ |
| w/o Traj-Vision | Trajectory | 0.5590 | 0.0690 | 0.8350 | 0.9050 | 0.7300 | 0.7100↓ | 0.3000↓ | 0.8000 | 0.5150 | 0.4650 | 0.7150 | 0.4950 |
| w/o SAT-Single | Global | 0.5345 | 0.0778 | 0.8600 | 0.9100 | 0.5550↓ | 0.4550↓ | 0.3800 | 0.7800 | 0.5150 | 0.4100↓ | 0.7200 | 0.4800 |
| w/o SAT-Multi | Global | 0.5420 | 0.0778 | 0.8500 | 0.8700 | 0.6200↓ | 0.6800↓ | 0.3400 | 0.6450↓ | 0.3500↓ | 0.3400↓ | 0.3950↓ | 0.2600↓ |
",
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+ {
+ "type": "text",
+ "text": "struction tuning data, leading to the training of the first open source MLLM. Following LLaVA, VILA [29] explore the effects of training pipelines and data formats during the pretraining stage. ShareGPT4v [6] further expand data scale by developing a superb caption model trained on high-quality caption data from GPT4-V. While general MLLM demonstrate strong visual understanding and reasoning capabilities [9, 21, 43, 47] in common scenarios, they often face challenges in many specialized fields such as medical applications and remote sensing tasks. Thus, domain-specific multi-modal large language models [42] are proposed, such as, dolphins [34] for autonomous driving, GeoChat [26] for remote sensing tasks, and various models for medical application [23]. In this paper, we propose the first MLLM for urban intelligence which can handle various data and diverse tasks in urban field.",
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+ "type": "text",
+ "text": "4.2. Multi-modal Model for Urban Study",
+ "text_level": 1,
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+ "text": "Urban research is an interdisciplinary field that exists multimodal data sources [10, 17, 35, 53, 57], including structured geospatial data [2], spatiotemporal series data [57], remote sensing data [35, 55] and street view data [3, 14, 54]. Inspired by the recent advances of MLLMs, researchers explore their potential in urban studies. For structured geospatial data, Balsebre et al. [1] and Feng et al. [16] propose various methods to convert structured geospatial data into a language-compatible format to enhance the geospatial knowledge of large language models. For remote sensing data [24, 33, 37, 51], Kuckreja et al. [26] and Zhang et al. [52] design various remote sensing instruction data to",
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+ "text": "fine-tune general MLLMs for various downstream remote sensing tasks. For street view data, Hao et al. [22] fine-tune CLIP model for improved urban indicator prediction by integrating street view data and remote sensing data. Liu et al. [32] evaluate the potential of multi-modal language model for urban socioeconomic sensing. For spatiotemporal series data, Li et al. [28] and Gong et al. [20] introduce domain-specific encoders to enhance LLM capabilities for spatiotemporal series modeling. Feng et al. [15] propose agentic framework to unleash the power of LLM for zero-shot mobility prediction. Unlike these works that focus on limited data types and specific tasks, our method is designed to process all these data types and address a wide range of urban tasks.",
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+ "text": "This work was supported in part by the National Key Research and Development Program of China under grant 2024YFC3307603, in part by the National Natural Science Foundation of China under grant U23B2030, in part by the China Postdoctoral Science Foundation under grant 2024M761670 and GZB20240384, in part by the Tsinghua University Shuimu Scholar Program under grant 2023SM235. This work was also sponsored by Tsinghua University-Toyota Research Center.",
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diff --git a/2025/UrbanLLaVA_ A Multi-modal Large Language Model for Urban Intelligence/04c8cc16-b9e6-46a8-b406-679b33839262_model.json b/2025/UrbanLLaVA_ A Multi-modal Large Language Model for Urban Intelligence/04c8cc16-b9e6-46a8-b406-679b33839262_model.json
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+ "content": "\\(^{\\dagger}\\)Department of Electronic Engineering, BNRist, Tsinghua University, Beijing, China \n\\(^{\\ddagger}\\)Department of Computer Science and Technology, Tsinghua University, Beijing, China \n\\(^{\\S}\\)School of Electronic and Information Engineering, Beijing Jiaotong University, China \n\\(^{\\text{¶}}\\)University of Helsinki, Finland \n{fengjie, liyong07}@tsinghua.edu.cn"
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+ "content": "Urban research involves a wide range of scenarios and tasks that require the understanding of multi-modal data. Current methods often focus on specific data types and lack a unified framework in urban field for processing them comprehensively. The recent success of multi-modal large language models (MLLMs) presents a promising opportunity to overcome this limitation. In this paper, we introduce UrbanLLaVA, a multi-modal large language model designed to process these four types of data simultaneously and achieve strong performance across diverse urban tasks compared with general MLLMs. In UrbanLLaVA, we first curate a diverse urban instruction dataset encompassing both single-modal and cross-modal urban data, spanning from location view to global view of urban environment. Additionally, we propose a multi-stage training framework that decouples spatial reasoning enhancement from domain knowledge learning, thereby improving the compatibility and downstream performance of UrbanLLaVA across diverse urban tasks. Finally, we also extend existing benchmark for urban research to assess the performance of MLLMs across a wide range of urban tasks. Experimental results from three cities demonstrate that UrbanLLaVA outperforms open-source and proprietary MLLMs in both single-modal tasks and complex cross-modal tasks and shows robust generalization abilities across cities. Source codes and data are openly accessible to the research community via https://github.com/tsinghua-fiblab/UrbanLLaVA."
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+ "content": "Figure 2. The framework of UrbanLLaVA, including UData, UTrain and UBench."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "time series [25]. For example, Ma et al. [34] develop a vision-language model as a conversational assistant for autonomous driving, Brohan et al. [4] introduce RT-2, a vision language model based end-to-end model for flexible robotics control, Li et al. [27] train LLaVA-Med for answering open-ended questions related to biomedicine images. Building on this trend, researchers have begun to explore the potential of MLLMs in urban studies [53]. As shown in the left part of Figure 1, notable examples include GeoChat [26], an early effort in creating MLLMs for remote sensing tasks; Mobility-LLM [20], which extends LLM with capabilities for trajectory modeling; and CityGPT [16], designed to process structured geospatial data with LLMs. In contrast to earlier urban data fusion methods developing in the deep learning era [53, 57], these recent studies incorporate various unimodal urban data into LLMs to create obtain MLLMs that maintain the powerful reasoning abilities and address diverse urban tasks within a single modality."
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+ "type": "text",
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+ "content": "However, these recent works focus solely on processing unimodal urban data and fall short of achieving a comprehensive understanding and modeling of urban system across diverse tasks involving multi-modal urban data. Unified modeling of multi-modal urban data poses significant challenges. The first challenge is the scarcity of high-quality data for cross-modality alignment. While previous works [16, 26] propose various methods for constructing"
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+ "content": "instruction tuning dataset for different types of unimodal urban data integrated with language, these efforts are insufficient for unified modeling across multiple modalities. A second challenge lies in the potential conflicts among diverse urban tasks across different modalities, which can lead to unstable training and inconsistent performance."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this paper, we introduce UrbanLLaVA, a multi-modal large language model designed to build comprehensive urban cognition and addressing a wide range of urban tasks, which is shown in the right part of Figure 1. In UrbanLLaVA, we first design UData, a systematic urban instruction data pipeline that enables the generation of high-quality synthetic data. In UData, data generation is meticulously structured to span multiple perspectives—from a localized view for single modality data to trajectory and global view for cross-modality data—capturing the inherently multi-faceted nature of urban system. To improve the training stability and model performance, we conduct extensive experiments to identify key factors impacting the training process and develop an effective three-stage training pipeline UTrain, based on these insights. In fact, the proposed multi-stage training framework can be viewed as a promising practice that explicitly decouples the learning of reasoning capabilities from domain-specific knowledge in MLLMs. Finally, we extend existing urban benchmarks to build a systematic urban benchmark UBench for evaluating the capabilities of MLLMs in tackling diverse urban"
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+ "content": "Figure 3. The thorough composition of UData in Beijing."
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+ "content": "tasks. In summary, our contributions are as follows,"
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+ "content": "- UrbanLLaVA is the first MLLM designed for the unified modeling of four major types of urban data, with the goal of fostering comprehensive understanding and effective task-solving for urban environments, to the best of our knowledge."
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+ "content": "- We conduct extensive experiments to identify the key factors influencing training and propose a three-stage training pipeline that ensures stable performance of UrbanLLaVA across a wide range of urban tasks involving multiple data modalities."
+ },
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+ "content": "- UrbanLLaVA demonstrates effective integration of multi-modal data, establishing comprehensive spatial cognition and outperforming general MLLMs across various urban tasks based on results from an enhanced urban task benchmark."
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+ "content": "2. Methods"
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+ "content": "As illustrated in Figure 2, UrbanLLaVA comprises three key components: 1) the data pipeline, UData, designed for generating diverse and high-quality urban instruction data across various urban scenarios; 2) the training pipeline, UTrain, which facilitates efficient and stable training across a wide range of urban tasks; 3) the evaluation benchmark, UBench, for evaluating the capabilities of MLLMs in multimodal urban tasks."
+ },
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+ "content": "2.1. UData: Constructing Urban Instruction Data from a Multi-View Perspective of Urban Space"
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+ "content": "Over the past decade, effectively integrating multi-modal urban data has emerged as a key research question in urban studies [57]. Building on the successes of MLLMs in various fields [49, 53], we extend the modelling of four types of urban data into a unified model, UrbanLLaVA, by constructing a diverse urban instruction data from a systematic view on the urban environment. Specifically, we organize the urban instruction data in a sequence that move from location view to a trajectory view, and finally to a global view. This approach ensures both broad spatial coverage and the integrity of relationships between different modalities in the final data. UData builds upon four kinds of original urban data: 1) the structured geospatial data from OpenStreetMap \\(^{1}\\); 2) public trajectory data, e.g., Foursquare-checkins [48] and OpenStreetMap traces \\(^{2}\\); 3) satellite images from GoogleEarth \\(^{3}\\); 4) street view images from GoogleMap \\(^{4}\\) and BaiduMap \\(^{5}\\). Before experiments, we collect original data from above platforms and using the following data pipeline to build instruction data. We follow the license of these platforms and ensure that the data is used only for academic research."
+ },
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+ "content": "2.1.1. Location View Data"
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+ "content": "In the location view data construction stage, we focus on structured geospatial data and single street view images. Following the recent practices [1, 16] for structured geospatial knowledge learning, we create geospatial instruction data by designing question templates that transform basic geospatial data into natural language question and answers. For single street view image, we synthesize three types of questions: 1) two types based on predefined templates populated with information from structured geospatial data, such as, location addresses and landmark details; 2) one general MLLM generated detailed description of the image content, following the common practice for image captioning [6]. Throughout the data construction, we maintain a core principle of integrating street view image content with structured geographical knowledge, such as consistency in location addresses and landmark descriptions."
+ },
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+ "content": "2.1.2. Trajectory View Data"
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+ "content": "Here, we construct the trajectory view data, which includes the geospatial data, trajectory data, and street view images. We start by creating two types of text-based trajectory data. The first type is generated by randomly sampling origin and destination points for routing, while the second type uses the real-world trajectory data collected from the public web"
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+ "content": "1https://www.openstreetmap.org"
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+ "content": "\\(^{2}\\)https://www.openstreetmap.org/traces"
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+ "bbox": [
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+ "angle": 0,
+ "content": "3https://earth.google.com/"
+ },
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+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "4https://www.google.com/maps"
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+ "bbox": [
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+ "angle": 0,
+ "content": "5https://map.baidu.com/"
+ },
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+ "bbox": [
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+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "source, including Foursquare-checkins and OpenStreetMap traces. To enhance geospatial context of trajectory data, we align the GPS coordinates from these original data sources with the structured geospatial data, using the textual addresses to represent locations within the trajectory. Additionally, we integrate street view images to enrich trajectory data, resulting two types of vision-augmented trajectory data. The first data extends the text-based trajectory data by incorporating street view images captured along the route (excluding intersections). We organize this data with the similar interleaved image-text format in VILA [29]. The second data builds on the navigation instruction format akin to the classic vision-language navigation task [5]. In this data, multiple street view images are presented at intersection during the trajectory, and the correct image is selected to guide the continuation of the journey."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.1.3. Global View Data"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Here, we present the construction of global view data designed to capture relationships among diverse data types over long distances, with street view images and satellite images as primary components and geospatial data serving as auxiliary support. Initially, we create a basic form of global view data by generating captions for single satellite image data enriched with structured geospatial data. Specifically, we define three types of data: 1) prompting general MLLM to produce detailed content description for individual satellite image; 2) sampling location address within satellite image and using a general LLM to summarize the spatial coverage of it based on these location address; 3) prompting general MLLM with land use ground-truth label to generate land use inference results with reason."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Furthermore, we introduce the multiple satellite images for more complex instruction data. The first task is to compare the building densities across multiple satellite images. The second task focuses on identifying functional point of interest within these images. For these tasks, we provide manually crafted reasoning steps in a chain-of-thoughts format, supported by structured geospatial data, to improve the alignment between satellite images and geospatial data. Finally, we design two tasks to strengthen the alignment between the street view images and satellite images. The first task is to select the correct satellite image from a set when given a street view image, requiring the model to understand and match content or address across both image types. The second, more challenging task involves pinpointing the location of the street view image within a specific satellite image, such as identifying it as located in the top-left region of satellite image."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Based on the data generation steps described before, we perform data quality checks and filtering on the synthesized data to ensure its quality."
+ },
+ {
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+ "angle": 0,
+ "content": "2.2. UTrain: A Multi-Stage Training Pipeline for Decoupling Reasoning and Knowledge Learning"
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
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+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. UTrain: three-stage training pipeline."
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Training UrbanLLaVA presents significant challenges due to the heterogeneity of multi-modal urban instruction data and the diversity of urban tasks. Achieving stable training and balancing performance across various tasks is notably difficult. We chose VILA[29] as the base model for our experiments and conduct extensive studies to identify key factors affecting training. We examine the impact of the training order of multi-modal data and trained components, observing minimal effects. However, we find that learning rate has significant effects on training stability and performance. Detailed results of them are provided in the section 3.3. Additionally, inspired by Dong et al. [12], we explore and propose an effective multi-stage training pipeline which is shown in the Figure 4."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "We first introduce three kinds of learning procedures: knowledge learning, task alignment and mixture learning. The knowledge learning procedure refers to the training process which UrbanLLaVA acquires foundational urban knowledge from various urban data, such as the information of geospatial data, pure textual trajectory, and detailed description of street view and satellite images. The task alignment learning focuses on equipping UrbanLLaVA with task-specific skills for urban applications, including vision-language navigation, trajectory prediction, chain-of-thoughts reasoning across multiple satellite and street view images. Finally, mixture learning represents the standard training method used by most MLLMs, which training by directly mixing all types of instruction data."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "During our experiments, we observe that different combination of various learning procedures significantly impact the training. Based on the observations, we propose a three-stage tuning pipeline to improve the training stability and performance on diverse urban tasks. This pipeline consists of three sequential stages: task alignment, knowledge learning, and finally mixture learning. Starting with a well-trained general MLLM as our base model, we first introduce the task alignment learning procedure, fine-tuning the model with diverse urban task related instructions to prepare it for various urban tasks. Through this phase, the model become familiar with a variety of urban tasks, lever"
+ },
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+ "content": "6212"
+ }
+ ],
+ [
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+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "aging its pre-existing general knowledge to complete them. However, familiarity with general knowledge alone is insufficient for effectively addressing diverse urban tasks, so we incorporate the second stage, knowledge learning procedure. This stage imparts specialized urban knowledge from multi-modal urban data that is essential for task resolution. Finally, we introduce the mixture learning stage to enhance the model's awareness of combining knowledge and skills for solving diverse urban tasks. Here, we resample 1/3 domain specific data from the first two stages and 1/3 general textual instruction data, e.g. ShareGPT \\(^{6}\\) and UltralChat [11], for final tuning."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "2.3. UBench: An Enhanced Multimodal Benchmark for Urban Intelligence Tasks"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To assess the potential of MLLMs in urban studies, City-Bench [18] and Urbench [56] have been recently introduced. Drawing from the diverse evaluation tasks in these two benchmarks, we reorganize and expand them to create the urban evaluation benchmark UBench, which includes 12 tasks for our experiments. All the evaluation tasks are presented in Table1. We select 6 of these tasks based on the utility of the evaluation data and their relevance to urban scenarios involving UrbanLLaVA's urban data. For structured geospatial data and trajectory modelling, we incorporate the GeoQA, trajectory prediction and navigation task from CityBench. For cross-view urban tasks involving both street view and satellite images, we adopt the image retrieval, camera localization, and scene comparison task from UrBench. In addition, we introduce 6 new tasks in UBench. Four of these tasks are designed for single street view and satellite images, including address inference for both image types, landmark recognition for street view images, and land use inference for satellite images. These single-image tasks are aligned with the urban instruction data, and we partition the original dataset into training and validation sets to prevent potential data leakage. Moreover, we build 2 additional tasks involving multiple images: 1) STV-Outlier, is a spatial consistency task for street view image, where multiple images from a single trajectory are compared to identify an outlier image not part of the trajectory; 2) SceneFunc, extends the scene comparison task from UrBench, challenging model to select the correct satellite image that fulfills specific functional requirements."
+ },
+ {
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+ "angle": 0,
+ "content": "3. Experiments"
+ },
+ {
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+ "angle": 0,
+ "content": "3.1. Settings"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We select Beijing, London and New York to conduct experiments. Due to the large volume of data, we select a region"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. Detailed information about UBench for Beijing, 'STV' refers to street view image, and 'SAT' refers to satellite image."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "content": "| Tasks | Data | Category | Metrics | Samples | Source |
| GeoQA | Geospatial Data | GeoQA | Avg. Accuracy | 1450 | CityBench |
| TrajPredict | Trajectory Data | Geo+Traj | Top-1 | 500 | CityBench |
| Navigation | Single STV | Geo+Traj | Success Rate | 50 | CityBench |
| SceneComp | Multi SAT | Geo+SAT | Accuracy | 200 | UrBench |
| ImgRetrieval | Multi STV & SAT | Geo+SS | Accuracy | 200 | UrBench |
| CameraLoc | Multi STV & SAT | Geo+SS | Accuracy | 200 | UrBench |
| STV-Address | Single STV | Geo+STV | Accuracy | 200 | UBench |
| STV-Landmark | Single STV | Geo+STV | Accuracy | 200 | UBench |
| SAT-Address | Single SAT | Geo+SAT | Accuracy | 200 | UBench |
| SAT-Landuse | Single SAT | Geo+SAT | Accuracy | 200 | UBench |
| STV-Outlier | Multi STV | Geo+STV | Accuracy | 200 | UBench |
| SceneFunc | Multi SAT | Geo+SAT | Accuracy | 200 | UBench |
"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "from each city to conduct experiments. The spatial coverage of each region is shown in supplementary material."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "MLLMs We consider the following MLLMs as baselines: Qwen2VL-7B/72B [41], InternVL2-8B/26B [7, 8], VILA1.5-3B/8B/13B [29], LLama3.2-11B/90B [36], and GPT4o and GPT4o-mini [40]. For open source MLLMs, we deploy them through VLMEvalKit [13]. The max output tokens are set to 1000, and the temperature is set as 0."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Metrics Table 1 contains all the metrics for UBench. For general evaluation tasks including LLaVA-Bench(In-the-Wild) [30], RealWorldQA [44], and MM-Vet [50], RealWorldQA uses accuracy as the metric, while LLaVA-Bench(In-the-Wild) and MM-Vet use rating score form GPT4o as the judgement."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Implementation We use codes from official repository 7 of VILA [29] for fine-tuning on a single 8xA100 node. The training parameters are set as follows: a learning rate of 1e-5, a maximum sequence length of 2048, a batch size of 8 per GPU, and one training epoch. Training UrbanLLaVA for Beijing on 4xA100 took a total of 10.7 hours."
+ },
+ {
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+ "angle": 0,
+ "content": "3.2. Main Results"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The main results of UrbanLLaVA on three cities are presented in Table 2. We use VILA1.5-8B as the default base model in most experiments and use UData with UTrain methods to fine-tune it to obtain the final model UrbanLLaVA."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We analyze the results in Beijing first. One point to note is that, since LLama3.2 series models currently do not support multi-image input, the results for evaluation tasks involving multiple images in the UBench are left blank. For models within the same series, the general trend is that larger parameter models tend to perform better, e.g., VILA1.5-13b significantly outperforms VILA1.5-3b on 5 out of 6 tasks, including both single modal and cross modal tasks. Additionally, we observe that the latest released Qwen2VL series models outperform the GPT4o se"
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+ "angle": 0,
+ "content": "\\(^{6}\\)https://huggingface.co/datasets/shareAI/ShareGPT-Chinese-English-90k"
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+ "bbox": [
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+ "angle": 0,
+ "content": "7https://github.com/NVlabs/VILA"
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+ "content": "Table 2. Results on UBench at Beijing, London, and New York. UrbanLLaVA significantly outperforms other baselines in most task across cities. Here, 'STV' denotes street view images related tasks, 'Geo' denotes geospatial data, 'Traj' denotes trajectory related task, 'SAT' denotes satellite images related tasks, and 'SS' denotes street view + satellite images. Detailed subtask and metrics can refer to Table 1."
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+ "type": "table",
+ "bbox": [
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+ "content": "| City Task Group | Beijing | London | New York |
| GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS | GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS | GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS |
| VILA1.5-3B | 0.3873 | 0.0200 | 0.3967 | 0.3200 | 0.2575 | 0.4362 | 0.0400 | 0.2557 | 0.2850 | 0.2725 | 0.3954 | 0.0400 | 0.4400 | 0.2713 | 0.2425 |
| VILA1.5-8B | 0.4322 | 0.0589 | 0.4300 | 0.3488 | 0.2425 | 0.4841 | 0.0884 | 0.4495 | 0.4575 | 0.2575 | 0.4575 | 0.1200 | 0.4983 | 0.3763 | 0.2525 |
| VILA1.5-13B | 0.4410 | 0.1156 | 0.5167 | 0.3638 | 0.2400 | 0.4592 | 0.1298 | 0.4991 | 0.4538 | 0.2625 | 0.4501 | 0.2350 | 0.5583 | 0.4025 | 0.2825 |
| InternVL2-8B | 0.4709 | 0.1578 | 0.4667 | 0.3313 | 0.2325 | 0.4973 | 0.1347 | 0.4477 | 0.4763 | 0.2400 | 0.4632 | 0.1830 | 0.4917 | 0.4175 | 0.2400 |
| InternVL2-26B | 0.4877 | 0.1478 | 0.4550 | 0.3825 | 0.2275 | 0.5168 | 0.1288 | 0.4923 | 0.5138 | 0.2425 | 0.4766 | 0.2240 | 0.5217 | 0.4738 | 0.2375 |
| Qwen2VL-7B | 0.4950 | 0.1389 | 0.4383 | 0.3638 | 0.2675 | 0.4991 | 0.1560 | 0.4381 | 0.4863 | 0.2775 | 0.4567 | 0.1700 | 0.5117 | 0.5100 | 0.2950 |
| Qwen2VL-72B | 0.5491 | 0.1611 | 0.5817 | 0.3588 | 0.2975 | 0.5802 | 0.2322 | 0.6375 | 0.4375 | 0.3250 | 0.5273 | 0.2540 | 0.6333 | 0.3788 | 0.3275 |
| LLaMA3.2-11B | 0.4229 | 0.0756 | 0.4375 | 0.3075 | / | 0.4804 | 0.1180 | 0.4000 | 0.3800 | / | 0.4127 | 0.1100 | 0.5200 | 0.2225 | / |
| LLaMA3.2-90B | 0.4502 | 0.1056 | 0.5325 | 0.2925 | / | 0.5659 | 0.2010 | 0.5450 | 0.4700 | / | 0.5234 | 0.1570 | 0.6825 | 0.3400 | / |
| GPT4o-mini | 0.4542 | 0.1622 | 0.4350 | 0.3800 | 0.2475 | 0.5357 | 0.1278 | 0.4752 | 0.5388 | 0.2675 | 0.5075 | 0.2320 | 0.5633 | 0.4775 | 0.2350 |
| GPT4o | 0.5479 | 0.1522 | 0.4300 | 0.4125 | 0.3025 | 0.6446 | 0.1300 | 0.5469 | 0.6050 | 0.2850 | 0.6232 | 0.2340 | 0.5767 | 0.5400 | 0.2900 |
| UrbanLLaVA-VILA1.5-8B | 0.5682 | 0.2800 | 0.8650 | 0.6663 | 0.7025 | 0.6399 | 0.2680 | 0.7500 | 0.7100 | 0.4325 | 0.5773 | 0.3060 | 0.8500 | 0.7725 | 0.5825 |
| vs. VILA1.5-8B | +31.47% | +375.38% | +101.16% | +91.03% | +189.69% | +32.18% | +203.17% | +66.85% | +55.19% | +67.96% | +26.19% | +155.00% | +70.57% | +105.32% | +130.69% |
| vs. Best Baseline | +3.48% | +72.63% | +48.70% | +61.53% | +132.23% | -0.73% | +15.42% | +17.65% | +17.36% | +33.08% | -7.37% | +20.47% | +24.54% | +43.06% | +77.86% |
"
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+ "content": "ries models on 2 tasks. These results demonstrate the validity and usability of our UBench. Our UrbanLLaVA shows marked improvements over all baselines across all tasks in UBench. Against the best baselines, UrbanLLaVA achieves performance gains ranging from \\(3.48\\%\\) to \\(132.23\\%\\) for each task. When compared to the base model VILA1.5-8B, the minimum increase is \\(31.47\\%\\) on the GeoQA task, while the maximum reaches an impressive \\(375.38\\%\\) on the Geo+Traj task. These results highlight the effectiveness of the proposed multi modal dataset, UData, which successfully equips smaller MLLMs with a variety of capabilities within urban space, achieving superior performance over all advanced general MLLMs."
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+ "content": "The results in New York and London are similar to those in Beijing. Out of 5 tasks, UrbanLLaVA@London and UrbanLLaVA@NewYork both perform best in 4 tasks. However, in GeoQA task, their performance is slightly inferior to GPT4o, with reductions of \\(-0.73\\%\\) and \\(-7.37\\%\\), respectively. For UrbanLLaVA's performance falling short of expectations on certain task, we speculate two possible reasons: first, the quality of relevant data in the two cities may be lower than that in Beijing, preventing the model from acquiring urban capabilities through learning in the training stage; second, the base model VILA1.5-8B may have comparatively weaker capabilities than commercial API GPT4o, e.g., for the GeoQA task, UrbanLLaVA@London outperforms VILA1.5-8B by \\(32.18\\%\\) but falls short of GPT4o by \\(0.73\\%\\)."
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+ "content": "Overall, the proposed UrbanLLaVA successfully enhance the performance of small MLLMs on diverse urban tasks."
+ },
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+ "content": "3.3. Effects of Training Strategies"
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+ "content": "Since UrbanLLaVA is trained with multi-modal urban instruction data, we conduct various experiments to explore a"
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+ "content": "stable and well-performing training strategies. Due to the limitation of space, we only report the multi-stage results here, more results on learning rate, modality and trained components can refer the supplementary material."
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+ "content": "We divide the training dataset into two categories: basic knowledge data and task format aligned data, aiming to develop a training pipeline that enables the model to perform stably and effectively on diverse urban tasks. As Figure 5a shows, 'Three stage: \\(\\mathrm{TA} \\rightarrow \\mathrm{K} \\rightarrow \\mathrm{Mix}\\)' performs best in most tasks and maintains reliable performance, surpassing the default tuning method for MLLMs. We also probe the effects of the order between knowledge learning and task alignment in Figure 5b and Figure 5c. We find that in two-stage training, \\(\\mathrm{K} \\rightarrow \\mathrm{TA}\\) slightly outperforms \\(\\mathrm{TA} \\rightarrow \\mathrm{K}\\). However, when the third mixture learning is added in a two-stage training model, having task alignment first achieves better results, surpassing the models in two-stage training. We hypothesize that this is because in the two-stage training, the model first learns the foundational knowledge and then learns how to solve specific tasks. In the three-stage training, the two-stage model that knowledge learning first and then task alignment already possesses considerable capabilities, so the impact of mixture training is not significant. However, for two-stage model that completes task alignment before knowledge learning, mixture learning can enhance its abilities, allowing it to recall how to solve urban tasks learned previously."
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+ "content": "On the whole, the proposed three-stage training pipeline UTrain integrates cross-modal data to achieve stable training and balanced performance across various urban tasks."
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+ "content": "3.4. Model Generalization Study"
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+ "content": "Here, we show that UrbanLLaVA can be generalized to different data distributions and tasks, which are crucial for"
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+ "content": "(a) The performance of three-stage tuning, gray part is the default tuning method for MLLMs."
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+ "content": "(b) The effects of the order between knowledge learning and task alignment in two-stage tuning."
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+ "content": "(c) The effects of the order between knowledge learning and task alignment in three-stage tuning."
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+ "bbox": [
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+ "content": "Figure 5. Performance of different training strategies. 'K' refers to knowledge learning, 'TA' refers to task alignment, and 'Mix' refers to mixture learning. 'One stage: K + TA' means knowledge learning and task alignment are merged in the same stage. 'Two stage: TA → K' means task alignment first then knowledge learning in the second stage. 'Three stage: TA → K → Mix' adds a step in the third stage: mixture learning. The tasks detailed in the table are those with significant differences across different training strategies, while 'Others' refers to other tasks in UBench with smaller differences."
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "general urban intelligence. As Table 3 shows, while our UrbanLLaVA performs well in diverse urban tasks, it also maintains the original stability in general scenarios, including LLaVA-Bench [30], RealWorldQA [44], and MMVet [50]. The results demonstrate that UrbanLLaVA is competitive in the dimension of various daily-life visual tasks, real-world spatial understanding and integrated capabilities which is the base for general urban intelligence."
+ },
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+ "type": "table_caption",
+ "bbox": [
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+ "content": "Table 3. General benchmark results. Rating Score refers to result from the LLM-as-a-judge method with GPT4o. For LLaVA-Bench, scores range from 0 to 100, for MM-Vet, scores range from 0.0 to 1.0. Higher scores indicate better performance."
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+ "angle": 0,
+ "content": "| Test@General | LLaVA-Bench (In-the-Wild) | RealWorldQA | MM-Vet |
| Metric | Rating Score | ACC | Rating Score |
| VILA1.5-8B | 60.75 | 0.3765 | 0.3518 |
| Ours-8B | 58.95 | 0.4052 | 0.3239 |
"
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+ "type": "text",
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+ "angle": 0,
+ "content": "Different cities exhibit various natural and artificial features. Thus, the transferability of urban model is important for its application. As Figure 6 shows, apart from in-domain capabilities empowering and performance improvement after learning, UrbanLLaVA can generalize to out-of-domain tasks in various cities. Here, we examined our model trained in the Beijing training set and it exhibits competitive capabilities when tested on London and New York benchmarks. We can see from Figure 6, performance improvements are observed across all tasks in London and New York. Notably, for challenging aspects such as trajectory and regional tasks, the enhancements are significant, indicating the presence of similarity structures across cities that go beyond simple, naive differences."
+ },
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+ "content": "3.5. Data Ablation Study"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Here, we investigate the influences of different data compositions, with results shown in Table 4. As outlined in Sec-"
+ },
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+ "bbox": [
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+ "content": "tion 2.1, the urban instruction data is divided into three different subsets: local view, trajectory view, and global view. We remove each subset individually and observe the resulting performance differences. Local view: It consists of textual urban geography denoted as CityQA and street view related data denoted as STV. Local view data is important for different tasks requiring intelligence about a local part of cities. Noticeable deterioration is observed in both single-modal and multi-modal tasks, indicating the importance of locality knowledge for overall urban understanding. Trajectory view: It describes the knowledge about continuous spaces in urban areas. It contains text-trajectory (random walk routing and real-world trajectories) and visual-trajectory (visual-language navigation instructions and random walk with visual input). Both text and multi-modal trajectory view datasets are essential for navigation task. It is also shown that trajectory view data is helpful for different tasks like SceneFunc and GeoQA. Global view: It includes a subset of single satellite images that focus on urban knowledge from a specific area, as well as a subset of multiple satellite images that highlight the correlations between different regions and cross alignment between satellite and street view images. Results show that they are essential to empower MLLM to handle urban tasks from a global view, e.g., ImgRetrieval and CameraLoc, while local capabilities are already competitive."
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+ "content": "4. Related Work"
+ },
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+ "angle": 0,
+ "content": "4.1. Multi-modal Large Language Model"
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+ "angle": 0,
+ "content": "Since the success of GPT4-V [39], MLLM [49] have become a major area of focus in research community, exemplified by the development of models like the LLaVA [30, 31], VILA [29], QwenVL [41] and InternVL [7, 8]. One of the most promising solution to develop advanced MLLM is constructing diverse and high-quality instruction dataset. For example, LLaVA [31] use GPT4-V to create visual in-"
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+ [
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+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 6. Learning from one city (Beijing) can be directly generalized to other cities (London and New York). In this figure, Baseline is VILA1.5-8b, and our UrbanLLaVA is only trained with the urban instruction data from Beijing."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 4. Ablation results on different urban instruction data compositions. The arrows indicate corresponding comparison with ours. Only significant differences are denoted. For TrajPredict task, the threshold is \\(1\\%\\), for other tasks, the threshold is \\(5\\%\\). All models are trained using the one-stage strategy to optimize experimental efficiency."
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+ "type": "table",
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+ "angle": 0,
+ "content": "| Task | Data View | GeoQA | TrajPredict | Address | Landmark | Address | LandUse | Navigation | STV-Outlier | SceneComp | SceneFunc | ImgRetrieval | CameraLoc |
| Metric | | Avg. Acc | Acc@1 | Acc | Acc | Acc | Acc | Success Rate | Acc | Acc | Acc | Acc | Acc |
| Ours | - | 0.5741 | 0.0711 | 0.8550 | 0.8750 | 0.7450 | 0.7850 | 0.3600 | 0.7800 | 0.5500 | 0.5050 | 0.7300 | 0.5100 |
| w/o CityQA | Local | 0.5409 | 0.0822↑ | 0.8700 | 0.8900 | 0.7150 | 0.6950↓ | 0.4000 | 0.8050 | 0.5400 | 0.5200 | 0.7750 | 0.5200 |
| w/o STV | Local | 0.5192↓ | 0.0622 | 0.4300↓ | 0.7300↓ | 0.4700↓ | 0.7200↓ | 0.4200↑ | 0.6700↓ | 0.4900↓ | 0.4550↓ | 0.6250↓ | 0.4250↓ |
| w/o Traj-Text&Nav | Trajectory | 0.4769↓ | 0.0644 | 0.8100 | 0.8800 | 0.6350↓ | 0.7050↓ | 0.0000↓ | 0.7600 | 0.4950↓ | 0.4300↓ | 0.6800↓ | 0.4600↓ |
| w/o Traj-Vision | Trajectory | 0.5590 | 0.0690 | 0.8350 | 0.9050 | 0.7300 | 0.7100↓ | 0.3000↓ | 0.8000 | 0.5150 | 0.4650 | 0.7150 | 0.4950 |
| w/o SAT-Single | Global | 0.5345 | 0.0778 | 0.8600 | 0.9100 | 0.5550↓ | 0.4550↓ | 0.3800 | 0.7800 | 0.5150 | 0.4100↓ | 0.7200 | 0.4800 |
| w/o SAT-Multi | Global | 0.5420 | 0.0778 | 0.8500 | 0.8700 | 0.6200↓ | 0.6800↓ | 0.3400 | 0.6450↓ | 0.3500↓ | 0.3400↓ | 0.3950↓ | 0.2600↓ |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "struction tuning data, leading to the training of the first open source MLLM. Following LLaVA, VILA [29] explore the effects of training pipelines and data formats during the pretraining stage. ShareGPT4v [6] further expand data scale by developing a superb caption model trained on high-quality caption data from GPT4-V. While general MLLM demonstrate strong visual understanding and reasoning capabilities [9, 21, 43, 47] in common scenarios, they often face challenges in many specialized fields such as medical applications and remote sensing tasks. Thus, domain-specific multi-modal large language models [42] are proposed, such as, dolphins [34] for autonomous driving, GeoChat [26] for remote sensing tasks, and various models for medical application [23]. In this paper, we propose the first MLLM for urban intelligence which can handle various data and diverse tasks in urban field."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Multi-modal Model for Urban Study"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Urban research is an interdisciplinary field that exists multimodal data sources [10, 17, 35, 53, 57], including structured geospatial data [2], spatiotemporal series data [57], remote sensing data [35, 55] and street view data [3, 14, 54]. Inspired by the recent advances of MLLMs, researchers explore their potential in urban studies. For structured geospatial data, Balsebre et al. [1] and Feng et al. [16] propose various methods to convert structured geospatial data into a language-compatible format to enhance the geospatial knowledge of large language models. For remote sensing data [24, 33, 37, 51], Kuckreja et al. [26] and Zhang et al. [52] design various remote sensing instruction data to"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.442,
+ 0.909,
+ 0.653
+ ],
+ "angle": 0,
+ "content": "fine-tune general MLLMs for various downstream remote sensing tasks. For street view data, Hao et al. [22] fine-tune CLIP model for improved urban indicator prediction by integrating street view data and remote sensing data. Liu et al. [32] evaluate the potential of multi-modal language model for urban socioeconomic sensing. For spatiotemporal series data, Li et al. [28] and Gong et al. [20] introduce domain-specific encoders to enhance LLM capabilities for spatiotemporal series modeling. Feng et al. [15] propose agentic framework to unleash the power of LLM for zero-shot mobility prediction. Unlike these works that focus on limited data types and specific tasks, our method is designed to process all these data types and address a wide range of urban tasks."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.689,
+ 0.909,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "In this paper, we propose UrbanLLaVA, a MLLM with enhanced urban spatial cognition by integrating four types of urban data and supporting a wide range of urban tasks. Our approach begins with the development of diverse and high-quality urban instruction data, spanning from local view to global view of urban environment. We then design a three-stage training pipeline to ensure the stable training and improved performance of model on diverse urban tasks. Experimental results from three cities on an extended urban benchmark highlight the effectiveness of UrbanLLaVA for integrating multi-modal urban data and solving urban tasks. In summary, UrbanLLaVA sheds lights for building the unified foundation model with powerful perception and reasoning abilities for general urban intelligence."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "6216"
+ }
+ ],
+ [
+ {
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+ "angle": 0,
+ "content": "6. Acknowledgment"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This work was supported in part by the National Key Research and Development Program of China under grant 2024YFC3307603, in part by the National Natural Science Foundation of China under grant U23B2030, in part by the China Postdoctoral Science Foundation under grant 2024M761670 and GZB20240384, in part by the Tsinghua University Shuimu Scholar Program under grant 2023SM235. This work was also sponsored by Tsinghua University-Toyota Research Center."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "References"
+ },
+ {
+ "type": "ref_text",
+ "bbox": [
+ 0.101,
+ 0.288,
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+ "content": "[54] Xin Zhang, Tianjian Ouyang, Yu Shang, Qingmin Liao, and Yong Li. UrbanMLLM: Joint learning of cross-view imagery for urban understanding, 2025. 8"
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+# UrbanLLaVA: A Multi-modal Large Language Model for Urban Intelligence
+
+Jie Feng†, Shengyuan Wang‡, Tianhui Liu§, Yanxin Xi¶, Yong Li†
+
+$^{\dagger}$ Department of Electronic Engineering, BNRist, Tsinghua University, Beijing, China
+ $^{\ddagger}$ Department of Computer Science and Technology, Tsinghua University, Beijing, China
+ $^{\S}$ School of Electronic and Information Engineering, Beijing Jiaotong University, China
+ $^{\text{¶}}$ University of Helsinki, Finland
+{fengjie, liyong07}@tsinghua.edu.cn
+
+# Abstract
+
+Urban research involves a wide range of scenarios and tasks that require the understanding of multi-modal data. Current methods often focus on specific data types and lack a unified framework in urban field for processing them comprehensively. The recent success of multi-modal large language models (MLLMs) presents a promising opportunity to overcome this limitation. In this paper, we introduce UrbanLLaVA, a multi-modal large language model designed to process these four types of data simultaneously and achieve strong performance across diverse urban tasks compared with general MLLMs. In UrbanLLaVA, we first curate a diverse urban instruction dataset encompassing both single-modal and cross-modal urban data, spanning from location view to global view of urban environment. Additionally, we propose a multi-stage training framework that decouples spatial reasoning enhancement from domain knowledge learning, thereby improving the compatibility and downstream performance of UrbanLLaVA across diverse urban tasks. Finally, we also extend existing benchmark for urban research to assess the performance of MLLMs across a wide range of urban tasks. Experimental results from three cities demonstrate that UrbanLLaVA outperforms open-source and proprietary MLLMs in both single-modal tasks and complex cross-modal tasks and shows robust generalization abilities across cities. Source codes and data are openly accessible to the research community via https://github.com/tsinghua-fiblab/UrbanLLaVA.
+
+# 1. Introduction
+
+Urban science [53, 57] and geographic science research[35] highlight that urban data spans multiple modalities, including urban visual data [14], geo-text [45], structured geospatial data [1, 2], and spatiotemporal series data [20, 28]. To
+
+
+Figure 1. Existing works vs. our UrbanLLaVA in urban research.
+
+gather, these data types capture the multi-faceted nature of urban environments, representing a wide range of spatial information and urban knowledge [35, 46, 57]. Integrating these multi-modal data into a cohesive framework is essential for developing a systematic understanding of urban spaces and advancing complex modeling architectures in urban research. However, the inherent heterogeneity of these diverse urban data presents substantial challenges for the integration. While numerous deep learning based methods have been proposed to fuse various cross-domain urban data [57], they are often designed for specific urban tasks, limiting their ability to achieve a comprehensive understanding of urban environment and advanced reasoning for real-world urban applications [46, 53].
+
+Recently, multi-modal large language models (MLLMs) [49] have made notable advancements by leveraging large language models (LLMs) [38] with build-in common sense and reasoning abilities as a central component for unifying the processing data across various modalities, such as images [31], speech [19], and
+
+
+Figure 2. The framework of UrbanLLaVA, including UData, UTrain and UBench.
+
+time series [25]. For example, Ma et al. [34] develop a vision-language model as a conversational assistant for autonomous driving, Brohan et al. [4] introduce RT-2, a vision language model based end-to-end model for flexible robotics control, Li et al. [27] train LLaVA-Med for answering open-ended questions related to biomedicine images. Building on this trend, researchers have begun to explore the potential of MLLMs in urban studies [53]. As shown in the left part of Figure 1, notable examples include GeoChat [26], an early effort in creating MLLMs for remote sensing tasks; Mobility-LLM [20], which extends LLM with capabilities for trajectory modeling; and CityGPT [16], designed to process structured geospatial data with LLMs. In contrast to earlier urban data fusion methods developing in the deep learning era [53, 57], these recent studies incorporate various unimodal urban data into LLMs to create obtain MLLMs that maintain the powerful reasoning abilities and address diverse urban tasks within a single modality.
+
+However, these recent works focus solely on processing unimodal urban data and fall short of achieving a comprehensive understanding and modeling of urban system across diverse tasks involving multi-modal urban data. Unified modeling of multi-modal urban data poses significant challenges. The first challenge is the scarcity of high-quality data for cross-modality alignment. While previous works [16, 26] propose various methods for constructing
+
+instruction tuning dataset for different types of unimodal urban data integrated with language, these efforts are insufficient for unified modeling across multiple modalities. A second challenge lies in the potential conflicts among diverse urban tasks across different modalities, which can lead to unstable training and inconsistent performance.
+
+In this paper, we introduce UrbanLLaVA, a multi-modal large language model designed to build comprehensive urban cognition and addressing a wide range of urban tasks, which is shown in the right part of Figure 1. In UrbanLLaVA, we first design UData, a systematic urban instruction data pipeline that enables the generation of high-quality synthetic data. In UData, data generation is meticulously structured to span multiple perspectives—from a localized view for single modality data to trajectory and global view for cross-modality data—capturing the inherently multi-faceted nature of urban system. To improve the training stability and model performance, we conduct extensive experiments to identify key factors impacting the training process and develop an effective three-stage training pipeline UTrain, based on these insights. In fact, the proposed multi-stage training framework can be viewed as a promising practice that explicitly decouples the learning of reasoning capabilities from domain-specific knowledge in MLLMs. Finally, we extend existing urban benchmarks to build a systematic urban benchmark UBench for evaluating the capabilities of MLLMs in tackling diverse urban
+
+
+Figure 3. The thorough composition of UData in Beijing.
+
+tasks. In summary, our contributions are as follows,
+
+- UrbanLLaVA is the first MLLM designed for the unified modeling of four major types of urban data, with the goal of fostering comprehensive understanding and effective task-solving for urban environments, to the best of our knowledge.
+- We conduct extensive experiments to identify the key factors influencing training and propose a three-stage training pipeline that ensures stable performance of UrbanLLaVA across a wide range of urban tasks involving multiple data modalities.
+- UrbanLLaVA demonstrates effective integration of multi-modal data, establishing comprehensive spatial cognition and outperforming general MLLMs across various urban tasks based on results from an enhanced urban task benchmark.
+
+# 2. Methods
+
+As illustrated in Figure 2, UrbanLLaVA comprises three key components: 1) the data pipeline, UData, designed for generating diverse and high-quality urban instruction data across various urban scenarios; 2) the training pipeline, UTrain, which facilitates efficient and stable training across a wide range of urban tasks; 3) the evaluation benchmark, UBench, for evaluating the capabilities of MLLMs in multimodal urban tasks.
+
+# 2.1. UData: Constructing Urban Instruction Data from a Multi-View Perspective of Urban Space
+
+Over the past decade, effectively integrating multi-modal urban data has emerged as a key research question in urban studies [57]. Building on the successes of MLLMs in various fields [49, 53], we extend the modelling of four types of urban data into a unified model, UrbanLLaVA, by constructing a diverse urban instruction data from a systematic view on the urban environment. Specifically, we organize the urban instruction data in a sequence that move from location view to a trajectory view, and finally to a global view. This approach ensures both broad spatial coverage and the integrity of relationships between different modalities in the final data. UData builds upon four kinds of original urban data: 1) the structured geospatial data from OpenStreetMap $^{1}$ ; 2) public trajectory data, e.g., Foursquare-checkins [48] and OpenStreetMap traces $^{2}$ ; 3) satellite images from GoogleEarth $^{3}$ ; 4) street view images from GoogleMap $^{4}$ and BaiduMap $^{5}$ . Before experiments, we collect original data from above platforms and using the following data pipeline to build instruction data. We follow the license of these platforms and ensure that the data is used only for academic research.
+
+# 2.1.1. Location View Data
+
+In the location view data construction stage, we focus on structured geospatial data and single street view images. Following the recent practices [1, 16] for structured geospatial knowledge learning, we create geospatial instruction data by designing question templates that transform basic geospatial data into natural language question and answers. For single street view image, we synthesize three types of questions: 1) two types based on predefined templates populated with information from structured geospatial data, such as, location addresses and landmark details; 2) one general MLLM generated detailed description of the image content, following the common practice for image captioning [6]. Throughout the data construction, we maintain a core principle of integrating street view image content with structured geographical knowledge, such as consistency in location addresses and landmark descriptions.
+
+# 2.1.2. Trajectory View Data
+
+Here, we construct the trajectory view data, which includes the geospatial data, trajectory data, and street view images. We start by creating two types of text-based trajectory data. The first type is generated by randomly sampling origin and destination points for routing, while the second type uses the real-world trajectory data collected from the public web
+
+source, including Foursquare-checkins and OpenStreetMap traces. To enhance geospatial context of trajectory data, we align the GPS coordinates from these original data sources with the structured geospatial data, using the textual addresses to represent locations within the trajectory. Additionally, we integrate street view images to enrich trajectory data, resulting two types of vision-augmented trajectory data. The first data extends the text-based trajectory data by incorporating street view images captured along the route (excluding intersections). We organize this data with the similar interleaved image-text format in VILA [29]. The second data builds on the navigation instruction format akin to the classic vision-language navigation task [5]. In this data, multiple street view images are presented at intersection during the trajectory, and the correct image is selected to guide the continuation of the journey.
+
+# 2.1.3. Global View Data
+
+Here, we present the construction of global view data designed to capture relationships among diverse data types over long distances, with street view images and satellite images as primary components and geospatial data serving as auxiliary support. Initially, we create a basic form of global view data by generating captions for single satellite image data enriched with structured geospatial data. Specifically, we define three types of data: 1) prompting general MLLM to produce detailed content description for individual satellite image; 2) sampling location address within satellite image and using a general LLM to summarize the spatial coverage of it based on these location address; 3) prompting general MLLM with land use ground-truth label to generate land use inference results with reason.
+
+Furthermore, we introduce the multiple satellite images for more complex instruction data. The first task is to compare the building densities across multiple satellite images. The second task focuses on identifying functional point of interest within these images. For these tasks, we provide manually crafted reasoning steps in a chain-of-thoughts format, supported by structured geospatial data, to improve the alignment between satellite images and geospatial data. Finally, we design two tasks to strengthen the alignment between the street view images and satellite images. The first task is to select the correct satellite image from a set when given a street view image, requiring the model to understand and match content or address across both image types. The second, more challenging task involves pinpointing the location of the street view image within a specific satellite image, such as identifying it as located in the top-left region of satellite image.
+
+Based on the data generation steps described before, we perform data quality checks and filtering on the synthesized data to ensure its quality.
+
+# 2.2. UTrain: A Multi-Stage Training Pipeline for Decoupling Reasoning and Knowledge Learning
+
+
+Figure 4. UTrain: three-stage training pipeline.
+
+Training UrbanLLaVA presents significant challenges due to the heterogeneity of multi-modal urban instruction data and the diversity of urban tasks. Achieving stable training and balancing performance across various tasks is notably difficult. We chose VILA[29] as the base model for our experiments and conduct extensive studies to identify key factors affecting training. We examine the impact of the training order of multi-modal data and trained components, observing minimal effects. However, we find that learning rate has significant effects on training stability and performance. Detailed results of them are provided in the section 3.3. Additionally, inspired by Dong et al. [12], we explore and propose an effective multi-stage training pipeline which is shown in the Figure 4.
+
+We first introduce three kinds of learning procedures: knowledge learning, task alignment and mixture learning. The knowledge learning procedure refers to the training process which UrbanLLaVA acquires foundational urban knowledge from various urban data, such as the information of geospatial data, pure textual trajectory, and detailed description of street view and satellite images. The task alignment learning focuses on equipping UrbanLLaVA with task-specific skills for urban applications, including vision-language navigation, trajectory prediction, chain-of-thoughts reasoning across multiple satellite and street view images. Finally, mixture learning represents the standard training method used by most MLLMs, which training by directly mixing all types of instruction data.
+
+During our experiments, we observe that different combination of various learning procedures significantly impact the training. Based on the observations, we propose a three-stage tuning pipeline to improve the training stability and performance on diverse urban tasks. This pipeline consists of three sequential stages: task alignment, knowledge learning, and finally mixture learning. Starting with a well-trained general MLLM as our base model, we first introduce the task alignment learning procedure, fine-tuning the model with diverse urban task related instructions to prepare it for various urban tasks. Through this phase, the model become familiar with a variety of urban tasks, lever
+
+aging its pre-existing general knowledge to complete them. However, familiarity with general knowledge alone is insufficient for effectively addressing diverse urban tasks, so we incorporate the second stage, knowledge learning procedure. This stage imparts specialized urban knowledge from multi-modal urban data that is essential for task resolution. Finally, we introduce the mixture learning stage to enhance the model's awareness of combining knowledge and skills for solving diverse urban tasks. Here, we resample 1/3 domain specific data from the first two stages and 1/3 general textual instruction data, e.g. ShareGPT $^{6}$ and UltralChat [11], for final tuning.
+
+# 2.3. UBench: An Enhanced Multimodal Benchmark for Urban Intelligence Tasks
+
+To assess the potential of MLLMs in urban studies, City-Bench [18] and Urbench [56] have been recently introduced. Drawing from the diverse evaluation tasks in these two benchmarks, we reorganize and expand them to create the urban evaluation benchmark UBench, which includes 12 tasks for our experiments. All the evaluation tasks are presented in Table1. We select 6 of these tasks based on the utility of the evaluation data and their relevance to urban scenarios involving UrbanLLaVA's urban data. For structured geospatial data and trajectory modelling, we incorporate the GeoQA, trajectory prediction and navigation task from CityBench. For cross-view urban tasks involving both street view and satellite images, we adopt the image retrieval, camera localization, and scene comparison task from UrBench. In addition, we introduce 6 new tasks in UBench. Four of these tasks are designed for single street view and satellite images, including address inference for both image types, landmark recognition for street view images, and land use inference for satellite images. These single-image tasks are aligned with the urban instruction data, and we partition the original dataset into training and validation sets to prevent potential data leakage. Moreover, we build 2 additional tasks involving multiple images: 1) STV-Outlier, is a spatial consistency task for street view image, where multiple images from a single trajectory are compared to identify an outlier image not part of the trajectory; 2) SceneFunc, extends the scene comparison task from UrBench, challenging model to select the correct satellite image that fulfills specific functional requirements.
+
+# 3. Experiments
+
+# 3.1. Settings
+
+We select Beijing, London and New York to conduct experiments. Due to the large volume of data, we select a region
+
+Table 1. Detailed information about UBench for Beijing, 'STV' refers to street view image, and 'SAT' refers to satellite image.
+
+| Tasks | Data | Category | Metrics | Samples | Source |
| GeoQA | Geospatial Data | GeoQA | Avg. Accuracy | 1450 | CityBench |
| TrajPredict | Trajectory Data | Geo+Traj | Top-1 | 500 | CityBench |
| Navigation | Single STV | Geo+Traj | Success Rate | 50 | CityBench |
| SceneComp | Multi SAT | Geo+SAT | Accuracy | 200 | UrBench |
| ImgRetrieval | Multi STV & SAT | Geo+SS | Accuracy | 200 | UrBench |
| CameraLoc | Multi STV & SAT | Geo+SS | Accuracy | 200 | UrBench |
| STV-Address | Single STV | Geo+STV | Accuracy | 200 | UBench |
| STV-Landmark | Single STV | Geo+STV | Accuracy | 200 | UBench |
| SAT-Address | Single SAT | Geo+SAT | Accuracy | 200 | UBench |
| SAT-Landuse | Single SAT | Geo+SAT | Accuracy | 200 | UBench |
| STV-Outlier | Multi STV | Geo+STV | Accuracy | 200 | UBench |
| SceneFunc | Multi SAT | Geo+SAT | Accuracy | 200 | UBench |
+
+from each city to conduct experiments. The spatial coverage of each region is shown in supplementary material.
+
+MLLMs We consider the following MLLMs as baselines: Qwen2VL-7B/72B [41], InternVL2-8B/26B [7, 8], VILA1.5-3B/8B/13B [29], LLama3.2-11B/90B [36], and GPT4o and GPT4o-mini [40]. For open source MLLMs, we deploy them through VLMEvalKit [13]. The max output tokens are set to 1000, and the temperature is set as 0.
+
+Metrics Table 1 contains all the metrics for UBench. For general evaluation tasks including LLaVA-Bench(In-the-Wild) [30], RealWorldQA [44], and MM-Vet [50], RealWorldQA uses accuracy as the metric, while LLaVA-Bench(In-the-Wild) and MM-Vet use rating score form GPT4o as the judgement.
+
+Implementation We use codes from official repository 7 of VILA [29] for fine-tuning on a single 8xA100 node. The training parameters are set as follows: a learning rate of 1e-5, a maximum sequence length of 2048, a batch size of 8 per GPU, and one training epoch. Training UrbanLLaVA for Beijing on 4xA100 took a total of 10.7 hours.
+
+# 3.2. Main Results
+
+The main results of UrbanLLaVA on three cities are presented in Table 2. We use VILA1.5-8B as the default base model in most experiments and use UData with UTrain methods to fine-tune it to obtain the final model UrbanLLaVA.
+
+We analyze the results in Beijing first. One point to note is that, since LLama3.2 series models currently do not support multi-image input, the results for evaluation tasks involving multiple images in the UBench are left blank. For models within the same series, the general trend is that larger parameter models tend to perform better, e.g., VILA1.5-13b significantly outperforms VILA1.5-3b on 5 out of 6 tasks, including both single modal and cross modal tasks. Additionally, we observe that the latest released Qwen2VL series models outperform the GPT4o se
+
+Table 2. Results on UBench at Beijing, London, and New York. UrbanLLaVA significantly outperforms other baselines in most task across cities. Here, 'STV' denotes street view images related tasks, 'Geo' denotes geospatial data, 'Traj' denotes trajectory related task, 'SAT' denotes satellite images related tasks, and 'SS' denotes street view + satellite images. Detailed subtask and metrics can refer to Table 1.
+
+| City Task Group | Beijing | London | New York |
| GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS | GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS | GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS |
| VILA1.5-3B | 0.3873 | 0.0200 | 0.3967 | 0.3200 | 0.2575 | 0.4362 | 0.0400 | 0.2557 | 0.2850 | 0.2725 | 0.3954 | 0.0400 | 0.4400 | 0.2713 | 0.2425 |
| VILA1.5-8B | 0.4322 | 0.0589 | 0.4300 | 0.3488 | 0.2425 | 0.4841 | 0.0884 | 0.4495 | 0.4575 | 0.2575 | 0.4575 | 0.1200 | 0.4983 | 0.3763 | 0.2525 |
| VILA1.5-13B | 0.4410 | 0.1156 | 0.5167 | 0.3638 | 0.2400 | 0.4592 | 0.1298 | 0.4991 | 0.4538 | 0.2625 | 0.4501 | 0.2350 | 0.5583 | 0.4025 | 0.2825 |
| InternVL2-8B | 0.4709 | 0.1578 | 0.4667 | 0.3313 | 0.2325 | 0.4973 | 0.1347 | 0.4477 | 0.4763 | 0.2400 | 0.4632 | 0.1830 | 0.4917 | 0.4175 | 0.2400 |
| InternVL2-26B | 0.4877 | 0.1478 | 0.4550 | 0.3825 | 0.2275 | 0.5168 | 0.1288 | 0.4923 | 0.5138 | 0.2425 | 0.4766 | 0.2240 | 0.5217 | 0.4738 | 0.2375 |
| Qwen2VL-7B | 0.4950 | 0.1389 | 0.4383 | 0.3638 | 0.2675 | 0.4991 | 0.1560 | 0.4381 | 0.4863 | 0.2775 | 0.4567 | 0.1700 | 0.5117 | 0.5100 | 0.2950 |
| Qwen2VL-72B | 0.5491 | 0.1611 | 0.5817 | 0.3588 | 0.2975 | 0.5802 | 0.2322 | 0.6375 | 0.4375 | 0.3250 | 0.5273 | 0.2540 | 0.6333 | 0.3788 | 0.3275 |
| LLaMA3.2-11B | 0.4229 | 0.0756 | 0.4375 | 0.3075 | / | 0.4804 | 0.1180 | 0.4000 | 0.3800 | / | 0.4127 | 0.1100 | 0.5200 | 0.2225 | / |
| LLaMA3.2-90B | 0.4502 | 0.1056 | 0.5325 | 0.2925 | / | 0.5659 | 0.2010 | 0.5450 | 0.4700 | / | 0.5234 | 0.1570 | 0.6825 | 0.3400 | / |
| GPT4o-mini | 0.4542 | 0.1622 | 0.4350 | 0.3800 | 0.2475 | 0.5357 | 0.1278 | 0.4752 | 0.5388 | 0.2675 | 0.5075 | 0.2320 | 0.5633 | 0.4775 | 0.2350 |
| GPT4o | 0.5479 | 0.1522 | 0.4300 | 0.4125 | 0.3025 | 0.6446 | 0.1300 | 0.5469 | 0.6050 | 0.2850 | 0.6232 | 0.2340 | 0.5767 | 0.5400 | 0.2900 |
| UrbanLLaVA-VILA1.5-8B | 0.5682 | 0.2800 | 0.8650 | 0.6663 | 0.7025 | 0.6399 | 0.2680 | 0.7500 | 0.7100 | 0.4325 | 0.5773 | 0.3060 | 0.8500 | 0.7725 | 0.5825 |
| vs. VILA1.5-8B | +31.47% | +375.38% | +101.16% | +91.03% | +189.69% | +32.18% | +203.17% | +66.85% | +55.19% | +67.96% | +26.19% | +155.00% | +70.57% | +105.32% | +130.69% |
| vs. Best Baseline | +3.48% | +72.63% | +48.70% | +61.53% | +132.23% | -0.73% | +15.42% | +17.65% | +17.36% | +33.08% | -7.37% | +20.47% | +24.54% | +43.06% | +77.86% |
+
+ries models on 2 tasks. These results demonstrate the validity and usability of our UBench. Our UrbanLLaVA shows marked improvements over all baselines across all tasks in UBench. Against the best baselines, UrbanLLaVA achieves performance gains ranging from $3.48\%$ to $132.23\%$ for each task. When compared to the base model VILA1.5-8B, the minimum increase is $31.47\%$ on the GeoQA task, while the maximum reaches an impressive $375.38\%$ on the Geo+Traj task. These results highlight the effectiveness of the proposed multi modal dataset, UData, which successfully equips smaller MLLMs with a variety of capabilities within urban space, achieving superior performance over all advanced general MLLMs.
+
+The results in New York and London are similar to those in Beijing. Out of 5 tasks, UrbanLLaVA@London and UrbanLLaVA@NewYork both perform best in 4 tasks. However, in GeoQA task, their performance is slightly inferior to GPT4o, with reductions of $-0.73\%$ and $-7.37\%$ , respectively. For UrbanLLaVA's performance falling short of expectations on certain task, we speculate two possible reasons: first, the quality of relevant data in the two cities may be lower than that in Beijing, preventing the model from acquiring urban capabilities through learning in the training stage; second, the base model VILA1.5-8B may have comparatively weaker capabilities than commercial API GPT4o, e.g., for the GeoQA task, UrbanLLaVA@London outperforms VILA1.5-8B by $32.18\%$ but falls short of GPT4o by $0.73\%$ .
+
+Overall, the proposed UrbanLLaVA successfully enhance the performance of small MLLMs on diverse urban tasks.
+
+# 3.3. Effects of Training Strategies
+
+Since UrbanLLaVA is trained with multi-modal urban instruction data, we conduct various experiments to explore a
+
+stable and well-performing training strategies. Due to the limitation of space, we only report the multi-stage results here, more results on learning rate, modality and trained components can refer the supplementary material.
+
+We divide the training dataset into two categories: basic knowledge data and task format aligned data, aiming to develop a training pipeline that enables the model to perform stably and effectively on diverse urban tasks. As Figure 5a shows, 'Three stage: $\mathrm{TA} \rightarrow \mathrm{K} \rightarrow \mathrm{Mix}$ ' performs best in most tasks and maintains reliable performance, surpassing the default tuning method for MLLMs. We also probe the effects of the order between knowledge learning and task alignment in Figure 5b and Figure 5c. We find that in two-stage training, $\mathrm{K} \rightarrow \mathrm{TA}$ slightly outperforms $\mathrm{TA} \rightarrow \mathrm{K}$ . However, when the third mixture learning is added in a two-stage training model, having task alignment first achieves better results, surpassing the models in two-stage training. We hypothesize that this is because in the two-stage training, the model first learns the foundational knowledge and then learns how to solve specific tasks. In the three-stage training, the two-stage model that knowledge learning first and then task alignment already possesses considerable capabilities, so the impact of mixture training is not significant. However, for two-stage model that completes task alignment before knowledge learning, mixture learning can enhance its abilities, allowing it to recall how to solve urban tasks learned previously.
+
+On the whole, the proposed three-stage training pipeline UTrain integrates cross-modal data to achieve stable training and balanced performance across various urban tasks.
+
+# 3.4. Model Generalization Study
+
+Here, we show that UrbanLLaVA can be generalized to different data distributions and tasks, which are crucial for
+
+
+(a) The performance of three-stage tuning, gray part is the default tuning method for MLLMs.
+
+
+Figure 5. Performance of different training strategies. 'K' refers to knowledge learning, 'TA' refers to task alignment, and 'Mix' refers to mixture learning. 'One stage: K + TA' means knowledge learning and task alignment are merged in the same stage. 'Two stage: TA → K' means task alignment first then knowledge learning in the second stage. 'Three stage: TA → K → Mix' adds a step in the third stage: mixture learning. The tasks detailed in the table are those with significant differences across different training strategies, while 'Others' refers to other tasks in UBench with smaller differences.
+
+
+(b) The effects of the order between knowledge learning and task alignment in two-stage tuning.
+(c) The effects of the order between knowledge learning and task alignment in three-stage tuning.
+
+general urban intelligence. As Table 3 shows, while our UrbanLLaVA performs well in diverse urban tasks, it also maintains the original stability in general scenarios, including LLaVA-Bench [30], RealWorldQA [44], and MMVet [50]. The results demonstrate that UrbanLLaVA is competitive in the dimension of various daily-life visual tasks, real-world spatial understanding and integrated capabilities which is the base for general urban intelligence.
+
+Table 3. General benchmark results. Rating Score refers to result from the LLM-as-a-judge method with GPT4o. For LLaVA-Bench, scores range from 0 to 100, for MM-Vet, scores range from 0.0 to 1.0. Higher scores indicate better performance.
+
+| Test@General | LLaVA-Bench (In-the-Wild) | RealWorldQA | MM-Vet |
| Metric | Rating Score | ACC | Rating Score |
| VILA1.5-8B | 60.75 | 0.3765 | 0.3518 |
| Ours-8B | 58.95 | 0.4052 | 0.3239 |
+
+Different cities exhibit various natural and artificial features. Thus, the transferability of urban model is important for its application. As Figure 6 shows, apart from in-domain capabilities empowering and performance improvement after learning, UrbanLLaVA can generalize to out-of-domain tasks in various cities. Here, we examined our model trained in the Beijing training set and it exhibits competitive capabilities when tested on London and New York benchmarks. We can see from Figure 6, performance improvements are observed across all tasks in London and New York. Notably, for challenging aspects such as trajectory and regional tasks, the enhancements are significant, indicating the presence of similarity structures across cities that go beyond simple, naive differences.
+
+# 3.5. Data Ablation Study
+
+Here, we investigate the influences of different data compositions, with results shown in Table 4. As outlined in Sec-
+
+tion 2.1, the urban instruction data is divided into three different subsets: local view, trajectory view, and global view. We remove each subset individually and observe the resulting performance differences. Local view: It consists of textual urban geography denoted as CityQA and street view related data denoted as STV. Local view data is important for different tasks requiring intelligence about a local part of cities. Noticeable deterioration is observed in both single-modal and multi-modal tasks, indicating the importance of locality knowledge for overall urban understanding. Trajectory view: It describes the knowledge about continuous spaces in urban areas. It contains text-trajectory (random walk routing and real-world trajectories) and visual-trajectory (visual-language navigation instructions and random walk with visual input). Both text and multi-modal trajectory view datasets are essential for navigation task. It is also shown that trajectory view data is helpful for different tasks like SceneFunc and GeoQA. Global view: It includes a subset of single satellite images that focus on urban knowledge from a specific area, as well as a subset of multiple satellite images that highlight the correlations between different regions and cross alignment between satellite and street view images. Results show that they are essential to empower MLLM to handle urban tasks from a global view, e.g., ImgRetrieval and CameraLoc, while local capabilities are already competitive.
+
+# 4. Related Work
+
+# 4.1. Multi-modal Large Language Model
+
+Since the success of GPT4-V [39], MLLM [49] have become a major area of focus in research community, exemplified by the development of models like the LLaVA [30, 31], VILA [29], QwenVL [41] and InternVL [7, 8]. One of the most promising solution to develop advanced MLLM is constructing diverse and high-quality instruction dataset. For example, LLaVA [31] use GPT4-V to create visual in-
+
+
+Figure 6. Learning from one city (Beijing) can be directly generalized to other cities (London and New York). In this figure, Baseline is VILA1.5-8b, and our UrbanLLaVA is only trained with the urban instruction data from Beijing.
+
+Table 4. Ablation results on different urban instruction data compositions. The arrows indicate corresponding comparison with ours. Only significant differences are denoted. For TrajPredict task, the threshold is $1\%$ , for other tasks, the threshold is $5\%$ . All models are trained using the one-stage strategy to optimize experimental efficiency.
+
+| Task | Data View | GeoQA | TrajPredict | Address | Landmark | Address | LandUse | Navigation | STV-Outlier | SceneComp | SceneFunc | ImgRetrieval | CameraLoc |
| Metric | | Avg. Acc | Acc@1 | Acc | Acc | Acc | Acc | Success Rate | Acc | Acc | Acc | Acc | Acc |
| Ours | - | 0.5741 | 0.0711 | 0.8550 | 0.8750 | 0.7450 | 0.7850 | 0.3600 | 0.7800 | 0.5500 | 0.5050 | 0.7300 | 0.5100 |
| w/o CityQA | Local | 0.5409 | 0.0822↑ | 0.8700 | 0.8900 | 0.7150 | 0.6950↓ | 0.4000 | 0.8050 | 0.5400 | 0.5200 | 0.7750 | 0.5200 |
| w/o STV | Local | 0.5192↓ | 0.0622 | 0.4300↓ | 0.7300↓ | 0.4700↓ | 0.7200↓ | 0.4200↑ | 0.6700↓ | 0.4900↓ | 0.4550↓ | 0.6250↓ | 0.4250↓ |
| w/o Traj-Text&Nav | Trajectory | 0.4769↓ | 0.0644 | 0.8100 | 0.8800 | 0.6350↓ | 0.7050↓ | 0.0000↓ | 0.7600 | 0.4950↓ | 0.4300↓ | 0.6800↓ | 0.4600↓ |
| w/o Traj-Vision | Trajectory | 0.5590 | 0.0690 | 0.8350 | 0.9050 | 0.7300 | 0.7100↓ | 0.3000↓ | 0.8000 | 0.5150 | 0.4650 | 0.7150 | 0.4950 |
| w/o SAT-Single | Global | 0.5345 | 0.0778 | 0.8600 | 0.9100 | 0.5550↓ | 0.4550↓ | 0.3800 | 0.7800 | 0.5150 | 0.4100↓ | 0.7200 | 0.4800 |
| w/o SAT-Multi | Global | 0.5420 | 0.0778 | 0.8500 | 0.8700 | 0.6200↓ | 0.6800↓ | 0.3400 | 0.6450↓ | 0.3500↓ | 0.3400↓ | 0.3950↓ | 0.2600↓ |
+
+struction tuning data, leading to the training of the first open source MLLM. Following LLaVA, VILA [29] explore the effects of training pipelines and data formats during the pretraining stage. ShareGPT4v [6] further expand data scale by developing a superb caption model trained on high-quality caption data from GPT4-V. While general MLLM demonstrate strong visual understanding and reasoning capabilities [9, 21, 43, 47] in common scenarios, they often face challenges in many specialized fields such as medical applications and remote sensing tasks. Thus, domain-specific multi-modal large language models [42] are proposed, such as, dolphins [34] for autonomous driving, GeoChat [26] for remote sensing tasks, and various models for medical application [23]. In this paper, we propose the first MLLM for urban intelligence which can handle various data and diverse tasks in urban field.
+
+# 4.2. Multi-modal Model for Urban Study
+
+Urban research is an interdisciplinary field that exists multimodal data sources [10, 17, 35, 53, 57], including structured geospatial data [2], spatiotemporal series data [57], remote sensing data [35, 55] and street view data [3, 14, 54]. Inspired by the recent advances of MLLMs, researchers explore their potential in urban studies. For structured geospatial data, Balsebre et al. [1] and Feng et al. [16] propose various methods to convert structured geospatial data into a language-compatible format to enhance the geospatial knowledge of large language models. For remote sensing data [24, 33, 37, 51], Kuckreja et al. [26] and Zhang et al. [52] design various remote sensing instruction data to
+
+fine-tune general MLLMs for various downstream remote sensing tasks. For street view data, Hao et al. [22] fine-tune CLIP model for improved urban indicator prediction by integrating street view data and remote sensing data. Liu et al. [32] evaluate the potential of multi-modal language model for urban socioeconomic sensing. For spatiotemporal series data, Li et al. [28] and Gong et al. [20] introduce domain-specific encoders to enhance LLM capabilities for spatiotemporal series modeling. Feng et al. [15] propose agentic framework to unleash the power of LLM for zero-shot mobility prediction. Unlike these works that focus on limited data types and specific tasks, our method is designed to process all these data types and address a wide range of urban tasks.
+
+# 5. Conclusion
+
+In this paper, we propose UrbanLLaVA, a MLLM with enhanced urban spatial cognition by integrating four types of urban data and supporting a wide range of urban tasks. Our approach begins with the development of diverse and high-quality urban instruction data, spanning from local view to global view of urban environment. We then design a three-stage training pipeline to ensure the stable training and improved performance of model on diverse urban tasks. Experimental results from three cities on an extended urban benchmark highlight the effectiveness of UrbanLLaVA for integrating multi-modal urban data and solving urban tasks. In summary, UrbanLLaVA sheds lights for building the unified foundation model with powerful perception and reasoning abilities for general urban intelligence.
+
+# 6. Acknowledgment
+
+This work was supported in part by the National Key Research and Development Program of China under grant 2024YFC3307603, in part by the National Natural Science Foundation of China under grant U23B2030, in part by the China Postdoctoral Science Foundation under grant 2024M761670 and GZB20240384, in part by the Tsinghua University Shuimu Scholar Program under grant 2023SM235. This work was also sponsored by Tsinghua University-Toyota Research Center.
+
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| GeoQA | Geospatial Data | GeoQA | Avg. Accuracy | 1450 | CityBench |
| TrajPredict | Trajectory Data | Geo+Traj | Top-1 | 500 | CityBench |
| Navigation | Single STV | Geo+Traj | Success Rate | 50 | CityBench |
| SceneComp | Multi SAT | Geo+SAT | Accuracy | 200 | UrBench |
| ImgRetrieval | Multi STV & SAT | Geo+SS | Accuracy | 200 | UrBench |
| CameraLoc | Multi STV & SAT | Geo+SS | Accuracy | 200 | UrBench |
| STV-Address | Single STV | Geo+STV | Accuracy | 200 | UBench |
| STV-Landmark | Single STV | Geo+STV | Accuracy | 200 | UBench |
| SAT-Address | Single SAT | Geo+SAT | Accuracy | 200 | UBench |
| SAT-Landuse | Single SAT | Geo+SAT | Accuracy | 200 | UBench |
| STV-Outlier | Multi STV | Geo+STV | Accuracy | 200 | UBench |
| SceneFunc | Multi SAT | Geo+SAT | Accuracy | 200 | UBench |
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| GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS | GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS | GeoQA | Geo+Traj | Geo+STV | Geo+SAT | Geo+SS |
| VILA1.5-3B | 0.3873 | 0.0200 | 0.3967 | 0.3200 | 0.2575 | 0.4362 | 0.0400 | 0.2557 | 0.2850 | 0.2725 | 0.3954 | 0.0400 | 0.4400 | 0.2713 | 0.2425 |
| VILA1.5-8B | 0.4322 | 0.0589 | 0.4300 | 0.3488 | 0.2425 | 0.4841 | 0.0884 | 0.4495 | 0.4575 | 0.2575 | 0.4575 | 0.1200 | 0.4983 | 0.3763 | 0.2525 |
| VILA1.5-13B | 0.4410 | 0.1156 | 0.5167 | 0.3638 | 0.2400 | 0.4592 | 0.1298 | 0.4991 | 0.4538 | 0.2625 | 0.4501 | 0.2350 | 0.5583 | 0.4025 | 0.2825 |
| InternVL2-8B | 0.4709 | 0.1578 | 0.4667 | 0.3313 | 0.2325 | 0.4973 | 0.1347 | 0.4477 | 0.4763 | 0.2400 | 0.4632 | 0.1830 | 0.4917 | 0.4175 | 0.2400 |
| InternVL2-26B | 0.4877 | 0.1478 | 0.4550 | 0.3825 | 0.2275 | 0.5168 | 0.1288 | 0.4923 | 0.5138 | 0.2425 | 0.4766 | 0.2240 | 0.5217 | 0.4738 | 0.2375 |
| Qwen2VL-7B | 0.4950 | 0.1389 | 0.4383 | 0.3638 | 0.2675 | 0.4991 | 0.1560 | 0.4381 | 0.4863 | 0.2775 | 0.4567 | 0.1700 | 0.5117 | 0.5100 | 0.2950 |
| Qwen2VL-72B | 0.5491 | 0.1611 | 0.5817 | 0.3588 | 0.2975 | 0.5802 | 0.2322 | 0.6375 | 0.4375 | 0.3250 | 0.5273 | 0.2540 | 0.6333 | 0.3788 | 0.3275 |
| LLaMA3.2-11B | 0.4229 | 0.0756 | 0.4375 | 0.3075 | / | 0.4804 | 0.1180 | 0.4000 | 0.3800 | / | 0.4127 | 0.1100 | 0.5200 | 0.2225 | / |
| LLaMA3.2-90B | 0.4502 | 0.1056 | 0.5325 | 0.2925 | / | 0.5659 | 0.2010 | 0.5450 | 0.4700 | / | 0.5234 | 0.1570 | 0.6825 | 0.3400 | / |
| GPT4o-mini | 0.4542 | 0.1622 | 0.4350 | 0.3800 | 0.2475 | 0.5357 | 0.1278 | 0.4752 | 0.5388 | 0.2675 | 0.5075 | 0.2320 | 0.5633 | 0.4775 | 0.2350 |
| GPT4o | 0.5479 | 0.1522 | 0.4300 | 0.4125 | 0.3025 | 0.6446 | 0.1300 | 0.5469 | 0.6050 | 0.2850 | 0.6232 | 0.2340 | 0.5767 | 0.5400 | 0.2900 |
| UrbanLLaVA-VILA1.5-8B | 0.5682 | 0.2800 | 0.8650 | 0.6663 | 0.7025 | 0.6399 | 0.2680 | 0.7500 | 0.7100 | 0.4325 | 0.5773 | 0.3060 | 0.8500 | 0.7725 | 0.5825 |
| vs. VILA1.5-8B | +31.47% | +375.38% | +101.16% | +91.03% | +189.69% | +32.18% | +203.17% | +66.85% | +55.19% | +67.96% | +26.19% | +155.00% | +70.57% | +105.32% | +130.69% |
| vs. Best Baseline | +3.48% | +72.63% | +48.70% | +61.53% | +132.23% | -0.73% | +15.42% | +17.65% | +17.36% | +33.08% | -7.37% | +20.47% | +24.54% | +43.06% | +77.86% |
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| Ours-8B | 58.95 | 0.4052 | 0.3239 |
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| Metric | | Avg. Acc | Acc@1 | Acc | Acc | Acc | Acc | Success Rate | Acc | Acc | Acc | Acc | Acc |
| Ours | - | 0.5741 | 0.0711 | 0.8550 | 0.8750 | 0.7450 | 0.7850 | 0.3600 | 0.7800 | 0.5500 | 0.5050 | 0.7300 | 0.5100 |
| w/o CityQA | Local | 0.5409 | 0.0822↑ | 0.8700 | 0.8900 | 0.7150 | 0.6950↓ | 0.4000 | 0.8050 | 0.5400 | 0.5200 | 0.7750 | 0.5200 |
| w/o STV | Local | 0.5192↓ | 0.0622 | 0.4300↓ | 0.7300↓ | 0.4700↓ | 0.7200↓ | 0.4200↑ | 0.6700↓ | 0.4900↓ | 0.4550↓ | 0.6250↓ | 0.4250↓ |
| w/o Traj-Text&Nav | Trajectory | 0.4769↓ | 0.0644 | 0.8100 | 0.8800 | 0.6350↓ | 0.7050↓ | 0.0000↓ | 0.7600 | 0.4950↓ | 0.4300↓ | 0.6800↓ | 0.4600↓ |
| w/o Traj-Vision | Trajectory | 0.5590 | 0.0690 | 0.8350 | 0.9050 | 0.7300 | 0.7100↓ | 0.3000↓ | 0.8000 | 0.5150 | 0.4650 | 0.7150 | 0.4950 |
| w/o SAT-Single | Global | 0.5345 | 0.0778 | 0.8600 | 0.9100 | 0.5550↓ | 0.4550↓ | 0.3800 | 0.7800 | 0.5150 | 0.4100↓ | 0.7200 | 0.4800 |
| w/o SAT-Multi | Global | 0.5420 | 0.0778 | 0.8500 | 0.8700 | 0.6200↓ | 0.6800↓ | 0.3400 | 0.6450↓ | 0.3500↓ | 0.3400↓ | 0.3950↓ | 0.2600↓ |
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+ "content": "Urban research is an interdisciplinary field that exists multimodal data sources [10, 17, 35, 53, 57], including structured geospatial data [2], spatiotemporal series data [57], remote sensing data [35, 55] and street view data [3, 14, 54]. Inspired by the recent advances of MLLMs, researchers explore their potential in urban studies. For structured geospatial data, Balsebre et al. [1] and Feng et al. [16] propose various methods to convert structured geospatial data into a language-compatible format to enhance the geospatial knowledge of large language models. For remote sensing data [24, 33, 37, 51], Kuckreja et al. [26] and Zhang et al. [52] design various remote sensing instruction data to"
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+ "content": "[52] Wei Zhang, Miaoxin Cai, Tong Zhang, Yin Zhuang, and Xuerui Mao. Earthgpt: A universal multi-modal large language model for multi-sensor image comprehension in remote sensing domain. IEEE Transactions on Geoscience and Remote Sensing, 2024. 8"
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diff --git a/2025/V.I.P. _ Iterative Online Preference Distillation for Efficient Video Diffusion Models/dd5c55db-7a1c-4c99-95eb-8d1eafcb989f_content_list.json b/2025/V.I.P. _ Iterative Online Preference Distillation for Efficient Video Diffusion Models/dd5c55db-7a1c-4c99-95eb-8d1eafcb989f_content_list.json
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+ "text": "V.I.P.: Iterative Online Preference Distillation for Efficient Video Diffusion Models",
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+ "type": "text",
+ "text": "Jisoo Kim Wooseok Seo Junwan Kim Seungho Park Sooyeon Park Youngjae Yu Yonsei University",
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "{jisoo6687，justin_seo，jw1510，gomi0904，dreamyou070，yjy}@yonsei.ac.kr",
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+ {
+ "type": "text",
+ "text": "Abstract",
+ "text_level": 1,
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+ ],
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+ },
+ {
+ "type": "text",
+ "text": "With growing interest in deploying text-to-video (T2V) models in resource-constrained environments, reducing their high computational cost has become crucial, leading to extensive research on pruning and knowledge distillation methods while maintaining performance. However, existing distillation methods primarily rely on supervised finetuning (SFT), which often leads to mode collapse as pruned models with reduced capacity fail to directly match the teacher's outputs, ultimately resulting in degraded quality. To address this challenge, we propose an effective distillation method, ReDPO, that integrates DPO and SFT. Our approach leverages DPO to guide the student model to focus on recovering only the targeted properties, rather than passively imitating the teacher, while also utilizing SFT to enhance overall performance. We additionally propose V.I.P., a novel framework for filtering and curating high-quality pair datasets, along with a step-by-step online approach for calibrated training. We validate our method on two leading T2V models, VideoCrafter2 andAnimateDiff, achieving parameter reduction of $36.2\\%$ and $67.5\\%$ each, while maintaining or even surpassing the performance of full models. Further experiments demonstrate the effectiveness of both ReDPO and V.I.P. framework in enabling efficient and high-quality video generation. Our code and videos are available at https://jiiiisoo.github.io/VIP.github.io/.",
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+ "type": "text",
+ "text": "1. Introduction",
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+ "text": "Recent advancements in video generation models have significantly improved their ability to produce high-fidelity and temporally coherent videos. However, these models typically require substantial computational costs and large memory footprints, which can be prohibitive for resource-constrained deployment. In particular, deploying on mobile phones or edge devices with strict memory and speed constraints often becomes infeasible with models of this scale.",
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+ "Figure 1. Conceptual visualization of generated videos and benchmark scores from pruned models distilled using V.I.P. and SFT. Only the model trained with V.I.P. generates correct concept (astronaut) with high-quality video, indicating strong text alignment, even surpassing the full model. This indicates that V.I.P. selectively improves red (weak) dimensions while preserving green (strong) ones, whereas SFT blindly mimics teacher; degrading even the previously better-performing aspects (text alignment)."
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+ "text": "To address these challenges, recent research has explored strategies such as pruning [19, 28, 38, 59] to develop lightweight models. However, since pruned models typically suffer from performance degradation compared to full models, knowledge distillation [20] has emerged as a prominent approach for preserving strong generative performance, where a smaller student model learns to approximate the output of a larger teacher model, achieving comparable performance while reducing computational cost.",
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+ "text": "Conventional knowledge distillation methods for diffusion models rely largely on naively imitating the teacher's",
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+ {
+ "type": "header",
+ "text": "CVF",
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+ "page_idx": 0
+ },
+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "outputs without addressing the limited capacity of the student model [6, 26, 58]. These approaches transfer knowledge in a direct but unstructured manner, forcing the student model to replicate the teacher's behavior indiscriminately. Due to the inherent capacity gap, such direct distillation—often performed by minimizing the distance between the teacher's and student's predictions or features—tends to result in a suboptimal results [5, 13, 41], as the student model lacks the expressiveness to fully reproduce the teacher's outputs [35]. Therefore, refining the learning objective is essential to ensure that the student allocates its limited capacity toward capturing critical generative patterns rather than blindly mimicking the teacher's outputs.",
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+ "text": "As a novel alternative to conventional methods with direct supervision, we propose leveraging preference learning, commonly represented by Direct Preference Optimization (DPO) [45], to improve diffusion model distillation. Unlike conventional approaches that enforce strict alignment with the teacher's outputs across all aspects, preference learning allows the student to selectively improve properties that degrade due to pruning while avoiding the unnecessary expenditure of its limited capacity on those that undergo only minor deterioration or even improve. Therefore, we formulate diffusion distillation as a preference learning task, where the teacher's outputs are treated as winning responses and the student's as losing responses. By learning from contrastive feedback, rather than direct supervision alone, the student model can prioritize recovering the most critical generative patterns that are negatively affected by pruning, rather than attempting to mimic the teacher indiscriminately. Given the unpredictability of pruning effects—where certain generative properties degrade while others persist or even strengthen [50, 57]—this approach enables a more adaptive and efficient transfer of knowledge.",
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+ "text": "To fully capitalize on the benefits of preference learning in diffusion model distillation, we introduce V.I.P., a step-by-step online distillation framework designed to iteratively guide the student model through progressive pruning. Unlike conventional one-shot pruning, which abruptly removes multiple model components and forces the student to compensate for drastic capacity loss, our approach adopts an iterative pruning strategy. At each stage, we selectively remove specific blocks, allowing the model to gradually adapt while maintaining generative capability. This step-by-step adaptation, by progressively updating the student model at each iteration rather than all at once, ensures that the student model is consistently updated and enhanced, enabling it to continually generate improved training data at each iteration. Consequently, this iterative approach not only mitigates the significant degradation typically resulted by one-shot pruning but also contributes to synthesizing high-quality preference pairs via improved student models.",
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+ "- We present a novel distillation loss ReDPO that integrates Direct Preference Optimization (DPO) into the diffusion framework, making it the first to employ preference learning for pruned diffusion models.",
+ "- We propose V.I.P., a framework that incorporates an on-policy data curation strategy and an online distillation method, allowing pruned models to recover lost features more effectively. By structuring pruning and distillation in stages, our approach ensures stable optimization and improved generative performance.",
+ "- Through extensive experiments, we demonstrate that our method significantly outperforms existing distillation approaches, even surpassing the full model in performance, while reducing parameters by $36.2\\%$ in VideoCrafter and $67.5\\%$ in theAnimateDiff motion module."
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+ "text": "2. Related Works",
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+ "text": "Text-to-video generation has gained considerable attention due to its broad potential for various applications. Early methods relied on traditional generative models such as Generative Adversarial Networks (GANs) [15] and Variational Autoencoders (VAEs) [27], but these approaches often produced low-quality, short videos. With the success of image diffusion models [21, 44, 48], recent methods extend them to video diffusion models by introducing additional temporal layers on top of the spatial layers in existing 2D diffusion models [3, 4, 7, 17, 29]. This approach effectively carries over the strong generative capabilities of image diffusion models to the video domain. However, while these advancements have enabled high-resolution video generation, their substantial computational costs, limiting practical use for real-world applications. To address this, we propose a distillation-based approach that reduces model size while keeping generative capabilities largely intact. Unlike prior methods that focus only on naive pruning or supervised fine-tuning, we introduce a targeted and adaptive mechanism to prioritize and recover the most critical generative properties sacrificed by aggressive pruning.",
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+ {
+ "type": "text",
+ "text": "Diffusion models are computationally intensive, requiring pruning-based optimization for efficiency. While pruning removes redundancy with minimal performance loss, it often requires further training. Some works [26, 30, 58, 62, 65] finetune pruned models with diffusion loss, which requires substantial data and computation. BK-SDM [26] introduces knowledge distillation [20] by minimizing the distance between noise predictions of pruned and original models. However, as such exact matching is limited due to reduced capacity [34], it further incorporates feature-level guidance. Recent work [57] improves upon this by incorpo",
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+ {
+ "type": "text",
+ "text": "rating adversarial loss, which sharpens distributions to mitigate capacity limitations. Yet, adversarial methods inherently lack precise control over where sharpness is applied, often leading to unintended distortions [33, 35] and mode collapse [61], posing stability challenges in practical applications. Moreover, only few methods explore such techniques for text-to-video diffusion, wherein temporal consistency and motion fidelity become challenge and prone to degeneration under pruning. To address this, we propose a stepwise pruning with a novel distillation process that (i) explicitly identifies the properties that the pruned model struggles with and (ii) guides the student to prioritize them in a more adaptive, preference-driven manner.",
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+ "text": "Preference learning is widely used to align generative models, especially large language models (LLMs), with human preferences [42, 66]. Traditional methods train a separate reward model using human preference data, which subsequently guides model refinement via reinforcement learning (RL) algorithms such as Proximal Policy Optimization (PPO) [49]. Recently, Direct Preference Optimization (DPO) [45] emerged as a more streamlined alternative, bypassing explicit reward model training and directly optimizing models against human preferences on pairwise datasets. The simplicity of its training process has popularized DPO, leading to various adaptations across text [1, 11, 22, 40], images [46, 54, 63], and videos [25, 37, 64]. Despite its widespread use, the application of preference learning in diffusion distillation remains largely understudied, due to the complexity of aligning iterative denoising steps with human preferences while maintaining generative capability. To the best of our knowledge, we are the first to tackle these challenges by introducing a preference-guided framework tailored for diffusion distillation. In doing so, we seamlessly integrate preference alignment with iterative pruning and online distillation, enabling our method to continuously curate training data at each stage and effectively remedy newly emerging weaknesses in the pruned model.",
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+ "text": "In this section, we propose V.I.P. (Video diffusion distillation via Iterative Preference learning), our distillation framework designed to efficiently transfer generative capabilities from high-capacity teacher diffusion models to their lightweight students. Motivated by limitations of standard distillation methods, we first highlight the need for explicit guidance into loss function (Sec. 3.1). We then describe two key building blocks, pruning algorithm (Sec. 3.2) and data curation (Sec. 3.3). Finally, we present V.I.P. (Sec. 3.4), which integrates our proposed loss ReDPO, and step-by-step distillation to better reallocate the student's limited capacity toward essential generative properties.",
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+ "Figure 2. Conceptual illustration of learned distributions from teacher and student models. Conventional distillation methods (SFT) result in overly smooth distributions in low-capacity students. Our proposed method (ReDPO) effectively reallocates the student's limited capacity toward the critical mode while preventing over-optimization."
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+ "text": "Figure 2 illustrates how a well-designed distillation loss helps capacity-constrained model effectively learn essential generative properties. Conventional distillation methods typically transfer knowledge by minimizing the $L_{2}$ distance between teacher and student predictions or feature representations [6, 26, 58], known as supervised fine-tuning (SFT). While this approach guarantees convergence in sufficiently expressive models, it fails to do so when applied to models with limited capacity. In such cases, SFT loss often leads to a distributional averaging, where student produces samples that do not exist in teacher's distribution. This occurs since minimizing SFT loss inherently prioritizes reducing overall error over preserving fine-grained details [5, 13], resulting in an oversmoothed generative process (green curve).",
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+ "text": "To address this, explicit guidance is required to help the student allocate its limited capacity to the most essential aspects of generation. We employ Direct Preference Optimization (DPO) [45] to guide the student toward selectively meaningful generative properties, rather than mimicking all aspects of the teacher indiscriminately and wasting capacity. This prevents the capacity-limited student model from collapsing to a distributional average and enables effective use of constrained capacity. Notably, pruned student models often exhibit selective degradation (blue curve) where some generative properties deteriorate while others remain unaffected or even improve. Using DPO, we can explicitly steer the student toward recovering these degraded properties rather than passively approximating the teacher's distribution, ensuring a targeted and efficient distillation process.",
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+ "text": "While DPO ideally enables the student model to allocate capacity more efficiently, a critical challenge is its inherent tendency to over-optimize [12, 39, 43]. This arises from the objective, maximizing the relative likelihood (i.e., the margin) between preferred and unpreferred responses. This can",
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+ "Figure 3. Overall architecture. Starting from a baseline model $M_0$ , we obtain a pruned model $M_1$ . Through a systemic evaluation & preference data synthesis, and a training process using ReDPO, we obtain a preference-learned model $M_1'$ . Then, $M_1'$ is pruned again to obtain $M_2$ , which will run through an iterative distillation process V.I.P.. Note that the teacher model is fixed to $M_0$ , while the student model $M_i$ is dynamically updated."
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+ "text": "lead to an imperfect reward distribution, particularly in uncertain regions, resulting degraded output quality and bias toward out-of-distribution samples [39] (purple curve).",
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+ "text": "To address this, we introduce the SFT loss as regularizer, encouraging the student to mimic the teacher without relying solely on learned reward distributions. This combination results in a more balanced distillation process, avoiding inefficient resource allocation while preventing overoptimization. Building on this motivation, we propose ReDPO, which successfully transfers knowledge from the teacher to the student (red curve). Section 3.4.1 provides a detailed explanation of ReDPO, while Supplementary Section E presents toy experiment validating of our motivation.",
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+ "text": "3.2. Pruning Algorithm",
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+ "text": "For pruning blocks of model, we first evaluate the impact by removing each block individually using VideoScore's [18] total score and select blocks that have minimal impact compared to the full model. Here, we identify the properties that show the performance drop relative to the full model as the target properties for recovery. After each training step, as shown in Algorithm 1 in the Supplementary Section C.1, the same pruning process is repeated as part of our step-by-step approach. This allows the model to progressively adapt to the full model's distribution, starting from easier settings by structurally pruning less impactful modules first, thereby facilitating a more effective learning process.",
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+ "text": "3.3. Data Curation",
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+ "text": "We perform dataset filtering in two phases: prompt filtering and video filtering. Given the strong impact of prompt quality and semantics on video generation [9, 14, 31], we first filter prompts for quality and relevance to the targeted attribute. Using the filtered set, we curate videos by generating and evaluating outputs from both full and pruned models, and form winning-losing pairs based on target property.",
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+ "text": "Prompt filtering. First, we select high-quality prompts suitable for video inference and well-aligned with the targeted property. Given long prompts are not well-suited for video generation, following [18], we retain prompts with 5 to 25 words and remove articles to maintain a balanced length. We then filter prompts that contain the targeted property through LLM-based filtering, ensuring they explicitly describe relevant aspects that rule-based methods often miss. For instance, to target dynamic degree, we select prompts including motion-related elements, such as object movement or camera motion. Further details on LLM prompting are provided in Supplementary Section F.",
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+ "text": "Video curation. Using the filtered prompts, we generate a set of videos with both the full model and the pruned model, then evaluate them with VideoScore, which serves as a reward model. Based on the resulting scores, we construct training pairs $(v_{\\mathrm{full}}, v_{\\mathrm{pruned}})$ where the teacher outperforms",
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+ "text": "17238",
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+ "type": "text",
+ "text": "the student for the targeted property $p$ , and also impose a minimum threshold $\\tau_{p}$ to prevent the inclusion of excessively low-quality samples.:",
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+ {
+ "type": "equation",
+ "text": "\n$$\nS (v _ {\\text {f u l l}}) > S (v _ {\\text {p r u n e d}}) > \\tau_ {p}, \\quad v _ {\\text {f u l l}} \\in V _ {\\text {f u l l}} ^ {p}, \\quad v _ {\\text {p r u n e d}} \\in V _ {\\text {p r u n e d}} ^ {p}\n$$\n",
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+ "type": "text",
+ "text": "where $S(v)$ represents the reward of video $v$ . This ensures that the winning sample is of high quality while effectively capturing cases where the pruned model underperforms. Further details are provided in Supplementary Section C.2",
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+ "type": "text",
+ "text": "3.4. Iterative Preference Distillation",
+ "text_level": 1,
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+ "type": "text",
+ "text": "Building on a pruned model and curated data, our proposed method, V.I.P., introduces two key components: integration of SFT into DPO and step-by-step online DPO learning.",
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+ "text": "As noted in Section 3.1, despite the advantages, DPO is prone to overoptimization, which can paradoxically degrade the output probability of winning responses. To address this, we integrate SFT into DPO as regularizer. Moreover, standard DPO operates offline, relying entirely on static datasets. In contrast, online methods like PPO [49] sample training data and update policy iteratively, and have been shown to outperform offline approaches [10, 24, 52, 53], motivating recent proposals for online DPO variants [8, 16]. Inspired by theses findings, and to avoid the degradation from one-shot pruning which leads to drastic capacity loss, we propose step-by-step online DPO learning that incrementally optimizes the student model using updated samples at each stage. To these ends, we propose ReDPO (Regularized Diffusion Preference Optimization) and V.I.P. (Video diffusion distillation via Iterative Preference Optimization), described in the following sections.",
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+ "text": "3.4.1. ReDPO",
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+ "text": "We enhance diffusion DPO loss [54] by incorporating SFT on preferred pairs as a regularizer, motivated by [39]. While the KL term in DPO imposes some constraints, it is insufficient to fully prevent overoptimization. SFT explicitly aligns student with distribution of preferred samples, reinforcing preference probability more effectively and improving generation quality.",
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+ "text": "We set $\\pi_{ref}$ as the full model and $\\pi_{\\theta}$ as the pruned model. The key idea behind ReDPO is that, given curated dataset, it selectively align the pruned model $\\pi_{\\theta}$ with the full model $\\pi_{ref}$ , while preserving aspects where the pruned model may already outperform the teacher.",
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+ "text": "To achieve this, objective $L_{diff - dpo}(\\theta)$ is as follows:",
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+ "text": "\n$$\n\\begin{array}{l} L _ {d i f f - d p o} (\\theta) = \\\\ - \\mathbb {E} _ {\\left(x _ {0} ^ {w}, x _ {0} ^ {l}\\right) \\sim \\mathcal {D}, t \\sim \\mathcal {U} (0, T), x _ {t} ^ {w} \\sim q \\left(x _ {t} ^ {w} \\mid x _ {0} ^ {w}\\right), x _ {t} ^ {l} \\sim q \\left(x _ {t} ^ {l} \\mid x _ {0} ^ {l}\\right)} \\\\ \\end{array}\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\log \\sigma (- \\beta T \\omega (\\lambda_ {t}) (1)\n$$\n",
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+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\left\\| \\boldsymbol {\\epsilon} ^ {w} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {w}, t\\right) \\right\\| _ {2} ^ {2} - \\left\\| \\boldsymbol {\\epsilon} ^ {w} - \\boldsymbol {\\epsilon} _ {\\operatorname {r e f}} \\left(\\boldsymbol {x} _ {t} ^ {w}, t\\right) \\right\\| _ {2} ^ {2} \\\\ - \\left(\\left\\| \\boldsymbol {\\epsilon} ^ {l} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {l}, t\\right)\\right\\| _ {2} ^ {2} - \\left\\| \\boldsymbol {\\epsilon} ^ {l} - \\boldsymbol {\\epsilon} _ {\\text {r e f}} \\left(\\boldsymbol {x} _ {t} ^ {l}, t\\right)\\right\\| _ {2} ^ {2}\\right)\\left. \\right)) \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "Here, $\\epsilon_{\\theta}(\\pmb{x}_t^w,t)$ and $\\epsilon_{ref}(\\pmb{x}_t^w,t)$ denote the noise predicted by $\\pi_{\\theta}$ and $\\pi_{ref}$ , respectively. The SFT regularization term on the preferred pair is defined as:",
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+ "type": "equation",
+ "text": "\n$$\nL _ {S F T} (\\theta) = \\left\\| \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {w}, t\\right) - \\boldsymbol {\\epsilon} _ {\\mathrm {r e f}} \\left(\\boldsymbol {x} _ {t} ^ {w}, t\\right) \\right\\| _ {2} ^ {2} \\tag {2}\n$$\n",
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+ "type": "text",
+ "text": "Therefore, our final ReDPO loss is as follows :",
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+ "text": "\n$$\nL _ {R e D P O} (\\theta) = L _ {d i f f - d p o} (\\theta) + w _ {S F T} L _ {S F T} (\\theta) \\tag {3}\n$$\n",
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+ "text": "$w_{SFT}$ is the weight of SFT loss. Furthermore, although ReDPO was specifically utilized for distillation task in this work, we emphasize that it can be applied robustly for general diffusion preference alignment purposes. We analyze the effect of $w_{SFT}$ in Supplementary Section D.1.",
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+ "type": "text",
+ "text": "3.4.2.V.I.P.",
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+ "text": "The overall workflow of V.I.P. is shown in Figure 3. We begin by pruning the full (teacher) model $M_0$ into a smaller model $M_1$ (Section 3.2). Both models $M_0$ and $M_1$ generate videos for the same targeted prompts (Section 3.3), forming winning (from $M_0$ ) and losing (from $M_1$ ) pairs. These pairs are used to distill knowledge from $M_0$ into the pruned model via our preference-based distillation loss ReDPO, resulting in trained pruned model, $M_1'$ . This refinement process repeats iteratively. The refined model $M_1'$ further pruned to $M_2$ . In each subsequent iteration, the full model $M_0$ continues to produce the winning samples, while the current pruned model (e.g., $M_2$ ) generates updated losing samples based on targeted prompts identified through systematic evaluation of its deficiencies. These dynamically updated pairs form the training data for the next round of distillation. This iterative, online distillation cycle ensures pruned models to progressively adapt by consistently targeting and mitigating their latest performance weaknesses.",
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+ "type": "text",
+ "text": "4. Experiments",
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+ "text": "In this section, we outline our evaluation approach. Section 4.1 describes the experimental setup, covering benchmarks, baseline models, datasets, and hyperparameters. Section 4.2 presents both quantitative and qualitative analyses across various settings, comparing V.I.P., SFT-based distillation, and the full (teacher) model. An ablation study in Section 4.3 highlights the impact of each components. Further experimental details are in Supplementary Section C.",
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+ "text": "4.1. Settings",
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+ "text": "Evaluation details. We evaluated our models using VideoScore [18] and VBench [23]. VideoScore is human preference-aligned model trained on human-annotated dataset, while VBench is preference-aligned for aesthetics but uses rule-based for other attributes. We used the official test sets provided by each models. To improve motion evaluation, we propose a revised dynamic score for VBench.",
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+ "type": "table",
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+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Model | Stage | Method | Visual Quality | Temporal Consistency | Dynamic Degree | Text Alignment | Average | Param(B) |
| VideoCrafter 2 | Full | 2.627 | 2.602 | 2.728 | 2.491 | 2.613 | 1.413 |
| Stage 1 | Pruned | 2.609 | 2.588 | 2.744 | 2.487 | 2.609 | 1.174 |
| ReDPO (ours) | 2.630 | 2.608 | 2.731 | 2.510 | 2.620 |
| Stage 2 | Pruned | 2.627 | 2.595 | 2.725 | 2.486 | 2.608 | 0.902 |
| ReDPO (ours) | 2.629 | 2.617 | 2.728 | 2.518 | 2.623 (+0.010) |
| AnimateDiff | Full | 2.575 | 2.505 | 2.684 | 2.486 | 2.563 | 0.453 |
| Stage 1 | Pruned | 2.561 | 2.494 | 2.713 | 2.488 | 2.564 | 0.309 |
| ReDPO (ours) | 2.579 | 2.524 | 2.685 | 2.499 | 2.572 |
| Stage 2 | Pruned | 2.553 | 2.478 | 2.718 | 2.470 | 2.555 | 0.219 |
| ReDPO (ours) | 2.583 | 2.525 | 2.688 | 2.496 | 2.573 |
| Stage 3 | Pruned | 2.552 | 2.469 | 2.736 | 2.505 | 2.566 | 0.147 |
| ReDPO (ours) | 2.569 | 2.513 | 2.695 | 2.496 | 2.568 (+0.005) |
",
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+ "type": "text",
+ "text": "Table 1. VideoScore results across stages with V.I.P. applied to two baseline models. The yellow-lighted scores indicate our target training property, while the blue numbers represent the average improvement achieved by V.I.P. compared to the full model. Our method not only successfully recovers performance lost due to pruning but also consistently surpasses the full model across nearly all evaluation criteria for both baselines. Our approach achieves these enhancements while reducing the parameter count by between $36.2\\%$ and $67.5\\%$ .",
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+ "text": "Noted in [32], high dynamic scores are not always ideal—some prompts naturally require static motion, and generating appropriate stillness can reflect better model understanding. However, many static prompts are included in VBench's dynamic set, making it difficult to fairly assess motion quality. To address this, we manually re-annotated the dynamic test set, labeling prompts as either static or dynamic. For static prompts, we assigned a dynamic score of zero, ensuring that models are rewarded for correctly generating still motion when appropriate.",
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+ "text": "Training details. We useAnimateDiff [17] and VideoCrafter [7] as baselines. Since both are trained on WebVid-10M [2], we filter prompts from this dataset to ensure distilled knowledge lies in pretrained training distribution. For pruning, sinceAnimateDiff uses a frozen Stable Diffusion 1.5 [47] U-Net as its backbone and only trains the motion module, we pruned the motion module exclusively. For VideoCrafter, we pruned entire blocks of U-Net. Both models were trained with $\\beta = 5000$ and learning rate $= 6\\mathrm{e - }6$ , following the setting of VideoDPO [37]. To match the scale of the DPO loss, we set the SFT weight to 1e4 forAnimateDiff and 1e6 for VideoCrafter. All experiments were conducted with a 2k prompt subset, batch size 2, and 2 training epochs per stage on 4 A100 GPUs.",
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+ "text": "4.2. Experimental Results",
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+ "text": "Our experimental results are presented in four parts. First, we compare pruned models trained with our method against both naively pruned and full models across two baselines. Second, we evaluate the effectiveness of our ReDPO loss",
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+ "type": "text",
+ "text": "against the standard distillation loss, SFT. Third, a user study evaluates how well our method aligns with human preferences compared to SFT and full model. Finally, we provide qualitative examples highlighting the advantages of V.I.P. over alternatives. In addition, we evaluate the effectiveness of V.I.P. under extreme conditions using a step-distilled model and address robustness toward potential bias from relying on single reward model by using other reward model, as detailed in Supplementary Sections D.3 and D.4.",
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+ "text": "Performance of V.I.P. Table 1 shows the results of applying our framework V.I.P. to VideoCraft2 and Animatediff, with targeted properties at each stage highlighted in yellow. In most cases, V.I.P. not only improves the explicitly targeted metric but also enhances other properties. Even though some stages show slight drops in dynamic scores, this reflects a natural trade-off, where higher temporal consistency can moderate motion dynamics. Importantly, ours maintain strong visual quality and temporal coherence. This aligns with previous studies [32, 56, 60], which report that excessive dynamic motion with low temporal consistency often degrades visual quality. These findings highlight that higher dynamics are not always preferable, and that achieving a balanced trade-off between motion and consistency is essential for generating high-quality videos.",
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+ "text": "Moreover, our final-stage results match or exceed the full model's performance in all metrics for VideoCrafter2, and show similar improvements for Animatediff. Notably, this is achieved with a $36.2\\%$ parameter reduction and a $21\\%$ TFLOPs drop $(9.4 \\rightarrow 7.4)$ for VideoCrafter2, and a $67.5\\%$ parameter reduction with a $33\\%$ TFLOPs drop $(4.9 \\rightarrow 3.3)$",
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+ "table_body": "| Model | Method | Quality Score | Semantic Score | Subject Consist. | Background Consist. | Temporal Flickering | Motion Smoothness | Dynamic Degree | Aesthetic Quality | Imaging Quality |
| VC2 | SFT | 82.1 | 72.2 | 96.9 | 98.1 | 98.4 | 98.3 | 38.9 | 62.4 | 67.4 |
| ReDPO | 82.3 | 73.9 | 97.5 | 98.2 | 98.2 | 98.1 | 41.7 | 62.6 | 67.7 |
| Full | 82.3 | 73.6 | 96.8 | 97.7 | 98.1 | 97.9 | 45.8 | 62.9 | 67.6 |
| AD | SFT | 81.0 | 74.7 | 98.2 | 97.8 | 98.1 | 98.3 | 20.8 | 65.2 | 66.5 |
| ReDPO | 81.3 | 76.8 | 97.8 | 97.9 | 97.9 | 98.3 | 22.2 | 66.5 | 66.9 |
| Full | 81.3 | 75.1 | 97.2 | 97.8 | 98.0 | 98.1 | 26.4 | 65.7 | 67.1 |
",
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+ "Table 2. Comparison against SFT across multiple models using the VBench evaluation. Although our primary focus is a human preference-aligned benchmark, we also assess our model's performance on the VBench test sets, which predominantly utilize rule-based measurements across criteria except for aesthetics. Our approach demonstrates robust performance in both Quality and Semantics, consistently outperforming or matching the baseline models and surpassing the SFT-based distillation across all core criteria."
+ ],
+ "table_footnote": [],
+ "table_body": "| Model | Method | Visual Quality | Temporal Consist. | Dynamic Degree | Text Align. |
| VC2 | SFT | 2.628 | 2.613 | 2.724 | 2.505 |
| ReDPO | 2.629 | 2.617 | 2.728 | 2.518 |
| Full | 2.627 | 2.602 | 2.728 | 2.491 |
| AD | SFT | 2.564 | 2.515 | 2.679 | 2.477 |
| ReDPO | 2.569 | 2.513 | 2.695 | 2.496 |
| Full | 2.575 | 2.505 | 2.684 | 2.486 |
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+ "text": "Table 3. Comparison against SFT across multiple models on Videoscore. Bold stands for first place, underline stands for second place. Our approach achieves at least second place in all criteria, surpassing both SFT-based distillation and the baseline.",
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+ "type": "text",
+ "text": "forAnimateDiff. These results indicate that our method preserves the strengths inherent in the pruned models, mitigates prior weaknesses, enabling pruned models to outperform full counterparts in both quality and efficiency.",
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+ "text": "Comparison with SFT. For fair comparison with SFT, we retained our pruning strategy, data curation procedure, and iterative online framework unchanged, replacing only our proposed ReDPO with the SFT loss. Tables 3 and 2 present results comparing SFT-based distillation with full models on VideoScore and VBenchmark test sets, respectively.",
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+ "text": "Compared to SFT, ReDPO consistently outperforms across most metrics on both VideoCraft2 and Animatediff. This is due to fundamental limitation of SFT, which drives distilled models toward averaged predictions under reduced capacity, resulting in blurry outputs and weaker motion dynamics. Such averaging adversely impacts text alignment and overall visual quality. Furthermore, since SFT explicitly attempts to replicate the full model's behavior, it inadvertently reduces properties that pruned models originally excelled, causing unnecessary performance deterioration. In contrast, our method explicitly targets degraded properties and allocates capacity more effectively,",
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+ "Figure 4. Results of User Study. The results demonstrate that ours outperforms other baselines, indicating that ReDPO effectively distills the underperforming dimensions from the full model."
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+ "text": "guiding the student to focus on essential aspects, resulting in consistently better performance than SFT.",
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+ "text": "User study. We also present the user study results in Figure 4, demonstrating that V.I.P. significantly outperforms both Full and SFT in terms of overall preference. This results demonstrate that the model trained with our ReDPO also effectively aligns with human preferences. Further details are provided in Supplementary Section C.4.",
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+ "text": "Visualization. As shown in Figure 5, the left illustrates results from VideoCrafter2 and the right fromAnimateDiff. In the left side of Figure 5, only our V.I.P. framework enables the model to generate a video including security guard, properly reflecting the given prompt while others fail to depict the intended concept. On the right side,AnimateDiff trained with ReDPO produces the highest visual quality and consistency. The spaceship retains detailed structure, and the background appears more vibrant. In contrast, SFT yields colorless, blurry frames with inconsistent motion where the tail of the spaceship changing across frames. The full model, while more colorful than SFT, also exhibits distortions in the spaceship shape and temporal inconsistency. Despite reduced parameters, V.I.P. framework enables high-quality generation through effective distillation. Further qualitative results can be found in Supplementary.",
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+ "Figure 5. Quantitative results of videos with VideoCrafter2 (left) andAnimateDiff (right) using the full and pruned model with different distillation methods. On the left, only the V.I.P.-trained model successfully generates a security guard, aligning with the prompt. On the right, the V.I.P. trained prunedAnimateDiff achieves the highest visual quality and consistency, whereas other models produce colorless spaceship and blurry outputs."
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+ "table_body": "| Model | Method | Visual Quality | Temporal Consist. | Dynamic Degree | Text Align. |
| VC2 | w/o SFT | 2.625 | 2.583 | 2.729 | 2.471 |
| w/o online | 2.626 | 2.603 | 2.719 | 2.483 |
| V.I.P. | 2.629 | 2.617 | 2.728 | 2.518 |
| AD | w/o SFT | 2.563 | 2.437 | 2.744 | 2.480 |
| w/o online | 2.564 | 2.506 | 2.670 | 2.498 |
| V.I.P. | 2.569 | 2.513 | 2.695 | 2.496 |
",
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+ "text": "Table 4. Results of ablation study. The model with our full V.I.P. outperforms other methods, demonstrating the effectiveness of ReDPO and iterative training.",
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+ "text": "4.3. Ablation Study",
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+ "text": "Table 4 presents the ablation study results on the impact of SFT implementation in our ReDPO loss and the effectiveness of our V.I.P. framework for the online setting. For SFT ablation, we kept the entire framework unchanged and modified only the loss function, and in the offline ablation, we removed all modules at once and trained using ReDPO.",
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+ "text": "When SFT is removed from ReDPO, we observe a performance drop across nearly all properties in Table 4, confirming that SFT plays a crucial role in maintaining performance. Although the dynamic degree is higher than ours, the drop in consistency indicates that poor motion quality videos are generated. As mentioned earlier, SFT is incorporated as DPO by directly maximizing the relative likelihood of preferred versus losing responses, which can paradoxically degrade the absolute quality of preferred outputs. Therefore, SFT helps explicitly constrain the preference",
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+ "text": "probability to be higher, ensuring high-quality generations.",
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+ "text": "Compared to offline setting, our method achieves superior performance across most properties. This highlights the effectiveness of progressively pruning modules and reducing capacity while analyzing degraded properties, rather than dropping the model's capacity all at once. Also, by iteratively generating datasets from pruned models in an on-policy manner, the model enables self-reflection, better aligning with the full model's distribution and produce high-quality videos. Details and additional evaluations are provided in Supplementary Section D.",
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+ "type": "text",
+ "text": "5. Conclusion",
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+ "text": "In this work, we introduced ReDPO, a novel distillation loss for diffusion models, and V.I.P., a new framework that integrates ReDPO into an online step-by-step distillation process. To overcome the limitations of conventional SFT-based distillation, we leverage preference learning through DPO to explicitly guide the model toward targeted property. To address DPO's tendency toward over-optimization, we incorporate SFT-based regularization term, resulting in more stable and effective training. Our ReDPO consistently outperform SFT in distillation quality, and when combined with our iterative online step-by-step distillation process, enables pruned model to achieve performance comparable to, and in some cases surpassing, the full model, while significantly reducing the number of parameters. This highlights the effectiveness of our approach in enhancing efficiency without compromising generative quality.",
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+ "type": "text",
+ "text": "Acknowledgements",
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+ "text": "This work was supported by an IITP grant funded by the Korean Government (MSIT) (No. RS-2020-II201361, Artificial Intelligence Graduate School Program (Yonsei University)) and Institute of Information Communications Technology Planning Evaluation (IITP) grants funded by the Korea government (MSIT) (No. RS-2024-00457882, AI Research Hub Project) and Culture, Sports and Tourism R&D Program through the Korea Creative Content Agency grant funded by the Ministry of Culture, Sports and Tourism in 2024 (Project Name:Development of multimodal UX evaluation platform technology for XR spatial responsive content optimization, Project Number: RS-2024-00361757) and Samsung Electronics Co., Ltd (No. IO240424-09660-01).",
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diff --git a/2025/V.I.P. _ Iterative Online Preference Distillation for Efficient Video Diffusion Models/dd5c55db-7a1c-4c99-95eb-8d1eafcb989f_model.json b/2025/V.I.P. _ Iterative Online Preference Distillation for Efficient Video Diffusion Models/dd5c55db-7a1c-4c99-95eb-8d1eafcb989f_model.json
new file mode 100644
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+++ b/2025/V.I.P. _ Iterative Online Preference Distillation for Efficient Video Diffusion Models/dd5c55db-7a1c-4c99-95eb-8d1eafcb989f_model.json
@@ -0,0 +1,2169 @@
+[
+ [
+ {
+ "type": "header",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "CVF"
+ },
+ {
+ "type": "header",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.235,
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+ "angle": 0,
+ "content": "V.I.P.: Iterative Online Preference Distillation for Efficient Video Diffusion Models"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Jisoo Kim Wooseok Seo Junwan Kim Seungho Park Sooyeon Park Youngjae Yu Yonsei University"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "{jisoo6687，justin_seo，jw1510，gomi0904，dreamyou070，yjy}@yonsei.ac.kr"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "Abstract"
+ },
+ {
+ "type": "text",
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+ 0.718
+ ],
+ "angle": 0,
+ "content": "With growing interest in deploying text-to-video (T2V) models in resource-constrained environments, reducing their high computational cost has become crucial, leading to extensive research on pruning and knowledge distillation methods while maintaining performance. However, existing distillation methods primarily rely on supervised finetuning (SFT), which often leads to mode collapse as pruned models with reduced capacity fail to directly match the teacher's outputs, ultimately resulting in degraded quality. To address this challenge, we propose an effective distillation method, ReDPO, that integrates DPO and SFT. Our approach leverages DPO to guide the student model to focus on recovering only the targeted properties, rather than passively imitating the teacher, while also utilizing SFT to enhance overall performance. We additionally propose V.I.P., a novel framework for filtering and curating high-quality pair datasets, along with a step-by-step online approach for calibrated training. We validate our method on two leading T2V models, VideoCrafter2 andAnimateDiff, achieving parameter reduction of \\(36.2\\%\\) and \\(67.5\\%\\) each, while maintaining or even surpassing the performance of full models. Further experiments demonstrate the effectiveness of both ReDPO and V.I.P. framework in enabling efficient and high-quality video generation. Our code and videos are available at https://jiiiisoo.github.io/VIP.github.io/."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Recent advancements in video generation models have significantly improved their ability to produce high-fidelity and temporally coherent videos. However, these models typically require substantial computational costs and large memory footprints, which can be prohibitive for resource-constrained deployment. In particular, deploying on mobile phones or edge devices with strict memory and speed constraints often becomes infeasible with models of this scale."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
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+ "type": "image_caption",
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+ "content": "Figure 1. Conceptual visualization of generated videos and benchmark scores from pruned models distilled using V.I.P. and SFT. Only the model trained with V.I.P. generates correct concept (astronaut) with high-quality video, indicating strong text alignment, even surpassing the full model. This indicates that V.I.P. selectively improves red (weak) dimensions while preserving green (strong) ones, whereas SFT blindly mimics teacher; degrading even the previously better-performing aspects (text alignment)."
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+ "content": "To address these challenges, recent research has explored strategies such as pruning [19, 28, 38, 59] to develop lightweight models. However, since pruned models typically suffer from performance degradation compared to full models, knowledge distillation [20] has emerged as a prominent approach for preserving strong generative performance, where a smaller student model learns to approximate the output of a larger teacher model, achieving comparable performance while reducing computational cost."
+ },
+ {
+ "type": "text",
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+ "content": "Conventional knowledge distillation methods for diffusion models rely largely on naively imitating the teacher's"
+ },
+ {
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+ "bbox": [
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+ "type": "text",
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+ "content": "outputs without addressing the limited capacity of the student model [6, 26, 58]. These approaches transfer knowledge in a direct but unstructured manner, forcing the student model to replicate the teacher's behavior indiscriminately. Due to the inherent capacity gap, such direct distillation—often performed by minimizing the distance between the teacher's and student's predictions or features—tends to result in a suboptimal results [5, 13, 41], as the student model lacks the expressiveness to fully reproduce the teacher's outputs [35]. Therefore, refining the learning objective is essential to ensure that the student allocates its limited capacity toward capturing critical generative patterns rather than blindly mimicking the teacher's outputs."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "As a novel alternative to conventional methods with direct supervision, we propose leveraging preference learning, commonly represented by Direct Preference Optimization (DPO) [45], to improve diffusion model distillation. Unlike conventional approaches that enforce strict alignment with the teacher's outputs across all aspects, preference learning allows the student to selectively improve properties that degrade due to pruning while avoiding the unnecessary expenditure of its limited capacity on those that undergo only minor deterioration or even improve. Therefore, we formulate diffusion distillation as a preference learning task, where the teacher's outputs are treated as winning responses and the student's as losing responses. By learning from contrastive feedback, rather than direct supervision alone, the student model can prioritize recovering the most critical generative patterns that are negatively affected by pruning, rather than attempting to mimic the teacher indiscriminately. Given the unpredictability of pruning effects—where certain generative properties degrade while others persist or even strengthen [50, 57]—this approach enables a more adaptive and efficient transfer of knowledge."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To fully capitalize on the benefits of preference learning in diffusion model distillation, we introduce V.I.P., a step-by-step online distillation framework designed to iteratively guide the student model through progressive pruning. Unlike conventional one-shot pruning, which abruptly removes multiple model components and forces the student to compensate for drastic capacity loss, our approach adopts an iterative pruning strategy. At each stage, we selectively remove specific blocks, allowing the model to gradually adapt while maintaining generative capability. This step-by-step adaptation, by progressively updating the student model at each iteration rather than all at once, ensures that the student model is consistently updated and enhanced, enabling it to continually generate improved training data at each iteration. Consequently, this iterative approach not only mitigates the significant degradation typically resulted by one-shot pruning but also contributes to synthesizing high-quality preference pairs via improved student models."
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Overall, our contributions are as follows:"
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+ "type": "text",
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+ "content": "- We present a novel distillation loss ReDPO that integrates Direct Preference Optimization (DPO) into the diffusion framework, making it the first to employ preference learning for pruned diffusion models."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We propose V.I.P., a framework that incorporates an on-policy data curation strategy and an online distillation method, allowing pruned models to recover lost features more effectively. By structuring pruning and distillation in stages, our approach ensures stable optimization and improved generative performance."
+ },
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+ "content": "- Through extensive experiments, we demonstrate that our method significantly outperforms existing distillation approaches, even surpassing the full model in performance, while reducing parameters by \\(36.2\\%\\) in VideoCrafter and \\(67.5\\%\\) in theAnimateDiff motion module."
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+ "content": "2. Related Works"
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+ "content": "2.1. Text to Video Generation"
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+ "content": "Text-to-video generation has gained considerable attention due to its broad potential for various applications. Early methods relied on traditional generative models such as Generative Adversarial Networks (GANs) [15] and Variational Autoencoders (VAEs) [27], but these approaches often produced low-quality, short videos. With the success of image diffusion models [21, 44, 48], recent methods extend them to video diffusion models by introducing additional temporal layers on top of the spatial layers in existing 2D diffusion models [3, 4, 7, 17, 29]. This approach effectively carries over the strong generative capabilities of image diffusion models to the video domain. However, while these advancements have enabled high-resolution video generation, their substantial computational costs, limiting practical use for real-world applications. To address this, we propose a distillation-based approach that reduces model size while keeping generative capabilities largely intact. Unlike prior methods that focus only on naive pruning or supervised fine-tuning, we introduce a targeted and adaptive mechanism to prioritize and recover the most critical generative properties sacrificed by aggressive pruning."
+ },
+ {
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+ "content": "2.2. Diffusion Distillation"
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+ "content": "Diffusion models are computationally intensive, requiring pruning-based optimization for efficiency. While pruning removes redundancy with minimal performance loss, it often requires further training. Some works [26, 30, 58, 62, 65] finetune pruned models with diffusion loss, which requires substantial data and computation. BK-SDM [26] introduces knowledge distillation [20] by minimizing the distance between noise predictions of pruned and original models. However, as such exact matching is limited due to reduced capacity [34], it further incorporates feature-level guidance. Recent work [57] improves upon this by incorpo"
+ },
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+ "content": "rating adversarial loss, which sharpens distributions to mitigate capacity limitations. Yet, adversarial methods inherently lack precise control over where sharpness is applied, often leading to unintended distortions [33, 35] and mode collapse [61], posing stability challenges in practical applications. Moreover, only few methods explore such techniques for text-to-video diffusion, wherein temporal consistency and motion fidelity become challenge and prone to degeneration under pruning. To address this, we propose a stepwise pruning with a novel distillation process that (i) explicitly identifies the properties that the pruned model struggles with and (ii) guides the student to prioritize them in a more adaptive, preference-driven manner."
+ },
+ {
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+ "angle": 0,
+ "content": "2.3. Preference Alignment Training"
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+ "angle": 0,
+ "content": "Preference learning is widely used to align generative models, especially large language models (LLMs), with human preferences [42, 66]. Traditional methods train a separate reward model using human preference data, which subsequently guides model refinement via reinforcement learning (RL) algorithms such as Proximal Policy Optimization (PPO) [49]. Recently, Direct Preference Optimization (DPO) [45] emerged as a more streamlined alternative, bypassing explicit reward model training and directly optimizing models against human preferences on pairwise datasets. The simplicity of its training process has popularized DPO, leading to various adaptations across text [1, 11, 22, 40], images [46, 54, 63], and videos [25, 37, 64]. Despite its widespread use, the application of preference learning in diffusion distillation remains largely understudied, due to the complexity of aligning iterative denoising steps with human preferences while maintaining generative capability. To the best of our knowledge, we are the first to tackle these challenges by introducing a preference-guided framework tailored for diffusion distillation. In doing so, we seamlessly integrate preference alignment with iterative pruning and online distillation, enabling our method to continuously curate training data at each stage and effectively remedy newly emerging weaknesses in the pruned model."
+ },
+ {
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+ "content": "3. Method"
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+ "content": "In this section, we propose V.I.P. (Video diffusion distillation via Iterative Preference learning), our distillation framework designed to efficiently transfer generative capabilities from high-capacity teacher diffusion models to their lightweight students. Motivated by limitations of standard distillation methods, we first highlight the need for explicit guidance into loss function (Sec. 3.1). We then describe two key building blocks, pruning algorithm (Sec. 3.2) and data curation (Sec. 3.3). Finally, we present V.I.P. (Sec. 3.4), which integrates our proposed loss ReDPO, and step-by-step distillation to better reallocate the student's limited capacity toward essential generative properties."
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+ "content": "3.1. Motivation"
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+ "content": "Figure 2. Conceptual illustration of learned distributions from teacher and student models. Conventional distillation methods (SFT) result in overly smooth distributions in low-capacity students. Our proposed method (ReDPO) effectively reallocates the student's limited capacity toward the critical mode while preventing over-optimization."
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+ "content": "Figure 2 illustrates how a well-designed distillation loss helps capacity-constrained model effectively learn essential generative properties. Conventional distillation methods typically transfer knowledge by minimizing the \\( L_{2} \\) distance between teacher and student predictions or feature representations [6, 26, 58], known as supervised fine-tuning (SFT). While this approach guarantees convergence in sufficiently expressive models, it fails to do so when applied to models with limited capacity. In such cases, SFT loss often leads to a distributional averaging, where student produces samples that do not exist in teacher's distribution. This occurs since minimizing SFT loss inherently prioritizes reducing overall error over preserving fine-grained details [5, 13], resulting in an oversmoothed generative process (green curve)."
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+ "angle": 0,
+ "content": "To address this, explicit guidance is required to help the student allocate its limited capacity to the most essential aspects of generation. We employ Direct Preference Optimization (DPO) [45] to guide the student toward selectively meaningful generative properties, rather than mimicking all aspects of the teacher indiscriminately and wasting capacity. This prevents the capacity-limited student model from collapsing to a distributional average and enables effective use of constrained capacity. Notably, pruned student models often exhibit selective degradation (blue curve) where some generative properties deteriorate while others remain unaffected or even improve. Using DPO, we can explicitly steer the student toward recovering these degraded properties rather than passively approximating the teacher's distribution, ensuring a targeted and efficient distillation process."
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+ "content": "While DPO ideally enables the student model to allocate capacity more efficiently, a critical challenge is its inherent tendency to over-optimize [12, 39, 43]. This arises from the objective, maximizing the relative likelihood (i.e., the margin) between preferred and unpreferred responses. This can"
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+ "content": "Figure 3. Overall architecture. Starting from a baseline model \\( M_0 \\), we obtain a pruned model \\( M_1 \\). Through a systemic evaluation & preference data synthesis, and a training process using ReDPO, we obtain a preference-learned model \\( M_1' \\). Then, \\( M_1' \\) is pruned again to obtain \\( M_2 \\), which will run through an iterative distillation process V.I.P.. Note that the teacher model is fixed to \\( M_0 \\), while the student model \\( M_i \\) is dynamically updated."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "lead to an imperfect reward distribution, particularly in uncertain regions, resulting degraded output quality and bias toward out-of-distribution samples [39] (purple curve)."
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+ "content": "To address this, we introduce the SFT loss as regularizer, encouraging the student to mimic the teacher without relying solely on learned reward distributions. This combination results in a more balanced distillation process, avoiding inefficient resource allocation while preventing overoptimization. Building on this motivation, we propose ReDPO, which successfully transfers knowledge from the teacher to the student (red curve). Section 3.4.1 provides a detailed explanation of ReDPO, while Supplementary Section E presents toy experiment validating of our motivation."
+ },
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+ "type": "title",
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+ "content": "3.2. Pruning Algorithm"
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+ "content": "For pruning blocks of model, we first evaluate the impact by removing each block individually using VideoScore's [18] total score and select blocks that have minimal impact compared to the full model. Here, we identify the properties that show the performance drop relative to the full model as the target properties for recovery. After each training step, as shown in Algorithm 1 in the Supplementary Section C.1, the same pruning process is repeated as part of our step-by-step approach. This allows the model to progressively adapt to the full model's distribution, starting from easier settings by structurally pruning less impactful modules first, thereby facilitating a more effective learning process."
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+ "content": "3.3. Data Curation"
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+ "content": "We perform dataset filtering in two phases: prompt filtering and video filtering. Given the strong impact of prompt quality and semantics on video generation [9, 14, 31], we first filter prompts for quality and relevance to the targeted attribute. Using the filtered set, we curate videos by generating and evaluating outputs from both full and pruned models, and form winning-losing pairs based on target property."
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+ "content": "Prompt filtering. First, we select high-quality prompts suitable for video inference and well-aligned with the targeted property. Given long prompts are not well-suited for video generation, following [18], we retain prompts with 5 to 25 words and remove articles to maintain a balanced length. We then filter prompts that contain the targeted property through LLM-based filtering, ensuring they explicitly describe relevant aspects that rule-based methods often miss. For instance, to target dynamic degree, we select prompts including motion-related elements, such as object movement or camera motion. Further details on LLM prompting are provided in Supplementary Section F."
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+ "content": "Video curation. Using the filtered prompts, we generate a set of videos with both the full model and the pruned model, then evaluate them with VideoScore, which serves as a reward model. Based on the resulting scores, we construct training pairs \\((v_{\\mathrm{full}}, v_{\\mathrm{pruned}})\\) where the teacher outperforms"
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+ "content": "the student for the targeted property \\( p \\), and also impose a minimum threshold \\( \\tau_{p} \\) to prevent the inclusion of excessively low-quality samples.:"
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+ "angle": 0,
+ "content": "\\[\nS (v _ {\\text {f u l l}}) > S (v _ {\\text {p r u n e d}}) > \\tau_ {p}, \\quad v _ {\\text {f u l l}} \\in V _ {\\text {f u l l}} ^ {p}, \\quad v _ {\\text {p r u n e d}} \\in V _ {\\text {p r u n e d}} ^ {p}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.177,
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+ ],
+ "angle": 0,
+ "content": "where \\( S(v) \\) represents the reward of video \\( v \\). This ensures that the winning sample is of high quality while effectively capturing cases where the pruned model underperforms. Further details are provided in Supplementary Section C.2"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.4. Iterative Preference Distillation"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Building on a pruned model and curated data, our proposed method, V.I.P., introduces two key components: integration of SFT into DPO and step-by-step online DPO learning."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "As noted in Section 3.1, despite the advantages, DPO is prone to overoptimization, which can paradoxically degrade the output probability of winning responses. To address this, we integrate SFT into DPO as regularizer. Moreover, standard DPO operates offline, relying entirely on static datasets. In contrast, online methods like PPO [49] sample training data and update policy iteratively, and have been shown to outperform offline approaches [10, 24, 52, 53], motivating recent proposals for online DPO variants [8, 16]. Inspired by theses findings, and to avoid the degradation from one-shot pruning which leads to drastic capacity loss, we propose step-by-step online DPO learning that incrementally optimizes the student model using updated samples at each stage. To these ends, we propose ReDPO (Regularized Diffusion Preference Optimization) and V.I.P. (Video diffusion distillation via Iterative Preference Optimization), described in the following sections."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
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+ ],
+ "angle": 0,
+ "content": "3.4.1. ReDPO"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.597,
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+ ],
+ "angle": 0,
+ "content": "We enhance diffusion DPO loss [54] by incorporating SFT on preferred pairs as a regularizer, motivated by [39]. While the KL term in DPO imposes some constraints, it is insufficient to fully prevent overoptimization. SFT explicitly aligns student with distribution of preferred samples, reinforcing preference probability more effectively and improving generation quality."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.703,
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+ ],
+ "angle": 0,
+ "content": "We set \\(\\pi_{ref}\\) as the full model and \\(\\pi_{\\theta}\\) as the pruned model. The key idea behind ReDPO is that, given curated dataset, it selectively align the pruned model \\(\\pi_{\\theta}\\) with the full model \\(\\pi_{ref}\\), while preserving aspects where the pruned model may already outperform the teacher."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To achieve this, objective \\( L_{diff - dpo}(\\theta) \\) is as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.113,
+ 0.807,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} L _ {d i f f - d p o} (\\theta) = \\\\ - \\mathbb {E} _ {\\left(x _ {0} ^ {w}, x _ {0} ^ {l}\\right) \\sim \\mathcal {D}, t \\sim \\mathcal {U} (0, T), x _ {t} ^ {w} \\sim q \\left(x _ {t} ^ {w} \\mid x _ {0} ^ {w}\\right), x _ {t} ^ {l} \\sim q \\left(x _ {t} ^ {l} \\mid x _ {0} ^ {l}\\right)} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.13,
+ 0.847,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\log \\sigma (- \\beta T \\omega (\\lambda_ {t}) (1)\n\\]"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.145,
+ 0.866,
+ 0.445,
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+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\left\\| \\boldsymbol {\\epsilon} ^ {w} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {w}, t\\right) \\right\\| _ {2} ^ {2} - \\left\\| \\boldsymbol {\\epsilon} ^ {w} - \\boldsymbol {\\epsilon} _ {\\operatorname {r e f}} \\left(\\boldsymbol {x} _ {t} ^ {w}, t\\right) \\right\\| _ {2} ^ {2} \\\\ - \\left(\\left\\| \\boldsymbol {\\epsilon} ^ {l} - \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {l}, t\\right)\\right\\| _ {2} ^ {2} - \\left\\| \\boldsymbol {\\epsilon} ^ {l} - \\boldsymbol {\\epsilon} _ {\\text {r e f}} \\left(\\boldsymbol {x} _ {t} ^ {l}, t\\right)\\right\\| _ {2} ^ {2}\\right)\\left. \\right)) \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Here, \\(\\epsilon_{\\theta}(\\pmb{x}_t^w,t)\\) and \\(\\epsilon_{ref}(\\pmb{x}_t^w,t)\\) denote the noise predicted by \\(\\pi_{\\theta}\\) and \\(\\pi_{ref}\\), respectively. The SFT regularization term on the preferred pair is defined as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.571,
+ 0.148,
+ 0.907,
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+ ],
+ "angle": 0,
+ "content": "\\[\nL _ {S F T} (\\theta) = \\left\\| \\boldsymbol {\\epsilon} _ {\\theta} \\left(\\boldsymbol {x} _ {t} ^ {w}, t\\right) - \\boldsymbol {\\epsilon} _ {\\mathrm {r e f}} \\left(\\boldsymbol {x} _ {t} ^ {w}, t\\right) \\right\\| _ {2} ^ {2} \\tag {2}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Therefore, our final ReDPO loss is as follows :"
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "\\[\nL _ {R e D P O} (\\theta) = L _ {d i f f - d p o} (\\theta) + w _ {S F T} L _ {S F T} (\\theta) \\tag {3}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "\\(w_{SFT}\\) is the weight of SFT loss. Furthermore, although ReDPO was specifically utilized for distillation task in this work, we emphasize that it can be applied robustly for general diffusion preference alignment purposes. We analyze the effect of \\(w_{SFT}\\) in Supplementary Section D.1."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "3.4.2.V.I.P."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.333,
+ 0.907,
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+ ],
+ "angle": 0,
+ "content": "The overall workflow of V.I.P. is shown in Figure 3. We begin by pruning the full (teacher) model \\( M_0 \\) into a smaller model \\( M_1 \\) (Section 3.2). Both models \\( M_0 \\) and \\( M_1 \\) generate videos for the same targeted prompts (Section 3.3), forming winning (from \\( M_0 \\)) and losing (from \\( M_1 \\)) pairs. These pairs are used to distill knowledge from \\( M_0 \\) into the pruned model via our preference-based distillation loss ReDPO, resulting in trained pruned model, \\( M_1' \\). This refinement process repeats iteratively. The refined model \\( M_1' \\) further pruned to \\( M_2 \\). In each subsequent iteration, the full model \\( M_0 \\) continues to produce the winning samples, while the current pruned model (e.g., \\( M_2 \\)) generates updated losing samples based on targeted prompts identified through systematic evaluation of its deficiencies. These dynamically updated pairs form the training data for the next round of distillation. This iterative, online distillation cycle ensures pruned models to progressively adapt by consistently targeting and mitigating their latest performance weaknesses."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4. Experiments"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ "angle": 0,
+ "content": "In this section, we outline our evaluation approach. Section 4.1 describes the experimental setup, covering benchmarks, baseline models, datasets, and hyperparameters. Section 4.2 presents both quantitative and qualitative analyses across various settings, comparing V.I.P., SFT-based distillation, and the full (teacher) model. An ablation study in Section 4.3 highlights the impact of each components. Further experimental details are in Supplementary Section C."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.1. Settings"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Evaluation details. We evaluated our models using VideoScore [18] and VBench [23]. VideoScore is human preference-aligned model trained on human-annotated dataset, while VBench is preference-aligned for aesthetics but uses rule-based for other attributes. We used the official test sets provided by each models. To improve motion evaluation, we propose a revised dynamic score for VBench."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Model | Stage | Method | Visual Quality | Temporal Consistency | Dynamic Degree | Text Alignment | Average | Param(B) |
| VideoCrafter 2 | Full | 2.627 | 2.602 | 2.728 | 2.491 | 2.613 | 1.413 |
| Stage 1 | Pruned | 2.609 | 2.588 | 2.744 | 2.487 | 2.609 | 1.174 |
| ReDPO (ours) | 2.630 | 2.608 | 2.731 | 2.510 | 2.620 |
| Stage 2 | Pruned | 2.627 | 2.595 | 2.725 | 2.486 | 2.608 | 0.902 |
| ReDPO (ours) | 2.629 | 2.617 | 2.728 | 2.518 | 2.623 (+0.010) |
| AnimateDiff | Full | 2.575 | 2.505 | 2.684 | 2.486 | 2.563 | 0.453 |
| Stage 1 | Pruned | 2.561 | 2.494 | 2.713 | 2.488 | 2.564 | 0.309 |
| ReDPO (ours) | 2.579 | 2.524 | 2.685 | 2.499 | 2.572 |
| Stage 2 | Pruned | 2.553 | 2.478 | 2.718 | 2.470 | 2.555 | 0.219 |
| ReDPO (ours) | 2.583 | 2.525 | 2.688 | 2.496 | 2.573 |
| Stage 3 | Pruned | 2.552 | 2.469 | 2.736 | 2.505 | 2.566 | 0.147 |
| ReDPO (ours) | 2.569 | 2.513 | 2.695 | 2.496 | 2.568 (+0.005) |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.089,
+ 0.335,
+ 0.908,
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+ ],
+ "angle": 0,
+ "content": "Table 1. VideoScore results across stages with V.I.P. applied to two baseline models. The yellow-lighted scores indicate our target training property, while the blue numbers represent the average improvement achieved by V.I.P. compared to the full model. Our method not only successfully recovers performance lost due to pruning but also consistently surpasses the full model across nearly all evaluation criteria for both baselines. Our approach achieves these enhancements while reducing the parameter count by between \\(36.2\\%\\) and \\(67.5\\%\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.418,
+ 0.487,
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+ ],
+ "angle": 0,
+ "content": "Noted in [32], high dynamic scores are not always ideal—some prompts naturally require static motion, and generating appropriate stillness can reflect better model understanding. However, many static prompts are included in VBench's dynamic set, making it difficult to fairly assess motion quality. To address this, we manually re-annotated the dynamic test set, labeling prompts as either static or dynamic. For static prompts, we assigned a dynamic score of zero, ensuring that models are rewarded for correctly generating still motion when appropriate."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.593,
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+ ],
+ "angle": 0,
+ "content": "Training details. We useAnimateDiff [17] and VideoCrafter [7] as baselines. Since both are trained on WebVid-10M [2], we filter prompts from this dataset to ensure distilled knowledge lies in pretrained training distribution. For pruning, sinceAnimateDiff uses a frozen Stable Diffusion 1.5 [47] U-Net as its backbone and only trains the motion module, we pruned the motion module exclusively. For VideoCrafter, we pruned entire blocks of U-Net. Both models were trained with \\(\\beta = 5000\\) and learning rate \\(= 6\\mathrm{e - }6\\), following the setting of VideoDPO [37]. To match the scale of the DPO loss, we set the SFT weight to 1e4 forAnimateDiff and 1e6 for VideoCrafter. All experiments were conducted with a 2k prompt subset, batch size 2, and 2 training epochs per stage on 4 A100 GPUs."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Experimental Results"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Our experimental results are presented in four parts. First, we compare pruned models trained with our method against both naively pruned and full models across two baselines. Second, we evaluate the effectiveness of our ReDPO loss"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.418,
+ 0.909,
+ 0.557
+ ],
+ "angle": 0,
+ "content": "against the standard distillation loss, SFT. Third, a user study evaluates how well our method aligns with human preferences compared to SFT and full model. Finally, we provide qualitative examples highlighting the advantages of V.I.P. over alternatives. In addition, we evaluate the effectiveness of V.I.P. under extreme conditions using a step-distilled model and address robustness toward potential bias from relying on single reward model by using other reward model, as detailed in Supplementary Sections D.3 and D.4."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ "angle": 0,
+ "content": "Performance of V.I.P. Table 1 shows the results of applying our framework V.I.P. to VideoCraft2 and Animatediff, with targeted properties at each stage highlighted in yellow. In most cases, V.I.P. not only improves the explicitly targeted metric but also enhances other properties. Even though some stages show slight drops in dynamic scores, this reflects a natural trade-off, where higher temporal consistency can moderate motion dynamics. Importantly, ours maintain strong visual quality and temporal coherence. This aligns with previous studies [32, 56, 60], which report that excessive dynamic motion with low temporal consistency often degrades visual quality. These findings highlight that higher dynamics are not always preferable, and that achieving a balanced trade-off between motion and consistency is essential for generating high-quality videos."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Moreover, our final-stage results match or exceed the full model's performance in all metrics for VideoCrafter2, and show similar improvements for Animatediff. Notably, this is achieved with a \\(36.2\\%\\) parameter reduction and a \\(21\\%\\) TFLOPs drop \\((9.4 \\rightarrow 7.4)\\) for VideoCrafter2, and a \\(67.5\\%\\) parameter reduction with a \\(33\\%\\) TFLOPs drop \\((4.9 \\rightarrow 3.3)\\)"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ }
+ ],
+ [
+ {
+ "type": "table",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "| Model | Method | Quality Score | Semantic Score | Subject Consist. | Background Consist. | Temporal Flickering | Motion Smoothness | Dynamic Degree | Aesthetic Quality | Imaging Quality |
| VC2 | SFT | 82.1 | 72.2 | 96.9 | 98.1 | 98.4 | 98.3 | 38.9 | 62.4 | 67.4 |
| ReDPO | 82.3 | 73.9 | 97.5 | 98.2 | 98.2 | 98.1 | 41.7 | 62.6 | 67.7 |
| Full | 82.3 | 73.6 | 96.8 | 97.7 | 98.1 | 97.9 | 45.8 | 62.9 | 67.6 |
| AD | SFT | 81.0 | 74.7 | 98.2 | 97.8 | 98.1 | 98.3 | 20.8 | 65.2 | 66.5 |
| ReDPO | 81.3 | 76.8 | 97.8 | 97.9 | 97.9 | 98.3 | 22.2 | 66.5 | 66.9 |
| Full | 81.3 | 75.1 | 97.2 | 97.8 | 98.0 | 98.1 | 26.4 | 65.7 | 67.1 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Comparison against SFT across multiple models using the VBench evaluation. Although our primary focus is a human preference-aligned benchmark, we also assess our model's performance on the VBench test sets, which predominantly utilize rule-based measurements across criteria except for aesthetics. Our approach demonstrates robust performance in both Quality and Semantics, consistently outperforming or matching the baseline models and surpassing the SFT-based distillation across all core criteria."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "| Model | Method | Visual Quality | Temporal Consist. | Dynamic Degree | Text Align. |
| VC2 | SFT | 2.628 | 2.613 | 2.724 | 2.505 |
| ReDPO | 2.629 | 2.617 | 2.728 | 2.518 |
| Full | 2.627 | 2.602 | 2.728 | 2.491 |
| AD | SFT | 2.564 | 2.515 | 2.679 | 2.477 |
| ReDPO | 2.569 | 2.513 | 2.695 | 2.496 |
| Full | 2.575 | 2.505 | 2.684 | 2.486 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Comparison against SFT across multiple models on Videoscore. Bold stands for first place, underline stands for second place. Our approach achieves at least second place in all criteria, surpassing both SFT-based distillation and the baseline."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "forAnimateDiff. These results indicate that our method preserves the strengths inherent in the pruned models, mitigates prior weaknesses, enabling pruned models to outperform full counterparts in both quality and efficiency."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.628,
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+ "angle": 0,
+ "content": "Comparison with SFT. For fair comparison with SFT, we retained our pruning strategy, data curation procedure, and iterative online framework unchanged, replacing only our proposed ReDPO with the SFT loss. Tables 3 and 2 present results comparing SFT-based distillation with full models on VideoScore and VBenchmark test sets, respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.72,
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+ 0.902
+ ],
+ "angle": 0,
+ "content": "Compared to SFT, ReDPO consistently outperforms across most metrics on both VideoCraft2 and Animatediff. This is due to fundamental limitation of SFT, which drives distilled models toward averaged predictions under reduced capacity, resulting in blurry outputs and weaker motion dynamics. Such averaging adversely impacts text alignment and overall visual quality. Furthermore, since SFT explicitly attempts to replicate the full model's behavior, it inadvertently reduces properties that pruned models originally excelled, causing unnecessary performance deterioration. In contrast, our method explicitly targets degraded properties and allocates capacity more effectively,"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.517,
+ 0.318,
+ 0.907,
+ 0.416
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.513,
+ 0.425,
+ 0.907,
+ 0.468
+ ],
+ "angle": 0,
+ "content": "Figure 4. Results of User Study. The results demonstrate that ours outperforms other baselines, indicating that ReDPO effectively distills the underperforming dimensions from the full model."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.513,
+ 0.495,
+ 0.907,
+ 0.527
+ ],
+ "angle": 0,
+ "content": "guiding the student to focus on essential aspects, resulting in consistently better performance than SFT."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.547,
+ 0.906,
+ 0.639
+ ],
+ "angle": 0,
+ "content": "User study. We also present the user study results in Figure 4, demonstrating that V.I.P. significantly outperforms both Full and SFT in terms of overall preference. This results demonstrate that the model trained with our ReDPO also effectively aligns with human preferences. Further details are provided in Supplementary Section C.4."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.659,
+ 0.907,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "Visualization. As shown in Figure 5, the left illustrates results from VideoCrafter2 and the right fromAnimateDiff. In the left side of Figure 5, only our V.I.P. framework enables the model to generate a video including security guard, properly reflecting the given prompt while others fail to depict the intended concept. On the right side,AnimateDiff trained with ReDPO produces the highest visual quality and consistency. The spaceship retains detailed structure, and the background appears more vibrant. In contrast, SFT yields colorless, blurry frames with inconsistent motion where the tail of the spaceship changing across frames. The full model, while more colorful than SFT, also exhibits distortions in the spaceship shape and temporal inconsistency. Despite reduced parameters, V.I.P. framework enables high-quality generation through effective distillation. Further qualitative results can be found in Supplementary."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "17241"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.092,
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.348,
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+ 0.406
+ ],
+ "angle": 0,
+ "content": "Figure 5. Quantitative results of videos with VideoCrafter2 (left) andAnimateDiff (right) using the full and pruned model with different distillation methods. On the left, only the V.I.P.-trained model successfully generates a security guard, aligning with the prompt. On the right, the V.I.P. trained prunedAnimateDiff achieves the highest visual quality and consistency, whereas other models produce colorless spaceship and blurry outputs."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "| Model | Method | Visual Quality | Temporal Consist. | Dynamic Degree | Text Align. |
| VC2 | w/o SFT | 2.625 | 2.583 | 2.729 | 2.471 |
| w/o online | 2.626 | 2.603 | 2.719 | 2.483 |
| V.I.P. | 2.629 | 2.617 | 2.728 | 2.518 |
| AD | w/o SFT | 2.563 | 2.437 | 2.744 | 2.480 |
| w/o online | 2.564 | 2.506 | 2.670 | 2.498 |
| V.I.P. | 2.569 | 2.513 | 2.695 | 2.496 |
"
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+ "content": "Table 4. Results of ablation study. The model with our full V.I.P. outperforms other methods, demonstrating the effectiveness of ReDPO and iterative training."
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+ "content": "Table 4 presents the ablation study results on the impact of SFT implementation in our ReDPO loss and the effectiveness of our V.I.P. framework for the online setting. For SFT ablation, we kept the entire framework unchanged and modified only the loss function, and in the offline ablation, we removed all modules at once and trained using ReDPO."
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+ "content": "When SFT is removed from ReDPO, we observe a performance drop across nearly all properties in Table 4, confirming that SFT plays a crucial role in maintaining performance. Although the dynamic degree is higher than ours, the drop in consistency indicates that poor motion quality videos are generated. As mentioned earlier, SFT is incorporated as DPO by directly maximizing the relative likelihood of preferred versus losing responses, which can paradoxically degrade the absolute quality of preferred outputs. Therefore, SFT helps explicitly constrain the preference"
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+ "angle": 0,
+ "content": "probability to be higher, ensuring high-quality generations."
+ },
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+ "content": "Compared to offline setting, our method achieves superior performance across most properties. This highlights the effectiveness of progressively pruning modules and reducing capacity while analyzing degraded properties, rather than dropping the model's capacity all at once. Also, by iteratively generating datasets from pruned models in an on-policy manner, the model enables self-reflection, better aligning with the full model's distribution and produce high-quality videos. Details and additional evaluations are provided in Supplementary Section D."
+ },
+ {
+ "type": "title",
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+ "content": "5. Conclusion"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this work, we introduced ReDPO, a novel distillation loss for diffusion models, and V.I.P., a new framework that integrates ReDPO into an online step-by-step distillation process. To overcome the limitations of conventional SFT-based distillation, we leverage preference learning through DPO to explicitly guide the model toward targeted property. To address DPO's tendency toward over-optimization, we incorporate SFT-based regularization term, resulting in more stable and effective training. Our ReDPO consistently outperform SFT in distillation quality, and when combined with our iterative online step-by-step distillation process, enables pruned model to achieve performance comparable to, and in some cases surpassing, the full model, while significantly reducing the number of parameters. This highlights the effectiveness of our approach in enhancing efficiency without compromising generative quality."
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+ "content": "Acknowledgements"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "This work was supported by an IITP grant funded by the Korean Government (MSIT) (No. RS-2020-II201361, Artificial Intelligence Graduate School Program (Yonsei University)) and Institute of Information Communications Technology Planning Evaluation (IITP) grants funded by the Korea government (MSIT) (No. RS-2024-00457882, AI Research Hub Project) and Culture, Sports and Tourism R&D Program through the Korea Creative Content Agency grant funded by the Ministry of Culture, Sports and Tourism in 2024 (Project Name:Development of multimodal UX evaluation platform technology for XR spatial responsive content optimization, Project Number: RS-2024-00361757) and Samsung Electronics Co., Ltd (No. IO240424-09660-01)."
+ },
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+ "angle": 0,
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+
+
+# V.I.P.: Iterative Online Preference Distillation for Efficient Video Diffusion Models
+
+Jisoo Kim Wooseok Seo Junwan Kim Seungho Park Sooyeon Park Youngjae Yu Yonsei University
+
+{jisoo6687，justin_seo，jw1510，gomi0904，dreamyou070，yjy}@yonsei.ac.kr
+
+# Abstract
+
+With growing interest in deploying text-to-video (T2V) models in resource-constrained environments, reducing their high computational cost has become crucial, leading to extensive research on pruning and knowledge distillation methods while maintaining performance. However, existing distillation methods primarily rely on supervised finetuning (SFT), which often leads to mode collapse as pruned models with reduced capacity fail to directly match the teacher's outputs, ultimately resulting in degraded quality. To address this challenge, we propose an effective distillation method, ReDPO, that integrates DPO and SFT. Our approach leverages DPO to guide the student model to focus on recovering only the targeted properties, rather than passively imitating the teacher, while also utilizing SFT to enhance overall performance. We additionally propose V.I.P., a novel framework for filtering and curating high-quality pair datasets, along with a step-by-step online approach for calibrated training. We validate our method on two leading T2V models, VideoCrafter2 andAnimateDiff, achieving parameter reduction of $36.2\%$ and $67.5\%$ each, while maintaining or even surpassing the performance of full models. Further experiments demonstrate the effectiveness of both ReDPO and V.I.P. framework in enabling efficient and high-quality video generation. Our code and videos are available at https://jiiiisoo.github.io/VIP.github.io/.
+
+# 1. Introduction
+
+Recent advancements in video generation models have significantly improved their ability to produce high-fidelity and temporally coherent videos. However, these models typically require substantial computational costs and large memory footprints, which can be prohibitive for resource-constrained deployment. In particular, deploying on mobile phones or edge devices with strict memory and speed constraints often becomes infeasible with models of this scale.
+
+
+Figure 1. Conceptual visualization of generated videos and benchmark scores from pruned models distilled using V.I.P. and SFT. Only the model trained with V.I.P. generates correct concept (astronaut) with high-quality video, indicating strong text alignment, even surpassing the full model. This indicates that V.I.P. selectively improves red (weak) dimensions while preserving green (strong) ones, whereas SFT blindly mimics teacher; degrading even the previously better-performing aspects (text alignment).
+
+To address these challenges, recent research has explored strategies such as pruning [19, 28, 38, 59] to develop lightweight models. However, since pruned models typically suffer from performance degradation compared to full models, knowledge distillation [20] has emerged as a prominent approach for preserving strong generative performance, where a smaller student model learns to approximate the output of a larger teacher model, achieving comparable performance while reducing computational cost.
+
+Conventional knowledge distillation methods for diffusion models rely largely on naively imitating the teacher's
+
+outputs without addressing the limited capacity of the student model [6, 26, 58]. These approaches transfer knowledge in a direct but unstructured manner, forcing the student model to replicate the teacher's behavior indiscriminately. Due to the inherent capacity gap, such direct distillation—often performed by minimizing the distance between the teacher's and student's predictions or features—tends to result in a suboptimal results [5, 13, 41], as the student model lacks the expressiveness to fully reproduce the teacher's outputs [35]. Therefore, refining the learning objective is essential to ensure that the student allocates its limited capacity toward capturing critical generative patterns rather than blindly mimicking the teacher's outputs.
+
+As a novel alternative to conventional methods with direct supervision, we propose leveraging preference learning, commonly represented by Direct Preference Optimization (DPO) [45], to improve diffusion model distillation. Unlike conventional approaches that enforce strict alignment with the teacher's outputs across all aspects, preference learning allows the student to selectively improve properties that degrade due to pruning while avoiding the unnecessary expenditure of its limited capacity on those that undergo only minor deterioration or even improve. Therefore, we formulate diffusion distillation as a preference learning task, where the teacher's outputs are treated as winning responses and the student's as losing responses. By learning from contrastive feedback, rather than direct supervision alone, the student model can prioritize recovering the most critical generative patterns that are negatively affected by pruning, rather than attempting to mimic the teacher indiscriminately. Given the unpredictability of pruning effects—where certain generative properties degrade while others persist or even strengthen [50, 57]—this approach enables a more adaptive and efficient transfer of knowledge.
+
+To fully capitalize on the benefits of preference learning in diffusion model distillation, we introduce V.I.P., a step-by-step online distillation framework designed to iteratively guide the student model through progressive pruning. Unlike conventional one-shot pruning, which abruptly removes multiple model components and forces the student to compensate for drastic capacity loss, our approach adopts an iterative pruning strategy. At each stage, we selectively remove specific blocks, allowing the model to gradually adapt while maintaining generative capability. This step-by-step adaptation, by progressively updating the student model at each iteration rather than all at once, ensures that the student model is consistently updated and enhanced, enabling it to continually generate improved training data at each iteration. Consequently, this iterative approach not only mitigates the significant degradation typically resulted by one-shot pruning but also contributes to synthesizing high-quality preference pairs via improved student models.
+
+Overall, our contributions are as follows:
+
+- We present a novel distillation loss ReDPO that integrates Direct Preference Optimization (DPO) into the diffusion framework, making it the first to employ preference learning for pruned diffusion models.
+- We propose V.I.P., a framework that incorporates an on-policy data curation strategy and an online distillation method, allowing pruned models to recover lost features more effectively. By structuring pruning and distillation in stages, our approach ensures stable optimization and improved generative performance.
+- Through extensive experiments, we demonstrate that our method significantly outperforms existing distillation approaches, even surpassing the full model in performance, while reducing parameters by $36.2\%$ in VideoCrafter and $67.5\%$ in theAnimateDiff motion module.
+
+# 2. Related Works
+
+# 2.1. Text to Video Generation
+
+Text-to-video generation has gained considerable attention due to its broad potential for various applications. Early methods relied on traditional generative models such as Generative Adversarial Networks (GANs) [15] and Variational Autoencoders (VAEs) [27], but these approaches often produced low-quality, short videos. With the success of image diffusion models [21, 44, 48], recent methods extend them to video diffusion models by introducing additional temporal layers on top of the spatial layers in existing 2D diffusion models [3, 4, 7, 17, 29]. This approach effectively carries over the strong generative capabilities of image diffusion models to the video domain. However, while these advancements have enabled high-resolution video generation, their substantial computational costs, limiting practical use for real-world applications. To address this, we propose a distillation-based approach that reduces model size while keeping generative capabilities largely intact. Unlike prior methods that focus only on naive pruning or supervised fine-tuning, we introduce a targeted and adaptive mechanism to prioritize and recover the most critical generative properties sacrificed by aggressive pruning.
+
+# 2.2. Diffusion Distillation
+
+Diffusion models are computationally intensive, requiring pruning-based optimization for efficiency. While pruning removes redundancy with minimal performance loss, it often requires further training. Some works [26, 30, 58, 62, 65] finetune pruned models with diffusion loss, which requires substantial data and computation. BK-SDM [26] introduces knowledge distillation [20] by minimizing the distance between noise predictions of pruned and original models. However, as such exact matching is limited due to reduced capacity [34], it further incorporates feature-level guidance. Recent work [57] improves upon this by incorpo
+
+rating adversarial loss, which sharpens distributions to mitigate capacity limitations. Yet, adversarial methods inherently lack precise control over where sharpness is applied, often leading to unintended distortions [33, 35] and mode collapse [61], posing stability challenges in practical applications. Moreover, only few methods explore such techniques for text-to-video diffusion, wherein temporal consistency and motion fidelity become challenge and prone to degeneration under pruning. To address this, we propose a stepwise pruning with a novel distillation process that (i) explicitly identifies the properties that the pruned model struggles with and (ii) guides the student to prioritize them in a more adaptive, preference-driven manner.
+
+# 2.3. Preference Alignment Training
+
+Preference learning is widely used to align generative models, especially large language models (LLMs), with human preferences [42, 66]. Traditional methods train a separate reward model using human preference data, which subsequently guides model refinement via reinforcement learning (RL) algorithms such as Proximal Policy Optimization (PPO) [49]. Recently, Direct Preference Optimization (DPO) [45] emerged as a more streamlined alternative, bypassing explicit reward model training and directly optimizing models against human preferences on pairwise datasets. The simplicity of its training process has popularized DPO, leading to various adaptations across text [1, 11, 22, 40], images [46, 54, 63], and videos [25, 37, 64]. Despite its widespread use, the application of preference learning in diffusion distillation remains largely understudied, due to the complexity of aligning iterative denoising steps with human preferences while maintaining generative capability. To the best of our knowledge, we are the first to tackle these challenges by introducing a preference-guided framework tailored for diffusion distillation. In doing so, we seamlessly integrate preference alignment with iterative pruning and online distillation, enabling our method to continuously curate training data at each stage and effectively remedy newly emerging weaknesses in the pruned model.
+
+# 3. Method
+
+In this section, we propose V.I.P. (Video diffusion distillation via Iterative Preference learning), our distillation framework designed to efficiently transfer generative capabilities from high-capacity teacher diffusion models to their lightweight students. Motivated by limitations of standard distillation methods, we first highlight the need for explicit guidance into loss function (Sec. 3.1). We then describe two key building blocks, pruning algorithm (Sec. 3.2) and data curation (Sec. 3.3). Finally, we present V.I.P. (Sec. 3.4), which integrates our proposed loss ReDPO, and step-by-step distillation to better reallocate the student's limited capacity toward essential generative properties.
+
+# 3.1. Motivation
+
+
+Figure 2. Conceptual illustration of learned distributions from teacher and student models. Conventional distillation methods (SFT) result in overly smooth distributions in low-capacity students. Our proposed method (ReDPO) effectively reallocates the student's limited capacity toward the critical mode while preventing over-optimization.
+
+
+
+Figure 2 illustrates how a well-designed distillation loss helps capacity-constrained model effectively learn essential generative properties. Conventional distillation methods typically transfer knowledge by minimizing the $L_{2}$ distance between teacher and student predictions or feature representations [6, 26, 58], known as supervised fine-tuning (SFT). While this approach guarantees convergence in sufficiently expressive models, it fails to do so when applied to models with limited capacity. In such cases, SFT loss often leads to a distributional averaging, where student produces samples that do not exist in teacher's distribution. This occurs since minimizing SFT loss inherently prioritizes reducing overall error over preserving fine-grained details [5, 13], resulting in an oversmoothed generative process (green curve).
+
+To address this, explicit guidance is required to help the student allocate its limited capacity to the most essential aspects of generation. We employ Direct Preference Optimization (DPO) [45] to guide the student toward selectively meaningful generative properties, rather than mimicking all aspects of the teacher indiscriminately and wasting capacity. This prevents the capacity-limited student model from collapsing to a distributional average and enables effective use of constrained capacity. Notably, pruned student models often exhibit selective degradation (blue curve) where some generative properties deteriorate while others remain unaffected or even improve. Using DPO, we can explicitly steer the student toward recovering these degraded properties rather than passively approximating the teacher's distribution, ensuring a targeted and efficient distillation process.
+
+While DPO ideally enables the student model to allocate capacity more efficiently, a critical challenge is its inherent tendency to over-optimize [12, 39, 43]. This arises from the objective, maximizing the relative likelihood (i.e., the margin) between preferred and unpreferred responses. This can
+
+
+Figure 3. Overall architecture. Starting from a baseline model $M_0$ , we obtain a pruned model $M_1$ . Through a systemic evaluation & preference data synthesis, and a training process using ReDPO, we obtain a preference-learned model $M_1'$ . Then, $M_1'$ is pruned again to obtain $M_2$ , which will run through an iterative distillation process V.I.P.. Note that the teacher model is fixed to $M_0$ , while the student model $M_i$ is dynamically updated.
+
+
+
+
+
+lead to an imperfect reward distribution, particularly in uncertain regions, resulting degraded output quality and bias toward out-of-distribution samples [39] (purple curve).
+
+To address this, we introduce the SFT loss as regularizer, encouraging the student to mimic the teacher without relying solely on learned reward distributions. This combination results in a more balanced distillation process, avoiding inefficient resource allocation while preventing overoptimization. Building on this motivation, we propose ReDPO, which successfully transfers knowledge from the teacher to the student (red curve). Section 3.4.1 provides a detailed explanation of ReDPO, while Supplementary Section E presents toy experiment validating of our motivation.
+
+# 3.2. Pruning Algorithm
+
+For pruning blocks of model, we first evaluate the impact by removing each block individually using VideoScore's [18] total score and select blocks that have minimal impact compared to the full model. Here, we identify the properties that show the performance drop relative to the full model as the target properties for recovery. After each training step, as shown in Algorithm 1 in the Supplementary Section C.1, the same pruning process is repeated as part of our step-by-step approach. This allows the model to progressively adapt to the full model's distribution, starting from easier settings by structurally pruning less impactful modules first, thereby facilitating a more effective learning process.
+
+# 3.3. Data Curation
+
+We perform dataset filtering in two phases: prompt filtering and video filtering. Given the strong impact of prompt quality and semantics on video generation [9, 14, 31], we first filter prompts for quality and relevance to the targeted attribute. Using the filtered set, we curate videos by generating and evaluating outputs from both full and pruned models, and form winning-losing pairs based on target property.
+
+Prompt filtering. First, we select high-quality prompts suitable for video inference and well-aligned with the targeted property. Given long prompts are not well-suited for video generation, following [18], we retain prompts with 5 to 25 words and remove articles to maintain a balanced length. We then filter prompts that contain the targeted property through LLM-based filtering, ensuring they explicitly describe relevant aspects that rule-based methods often miss. For instance, to target dynamic degree, we select prompts including motion-related elements, such as object movement or camera motion. Further details on LLM prompting are provided in Supplementary Section F.
+
+Video curation. Using the filtered prompts, we generate a set of videos with both the full model and the pruned model, then evaluate them with VideoScore, which serves as a reward model. Based on the resulting scores, we construct training pairs $(v_{\mathrm{full}}, v_{\mathrm{pruned}})$ where the teacher outperforms
+
+the student for the targeted property $p$ , and also impose a minimum threshold $\tau_{p}$ to prevent the inclusion of excessively low-quality samples.:
+
+$$
+S (v _ {\text {f u l l}}) > S (v _ {\text {p r u n e d}}) > \tau_ {p}, \quad v _ {\text {f u l l}} \in V _ {\text {f u l l}} ^ {p}, \quad v _ {\text {p r u n e d}} \in V _ {\text {p r u n e d}} ^ {p}
+$$
+
+where $S(v)$ represents the reward of video $v$ . This ensures that the winning sample is of high quality while effectively capturing cases where the pruned model underperforms. Further details are provided in Supplementary Section C.2
+
+# 3.4. Iterative Preference Distillation
+
+Building on a pruned model and curated data, our proposed method, V.I.P., introduces two key components: integration of SFT into DPO and step-by-step online DPO learning.
+
+As noted in Section 3.1, despite the advantages, DPO is prone to overoptimization, which can paradoxically degrade the output probability of winning responses. To address this, we integrate SFT into DPO as regularizer. Moreover, standard DPO operates offline, relying entirely on static datasets. In contrast, online methods like PPO [49] sample training data and update policy iteratively, and have been shown to outperform offline approaches [10, 24, 52, 53], motivating recent proposals for online DPO variants [8, 16]. Inspired by theses findings, and to avoid the degradation from one-shot pruning which leads to drastic capacity loss, we propose step-by-step online DPO learning that incrementally optimizes the student model using updated samples at each stage. To these ends, we propose ReDPO (Regularized Diffusion Preference Optimization) and V.I.P. (Video diffusion distillation via Iterative Preference Optimization), described in the following sections.
+
+# 3.4.1. ReDPO
+
+We enhance diffusion DPO loss [54] by incorporating SFT on preferred pairs as a regularizer, motivated by [39]. While the KL term in DPO imposes some constraints, it is insufficient to fully prevent overoptimization. SFT explicitly aligns student with distribution of preferred samples, reinforcing preference probability more effectively and improving generation quality.
+
+We set $\pi_{ref}$ as the full model and $\pi_{\theta}$ as the pruned model. The key idea behind ReDPO is that, given curated dataset, it selectively align the pruned model $\pi_{\theta}$ with the full model $\pi_{ref}$ , while preserving aspects where the pruned model may already outperform the teacher.
+
+To achieve this, objective $L_{diff - dpo}(\theta)$ is as follows:
+
+$$
+\begin{array}{l} L _ {d i f f - d p o} (\theta) = \\ - \mathbb {E} _ {\left(x _ {0} ^ {w}, x _ {0} ^ {l}\right) \sim \mathcal {D}, t \sim \mathcal {U} (0, T), x _ {t} ^ {w} \sim q \left(x _ {t} ^ {w} \mid x _ {0} ^ {w}\right), x _ {t} ^ {l} \sim q \left(x _ {t} ^ {l} \mid x _ {0} ^ {l}\right)} \\ \end{array}
+$$
+
+$$
+\log \sigma (- \beta T \omega (\lambda_ {t}) (1)
+$$
+
+$$
+\begin{array}{l} \left\| \boldsymbol {\epsilon} ^ {w} - \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t} ^ {w}, t\right) \right\| _ {2} ^ {2} - \left\| \boldsymbol {\epsilon} ^ {w} - \boldsymbol {\epsilon} _ {\operatorname {r e f}} \left(\boldsymbol {x} _ {t} ^ {w}, t\right) \right\| _ {2} ^ {2} \\ - \left(\left\| \boldsymbol {\epsilon} ^ {l} - \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t} ^ {l}, t\right)\right\| _ {2} ^ {2} - \left\| \boldsymbol {\epsilon} ^ {l} - \boldsymbol {\epsilon} _ {\text {r e f}} \left(\boldsymbol {x} _ {t} ^ {l}, t\right)\right\| _ {2} ^ {2}\right)\left. \right)) \\ \end{array}
+$$
+
+Here, $\epsilon_{\theta}(\pmb{x}_t^w,t)$ and $\epsilon_{ref}(\pmb{x}_t^w,t)$ denote the noise predicted by $\pi_{\theta}$ and $\pi_{ref}$ , respectively. The SFT regularization term on the preferred pair is defined as:
+
+$$
+L _ {S F T} (\theta) = \left\| \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t} ^ {w}, t\right) - \boldsymbol {\epsilon} _ {\mathrm {r e f}} \left(\boldsymbol {x} _ {t} ^ {w}, t\right) \right\| _ {2} ^ {2} \tag {2}
+$$
+
+Therefore, our final ReDPO loss is as follows :
+
+$$
+L _ {R e D P O} (\theta) = L _ {d i f f - d p o} (\theta) + w _ {S F T} L _ {S F T} (\theta) \tag {3}
+$$
+
+$w_{SFT}$ is the weight of SFT loss. Furthermore, although ReDPO was specifically utilized for distillation task in this work, we emphasize that it can be applied robustly for general diffusion preference alignment purposes. We analyze the effect of $w_{SFT}$ in Supplementary Section D.1.
+
+# 3.4.2.V.I.P.
+
+The overall workflow of V.I.P. is shown in Figure 3. We begin by pruning the full (teacher) model $M_0$ into a smaller model $M_1$ (Section 3.2). Both models $M_0$ and $M_1$ generate videos for the same targeted prompts (Section 3.3), forming winning (from $M_0$ ) and losing (from $M_1$ ) pairs. These pairs are used to distill knowledge from $M_0$ into the pruned model via our preference-based distillation loss ReDPO, resulting in trained pruned model, $M_1'$ . This refinement process repeats iteratively. The refined model $M_1'$ further pruned to $M_2$ . In each subsequent iteration, the full model $M_0$ continues to produce the winning samples, while the current pruned model (e.g., $M_2$ ) generates updated losing samples based on targeted prompts identified through systematic evaluation of its deficiencies. These dynamically updated pairs form the training data for the next round of distillation. This iterative, online distillation cycle ensures pruned models to progressively adapt by consistently targeting and mitigating their latest performance weaknesses.
+
+# 4. Experiments
+
+In this section, we outline our evaluation approach. Section 4.1 describes the experimental setup, covering benchmarks, baseline models, datasets, and hyperparameters. Section 4.2 presents both quantitative and qualitative analyses across various settings, comparing V.I.P., SFT-based distillation, and the full (teacher) model. An ablation study in Section 4.3 highlights the impact of each components. Further experimental details are in Supplementary Section C.
+
+# 4.1. Settings
+
+Evaluation details. We evaluated our models using VideoScore [18] and VBench [23]. VideoScore is human preference-aligned model trained on human-annotated dataset, while VBench is preference-aligned for aesthetics but uses rule-based for other attributes. We used the official test sets provided by each models. To improve motion evaluation, we propose a revised dynamic score for VBench.
+
+| Model | Stage | Method | Visual Quality | Temporal Consistency | Dynamic Degree | Text Alignment | Average | Param(B) |
| VideoCrafter 2 | Full | 2.627 | 2.602 | 2.728 | 2.491 | 2.613 | 1.413 |
| Stage 1 | Pruned | 2.609 | 2.588 | 2.744 | 2.487 | 2.609 | 1.174 |
| ReDPO (ours) | 2.630 | 2.608 | 2.731 | 2.510 | 2.620 |
| Stage 2 | Pruned | 2.627 | 2.595 | 2.725 | 2.486 | 2.608 | 0.902 |
| ReDPO (ours) | 2.629 | 2.617 | 2.728 | 2.518 | 2.623 (+0.010) |
| AnimateDiff | Full | 2.575 | 2.505 | 2.684 | 2.486 | 2.563 | 0.453 |
| Stage 1 | Pruned | 2.561 | 2.494 | 2.713 | 2.488 | 2.564 | 0.309 |
| ReDPO (ours) | 2.579 | 2.524 | 2.685 | 2.499 | 2.572 |
| Stage 2 | Pruned | 2.553 | 2.478 | 2.718 | 2.470 | 2.555 | 0.219 |
| ReDPO (ours) | 2.583 | 2.525 | 2.688 | 2.496 | 2.573 |
| Stage 3 | Pruned | 2.552 | 2.469 | 2.736 | 2.505 | 2.566 | 0.147 |
| ReDPO (ours) | 2.569 | 2.513 | 2.695 | 2.496 | 2.568 (+0.005) |
+
+Table 1. VideoScore results across stages with V.I.P. applied to two baseline models. The yellow-lighted scores indicate our target training property, while the blue numbers represent the average improvement achieved by V.I.P. compared to the full model. Our method not only successfully recovers performance lost due to pruning but also consistently surpasses the full model across nearly all evaluation criteria for both baselines. Our approach achieves these enhancements while reducing the parameter count by between $36.2\%$ and $67.5\%$ .
+
+Noted in [32], high dynamic scores are not always ideal—some prompts naturally require static motion, and generating appropriate stillness can reflect better model understanding. However, many static prompts are included in VBench's dynamic set, making it difficult to fairly assess motion quality. To address this, we manually re-annotated the dynamic test set, labeling prompts as either static or dynamic. For static prompts, we assigned a dynamic score of zero, ensuring that models are rewarded for correctly generating still motion when appropriate.
+
+Training details. We useAnimateDiff [17] and VideoCrafter [7] as baselines. Since both are trained on WebVid-10M [2], we filter prompts from this dataset to ensure distilled knowledge lies in pretrained training distribution. For pruning, sinceAnimateDiff uses a frozen Stable Diffusion 1.5 [47] U-Net as its backbone and only trains the motion module, we pruned the motion module exclusively. For VideoCrafter, we pruned entire blocks of U-Net. Both models were trained with $\beta = 5000$ and learning rate $= 6\mathrm{e - }6$ , following the setting of VideoDPO [37]. To match the scale of the DPO loss, we set the SFT weight to 1e4 forAnimateDiff and 1e6 for VideoCrafter. All experiments were conducted with a 2k prompt subset, batch size 2, and 2 training epochs per stage on 4 A100 GPUs.
+
+# 4.2. Experimental Results
+
+Our experimental results are presented in four parts. First, we compare pruned models trained with our method against both naively pruned and full models across two baselines. Second, we evaluate the effectiveness of our ReDPO loss
+
+against the standard distillation loss, SFT. Third, a user study evaluates how well our method aligns with human preferences compared to SFT and full model. Finally, we provide qualitative examples highlighting the advantages of V.I.P. over alternatives. In addition, we evaluate the effectiveness of V.I.P. under extreme conditions using a step-distilled model and address robustness toward potential bias from relying on single reward model by using other reward model, as detailed in Supplementary Sections D.3 and D.4.
+
+Performance of V.I.P. Table 1 shows the results of applying our framework V.I.P. to VideoCraft2 and Animatediff, with targeted properties at each stage highlighted in yellow. In most cases, V.I.P. not only improves the explicitly targeted metric but also enhances other properties. Even though some stages show slight drops in dynamic scores, this reflects a natural trade-off, where higher temporal consistency can moderate motion dynamics. Importantly, ours maintain strong visual quality and temporal coherence. This aligns with previous studies [32, 56, 60], which report that excessive dynamic motion with low temporal consistency often degrades visual quality. These findings highlight that higher dynamics are not always preferable, and that achieving a balanced trade-off between motion and consistency is essential for generating high-quality videos.
+
+Moreover, our final-stage results match or exceed the full model's performance in all metrics for VideoCrafter2, and show similar improvements for Animatediff. Notably, this is achieved with a $36.2\%$ parameter reduction and a $21\%$ TFLOPs drop $(9.4 \rightarrow 7.4)$ for VideoCrafter2, and a $67.5\%$ parameter reduction with a $33\%$ TFLOPs drop $(4.9 \rightarrow 3.3)$
+
+| Model | Method | Quality Score | Semantic Score | Subject Consist. | Background Consist. | Temporal Flickering | Motion Smoothness | Dynamic Degree | Aesthetic Quality | Imaging Quality |
| VC2 | SFT | 82.1 | 72.2 | 96.9 | 98.1 | 98.4 | 98.3 | 38.9 | 62.4 | 67.4 |
| ReDPO | 82.3 | 73.9 | 97.5 | 98.2 | 98.2 | 98.1 | 41.7 | 62.6 | 67.7 |
| Full | 82.3 | 73.6 | 96.8 | 97.7 | 98.1 | 97.9 | 45.8 | 62.9 | 67.6 |
| AD | SFT | 81.0 | 74.7 | 98.2 | 97.8 | 98.1 | 98.3 | 20.8 | 65.2 | 66.5 |
| ReDPO | 81.3 | 76.8 | 97.8 | 97.9 | 97.9 | 98.3 | 22.2 | 66.5 | 66.9 |
| Full | 81.3 | 75.1 | 97.2 | 97.8 | 98.0 | 98.1 | 26.4 | 65.7 | 67.1 |
+
+Table 2. Comparison against SFT across multiple models using the VBench evaluation. Although our primary focus is a human preference-aligned benchmark, we also assess our model's performance on the VBench test sets, which predominantly utilize rule-based measurements across criteria except for aesthetics. Our approach demonstrates robust performance in both Quality and Semantics, consistently outperforming or matching the baseline models and surpassing the SFT-based distillation across all core criteria.
+
+| Model | Method | Visual Quality | Temporal Consist. | Dynamic Degree | Text Align. |
| VC2 | SFT | 2.628 | 2.613 | 2.724 | 2.505 |
| ReDPO | 2.629 | 2.617 | 2.728 | 2.518 |
| Full | 2.627 | 2.602 | 2.728 | 2.491 |
| AD | SFT | 2.564 | 2.515 | 2.679 | 2.477 |
| ReDPO | 2.569 | 2.513 | 2.695 | 2.496 |
| Full | 2.575 | 2.505 | 2.684 | 2.486 |
+
+Table 3. Comparison against SFT across multiple models on Videoscore. Bold stands for first place, underline stands for second place. Our approach achieves at least second place in all criteria, surpassing both SFT-based distillation and the baseline.
+
+forAnimateDiff. These results indicate that our method preserves the strengths inherent in the pruned models, mitigates prior weaknesses, enabling pruned models to outperform full counterparts in both quality and efficiency.
+
+Comparison with SFT. For fair comparison with SFT, we retained our pruning strategy, data curation procedure, and iterative online framework unchanged, replacing only our proposed ReDPO with the SFT loss. Tables 3 and 2 present results comparing SFT-based distillation with full models on VideoScore and VBenchmark test sets, respectively.
+
+Compared to SFT, ReDPO consistently outperforms across most metrics on both VideoCraft2 and Animatediff. This is due to fundamental limitation of SFT, which drives distilled models toward averaged predictions under reduced capacity, resulting in blurry outputs and weaker motion dynamics. Such averaging adversely impacts text alignment and overall visual quality. Furthermore, since SFT explicitly attempts to replicate the full model's behavior, it inadvertently reduces properties that pruned models originally excelled, causing unnecessary performance deterioration. In contrast, our method explicitly targets degraded properties and allocates capacity more effectively,
+
+
+Figure 4. Results of User Study. The results demonstrate that ours outperforms other baselines, indicating that ReDPO effectively distills the underperforming dimensions from the full model.
+
+guiding the student to focus on essential aspects, resulting in consistently better performance than SFT.
+
+User study. We also present the user study results in Figure 4, demonstrating that V.I.P. significantly outperforms both Full and SFT in terms of overall preference. This results demonstrate that the model trained with our ReDPO also effectively aligns with human preferences. Further details are provided in Supplementary Section C.4.
+
+Visualization. As shown in Figure 5, the left illustrates results from VideoCrafter2 and the right fromAnimateDiff. In the left side of Figure 5, only our V.I.P. framework enables the model to generate a video including security guard, properly reflecting the given prompt while others fail to depict the intended concept. On the right side,AnimateDiff trained with ReDPO produces the highest visual quality and consistency. The spaceship retains detailed structure, and the background appears more vibrant. In contrast, SFT yields colorless, blurry frames with inconsistent motion where the tail of the spaceship changing across frames. The full model, while more colorful than SFT, also exhibits distortions in the spaceship shape and temporal inconsistency. Despite reduced parameters, V.I.P. framework enables high-quality generation through effective distillation. Further qualitative results can be found in Supplementary.
+
+
+Figure 5. Quantitative results of videos with VideoCrafter2 (left) andAnimateDiff (right) using the full and pruned model with different distillation methods. On the left, only the V.I.P.-trained model successfully generates a security guard, aligning with the prompt. On the right, the V.I.P. trained prunedAnimateDiff achieves the highest visual quality and consistency, whereas other models produce colorless spaceship and blurry outputs.
+
+| Model | Method | Visual Quality | Temporal Consist. | Dynamic Degree | Text Align. |
| VC2 | w/o SFT | 2.625 | 2.583 | 2.729 | 2.471 |
| w/o online | 2.626 | 2.603 | 2.719 | 2.483 |
| V.I.P. | 2.629 | 2.617 | 2.728 | 2.518 |
| AD | w/o SFT | 2.563 | 2.437 | 2.744 | 2.480 |
| w/o online | 2.564 | 2.506 | 2.670 | 2.498 |
| V.I.P. | 2.569 | 2.513 | 2.695 | 2.496 |
+
+Table 4. Results of ablation study. The model with our full V.I.P. outperforms other methods, demonstrating the effectiveness of ReDPO and iterative training.
+
+# 4.3. Ablation Study
+
+Table 4 presents the ablation study results on the impact of SFT implementation in our ReDPO loss and the effectiveness of our V.I.P. framework for the online setting. For SFT ablation, we kept the entire framework unchanged and modified only the loss function, and in the offline ablation, we removed all modules at once and trained using ReDPO.
+
+When SFT is removed from ReDPO, we observe a performance drop across nearly all properties in Table 4, confirming that SFT plays a crucial role in maintaining performance. Although the dynamic degree is higher than ours, the drop in consistency indicates that poor motion quality videos are generated. As mentioned earlier, SFT is incorporated as DPO by directly maximizing the relative likelihood of preferred versus losing responses, which can paradoxically degrade the absolute quality of preferred outputs. Therefore, SFT helps explicitly constrain the preference
+
+probability to be higher, ensuring high-quality generations.
+
+Compared to offline setting, our method achieves superior performance across most properties. This highlights the effectiveness of progressively pruning modules and reducing capacity while analyzing degraded properties, rather than dropping the model's capacity all at once. Also, by iteratively generating datasets from pruned models in an on-policy manner, the model enables self-reflection, better aligning with the full model's distribution and produce high-quality videos. Details and additional evaluations are provided in Supplementary Section D.
+
+# 5. Conclusion
+
+In this work, we introduced ReDPO, a novel distillation loss for diffusion models, and V.I.P., a new framework that integrates ReDPO into an online step-by-step distillation process. To overcome the limitations of conventional SFT-based distillation, we leverage preference learning through DPO to explicitly guide the model toward targeted property. To address DPO's tendency toward over-optimization, we incorporate SFT-based regularization term, resulting in more stable and effective training. Our ReDPO consistently outperform SFT in distillation quality, and when combined with our iterative online step-by-step distillation process, enables pruned model to achieve performance comparable to, and in some cases surpassing, the full model, while significantly reducing the number of parameters. This highlights the effectiveness of our approach in enhancing efficiency without compromising generative quality.
+
+# Acknowledgements
+
+This work was supported by an IITP grant funded by the Korean Government (MSIT) (No. RS-2020-II201361, Artificial Intelligence Graduate School Program (Yonsei University)) and Institute of Information Communications Technology Planning Evaluation (IITP) grants funded by the Korea government (MSIT) (No. RS-2024-00457882, AI Research Hub Project) and Culture, Sports and Tourism R&D Program through the Korea Creative Content Agency grant funded by the Ministry of Culture, Sports and Tourism in 2024 (Project Name:Development of multimodal UX evaluation platform technology for XR spatial responsive content optimization, Project Number: RS-2024-00361757) and Samsung Electronics Co., Ltd (No. IO240424-09660-01).
+
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+ "html": "| Model | Stage | Method | Visual Quality | Temporal Consistency | Dynamic Degree | Text Alignment | Average | Param(B) |
| VideoCrafter 2 | Full | 2.627 | 2.602 | 2.728 | 2.491 | 2.613 | 1.413 |
| Stage 1 | Pruned | 2.609 | 2.588 | 2.744 | 2.487 | 2.609 | 1.174 |
| ReDPO (ours) | 2.630 | 2.608 | 2.731 | 2.510 | 2.620 |
| Stage 2 | Pruned | 2.627 | 2.595 | 2.725 | 2.486 | 2.608 | 0.902 |
| ReDPO (ours) | 2.629 | 2.617 | 2.728 | 2.518 | 2.623 (+0.010) |
| AnimateDiff | Full | 2.575 | 2.505 | 2.684 | 2.486 | 2.563 | 0.453 |
| Stage 1 | Pruned | 2.561 | 2.494 | 2.713 | 2.488 | 2.564 | 0.309 |
| ReDPO (ours) | 2.579 | 2.524 | 2.685 | 2.499 | 2.572 |
| Stage 2 | Pruned | 2.553 | 2.478 | 2.718 | 2.470 | 2.555 | 0.219 |
| ReDPO (ours) | 2.583 | 2.525 | 2.688 | 2.496 | 2.573 |
| Stage 3 | Pruned | 2.552 | 2.469 | 2.736 | 2.505 | 2.566 | 0.147 |
| ReDPO (ours) | 2.569 | 2.513 | 2.695 | 2.496 | 2.568 (+0.005) |
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+ "content": ", following the setting of VideoDPO [37]. To match the scale of the DPO loss, we set the SFT weight to 1e4 forAnimateDiff and 1e6 for VideoCrafter. All experiments were conducted with a 2k prompt subset, batch size 2, and 2 training epochs per stage on 4 A100 GPUs."
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| ReDPO | 82.3 | 73.9 | 97.5 | 98.2 | 98.2 | 98.1 | 41.7 | 62.6 | 67.7 |
| Full | 82.3 | 73.6 | 96.8 | 97.7 | 98.1 | 97.9 | 45.8 | 62.9 | 67.6 |
| AD | SFT | 81.0 | 74.7 | 98.2 | 97.8 | 98.1 | 98.3 | 20.8 | 65.2 | 66.5 |
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| Full | 2.627 | 2.602 | 2.728 | 2.491 |
| AD | SFT | 2.564 | 2.515 | 2.679 | 2.477 |
| ReDPO | 2.569 | 2.513 | 2.695 | 2.496 |
| Full | 2.575 | 2.505 | 2.684 | 2.486 |
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| VC2 | w/o SFT | 2.625 | 2.583 | 2.729 | 2.471 |
| w/o online | 2.626 | 2.603 | 2.719 | 2.483 |
| V.I.P. | 2.629 | 2.617 | 2.728 | 2.518 |
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+ "content": "[1] Mohammad Gheshlaghi Azar, Zhaohan Daniel Guo, Bilal Piot, Remi Munos, Mark Rowland, Michal Valko, and Daniele Calandriello. A general theoretical paradigm to understand learning from human preferences. In International Conference on Artificial Intelligence and Statistics, pages 4447-4455. PMLR, 2024. 3"
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diff --git a/2025/V2M4_ 4D Mesh Animation Reconstruction from a Single Monocular Video/b113d5c5-a844-4d39-a907-37bd11792160_content_list.json b/2025/V2M4_ 4D Mesh Animation Reconstruction from a Single Monocular Video/b113d5c5-a844-4d39-a907-37bd11792160_content_list.json
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+ {
+ "type": "text",
+ "text": "V2M4: 4D Mesh Animation Reconstruction from a Single Monocular Video",
+ "text_level": 1,
+ "bbox": [
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+ "type": "text",
+ "text": "Jianqi Chen",
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+ "text": "Biao Zhang Xiangjun Tang KAUST",
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Peter Wonka",
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+ ],
+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "{jianqi.chen, biao.zhang, xiangjun.tang, peter.wonka}@kaust.edu.sa",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "image",
+ "img_path": "images/3cf64049a37a5ee74217e0ef9594552e22103d0b9c9a0e3cdcebc83233bb0293.jpg",
+ "image_caption": [
+ "Figure 1. Given a monocular video, our method can output a high-quality 4D mesh asset readily usable in graphics and game software."
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Abstract",
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+ "bbox": [
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+ {
+ "type": "text",
+ "text": "We present V2M4, a novel 4D reconstruction method that directly generates a usable 4D mesh animation asset from a single monocular video. Unlike existing approaches that rely on priors from multi-view image and video generation models, our method is based on native 3D mesh generation models. Naively applying 3D mesh generation models to generate a mesh for each frame in a 4D task can lead to issues such as incorrect mesh poses, misalignment of mesh appearance, and inconsistencies in mesh geometry and texture maps. To address these problems, we propose a structured workflow that includes camera search and mesh reposing, condition embedding optimization for mesh appearance refinement, pairwise mesh registration for topology consistency, and global texture map optimization for texture consistency. Our method outputs high-quality 4D animated assets that are compatible with mainstream graphics and game software. Experimental results across a variety of animation types and motion amplitudes demonstrate the generalization and effectiveness of our method. https://windvchen.github.io/V2M4.",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "1. Introduction",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
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+ "text": "Creating 4D mesh animations is a challenging task. Unlike the synthesis of 3D geometry or 2D images, the scarcity of 4D mesh animations makes it difficult to employ a learning-based framework. Monocular videos provide rich motion cues, making them a potential source for animation reconstruction. However, reconstructing 4D mesh animations from single-view videos remains an underexplored problem, posing challenges in addressing the ambiguity in single-view video and maintaining both visual and topological consistency over time.",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Existing methods [14, 15, 31, 32, 40, 47, 49, 54, 56, 59, 62] have explored animation reconstruction based on implicit representations such as NeRF [24] or topology-independent representations like Gaussian Splatting [17]. To mitigate occlusions and ambiguities in single-view videos, these approaches leverage knowledge embedded in multi-view image diffusion [22, 36, 43] and video diffusion [1, 11]. While these methods are viable alternatives, they face disadvantages, such as the difficulty of ensuring 3D consistency in multi-view image diffusion and video diffusion. Additionally, converting these implicit and",
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+ "text": "CVF",
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+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+ "bbox": [
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+ "text": "11643",
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+ {
+ "type": "text",
+ "text": "topology-independent representations into a mesh representation remains challenging. These factors complicate the use of these methods to obtain a mesh animation that maintains a fine-grained geometric shape and preserves interframe topological consistency.",
+ "bbox": [
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+ "text": "In this work, we propose V2M4, a method that directly reconstructs a 4D animated mesh from a fixed-viewpoint monocular video. Unlike existing approaches that rely on multi-view image and video diffusion models, our method leverages recent advancements in native 3D mesh reconstruction [12, 48], enabling explicit mesh generation with good shape without the need to convert from other representations. A naive approach to using 3D mesh reconstruction for 4D animation involves generating a mesh for each frame independently. However, this strategy presents several challenges. Chief among these is the uncertainty of the generated mesh pose, where random face orientations and positions lead to misalignment with the video frames. Additionally, there are issues of appearance misalignment, where the generated meshes fail to match the object's appearance in the video. Furthermore, inconsistencies in geometry and topology result in varying mesh structures across frames, and differences in texture maps disrupt the visual continuity of the animation.",
+ "bbox": [
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+ "text": "To tackle these challenges, we introduce a structured approach that effectively extends the 3D mesh reconstruction model to the 4D mesh animation task. First, we develop a mesh reposing strategy. In this step, we search for camera poses for each reconstructed mesh to ensure semantic alignment with the input video frame by combining particle swarm optimization with a dense stereo reconstruction model's prior. We then re-pose the meshes by applying inverse camera transformations. Second, we refine the appearance of the meshes by optimizing the negative condition embedding of the 3D reconstruction model, enhancing consistency with the video frames. Third, we enforce geometry consistency by selecting the first-frame mesh as a rest pose and introducing a global-to-local mesh registration approach using differential rendering and geometric constraints. Fourth, we optimize a global texture map to ensure texture consistency based on the rendering views of the reconstructed meshes. Finally, we keyframe the meshes and interpolate vertex positions between frames to achieve smoother animation, integrating the results into a GLTF [7] animated file, which is compatible with mainstream graphics software. Fig. 1 displays some of our results. Our main contributions are as follows:",
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+ "- We introduce the use of native 3D mesh reconstruction models for 4D animated asset generation, enabling the direct creation of explicit 4D meshes with consistent geometry, shared textures, and video-aligned object motions from a fixed-viewpoint monocular video.",
+ "- We propose V2M4, a practical and efficient framework"
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+ "type": "table",
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+ "table_caption": [],
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+ "table_body": "| Method | 3D Prior Source | Reconstruction Process | Output Format |
| Consistent4D | MV Image and Video Diffusion | Optimization | NeRF |
| STAG4D | MV Image Diffusion | Optimization | GS |
| Diffusion2 | MV Image and Video Diffusion | Optimization | GS |
| EG4D | MV Image and Video Diffusion | Optimization | GS |
| Animate3D | MV-Video Diffusion | Optimization | GS |
| 4Diffusion | MV-Video Diffusion | Optimization | NeRF |
| Diffusion4D | MV-Video Diffusion | Optimization | GS |
| SV4D | MV-Video Diffusion | Optimization | NeRF |
| AR4D | MV Image Diffusion | Recon Network | GS |
| L4GM | MV Image Diffusion | Recon Network | GS |
| DreamMesh4D | MV Image Diffusion | Optimization | Mesh & GS |
| V2M4 (Ours) | Native 3D Mesh Diffusion Model | - | Mesh |
",
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+ {
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+ "text": "Table 1. Comparison of V2M4 with Existing 4D Reconstruction Methods. “-” indicates the absence of an intermediate reconstruction phase. Not all existing 4D methods are listed, but other approaches are generally similar to those included in the table.",
+ "bbox": [
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+ "type": "text",
+ "text": "that addresses key challenges associated with using 3D mesh reconstruction models for 4D mesh reconstruction, including incorrect mesh positioning, appearance misalignment, geometry inconsistencies, and texture inconsistencies.",
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+ "text": "- We conduct extensive evaluations on diverse animations, including humanoid and animal motions, covering a range of motion amplitudes from subtle movements to large-scale motions. The results demonstrate the effectiveness and generalizability of our approach.",
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+ "text": "2. Related Works",
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+ "text": "Multi-view and Video Diffusion Models. Building on the success of image diffusion models [10, 33], recent works have increasingly focused on the generation of other modalities, such as multi-view images [22, 36, 43] and videos [8, 11, 37]. In multi-view diffusion models, networks predict the 3D structure of an object from an input image. For instance, Zero123 [22] can generate a rendering of an object from a novel camera viewpoint by taking an input image and a target camera pose transition. Subsequent works, such as ImageDream [45] and SyncDream [23], further advance this direction by generating multi-view images in a single forward pass from a single input image. Video diffusion models have seen even more rapid development, driven by the availability of large-scale video datasets. Methods such as Dynamiccafter [50] and Stable Video Diffusion [1] can generate high-quality videos and enable smooth interpolation between frames.",
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+ "type": "text",
+ "text": "Video-to-4D Reconstruction Models. Due to the scarcity of 4D animated assets, existing research primarily leverages priors learned from multi-view and video generative models to ensure spatial and temporal consistency in reconstructed 4D animations. Consistent4D [14] employs Score Distillation Sampling (SDS) with signals from both pretrained multi-view and video diffusion models. STAG4D [56] follows a similar approach but introduces",
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+ "text": "an inter-frame key-value mixing mechanism during the denoising process to enhance sequence consistency. To avoid SDS, AR4D [65] instead proposes deforming the initial frame's Gaussian Splats while utilizing priors from multi-view generation models. Diffusion $^{2}$ [54] and EG4D [40] modify the sampling or attention mechanisms to integrate prior knowledge from multi-view image and video diffusion models without relying on SDS. Animate3D [15] and 4Diffusion [59] train multi-view video diffusion models that generate more consistent images for improved SDS optimization. Similarly, Diffusion4D [21] and SV4D [49] also train multi-view video generation models but directly optimize Gaussian Splatting or NeRF on the generated images without SDS. L4GM [32] takes a different approach by training a network that outputs 4D Gaussian Splats given multiview images. However, all of these methods do not output meshes, as discussed in Sec. 1. An alternative approach, DreamMesh4D [20], introduces a hybrid Gaussian-Mesh representation capable of outputting meshes, though it still relies on multi-view and video diffusion model priors and adopts SDS optimization. Other works [39, 52, 53] also attempt to reconstruct meshes from videos but require significantly more input, such as multiple video clips, rendering camera poses, skeletons, or categorical dense feature descriptors, rather than just a single monocular video.",
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+ "text": "Large Native 3D Mesh Generation Models. Unlike previous indirect 3D generative methods, which either generate multi-view images [23, 41, 45] or implicit representations [51, 57, 58, 64], recent work [12, 48] focuses on directly generating usable meshes by adopting differentiable meshing techniques such as FlexiCubes [35] or DMTet [34]. Instead, they directly predict grid attributes and generate explicit meshes. By training on large collections of synthesized 3D assets, the method achieves impressive generation results conditioned on images.",
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+ "text": "Ours versus Others. Different from most existing methods that rely on priors from multi-view image or video diffusion models and use NeRF or Gaussian Splitting as representations, we pioneer the use of native 3D mesh generation models for 4D animation reconstruction. Our approach only requires a single monocular video with a fixed camera pose as input, without the need for SDS, and outputs a 4D mesh animation file with consistent geometry and texture. Table 1 illustrates how our approach differs from previous works.",
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+ "text": "3. Preliminaries",
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+ "text": "Our method builds upon TRELLIS [48], a recently introduced and powerful 3D generation model (we also evaluate our method using more advanced 3D generators, as detailed in Appendix B). TRELLIS encodes 3D assets into a structured latent representation (SLAT), which consists of a",
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+ "text": "sparse 3D grid embedding both geometric and appearance information. The 3D reconstruction process in TRELLIS can be broadly divided into two phases. In the first phase, TRELLIS employs rectified flow [3] to generate a 3D voxel grid, where the voxel values indicate the object's occupancies. By applying a threshold, TRELLIS extracts a sparse voxel representation. In the second phase, a sparse rectified flow transformer is used to generate the object's SLAT from this sparse voxel grid. Both phases are conditioned on visual features extracted from the input image using DINOv2 [28], along with a negative condition based on the classifier-free technique [9]. The SLAT can then be processed by three independent decoders, which generate meshes, Gaussian Splats [17], and Radiance Fields [6], respectively. For mesh decoding, TRELLIS predicts both the signed distance field (SDF) grid and the parameters of differentiable FlexiCubes [35], enabling the conversion from the SDF into a mesh. Instead of using the predicted mesh vertex colors from the mesh decoder, TRELLIS employs xatlas [55] to compute UV maps of the mesh and then bakes a high-resolution texture map using multi-view observations of its Gaussian Splats.",
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+ "text": "Given a reference monocular video sequence of length $T$ , denoted as $V_{\\mathrm{ref}} = \\{V_{\\mathrm{ref},t}\\}_{t=1}^{T}$ , which captures an object from a fixed camera pose, our method generates a directly usable 4D animated asset. This asset comprises a static mesh $\\mathcal{M}$ with vertices $\\mathcal{V} = \\{\\mathbf{v}_1,\\mathbf{v}_2,\\dots,\\mathbf{v}_N\\}$ (or simply $\\mathcal{V}\\in \\mathbb{R}^{N\\times 3}$ ) and faces $\\mathcal{F}\\subset \\mathcal{V}\\times \\mathcal{V}\\times \\mathcal{V}$ , a texture map $\\mathcal{T}$ , and a deformation tensor $\\mathcal{D}\\in \\mathbb{R}^{T\\times N\\times 3}$ that records the vertices' deformations over time. Initially, each video frame is processed through an image-conditioned 3D generation model, resulting in a set of initial 3D meshes, denoted as $\\widetilde{\\mathcal{M}}_{\\mathrm{init}} = \\{\\widetilde{\\mathcal{M}}_1,\\widetilde{\\mathcal{M}}_2,\\ldots ,\\widetilde{\\mathcal{M}}_T\\}$ . These meshes exhibit inconsistencies with $V_{\\mathrm{ref}}$ as well as inter-mesh texture and geometry discrepancies, rendering them unsuitable for direct conversion into a usable 4D asset. To address these issues, our method employs a five-step workflow: repositioning the mesh for accurate object movement (Sec. 4.1), refining object appearance (Sec. 4.2), ensuring inter-frame mesh geometry consistency (Sec. 4.3), maintaining inter-frame mesh texture consistency (Sec. 4.3), and ultimately converting the 3D assets into 4D assets (Sec. 4.5). The complete workflow is illustrated in Fig. 2.",
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+ "text": "Due to the setup of training TRELLIS, the initial meshes $\\widetilde{\\mathcal{M}}_{\\mathrm{init}}$ often tend to have a canonical face orientation along one axis (as illustrated in Fig. 2), and their positions may also sometimes be canonicalized to the origin of the coordinate system. This results in a significant loss of object motion information, such as translation and rotation. To re",
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+ "Figure 2. The Workflow of V2M4. Upon receiving a video sequence $V_{\\mathrm{ref}}$ , we generate coarse 3D meshes for each frame, denoted as $\\widetilde{\\mathcal{M}}_{\\{1,\\dots,t\\}}$ . These initial meshes do not accurately capture the object's movement and appearance as depicted in the input video, and they exhibit inconsistencies in topology and texture. Our method employs a five-stage process: (1) Repose the mesh to accurately reflect object movement; (2) Refine the mesh appearance based on the reference video frames; (3) Ensure inter-mesh topology consistency through mesh registration; (4) Optimize a globally shared texture map across all meshes; (5) Keyframe the meshes, perform interpolation, and convert them into a directly usable 4D animation asset."
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+ "text": "cover these motions, we propose first determining the camera pose $\\mathcal{C} \\in \\mathbb{R}^6 = \\{\\mathrm{yaw},\\mathrm{pitch},\\mathrm{radius},\\mathrm{lookat}_{x,y,z}\\}$ for each reconstructed mesh $\\widetilde{\\mathcal{M}}_t$ , ensuring the rendered view is semantically similar to the corresponding video frame. Then, we can invert the camera pose and apply the transformation to the mesh, effectively recovering mesh motion from the camera motion.",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "Since directly optimizing camera parameters via gradient descent from a random starting point using differentiable rendering tools like Nvdiffrast [18] often leads to poor local minima, we propose a more robust camera pose search strategy. Specifically, we begin by sampling a large number of camera positions around the object and selecting the top $n$ positions that exhibit high similarity to the reference video frame, denoted as $V_{\\mathrm{ref},t}$ . We then utilize a pretrained dense stereo model to process the rendering views under these $n$ cameras and $V_{\\mathrm{ref},t}$ , obtaining the predicted point clouds for each view. Next, we design to extract the camera pose $C_{\\mathrm{ref},t,\\mathrm{DUSt3R}}$ for the reference image from these point clouds. This pose $C_{\\mathrm{ref},t,\\mathrm{DUSt3R}}$ is added back to the initial pool of camera pose candidates, and we employ the Particle Swarm Optimization (PSO) algorithm to refine this into a more accurate camera pose $C_{\\mathrm{ref},t,\\mathrm{PSO}}$ . Subsequently, we further refine the camera pose using gradient descent optimization, starting from the improved point $C_{\\mathrm{ref},t,\\mathrm{PSO}}$ , to obtain the final $C_{\\mathrm{ref},t}$ . Finally, we derive the camera motion from $C_{\\mathrm{ref},t}$ , invert it, and apply this transformation to $\\widetilde{\\mathcal{M}}_t$ to obtain $\\widetilde{\\mathcal{M}}_{\\mathrm{repose},t}$ . The entire workflow is detailed in Algorithm 1.",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "Below, we provide more details about the three key com",
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Algorithm 1 Camera Search and Mesh Re-Pose",
+ "text_level": 1,
+ "bbox": [
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+ {
+ "type": "text",
+ "text": "Require: Initial mesh $\\widetilde{\\mathcal{M}}_t$ , reference frame $V_{\\mathrm{ref},t}$ at time $t$ , pretrained dense stereo reconstruction model DUSt3R",
+ "bbox": [
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+ "type": "list",
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+ "list_items": [
+ "1: Initialize a set of sampled camera poses $P_0$",
+ "2: Select the top $n$ camera poses based on similarity to $V_{\\mathrm{ref},t}$ . Render views under these poses and input them, along with $V_{\\mathrm{ref},t}$ , into the DUSt3R",
+ "3: DUSt3R Estimation: Align DUSt3R-predicted point clouds with ground-truth point clouds",
+ "4: Optimize the camera extrinsic matrix to derive $\\mathcal{C}_{\\mathrm{ref},t,\\mathrm{DUS3R}}$",
+ "5: PSO Search: Add $C_{\\mathrm{ref},t,\\mathrm{DUS3R}}$ to the top $K$ camera poses from $P_0$ , then apply PSO",
+ "6: Select the best camera pose $C_{\\mathrm{ref},t,\\mathrm{PSO}}$ after iterations",
+ "7: Gradient Descent Refinement: Refine by minimizing mask discrepancy with $V_{\\mathrm{ref},t}$",
+ "8: Obtain the final optimized camera pose $\\mathcal{C}_{\\mathrm{ref},t}$",
+ "9: Mesh Re-pose: Apply the inverse of $\\mathcal{C}_{\\mathrm{ref},t}$ to $\\widetilde{\\mathcal{M}}_t$ to obtain $\\widetilde{\\mathcal{M}}_{\\mathrm{repose},t}$",
+ "10: return Re-posed mesh $\\widetilde{\\mathcal{M}}_{\\mathrm{repose},t}$"
+ ],
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "ponents involved.",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "text",
+ "text": "Camera Search Using Particle Swarm Optimization. We use PSO [16] algorithm to search for the aligned camera pose. To effectively explore the search space and avoid the local minima problem encountered with direct gradient descent, we sample $P$ particles (camera poses) around the object. The sampling strategy is designed to ensure that the",
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+ "page_idx": 3
+ },
+ {
+ "type": "page_number",
+ "text": "11646",
+ "bbox": [
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+ "page_idx": 3
+ },
+ {
+ "type": "image",
+ "img_path": "images/b21666e140aaee52493e0d6fee8287e21162d89078cafa328757e18e40d13cea.jpg",
+ "image_caption": [
+ "Figure 3. Camera Pose Extraction from Dense Stereo Reconstruction for $V_{\\mathrm{ref},t}$ . We first obtain estimated point clouds $\\overline{\\mathrm{PC}}_{\\mathrm{ref}}$ and $\\overline{\\mathrm{PC}}_{\\mathrm{rend}}$ from the DUSt3R model for reference video frame $V_{\\mathrm{ref},t}$ and rendering views $V_{\\mathrm{rend}}$ . We then align $\\overline{\\mathrm{PC}}_{\\mathrm{rend}}$ with the point clouds $\\mathrm{PC}_{\\mathrm{rend}}$ obtained from mesh $\\widetilde{\\mathcal{M}}_t$ during rasterization (Note the differences in axis direction and scale depicted in the figure.). This transformation is then applied to $\\overline{\\mathrm{PC}}_{\\mathrm{ref}}$ , resulting in the transformed $\\mathrm{PC}_{\\mathrm{ref}}$ . Finally, we optimize to determine the camera pose $C_{\\mathrm{ref},t}$ that ensures accurate mapping from 3D to 2D points."
+ ],
+ "image_footnote": [],
+ "bbox": [
+ 94,
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+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "yaw and pitch values are uniformly distributed over a unit sphere, while the radius is sampled according to the surface area of the sphere along with its radius. The $\\mathrm{lookat}_{x,y,z}$ values are uniformly sampled within a predefined range. For the objective function, we utilize DreamSim [5], which is more effective at evaluating the similarity between the rendered view of the imperfectly reconstructed mesh and the reference video frame, compared to conventional methods like MSE or LPIPS [61]. The positions of the particles (camera pose values) are iteratively updated based on both their individual best-known position and the best-known position of the entire swarm, with added noise randomness. The final best one is selected as the reference image's camera pose $C_{\\mathrm{ref},t,\\mathrm{PSO}}$ .",
+ "bbox": [
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+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Knowledge Utilization from Dense Stereo Reconstruction Model. To enhance the robustness of the PSO search, we leverage prior knowledge from a pretrained dense stereo model, specifically DUSt3R [46]. DUSt3R can predict inter-frame camera motion and 3D point positions corresponding to each view's 2D pixels. While a straightforward approach would involve feeding both the reference video frame $V_{\\mathrm{ref},t}$ and a set of rendered views $V_{\\mathrm{rend},\\{1,\\dots,n\\}}$ around $\\widetilde{\\mathcal{M}}_t$ into DUSt3R and using the predicted relative camera motion to estimate the camera pose of $V_{\\mathrm{ref},t}$ , this poses challenges. Differences in camera models and coordinate settings, such as scale and orientation, complicate matrix conversions, and semantic discrepancies between $V_{\\mathrm{ref},t}$ and $V_{\\mathrm{rend},\\{1,\\dots,n\\}}$ can lead to inaccurate motion predictions. To overcome these issues, we focus on the point clouds estimated by DUSt3R instead of relying on the predicted cam",
+ "bbox": [
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+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "era motions. Let $\\overline{\\mathrm{PC}}_{\\mathrm{ref}}$ and $\\overline{\\mathrm{PC}}_{\\mathrm{rend},\\{1,\\dots,n\\}}$ represent the predicted point clouds for $V_{\\mathrm{ref},t}$ and $V_{\\mathrm{rend},\\{1,\\dots,n\\}}$ , respectively. Given that the camera model, camera poses, and $\\widetilde{\\mathcal{M}}_t$ are known for rendering $V_{\\mathrm{rend},\\{1,\\dots,n\\}}$ , we can derive the ground-truth point clouds in our coordinate system, denoted as $\\mathrm{PC}_{\\mathrm{rend},\\{1,\\dots,n\\}}$ . We align the predicted point clouds with the ground truth using a global transformation (rotation, translation, and scale) optimized via Chamfer distance [4]. Applying this transformation to $\\overline{\\mathrm{PC}}_{\\mathrm{ref}}$ , we obtain $\\mathrm{PC}_{\\mathrm{ref}}$ . Ideally, with the correct camera pose $\\mathcal{C}_{\\mathrm{ref},t}$ , the 3D positions of $\\mathrm{PC}_{\\mathrm{ref}}$ should project onto the 2D pixel coordinates of $V_{\\mathrm{ref},t}$ . We optimize the camera's extrinsic matrix to ensure this alignment, thereby deriving the reference image camera pose $\\mathcal{C}_{\\mathrm{ref},t}$ from the extrinsic matrix.",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Camera Refinement via Gradient Descent. Given an approximately aligned camera pose where the rendering view matches $V_{\\mathrm{ref},t}$ , we further refine this alignment by applying gradient descent optimization on the camera pose. Specifically, we minimize the discrepancy between the mask region of the rendering view—defined as the pixels covered by the object during rasterization—and the object region in $V_{\\mathrm{ref},t}$ . With a well-initialized starting point, the gradient descent efficiently converges to a near-optimal solution for $\\mathcal{C}_{\\mathrm{ref},t}$ .",
+ "bbox": [
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+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "4.2. Mesh Appearance Refinement via Negative Condition Embedding Optimization",
+ "text_level": 1,
+ "bbox": [
+ 511,
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+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "With $\\mathcal{C}_{\\mathrm{ref},t}$ , the object's viewpoint is now synchronized with the video frame. This alignment allows us to leverage supervision from $V_{\\mathrm{ref},t}$ to improve the consistency of the mesh appearance with the input video. Inspired by techniques in image editing [2, 26], we propose optimizing the negative condition embedding during the second phase of TRELLIS inference (described in Sec. 3). This optimization preserves the priors learned by the network, as opposed to directly optimizing the final output SLAT. We begin optimization after a few denoising steps with the sparse flow transformer, ensuring that the object's structure is roughly generated. The optimization objective is to maximize similarity (measured by DreamSim, MSE, and LPIPS, with a regularization term to prevent significant deviation from the initial values) between the rendered view of the decoded SLAT (both mesh and Gaussian splats) under the camera pose $\\mathcal{C}_{\\mathrm{ref},t}$ and the reference video frame $V_{\\mathrm{ref},t}$ . The optimization is performed over multiple iterations for each denoising timestep. We denote the refined mesh as $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t}$ .",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "4.3. Consistent Topology via Iterative Pairwise Registration",
+ "text_level": 1,
+ "bbox": [
+ 511,
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+ ],
+ "page_idx": 4
+ },
+ {
+ "type": "text",
+ "text": "Due to the inherent randomness of the generation model, reconstructed meshes from adjacent video frames often exhibit variations in topology, such as differing numbers of vertices and faces, as well as changes in vertex and edge",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "page_number",
+ "text": "11647",
+ "bbox": [
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+ "page_idx": 4
+ },
+ {
+ "type": "image",
+ "img_path": "images/a8bff1abfae602141b6f391586bca53e061732ec65007b0adaf5d874a6f35366.jpg",
+ "image_caption": [
+ "(a) Mesh 1"
+ ],
+ "image_footnote": [],
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "image",
+ "img_path": "images/e6c4660c9797127365a0460e84216c6042e90dcd738434078327a2cc526dbafc.jpg",
+ "image_caption": [
+ "(b) Mesh 2 - Registered from Mesh 1",
+ "Figure 4. Comparison of Vertex Positions Between Original and Registered Meshes. We compare the vertex correspondences between mesh 1 and mesh 2, where mesh 2 is registered from mesh 1. To visualize these correspondences, we use the vertex normals of mesh 1 to color both meshes, highlighting their alignment."
+ ],
+ "image_footnote": [],
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "connectivity. To create a valid 4D animation asset with consistent geometry, we propose an iterative pairwise registration approach. For two consecutive meshes after refinement, $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t}$ and $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t + 1}$ , we begin by treating $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t}$ as a rigid body. We optimize its global transformation (rotation, translation, and scale) to align it with $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t + 1}$ using Chamfer distance and a differentiable rendering loss. After achieving global registration, we refine the alignment using the preconditioned optimization proposed by [27], which allows for fast and smooth convergence in the inverse reconstruction process. However, the differentiable rendering loss from [27] can struggle with regions undergoing large deformations or containing long, thin structures. To improve registration in these areas, we incorporate the As-Rigid-As-Possible (ARAP) constraint [13] alongside the Chamfer distance for enhanced local registration. Through these global and local alignment steps, we obtain a deformed version $\\widetilde{\\mathcal{M}}_t^\\prime$ (with vertices $\\nu_{t}^{\\prime}$ and faces $\\mathcal{F}_t^\\prime$ ) of $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t}$ ( $\\nu_{t}$ and faces $\\mathcal{F}_t$ ), ensuring that the number and topology are identical ( $\\nu_{t}^{\\prime} = \\nu_{t}$ , $\\mathcal{F}_t^\\prime = \\mathcal{F}_t$ ) and closely resemble the shape of $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t + 1}$ . We then replace the initial $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t + 1}$ with the deformed $\\widetilde{\\mathcal{M}}_t^\\prime$ . In practice, we designate $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},1}$ as the rest pose and iteratively apply the registration process across consecutive frames. This ensures consistent geometry across all meshes $\\widetilde{\\mathcal{M}}_{\\{1,\\dots,T\\}}^{\\prime}$ .",
+ "bbox": [
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4.4. Consistent Texture Map via Weighted Optimization",
+ "text_level": 1,
+ "bbox": [
+ 89,
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+ ],
+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "After the mesh registration process outlined in Sec. 4.3, we observe that the deformed vertices maintain their correspondence to the initial parts of the object. For instance, vertices representing the left side of the face remain aligned with the left face region (as illustrated in Fig. 4). Therefore, we directly inherit the texture map and UV coordinates of $\\widetilde{\\mathcal{M}}_1'$ for the subsequent meshes $\\widetilde{\\mathcal{M}}_{\\{2,\\dots,T\\}}^{\\prime}$ . To refine the texture and minimize artifacts, we further optimize the texture map using multi-view renderings of Gaussian splats generated alongside $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},1}$ (see Sec. 3), while using a single view",
+ "bbox": [
+ 89,
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+ "page_idx": 5
+ },
+ {
+ "type": "table",
+ "img_path": "images/af5c59836facb552e77b530dd9e20760036fd14c92fe44d4c60b00620de2eec7.jpg",
+ "table_caption": [],
+ "table_footnote": [],
+ "table_body": "| Simple | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8905 | 0.1597 | 1342.66 | 0.1282 |
| DreamMesh4D | 0.8692 | 0.1019 | 914.28 | 0.0937 |
| V2M4 (Ours) | 0.9259 | 0.1017 | 825.59 | 0.0688 |
| Complex | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8887 | 0.1265 | 1216.19 | 0.1492 |
| DreamMesh4D | 0.8256 | 0.0804 | 1079.02 | 0.1850 |
| V2M4 (Ours) | 0.9008 | 0.0747 | 666.04 | 0.1220 |
| All | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8891 | 0.1352 | 1014.45 | 0.1438 |
| DreamMesh4D | 0.8369 | 0.0860 | 855.29 | 0.1613 |
| V2M4 (Ours) | 0.9073 | 0.0817 | 576.73 | 0.1082 |
",
+ "bbox": [
+ 514,
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+ "page_idx": 5
+ },
+ {
+ "type": "table",
+ "img_path": "images/26cf732d567988cfb7688272176806d36e097de84f9adb7dbd721f3564a38e57.jpg",
+ "table_caption": [
+ "Table 2. Quantitative Evaluation of Different Methods. All metrics are computed using the rendering view of the reconstructed meshes. \"Simple\" refers to the Consistent4D data, which consists of simple objects with subtle movements, while \"Complex\" refers to data collected online featuring more complex objects and large-scale movements. \"All\" represents the combined evaluation on both subsets. The best results are in bold."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | Naïve TRELLIS | DreamMesh4D | V2M4 (Ours) |
| Time | 40s | 3 min | 60s |
",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Table 3. Average Reconstruction Time per Frame. The displayed time represents the average time taken to reconstruct each frame across an animation sequence. Detailed timing for each step of our method is provided in Appendix A.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "under $\\mathcal{C}_{\\mathrm{ref},t}$ for Gaussian splats of the subsequent meshes $\\widetilde{\\mathcal{M}}_{\\mathrm{refine},\\{2,\\dots,T\\}}$ . This setting is to ensure that all parts of the object are captured, even those that might not be visible in the video. We apply higher weights to views from $\\mathcal{C}_{\\mathrm{ref}}$ to ensure accurate alignment with the reference view $V_{\\mathrm{ref}}$ . This optimization results in a globally shared texture map $\\mathcal{T}$ for all meshes $\\widetilde{\\mathcal{M}}_{\\{1,\\dots,T\\}}^{\\prime}$ .",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "4.5. Mesh Interpolation and 4D Asset Conversion",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Since adjacent video frames, such as $V_{\\mathrm{ref},t}$ and $V_{\\mathrm{ref},t + 1}$ , are typically quite similar, we downsample the time dimension in our practical implementation by selecting every $i_{\\mathrm{th}}$ frame to reconstruct the mesh. This results in a time-reduced mesh sequence. To ensure smooth mesh animation, we linearly interpolate the vertex positions between every two adjacent reconstructed meshes, aligning them with the time resolution of $V_{\\mathrm{ref}}$ . Next, we convert the upsampled meshes $\\widetilde{\\mathcal{M}}_{\\{1,\\dots,T\\}}^{\\prime}$ into the mesh $\\widetilde{\\mathcal{M}}_1^\\prime$ plus a deformation tensor $\\mathcal{D}\\in \\mathbb{R}^{T\\times N\\times 3}$ , which stores the vertices' deformation over time. By keyframing these offsets and using the globally shared texture map $\\mathcal{T}$ , we can generate a GLTF animation file that is compatible with graphics and game engines.",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "5. Experiments",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "5.1. Experimental Setup",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "text",
+ "text": "Please refer to Appendix A for implementation details, and to Appendix B & D for comprehensive ablation studies (including experiments with more advanced 3D genera",
+ "bbox": [
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+ "page_idx": 5
+ },
+ {
+ "type": "page_number",
+ "text": "11648",
+ "bbox": [
+ 480,
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+ "page_idx": 5
+ },
+ {
+ "type": "image",
+ "img_path": "images/1fc8b2e67fda55f2d1dc4b70cb689d3fe5376301f0e8cbb08187f637ae1ae4a8.jpg",
+ "image_caption": [
+ "Figure 5. Qualitative Evaluation of Different Methods. We show both the color and normal views of the reconstructed meshes. The first two samples are from the Consistent4D dataset, while the rest are from our collected data. Each sample includes two timestamps for quick comparison. Please zoom in for a clearer view. For more results and animations, see the Supplementary Files."
+ ],
+ "image_footnote": [],
+ "bbox": [
+ 86,
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+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "tion models such as Hunyuan3D-2.0 [63], TripoSG [19], and advanced dense stereo reconstruction models like VGGT [44]), as well as additional visual results.",
+ "bbox": [
+ 89,
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+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "Datasets. We constructed a benchmark comprising 40 animation videos. Specifically, we first collected 20 animation videos from Consistent4D [14], which feature sim",
+ "bbox": [
+ 89,
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+ 483,
+ 900
+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "text",
+ "text": "ple object topologies with subtle movements. Additionally, we gathered 20 animation videos from Mixamo [25] and Sketchfab [38] to include larger-scale object movements and more complex object topologies (with sequences containing more than 200 frames), thus providing a diverse test set for assessing reconstruction performance. Our bench-",
+ "bbox": [
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+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "page_number",
+ "text": "11649",
+ "bbox": [
+ 478,
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+ ],
+ "page_idx": 6
+ },
+ {
+ "type": "image",
+ "img_path": "images/a131bb4e827fbbb26d7b3c6d668d64095b373ad4d39c7627d199dc5b56be6891.jpg",
+ "image_caption": [
+ "Figure 6. Multi-View Object Geometry Comparison with L4GM. For L4GM, we present the multi-view Gaussian Splats rendering views, while for our method, we display the multi-view rendering views of our mesh. Please zoom in for a clearer view."
+ ],
+ "image_footnote": [],
+ "bbox": [
+ 91,
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+ 243
+ ],
+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "mark is much larger and more varied than those used in existing works [14, 20, 56], which evaluate only 7 test samples (each with just 32 frames). Sample frames from our benchmark can be found in Appendix D. Since existing video segmentation methods [30] can easily extract foreground object regions, the dataset has been pre-processed to remove backgrounds. This ensures that the evaluation remains focused on reconstruction quality rather than segmentation challenges.",
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "Evaluation Metrics. To evaluate the reconstruction quality, we adopt metrics commonly used in 4D works [32, 56], including CLIP [29], LPIPS [60], and FVD [42], to assess the visual quality of the reconstructed 4D animation through video-to-rendering evaluation. We also include DreamSim [5] due to its excellent performance in evaluating semantic similarity. All these metrics are calculated between the input video frames and the rendered video frames of the reconstructed mesh with an aligned camera viewpoint. Please see Appendix A for details on the metric settings.",
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
+ "type": "text",
+ "text": "5.2. Comparisons",
+ "text_level": 1,
+ "bbox": [
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+ "page_idx": 7
+ },
+ {
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+ "text": "Quantitative Evaluation. Since V2M4 directly outputs 4D meshes and most existing 4D works focus on single NeRF or Gaussian Splats outputs, we ensure fair comparisons by evaluating our method against the recent DreamMesh4D [20], which outputs both Gaussian Splats and 4D meshes. We also compare our results with the naive TRELLIS [48], which reconstructs each video frame individually. Table 2 presents the quantitative performance results on our benchmark. For comprehensiveness, we separately display results on Consistent4D data, which features simple topology and subtle movement, and our additional data from Mixamo and Sketchfab, which includes complex topology, intense movement, and longer movement durations. From the results, V2M4 outperforms both other methods, achieving superior performance across all metrics. Additionally, we report processing times in Table 3. Thanks to our interpolation design detailed in Sec-",
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+ "text": "tion 4.5, our method processes each frame in approximately one minute on average, adding little to the naive TRELIS processing time, while being significantly faster than DreamMesh4D.",
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+ "text": "Qualitative Evaluation. Fig. 5 show qualitative visual results of the reconstructed meshes across different methods on the Consistent4D data and the newly collected data. We present both the rendering color view and normal view of the meshes. From these visuals, V2M4 produces mesh results with significantly better appearance and topology than DreamMesh4D, and they are much more aligned with the reference videos. These findings verify that V2M4 is effective and generalizable, capable of reconstructing high-quality, usable 4D mesh animations from monocular videos.",
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+ "text": "Additionally, to further highlight the advantages of basing the 4D reconstruction task on native 3D mesh models, we qualitatively compare our method with a current powerful 4D Gaussian Splatting reconstruction method, L4GM [32], which explicitly trains a multi-view Gaussian Splatting network. In Fig. 6, we display the multi-view rendering views of our mesh and Gaussian Splats for several cases. We observe that V2M4 preserves more accurate model geometry than L4GM, underscoring the promise of using native 3D mesh generation models for 4D tasks.",
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+ "text": "While our method effectively reconstructs 4D mesh animations from input videos in many scenarios, it has several limitations. First, since our approach is based on TRELLIS, our method may suffer from performance issues when TRELLIS outputs poor 3D reconstructions (see further analysis in Appendix B). Second, artifacts can occur when reconstructing animations with topology changes, as we enforce topology consistency by registering the first mesh to subsequent frames. Third, using a fixed sampling rate, as discussed in Section 4.5, can be inefficient due to variable motion dynamics—sometimes moving slowly and other times rapidly. Future work could benefit from incorporating adaptive sampling techniques.",
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+ "text": "In this work, we propose a 4D reconstruction method capable of directly generating usable 4D mesh animation assets. Our method is built upon a 3D mesh generation model and addresses key challenges, including misalignment between the reconstructed mesh and the input video in terms of pose and appearance, as well as inconsistencies in geometry and texture throughout the animation. Our approach successfully produces high-quality mesh animation files that are compatible with graphics and game software. We believe this work offers a promising solution by enabling direct 4D mesh generation.",
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+ "content": "We present V2M4, a novel 4D reconstruction method that directly generates a usable 4D mesh animation asset from a single monocular video. Unlike existing approaches that rely on priors from multi-view image and video generation models, our method is based on native 3D mesh generation models. Naively applying 3D mesh generation models to generate a mesh for each frame in a 4D task can lead to issues such as incorrect mesh poses, misalignment of mesh appearance, and inconsistencies in mesh geometry and texture maps. To address these problems, we propose a structured workflow that includes camera search and mesh reposing, condition embedding optimization for mesh appearance refinement, pairwise mesh registration for topology consistency, and global texture map optimization for texture consistency. Our method outputs high-quality 4D animated assets that are compatible with mainstream graphics and game software. Experimental results across a variety of animation types and motion amplitudes demonstrate the generalization and effectiveness of our method. https://windvchen.github.io/V2M4."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "1. Introduction"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Creating 4D mesh animations is a challenging task. Unlike the synthesis of 3D geometry or 2D images, the scarcity of 4D mesh animations makes it difficult to employ a learning-based framework. Monocular videos provide rich motion cues, making them a potential source for animation reconstruction. However, reconstructing 4D mesh animations from single-view videos remains an underexplored problem, posing challenges in addressing the ambiguity in single-view video and maintaining both visual and topological consistency over time."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Existing methods [14, 15, 31, 32, 40, 47, 49, 54, 56, 59, 62] have explored animation reconstruction based on implicit representations such as NeRF [24] or topology-independent representations like Gaussian Splatting [17]. To mitigate occlusions and ambiguities in single-view videos, these approaches leverage knowledge embedded in multi-view image diffusion [22, 36, 43] and video diffusion [1, 11]. While these methods are viable alternatives, they face disadvantages, such as the difficulty of ensuring 3D consistency in multi-view image diffusion and video diffusion. Additionally, converting these implicit and"
+ },
+ {
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+ [
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "topology-independent representations into a mesh representation remains challenging. These factors complicate the use of these methods to obtain a mesh animation that maintains a fine-grained geometric shape and preserves interframe topological consistency."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this work, we propose V2M4, a method that directly reconstructs a 4D animated mesh from a fixed-viewpoint monocular video. Unlike existing approaches that rely on multi-view image and video diffusion models, our method leverages recent advancements in native 3D mesh reconstruction [12, 48], enabling explicit mesh generation with good shape without the need to convert from other representations. A naive approach to using 3D mesh reconstruction for 4D animation involves generating a mesh for each frame independently. However, this strategy presents several challenges. Chief among these is the uncertainty of the generated mesh pose, where random face orientations and positions lead to misalignment with the video frames. Additionally, there are issues of appearance misalignment, where the generated meshes fail to match the object's appearance in the video. Furthermore, inconsistencies in geometry and topology result in varying mesh structures across frames, and differences in texture maps disrupt the visual continuity of the animation."
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To tackle these challenges, we introduce a structured approach that effectively extends the 3D mesh reconstruction model to the 4D mesh animation task. First, we develop a mesh reposing strategy. In this step, we search for camera poses for each reconstructed mesh to ensure semantic alignment with the input video frame by combining particle swarm optimization with a dense stereo reconstruction model's prior. We then re-pose the meshes by applying inverse camera transformations. Second, we refine the appearance of the meshes by optimizing the negative condition embedding of the 3D reconstruction model, enhancing consistency with the video frames. Third, we enforce geometry consistency by selecting the first-frame mesh as a rest pose and introducing a global-to-local mesh registration approach using differential rendering and geometric constraints. Fourth, we optimize a global texture map to ensure texture consistency based on the rendering views of the reconstructed meshes. Finally, we keyframe the meshes and interpolate vertex positions between frames to achieve smoother animation, integrating the results into a GLTF [7] animated file, which is compatible with mainstream graphics software. Fig. 1 displays some of our results. Our main contributions are as follows:"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We introduce the use of native 3D mesh reconstruction models for 4D animated asset generation, enabling the direct creation of explicit 4D meshes with consistent geometry, shared textures, and video-aligned object motions from a fixed-viewpoint monocular video."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We propose V2M4, a practical and efficient framework"
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+ "type": "list",
+ "bbox": [
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+ "type": "table",
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+ "content": "| Method | 3D Prior Source | Reconstruction Process | Output Format |
| Consistent4D | MV Image and Video Diffusion | Optimization | NeRF |
| STAG4D | MV Image Diffusion | Optimization | GS |
| Diffusion2 | MV Image and Video Diffusion | Optimization | GS |
| EG4D | MV Image and Video Diffusion | Optimization | GS |
| Animate3D | MV-Video Diffusion | Optimization | GS |
| 4Diffusion | MV-Video Diffusion | Optimization | NeRF |
| Diffusion4D | MV-Video Diffusion | Optimization | GS |
| SV4D | MV-Video Diffusion | Optimization | NeRF |
| AR4D | MV Image Diffusion | Recon Network | GS |
| L4GM | MV Image Diffusion | Recon Network | GS |
| DreamMesh4D | MV Image Diffusion | Optimization | Mesh & GS |
| V2M4 (Ours) | Native 3D Mesh Diffusion Model | - | Mesh |
"
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+ "content": "Table 1. Comparison of V2M4 with Existing 4D Reconstruction Methods. “-” indicates the absence of an intermediate reconstruction phase. Not all existing 4D methods are listed, but other approaches are generally similar to those included in the table."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "that addresses key challenges associated with using 3D mesh reconstruction models for 4D mesh reconstruction, including incorrect mesh positioning, appearance misalignment, geometry inconsistencies, and texture inconsistencies."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "- We conduct extensive evaluations on diverse animations, including humanoid and animal motions, covering a range of motion amplitudes from subtle movements to large-scale motions. The results demonstrate the effectiveness and generalizability of our approach."
+ },
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+ "type": "title",
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+ "content": "2. Related Works"
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "Multi-view and Video Diffusion Models. Building on the success of image diffusion models [10, 33], recent works have increasingly focused on the generation of other modalities, such as multi-view images [22, 36, 43] and videos [8, 11, 37]. In multi-view diffusion models, networks predict the 3D structure of an object from an input image. For instance, Zero123 [22] can generate a rendering of an object from a novel camera viewpoint by taking an input image and a target camera pose transition. Subsequent works, such as ImageDream [45] and SyncDream [23], further advance this direction by generating multi-view images in a single forward pass from a single input image. Video diffusion models have seen even more rapid development, driven by the availability of large-scale video datasets. Methods such as Dynamiccafter [50] and Stable Video Diffusion [1] can generate high-quality videos and enable smooth interpolation between frames."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Video-to-4D Reconstruction Models. Due to the scarcity of 4D animated assets, existing research primarily leverages priors learned from multi-view and video generative models to ensure spatial and temporal consistency in reconstructed 4D animations. Consistent4D [14] employs Score Distillation Sampling (SDS) with signals from both pretrained multi-view and video diffusion models. STAG4D [56] follows a similar approach but introduces"
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+ {
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+ "bbox": [
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+ "type": "text",
+ "bbox": [
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+ "content": "an inter-frame key-value mixing mechanism during the denoising process to enhance sequence consistency. To avoid SDS, AR4D [65] instead proposes deforming the initial frame's Gaussian Splats while utilizing priors from multi-view generation models. Diffusion\\(^{2}\\) [54] and EG4D [40] modify the sampling or attention mechanisms to integrate prior knowledge from multi-view image and video diffusion models without relying on SDS. Animate3D [15] and 4Diffusion [59] train multi-view video diffusion models that generate more consistent images for improved SDS optimization. Similarly, Diffusion4D [21] and SV4D [49] also train multi-view video generation models but directly optimize Gaussian Splatting or NeRF on the generated images without SDS. L4GM [32] takes a different approach by training a network that outputs 4D Gaussian Splats given multiview images. However, all of these methods do not output meshes, as discussed in Sec. 1. An alternative approach, DreamMesh4D [20], introduces a hybrid Gaussian-Mesh representation capable of outputting meshes, though it still relies on multi-view and video diffusion model priors and adopts SDS optimization. Other works [39, 52, 53] also attempt to reconstruct meshes from videos but require significantly more input, such as multiple video clips, rendering camera poses, skeletons, or categorical dense feature descriptors, rather than just a single monocular video."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Large Native 3D Mesh Generation Models. Unlike previous indirect 3D generative methods, which either generate multi-view images [23, 41, 45] or implicit representations [51, 57, 58, 64], recent work [12, 48] focuses on directly generating usable meshes by adopting differentiable meshing techniques such as FlexiCubes [35] or DMTet [34]. Instead, they directly predict grid attributes and generate explicit meshes. By training on large collections of synthesized 3D assets, the method achieves impressive generation results conditioned on images."
+ },
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+ "type": "text",
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+ "content": "Ours versus Others. Different from most existing methods that rely on priors from multi-view image or video diffusion models and use NeRF or Gaussian Splitting as representations, we pioneer the use of native 3D mesh generation models for 4D animation reconstruction. Our approach only requires a single monocular video with a fixed camera pose as input, without the need for SDS, and outputs a 4D mesh animation file with consistent geometry and texture. Table 1 illustrates how our approach differs from previous works."
+ },
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+ "content": "3. Preliminaries"
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+ "content": "Our method builds upon TRELLIS [48], a recently introduced and powerful 3D generation model (we also evaluate our method using more advanced 3D generators, as detailed in Appendix B). TRELLIS encodes 3D assets into a structured latent representation (SLAT), which consists of a"
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "sparse 3D grid embedding both geometric and appearance information. The 3D reconstruction process in TRELLIS can be broadly divided into two phases. In the first phase, TRELLIS employs rectified flow [3] to generate a 3D voxel grid, where the voxel values indicate the object's occupancies. By applying a threshold, TRELLIS extracts a sparse voxel representation. In the second phase, a sparse rectified flow transformer is used to generate the object's SLAT from this sparse voxel grid. Both phases are conditioned on visual features extracted from the input image using DINOv2 [28], along with a negative condition based on the classifier-free technique [9]. The SLAT can then be processed by three independent decoders, which generate meshes, Gaussian Splats [17], and Radiance Fields [6], respectively. For mesh decoding, TRELLIS predicts both the signed distance field (SDF) grid and the parameters of differentiable FlexiCubes [35], enabling the conversion from the SDF into a mesh. Instead of using the predicted mesh vertex colors from the mesh decoder, TRELLIS employs xatlas [55] to compute UV maps of the mesh and then bakes a high-resolution texture map using multi-view observations of its Gaussian Splats."
+ },
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+ "content": "4. Method"
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+ "content": "Given a reference monocular video sequence of length \\(T\\), denoted as \\(V_{\\mathrm{ref}} = \\{V_{\\mathrm{ref},t}\\}_{t=1}^{T}\\), which captures an object from a fixed camera pose, our method generates a directly usable 4D animated asset. This asset comprises a static mesh \\(\\mathcal{M}\\) with vertices \\(\\mathcal{V} = \\{\\mathbf{v}_1,\\mathbf{v}_2,\\dots,\\mathbf{v}_N\\}\\) (or simply \\(\\mathcal{V}\\in \\mathbb{R}^{N\\times 3}\\)) and faces \\(\\mathcal{F}\\subset \\mathcal{V}\\times \\mathcal{V}\\times \\mathcal{V}\\), a texture map \\(\\mathcal{T}\\), and a deformation tensor \\(\\mathcal{D}\\in \\mathbb{R}^{T\\times N\\times 3}\\) that records the vertices' deformations over time. Initially, each video frame is processed through an image-conditioned 3D generation model, resulting in a set of initial 3D meshes, denoted as \\(\\widetilde{\\mathcal{M}}_{\\mathrm{init}} = \\{\\widetilde{\\mathcal{M}}_1,\\widetilde{\\mathcal{M}}_2,\\ldots ,\\widetilde{\\mathcal{M}}_T\\}\\). These meshes exhibit inconsistencies with \\(V_{\\mathrm{ref}}\\) as well as inter-mesh texture and geometry discrepancies, rendering them unsuitable for direct conversion into a usable 4D asset. To address these issues, our method employs a five-step workflow: repositioning the mesh for accurate object movement (Sec. 4.1), refining object appearance (Sec. 4.2), ensuring inter-frame mesh geometry consistency (Sec. 4.3), maintaining inter-frame mesh texture consistency (Sec. 4.3), and ultimately converting the 3D assets into 4D assets (Sec. 4.5). The complete workflow is illustrated in Fig. 2."
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+ "content": "4.1. Camera Search and Mesh Re-Pose"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Due to the setup of training TRELLIS, the initial meshes \\(\\widetilde{\\mathcal{M}}_{\\mathrm{init}}\\) often tend to have a canonical face orientation along one axis (as illustrated in Fig. 2), and their positions may also sometimes be canonicalized to the origin of the coordinate system. This results in a significant loss of object motion information, such as translation and rotation. To re"
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+ [
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+ "type": "image_caption",
+ "bbox": [
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+ "content": "Figure 2. The Workflow of V2M4. Upon receiving a video sequence \\(V_{\\mathrm{ref}}\\), we generate coarse 3D meshes for each frame, denoted as \\(\\widetilde{\\mathcal{M}}_{\\{1,\\dots,t\\}}\\). These initial meshes do not accurately capture the object's movement and appearance as depicted in the input video, and they exhibit inconsistencies in topology and texture. Our method employs a five-stage process: (1) Repose the mesh to accurately reflect object movement; (2) Refine the mesh appearance based on the reference video frames; (3) Ensure inter-mesh topology consistency through mesh registration; (4) Optimize a globally shared texture map across all meshes; (5) Keyframe the meshes, perform interpolation, and convert them into a directly usable 4D animation asset."
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+ "bbox": [
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+ "angle": 0,
+ "content": "cover these motions, we propose first determining the camera pose \\(\\mathcal{C} \\in \\mathbb{R}^6 = \\{\\mathrm{yaw},\\mathrm{pitch},\\mathrm{radius},\\mathrm{lookat}_{x,y,z}\\}\\) for each reconstructed mesh \\(\\widetilde{\\mathcal{M}}_t\\), ensuring the rendered view is semantically similar to the corresponding video frame. Then, we can invert the camera pose and apply the transformation to the mesh, effectively recovering mesh motion from the camera motion."
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+ "bbox": [
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+ "angle": 0,
+ "content": "Since directly optimizing camera parameters via gradient descent from a random starting point using differentiable rendering tools like Nvdiffrast [18] often leads to poor local minima, we propose a more robust camera pose search strategy. Specifically, we begin by sampling a large number of camera positions around the object and selecting the top \\( n \\) positions that exhibit high similarity to the reference video frame, denoted as \\( V_{\\mathrm{ref},t} \\). We then utilize a pretrained dense stereo model to process the rendering views under these \\( n \\) cameras and \\( V_{\\mathrm{ref},t} \\), obtaining the predicted point clouds for each view. Next, we design to extract the camera pose \\( C_{\\mathrm{ref},t,\\mathrm{DUSt3R}} \\) for the reference image from these point clouds. This pose \\( C_{\\mathrm{ref},t,\\mathrm{DUSt3R}} \\) is added back to the initial pool of camera pose candidates, and we employ the Particle Swarm Optimization (PSO) algorithm to refine this into a more accurate camera pose \\( C_{\\mathrm{ref},t,\\mathrm{PSO}} \\). Subsequently, we further refine the camera pose using gradient descent optimization, starting from the improved point \\( C_{\\mathrm{ref},t,\\mathrm{PSO}} \\), to obtain the final \\( C_{\\mathrm{ref},t} \\). Finally, we derive the camera motion from \\( C_{\\mathrm{ref},t} \\), invert it, and apply this transformation to \\( \\widetilde{\\mathcal{M}}_t \\) to obtain \\( \\widetilde{\\mathcal{M}}_{\\mathrm{repose},t} \\). The entire workflow is detailed in Algorithm 1."
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+ "angle": 0,
+ "content": "Below, we provide more details about the three key com"
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+ "content": "Algorithm 1 Camera Search and Mesh Re-Pose"
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+ "angle": 0,
+ "content": "Require: Initial mesh \\(\\widetilde{\\mathcal{M}}_t\\), reference frame \\(V_{\\mathrm{ref},t}\\) at time \\(t\\), pretrained dense stereo reconstruction model DUSt3R"
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+ "content": "1: Initialize a set of sampled camera poses \\( P_0 \\)"
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+ "content": "2: Select the top \\( n \\) camera poses based on similarity to \\( V_{\\mathrm{ref},t} \\). Render views under these poses and input them, along with \\( V_{\\mathrm{ref},t} \\), into the DUSt3R"
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+ "content": "3: DUSt3R Estimation: Align DUSt3R-predicted point clouds with ground-truth point clouds"
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+ "angle": 0,
+ "content": "4: Optimize the camera extrinsic matrix to derive \\(\\mathcal{C}_{\\mathrm{ref},t,\\mathrm{DUS3R}}\\)"
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+ "angle": 0,
+ "content": "5: PSO Search: Add \\( C_{\\mathrm{ref},t,\\mathrm{DUS3R}} \\) to the top \\( K \\) camera poses from \\( P_0 \\), then apply PSO"
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+ "angle": 0,
+ "content": "6: Select the best camera pose \\( C_{\\mathrm{ref},t,\\mathrm{PSO}} \\) after iterations"
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+ "angle": 0,
+ "content": "7: Gradient Descent Refinement: Refine by minimizing mask discrepancy with \\( V_{\\mathrm{ref},t} \\)"
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+ "angle": 0,
+ "content": "8: Obtain the final optimized camera pose \\( \\mathcal{C}_{\\mathrm{ref},t} \\)"
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+ "angle": 0,
+ "content": "9: Mesh Re-pose: Apply the inverse of \\( \\mathcal{C}_{\\mathrm{ref},t} \\) to \\( \\widetilde{\\mathcal{M}}_t \\) to obtain \\( \\widetilde{\\mathcal{M}}_{\\mathrm{repose},t} \\)"
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+ "angle": 0,
+ "content": "10: return Re-posed mesh \\(\\widetilde{\\mathcal{M}}_{\\mathrm{repose},t}\\)"
+ },
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+ "type": "list",
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+ "angle": 0,
+ "content": "ponents involved."
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+ "angle": 0,
+ "content": "Camera Search Using Particle Swarm Optimization. We use PSO [16] algorithm to search for the aligned camera pose. To effectively explore the search space and avoid the local minima problem encountered with direct gradient descent, we sample \\(P\\) particles (camera poses) around the object. The sampling strategy is designed to ensure that the"
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+ "angle": 0,
+ "content": "Figure 3. Camera Pose Extraction from Dense Stereo Reconstruction for \\( V_{\\mathrm{ref},t} \\). We first obtain estimated point clouds \\( \\overline{\\mathrm{PC}}_{\\mathrm{ref}} \\) and \\( \\overline{\\mathrm{PC}}_{\\mathrm{rend}} \\) from the DUSt3R model for reference video frame \\( V_{\\mathrm{ref},t} \\) and rendering views \\( V_{\\mathrm{rend}} \\). We then align \\( \\overline{\\mathrm{PC}}_{\\mathrm{rend}} \\) with the point clouds \\( \\mathrm{PC}_{\\mathrm{rend}} \\) obtained from mesh \\( \\widetilde{\\mathcal{M}}_t \\) during rasterization (Note the differences in axis direction and scale depicted in the figure.). This transformation is then applied to \\( \\overline{\\mathrm{PC}}_{\\mathrm{ref}} \\), resulting in the transformed \\( \\mathrm{PC}_{\\mathrm{ref}} \\). Finally, we optimize to determine the camera pose \\( C_{\\mathrm{ref},t} \\) that ensures accurate mapping from 3D to 2D points."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.434,
+ 0.483,
+ 0.648
+ ],
+ "angle": 0,
+ "content": "yaw and pitch values are uniformly distributed over a unit sphere, while the radius is sampled according to the surface area of the sphere along with its radius. The \\(\\mathrm{lookat}_{x,y,z}\\) values are uniformly sampled within a predefined range. For the objective function, we utilize DreamSim [5], which is more effective at evaluating the similarity between the rendered view of the imperfectly reconstructed mesh and the reference video frame, compared to conventional methods like MSE or LPIPS [61]. The positions of the particles (camera pose values) are iteratively updated based on both their individual best-known position and the best-known position of the entire swarm, with added noise randomness. The final best one is selected as the reference image's camera pose \\(C_{\\mathrm{ref},t,\\mathrm{PSO}}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.656,
+ 0.483,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "Knowledge Utilization from Dense Stereo Reconstruction Model. To enhance the robustness of the PSO search, we leverage prior knowledge from a pretrained dense stereo model, specifically DUSt3R [46]. DUSt3R can predict inter-frame camera motion and 3D point positions corresponding to each view's 2D pixels. While a straightforward approach would involve feeding both the reference video frame \\( V_{\\mathrm{ref},t} \\) and a set of rendered views \\( V_{\\mathrm{rend},\\{1,\\dots,n\\}} \\) around \\( \\widetilde{\\mathcal{M}}_t \\) into DUSt3R and using the predicted relative camera motion to estimate the camera pose of \\( V_{\\mathrm{ref},t} \\), this poses challenges. Differences in camera models and coordinate settings, such as scale and orientation, complicate matrix conversions, and semantic discrepancies between \\( V_{\\mathrm{ref},t} \\) and \\( V_{\\mathrm{rend},\\{1,\\dots,n\\}} \\) can lead to inaccurate motion predictions. To overcome these issues, we focus on the point clouds estimated by DUSt3R instead of relying on the predicted cam"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.091,
+ 0.905,
+ 0.305
+ ],
+ "angle": 0,
+ "content": "era motions. Let \\(\\overline{\\mathrm{PC}}_{\\mathrm{ref}}\\) and \\(\\overline{\\mathrm{PC}}_{\\mathrm{rend},\\{1,\\dots,n\\}}\\) represent the predicted point clouds for \\(V_{\\mathrm{ref},t}\\) and \\(V_{\\mathrm{rend},\\{1,\\dots,n\\}}\\), respectively. Given that the camera model, camera poses, and \\(\\widetilde{\\mathcal{M}}_t\\) are known for rendering \\(V_{\\mathrm{rend},\\{1,\\dots,n\\}}\\), we can derive the ground-truth point clouds in our coordinate system, denoted as \\(\\mathrm{PC}_{\\mathrm{rend},\\{1,\\dots,n\\}}\\). We align the predicted point clouds with the ground truth using a global transformation (rotation, translation, and scale) optimized via Chamfer distance [4]. Applying this transformation to \\(\\overline{\\mathrm{PC}}_{\\mathrm{ref}}\\), we obtain \\(\\mathrm{PC}_{\\mathrm{ref}}\\). Ideally, with the correct camera pose \\(\\mathcal{C}_{\\mathrm{ref},t}\\), the 3D positions of \\(\\mathrm{PC}_{\\mathrm{ref}}\\) should project onto the 2D pixel coordinates of \\(V_{\\mathrm{ref},t}\\). We optimize the camera's extrinsic matrix to ensure this alignment, thereby deriving the reference image camera pose \\(\\mathcal{C}_{\\mathrm{ref},t}\\) from the extrinsic matrix."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.31,
+ 0.905,
+ 0.462
+ ],
+ "angle": 0,
+ "content": "Camera Refinement via Gradient Descent. Given an approximately aligned camera pose where the rendering view matches \\( V_{\\mathrm{ref},t} \\), we further refine this alignment by applying gradient descent optimization on the camera pose. Specifically, we minimize the discrepancy between the mask region of the rendering view—defined as the pixels covered by the object during rasterization—and the object region in \\( V_{\\mathrm{ref},t} \\). With a well-initialized starting point, the gradient descent efficiently converges to a near-optimal solution for \\( \\mathcal{C}_{\\mathrm{ref},t} \\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.469,
+ 0.905,
+ 0.501
+ ],
+ "angle": 0,
+ "content": "4.2. Mesh Appearance Refinement via Negative Condition Embedding Optimization"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.507,
+ 0.905,
+ 0.796
+ ],
+ "angle": 0,
+ "content": "With \\(\\mathcal{C}_{\\mathrm{ref},t}\\), the object's viewpoint is now synchronized with the video frame. This alignment allows us to leverage supervision from \\(V_{\\mathrm{ref},t}\\) to improve the consistency of the mesh appearance with the input video. Inspired by techniques in image editing [2, 26], we propose optimizing the negative condition embedding during the second phase of TRELLIS inference (described in Sec. 3). This optimization preserves the priors learned by the network, as opposed to directly optimizing the final output SLAT. We begin optimization after a few denoising steps with the sparse flow transformer, ensuring that the object's structure is roughly generated. The optimization objective is to maximize similarity (measured by DreamSim, MSE, and LPIPS, with a regularization term to prevent significant deviation from the initial values) between the rendered view of the decoded SLAT (both mesh and Gaussian splats) under the camera pose \\(\\mathcal{C}_{\\mathrm{ref},t}\\) and the reference video frame \\(V_{\\mathrm{ref},t}\\). The optimization is performed over multiple iterations for each denoising timestep. We denote the refined mesh as \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t}\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.803,
+ 0.905,
+ 0.833
+ ],
+ "angle": 0,
+ "content": "4.3. Consistent Topology via Iterative Pairwise Registration"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.84,
+ 0.908,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "Due to the inherent randomness of the generation model, reconstructed meshes from adjacent video frames often exhibit variations in topology, such as differing numbers of vertices and faces, as well as changes in vertex and edge"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.48,
+ 0.949,
+ 0.518,
+ 0.961
+ ],
+ "angle": 0,
+ "content": "11647"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.131,
+ 0.088,
+ 0.272,
+ 0.209
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.154,
+ 0.211,
+ 0.207,
+ 0.221
+ ],
+ "angle": 0,
+ "content": "(a) Mesh 1"
+ },
+ {
+ "type": "image",
+ "bbox": [
+ 0.274,
+ 0.088,
+ 0.438,
+ 0.213
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.253,
+ 0.212,
+ 0.434,
+ 0.222
+ ],
+ "angle": 0,
+ "content": "(b) Mesh 2 - Registered from Mesh 1"
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.226,
+ 0.483,
+ 0.298
+ ],
+ "angle": 0,
+ "content": "Figure 4. Comparison of Vertex Positions Between Original and Registered Meshes. We compare the vertex correspondences between mesh 1 and mesh 2, where mesh 2 is registered from mesh 1. To visualize these correspondences, we use the vertex normals of mesh 1 to color both meshes, highlighting their alignment."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.093,
+ 0.303,
+ 0.485,
+ 0.701
+ ],
+ "angle": 0,
+ "content": "connectivity. To create a valid 4D animation asset with consistent geometry, we propose an iterative pairwise registration approach. For two consecutive meshes after refinement, \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t}\\) and \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t + 1}\\), we begin by treating \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t}\\) as a rigid body. We optimize its global transformation (rotation, translation, and scale) to align it with \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t + 1}\\) using Chamfer distance and a differentiable rendering loss. After achieving global registration, we refine the alignment using the preconditioned optimization proposed by [27], which allows for fast and smooth convergence in the inverse reconstruction process. However, the differentiable rendering loss from [27] can struggle with regions undergoing large deformations or containing long, thin structures. To improve registration in these areas, we incorporate the As-Rigid-As-Possible (ARAP) constraint [13] alongside the Chamfer distance for enhanced local registration. Through these global and local alignment steps, we obtain a deformed version \\(\\widetilde{\\mathcal{M}}_t^\\prime\\) (with vertices \\(\\nu_{t}^{\\prime}\\) and faces \\(\\mathcal{F}_t^\\prime\\)) of \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t}\\) (\\(\\nu_{t}\\) and faces \\(\\mathcal{F}_t\\)), ensuring that the number and topology are identical (\\(\\nu_{t}^{\\prime} = \\nu_{t}\\), \\(\\mathcal{F}_t^\\prime = \\mathcal{F}_t\\)) and closely resemble the shape of \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t + 1}\\). We then replace the initial \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},t + 1}\\) with the deformed \\(\\widetilde{\\mathcal{M}}_t^\\prime\\). In practice, we designate \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},1}\\) as the rest pose and iteratively apply the registration process across consecutive frames. This ensures consistent geometry across all meshes \\(\\widetilde{\\mathcal{M}}_{\\{1,\\dots,T\\}}^{\\prime}\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.09,
+ 0.708,
+ 0.483,
+ 0.739
+ ],
+ "angle": 0,
+ "content": "4.4. Consistent Texture Map via Weighted Optimization"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.745,
+ 0.483,
+ 0.902
+ ],
+ "angle": 0,
+ "content": "After the mesh registration process outlined in Sec. 4.3, we observe that the deformed vertices maintain their correspondence to the initial parts of the object. For instance, vertices representing the left side of the face remain aligned with the left face region (as illustrated in Fig. 4). Therefore, we directly inherit the texture map and UV coordinates of \\(\\widetilde{\\mathcal{M}}_1'\\) for the subsequent meshes \\(\\widetilde{\\mathcal{M}}_{\\{2,\\dots,T\\}}^{\\prime}\\). To refine the texture and minimize artifacts, we further optimize the texture map using multi-view renderings of Gaussian splats generated alongside \\(\\widetilde{\\mathcal{M}}_{\\mathrm{refine},1}\\) (see Sec. 3), while using a single view"
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.515,
+ 0.088,
+ 0.911,
+ 0.235
+ ],
+ "angle": 0,
+ "content": "| Simple | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8905 | 0.1597 | 1342.66 | 0.1282 |
| DreamMesh4D | 0.8692 | 0.1019 | 914.28 | 0.0937 |
| V2M4 (Ours) | 0.9259 | 0.1017 | 825.59 | 0.0688 |
| Complex | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8887 | 0.1265 | 1216.19 | 0.1492 |
| DreamMesh4D | 0.8256 | 0.0804 | 1079.02 | 0.1850 |
| V2M4 (Ours) | 0.9008 | 0.0747 | 666.04 | 0.1220 |
| All | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8891 | 0.1352 | 1014.45 | 0.1438 |
| DreamMesh4D | 0.8369 | 0.0860 | 855.29 | 0.1613 |
| V2M4 (Ours) | 0.9073 | 0.0817 | 576.73 | 0.1082 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.512,
+ 0.239,
+ 0.907,
+ 0.337
+ ],
+ "angle": 0,
+ "content": "Table 2. Quantitative Evaluation of Different Methods. All metrics are computed using the rendering view of the reconstructed meshes. \"Simple\" refers to the Consistent4D data, which consists of simple objects with subtle movements, while \"Complex\" refers to data collected online featuring more complex objects and large-scale movements. \"All\" represents the combined evaluation on both subsets. The best results are in bold."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.551,
+ 0.345,
+ 0.866,
+ 0.38
+ ],
+ "angle": 0,
+ "content": "| Method | Naïve TRELLIS | DreamMesh4D | V2M4 (Ours) |
| Time | 40s | 3 min | 60s |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.384,
+ 0.907,
+ 0.442
+ ],
+ "angle": 0,
+ "content": "Table 3. Average Reconstruction Time per Frame. The displayed time represents the average time taken to reconstruct each frame across an animation sequence. Detailed timing for each step of our method is provided in Appendix A."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.448,
+ 0.907,
+ 0.563
+ ],
+ "angle": 0,
+ "content": "under \\( \\mathcal{C}_{\\mathrm{ref},t} \\) for Gaussian splats of the subsequent meshes \\( \\widetilde{\\mathcal{M}}_{\\mathrm{refine},\\{2,\\dots,T\\}} \\). This setting is to ensure that all parts of the object are captured, even those that might not be visible in the video. We apply higher weights to views from \\( \\mathcal{C}_{\\mathrm{ref}} \\) to ensure accurate alignment with the reference view \\( V_{\\mathrm{ref}} \\). This optimization results in a globally shared texture map \\( \\mathcal{T} \\) for all meshes \\( \\widetilde{\\mathcal{M}}_{\\{1,\\dots,T\\}}^{\\prime} \\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.57,
+ 0.896,
+ 0.587
+ ],
+ "angle": 0,
+ "content": "4.5. Mesh Interpolation and 4D Asset Conversion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.593,
+ 0.907,
+ 0.795
+ ],
+ "angle": 0,
+ "content": "Since adjacent video frames, such as \\( V_{\\mathrm{ref},t} \\) and \\( V_{\\mathrm{ref},t + 1} \\), are typically quite similar, we downsample the time dimension in our practical implementation by selecting every \\( i_{\\mathrm{th}} \\) frame to reconstruct the mesh. This results in a time-reduced mesh sequence. To ensure smooth mesh animation, we linearly interpolate the vertex positions between every two adjacent reconstructed meshes, aligning them with the time resolution of \\( V_{\\mathrm{ref}} \\). Next, we convert the upsampled meshes \\( \\widetilde{\\mathcal{M}}_{\\{1,\\dots,T\\}}^{\\prime} \\) into the mesh \\( \\widetilde{\\mathcal{M}}_1^\\prime \\) plus a deformation tensor \\( \\mathcal{D}\\in \\mathbb{R}^{T\\times N\\times 3} \\), which stores the vertices' deformation over time. By keyframing these offsets and using the globally shared texture map \\( \\mathcal{T} \\), we can generate a GLTF animation file that is compatible with graphics and game engines."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.808,
+ 0.646,
+ 0.825
+ ],
+ "angle": 0,
+ "content": "5. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.833,
+ 0.704,
+ 0.85
+ ],
+ "angle": 0,
+ "content": "5.1. Experimental Setup"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.856,
+ 0.907,
+ 0.903
+ ],
+ "angle": 0,
+ "content": "Please refer to Appendix A for implementation details, and to Appendix B & D for comprehensive ablation studies (including experiments with more advanced 3D genera"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.481,
+ 0.949,
+ 0.519,
+ 0.961
+ ],
+ "angle": 0,
+ "content": "11648"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.087,
+ 0.085,
+ 0.905,
+ 0.727
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.728,
+ 0.908,
+ 0.77
+ ],
+ "angle": 0,
+ "content": "Figure 5. Qualitative Evaluation of Different Methods. We show both the color and normal views of the reconstructed meshes. The first two samples are from the Consistent4D dataset, while the rest are from our collected data. Each sample includes two timestamps for quick comparison. Please zoom in for a clearer view. For more results and animations, see the Supplementary Files."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.796,
+ 0.483,
+ 0.842
+ ],
+ "angle": 0,
+ "content": "tion models such as Hunyuan3D-2.0 [63], TripoSG [19], and advanced dense stereo reconstruction models like VGGT [44]), as well as additional visual results."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.856,
+ 0.484,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Datasets. We constructed a benchmark comprising 40 animation videos. Specifically, we first collected 20 animation videos from Consistent4D [14], which feature sim"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.796,
+ 0.907,
+ 0.888
+ ],
+ "angle": 0,
+ "content": "ple object topologies with subtle movements. Additionally, we gathered 20 animation videos from Mixamo [25] and Sketchfab [38] to include larger-scale object movements and more complex object topologies (with sequences containing more than 200 frames), thus providing a diverse test set for assessing reconstruction performance. Our bench-"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.48,
+ 0.949,
+ 0.52,
+ 0.961
+ ],
+ "angle": 0,
+ "content": "11649"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.093,
+ 0.09,
+ 0.482,
+ 0.244
+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
+ 0.247,
+ 0.485,
+ 0.304
+ ],
+ "angle": 0,
+ "content": "Figure 6. Multi-View Object Geometry Comparison with L4GM. For L4GM, we present the multi-view Gaussian Splats rendering views, while for our method, we display the multi-view rendering views of our mesh. Please zoom in for a clearer view."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.317,
+ 0.483,
+ 0.455
+ ],
+ "angle": 0,
+ "content": "mark is much larger and more varied than those used in existing works [14, 20, 56], which evaluate only 7 test samples (each with just 32 frames). Sample frames from our benchmark can be found in Appendix D. Since existing video segmentation methods [30] can easily extract foreground object regions, the dataset has been pre-processed to remove backgrounds. This ensures that the evaluation remains focused on reconstruction quality rather than segmentation challenges."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.461,
+ 0.484,
+ 0.613
+ ],
+ "angle": 0,
+ "content": "Evaluation Metrics. To evaluate the reconstruction quality, we adopt metrics commonly used in 4D works [32, 56], including CLIP [29], LPIPS [60], and FVD [42], to assess the visual quality of the reconstructed 4D animation through video-to-rendering evaluation. We also include DreamSim [5] due to its excellent performance in evaluating semantic similarity. All these metrics are calculated between the input video frames and the rendered video frames of the reconstructed mesh with an aligned camera viewpoint. Please see Appendix A for details on the metric settings."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.091,
+ 0.622,
+ 0.233,
+ 0.639
+ ],
+ "angle": 0,
+ "content": "5.2. Comparisons"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.644,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Quantitative Evaluation. Since V2M4 directly outputs 4D meshes and most existing 4D works focus on single NeRF or Gaussian Splats outputs, we ensure fair comparisons by evaluating our method against the recent DreamMesh4D [20], which outputs both Gaussian Splats and 4D meshes. We also compare our results with the naive TRELLIS [48], which reconstructs each video frame individually. Table 2 presents the quantitative performance results on our benchmark. For comprehensiveness, we separately display results on Consistent4D data, which features simple topology and subtle movement, and our additional data from Mixamo and Sketchfab, which includes complex topology, intense movement, and longer movement durations. From the results, V2M4 outperforms both other methods, achieving superior performance across all metrics. Additionally, we report processing times in Table 3. Thanks to our interpolation design detailed in Sec-"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.092,
+ 0.905,
+ 0.152
+ ],
+ "angle": 0,
+ "content": "tion 4.5, our method processes each frame in approximately one minute on average, adding little to the naive TRELIS processing time, while being significantly faster than DreamMesh4D."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.157,
+ 0.907,
+ 0.308
+ ],
+ "angle": 0,
+ "content": "Qualitative Evaluation. Fig. 5 show qualitative visual results of the reconstructed meshes across different methods on the Consistent4D data and the newly collected data. We present both the rendering color view and normal view of the meshes. From these visuals, V2M4 produces mesh results with significantly better appearance and topology than DreamMesh4D, and they are much more aligned with the reference videos. These findings verify that V2M4 is effective and generalizable, capable of reconstructing high-quality, usable 4D mesh animations from monocular videos."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.309,
+ 0.909,
+ 0.461
+ ],
+ "angle": 0,
+ "content": "Additionally, to further highlight the advantages of basing the 4D reconstruction task on native 3D mesh models, we qualitatively compare our method with a current powerful 4D Gaussian Splatting reconstruction method, L4GM [32], which explicitly trains a multi-view Gaussian Splatting network. In Fig. 6, we display the multi-view rendering views of our mesh and Gaussian Splats for several cases. We observe that V2M4 preserves more accurate model geometry than L4GM, underscoring the promise of using native 3D mesh generation models for 4D tasks."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.469,
+ 0.642,
+ 0.485
+ ],
+ "angle": 0,
+ "content": "5.3. Limitations"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.491,
+ 0.909,
+ 0.69
+ ],
+ "angle": 0,
+ "content": "While our method effectively reconstructs 4D mesh animations from input videos in many scenarios, it has several limitations. First, since our approach is based on TRELLIS, our method may suffer from performance issues when TRELLIS outputs poor 3D reconstructions (see further analysis in Appendix B). Second, artifacts can occur when reconstructing animations with topology changes, as we enforce topology consistency by registering the first mesh to subsequent frames. Third, using a fixed sampling rate, as discussed in Section 4.5, can be inefficient due to variable motion dynamics—sometimes moving slowly and other times rapidly. Future work could benefit from incorporating adaptive sampling techniques."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
+ 0.701,
+ 0.634,
+ 0.717
+ ],
+ "angle": 0,
+ "content": "6. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.726,
+ 0.909,
+ 0.893
+ ],
+ "angle": 0,
+ "content": "In this work, we propose a 4D reconstruction method capable of directly generating usable 4D mesh animation assets. Our method is built upon a 3D mesh generation model and addresses key challenges, including misalignment between the reconstructed mesh and the input video in terms of pose and appearance, as well as inconsistencies in geometry and texture throughout the animation. Our approach successfully produces high-quality mesh animation files that are compatible with graphics and game software. We believe this work offers a promising solution by enabling direct 4D mesh generation."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
+ 0.48,
+ 0.949,
+ 0.521,
+ 0.961
+ ],
+ "angle": 0,
+ "content": "11650"
+ }
+ ],
+ [
+ {
+ "type": "title",
+ "bbox": [
+ 0.092,
+ 0.091,
+ 0.26,
+ 0.108
+ ],
+ "angle": 0,
+ "content": "Acknowledgements"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.091,
+ 0.117,
+ 0.486,
+ 0.162
+ ],
+ "angle": 0,
+ "content": "This work was supported by funding from King Abdullah University of Science and Technology (KAUST) — Center of Excellence for Generative AI, under award number 5940."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.093,
+ 0.181,
+ 0.188,
+ 0.197
+ ],
+ "angle": 0,
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+# V2M4: 4D Mesh Animation Reconstruction from a Single Monocular Video
+
+Jianqi Chen
+
+Biao Zhang Xiangjun Tang KAUST
+
+Peter Wonka
+
+{jianqi.chen, biao.zhang, xiangjun.tang, peter.wonka}@kaust.edu.sa
+
+
+Figure 1. Given a monocular video, our method can output a high-quality 4D mesh asset readily usable in graphics and game software.
+
+# Abstract
+
+We present V2M4, a novel 4D reconstruction method that directly generates a usable 4D mesh animation asset from a single monocular video. Unlike existing approaches that rely on priors from multi-view image and video generation models, our method is based on native 3D mesh generation models. Naively applying 3D mesh generation models to generate a mesh for each frame in a 4D task can lead to issues such as incorrect mesh poses, misalignment of mesh appearance, and inconsistencies in mesh geometry and texture maps. To address these problems, we propose a structured workflow that includes camera search and mesh reposing, condition embedding optimization for mesh appearance refinement, pairwise mesh registration for topology consistency, and global texture map optimization for texture consistency. Our method outputs high-quality 4D animated assets that are compatible with mainstream graphics and game software. Experimental results across a variety of animation types and motion amplitudes demonstrate the generalization and effectiveness of our method. https://windvchen.github.io/V2M4.
+
+# 1. Introduction
+
+Creating 4D mesh animations is a challenging task. Unlike the synthesis of 3D geometry or 2D images, the scarcity of 4D mesh animations makes it difficult to employ a learning-based framework. Monocular videos provide rich motion cues, making them a potential source for animation reconstruction. However, reconstructing 4D mesh animations from single-view videos remains an underexplored problem, posing challenges in addressing the ambiguity in single-view video and maintaining both visual and topological consistency over time.
+
+Existing methods [14, 15, 31, 32, 40, 47, 49, 54, 56, 59, 62] have explored animation reconstruction based on implicit representations such as NeRF [24] or topology-independent representations like Gaussian Splatting [17]. To mitigate occlusions and ambiguities in single-view videos, these approaches leverage knowledge embedded in multi-view image diffusion [22, 36, 43] and video diffusion [1, 11]. While these methods are viable alternatives, they face disadvantages, such as the difficulty of ensuring 3D consistency in multi-view image diffusion and video diffusion. Additionally, converting these implicit and
+
+topology-independent representations into a mesh representation remains challenging. These factors complicate the use of these methods to obtain a mesh animation that maintains a fine-grained geometric shape and preserves interframe topological consistency.
+
+In this work, we propose V2M4, a method that directly reconstructs a 4D animated mesh from a fixed-viewpoint monocular video. Unlike existing approaches that rely on multi-view image and video diffusion models, our method leverages recent advancements in native 3D mesh reconstruction [12, 48], enabling explicit mesh generation with good shape without the need to convert from other representations. A naive approach to using 3D mesh reconstruction for 4D animation involves generating a mesh for each frame independently. However, this strategy presents several challenges. Chief among these is the uncertainty of the generated mesh pose, where random face orientations and positions lead to misalignment with the video frames. Additionally, there are issues of appearance misalignment, where the generated meshes fail to match the object's appearance in the video. Furthermore, inconsistencies in geometry and topology result in varying mesh structures across frames, and differences in texture maps disrupt the visual continuity of the animation.
+
+To tackle these challenges, we introduce a structured approach that effectively extends the 3D mesh reconstruction model to the 4D mesh animation task. First, we develop a mesh reposing strategy. In this step, we search for camera poses for each reconstructed mesh to ensure semantic alignment with the input video frame by combining particle swarm optimization with a dense stereo reconstruction model's prior. We then re-pose the meshes by applying inverse camera transformations. Second, we refine the appearance of the meshes by optimizing the negative condition embedding of the 3D reconstruction model, enhancing consistency with the video frames. Third, we enforce geometry consistency by selecting the first-frame mesh as a rest pose and introducing a global-to-local mesh registration approach using differential rendering and geometric constraints. Fourth, we optimize a global texture map to ensure texture consistency based on the rendering views of the reconstructed meshes. Finally, we keyframe the meshes and interpolate vertex positions between frames to achieve smoother animation, integrating the results into a GLTF [7] animated file, which is compatible with mainstream graphics software. Fig. 1 displays some of our results. Our main contributions are as follows:
+
+- We introduce the use of native 3D mesh reconstruction models for 4D animated asset generation, enabling the direct creation of explicit 4D meshes with consistent geometry, shared textures, and video-aligned object motions from a fixed-viewpoint monocular video.
+- We propose V2M4, a practical and efficient framework
+
+| Method | 3D Prior Source | Reconstruction Process | Output Format |
| Consistent4D | MV Image and Video Diffusion | Optimization | NeRF |
| STAG4D | MV Image Diffusion | Optimization | GS |
| Diffusion2 | MV Image and Video Diffusion | Optimization | GS |
| EG4D | MV Image and Video Diffusion | Optimization | GS |
| Animate3D | MV-Video Diffusion | Optimization | GS |
| 4Diffusion | MV-Video Diffusion | Optimization | NeRF |
| Diffusion4D | MV-Video Diffusion | Optimization | GS |
| SV4D | MV-Video Diffusion | Optimization | NeRF |
| AR4D | MV Image Diffusion | Recon Network | GS |
| L4GM | MV Image Diffusion | Recon Network | GS |
| DreamMesh4D | MV Image Diffusion | Optimization | Mesh & GS |
| V2M4 (Ours) | Native 3D Mesh Diffusion Model | - | Mesh |
+
+Table 1. Comparison of V2M4 with Existing 4D Reconstruction Methods. “-” indicates the absence of an intermediate reconstruction phase. Not all existing 4D methods are listed, but other approaches are generally similar to those included in the table.
+
+that addresses key challenges associated with using 3D mesh reconstruction models for 4D mesh reconstruction, including incorrect mesh positioning, appearance misalignment, geometry inconsistencies, and texture inconsistencies.
+
+- We conduct extensive evaluations on diverse animations, including humanoid and animal motions, covering a range of motion amplitudes from subtle movements to large-scale motions. The results demonstrate the effectiveness and generalizability of our approach.
+
+# 2. Related Works
+
+Multi-view and Video Diffusion Models. Building on the success of image diffusion models [10, 33], recent works have increasingly focused on the generation of other modalities, such as multi-view images [22, 36, 43] and videos [8, 11, 37]. In multi-view diffusion models, networks predict the 3D structure of an object from an input image. For instance, Zero123 [22] can generate a rendering of an object from a novel camera viewpoint by taking an input image and a target camera pose transition. Subsequent works, such as ImageDream [45] and SyncDream [23], further advance this direction by generating multi-view images in a single forward pass from a single input image. Video diffusion models have seen even more rapid development, driven by the availability of large-scale video datasets. Methods such as Dynamiccafter [50] and Stable Video Diffusion [1] can generate high-quality videos and enable smooth interpolation between frames.
+
+Video-to-4D Reconstruction Models. Due to the scarcity of 4D animated assets, existing research primarily leverages priors learned from multi-view and video generative models to ensure spatial and temporal consistency in reconstructed 4D animations. Consistent4D [14] employs Score Distillation Sampling (SDS) with signals from both pretrained multi-view and video diffusion models. STAG4D [56] follows a similar approach but introduces
+
+an inter-frame key-value mixing mechanism during the denoising process to enhance sequence consistency. To avoid SDS, AR4D [65] instead proposes deforming the initial frame's Gaussian Splats while utilizing priors from multi-view generation models. Diffusion $^{2}$ [54] and EG4D [40] modify the sampling or attention mechanisms to integrate prior knowledge from multi-view image and video diffusion models without relying on SDS. Animate3D [15] and 4Diffusion [59] train multi-view video diffusion models that generate more consistent images for improved SDS optimization. Similarly, Diffusion4D [21] and SV4D [49] also train multi-view video generation models but directly optimize Gaussian Splatting or NeRF on the generated images without SDS. L4GM [32] takes a different approach by training a network that outputs 4D Gaussian Splats given multiview images. However, all of these methods do not output meshes, as discussed in Sec. 1. An alternative approach, DreamMesh4D [20], introduces a hybrid Gaussian-Mesh representation capable of outputting meshes, though it still relies on multi-view and video diffusion model priors and adopts SDS optimization. Other works [39, 52, 53] also attempt to reconstruct meshes from videos but require significantly more input, such as multiple video clips, rendering camera poses, skeletons, or categorical dense feature descriptors, rather than just a single monocular video.
+
+Large Native 3D Mesh Generation Models. Unlike previous indirect 3D generative methods, which either generate multi-view images [23, 41, 45] or implicit representations [51, 57, 58, 64], recent work [12, 48] focuses on directly generating usable meshes by adopting differentiable meshing techniques such as FlexiCubes [35] or DMTet [34]. Instead, they directly predict grid attributes and generate explicit meshes. By training on large collections of synthesized 3D assets, the method achieves impressive generation results conditioned on images.
+
+Ours versus Others. Different from most existing methods that rely on priors from multi-view image or video diffusion models and use NeRF or Gaussian Splitting as representations, we pioneer the use of native 3D mesh generation models for 4D animation reconstruction. Our approach only requires a single monocular video with a fixed camera pose as input, without the need for SDS, and outputs a 4D mesh animation file with consistent geometry and texture. Table 1 illustrates how our approach differs from previous works.
+
+# 3. Preliminaries
+
+Our method builds upon TRELLIS [48], a recently introduced and powerful 3D generation model (we also evaluate our method using more advanced 3D generators, as detailed in Appendix B). TRELLIS encodes 3D assets into a structured latent representation (SLAT), which consists of a
+
+sparse 3D grid embedding both geometric and appearance information. The 3D reconstruction process in TRELLIS can be broadly divided into two phases. In the first phase, TRELLIS employs rectified flow [3] to generate a 3D voxel grid, where the voxel values indicate the object's occupancies. By applying a threshold, TRELLIS extracts a sparse voxel representation. In the second phase, a sparse rectified flow transformer is used to generate the object's SLAT from this sparse voxel grid. Both phases are conditioned on visual features extracted from the input image using DINOv2 [28], along with a negative condition based on the classifier-free technique [9]. The SLAT can then be processed by three independent decoders, which generate meshes, Gaussian Splats [17], and Radiance Fields [6], respectively. For mesh decoding, TRELLIS predicts both the signed distance field (SDF) grid and the parameters of differentiable FlexiCubes [35], enabling the conversion from the SDF into a mesh. Instead of using the predicted mesh vertex colors from the mesh decoder, TRELLIS employs xatlas [55] to compute UV maps of the mesh and then bakes a high-resolution texture map using multi-view observations of its Gaussian Splats.
+
+# 4. Method
+
+Given a reference monocular video sequence of length $T$ , denoted as $V_{\mathrm{ref}} = \{V_{\mathrm{ref},t}\}_{t=1}^{T}$ , which captures an object from a fixed camera pose, our method generates a directly usable 4D animated asset. This asset comprises a static mesh $\mathcal{M}$ with vertices $\mathcal{V} = \{\mathbf{v}_1,\mathbf{v}_2,\dots,\mathbf{v}_N\}$ (or simply $\mathcal{V}\in \mathbb{R}^{N\times 3}$ ) and faces $\mathcal{F}\subset \mathcal{V}\times \mathcal{V}\times \mathcal{V}$ , a texture map $\mathcal{T}$ , and a deformation tensor $\mathcal{D}\in \mathbb{R}^{T\times N\times 3}$ that records the vertices' deformations over time. Initially, each video frame is processed through an image-conditioned 3D generation model, resulting in a set of initial 3D meshes, denoted as $\widetilde{\mathcal{M}}_{\mathrm{init}} = \{\widetilde{\mathcal{M}}_1,\widetilde{\mathcal{M}}_2,\ldots ,\widetilde{\mathcal{M}}_T\}$ . These meshes exhibit inconsistencies with $V_{\mathrm{ref}}$ as well as inter-mesh texture and geometry discrepancies, rendering them unsuitable for direct conversion into a usable 4D asset. To address these issues, our method employs a five-step workflow: repositioning the mesh for accurate object movement (Sec. 4.1), refining object appearance (Sec. 4.2), ensuring inter-frame mesh geometry consistency (Sec. 4.3), maintaining inter-frame mesh texture consistency (Sec. 4.3), and ultimately converting the 3D assets into 4D assets (Sec. 4.5). The complete workflow is illustrated in Fig. 2.
+
+# 4.1. Camera Search and Mesh Re-Pose
+
+Due to the setup of training TRELLIS, the initial meshes $\widetilde{\mathcal{M}}_{\mathrm{init}}$ often tend to have a canonical face orientation along one axis (as illustrated in Fig. 2), and their positions may also sometimes be canonicalized to the origin of the coordinate system. This results in a significant loss of object motion information, such as translation and rotation. To re
+
+
+Figure 2. The Workflow of V2M4. Upon receiving a video sequence $V_{\mathrm{ref}}$ , we generate coarse 3D meshes for each frame, denoted as $\widetilde{\mathcal{M}}_{\{1,\dots,t\}}$ . These initial meshes do not accurately capture the object's movement and appearance as depicted in the input video, and they exhibit inconsistencies in topology and texture. Our method employs a five-stage process: (1) Repose the mesh to accurately reflect object movement; (2) Refine the mesh appearance based on the reference video frames; (3) Ensure inter-mesh topology consistency through mesh registration; (4) Optimize a globally shared texture map across all meshes; (5) Keyframe the meshes, perform interpolation, and convert them into a directly usable 4D animation asset.
+
+cover these motions, we propose first determining the camera pose $\mathcal{C} \in \mathbb{R}^6 = \{\mathrm{yaw},\mathrm{pitch},\mathrm{radius},\mathrm{lookat}_{x,y,z}\}$ for each reconstructed mesh $\widetilde{\mathcal{M}}_t$ , ensuring the rendered view is semantically similar to the corresponding video frame. Then, we can invert the camera pose and apply the transformation to the mesh, effectively recovering mesh motion from the camera motion.
+
+Since directly optimizing camera parameters via gradient descent from a random starting point using differentiable rendering tools like Nvdiffrast [18] often leads to poor local minima, we propose a more robust camera pose search strategy. Specifically, we begin by sampling a large number of camera positions around the object and selecting the top $n$ positions that exhibit high similarity to the reference video frame, denoted as $V_{\mathrm{ref},t}$ . We then utilize a pretrained dense stereo model to process the rendering views under these $n$ cameras and $V_{\mathrm{ref},t}$ , obtaining the predicted point clouds for each view. Next, we design to extract the camera pose $C_{\mathrm{ref},t,\mathrm{DUSt3R}}$ for the reference image from these point clouds. This pose $C_{\mathrm{ref},t,\mathrm{DUSt3R}}$ is added back to the initial pool of camera pose candidates, and we employ the Particle Swarm Optimization (PSO) algorithm to refine this into a more accurate camera pose $C_{\mathrm{ref},t,\mathrm{PSO}}$ . Subsequently, we further refine the camera pose using gradient descent optimization, starting from the improved point $C_{\mathrm{ref},t,\mathrm{PSO}}$ , to obtain the final $C_{\mathrm{ref},t}$ . Finally, we derive the camera motion from $C_{\mathrm{ref},t}$ , invert it, and apply this transformation to $\widetilde{\mathcal{M}}_t$ to obtain $\widetilde{\mathcal{M}}_{\mathrm{repose},t}$ . The entire workflow is detailed in Algorithm 1.
+
+Below, we provide more details about the three key com
+
+# Algorithm 1 Camera Search and Mesh Re-Pose
+
+Require: Initial mesh $\widetilde{\mathcal{M}}_t$ , reference frame $V_{\mathrm{ref},t}$ at time $t$ , pretrained dense stereo reconstruction model DUSt3R
+
+1: Initialize a set of sampled camera poses $P_0$
+2: Select the top $n$ camera poses based on similarity to $V_{\mathrm{ref},t}$ . Render views under these poses and input them, along with $V_{\mathrm{ref},t}$ , into the DUSt3R
+3: DUSt3R Estimation: Align DUSt3R-predicted point clouds with ground-truth point clouds
+4: Optimize the camera extrinsic matrix to derive $\mathcal{C}_{\mathrm{ref},t,\mathrm{DUS3R}}$
+5: PSO Search: Add $C_{\mathrm{ref},t,\mathrm{DUS3R}}$ to the top $K$ camera poses from $P_0$ , then apply PSO
+6: Select the best camera pose $C_{\mathrm{ref},t,\mathrm{PSO}}$ after iterations
+7: Gradient Descent Refinement: Refine by minimizing mask discrepancy with $V_{\mathrm{ref},t}$
+8: Obtain the final optimized camera pose $\mathcal{C}_{\mathrm{ref},t}$
+9: Mesh Re-pose: Apply the inverse of $\mathcal{C}_{\mathrm{ref},t}$ to $\widetilde{\mathcal{M}}_t$ to obtain $\widetilde{\mathcal{M}}_{\mathrm{repose},t}$
+10: return Re-posed mesh $\widetilde{\mathcal{M}}_{\mathrm{repose},t}$
+
+ponents involved.
+
+Camera Search Using Particle Swarm Optimization. We use PSO [16] algorithm to search for the aligned camera pose. To effectively explore the search space and avoid the local minima problem encountered with direct gradient descent, we sample $P$ particles (camera poses) around the object. The sampling strategy is designed to ensure that the
+
+
+Figure 3. Camera Pose Extraction from Dense Stereo Reconstruction for $V_{\mathrm{ref},t}$ . We first obtain estimated point clouds $\overline{\mathrm{PC}}_{\mathrm{ref}}$ and $\overline{\mathrm{PC}}_{\mathrm{rend}}$ from the DUSt3R model for reference video frame $V_{\mathrm{ref},t}$ and rendering views $V_{\mathrm{rend}}$ . We then align $\overline{\mathrm{PC}}_{\mathrm{rend}}$ with the point clouds $\mathrm{PC}_{\mathrm{rend}}$ obtained from mesh $\widetilde{\mathcal{M}}_t$ during rasterization (Note the differences in axis direction and scale depicted in the figure.). This transformation is then applied to $\overline{\mathrm{PC}}_{\mathrm{ref}}$ , resulting in the transformed $\mathrm{PC}_{\mathrm{ref}}$ . Finally, we optimize to determine the camera pose $C_{\mathrm{ref},t}$ that ensures accurate mapping from 3D to 2D points.
+
+yaw and pitch values are uniformly distributed over a unit sphere, while the radius is sampled according to the surface area of the sphere along with its radius. The $\mathrm{lookat}_{x,y,z}$ values are uniformly sampled within a predefined range. For the objective function, we utilize DreamSim [5], which is more effective at evaluating the similarity between the rendered view of the imperfectly reconstructed mesh and the reference video frame, compared to conventional methods like MSE or LPIPS [61]. The positions of the particles (camera pose values) are iteratively updated based on both their individual best-known position and the best-known position of the entire swarm, with added noise randomness. The final best one is selected as the reference image's camera pose $C_{\mathrm{ref},t,\mathrm{PSO}}$ .
+
+Knowledge Utilization from Dense Stereo Reconstruction Model. To enhance the robustness of the PSO search, we leverage prior knowledge from a pretrained dense stereo model, specifically DUSt3R [46]. DUSt3R can predict inter-frame camera motion and 3D point positions corresponding to each view's 2D pixels. While a straightforward approach would involve feeding both the reference video frame $V_{\mathrm{ref},t}$ and a set of rendered views $V_{\mathrm{rend},\{1,\dots,n\}}$ around $\widetilde{\mathcal{M}}_t$ into DUSt3R and using the predicted relative camera motion to estimate the camera pose of $V_{\mathrm{ref},t}$ , this poses challenges. Differences in camera models and coordinate settings, such as scale and orientation, complicate matrix conversions, and semantic discrepancies between $V_{\mathrm{ref},t}$ and $V_{\mathrm{rend},\{1,\dots,n\}}$ can lead to inaccurate motion predictions. To overcome these issues, we focus on the point clouds estimated by DUSt3R instead of relying on the predicted cam
+
+era motions. Let $\overline{\mathrm{PC}}_{\mathrm{ref}}$ and $\overline{\mathrm{PC}}_{\mathrm{rend},\{1,\dots,n\}}$ represent the predicted point clouds for $V_{\mathrm{ref},t}$ and $V_{\mathrm{rend},\{1,\dots,n\}}$ , respectively. Given that the camera model, camera poses, and $\widetilde{\mathcal{M}}_t$ are known for rendering $V_{\mathrm{rend},\{1,\dots,n\}}$ , we can derive the ground-truth point clouds in our coordinate system, denoted as $\mathrm{PC}_{\mathrm{rend},\{1,\dots,n\}}$ . We align the predicted point clouds with the ground truth using a global transformation (rotation, translation, and scale) optimized via Chamfer distance [4]. Applying this transformation to $\overline{\mathrm{PC}}_{\mathrm{ref}}$ , we obtain $\mathrm{PC}_{\mathrm{ref}}$ . Ideally, with the correct camera pose $\mathcal{C}_{\mathrm{ref},t}$ , the 3D positions of $\mathrm{PC}_{\mathrm{ref}}$ should project onto the 2D pixel coordinates of $V_{\mathrm{ref},t}$ . We optimize the camera's extrinsic matrix to ensure this alignment, thereby deriving the reference image camera pose $\mathcal{C}_{\mathrm{ref},t}$ from the extrinsic matrix.
+
+Camera Refinement via Gradient Descent. Given an approximately aligned camera pose where the rendering view matches $V_{\mathrm{ref},t}$ , we further refine this alignment by applying gradient descent optimization on the camera pose. Specifically, we minimize the discrepancy between the mask region of the rendering view—defined as the pixels covered by the object during rasterization—and the object region in $V_{\mathrm{ref},t}$ . With a well-initialized starting point, the gradient descent efficiently converges to a near-optimal solution for $\mathcal{C}_{\mathrm{ref},t}$ .
+
+# 4.2. Mesh Appearance Refinement via Negative Condition Embedding Optimization
+
+With $\mathcal{C}_{\mathrm{ref},t}$ , the object's viewpoint is now synchronized with the video frame. This alignment allows us to leverage supervision from $V_{\mathrm{ref},t}$ to improve the consistency of the mesh appearance with the input video. Inspired by techniques in image editing [2, 26], we propose optimizing the negative condition embedding during the second phase of TRELLIS inference (described in Sec. 3). This optimization preserves the priors learned by the network, as opposed to directly optimizing the final output SLAT. We begin optimization after a few denoising steps with the sparse flow transformer, ensuring that the object's structure is roughly generated. The optimization objective is to maximize similarity (measured by DreamSim, MSE, and LPIPS, with a regularization term to prevent significant deviation from the initial values) between the rendered view of the decoded SLAT (both mesh and Gaussian splats) under the camera pose $\mathcal{C}_{\mathrm{ref},t}$ and the reference video frame $V_{\mathrm{ref},t}$ . The optimization is performed over multiple iterations for each denoising timestep. We denote the refined mesh as $\widetilde{\mathcal{M}}_{\mathrm{refine},t}$ .
+
+# 4.3. Consistent Topology via Iterative Pairwise Registration
+
+Due to the inherent randomness of the generation model, reconstructed meshes from adjacent video frames often exhibit variations in topology, such as differing numbers of vertices and faces, as well as changes in vertex and edge
+
+
+(a) Mesh 1
+
+
+(b) Mesh 2 - Registered from Mesh 1
+Figure 4. Comparison of Vertex Positions Between Original and Registered Meshes. We compare the vertex correspondences between mesh 1 and mesh 2, where mesh 2 is registered from mesh 1. To visualize these correspondences, we use the vertex normals of mesh 1 to color both meshes, highlighting their alignment.
+
+connectivity. To create a valid 4D animation asset with consistent geometry, we propose an iterative pairwise registration approach. For two consecutive meshes after refinement, $\widetilde{\mathcal{M}}_{\mathrm{refine},t}$ and $\widetilde{\mathcal{M}}_{\mathrm{refine},t + 1}$ , we begin by treating $\widetilde{\mathcal{M}}_{\mathrm{refine},t}$ as a rigid body. We optimize its global transformation (rotation, translation, and scale) to align it with $\widetilde{\mathcal{M}}_{\mathrm{refine},t + 1}$ using Chamfer distance and a differentiable rendering loss. After achieving global registration, we refine the alignment using the preconditioned optimization proposed by [27], which allows for fast and smooth convergence in the inverse reconstruction process. However, the differentiable rendering loss from [27] can struggle with regions undergoing large deformations or containing long, thin structures. To improve registration in these areas, we incorporate the As-Rigid-As-Possible (ARAP) constraint [13] alongside the Chamfer distance for enhanced local registration. Through these global and local alignment steps, we obtain a deformed version $\widetilde{\mathcal{M}}_t^\prime$ (with vertices $\nu_{t}^{\prime}$ and faces $\mathcal{F}_t^\prime$ ) of $\widetilde{\mathcal{M}}_{\mathrm{refine},t}$ ( $\nu_{t}$ and faces $\mathcal{F}_t$ ), ensuring that the number and topology are identical ( $\nu_{t}^{\prime} = \nu_{t}$ , $\mathcal{F}_t^\prime = \mathcal{F}_t$ ) and closely resemble the shape of $\widetilde{\mathcal{M}}_{\mathrm{refine},t + 1}$ . We then replace the initial $\widetilde{\mathcal{M}}_{\mathrm{refine},t + 1}$ with the deformed $\widetilde{\mathcal{M}}_t^\prime$ . In practice, we designate $\widetilde{\mathcal{M}}_{\mathrm{refine},1}$ as the rest pose and iteratively apply the registration process across consecutive frames. This ensures consistent geometry across all meshes $\widetilde{\mathcal{M}}_{\{1,\dots,T\}}^{\prime}$ .
+
+# 4.4. Consistent Texture Map via Weighted Optimization
+
+After the mesh registration process outlined in Sec. 4.3, we observe that the deformed vertices maintain their correspondence to the initial parts of the object. For instance, vertices representing the left side of the face remain aligned with the left face region (as illustrated in Fig. 4). Therefore, we directly inherit the texture map and UV coordinates of $\widetilde{\mathcal{M}}_1'$ for the subsequent meshes $\widetilde{\mathcal{M}}_{\{2,\dots,T\}}^{\prime}$ . To refine the texture and minimize artifacts, we further optimize the texture map using multi-view renderings of Gaussian splats generated alongside $\widetilde{\mathcal{M}}_{\mathrm{refine},1}$ (see Sec. 3), while using a single view
+
+| Simple | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8905 | 0.1597 | 1342.66 | 0.1282 |
| DreamMesh4D | 0.8692 | 0.1019 | 914.28 | 0.0937 |
| V2M4 (Ours) | 0.9259 | 0.1017 | 825.59 | 0.0688 |
| Complex | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8887 | 0.1265 | 1216.19 | 0.1492 |
| DreamMesh4D | 0.8256 | 0.0804 | 1079.02 | 0.1850 |
| V2M4 (Ours) | 0.9008 | 0.0747 | 666.04 | 0.1220 |
| All | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8891 | 0.1352 | 1014.45 | 0.1438 |
| DreamMesh4D | 0.8369 | 0.0860 | 855.29 | 0.1613 |
| V2M4 (Ours) | 0.9073 | 0.0817 | 576.73 | 0.1082 |
+
+Table 2. Quantitative Evaluation of Different Methods. All metrics are computed using the rendering view of the reconstructed meshes. "Simple" refers to the Consistent4D data, which consists of simple objects with subtle movements, while "Complex" refers to data collected online featuring more complex objects and large-scale movements. "All" represents the combined evaluation on both subsets. The best results are in bold.
+
+| Method | Naïve TRELLIS | DreamMesh4D | V2M4 (Ours) |
| Time | 40s | 3 min | 60s |
+
+Table 3. Average Reconstruction Time per Frame. The displayed time represents the average time taken to reconstruct each frame across an animation sequence. Detailed timing for each step of our method is provided in Appendix A.
+
+under $\mathcal{C}_{\mathrm{ref},t}$ for Gaussian splats of the subsequent meshes $\widetilde{\mathcal{M}}_{\mathrm{refine},\{2,\dots,T\}}$ . This setting is to ensure that all parts of the object are captured, even those that might not be visible in the video. We apply higher weights to views from $\mathcal{C}_{\mathrm{ref}}$ to ensure accurate alignment with the reference view $V_{\mathrm{ref}}$ . This optimization results in a globally shared texture map $\mathcal{T}$ for all meshes $\widetilde{\mathcal{M}}_{\{1,\dots,T\}}^{\prime}$ .
+
+# 4.5. Mesh Interpolation and 4D Asset Conversion
+
+Since adjacent video frames, such as $V_{\mathrm{ref},t}$ and $V_{\mathrm{ref},t + 1}$ , are typically quite similar, we downsample the time dimension in our practical implementation by selecting every $i_{\mathrm{th}}$ frame to reconstruct the mesh. This results in a time-reduced mesh sequence. To ensure smooth mesh animation, we linearly interpolate the vertex positions between every two adjacent reconstructed meshes, aligning them with the time resolution of $V_{\mathrm{ref}}$ . Next, we convert the upsampled meshes $\widetilde{\mathcal{M}}_{\{1,\dots,T\}}^{\prime}$ into the mesh $\widetilde{\mathcal{M}}_1^\prime$ plus a deformation tensor $\mathcal{D}\in \mathbb{R}^{T\times N\times 3}$ , which stores the vertices' deformation over time. By keyframing these offsets and using the globally shared texture map $\mathcal{T}$ , we can generate a GLTF animation file that is compatible with graphics and game engines.
+
+# 5. Experiments
+
+# 5.1. Experimental Setup
+
+Please refer to Appendix A for implementation details, and to Appendix B & D for comprehensive ablation studies (including experiments with more advanced 3D genera
+
+
+Figure 5. Qualitative Evaluation of Different Methods. We show both the color and normal views of the reconstructed meshes. The first two samples are from the Consistent4D dataset, while the rest are from our collected data. Each sample includes two timestamps for quick comparison. Please zoom in for a clearer view. For more results and animations, see the Supplementary Files.
+
+tion models such as Hunyuan3D-2.0 [63], TripoSG [19], and advanced dense stereo reconstruction models like VGGT [44]), as well as additional visual results.
+
+Datasets. We constructed a benchmark comprising 40 animation videos. Specifically, we first collected 20 animation videos from Consistent4D [14], which feature sim
+
+ple object topologies with subtle movements. Additionally, we gathered 20 animation videos from Mixamo [25] and Sketchfab [38] to include larger-scale object movements and more complex object topologies (with sequences containing more than 200 frames), thus providing a diverse test set for assessing reconstruction performance. Our bench-
+
+
+Figure 6. Multi-View Object Geometry Comparison with L4GM. For L4GM, we present the multi-view Gaussian Splats rendering views, while for our method, we display the multi-view rendering views of our mesh. Please zoom in for a clearer view.
+
+mark is much larger and more varied than those used in existing works [14, 20, 56], which evaluate only 7 test samples (each with just 32 frames). Sample frames from our benchmark can be found in Appendix D. Since existing video segmentation methods [30] can easily extract foreground object regions, the dataset has been pre-processed to remove backgrounds. This ensures that the evaluation remains focused on reconstruction quality rather than segmentation challenges.
+
+Evaluation Metrics. To evaluate the reconstruction quality, we adopt metrics commonly used in 4D works [32, 56], including CLIP [29], LPIPS [60], and FVD [42], to assess the visual quality of the reconstructed 4D animation through video-to-rendering evaluation. We also include DreamSim [5] due to its excellent performance in evaluating semantic similarity. All these metrics are calculated between the input video frames and the rendered video frames of the reconstructed mesh with an aligned camera viewpoint. Please see Appendix A for details on the metric settings.
+
+# 5.2. Comparisons
+
+Quantitative Evaluation. Since V2M4 directly outputs 4D meshes and most existing 4D works focus on single NeRF or Gaussian Splats outputs, we ensure fair comparisons by evaluating our method against the recent DreamMesh4D [20], which outputs both Gaussian Splats and 4D meshes. We also compare our results with the naive TRELLIS [48], which reconstructs each video frame individually. Table 2 presents the quantitative performance results on our benchmark. For comprehensiveness, we separately display results on Consistent4D data, which features simple topology and subtle movement, and our additional data from Mixamo and Sketchfab, which includes complex topology, intense movement, and longer movement durations. From the results, V2M4 outperforms both other methods, achieving superior performance across all metrics. Additionally, we report processing times in Table 3. Thanks to our interpolation design detailed in Sec-
+
+tion 4.5, our method processes each frame in approximately one minute on average, adding little to the naive TRELIS processing time, while being significantly faster than DreamMesh4D.
+
+Qualitative Evaluation. Fig. 5 show qualitative visual results of the reconstructed meshes across different methods on the Consistent4D data and the newly collected data. We present both the rendering color view and normal view of the meshes. From these visuals, V2M4 produces mesh results with significantly better appearance and topology than DreamMesh4D, and they are much more aligned with the reference videos. These findings verify that V2M4 is effective and generalizable, capable of reconstructing high-quality, usable 4D mesh animations from monocular videos.
+
+Additionally, to further highlight the advantages of basing the 4D reconstruction task on native 3D mesh models, we qualitatively compare our method with a current powerful 4D Gaussian Splatting reconstruction method, L4GM [32], which explicitly trains a multi-view Gaussian Splatting network. In Fig. 6, we display the multi-view rendering views of our mesh and Gaussian Splats for several cases. We observe that V2M4 preserves more accurate model geometry than L4GM, underscoring the promise of using native 3D mesh generation models for 4D tasks.
+
+# 5.3. Limitations
+
+While our method effectively reconstructs 4D mesh animations from input videos in many scenarios, it has several limitations. First, since our approach is based on TRELLIS, our method may suffer from performance issues when TRELLIS outputs poor 3D reconstructions (see further analysis in Appendix B). Second, artifacts can occur when reconstructing animations with topology changes, as we enforce topology consistency by registering the first mesh to subsequent frames. Third, using a fixed sampling rate, as discussed in Section 4.5, can be inefficient due to variable motion dynamics—sometimes moving slowly and other times rapidly. Future work could benefit from incorporating adaptive sampling techniques.
+
+# 6. Conclusion
+
+In this work, we propose a 4D reconstruction method capable of directly generating usable 4D mesh animation assets. Our method is built upon a 3D mesh generation model and addresses key challenges, including misalignment between the reconstructed mesh and the input video in terms of pose and appearance, as well as inconsistencies in geometry and texture throughout the animation. Our approach successfully produces high-quality mesh animation files that are compatible with graphics and game software. We believe this work offers a promising solution by enabling direct 4D mesh generation.
+
+# Acknowledgements
+
+This work was supported by funding from King Abdullah University of Science and Technology (KAUST) — Center of Excellence for Generative AI, under award number 5940.
+
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| Consistent4D | MV Image and Video Diffusion | Optimization | NeRF |
| STAG4D | MV Image Diffusion | Optimization | GS |
| Diffusion2 | MV Image and Video Diffusion | Optimization | GS |
| EG4D | MV Image and Video Diffusion | Optimization | GS |
| Animate3D | MV-Video Diffusion | Optimization | GS |
| 4Diffusion | MV-Video Diffusion | Optimization | NeRF |
| Diffusion4D | MV-Video Diffusion | Optimization | GS |
| SV4D | MV-Video Diffusion | Optimization | NeRF |
| AR4D | MV Image Diffusion | Recon Network | GS |
| L4GM | MV Image Diffusion | Recon Network | GS |
| DreamMesh4D | MV Image Diffusion | Optimization | Mesh & GS |
| V2M4 (Ours) | Native 3D Mesh Diffusion Model | - | Mesh |
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+ "content": "Our method builds upon TRELLIS [48], a recently introduced and powerful 3D generation model (we also evaluate our method using more advanced 3D generators, as detailed in Appendix B). TRELLIS encodes 3D assets into a structured latent representation (SLAT), which consists of a"
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+ "content": "sparse 3D grid embedding both geometric and appearance information. The 3D reconstruction process in TRELLIS can be broadly divided into two phases. In the first phase, TRELLIS employs rectified flow [3] to generate a 3D voxel grid, where the voxel values indicate the object's occupancies. By applying a threshold, TRELLIS extracts a sparse voxel representation. In the second phase, a sparse rectified flow transformer is used to generate the object's SLAT from this sparse voxel grid. Both phases are conditioned on visual features extracted from the input image using DINOv2 [28], along with a negative condition based on the classifier-free technique [9]. The SLAT can then be processed by three independent decoders, which generate meshes, Gaussian Splats [17], and Radiance Fields [6], respectively. For mesh decoding, TRELLIS predicts both the signed distance field (SDF) grid and the parameters of differentiable FlexiCubes [35], enabling the conversion from the SDF into a mesh. Instead of using the predicted mesh vertex colors from the mesh decoder, TRELLIS employs xatlas [55] to compute UV maps of the mesh and then bakes a high-resolution texture map using multi-view observations of its Gaussian Splats."
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+ "content": " that records the vertices' deformations over time. Initially, each video frame is processed through an image-conditioned 3D generation model, resulting in a set of initial 3D meshes, denoted as "
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+ "content": " as well as inter-mesh texture and geometry discrepancies, rendering them unsuitable for direct conversion into a usable 4D asset. To address these issues, our method employs a five-step workflow: repositioning the mesh for accurate object movement (Sec. 4.1), refining object appearance (Sec. 4.2), ensuring inter-frame mesh geometry consistency (Sec. 4.3), maintaining inter-frame mesh texture consistency (Sec. 4.3), and ultimately converting the 3D assets into 4D assets (Sec. 4.5). The complete workflow is illustrated in Fig. 2."
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+ "content": ". Render views under these poses and input them, along with "
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+ "content": " can lead to inaccurate motion predictions. To overcome these issues, we focus on the point clouds estimated by DUSt3R instead of relying on the predicted cam"
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+ "type": "text",
+ "content": "connectivity. To create a valid 4D animation asset with consistent geometry, we propose an iterative pairwise registration approach. For two consecutive meshes after refinement, "
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+ "type": "text",
+ "content": " using Chamfer distance and a differentiable rendering loss. After achieving global registration, we refine the alignment using the preconditioned optimization proposed by [27], which allows for fast and smooth convergence in the inverse reconstruction process. However, the differentiable rendering loss from [27] can struggle with regions undergoing large deformations or containing long, thin structures. To improve registration in these areas, we incorporate the As-Rigid-As-Possible (ARAP) constraint [13] alongside the Chamfer distance for enhanced local registration. Through these global and local alignment steps, we obtain a deformed version "
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+ "content": " and faces "
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+ "type": "text",
+ "content": "), ensuring that the number and topology are identical ("
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+ "type": "inline_equation",
+ "content": "\\nu_{t}^{\\prime} = \\nu_{t}"
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+ "type": "inline_equation",
+ "content": "\\mathcal{F}_t^\\prime = \\mathcal{F}_t"
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+ {
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+ "type": "text",
+ "content": ") and closely resemble the shape of "
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+ "type": "inline_equation",
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+ "content": ". We then replace the initial "
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+ "type": "inline_equation",
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+ "type": "text",
+ "content": ". In practice, we designate "
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+ "type": "text",
+ "content": " as the rest pose and iteratively apply the registration process across consecutive frames. This ensures consistent geometry across all meshes "
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| Naïve TRELLIS | 0.8905 | 0.1597 | 1342.66 | 0.1282 |
| DreamMesh4D | 0.8692 | 0.1019 | 914.28 | 0.0937 |
| V2M4 (Ours) | 0.9259 | 0.1017 | 825.59 | 0.0688 |
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| Naïve TRELLIS | 0.8887 | 0.1265 | 1216.19 | 0.1492 |
| DreamMesh4D | 0.8256 | 0.0804 | 1079.02 | 0.1850 |
| V2M4 (Ours) | 0.9008 | 0.0747 | 666.04 | 0.1220 |
| All | Method | CLIP↑ | LPIPS↓ | FVD↓ | DreamSim↓ |
| Naïve TRELLIS | 0.8891 | 0.1352 | 1014.45 | 0.1438 |
| DreamMesh4D | 0.8369 | 0.0860 | 855.29 | 0.1613 |
| V2M4 (Ours) | 0.9073 | 0.0817 | 576.73 | 0.1082 |
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| Time | 40s | 3 min | 60s |
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diff --git a/2025/V2PE_ Improving Multimodal Long-Context Capability of Vision-Language Models with Variable Visual Position Encoding/75b04339-69b5-48e5-a71f-b17b99c6243a_content_list.json b/2025/V2PE_ Improving Multimodal Long-Context Capability of Vision-Language Models with Variable Visual Position Encoding/75b04339-69b5-48e5-a71f-b17b99c6243a_content_list.json
new file mode 100644
index 0000000000000000000000000000000000000000..0a831520775ff3938412468d00118811b0674f9d
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+ "text": "V2PE: Improving Multimodal Long-Context Capability of Vision-Language Models with Variable Visual Position Encoding",
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+ "text": "Junqi Ge $^{1,4*}$ , Ziyi Chen $^{1,4*}$ , Jintao Lin $^{3,4*}$ , Jinguo Zhu $^{4*}$ , Xihui Liu $^{3}$ , Jifeng Dai $^{1,4}$ , Xizhou Zhu $^{1,2,4\\dagger}$",
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+ "text": "$^{1}$ Tsinghua University $^{2}$ SenseTime Research $^{3}$ University of Hong Kong $^{4}$ Shanghai AI Laboratory",
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+ "text": "Vision-Language Models (VLMs) have shown promising capabilities in handling various multimodal tasks, yet they struggle in long-context scenarios, particularly tasks involving videos, high-resolution images, or lengthy image-text documents. In our work, we first conduct an empirical analysis of VLMs' long-context capabilities using our augmented long-context multimodal datasets. Our findings reveal that directly applying the positional encoding mechanism used for textual tokens to visual tokens is suboptimal, and VLM performance degrades sharply when the position encoding exceeds the model's context window. To address this, we propose Variable Visual Position Encoding (V2PE), a novel positional encoding approach that employs variable and smaller increments for visual tokens, enabling more efficient management of long multimodal sequences. Our experiments demonstrate the effectiveness of V2PE in enhancing VLMs' ability to effectively understand and reason over long multimodal contexts. We further integrate V2PE with our augmented long-context multimodal datasets to fine-tune the open-source VLMs. The fine-tuned model achieves strong performance on both standard and long-context multimodal tasks. Notably, when the sequence length of the training dataset is increased to 256K tokens, the model is capable of processing multimodal sequences up to 1M tokens, highlighting its potential for real-world long-context applications. We shall release the code, model weights, and datasets to facilitate further research.",
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+ "text": "1. Introduction",
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+ "text": "With the rapid advancement of Large Language Models (LLMs) [14, 29, 83, 99, 108], Vision-Language Models (VLMs) have made substantial strides [19, 82, 103, 115], excelling at tasks like visual captioning [17], visual question answering [78], and complex visual reasoning [136]. Despite this progress, existing research [112, 119, 132, 144]",
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+ "Figure 1. Performance on the image retrieval task using a token length of up to 1M on MM-NIAH [119] across different VLMs. The GPT-4o [81] version is 2024-08-06, while InternVL2-2B [20] models are both fine-tuned from the official release, using our augmented data, with token lengths reaching up to 256K per sample."
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+ "text": "reveals that VLMs struggle to generalize effectively when confronted with multimodal long-sequence inputs (e.g., long videos [121, 126], high-resolution images [45, 122], and lengthy image-text documents [3, 105, 151]). This limitation emerges even in relatively straightforward, such as object counting and passkey duplication, significantly restricting VLMs' potential applications and impeding the enhancement of user experience [22, 114, 119, 120].",
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+ "text": "Recent efforts have attempted to extend VLMs' capabilities to process multiple images or handle long multimodal sequences. However, these approaches either permit only a small number of images (typically fewer than five) [52, 65, 149] or primarily target video data (e.g., LongVA [144], LongVILA [132], LongLLAVA [120], VideoXL [93]). These studies are only limited to specific application scenarios, highlighting the challenges VLMs face in handling complex and long-sequence multimodal data, which makes a key research question particularly urgent: Why do VLMs perform poorly in long-context scenarios, and how can we unlock their capacity for comprehensive multimodal understanding and reasoning over long sequences?",
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+ "text": "To investigate this, we first construct a large-scale pool of long-context multimodal datasets to evaluate and analyze VLM capabilities systematically. By extending the se",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "image_caption": [
+ "Figure 2. Illustration from our proposed Variable Visual Position Encoding (V2PE). Unlike the standard position encoding used in most VLMs, which shares the same stepwise positional increment for both visual and textual tokens, our proposed Variable Visual Positional Encoding (V2PE) uses smaller and variable positional increments specifically for visual tokens compared to textual tokens. This flexible design enables VLMs to handle long-context multimodal sequences within a limited context window."
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+ {
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+ "text": "quence length of existing instruction-tuning datasets (e.g., DocVQA [78], ChartQA [77], SQA [72]) to 32K-64K tokens, we adapt these datasets specifically to train and validate VLMs for enhanced long-context capabilities. We also extend long-context benchmarks from 64K to 1M tokens (e.g., by employing the official MM-NIAH [119] curation code) to validate VLM performance with longer contexts, providing a deeper understanding of the limitations.",
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+ "text": "Our empirical analysis shows that the design of positional encodings of visual tokens plays an essential role in long-context scenarios, which is often overlooked in previous studies. Specifically, (1) directly applying the LLM positional encoding mechanism to visual tokens is suboptimal, and (2) the performance of VLMs degrades significantly when positional encodings for visual tokens exceed the trained context window, and previous position encoding extension methods applicable to LLMs provide only marginal improvements. These findings highlight the need for specialized positional encoding methods to manage visual tokens in long-context multimodal scenarios effectively.",
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+ "text": "To address these challenges, we propose Variable Visual Position Encoding (V2PE), a novel approach for handling visual token positions in VLMs. Considering the continuity nature of pixel space, adjacent visual tokens exhibit greater similarity than adjacent text tokens. Thus, V2PE uses smaller positional increments for visual tokens than text tokens (see Fig. 2). Furthermore, V2PE employs variable positional increments for visual tokens during training, enabling the model to learn and adapt to position encoding in various scenarios. This variable adjustment allows the model to effectively handle different numbers and complexities of image inputs during inference, thereby enhancing its stability and adaptability in long-context processing.",
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+ "text": "In experiments, we apply V2PE to enhance the long-context capability of open-source VLMs [19, 20], and fine-tune them using our extended multimodal datasets. The resulting models not only maintain strong performance on standard short-context multimodal benchmarks, but also excel in tasks requiring long-context handling, which outperform traditional token compression and other position encoding extension methods. In particular, after further fine-tuning on multimodal sequences up to 256K tokens, our model achieves promising performance in multimodal retrieval tasks involving sequences as long as 1M tokens, as shown in Fig. 1. The main contributions of this paper are as follows:",
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+ "- We construct mixed datasets to improve VLMs' long-context capability by augmenting existing multimodal instruction tuning datasets and conduct a thorough investigation into why current VLMs struggle with long-context multimodal inputs, revealing that directly applying LLM positional encoding to visual tokens is ineffective.",
+ "- We propose Variable Visual Position Encoding (V2PE), a novel positional encoding strategy that employs variable and smaller increments for visual tokens, significantly enhancing VLMs' ability to understand and reason over extended multimodal contexts.",
+ "- We apply our V2PE method and extend training data on the open-source VLMs. The fine-tuned VLMs perform exceptionally well on both general multimodal benchmarks and long-context multimodal tasks, with the capacity to handle sequences of up to 1M tokens, significantly longer than training sequence."
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+ "text": "2. Related Works",
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+ "text": "Vision-Language Models (VLMs). With the development of Large Language Models (LLMs) [6, 10, 14, 36, 83, 99, 101, 104, 107, 108, 123, 124, 134, 148], the integration of vision and language modalities is significantly catalyzed. This progress gives rise to Vision-Language Models (VLM), which can perceive visual contents, conduct visual reasoning, and engage in multi-modal dialogue with humans. Both proprietary commercial VLMs [5, 51, 79, 82, 95, 102, 103, 129] and open-source VLMs [46, 73, 75, 106, 113] have witnessed this significant evolution. For commercial entities, GPT-4V [82] incorporates visual inputs to extend GPT-4 [83] with capabilities of handling multi-modal content, while Google's Gemini series [102, 103] are able to process 1 million multi-modal tokens with significant performance. For open-source initiatives, BLIP series [27, 58, 59], LLaVA series [63–65], Qwen-VL series [7, 115], MiniCPM-V series [135], InternVL series [19, 20, 39], and others [9, 25, 26, 34, 35, 48, 61, 71, 86, 117, 140, 142] have also impacted the AGI landscape in the research community by linking large language models [6, 14, 107] and large vision models [4, 19, 30, 89] in processing both vi",
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+ "text": "21071",
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+ "img_path": "images/6efc0a6faf529ac2b89de497d48345dce486c3d0046dd9fc7688ca54b12d150e.jpg",
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+ "Figure 3. Statistics of our mixed training dataset (Long-MR, Long-VQA, and short SFT from InternVL2). The left and right figures illustrate the distributions of token counts and image counts per training sample, respectively."
+ ],
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+ "text": "sual and textual modality. Specifically, there are also some works advance VLMs' power by improving the scale and quality of data [15, 42, 68], training on high-resolution images [45, 122] or optimizing vision foundation models [19, 139].",
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+ "text": "Long Context Modeling. Due to practical demands, a large body of research [13, 21, 47, 67, 69, 143, 147] has been developed to extend the context length of LLMs. One mainstream direction is to increase the length of LLM's context window by extrapolation of position encoding [11, 16, 32, 85, 87, 96, 97, 146, 150], which allows the LLM to process unseen positions during inference. Another line of research focuses on alleviating the complexity of self-attention by using sparse attention [8, 18, 23, 31, 88, 138], linear-complexity state-space modules [40, 41], or approximate attention computation [24, 55, 91, 116] as the alternatives for dense global attention. The context can also be extended by utilizing external memory to retrieve relevant tokens from the compression of past inputs, such as chunked input [80, 118, 131, 141] or cached KV activations [2, 49, 109, 127, 128]. Other works [43, 127, 130] also adopt sliding windows to achieve an infinite context by only maintaining the activations for the very first and the latest tokens. Recent efforts [52, 120, 132, 144] aim to improve VLMs' ability to process multiple images and long multimodal sequences. However, these studies are often limited to specific applications, revealing challenges faced by VLMs in processing complex and long-context data.",
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+ "text": "Position Encoding in Transformer. To address the lack of sequential information inherent in self-attention mechanisms, Transformers [110] utilize position encoding as a fundamental component to provide position information. The common position encoding design can be broadly categorized into absolute position encoding (APE) and relative position encoding (RPE). The absolute position encoding [12, 53, 56, 110, 111, 145] is simple and intuitive, as it embeds each absolute position position into a position vector which is then added into the representation of input sequences, but this strategy cannot be applied effectively for long sequences. To improve the modeling of long-term dependencies, relative positional encod",
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+ "text": "ing [28, 74, 87, 90, 92, 98, 100, 133] focuses on utilizing distance between tokens as the position information. Some research works [44, 87, 100] aim to utilize relative position for length extrapolation to train Transformers on short sequences and inference on longer contexts. Another research direction is Rotary Position Encoding (RoPE), which embeds position information by rotating the key-query products according to their relative distances. Methods like Position Interpolation [16], NTK-Aware scaling [11], and LongRoPE [32] make progress on top of RoPE [98] to improve its poor extrapolation capability for longer sequences. For VLMs, most studies [7, 20, 132] adopt the same position embedding methods used in LLMs, and there are also some works [38, 76, 125] to explore different diagrams of the positional encoding schemes.",
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+ "text": "3. Method",
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+ "text": "3.1. Augmented Long-context Multimodal Datasets",
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+ "text": "We introduce two augmented long-context multimodal datasets: Long Visual Question Answering and Long multimodal Retrieval. These datasets aim to enhance VLMs' long-context training and establish a systematic evaluation framework, thereby addressing the challenges associated with long-context understanding that extend beyond the scope of existing training data.",
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+ "text": "Long Visual Question Answering (Long-VQA). The Long-VQA dataset aims to evaluate the capabilities of VLMs in understanding and reasoning over long multimodal sequences within general visual question-answering tasks. We extended 17 widely adopted datasets (e.g., DocVQA [78], GQA [50], SQA [72]), expanding their context from short sequences to those containing up to 64K tokens. The tasks involve answering questions that require commonsense reasoning, factual knowledge, and interpretation of visual information from charts, documents, and real-world texts.",
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+ "text": "To extend existing datasets, we interleaved images from multiple samples into a single input, increasing sequence length and complexity to simulate real-world scenarios involving extraneous information. To reduce ambiguity, we refined questions to be more specific, incorporating instructions like \"Based on page $n$ , answer the following question\", which helps models focus on relevant content.",
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+ "text": "Long-VQA contains 533K samples: 392K for training (up to 32K tokens) and 141K for validation (up to 64K tokens) to evaluate the generalization to longer contexts.",
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+ "text": "Long Multimodal Retrieval (Long-MR). Inspired by MM-NIAH (Multimodal Needle-in-a-Haystack) [119], we developed Long-MR by inserting a target image or textual segment into sequences of interleaved images and texts. Long-MR evaluates VLMs' ability to retrieve specific targets from ultra-long multimodal sequences, requiring mod-",
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+ "text": "els to locate the inserted \"needle\" and answer associated questions. We generated two subsets of Long-MR: Long-MR-32K (488K samples, sequences up to 32K tokens) and Long-MR-256K (50K samples, sequences up to 256K tokens), following the data construction process of MM-NIAH.",
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+ "text": "To assess the limitation of VLMs' long-context capabilities, we further extended MM-NIAH evaluation benchmark following the official code[84], generating testing samples with sequence lengths ranging from 64K to 1M tokens, named after MM-NIAH1M benchmark. This pushes the testing capacity beyond the original MM-NIAH, which is limited to sequences up to 64K tokens.",
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+ "text": "We combined the training splits of Long-VQA and Long-MR with short-context instruction-tuning datasets, as utilized in InternVL2, to create a mixed training set for our experiments. Fig. 3 illustrates the distribution of token sequence lengths and the number of images in the mixed training dataset, highlighting our focus on long-context samples.",
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+ "text": "More details about the construction process, examples, and statistics of the datasets are provided in Appendix Sec. C.",
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+ "text": "3.2. Variable Visual Position Encoding",
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+ "text": "Position Encoding in Vision-Language Models. Position encoding is essential in transformer architectures, enabling models to capture sequential relationships by providing tokens with positional information. It usually involves two sequential steps: Position Index Derivation $f_{\\mathrm{pos}}$ , which assigns a positional index $p_i$ to each token $x_i$ , and Position Embedding Computation $g_{\\mathrm{emb}}$ , which transforms these indices into position embeddings that influence the attention mechanism.",
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+ "text": "Formally, the multimodal input in VLMs can be represented as a sequence of $N$ interleaved textual and visual tokens:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {X} = \\left[ x _ {0}, x _ {1}, \\dots , x _ {N - 1} \\right], \\tag {1}\n$$\n",
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+ "text": "where each token $x_{i}$ is either a textual token $x_{i}^{\\mathrm{txt}}$ or a visual token $x_{i}^{\\mathrm{vis}}$ .",
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+ "text": "The Position Index Derivation function $f_{\\mathrm{pos}}$ is recursively defined to capture the sequential nature of token positions:",
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+ "type": "equation",
+ "text": "\n$$\np _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} i = 0, \\\\ f _ {\\text {p o s}} \\left(p _ {i - 1}, x _ {i}\\right), & \\text {f o r} i = 1, 2, \\dots , N - 1. \\end{array} \\right. \\tag {2}\n$$\n",
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+ "text": "In existing LLMs and VLMs, the position index increments uniformly by 1 for each token, regardless of its modality:",
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+ "text": "\n$$\np _ {i} = p _ {i - 1} + 1, \\quad \\text {f o r} i = 1, 2, \\dots , N - 1. \\tag {3}\n$$\n",
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+ "text": "The Position Embedding Computation $g_{\\mathrm{emb}}$ then transforms these position indices into embeddings. VLMs typically adopt the same position embedding methods used in",
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+ "text": "Large Language Models (LLMs), such as Relative Position Encoding [92] or Rotary Position Embedding (RoPE) [98]. These embeddings are incorporated into the token representations at each layer to provide positional context during attention computations. For instance, in RoPE encoding, the token representation $\\mathbf{h}_i$ integrates positional information as:",
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+ "text": "\n$$\n\\mathbf {h} _ {i} ^ {\\prime} = \\mathbf {h} _ {i} \\otimes g _ {\\mathrm {e m b}} \\left(p _ {i}\\right), \\tag {4}\n$$\n",
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+ "text": "where $\\otimes$ represents element-wise multiplication, and $\\mathbf{h}_i^{\\prime}$ is subsequently used as query or key embeddings in the Transformer attention mechanism.",
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+ "text": "Variable Position Index Derivation. The uniform increment of position indices in current VLMs does not account for the differences in information complexity and redundancy between textual and visual tokens. Visual tokens often exhibit higher redundancy and greater similarity with adjacent tokens, suggesting they may require smaller positional increments than textual tokens. Moreover, the large number of visual tokens can cause position indices to exceed the model's pre-trained context window, leading to degraded performance.",
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+ "text": "To address these issues, we propose a modality-specific recursive function for position index derivation, assigning position indices differently for textual and visual tokens:",
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+ "text": "\n$$\np _ {i} = p _ {i - 1} + \\left\\{ \\begin{array}{l l} 1, & \\text {i f} x _ {i} \\text {i s a t e x t u a l t o k e n ,} \\\\ \\delta , & \\text {i f} x _ {i} \\text {i s a v i s u a l t o k e n ,} \\end{array} \\right. \\tag {5}\n$$\n",
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+ "text": "where $\\delta$ is a smaller increment ( $\\delta < 1$ ) that reduces the rate at which position indices increase for visual tokens. The standard increment of 1 is retained for textual tokens to maintain their positional distinctions.",
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+ "text": "During training in our experiments, $\\delta$ is randomly selected for each image from a set of fractional values:",
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+ "text": "\n$$\n\\delta \\in \\Delta = \\left\\{1, \\frac {1}{2}, \\frac {1}{4}, \\frac {1}{8}, \\frac {1}{1 6}, \\frac {1}{3 2}, \\frac {1}{6 4}, \\frac {1}{1 2 8}, \\frac {1}{2 5 6} \\right\\}. \\tag {6}\n$$\n",
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+ "text": "Note that, $\\delta$ remains constant within a single image to preserve the relative positional relationships among its visual tokens. For inputs containing multiple images, $\\delta$ can be independently chosen for each image.",
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+ "text": "During inference, $\\delta$ can be flexibly selected based on the input sequence length, allowing us to balance task performance and ensure that position indices remain within the model's valid context range. Specifically, for long input sequences, a smaller $\\delta$ can be employed to control the increase in position indices, preventing from exceeding the trained positional embedding range, as illustrated in Fig. 2.",
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+ "text": "Discussion and Comparison with Previous Methods. Our Variable Visual Position Encoding (V2PE) offers several advantages over existing long-context methods:",
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+ "text": "21073",
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+ "img_path": "images/c11cbc9a3bd76e191d50b5bf2d051c43be725f370afae6670eff5467b944eb7c.jpg",
+ "image_caption": [
+ "Figure 4. Performance on Long-VQA (long) with sequence lengths up to $32\\mathrm{K}$ tokens and its corresponding standard VQA (short) benchmarks. Compared with GPT-4o and InternVL2-FT-Short, the InternVL2-FT-32K, enhanced with our proposed Long-VQA dataset, effectively narrows the performance gap between short and long-context tasks."
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+ "image_caption": [
+ "Figure 5. Performance on image retrieval task in MM-NIAH (left) and QA task in Long-VQA (right) with different positional increments. Additionally, we include the results of InternVL2-FT-32K when utilizing linear interpolation (linear) [16] and NTK-Aware Scaled RoPE (NTK) [11] position encoding extension methods."
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+ "text": "1) Unlike approaches that reduce the number of visual tokens through attention pooling or feature pooling, which potentially result in information loss, V2PE retains all visual tokens within the VLM, preserving the richness and granularity of visual content.",
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+ "text": "2) Position encoding extension methods (e.g., Positional Interpolation [16] and Extrapolation [96]) adjust position embeddings during inference to accommodate longer sequences. However, extrapolation extends position indices beyond the model's trained range, while interpolation methods (linear [16] / NTK-aware [11]) face performance degradation with unseen position increment, potentially requiring additional fine-tuning [85]. In contrast, V2PE allows the VLM to adapt position indices with arbitrary intervals while evaluating zero-shot in longer contexts by dynamically selecting $\\delta$ during training. This strategy avoids unexpected position embeddings, ensures consistent model performance across varying input lengths and avoids additional fine-tuning in longer contexts.",
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+ "type": "text",
+ "text": "4. Experiment",
+ "text_level": 1,
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+ "type": "text",
+ "text": "4.1. Analysis of VLMs' Long-Context Capabilities",
+ "text_level": 1,
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+ "type": "text",
+ "text": "We first analyze the long-context capabilities of existing VLM by using our constructed long-context multimodal datasets (see Sec. 3.1). Note that this sub-section does not use V2PE.",
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+ "type": "text",
+ "text": "Experimental Setup. We fine-tune InternVL2-2B on two different training datasets and obtain four finetuned models: 1) InternVL2-FT-Short: This model is fine-tuned on",
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+ "type": "table",
+ "img_path": "images/c6334eabc1d9bcfa6903546e45e6b64e5ec4a98b90a9d620ba6acbd9a2d38dec.jpg",
+ "table_caption": [
+ "Table 1. Performance on Long-VQA task with sequence lengths up to 64K tokens at various positional increments $\\delta$ ."
+ ],
+ "table_footnote": [],
+ "table_body": "| Model | δ | 16K | 32K | 40K | 48K | 56K | 64K | Avg |
| InternVL2-2B | - | 52.8 | 27.3 | 23.0 | 23.9 | 22.6 | 21.0 | 28.4 |
| InternVL2-FT-32K | - | 63.0 | 56.1 | 38.3 | 35.5 | 34.6 | 30.6 | 43.0 |
| InternVL2-V2PE-32K | 1/256 | 58.2 | 52.8 | 48.1 | 45.4 | 43.8 | 40.3 | 48.1 |
| 1/128 | 60.0 | 53.7 | 49.5 | 46.5 | 45.3 | 41.3 | 49.4 |
| 1/64 | 61.0 | 54.5 | 50.1 | 47.4 | 45.9 | 42.2 | 50.2 |
| 1/32 | 61.9 | 55.4 | 51.4 | 47.5 | 46.4 | 42.3 | 50.8 |
| 1/16 | 62.9 | 55.6 | 51.2 | 48.3 | 47.0 | 42.5 | 51.3 |
| 1/8 | 63.2 | 55.8 | 52.0 | 47.6 | 45.8 | 41.9 | 51.1 |
| 1/4 | 63.4 | 55.7 | 51.3 | 47.0 | 45.1 | 39.7 | 50.4 |
| 1/2 | 63.3 | 54.9 | 46.8 | 36.8 | 33.3 | 29.2 | 44.1 |
| 1/1 | 62.3 | 49.0 | 30.0 | 26.5 | 27.0 | 25.9 | 36.8 |
| InternVL2-FT-32K (Linear [16]) | - | 62.5 | 51.3 | 42.1 | 34.7 | 31.4 | 25.9 | 40.9 |
| InternVL2-FT-32K (NTK [11]) | - | 63.2 | 54.2 | 44.9 | 41.0 | 40.4 | 34.3 | 45.3 |
",
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+ "type": "text",
+ "text": "the original instruction-tuning dataset (short-context) used by InternVL2-2B. It serves as a baseline to evaluate performance without exposure to long-context data. 2) InternVL2-FT-32K: This model is fine-tuned on a mixed training dataset introduced in Sec. 3.1, incorporating our augmented long-context training data to enhance its long-context capacity. 3) InternVL2-32K-s1/16: To explore the effect of positional encoding increments on visual tokens, we reduce the positional increment to 1/16 for visual tokens, holding it fixed across training and inference, while maintaining training on the same mixed dataset as InternVL2-FT-32K. 4) InternVL2-32K-s1/256: Similarly, we further reduce the positional increments to 1/256 and keep it fixed to examine its impact. Notably, the positional increments for this model also remain fixed during training, without using V2PE.",
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+ "type": "text",
+ "text": "Evaluation Benchmarks. All models are evaluated on the Long-VQA validation split and the MM-NIAH benchmark. Additionally, performance on the standard multimodal VQA benchmarks is assessed if needed.",
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+ "text": "Effectiveness of Augmented Long-Context Multimodal Data. We compare the performance of InternVL2-FT-Short and InternVL2-FT-32K on both the Long-VQA validation set and standard short-context benchmarks, as shown in Fig. 4. The results reveal that InternVL2-FT-Short, which is trained exclusively on short-context data, performs competitively on standard benchmarks but suffers significant degradation on long-context tasks. Even advanced models, such as GPT-4o, exhibit notable declines when the input to",
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+ {
+ "type": "page_number",
+ "text": "21074",
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+ {
+ "type": "table",
+ "img_path": "images/7bf8ce6414b8d4a9b0e35073c1add4f3b824497c450098ae5a435bd460604326.jpg",
+ "table_caption": [
+ "Table 2. Performance on standard VQA benchmarks with different positional increment $\\delta$ . The highest score is marked in bold."
+ ],
+ "table_footnote": [],
+ "table_body": "| Model | δ | ChartQA | DocVQA | AI2D | InfoVQA | SQA | POPE | MMMUval | MMBenchEN | SEEDI | Avg |
| InternVL2-2B | - | 71.7 | 86.9 | 74.1 | 58.9 | 94.1 | 85.2 | 36.3 | 73.4 | 70.9 | 72.4 |
| InternVL2-FT-Short | - | 76.0 | 85.7 | 74.0 | 57.1 | 94.0 | 88.9 | 34.8 | 73.0 | 66.6 | 72.2 |
| InternVL2-FT-32K | - | 75.6 | 84.8 | 73.6 | 56.5 | 94.7 | 88.7 | 35.3 | 73.8 | 65.1 | 72.0 |
| InternVL2-V2PE-32K | 1/256 | 76.2 | 81.6 | 72.3 | 51.7 | 94.3 | 88.0 | 35.7 | 73.2 | 71.0 | 71.6 |
| 1/128 | 76.5 | 82.3 | 72.6 | 52.9 | 94.2 | 88.1 | 34.7 | 73.5 | 70.9 | 71.7 |
| 1/64 | 76.4 | 83.0 | 72.6 | 53.6 | 94.4 | 88.0 | 35.4 | 73.4 | 70.8 | 72.0 |
| 1/32 | 76.9 | 83.6 | 72.6 | 54.3 | 94.3 | 88.1 | 35.7 | 73.3 | 71.0 | 72.2 |
| 1/16 | 77.2 | 84.3 | 73.0 | 55.2 | 94.5 | 88.1 | 35.7 | 73.3 | 71.0 | 72.5 |
| 1/8 | 77.0 | 84.6 | 73.1 | 55.4 | 94.6 | 88.1 | 36.0 | 72.9 | 71.0 | 72.5 |
| 1/4 | 77.3 | 84.7 | 73.3 | 56.5 | 94.6 | 88.2 | 36.0 | 73.6 | 71.0 | 72.8 |
| 1/2 | 76.8 | 84.9 | 73.5 | 56.0 | 94.9 | 88.7 | 35.8 | 73.8 | 71.2 | 72.9 |
| 1/1 | 76.6 | 84.9 | 73.7 | 55.2 | 94.8 | 88.4 | 36.1 | 73.7 | 71.1 | 72.7 |
",
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+ {
+ "type": "table",
+ "img_path": "images/48c692dcb41f257c329190b229e9de7fa9a5b5279356dfa987a12351cc2cb889.jpg",
+ "table_caption": [
+ "Table 3. Performance on the image retrieval task in MM-NIAH with token lengths up to 1M at various position increments $\\delta$ . Test samples exceeding ${64}\\mathrm{\\;K}$ tokens are from our extended $\\mathrm{{MM}} - {\\mathrm{{NIAH}}}_{1\\mathrm{M}}$ . The designation \"NA\" indicates that the GPT-4 results are not applicable due to the extremely long context length."
+ ],
+ "table_footnote": [],
+ "table_body": "| Model | δ | 1K | 16K | 32K | 64K | 128K | 256K | 512K | 1M |
| InternVL2-2B | - | 23.9 | 33.7 | 28.7 | 26.0 | 17.3 | 21.8 | 5.3 | 0.0 |
| GPT-4o | - | 100.0 | 90.4 | 100.0 | 92.7 | 62.1 | 60.0 | 58.6 | NA |
| InternVL2-V2PE-32K | 1/256 | 100.0 | 84.7 | 79.3 | 81.5 | 61.2 | 56.9 | 36.7 | 6.0 |
| 1/64 | 96.0 | 83.9 | 78.1 | 79.5 | 43.6 | 39.3 | 23.4 | 3.4 |
| 1/16 | 96.0 | 82.4 | 73.1 | 65.4 | 57.6 | 41.3 | 19.8 | 0.0 |
| 1/4 | 96.0 | 84.2 | 76.2 | 57.6 | 48.9 | 21.5 | 2.8 | 0.0 |
| 1/1 | 83.0 | 61.2 | 42.0 | 27.5 | 25.5 | 1.5 | 0.0 | 0.0 |
| InternVL2-V2PE-256K | 1/256 | 96.0 | 97.1 | 96.6 | 97.1 | 99.1 | 95.7 | 95.1 | 64.5 |
| 1/64 | 96.0 | 94.7 | 96.6 | 97.1 | 97.1 | 94.1 | 94.1 | 62.8 |
| 1/16 | 96.0 | 94.7 | 93.1 | 94.2 | 100 | 96.2 | 92.9 | 45.1 |
| 1/4 | 96.0 | 94.4 | 100.0 | 97.1 | 75.5 | 75.2 | 38.3 | 2.5 |
| 1/1 | 91.0 | 92.8 | 96.6 | 93.1 | 56.1 | 3.7 | 10.8 | 0.0 |
| InternVL2-FT-32K with linear interpolation | - | 85.3 | 76.0 | 56.0 | 34.7 | 26.4 | 21.9 | 16.3 | 0.5 |
| InternVL2-FT-32K with NTK interpolation | - | 78.3 | 70.7 | 39.8 | 25.7 | 12.3 | 16.8 | 14.8 | 0.0 |
",
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+ },
+ {
+ "type": "text",
+ "text": "ken count is increased, underscoring a common limitation in handling extended sequences. In contrast, InternVL2-FT32K, trained on the mixed dataset including long-context data, effectively narrows the performance gap between short and long-context tasks. This suggests it is difficult for short-context VLMs to inherently generalize to long-context multimodal tasks without further finetuning. Targeted exposure to long-context data is crucial for achieving robust performance across varying input lengths.",
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+ {
+ "type": "text",
+ "text": "Impact of Visual Position Encoding. To assess the impact of position encoding increments for visual tokens, we evaluate the models InternVL2-FT-32K, InternVL2-32K-s1/16, and InternVL2-32K-s1/256 on both the Long-VQA validation set and MM-NIAH benchmark.",
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+ {
+ "type": "text",
+ "text": "Experimental results, presented in Fig. 5, indicate that InternVL2-FT-32K continues to experience performance degradation as input token sequences grow up to $64\\mathrm{K}$ tokens, despite being trained on sequences up to $32\\mathrm{K}$ tokens. When the input sequence length exceeds the maximum token count during training, performance declines sharply. Even applying positional encoding extension techniques developed for large language models (LLMs) give limited benefits. However, models with reduced positional increments for visual tokens show significant improvements. Both InternVL2-32K-s1/16 and InternVL2",
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+ "type": "text",
+ "text": "32K-s1/256 maintain stable performance. We hypothesize that reducing the position increments by factors of 16 and 256 effectively prevents the position indices of visual tokens from exceeding the model's trained context window, thereby mitigating performance decline.",
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+ "type": "text",
+ "text": "4.2. Effectiveness of Our Proposed V2PE",
+ "text_level": 1,
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+ "text": "Experimental Setup. We fine-tune the InternVL2-2B model using our proposed V2PE method in a two-stage training procedure. 1) In the first stage, we fine-tune the released InternVL2-2B model on our mixed training dataset, incorporating V2PE. During training, as described in Eq. 6, the positional increment $\\delta$ is randomly selected, enabling the model to adapt to varying positional increments for visual tokens flexibly. The model obtained after this stage is denoted as InternVL2-V2PE-32K. 2) In the second stage, we further fine-tune the model on the Long-MR-256K dataset, with sequence lengths up to 256K tokens. To preserve the model's general performance in shorter context, we retain $50\\%$ of the data from the first stage. To optimize memory usage, we apply the Ring Attention [66], enabling model parallelism across multiple GPUs. The model obtained after the second stage is denoted as InternVL2-V2PE-256K.",
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+ "type": "text",
+ "text": "Evaluation Benchmarks. We evaluate our trained models on various long-context and standard benchmarks, in",
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+ "text": "21075",
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+ "table_caption": [
+ "Table 4. Comparison with existing MLLMs on general MLLM benchmarks. \"#Param\" denotes the number of parameters. The designation \"—\" indicates that the corresponding score is not released. Numbers in gray are results evaluated by ourselves. $\\delta$ is fixed $1/2$ during testing."
+ ],
+ "table_footnote": [],
+ "table_body": "| Model | #Param | ChartQA | DocVQA | AI2D | InfoVQA | SQA | POPE | MMMUval | MMBenchEn | SEEDi | Avg |
| InternVL2-2B [20] | 2.0B | 71.7 | 86.9 | 74.1 | 58.9 | 94.1 | 85.2 | 36.3 | 73.4 | 70.9 | 72.4 |
| InternVL2-2B-FT32K | 2.0B | 75.6 | 84.9 | 73.7 | 56.5 | 94.7 | 88.5 | 35.3 | 73.4 | 70.9 | 71.1 |
| DeepSeek-VL-1.3B [71] | 2.0B | 47.4 | 36.5 | 51.5 | 20.6 | 68.4 | 85.9 | 33.8 | 66.4 | 66.0 | 52.9 |
| Qwen2-VL-2B [115] | 2.0B | 73.5 | 90.1 | 74.7 | 65.5 | 77.7 | 88.2 | 41.1 | 74.9 | 72.9 | 73.1 |
| Aquila-VL-2B [42] | 2.2B | 32.0 | 85.0 | 75.1 | 58.3 | 95.1 | 83.1 | 46.9 | 79.0 | 73.9 | 69.8 |
| MiniCPM-V-2 [135] | 2.8B | 55.6 | 71.9 | 62.9 | 36.0 | 80.7 | 86.3 | 38.2 | 64.1 | 67.1 | 62.5 |
| Vinterm-3B-beta [33] | 3.7B | 68.3 | 78.1 | 69.1 | 52.2 | 75.0 | 87.4 | 46.7 | 70.6 | 70.0 | 68.6 |
| Llama 3.2 11B [108] | 11B | 83.4 | 88.4 | 91.1 | - | - | - | 50.7 | 68.0 | - | - |
| Qwen2-VL-72B [115] | 73B | 88.3 | 96.5 | 88.1 | 84.5 | 91.2 | 87.2 | 64.5 | 86.9 | 77.9 | 85.0 |
| GPT-4o [81] | - | 85.7 | 92.8 | 84.7 | - | 90.1 | 97.2 | 69.1 | 82.1 | 76.7 | - |
| InternVL2-V2PE-32K (δ = 1/2) | 2.0B | 76.8 | 84.9 | 73.5 | 56.0 | 94.9 | 88.7 | 35.8 | 73.8 | 71.2 | 72.9 |
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+ "img_path": "images/1a2dd56962cf1f396d7725e53ddfc175be4b48fa8593a887a0fa2a6fe789fbe0.jpg",
+ "table_caption": [
+ "Table 5. Comparison with existing MLLMs on long context MLLM benchmarks. “#Param” denotes the number of parameters. The designation “-” indicates that the corresponding score is not released. Numbers in gray are results evaluated by ourselves. $\\delta$ is fixed 1/256 during testing."
+ ],
+ "table_footnote": [],
+ "table_body": "| Model | #Param | MM-NIAH | Milebench | VideoMME |
| Image | Text | Avg | T | S | NI | Avg |
| InternVL2-2B [20] | 2.0B | 23.0 | 18.9 | 21.0 | 58.2 | 54.5 | 37.0 | 49.9 | 48.2 |
| InternVL2-2B-FT32K | 2.0B | 73.0 | 81.1 | 77.05 | 63.6 | 56.0 | 96.2 | 71.9 | 47.8 |
| Phi-3-Vision [1] | 2.7B | 24.9 | 26.3 | 25.6 | 46.9 | 50.0 | 73.8 | 56.9 | 40.7 |
| LongLLaVA [120] | 9B | 28.8 | 57.1 | 43.0 | 47.3 | 46.8 | 50.0 | 48.0 | 43.7 |
| LongLLaVA [120] | 13B | 27.7 | 55.7 | 41.7 | 52.7 | 52.1 | 50.0 | 51.6 | 51.6 |
| VILA1.5 [62] | 13B | 5.4 | 11.0 | 8.2 | 21.4 | 48.5 | 7.7 | 25.9 | 47.4 |
| LongVILA [132] | 7B | 33.7 | 34.1 | 33.9 | 65.3 | 55.1 | 91.9 | 70.8 | 60.1 |
| Gemini-1.5 [103] | - | 28.5 | 82.1 | 55.2 | 50.2 | 58.3 | 97.9 | 68.8 | 69.6 |
| GPT-4o [81] | - | 52.3 | 75.0 | 63.7 | 56.2 | 63.5 | 99.8 | 73.2 | 64.7 |
| Claude3-Opus [5] | - | - | - | - | 37.4 | 48.1 | 85.3 | 56.9 | 59.7 |
| InternVL2-V2PE-32K (δ = 1/256) | 2.0B | 78.1 | 85.5 | 81.8 | 65.3 | 55.1 | 96.7 | 72.4 | 52.3 |
",
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+ {
+ "type": "text",
+ "text": "cluding the Long-VQA validation split, MM-NIAH [119] (including our augmented MM-NIAH $_{1\\mathrm{M}}$ ), and widely used VQA benchmarks such as ChartQA [77], DocVQA [78], AI2D [54], InfoQA [54], SQA [72], POPE [60], MMMU [137], MMBench $_{EN}$ [70], and SEED $_{Image}$ [57]. To systematically assess VLMs' performance on long-context tasks, we also compare our model with other state-of-the-art models on two additional long-context benchmarks: MileBench [94] for multi-image and video understanding, and Video-MME [37] for video analysis tasks.",
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+ "type": "text",
+ "text": "Effectiveness of V2PE. We compare the performance of InternVL2-V2PE-32K and InternVL2-V2PE-256K on the Long-VQA validation split, MM-NIAH (including MM $\\mathrm{NIAH}_{1\\mathrm{M}}$ ), and other standard multimodal benchmarks. The results are shown in Tab. 1, Tab. 2, and Tab. 3.",
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+ {
+ "type": "text",
+ "text": "We demonstrate how varying positional increments impact the models' performance on these benchmarks. Specifically, $\\mathrm{MM - NIAH_{1M}}$ is evaluated on the image-retrieval task where both the \"needle\" and \"question\" are images, posing a stringent challenge for multimodal models to handle visual tokens in long-context sequences.",
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+ "text": "On standard short-context benchmarks (see Fig. 2), V2PE does not offer obvious advantages. We observe a performance drop on specific tasks, such as DocVQA and InfoQA, when the positional increment is reduced. In Appendix Sec. A, we investigate this issue by applying V2PE in the pre-training stage of VLMs. The results indicate that the marginal benefits of V2PE on short-context benchmarks",
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+ {
+ "type": "text",
+ "text": "stem from the fact that InternVL2 was pre-trained and fine-tuned (SFT) using the default position encoding, making it inherently adapted to $\\delta = 1$ .",
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+ "text": "However, on long-context benchmarks like Long-VQA and MM-NIAH (see Fig. 1 and Fig. 3), V2PE demonstrates a clear advantage. For instance, on Long-VQA, the best performance is typically achieved when the positional increments are reduced to around 1/8 or 1/16. Moreover, as the token sequence length increases, smaller positional increments tend to be optimal.",
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+ "text": "In the MM-NIAH benchmark, involving longer token sequences, V2PE demonstrates optimal performance with positional increments of 1/256. Notably, InternVL2-V2PE-32K markedly enhances performance on sequences of 256K tokens, boosting scores from 1.5 to 56.9. This enhancement is also evident in InternVL2-V2PE-256K, which records the highest scores across various token sequence lengths when using a positional increment of 1/256. For sequences of 512K tokens, the score surges from 10.8 to 95.1. Additionally, with the same positional increment of 1/256, the InternVL2-V2PE-256K model attains a significant score of 64.5 on sequences reaching 1M tokens.",
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+ "type": "text",
+ "text": "From our previous experimental results, we observe a qualitative relationship among the choice of $\\delta$ , the context length, and model performance: with longer context, selecting a smaller $\\delta$ improves model's performance. Therefore, in later experiments, we set $\\delta$ to $1/2$ for evaluating general and $1/256$ for long context benchmarks respectively, based",
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+ "text": "21076",
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+ },
+ {
+ "type": "image",
+ "img_path": "images/676a6532cc4279c27cacc620614f78b1b370addc41c347bb0e375d62c3fe0e2b.jpg",
+ "image_caption": [
+ "Figure 6. Performance on MM-NIAH benchmarks with different position encoding strategies across six task types: \"image retrieval\", \"text retrieval\", \"image counting\", \"text counting\", \"image reasoning\" and \"text reasoning\". \"Image only\", \"Text only\", \"Both\" and \"Baseline\" represent applying V2PE to visual tokens, textual tokens, both simultaneously, and neither, respectively."
+ ],
+ "image_footnote": [],
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+ {
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+ "img_path": "images/0177132ca5dcd2bc9f61c36e03bb605b57ef7450813096dd9ed965c8038c923f.jpg",
+ "image_caption": [
+ "Figure 7. Performance on image retrieval task in MM-NIAH benchmark using V2PE and token compression strategies. Token compression reduces the number of visual tokens by a ratio $\\delta$ , whereas V2PE employs a smaller positional increment $\\delta$ while preserving all visual tokens."
+ ],
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+ "text": "on the context length. Furthermore, we provide theoretical analysis on optimal $\\delta$ selection in the Appendix Sec. B",
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+ "type": "text",
+ "text": "4.3. Comparison with Other VLMs.",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "We evaluate the performance of InternVL2-V2PE-32K against state-of-the-art vision-language models (VLMs) on both standard and long-context multimodal benchmarks, with results presented in Tab. 4 and Tab. 5, respectively. Despite built on a relatively small 2B-parameter model and incorporating a substantial amount of long-context training data, InternVL2-V2PE-32K retains highly competitive results on standard short-context multimodal benchmarks.",
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+ "type": "text",
+ "text": "On long-context multimodal benchmarks, the model performs exceptionally well, demonstrating that V2PE can significantly enhance long-context abilities even built on a relative small model. These results validate the potential of V2PE for improving the performance of VLMs on a wide range of long-context multimodal tasks.",
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+ "text": "4.4. Ablation Study",
+ "text_level": 1,
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+ "text": "Can V2PE be applied to textual tokens? We evaluate the impact of V2PE on visual tokens, textual tokens, both concurrently, and neither, with results on six MM-NIAH tasks presented in Fig. 6. Applying V2PE solely to textual tokens yields marginal improvements in language understanding but degrades performance on vision-centric tasks. When applied to both modalities, model performance exhibits instability. Notably, restricting V2PE to visual tokens consistently enhances performance across all tasks.",
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+ "Figure 8. Performance on image retrieval task in MM-NIAH benchmark with variable versus fixed position increments for visual tokens in the VLMs. \"Variable\" denotes training with variable increments, allowing evaluation with arbitrary fixed $\\delta$ , while \"Fixed\" means training and evaluating with the same fixed $\\delta$ ."
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+ "text": "Is V2PE equivalent to visual token compression? We also compare V2PE with the token compression strategy, where visual tokens undergo pooling operations to reduce token number, allowing more images to be processed ideally. We test various compression ratios and evaluate the model's performance on the MM-NIAH image retrieval task. The results, shown in Fig. 7, reveal that while token compression results in a rapid performance drop when the number of visual tokens is reduced 16 times or more, our method demonstrates stable performance across all settings.",
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+ "text": "Can positional increment be fixed during training? We train a set of InternVL2-FT-32K models with both V2PE method and fixed positional increments under the same settings. Their performance in the image retrieval task of the MM-NIAH benchmark is shown in Fig. 8. The results indicate that fixing the positional increment does not lead to optimal task performance. In contrast, the variable adjustment of positional increments provides consistent improvements.",
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+ "text": "Is V2PE superior to the position encoding extension methods? To compare V2PE with existing position encoding extension methods, we evaluated both InternVL2-V2PE-32K and InternVL2-FT-32K models using two widely adopted position extension techniques: linear interpolation and NTK-Aware Scaled RoPE. The results, presented in Fig. 5, Tab. 1, and Tab. 3, show that V2PE not only offers greater stability but also achieves superior task performance, especially in long-context scenarios.",
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+ "text": "5. Conclusion",
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+ "text": "We investigate the long-context capabilities of the existing VLMs, using our augmented long-context datasets, and find that positional encoding for visual tokens is critical for the long-context capabilities of VLMs. Based on this observation, we introduce V2PE, a novel position encoding strategy that applies smaller, variable positional increments to visual tokens, enabling more efficient handling of long-context multimodal sequences. By leveraging V2PE and our augmented long-context datasets, we fine-tune the open-source VLMs successfully, which shows significant improvements on both general and long-context multimodal benchmarks.",
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+ "type": "text",
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+ "content": "With the rapid advancement of Large Language Models (LLMs) [14, 29, 83, 99, 108], Vision-Language Models (VLMs) have made substantial strides [19, 82, 103, 115], excelling at tasks like visual captioning [17], visual question answering [78], and complex visual reasoning [136]. Despite this progress, existing research [112, 119, 132, 144]"
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+ "content": "Figure 1. Performance on the image retrieval task using a token length of up to 1M on MM-NIAH [119] across different VLMs. The GPT-4o [81] version is 2024-08-06, while InternVL2-2B [20] models are both fine-tuned from the official release, using our augmented data, with token lengths reaching up to 256K per sample."
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+ "type": "text",
+ "bbox": [
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+ "content": "reveals that VLMs struggle to generalize effectively when confronted with multimodal long-sequence inputs (e.g., long videos [121, 126], high-resolution images [45, 122], and lengthy image-text documents [3, 105, 151]). This limitation emerges even in relatively straightforward, such as object counting and passkey duplication, significantly restricting VLMs' potential applications and impeding the enhancement of user experience [22, 114, 119, 120]."
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+ "content": "Recent efforts have attempted to extend VLMs' capabilities to process multiple images or handle long multimodal sequences. However, these approaches either permit only a small number of images (typically fewer than five) [52, 65, 149] or primarily target video data (e.g., LongVA [144], LongVILA [132], LongLLAVA [120], VideoXL [93]). These studies are only limited to specific application scenarios, highlighting the challenges VLMs face in handling complex and long-sequence multimodal data, which makes a key research question particularly urgent: Why do VLMs perform poorly in long-context scenarios, and how can we unlock their capacity for comprehensive multimodal understanding and reasoning over long sequences?"
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+ "content": "To investigate this, we first construct a large-scale pool of long-context multimodal datasets to evaluate and analyze VLM capabilities systematically. By extending the se"
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+ "content": "Figure 2. Illustration from our proposed Variable Visual Position Encoding (V2PE). Unlike the standard position encoding used in most VLMs, which shares the same stepwise positional increment for both visual and textual tokens, our proposed Variable Visual Positional Encoding (V2PE) uses smaller and variable positional increments specifically for visual tokens compared to textual tokens. This flexible design enables VLMs to handle long-context multimodal sequences within a limited context window."
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+ "content": "quence length of existing instruction-tuning datasets (e.g., DocVQA [78], ChartQA [77], SQA [72]) to 32K-64K tokens, we adapt these datasets specifically to train and validate VLMs for enhanced long-context capabilities. We also extend long-context benchmarks from 64K to 1M tokens (e.g., by employing the official MM-NIAH [119] curation code) to validate VLM performance with longer contexts, providing a deeper understanding of the limitations."
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+ "content": "Our empirical analysis shows that the design of positional encodings of visual tokens plays an essential role in long-context scenarios, which is often overlooked in previous studies. Specifically, (1) directly applying the LLM positional encoding mechanism to visual tokens is suboptimal, and (2) the performance of VLMs degrades significantly when positional encodings for visual tokens exceed the trained context window, and previous position encoding extension methods applicable to LLMs provide only marginal improvements. These findings highlight the need for specialized positional encoding methods to manage visual tokens in long-context multimodal scenarios effectively."
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+ "content": "To address these challenges, we propose Variable Visual Position Encoding (V2PE), a novel approach for handling visual token positions in VLMs. Considering the continuity nature of pixel space, adjacent visual tokens exhibit greater similarity than adjacent text tokens. Thus, V2PE uses smaller positional increments for visual tokens than text tokens (see Fig. 2). Furthermore, V2PE employs variable positional increments for visual tokens during training, enabling the model to learn and adapt to position encoding in various scenarios. This variable adjustment allows the model to effectively handle different numbers and complexities of image inputs during inference, thereby enhancing its stability and adaptability in long-context processing."
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+ "content": "In experiments, we apply V2PE to enhance the long-context capability of open-source VLMs [19, 20], and fine-tune them using our extended multimodal datasets. The resulting models not only maintain strong performance on standard short-context multimodal benchmarks, but also excel in tasks requiring long-context handling, which outperform traditional token compression and other position encoding extension methods. In particular, after further fine-tuning on multimodal sequences up to 256K tokens, our model achieves promising performance in multimodal retrieval tasks involving sequences as long as 1M tokens, as shown in Fig. 1. The main contributions of this paper are as follows:"
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+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We construct mixed datasets to improve VLMs' long-context capability by augmenting existing multimodal instruction tuning datasets and conduct a thorough investigation into why current VLMs struggle with long-context multimodal inputs, revealing that directly applying LLM positional encoding to visual tokens is ineffective."
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+ "type": "text",
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+ "angle": 0,
+ "content": "- We propose Variable Visual Position Encoding (V2PE), a novel positional encoding strategy that employs variable and smaller increments for visual tokens, significantly enhancing VLMs' ability to understand and reason over extended multimodal contexts."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "- We apply our V2PE method and extend training data on the open-source VLMs. The fine-tuned VLMs perform exceptionally well on both general multimodal benchmarks and long-context multimodal tasks, with the capacity to handle sequences of up to 1M tokens, significantly longer than training sequence."
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+ "content": "2. Related Works"
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+ "type": "text",
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+ "content": "Vision-Language Models (VLMs). With the development of Large Language Models (LLMs) [6, 10, 14, 36, 83, 99, 101, 104, 107, 108, 123, 124, 134, 148], the integration of vision and language modalities is significantly catalyzed. This progress gives rise to Vision-Language Models (VLM), which can perceive visual contents, conduct visual reasoning, and engage in multi-modal dialogue with humans. Both proprietary commercial VLMs [5, 51, 79, 82, 95, 102, 103, 129] and open-source VLMs [46, 73, 75, 106, 113] have witnessed this significant evolution. For commercial entities, GPT-4V [82] incorporates visual inputs to extend GPT-4 [83] with capabilities of handling multi-modal content, while Google's Gemini series [102, 103] are able to process 1 million multi-modal tokens with significant performance. For open-source initiatives, BLIP series [27, 58, 59], LLaVA series [63–65], Qwen-VL series [7, 115], MiniCPM-V series [135], InternVL series [19, 20, 39], and others [9, 25, 26, 34, 35, 48, 61, 71, 86, 117, 140, 142] have also impacted the AGI landscape in the research community by linking large language models [6, 14, 107] and large vision models [4, 19, 30, 89] in processing both vi"
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+ "content": "Figure 3. Statistics of our mixed training dataset (Long-MR, Long-VQA, and short SFT from InternVL2). The left and right figures illustrate the distributions of token counts and image counts per training sample, respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "sual and textual modality. Specifically, there are also some works advance VLMs' power by improving the scale and quality of data [15, 42, 68], training on high-resolution images [45, 122] or optimizing vision foundation models [19, 139]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Long Context Modeling. Due to practical demands, a large body of research [13, 21, 47, 67, 69, 143, 147] has been developed to extend the context length of LLMs. One mainstream direction is to increase the length of LLM's context window by extrapolation of position encoding [11, 16, 32, 85, 87, 96, 97, 146, 150], which allows the LLM to process unseen positions during inference. Another line of research focuses on alleviating the complexity of self-attention by using sparse attention [8, 18, 23, 31, 88, 138], linear-complexity state-space modules [40, 41], or approximate attention computation [24, 55, 91, 116] as the alternatives for dense global attention. The context can also be extended by utilizing external memory to retrieve relevant tokens from the compression of past inputs, such as chunked input [80, 118, 131, 141] or cached KV activations [2, 49, 109, 127, 128]. Other works [43, 127, 130] also adopt sliding windows to achieve an infinite context by only maintaining the activations for the very first and the latest tokens. Recent efforts [52, 120, 132, 144] aim to improve VLMs' ability to process multiple images and long multimodal sequences. However, these studies are often limited to specific applications, revealing challenges faced by VLMs in processing complex and long-context data."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Position Encoding in Transformer. To address the lack of sequential information inherent in self-attention mechanisms, Transformers [110] utilize position encoding as a fundamental component to provide position information. The common position encoding design can be broadly categorized into absolute position encoding (APE) and relative position encoding (RPE). The absolute position encoding [12, 53, 56, 110, 111, 145] is simple and intuitive, as it embeds each absolute position position into a position vector which is then added into the representation of input sequences, but this strategy cannot be applied effectively for long sequences. To improve the modeling of long-term dependencies, relative positional encod"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "ing [28, 74, 87, 90, 92, 98, 100, 133] focuses on utilizing distance between tokens as the position information. Some research works [44, 87, 100] aim to utilize relative position for length extrapolation to train Transformers on short sequences and inference on longer contexts. Another research direction is Rotary Position Encoding (RoPE), which embeds position information by rotating the key-query products according to their relative distances. Methods like Position Interpolation [16], NTK-Aware scaling [11], and LongRoPE [32] make progress on top of RoPE [98] to improve its poor extrapolation capability for longer sequences. For VLMs, most studies [7, 20, 132] adopt the same position embedding methods used in LLMs, and there are also some works [38, 76, 125] to explore different diagrams of the positional encoding schemes."
+ },
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+ "content": "3. Method"
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+ "content": "3.1. Augmented Long-context Multimodal Datasets"
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+ "content": "We introduce two augmented long-context multimodal datasets: Long Visual Question Answering and Long multimodal Retrieval. These datasets aim to enhance VLMs' long-context training and establish a systematic evaluation framework, thereby addressing the challenges associated with long-context understanding that extend beyond the scope of existing training data."
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+ "content": "Long Visual Question Answering (Long-VQA). The Long-VQA dataset aims to evaluate the capabilities of VLMs in understanding and reasoning over long multimodal sequences within general visual question-answering tasks. We extended 17 widely adopted datasets (e.g., DocVQA [78], GQA [50], SQA [72]), expanding their context from short sequences to those containing up to 64K tokens. The tasks involve answering questions that require commonsense reasoning, factual knowledge, and interpretation of visual information from charts, documents, and real-world texts."
+ },
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+ "content": "To extend existing datasets, we interleaved images from multiple samples into a single input, increasing sequence length and complexity to simulate real-world scenarios involving extraneous information. To reduce ambiguity, we refined questions to be more specific, incorporating instructions like \"Based on page \\( n \\), answer the following question\", which helps models focus on relevant content."
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+ "angle": 0,
+ "content": "Long-VQA contains 533K samples: 392K for training (up to 32K tokens) and 141K for validation (up to 64K tokens) to evaluate the generalization to longer contexts."
+ },
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+ "type": "text",
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+ "content": "Long Multimodal Retrieval (Long-MR). Inspired by MM-NIAH (Multimodal Needle-in-a-Haystack) [119], we developed Long-MR by inserting a target image or textual segment into sequences of interleaved images and texts. Long-MR evaluates VLMs' ability to retrieve specific targets from ultra-long multimodal sequences, requiring mod-"
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+ "content": "els to locate the inserted \"needle\" and answer associated questions. We generated two subsets of Long-MR: Long-MR-32K (488K samples, sequences up to 32K tokens) and Long-MR-256K (50K samples, sequences up to 256K tokens), following the data construction process of MM-NIAH."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To assess the limitation of VLMs' long-context capabilities, we further extended MM-NIAH evaluation benchmark following the official code[84], generating testing samples with sequence lengths ranging from 64K to 1M tokens, named after MM-NIAH1M benchmark. This pushes the testing capacity beyond the original MM-NIAH, which is limited to sequences up to 64K tokens."
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+ "content": "We combined the training splits of Long-VQA and Long-MR with short-context instruction-tuning datasets, as utilized in InternVL2, to create a mixed training set for our experiments. Fig. 3 illustrates the distribution of token sequence lengths and the number of images in the mixed training dataset, highlighting our focus on long-context samples."
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+ "content": "More details about the construction process, examples, and statistics of the datasets are provided in Appendix Sec. C."
+ },
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+ "content": "3.2. Variable Visual Position Encoding"
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+ "content": "Position Encoding in Vision-Language Models. Position encoding is essential in transformer architectures, enabling models to capture sequential relationships by providing tokens with positional information. It usually involves two sequential steps: Position Index Derivation \\( f_{\\mathrm{pos}} \\), which assigns a positional index \\( p_i \\) to each token \\( x_i \\), and Position Embedding Computation \\( g_{\\mathrm{emb}} \\), which transforms these indices into position embeddings that influence the attention mechanism."
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+ "content": "Formally, the multimodal input in VLMs can be represented as a sequence of \\(N\\) interleaved textual and visual tokens:"
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+ "content": "\\[\n\\mathbf {X} = \\left[ x _ {0}, x _ {1}, \\dots , x _ {N - 1} \\right], \\tag {1}\n\\]"
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+ "content": "where each token \\( x_{i} \\) is either a textual token \\( x_{i}^{\\mathrm{txt}} \\) or a visual token \\( x_{i}^{\\mathrm{vis}} \\)."
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+ "content": "The Position Index Derivation function \\( f_{\\mathrm{pos}} \\) is recursively defined to capture the sequential nature of token positions:"
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+ "angle": 0,
+ "content": "\\[\np _ {i} = \\left\\{ \\begin{array}{l l} 0, & \\text {i f} i = 0, \\\\ f _ {\\text {p o s}} \\left(p _ {i - 1}, x _ {i}\\right), & \\text {f o r} i = 1, 2, \\dots , N - 1. \\end{array} \\right. \\tag {2}\n\\]"
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+ "content": "In existing LLMs and VLMs, the position index increments uniformly by 1 for each token, regardless of its modality:"
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+ "content": "\\[\np _ {i} = p _ {i - 1} + 1, \\quad \\text {f o r} i = 1, 2, \\dots , N - 1. \\tag {3}\n\\]"
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+ "content": "The Position Embedding Computation \\( g_{\\mathrm{emb}} \\) then transforms these position indices into embeddings. VLMs typically adopt the same position embedding methods used in"
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+ "content": "Large Language Models (LLMs), such as Relative Position Encoding [92] or Rotary Position Embedding (RoPE) [98]. These embeddings are incorporated into the token representations at each layer to provide positional context during attention computations. For instance, in RoPE encoding, the token representation \\(\\mathbf{h}_i\\) integrates positional information as:"
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+ "content": "\\[\n\\mathbf {h} _ {i} ^ {\\prime} = \\mathbf {h} _ {i} \\otimes g _ {\\mathrm {e m b}} \\left(p _ {i}\\right), \\tag {4}\n\\]"
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+ "content": "where \\(\\otimes\\) represents element-wise multiplication, and \\(\\mathbf{h}_i^{\\prime}\\) is subsequently used as query or key embeddings in the Transformer attention mechanism."
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+ "content": "Variable Position Index Derivation. The uniform increment of position indices in current VLMs does not account for the differences in information complexity and redundancy between textual and visual tokens. Visual tokens often exhibit higher redundancy and greater similarity with adjacent tokens, suggesting they may require smaller positional increments than textual tokens. Moreover, the large number of visual tokens can cause position indices to exceed the model's pre-trained context window, leading to degraded performance."
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+ "content": "To address these issues, we propose a modality-specific recursive function for position index derivation, assigning position indices differently for textual and visual tokens:"
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+ "content": "\\[\np _ {i} = p _ {i - 1} + \\left\\{ \\begin{array}{l l} 1, & \\text {i f} x _ {i} \\text {i s a t e x t u a l t o k e n ,} \\\\ \\delta , & \\text {i f} x _ {i} \\text {i s a v i s u a l t o k e n ,} \\end{array} \\right. \\tag {5}\n\\]"
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+ "content": "where \\(\\delta\\) is a smaller increment (\\(\\delta < 1\\)) that reduces the rate at which position indices increase for visual tokens. The standard increment of 1 is retained for textual tokens to maintain their positional distinctions."
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+ "content": "During training in our experiments, \\(\\delta\\) is randomly selected for each image from a set of fractional values:"
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+ "content": "\\[\n\\delta \\in \\Delta = \\left\\{1, \\frac {1}{2}, \\frac {1}{4}, \\frac {1}{8}, \\frac {1}{1 6}, \\frac {1}{3 2}, \\frac {1}{6 4}, \\frac {1}{1 2 8}, \\frac {1}{2 5 6} \\right\\}. \\tag {6}\n\\]"
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+ "content": "Note that, \\(\\delta\\) remains constant within a single image to preserve the relative positional relationships among its visual tokens. For inputs containing multiple images, \\(\\delta\\) can be independently chosen for each image."
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+ "content": "During inference, \\(\\delta\\) can be flexibly selected based on the input sequence length, allowing us to balance task performance and ensure that position indices remain within the model's valid context range. Specifically, for long input sequences, a smaller \\(\\delta\\) can be employed to control the increase in position indices, preventing from exceeding the trained positional embedding range, as illustrated in Fig. 2."
+ },
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+ "content": "Discussion and Comparison with Previous Methods. Our Variable Visual Position Encoding (V2PE) offers several advantages over existing long-context methods:"
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 4. Performance on Long-VQA (long) with sequence lengths up to \\(32\\mathrm{K}\\) tokens and its corresponding standard VQA (short) benchmarks. Compared with GPT-4o and InternVL2-FT-Short, the InternVL2-FT-32K, enhanced with our proposed Long-VQA dataset, effectively narrows the performance gap between short and long-context tasks."
+ },
+ {
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+ "bbox": [
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+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 5. Performance on image retrieval task in MM-NIAH (left) and QA task in Long-VQA (right) with different positional increments. Additionally, we include the results of InternVL2-FT-32K when utilizing linear interpolation (linear) [16] and NTK-Aware Scaled RoPE (NTK) [11] position encoding extension methods."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "1) Unlike approaches that reduce the number of visual tokens through attention pooling or feature pooling, which potentially result in information loss, V2PE retains all visual tokens within the VLM, preserving the richness and granularity of visual content."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "2) Position encoding extension methods (e.g., Positional Interpolation [16] and Extrapolation [96]) adjust position embeddings during inference to accommodate longer sequences. However, extrapolation extends position indices beyond the model's trained range, while interpolation methods (linear [16] / NTK-aware [11]) face performance degradation with unseen position increment, potentially requiring additional fine-tuning [85]. In contrast, V2PE allows the VLM to adapt position indices with arbitrary intervals while evaluating zero-shot in longer contexts by dynamically selecting \\(\\delta\\) during training. This strategy avoids unexpected position embeddings, ensures consistent model performance across varying input lengths and avoids additional fine-tuning in longer contexts."
+ },
+ {
+ "type": "title",
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+ "content": "4. Experiment"
+ },
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+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.1. Analysis of VLMs' Long-Context Capabilities"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "We first analyze the long-context capabilities of existing VLM by using our constructed long-context multimodal datasets (see Sec. 3.1). Note that this sub-section does not use V2PE."
+ },
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+ "bbox": [
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+ "content": "Experimental Setup. We fine-tune InternVL2-2B on two different training datasets and obtain four finetuned models: 1) InternVL2-FT-Short: This model is fine-tuned on"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. Performance on Long-VQA task with sequence lengths up to 64K tokens at various positional increments \\(\\delta\\)."
+ },
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+ "content": "| Model | δ | 16K | 32K | 40K | 48K | 56K | 64K | Avg |
| InternVL2-2B | - | 52.8 | 27.3 | 23.0 | 23.9 | 22.6 | 21.0 | 28.4 |
| InternVL2-FT-32K | - | 63.0 | 56.1 | 38.3 | 35.5 | 34.6 | 30.6 | 43.0 |
| InternVL2-V2PE-32K | 1/256 | 58.2 | 52.8 | 48.1 | 45.4 | 43.8 | 40.3 | 48.1 |
| 1/128 | 60.0 | 53.7 | 49.5 | 46.5 | 45.3 | 41.3 | 49.4 |
| 1/64 | 61.0 | 54.5 | 50.1 | 47.4 | 45.9 | 42.2 | 50.2 |
| 1/32 | 61.9 | 55.4 | 51.4 | 47.5 | 46.4 | 42.3 | 50.8 |
| 1/16 | 62.9 | 55.6 | 51.2 | 48.3 | 47.0 | 42.5 | 51.3 |
| 1/8 | 63.2 | 55.8 | 52.0 | 47.6 | 45.8 | 41.9 | 51.1 |
| 1/4 | 63.4 | 55.7 | 51.3 | 47.0 | 45.1 | 39.7 | 50.4 |
| 1/2 | 63.3 | 54.9 | 46.8 | 36.8 | 33.3 | 29.2 | 44.1 |
| 1/1 | 62.3 | 49.0 | 30.0 | 26.5 | 27.0 | 25.9 | 36.8 |
| InternVL2-FT-32K (Linear [16]) | - | 62.5 | 51.3 | 42.1 | 34.7 | 31.4 | 25.9 | 40.9 |
| InternVL2-FT-32K (NTK [11]) | - | 63.2 | 54.2 | 44.9 | 41.0 | 40.4 | 34.3 | 45.3 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.479,
+ 0.907,
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+ "angle": 0,
+ "content": "the original instruction-tuning dataset (short-context) used by InternVL2-2B. It serves as a baseline to evaluate performance without exposure to long-context data. 2) InternVL2-FT-32K: This model is fine-tuned on a mixed training dataset introduced in Sec. 3.1, incorporating our augmented long-context training data to enhance its long-context capacity. 3) InternVL2-32K-s1/16: To explore the effect of positional encoding increments on visual tokens, we reduce the positional increment to 1/16 for visual tokens, holding it fixed across training and inference, while maintaining training on the same mixed dataset as InternVL2-FT-32K. 4) InternVL2-32K-s1/256: Similarly, we further reduce the positional increments to 1/256 and keep it fixed to examine its impact. Notably, the positional increments for this model also remain fixed during training, without using V2PE."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Evaluation Benchmarks. All models are evaluated on the Long-VQA validation split and the MM-NIAH benchmark. Additionally, performance on the standard multimodal VQA benchmarks is assessed if needed."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Effectiveness of Augmented Long-Context Multimodal Data. We compare the performance of InternVL2-FT-Short and InternVL2-FT-32K on both the Long-VQA validation set and standard short-context benchmarks, as shown in Fig. 4. The results reveal that InternVL2-FT-Short, which is trained exclusively on short-context data, performs competitively on standard benchmarks but suffers significant degradation on long-context tasks. Even advanced models, such as GPT-4o, exhibit notable declines when the input to"
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+ [
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+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Performance on standard VQA benchmarks with different positional increment \\( \\delta \\) . The highest score is marked in bold."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Model | δ | ChartQA | DocVQA | AI2D | InfoVQA | SQA | POPE | MMMUval | MMBenchEN | SEEDI | Avg |
| InternVL2-2B | - | 71.7 | 86.9 | 74.1 | 58.9 | 94.1 | 85.2 | 36.3 | 73.4 | 70.9 | 72.4 |
| InternVL2-FT-Short | - | 76.0 | 85.7 | 74.0 | 57.1 | 94.0 | 88.9 | 34.8 | 73.0 | 66.6 | 72.2 |
| InternVL2-FT-32K | - | 75.6 | 84.8 | 73.6 | 56.5 | 94.7 | 88.7 | 35.3 | 73.8 | 65.1 | 72.0 |
| InternVL2-V2PE-32K | 1/256 | 76.2 | 81.6 | 72.3 | 51.7 | 94.3 | 88.0 | 35.7 | 73.2 | 71.0 | 71.6 |
| 1/128 | 76.5 | 82.3 | 72.6 | 52.9 | 94.2 | 88.1 | 34.7 | 73.5 | 70.9 | 71.7 |
| 1/64 | 76.4 | 83.0 | 72.6 | 53.6 | 94.4 | 88.0 | 35.4 | 73.4 | 70.8 | 72.0 |
| 1/32 | 76.9 | 83.6 | 72.6 | 54.3 | 94.3 | 88.1 | 35.7 | 73.3 | 71.0 | 72.2 |
| 1/16 | 77.2 | 84.3 | 73.0 | 55.2 | 94.5 | 88.1 | 35.7 | 73.3 | 71.0 | 72.5 |
| 1/8 | 77.0 | 84.6 | 73.1 | 55.4 | 94.6 | 88.1 | 36.0 | 72.9 | 71.0 | 72.5 |
| 1/4 | 77.3 | 84.7 | 73.3 | 56.5 | 94.6 | 88.2 | 36.0 | 73.6 | 71.0 | 72.8 |
| 1/2 | 76.8 | 84.9 | 73.5 | 56.0 | 94.9 | 88.7 | 35.8 | 73.8 | 71.2 | 72.9 |
| 1/1 | 76.6 | 84.9 | 73.7 | 55.2 | 94.8 | 88.4 | 36.1 | 73.7 | 71.1 | 72.7 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Performance on the image retrieval task in MM-NIAH with token lengths up to 1M at various position increments \\( \\delta \\) . Test samples exceeding \\( {64}\\mathrm{\\;K} \\) tokens are from our extended \\( \\mathrm{{MM}} - {\\mathrm{{NIAH}}}_{1\\mathrm{M}} \\) . The designation \"NA\" indicates that the GPT-4 results are not applicable due to the extremely long context length."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Model | δ | 1K | 16K | 32K | 64K | 128K | 256K | 512K | 1M |
| InternVL2-2B | - | 23.9 | 33.7 | 28.7 | 26.0 | 17.3 | 21.8 | 5.3 | 0.0 |
| GPT-4o | - | 100.0 | 90.4 | 100.0 | 92.7 | 62.1 | 60.0 | 58.6 | NA |
| InternVL2-V2PE-32K | 1/256 | 100.0 | 84.7 | 79.3 | 81.5 | 61.2 | 56.9 | 36.7 | 6.0 |
| 1/64 | 96.0 | 83.9 | 78.1 | 79.5 | 43.6 | 39.3 | 23.4 | 3.4 |
| 1/16 | 96.0 | 82.4 | 73.1 | 65.4 | 57.6 | 41.3 | 19.8 | 0.0 |
| 1/4 | 96.0 | 84.2 | 76.2 | 57.6 | 48.9 | 21.5 | 2.8 | 0.0 |
| 1/1 | 83.0 | 61.2 | 42.0 | 27.5 | 25.5 | 1.5 | 0.0 | 0.0 |
| InternVL2-V2PE-256K | 1/256 | 96.0 | 97.1 | 96.6 | 97.1 | 99.1 | 95.7 | 95.1 | 64.5 |
| 1/64 | 96.0 | 94.7 | 96.6 | 97.1 | 97.1 | 94.1 | 94.1 | 62.8 |
| 1/16 | 96.0 | 94.7 | 93.1 | 94.2 | 100 | 96.2 | 92.9 | 45.1 |
| 1/4 | 96.0 | 94.4 | 100.0 | 97.1 | 75.5 | 75.2 | 38.3 | 2.5 |
| 1/1 | 91.0 | 92.8 | 96.6 | 93.1 | 56.1 | 3.7 | 10.8 | 0.0 |
| InternVL2-FT-32K with linear interpolation | - | 85.3 | 76.0 | 56.0 | 34.7 | 26.4 | 21.9 | 16.3 | 0.5 |
| InternVL2-FT-32K with NTK interpolation | - | 78.3 | 70.7 | 39.8 | 25.7 | 12.3 | 16.8 | 14.8 | 0.0 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.51,
+ 0.482,
+ 0.646
+ ],
+ "angle": 0,
+ "content": "ken count is increased, underscoring a common limitation in handling extended sequences. In contrast, InternVL2-FT32K, trained on the mixed dataset including long-context data, effectively narrows the performance gap between short and long-context tasks. This suggests it is difficult for short-context VLMs to inherently generalize to long-context multimodal tasks without further finetuning. Targeted exposure to long-context data is crucial for achieving robust performance across varying input lengths."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.652,
+ 0.483,
+ 0.728
+ ],
+ "angle": 0,
+ "content": "Impact of Visual Position Encoding. To assess the impact of position encoding increments for visual tokens, we evaluate the models InternVL2-FT-32K, InternVL2-32K-s1/16, and InternVL2-32K-s1/256 on both the Long-VQA validation set and MM-NIAH benchmark."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
+ 0.735,
+ 0.483,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Experimental results, presented in Fig. 5, indicate that InternVL2-FT-32K continues to experience performance degradation as input token sequences grow up to \\(64\\mathrm{K}\\) tokens, despite being trained on sequences up to \\(32\\mathrm{K}\\) tokens. When the input sequence length exceeds the maximum token count during training, performance declines sharply. Even applying positional encoding extension techniques developed for large language models (LLMs) give limited benefits. However, models with reduced positional increments for visual tokens show significant improvements. Both InternVL2-32K-s1/16 and InternVL2"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.51,
+ 0.907,
+ 0.587
+ ],
+ "angle": 0,
+ "content": "32K-s1/256 maintain stable performance. We hypothesize that reducing the position increments by factors of 16 and 256 effectively prevents the position indices of visual tokens from exceeding the model's trained context window, thereby mitigating performance decline."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Effectiveness of Our Proposed V2PE"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.625,
+ 0.907,
+ 0.867
+ ],
+ "angle": 0,
+ "content": "Experimental Setup. We fine-tune the InternVL2-2B model using our proposed V2PE method in a two-stage training procedure. 1) In the first stage, we fine-tune the released InternVL2-2B model on our mixed training dataset, incorporating V2PE. During training, as described in Eq. 6, the positional increment \\(\\delta\\) is randomly selected, enabling the model to adapt to varying positional increments for visual tokens flexibly. The model obtained after this stage is denoted as InternVL2-V2PE-32K. 2) In the second stage, we further fine-tune the model on the Long-MR-256K dataset, with sequence lengths up to 256K tokens. To preserve the model's general performance in shorter context, we retain \\(50\\%\\) of the data from the first stage. To optimize memory usage, we apply the Ring Attention [66], enabling model parallelism across multiple GPUs. The model obtained after the second stage is denoted as InternVL2-V2PE-256K."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.871,
+ 0.906,
+ 0.901
+ ],
+ "angle": 0,
+ "content": "Evaluation Benchmarks. We evaluate our trained models on various long-context and standard benchmarks, in"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "content": "21075"
+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.09,
+ 0.089,
+ 0.908,
+ 0.119
+ ],
+ "angle": 0,
+ "content": "Table 4. Comparison with existing MLLMs on general MLLM benchmarks. \"#Param\" denotes the number of parameters. The designation \"—\" indicates that the corresponding score is not released. Numbers in gray are results evaluated by ourselves. \\( \\delta \\) is fixed \\( 1/2 \\) during testing."
+ },
+ {
+ "type": "table",
+ "bbox": [
+ 0.214,
+ 0.121,
+ 0.782,
+ 0.261
+ ],
+ "angle": 0,
+ "content": "| Model | #Param | ChartQA | DocVQA | AI2D | InfoVQA | SQA | POPE | MMMUval | MMBenchEn | SEEDi | Avg |
| InternVL2-2B [20] | 2.0B | 71.7 | 86.9 | 74.1 | 58.9 | 94.1 | 85.2 | 36.3 | 73.4 | 70.9 | 72.4 |
| InternVL2-2B-FT32K | 2.0B | 75.6 | 84.9 | 73.7 | 56.5 | 94.7 | 88.5 | 35.3 | 73.4 | 70.9 | 71.1 |
| DeepSeek-VL-1.3B [71] | 2.0B | 47.4 | 36.5 | 51.5 | 20.6 | 68.4 | 85.9 | 33.8 | 66.4 | 66.0 | 52.9 |
| Qwen2-VL-2B [115] | 2.0B | 73.5 | 90.1 | 74.7 | 65.5 | 77.7 | 88.2 | 41.1 | 74.9 | 72.9 | 73.1 |
| Aquila-VL-2B [42] | 2.2B | 32.0 | 85.0 | 75.1 | 58.3 | 95.1 | 83.1 | 46.9 | 79.0 | 73.9 | 69.8 |
| MiniCPM-V-2 [135] | 2.8B | 55.6 | 71.9 | 62.9 | 36.0 | 80.7 | 86.3 | 38.2 | 64.1 | 67.1 | 62.5 |
| Vinterm-3B-beta [33] | 3.7B | 68.3 | 78.1 | 69.1 | 52.2 | 75.0 | 87.4 | 46.7 | 70.6 | 70.0 | 68.6 |
| Llama 3.2 11B [108] | 11B | 83.4 | 88.4 | 91.1 | - | - | - | 50.7 | 68.0 | - | - |
| Qwen2-VL-72B [115] | 73B | 88.3 | 96.5 | 88.1 | 84.5 | 91.2 | 87.2 | 64.5 | 86.9 | 77.9 | 85.0 |
| GPT-4o [81] | - | 85.7 | 92.8 | 84.7 | - | 90.1 | 97.2 | 69.1 | 82.1 | 76.7 | - |
| InternVL2-V2PE-32K (δ = 1/2) | 2.0B | 76.8 | 84.9 | 73.5 | 56.0 | 94.9 | 88.7 | 35.8 | 73.8 | 71.2 | 72.9 |
"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.089,
+ 0.267,
+ 0.908,
+ 0.31
+ ],
+ "angle": 0,
+ "content": "Table 5. Comparison with existing MLLMs on long context MLLM benchmarks. “#Param” denotes the number of parameters. The designation “-” indicates that the corresponding score is not released. Numbers in gray are results evaluated by ourselves. \\(\\delta\\) is fixed 1/256 during testing."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ 0.457
+ ],
+ "angle": 0,
+ "content": "| Model | #Param | MM-NIAH | Milebench | VideoMME |
| Image | Text | Avg | T | S | NI | Avg |
| InternVL2-2B [20] | 2.0B | 23.0 | 18.9 | 21.0 | 58.2 | 54.5 | 37.0 | 49.9 | 48.2 |
| InternVL2-2B-FT32K | 2.0B | 73.0 | 81.1 | 77.05 | 63.6 | 56.0 | 96.2 | 71.9 | 47.8 |
| Phi-3-Vision [1] | 2.7B | 24.9 | 26.3 | 25.6 | 46.9 | 50.0 | 73.8 | 56.9 | 40.7 |
| LongLLaVA [120] | 9B | 28.8 | 57.1 | 43.0 | 47.3 | 46.8 | 50.0 | 48.0 | 43.7 |
| LongLLaVA [120] | 13B | 27.7 | 55.7 | 41.7 | 52.7 | 52.1 | 50.0 | 51.6 | 51.6 |
| VILA1.5 [62] | 13B | 5.4 | 11.0 | 8.2 | 21.4 | 48.5 | 7.7 | 25.9 | 47.4 |
| LongVILA [132] | 7B | 33.7 | 34.1 | 33.9 | 65.3 | 55.1 | 91.9 | 70.8 | 60.1 |
| Gemini-1.5 [103] | - | 28.5 | 82.1 | 55.2 | 50.2 | 58.3 | 97.9 | 68.8 | 69.6 |
| GPT-4o [81] | - | 52.3 | 75.0 | 63.7 | 56.2 | 63.5 | 99.8 | 73.2 | 64.7 |
| Claude3-Opus [5] | - | - | - | - | 37.4 | 48.1 | 85.3 | 56.9 | 59.7 |
| InternVL2-V2PE-32K (δ = 1/256) | 2.0B | 78.1 | 85.5 | 81.8 | 65.3 | 55.1 | 96.7 | 72.4 | 52.3 |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.467,
+ 0.483,
+ 0.619
+ ],
+ "angle": 0,
+ "content": "cluding the Long-VQA validation split, MM-NIAH [119] (including our augmented MM-NIAH\\(_{1\\mathrm{M}}\\)), and widely used VQA benchmarks such as ChartQA [77], DocVQA [78], AI2D [54], InfoQA [54], SQA [72], POPE [60], MMMU [137], MMBench\\(_{EN}\\) [70], and SEED\\(_{Image}\\) [57]. To systematically assess VLMs' performance on long-context tasks, we also compare our model with other state-of-the-art models on two additional long-context benchmarks: MileBench [94] for multi-image and video understanding, and Video-MME [37] for video analysis tasks."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.623,
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+ 0.699
+ ],
+ "angle": 0,
+ "content": "Effectiveness of V2PE. We compare the performance of InternVL2-V2PE-32K and InternVL2-V2PE-256K on the Long-VQA validation split, MM-NIAH (including MM\\(\\mathrm{NIAH}_{1\\mathrm{M}}\\)), and other standard multimodal benchmarks. The results are shown in Tab. 1, Tab. 2, and Tab. 3."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.702,
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+ 0.793
+ ],
+ "angle": 0,
+ "content": "We demonstrate how varying positional increments impact the models' performance on these benchmarks. Specifically, \\(\\mathrm{MM - NIAH_{1M}}\\) is evaluated on the image-retrieval task where both the \"needle\" and \"question\" are images, posing a stringent challenge for multimodal models to handle visual tokens in long-context sequences."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "On standard short-context benchmarks (see Fig. 2), V2PE does not offer obvious advantages. We observe a performance drop on specific tasks, such as DocVQA and InfoQA, when the positional increment is reduced. In Appendix Sec. A, we investigate this issue by applying V2PE in the pre-training stage of VLMs. The results indicate that the marginal benefits of V2PE on short-context benchmarks"
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+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "stem from the fact that InternVL2 was pre-trained and fine-tuned (SFT) using the default position encoding, making it inherently adapted to \\(\\delta = 1\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "However, on long-context benchmarks like Long-VQA and MM-NIAH (see Fig. 1 and Fig. 3), V2PE demonstrates a clear advantage. For instance, on Long-VQA, the best performance is typically achieved when the positional increments are reduced to around 1/8 or 1/16. Moreover, as the token sequence length increases, smaller positional increments tend to be optimal."
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "In the MM-NIAH benchmark, involving longer token sequences, V2PE demonstrates optimal performance with positional increments of 1/256. Notably, InternVL2-V2PE-32K markedly enhances performance on sequences of 256K tokens, boosting scores from 1.5 to 56.9. This enhancement is also evident in InternVL2-V2PE-256K, which records the highest scores across various token sequence lengths when using a positional increment of 1/256. For sequences of 512K tokens, the score surges from 10.8 to 95.1. Additionally, with the same positional increment of 1/256, the InternVL2-V2PE-256K model attains a significant score of 64.5 on sequences reaching 1M tokens."
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "From our previous experimental results, we observe a qualitative relationship among the choice of \\(\\delta\\), the context length, and model performance: with longer context, selecting a smaller \\(\\delta\\) improves model's performance. Therefore, in later experiments, we set \\(\\delta\\) to \\(1/2\\) for evaluating general and \\(1/256\\) for long context benchmarks respectively, based"
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+ [
+ {
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 6. Performance on MM-NIAH benchmarks with different position encoding strategies across six task types: \"image retrieval\", \"text retrieval\", \"image counting\", \"text counting\", \"image reasoning\" and \"text reasoning\". \"Image only\", \"Text only\", \"Both\" and \"Baseline\" represent applying V2PE to visual tokens, textual tokens, both simultaneously, and neither, respectively."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
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+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 7. Performance on image retrieval task in MM-NIAH benchmark using V2PE and token compression strategies. Token compression reduces the number of visual tokens by a ratio \\(\\delta\\), whereas V2PE employs a smaller positional increment \\(\\delta\\) while preserving all visual tokens."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "on the context length. Furthermore, we provide theoretical analysis on optimal \\(\\delta\\) selection in the Appendix Sec. B"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "content": "4.3. Comparison with Other VLMs."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "We evaluate the performance of InternVL2-V2PE-32K against state-of-the-art vision-language models (VLMs) on both standard and long-context multimodal benchmarks, with results presented in Tab. 4 and Tab. 5, respectively. Despite built on a relatively small 2B-parameter model and incorporating a substantial amount of long-context training data, InternVL2-V2PE-32K retains highly competitive results on standard short-context multimodal benchmarks."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "On long-context multimodal benchmarks, the model performs exceptionally well, demonstrating that V2PE can significantly enhance long-context abilities even built on a relative small model. These results validate the potential of V2PE for improving the performance of VLMs on a wide range of long-context multimodal tasks."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.4. Ablation Study"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Can V2PE be applied to textual tokens? We evaluate the impact of V2PE on visual tokens, textual tokens, both concurrently, and neither, with results on six MM-NIAH tasks presented in Fig. 6. Applying V2PE solely to textual tokens yields marginal improvements in language understanding but degrades performance on vision-centric tasks. When applied to both modalities, model performance exhibits instability. Notably, restricting V2PE to visual tokens consistently enhances performance across all tasks."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "Figure 8. Performance on image retrieval task in MM-NIAH benchmark with variable versus fixed position increments for visual tokens in the VLMs. \"Variable\" denotes training with variable increments, allowing evaluation with arbitrary fixed \\(\\delta\\), while \"Fixed\" means training and evaluating with the same fixed \\(\\delta\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Is V2PE equivalent to visual token compression? We also compare V2PE with the token compression strategy, where visual tokens undergo pooling operations to reduce token number, allowing more images to be processed ideally. We test various compression ratios and evaluate the model's performance on the MM-NIAH image retrieval task. The results, shown in Fig. 7, reveal that while token compression results in a rapid performance drop when the number of visual tokens is reduced 16 times or more, our method demonstrates stable performance across all settings."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "Can positional increment be fixed during training? We train a set of InternVL2-FT-32K models with both V2PE method and fixed positional increments under the same settings. Their performance in the image retrieval task of the MM-NIAH benchmark is shown in Fig. 8. The results indicate that fixing the positional increment does not lead to optimal task performance. In contrast, the variable adjustment of positional increments provides consistent improvements."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.558,
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+ ],
+ "angle": 0,
+ "content": "Is V2PE superior to the position encoding extension methods? To compare V2PE with existing position encoding extension methods, we evaluated both InternVL2-V2PE-32K and InternVL2-FT-32K models using two widely adopted position extension techniques: linear interpolation and NTK-Aware Scaled RoPE. The results, presented in Fig. 5, Tab. 1, and Tab. 3, show that V2PE not only offers greater stability but also achieves superior task performance, especially in long-context scenarios."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Conclusion"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.733,
+ 0.906,
+ 0.888
+ ],
+ "angle": 0,
+ "content": "We investigate the long-context capabilities of the existing VLMs, using our augmented long-context datasets, and find that positional encoding for visual tokens is critical for the long-context capabilities of VLMs. Based on this observation, we introduce V2PE, a novel position encoding strategy that applies smaller, variable positional increments to visual tokens, enabling more efficient handling of long-context multimodal sequences. By leveraging V2PE and our augmented long-context datasets, we fine-tune the open-source VLMs successfully, which shows significant improvements on both general and long-context multimodal benchmarks."
+ },
+ {
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+ [
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+ "angle": 0,
+ "content": "References"
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+# V2PE: Improving Multimodal Long-Context Capability of Vision-Language Models with Variable Visual Position Encoding
+
+Junqi Ge $^{1,4*}$ , Ziyi Chen $^{1,4*}$ , Jintao Lin $^{3,4*}$ , Jinguo Zhu $^{4*}$ , Xihui Liu $^{3}$ , Jifeng Dai $^{1,4}$ , Xizhou Zhu $^{1,2,4\dagger}$
+
+$^{1}$ Tsinghua University $^{2}$ SenseTime Research $^{3}$ University of Hong Kong $^{4}$ Shanghai AI Laboratory
+
+# Abstract
+
+Vision-Language Models (VLMs) have shown promising capabilities in handling various multimodal tasks, yet they struggle in long-context scenarios, particularly tasks involving videos, high-resolution images, or lengthy image-text documents. In our work, we first conduct an empirical analysis of VLMs' long-context capabilities using our augmented long-context multimodal datasets. Our findings reveal that directly applying the positional encoding mechanism used for textual tokens to visual tokens is suboptimal, and VLM performance degrades sharply when the position encoding exceeds the model's context window. To address this, we propose Variable Visual Position Encoding (V2PE), a novel positional encoding approach that employs variable and smaller increments for visual tokens, enabling more efficient management of long multimodal sequences. Our experiments demonstrate the effectiveness of V2PE in enhancing VLMs' ability to effectively understand and reason over long multimodal contexts. We further integrate V2PE with our augmented long-context multimodal datasets to fine-tune the open-source VLMs. The fine-tuned model achieves strong performance on both standard and long-context multimodal tasks. Notably, when the sequence length of the training dataset is increased to 256K tokens, the model is capable of processing multimodal sequences up to 1M tokens, highlighting its potential for real-world long-context applications. We shall release the code, model weights, and datasets to facilitate further research.
+
+# 1. Introduction
+
+With the rapid advancement of Large Language Models (LLMs) [14, 29, 83, 99, 108], Vision-Language Models (VLMs) have made substantial strides [19, 82, 103, 115], excelling at tasks like visual captioning [17], visual question answering [78], and complex visual reasoning [136]. Despite this progress, existing research [112, 119, 132, 144]
+
+
+Figure 1. Performance on the image retrieval task using a token length of up to 1M on MM-NIAH [119] across different VLMs. The GPT-4o [81] version is 2024-08-06, while InternVL2-2B [20] models are both fine-tuned from the official release, using our augmented data, with token lengths reaching up to 256K per sample.
+
+reveals that VLMs struggle to generalize effectively when confronted with multimodal long-sequence inputs (e.g., long videos [121, 126], high-resolution images [45, 122], and lengthy image-text documents [3, 105, 151]). This limitation emerges even in relatively straightforward, such as object counting and passkey duplication, significantly restricting VLMs' potential applications and impeding the enhancement of user experience [22, 114, 119, 120].
+
+Recent efforts have attempted to extend VLMs' capabilities to process multiple images or handle long multimodal sequences. However, these approaches either permit only a small number of images (typically fewer than five) [52, 65, 149] or primarily target video data (e.g., LongVA [144], LongVILA [132], LongLLAVA [120], VideoXL [93]). These studies are only limited to specific application scenarios, highlighting the challenges VLMs face in handling complex and long-sequence multimodal data, which makes a key research question particularly urgent: Why do VLMs perform poorly in long-context scenarios, and how can we unlock their capacity for comprehensive multimodal understanding and reasoning over long sequences?
+
+To investigate this, we first construct a large-scale pool of long-context multimodal datasets to evaluate and analyze VLM capabilities systematically. By extending the se
+
+
+Figure 2. Illustration from our proposed Variable Visual Position Encoding (V2PE). Unlike the standard position encoding used in most VLMs, which shares the same stepwise positional increment for both visual and textual tokens, our proposed Variable Visual Positional Encoding (V2PE) uses smaller and variable positional increments specifically for visual tokens compared to textual tokens. This flexible design enables VLMs to handle long-context multimodal sequences within a limited context window.
+
+quence length of existing instruction-tuning datasets (e.g., DocVQA [78], ChartQA [77], SQA [72]) to 32K-64K tokens, we adapt these datasets specifically to train and validate VLMs for enhanced long-context capabilities. We also extend long-context benchmarks from 64K to 1M tokens (e.g., by employing the official MM-NIAH [119] curation code) to validate VLM performance with longer contexts, providing a deeper understanding of the limitations.
+
+Our empirical analysis shows that the design of positional encodings of visual tokens plays an essential role in long-context scenarios, which is often overlooked in previous studies. Specifically, (1) directly applying the LLM positional encoding mechanism to visual tokens is suboptimal, and (2) the performance of VLMs degrades significantly when positional encodings for visual tokens exceed the trained context window, and previous position encoding extension methods applicable to LLMs provide only marginal improvements. These findings highlight the need for specialized positional encoding methods to manage visual tokens in long-context multimodal scenarios effectively.
+
+To address these challenges, we propose Variable Visual Position Encoding (V2PE), a novel approach for handling visual token positions in VLMs. Considering the continuity nature of pixel space, adjacent visual tokens exhibit greater similarity than adjacent text tokens. Thus, V2PE uses smaller positional increments for visual tokens than text tokens (see Fig. 2). Furthermore, V2PE employs variable positional increments for visual tokens during training, enabling the model to learn and adapt to position encoding in various scenarios. This variable adjustment allows the model to effectively handle different numbers and complexities of image inputs during inference, thereby enhancing its stability and adaptability in long-context processing.
+
+In experiments, we apply V2PE to enhance the long-context capability of open-source VLMs [19, 20], and fine-tune them using our extended multimodal datasets. The resulting models not only maintain strong performance on standard short-context multimodal benchmarks, but also excel in tasks requiring long-context handling, which outperform traditional token compression and other position encoding extension methods. In particular, after further fine-tuning on multimodal sequences up to 256K tokens, our model achieves promising performance in multimodal retrieval tasks involving sequences as long as 1M tokens, as shown in Fig. 1. The main contributions of this paper are as follows:
+
+- We construct mixed datasets to improve VLMs' long-context capability by augmenting existing multimodal instruction tuning datasets and conduct a thorough investigation into why current VLMs struggle with long-context multimodal inputs, revealing that directly applying LLM positional encoding to visual tokens is ineffective.
+- We propose Variable Visual Position Encoding (V2PE), a novel positional encoding strategy that employs variable and smaller increments for visual tokens, significantly enhancing VLMs' ability to understand and reason over extended multimodal contexts.
+- We apply our V2PE method and extend training data on the open-source VLMs. The fine-tuned VLMs perform exceptionally well on both general multimodal benchmarks and long-context multimodal tasks, with the capacity to handle sequences of up to 1M tokens, significantly longer than training sequence.
+
+# 2. Related Works
+
+Vision-Language Models (VLMs). With the development of Large Language Models (LLMs) [6, 10, 14, 36, 83, 99, 101, 104, 107, 108, 123, 124, 134, 148], the integration of vision and language modalities is significantly catalyzed. This progress gives rise to Vision-Language Models (VLM), which can perceive visual contents, conduct visual reasoning, and engage in multi-modal dialogue with humans. Both proprietary commercial VLMs [5, 51, 79, 82, 95, 102, 103, 129] and open-source VLMs [46, 73, 75, 106, 113] have witnessed this significant evolution. For commercial entities, GPT-4V [82] incorporates visual inputs to extend GPT-4 [83] with capabilities of handling multi-modal content, while Google's Gemini series [102, 103] are able to process 1 million multi-modal tokens with significant performance. For open-source initiatives, BLIP series [27, 58, 59], LLaVA series [63–65], Qwen-VL series [7, 115], MiniCPM-V series [135], InternVL series [19, 20, 39], and others [9, 25, 26, 34, 35, 48, 61, 71, 86, 117, 140, 142] have also impacted the AGI landscape in the research community by linking large language models [6, 14, 107] and large vision models [4, 19, 30, 89] in processing both vi
+
+
+Figure 3. Statistics of our mixed training dataset (Long-MR, Long-VQA, and short SFT from InternVL2). The left and right figures illustrate the distributions of token counts and image counts per training sample, respectively.
+
+sual and textual modality. Specifically, there are also some works advance VLMs' power by improving the scale and quality of data [15, 42, 68], training on high-resolution images [45, 122] or optimizing vision foundation models [19, 139].
+
+Long Context Modeling. Due to practical demands, a large body of research [13, 21, 47, 67, 69, 143, 147] has been developed to extend the context length of LLMs. One mainstream direction is to increase the length of LLM's context window by extrapolation of position encoding [11, 16, 32, 85, 87, 96, 97, 146, 150], which allows the LLM to process unseen positions during inference. Another line of research focuses on alleviating the complexity of self-attention by using sparse attention [8, 18, 23, 31, 88, 138], linear-complexity state-space modules [40, 41], or approximate attention computation [24, 55, 91, 116] as the alternatives for dense global attention. The context can also be extended by utilizing external memory to retrieve relevant tokens from the compression of past inputs, such as chunked input [80, 118, 131, 141] or cached KV activations [2, 49, 109, 127, 128]. Other works [43, 127, 130] also adopt sliding windows to achieve an infinite context by only maintaining the activations for the very first and the latest tokens. Recent efforts [52, 120, 132, 144] aim to improve VLMs' ability to process multiple images and long multimodal sequences. However, these studies are often limited to specific applications, revealing challenges faced by VLMs in processing complex and long-context data.
+
+Position Encoding in Transformer. To address the lack of sequential information inherent in self-attention mechanisms, Transformers [110] utilize position encoding as a fundamental component to provide position information. The common position encoding design can be broadly categorized into absolute position encoding (APE) and relative position encoding (RPE). The absolute position encoding [12, 53, 56, 110, 111, 145] is simple and intuitive, as it embeds each absolute position position into a position vector which is then added into the representation of input sequences, but this strategy cannot be applied effectively for long sequences. To improve the modeling of long-term dependencies, relative positional encod
+
+ing [28, 74, 87, 90, 92, 98, 100, 133] focuses on utilizing distance between tokens as the position information. Some research works [44, 87, 100] aim to utilize relative position for length extrapolation to train Transformers on short sequences and inference on longer contexts. Another research direction is Rotary Position Encoding (RoPE), which embeds position information by rotating the key-query products according to their relative distances. Methods like Position Interpolation [16], NTK-Aware scaling [11], and LongRoPE [32] make progress on top of RoPE [98] to improve its poor extrapolation capability for longer sequences. For VLMs, most studies [7, 20, 132] adopt the same position embedding methods used in LLMs, and there are also some works [38, 76, 125] to explore different diagrams of the positional encoding schemes.
+
+# 3. Method
+
+# 3.1. Augmented Long-context Multimodal Datasets
+
+We introduce two augmented long-context multimodal datasets: Long Visual Question Answering and Long multimodal Retrieval. These datasets aim to enhance VLMs' long-context training and establish a systematic evaluation framework, thereby addressing the challenges associated with long-context understanding that extend beyond the scope of existing training data.
+
+Long Visual Question Answering (Long-VQA). The Long-VQA dataset aims to evaluate the capabilities of VLMs in understanding and reasoning over long multimodal sequences within general visual question-answering tasks. We extended 17 widely adopted datasets (e.g., DocVQA [78], GQA [50], SQA [72]), expanding their context from short sequences to those containing up to 64K tokens. The tasks involve answering questions that require commonsense reasoning, factual knowledge, and interpretation of visual information from charts, documents, and real-world texts.
+
+To extend existing datasets, we interleaved images from multiple samples into a single input, increasing sequence length and complexity to simulate real-world scenarios involving extraneous information. To reduce ambiguity, we refined questions to be more specific, incorporating instructions like "Based on page $n$ , answer the following question", which helps models focus on relevant content.
+
+Long-VQA contains 533K samples: 392K for training (up to 32K tokens) and 141K for validation (up to 64K tokens) to evaluate the generalization to longer contexts.
+
+Long Multimodal Retrieval (Long-MR). Inspired by MM-NIAH (Multimodal Needle-in-a-Haystack) [119], we developed Long-MR by inserting a target image or textual segment into sequences of interleaved images and texts. Long-MR evaluates VLMs' ability to retrieve specific targets from ultra-long multimodal sequences, requiring mod-
+
+els to locate the inserted "needle" and answer associated questions. We generated two subsets of Long-MR: Long-MR-32K (488K samples, sequences up to 32K tokens) and Long-MR-256K (50K samples, sequences up to 256K tokens), following the data construction process of MM-NIAH.
+
+To assess the limitation of VLMs' long-context capabilities, we further extended MM-NIAH evaluation benchmark following the official code[84], generating testing samples with sequence lengths ranging from 64K to 1M tokens, named after MM-NIAH1M benchmark. This pushes the testing capacity beyond the original MM-NIAH, which is limited to sequences up to 64K tokens.
+
+We combined the training splits of Long-VQA and Long-MR with short-context instruction-tuning datasets, as utilized in InternVL2, to create a mixed training set for our experiments. Fig. 3 illustrates the distribution of token sequence lengths and the number of images in the mixed training dataset, highlighting our focus on long-context samples.
+
+More details about the construction process, examples, and statistics of the datasets are provided in Appendix Sec. C.
+
+# 3.2. Variable Visual Position Encoding
+
+Position Encoding in Vision-Language Models. Position encoding is essential in transformer architectures, enabling models to capture sequential relationships by providing tokens with positional information. It usually involves two sequential steps: Position Index Derivation $f_{\mathrm{pos}}$ , which assigns a positional index $p_i$ to each token $x_i$ , and Position Embedding Computation $g_{\mathrm{emb}}$ , which transforms these indices into position embeddings that influence the attention mechanism.
+
+Formally, the multimodal input in VLMs can be represented as a sequence of $N$ interleaved textual and visual tokens:
+
+$$
+\mathbf {X} = \left[ x _ {0}, x _ {1}, \dots , x _ {N - 1} \right], \tag {1}
+$$
+
+where each token $x_{i}$ is either a textual token $x_{i}^{\mathrm{txt}}$ or a visual token $x_{i}^{\mathrm{vis}}$ .
+
+The Position Index Derivation function $f_{\mathrm{pos}}$ is recursively defined to capture the sequential nature of token positions:
+
+$$
+p _ {i} = \left\{ \begin{array}{l l} 0, & \text {i f} i = 0, \\ f _ {\text {p o s}} \left(p _ {i - 1}, x _ {i}\right), & \text {f o r} i = 1, 2, \dots , N - 1. \end{array} \right. \tag {2}
+$$
+
+In existing LLMs and VLMs, the position index increments uniformly by 1 for each token, regardless of its modality:
+
+$$
+p _ {i} = p _ {i - 1} + 1, \quad \text {f o r} i = 1, 2, \dots , N - 1. \tag {3}
+$$
+
+The Position Embedding Computation $g_{\mathrm{emb}}$ then transforms these position indices into embeddings. VLMs typically adopt the same position embedding methods used in
+
+Large Language Models (LLMs), such as Relative Position Encoding [92] or Rotary Position Embedding (RoPE) [98]. These embeddings are incorporated into the token representations at each layer to provide positional context during attention computations. For instance, in RoPE encoding, the token representation $\mathbf{h}_i$ integrates positional information as:
+
+$$
+\mathbf {h} _ {i} ^ {\prime} = \mathbf {h} _ {i} \otimes g _ {\mathrm {e m b}} \left(p _ {i}\right), \tag {4}
+$$
+
+where $\otimes$ represents element-wise multiplication, and $\mathbf{h}_i^{\prime}$ is subsequently used as query or key embeddings in the Transformer attention mechanism.
+
+Variable Position Index Derivation. The uniform increment of position indices in current VLMs does not account for the differences in information complexity and redundancy between textual and visual tokens. Visual tokens often exhibit higher redundancy and greater similarity with adjacent tokens, suggesting they may require smaller positional increments than textual tokens. Moreover, the large number of visual tokens can cause position indices to exceed the model's pre-trained context window, leading to degraded performance.
+
+To address these issues, we propose a modality-specific recursive function for position index derivation, assigning position indices differently for textual and visual tokens:
+
+$$
+p _ {i} = p _ {i - 1} + \left\{ \begin{array}{l l} 1, & \text {i f} x _ {i} \text {i s a t e x t u a l t o k e n ,} \\ \delta , & \text {i f} x _ {i} \text {i s a v i s u a l t o k e n ,} \end{array} \right. \tag {5}
+$$
+
+where $\delta$ is a smaller increment ( $\delta < 1$ ) that reduces the rate at which position indices increase for visual tokens. The standard increment of 1 is retained for textual tokens to maintain their positional distinctions.
+
+During training in our experiments, $\delta$ is randomly selected for each image from a set of fractional values:
+
+$$
+\delta \in \Delta = \left\{1, \frac {1}{2}, \frac {1}{4}, \frac {1}{8}, \frac {1}{1 6}, \frac {1}{3 2}, \frac {1}{6 4}, \frac {1}{1 2 8}, \frac {1}{2 5 6} \right\}. \tag {6}
+$$
+
+Note that, $\delta$ remains constant within a single image to preserve the relative positional relationships among its visual tokens. For inputs containing multiple images, $\delta$ can be independently chosen for each image.
+
+During inference, $\delta$ can be flexibly selected based on the input sequence length, allowing us to balance task performance and ensure that position indices remain within the model's valid context range. Specifically, for long input sequences, a smaller $\delta$ can be employed to control the increase in position indices, preventing from exceeding the trained positional embedding range, as illustrated in Fig. 2.
+
+Discussion and Comparison with Previous Methods. Our Variable Visual Position Encoding (V2PE) offers several advantages over existing long-context methods:
+
+
+Figure 4. Performance on Long-VQA (long) with sequence lengths up to $32\mathrm{K}$ tokens and its corresponding standard VQA (short) benchmarks. Compared with GPT-4o and InternVL2-FT-Short, the InternVL2-FT-32K, enhanced with our proposed Long-VQA dataset, effectively narrows the performance gap between short and long-context tasks.
+
+
+
+
+
+
+Figure 5. Performance on image retrieval task in MM-NIAH (left) and QA task in Long-VQA (right) with different positional increments. Additionally, we include the results of InternVL2-FT-32K when utilizing linear interpolation (linear) [16] and NTK-Aware Scaled RoPE (NTK) [11] position encoding extension methods.
+
+
+
+1) Unlike approaches that reduce the number of visual tokens through attention pooling or feature pooling, which potentially result in information loss, V2PE retains all visual tokens within the VLM, preserving the richness and granularity of visual content.
+
+2) Position encoding extension methods (e.g., Positional Interpolation [16] and Extrapolation [96]) adjust position embeddings during inference to accommodate longer sequences. However, extrapolation extends position indices beyond the model's trained range, while interpolation methods (linear [16] / NTK-aware [11]) face performance degradation with unseen position increment, potentially requiring additional fine-tuning [85]. In contrast, V2PE allows the VLM to adapt position indices with arbitrary intervals while evaluating zero-shot in longer contexts by dynamically selecting $\delta$ during training. This strategy avoids unexpected position embeddings, ensures consistent model performance across varying input lengths and avoids additional fine-tuning in longer contexts.
+
+# 4. Experiment
+
+# 4.1. Analysis of VLMs' Long-Context Capabilities
+
+We first analyze the long-context capabilities of existing VLM by using our constructed long-context multimodal datasets (see Sec. 3.1). Note that this sub-section does not use V2PE.
+
+Experimental Setup. We fine-tune InternVL2-2B on two different training datasets and obtain four finetuned models: 1) InternVL2-FT-Short: This model is fine-tuned on
+
+Table 1. Performance on Long-VQA task with sequence lengths up to 64K tokens at various positional increments $\delta$ .
+
+| Model | δ | 16K | 32K | 40K | 48K | 56K | 64K | Avg |
| InternVL2-2B | - | 52.8 | 27.3 | 23.0 | 23.9 | 22.6 | 21.0 | 28.4 |
| InternVL2-FT-32K | - | 63.0 | 56.1 | 38.3 | 35.5 | 34.6 | 30.6 | 43.0 |
| InternVL2-V2PE-32K | 1/256 | 58.2 | 52.8 | 48.1 | 45.4 | 43.8 | 40.3 | 48.1 |
| 1/128 | 60.0 | 53.7 | 49.5 | 46.5 | 45.3 | 41.3 | 49.4 |
| 1/64 | 61.0 | 54.5 | 50.1 | 47.4 | 45.9 | 42.2 | 50.2 |
| 1/32 | 61.9 | 55.4 | 51.4 | 47.5 | 46.4 | 42.3 | 50.8 |
| 1/16 | 62.9 | 55.6 | 51.2 | 48.3 | 47.0 | 42.5 | 51.3 |
| 1/8 | 63.2 | 55.8 | 52.0 | 47.6 | 45.8 | 41.9 | 51.1 |
| 1/4 | 63.4 | 55.7 | 51.3 | 47.0 | 45.1 | 39.7 | 50.4 |
| 1/2 | 63.3 | 54.9 | 46.8 | 36.8 | 33.3 | 29.2 | 44.1 |
| 1/1 | 62.3 | 49.0 | 30.0 | 26.5 | 27.0 | 25.9 | 36.8 |
| InternVL2-FT-32K (Linear [16]) | - | 62.5 | 51.3 | 42.1 | 34.7 | 31.4 | 25.9 | 40.9 |
| InternVL2-FT-32K (NTK [11]) | - | 63.2 | 54.2 | 44.9 | 41.0 | 40.4 | 34.3 | 45.3 |
+
+the original instruction-tuning dataset (short-context) used by InternVL2-2B. It serves as a baseline to evaluate performance without exposure to long-context data. 2) InternVL2-FT-32K: This model is fine-tuned on a mixed training dataset introduced in Sec. 3.1, incorporating our augmented long-context training data to enhance its long-context capacity. 3) InternVL2-32K-s1/16: To explore the effect of positional encoding increments on visual tokens, we reduce the positional increment to 1/16 for visual tokens, holding it fixed across training and inference, while maintaining training on the same mixed dataset as InternVL2-FT-32K. 4) InternVL2-32K-s1/256: Similarly, we further reduce the positional increments to 1/256 and keep it fixed to examine its impact. Notably, the positional increments for this model also remain fixed during training, without using V2PE.
+
+Evaluation Benchmarks. All models are evaluated on the Long-VQA validation split and the MM-NIAH benchmark. Additionally, performance on the standard multimodal VQA benchmarks is assessed if needed.
+
+Effectiveness of Augmented Long-Context Multimodal Data. We compare the performance of InternVL2-FT-Short and InternVL2-FT-32K on both the Long-VQA validation set and standard short-context benchmarks, as shown in Fig. 4. The results reveal that InternVL2-FT-Short, which is trained exclusively on short-context data, performs competitively on standard benchmarks but suffers significant degradation on long-context tasks. Even advanced models, such as GPT-4o, exhibit notable declines when the input to
+
+Table 2. Performance on standard VQA benchmarks with different positional increment $\delta$ . The highest score is marked in bold.
+
+| Model | δ | ChartQA | DocVQA | AI2D | InfoVQA | SQA | POPE | MMMUval | MMBenchEN | SEEDI | Avg |
| InternVL2-2B | - | 71.7 | 86.9 | 74.1 | 58.9 | 94.1 | 85.2 | 36.3 | 73.4 | 70.9 | 72.4 |
| InternVL2-FT-Short | - | 76.0 | 85.7 | 74.0 | 57.1 | 94.0 | 88.9 | 34.8 | 73.0 | 66.6 | 72.2 |
| InternVL2-FT-32K | - | 75.6 | 84.8 | 73.6 | 56.5 | 94.7 | 88.7 | 35.3 | 73.8 | 65.1 | 72.0 |
| InternVL2-V2PE-32K | 1/256 | 76.2 | 81.6 | 72.3 | 51.7 | 94.3 | 88.0 | 35.7 | 73.2 | 71.0 | 71.6 |
| 1/128 | 76.5 | 82.3 | 72.6 | 52.9 | 94.2 | 88.1 | 34.7 | 73.5 | 70.9 | 71.7 |
| 1/64 | 76.4 | 83.0 | 72.6 | 53.6 | 94.4 | 88.0 | 35.4 | 73.4 | 70.8 | 72.0 |
| 1/32 | 76.9 | 83.6 | 72.6 | 54.3 | 94.3 | 88.1 | 35.7 | 73.3 | 71.0 | 72.2 |
| 1/16 | 77.2 | 84.3 | 73.0 | 55.2 | 94.5 | 88.1 | 35.7 | 73.3 | 71.0 | 72.5 |
| 1/8 | 77.0 | 84.6 | 73.1 | 55.4 | 94.6 | 88.1 | 36.0 | 72.9 | 71.0 | 72.5 |
| 1/4 | 77.3 | 84.7 | 73.3 | 56.5 | 94.6 | 88.2 | 36.0 | 73.6 | 71.0 | 72.8 |
| 1/2 | 76.8 | 84.9 | 73.5 | 56.0 | 94.9 | 88.7 | 35.8 | 73.8 | 71.2 | 72.9 |
| 1/1 | 76.6 | 84.9 | 73.7 | 55.2 | 94.8 | 88.4 | 36.1 | 73.7 | 71.1 | 72.7 |
+
+Table 3. Performance on the image retrieval task in MM-NIAH with token lengths up to 1M at various position increments $\delta$ . Test samples exceeding ${64}\mathrm{\;K}$ tokens are from our extended $\mathrm{{MM}} - {\mathrm{{NIAH}}}_{1\mathrm{M}}$ . The designation "NA" indicates that the GPT-4 results are not applicable due to the extremely long context length.
+
+| Model | δ | 1K | 16K | 32K | 64K | 128K | 256K | 512K | 1M |
| InternVL2-2B | - | 23.9 | 33.7 | 28.7 | 26.0 | 17.3 | 21.8 | 5.3 | 0.0 |
| GPT-4o | - | 100.0 | 90.4 | 100.0 | 92.7 | 62.1 | 60.0 | 58.6 | NA |
| InternVL2-V2PE-32K | 1/256 | 100.0 | 84.7 | 79.3 | 81.5 | 61.2 | 56.9 | 36.7 | 6.0 |
| 1/64 | 96.0 | 83.9 | 78.1 | 79.5 | 43.6 | 39.3 | 23.4 | 3.4 |
| 1/16 | 96.0 | 82.4 | 73.1 | 65.4 | 57.6 | 41.3 | 19.8 | 0.0 |
| 1/4 | 96.0 | 84.2 | 76.2 | 57.6 | 48.9 | 21.5 | 2.8 | 0.0 |
| 1/1 | 83.0 | 61.2 | 42.0 | 27.5 | 25.5 | 1.5 | 0.0 | 0.0 |
| InternVL2-V2PE-256K | 1/256 | 96.0 | 97.1 | 96.6 | 97.1 | 99.1 | 95.7 | 95.1 | 64.5 |
| 1/64 | 96.0 | 94.7 | 96.6 | 97.1 | 97.1 | 94.1 | 94.1 | 62.8 |
| 1/16 | 96.0 | 94.7 | 93.1 | 94.2 | 100 | 96.2 | 92.9 | 45.1 |
| 1/4 | 96.0 | 94.4 | 100.0 | 97.1 | 75.5 | 75.2 | 38.3 | 2.5 |
| 1/1 | 91.0 | 92.8 | 96.6 | 93.1 | 56.1 | 3.7 | 10.8 | 0.0 |
| InternVL2-FT-32K with linear interpolation | - | 85.3 | 76.0 | 56.0 | 34.7 | 26.4 | 21.9 | 16.3 | 0.5 |
| InternVL2-FT-32K with NTK interpolation | - | 78.3 | 70.7 | 39.8 | 25.7 | 12.3 | 16.8 | 14.8 | 0.0 |
+
+ken count is increased, underscoring a common limitation in handling extended sequences. In contrast, InternVL2-FT32K, trained on the mixed dataset including long-context data, effectively narrows the performance gap between short and long-context tasks. This suggests it is difficult for short-context VLMs to inherently generalize to long-context multimodal tasks without further finetuning. Targeted exposure to long-context data is crucial for achieving robust performance across varying input lengths.
+
+Impact of Visual Position Encoding. To assess the impact of position encoding increments for visual tokens, we evaluate the models InternVL2-FT-32K, InternVL2-32K-s1/16, and InternVL2-32K-s1/256 on both the Long-VQA validation set and MM-NIAH benchmark.
+
+Experimental results, presented in Fig. 5, indicate that InternVL2-FT-32K continues to experience performance degradation as input token sequences grow up to $64\mathrm{K}$ tokens, despite being trained on sequences up to $32\mathrm{K}$ tokens. When the input sequence length exceeds the maximum token count during training, performance declines sharply. Even applying positional encoding extension techniques developed for large language models (LLMs) give limited benefits. However, models with reduced positional increments for visual tokens show significant improvements. Both InternVL2-32K-s1/16 and InternVL2
+
+32K-s1/256 maintain stable performance. We hypothesize that reducing the position increments by factors of 16 and 256 effectively prevents the position indices of visual tokens from exceeding the model's trained context window, thereby mitigating performance decline.
+
+# 4.2. Effectiveness of Our Proposed V2PE
+
+Experimental Setup. We fine-tune the InternVL2-2B model using our proposed V2PE method in a two-stage training procedure. 1) In the first stage, we fine-tune the released InternVL2-2B model on our mixed training dataset, incorporating V2PE. During training, as described in Eq. 6, the positional increment $\delta$ is randomly selected, enabling the model to adapt to varying positional increments for visual tokens flexibly. The model obtained after this stage is denoted as InternVL2-V2PE-32K. 2) In the second stage, we further fine-tune the model on the Long-MR-256K dataset, with sequence lengths up to 256K tokens. To preserve the model's general performance in shorter context, we retain $50\%$ of the data from the first stage. To optimize memory usage, we apply the Ring Attention [66], enabling model parallelism across multiple GPUs. The model obtained after the second stage is denoted as InternVL2-V2PE-256K.
+
+Evaluation Benchmarks. We evaluate our trained models on various long-context and standard benchmarks, in
+
+Table 4. Comparison with existing MLLMs on general MLLM benchmarks. "#Param" denotes the number of parameters. The designation "—" indicates that the corresponding score is not released. Numbers in gray are results evaluated by ourselves. $\delta$ is fixed $1/2$ during testing.
+
+| Model | #Param | ChartQA | DocVQA | AI2D | InfoVQA | SQA | POPE | MMMUval | MMBenchEn | SEEDi | Avg |
| InternVL2-2B [20] | 2.0B | 71.7 | 86.9 | 74.1 | 58.9 | 94.1 | 85.2 | 36.3 | 73.4 | 70.9 | 72.4 |
| InternVL2-2B-FT32K | 2.0B | 75.6 | 84.9 | 73.7 | 56.5 | 94.7 | 88.5 | 35.3 | 73.4 | 70.9 | 71.1 |
| DeepSeek-VL-1.3B [71] | 2.0B | 47.4 | 36.5 | 51.5 | 20.6 | 68.4 | 85.9 | 33.8 | 66.4 | 66.0 | 52.9 |
| Qwen2-VL-2B [115] | 2.0B | 73.5 | 90.1 | 74.7 | 65.5 | 77.7 | 88.2 | 41.1 | 74.9 | 72.9 | 73.1 |
| Aquila-VL-2B [42] | 2.2B | 32.0 | 85.0 | 75.1 | 58.3 | 95.1 | 83.1 | 46.9 | 79.0 | 73.9 | 69.8 |
| MiniCPM-V-2 [135] | 2.8B | 55.6 | 71.9 | 62.9 | 36.0 | 80.7 | 86.3 | 38.2 | 64.1 | 67.1 | 62.5 |
| Vinterm-3B-beta [33] | 3.7B | 68.3 | 78.1 | 69.1 | 52.2 | 75.0 | 87.4 | 46.7 | 70.6 | 70.0 | 68.6 |
| Llama 3.2 11B [108] | 11B | 83.4 | 88.4 | 91.1 | - | - | - | 50.7 | 68.0 | - | - |
| Qwen2-VL-72B [115] | 73B | 88.3 | 96.5 | 88.1 | 84.5 | 91.2 | 87.2 | 64.5 | 86.9 | 77.9 | 85.0 |
| GPT-4o [81] | - | 85.7 | 92.8 | 84.7 | - | 90.1 | 97.2 | 69.1 | 82.1 | 76.7 | - |
| InternVL2-V2PE-32K (δ = 1/2) | 2.0B | 76.8 | 84.9 | 73.5 | 56.0 | 94.9 | 88.7 | 35.8 | 73.8 | 71.2 | 72.9 |
+
+Table 5. Comparison with existing MLLMs on long context MLLM benchmarks. “#Param” denotes the number of parameters. The designation “-” indicates that the corresponding score is not released. Numbers in gray are results evaluated by ourselves. $\delta$ is fixed 1/256 during testing.
+
+| Model | #Param | MM-NIAH | Milebench | VideoMME |
| Image | Text | Avg | T | S | NI | Avg |
| InternVL2-2B [20] | 2.0B | 23.0 | 18.9 | 21.0 | 58.2 | 54.5 | 37.0 | 49.9 | 48.2 |
| InternVL2-2B-FT32K | 2.0B | 73.0 | 81.1 | 77.05 | 63.6 | 56.0 | 96.2 | 71.9 | 47.8 |
| Phi-3-Vision [1] | 2.7B | 24.9 | 26.3 | 25.6 | 46.9 | 50.0 | 73.8 | 56.9 | 40.7 |
| LongLLaVA [120] | 9B | 28.8 | 57.1 | 43.0 | 47.3 | 46.8 | 50.0 | 48.0 | 43.7 |
| LongLLaVA [120] | 13B | 27.7 | 55.7 | 41.7 | 52.7 | 52.1 | 50.0 | 51.6 | 51.6 |
| VILA1.5 [62] | 13B | 5.4 | 11.0 | 8.2 | 21.4 | 48.5 | 7.7 | 25.9 | 47.4 |
| LongVILA [132] | 7B | 33.7 | 34.1 | 33.9 | 65.3 | 55.1 | 91.9 | 70.8 | 60.1 |
| Gemini-1.5 [103] | - | 28.5 | 82.1 | 55.2 | 50.2 | 58.3 | 97.9 | 68.8 | 69.6 |
| GPT-4o [81] | - | 52.3 | 75.0 | 63.7 | 56.2 | 63.5 | 99.8 | 73.2 | 64.7 |
| Claude3-Opus [5] | - | - | - | - | 37.4 | 48.1 | 85.3 | 56.9 | 59.7 |
| InternVL2-V2PE-32K (δ = 1/256) | 2.0B | 78.1 | 85.5 | 81.8 | 65.3 | 55.1 | 96.7 | 72.4 | 52.3 |
+
+cluding the Long-VQA validation split, MM-NIAH [119] (including our augmented MM-NIAH $_{1\mathrm{M}}$ ), and widely used VQA benchmarks such as ChartQA [77], DocVQA [78], AI2D [54], InfoQA [54], SQA [72], POPE [60], MMMU [137], MMBench $_{EN}$ [70], and SEED $_{Image}$ [57]. To systematically assess VLMs' performance on long-context tasks, we also compare our model with other state-of-the-art models on two additional long-context benchmarks: MileBench [94] for multi-image and video understanding, and Video-MME [37] for video analysis tasks.
+
+Effectiveness of V2PE. We compare the performance of InternVL2-V2PE-32K and InternVL2-V2PE-256K on the Long-VQA validation split, MM-NIAH (including MM $\mathrm{NIAH}_{1\mathrm{M}}$ ), and other standard multimodal benchmarks. The results are shown in Tab. 1, Tab. 2, and Tab. 3.
+
+We demonstrate how varying positional increments impact the models' performance on these benchmarks. Specifically, $\mathrm{MM - NIAH_{1M}}$ is evaluated on the image-retrieval task where both the "needle" and "question" are images, posing a stringent challenge for multimodal models to handle visual tokens in long-context sequences.
+
+On standard short-context benchmarks (see Fig. 2), V2PE does not offer obvious advantages. We observe a performance drop on specific tasks, such as DocVQA and InfoQA, when the positional increment is reduced. In Appendix Sec. A, we investigate this issue by applying V2PE in the pre-training stage of VLMs. The results indicate that the marginal benefits of V2PE on short-context benchmarks
+
+stem from the fact that InternVL2 was pre-trained and fine-tuned (SFT) using the default position encoding, making it inherently adapted to $\delta = 1$ .
+
+However, on long-context benchmarks like Long-VQA and MM-NIAH (see Fig. 1 and Fig. 3), V2PE demonstrates a clear advantage. For instance, on Long-VQA, the best performance is typically achieved when the positional increments are reduced to around 1/8 or 1/16. Moreover, as the token sequence length increases, smaller positional increments tend to be optimal.
+
+In the MM-NIAH benchmark, involving longer token sequences, V2PE demonstrates optimal performance with positional increments of 1/256. Notably, InternVL2-V2PE-32K markedly enhances performance on sequences of 256K tokens, boosting scores from 1.5 to 56.9. This enhancement is also evident in InternVL2-V2PE-256K, which records the highest scores across various token sequence lengths when using a positional increment of 1/256. For sequences of 512K tokens, the score surges from 10.8 to 95.1. Additionally, with the same positional increment of 1/256, the InternVL2-V2PE-256K model attains a significant score of 64.5 on sequences reaching 1M tokens.
+
+From our previous experimental results, we observe a qualitative relationship among the choice of $\delta$ , the context length, and model performance: with longer context, selecting a smaller $\delta$ improves model's performance. Therefore, in later experiments, we set $\delta$ to $1/2$ for evaluating general and $1/256$ for long context benchmarks respectively, based
+
+
+Figure 6. Performance on MM-NIAH benchmarks with different position encoding strategies across six task types: "image retrieval", "text retrieval", "image counting", "text counting", "image reasoning" and "text reasoning". "Image only", "Text only", "Both" and "Baseline" represent applying V2PE to visual tokens, textual tokens, both simultaneously, and neither, respectively.
+
+
+Figure 7. Performance on image retrieval task in MM-NIAH benchmark using V2PE and token compression strategies. Token compression reduces the number of visual tokens by a ratio $\delta$ , whereas V2PE employs a smaller positional increment $\delta$ while preserving all visual tokens.
+
+on the context length. Furthermore, we provide theoretical analysis on optimal $\delta$ selection in the Appendix Sec. B
+
+# 4.3. Comparison with Other VLMs.
+
+We evaluate the performance of InternVL2-V2PE-32K against state-of-the-art vision-language models (VLMs) on both standard and long-context multimodal benchmarks, with results presented in Tab. 4 and Tab. 5, respectively. Despite built on a relatively small 2B-parameter model and incorporating a substantial amount of long-context training data, InternVL2-V2PE-32K retains highly competitive results on standard short-context multimodal benchmarks.
+
+On long-context multimodal benchmarks, the model performs exceptionally well, demonstrating that V2PE can significantly enhance long-context abilities even built on a relative small model. These results validate the potential of V2PE for improving the performance of VLMs on a wide range of long-context multimodal tasks.
+
+# 4.4. Ablation Study
+
+Can V2PE be applied to textual tokens? We evaluate the impact of V2PE on visual tokens, textual tokens, both concurrently, and neither, with results on six MM-NIAH tasks presented in Fig. 6. Applying V2PE solely to textual tokens yields marginal improvements in language understanding but degrades performance on vision-centric tasks. When applied to both modalities, model performance exhibits instability. Notably, restricting V2PE to visual tokens consistently enhances performance across all tasks.
+
+
+Figure 8. Performance on image retrieval task in MM-NIAH benchmark with variable versus fixed position increments for visual tokens in the VLMs. "Variable" denotes training with variable increments, allowing evaluation with arbitrary fixed $\delta$ , while "Fixed" means training and evaluating with the same fixed $\delta$ .
+
+Is V2PE equivalent to visual token compression? We also compare V2PE with the token compression strategy, where visual tokens undergo pooling operations to reduce token number, allowing more images to be processed ideally. We test various compression ratios and evaluate the model's performance on the MM-NIAH image retrieval task. The results, shown in Fig. 7, reveal that while token compression results in a rapid performance drop when the number of visual tokens is reduced 16 times or more, our method demonstrates stable performance across all settings.
+
+Can positional increment be fixed during training? We train a set of InternVL2-FT-32K models with both V2PE method and fixed positional increments under the same settings. Their performance in the image retrieval task of the MM-NIAH benchmark is shown in Fig. 8. The results indicate that fixing the positional increment does not lead to optimal task performance. In contrast, the variable adjustment of positional increments provides consistent improvements.
+
+Is V2PE superior to the position encoding extension methods? To compare V2PE with existing position encoding extension methods, we evaluated both InternVL2-V2PE-32K and InternVL2-FT-32K models using two widely adopted position extension techniques: linear interpolation and NTK-Aware Scaled RoPE. The results, presented in Fig. 5, Tab. 1, and Tab. 3, show that V2PE not only offers greater stability but also achieves superior task performance, especially in long-context scenarios.
+
+# 5. Conclusion
+
+We investigate the long-context capabilities of the existing VLMs, using our augmented long-context datasets, and find that positional encoding for visual tokens is critical for the long-context capabilities of VLMs. Based on this observation, we introduce V2PE, a novel position encoding strategy that applies smaller, variable positional increments to visual tokens, enabling more efficient handling of long-context multimodal sequences. By leveraging V2PE and our augmented long-context datasets, we fine-tune the open-source VLMs successfully, which shows significant improvements on both general and long-context multimodal benchmarks.
+
+# References
+
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+[2] Muhammad Adnan, Akhil Arunkumar, Gaurav Jain, Prashant Nair, Ilya Soloveychik, and Purushotham Kamath. Keyformer: Kv cache reduction through key tokens selection for efficient generative inference. Proceedings of Machine Learning and Systems, 6:114-127, 2024. 3
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+[4] Dosovitskiy Alexey. An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv: 2010.11929, 2020. 2
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| InternVL2-2B | - | 52.8 | 27.3 | 23.0 | 23.9 | 22.6 | 21.0 | 28.4 |
| InternVL2-FT-32K | - | 63.0 | 56.1 | 38.3 | 35.5 | 34.6 | 30.6 | 43.0 |
| InternVL2-V2PE-32K | 1/256 | 58.2 | 52.8 | 48.1 | 45.4 | 43.8 | 40.3 | 48.1 |
| 1/128 | 60.0 | 53.7 | 49.5 | 46.5 | 45.3 | 41.3 | 49.4 |
| 1/64 | 61.0 | 54.5 | 50.1 | 47.4 | 45.9 | 42.2 | 50.2 |
| 1/32 | 61.9 | 55.4 | 51.4 | 47.5 | 46.4 | 42.3 | 50.8 |
| 1/16 | 62.9 | 55.6 | 51.2 | 48.3 | 47.0 | 42.5 | 51.3 |
| 1/8 | 63.2 | 55.8 | 52.0 | 47.6 | 45.8 | 41.9 | 51.1 |
| 1/4 | 63.4 | 55.7 | 51.3 | 47.0 | 45.1 | 39.7 | 50.4 |
| 1/2 | 63.3 | 54.9 | 46.8 | 36.8 | 33.3 | 29.2 | 44.1 |
| 1/1 | 62.3 | 49.0 | 30.0 | 26.5 | 27.0 | 25.9 | 36.8 |
| InternVL2-FT-32K (Linear [16]) | - | 62.5 | 51.3 | 42.1 | 34.7 | 31.4 | 25.9 | 40.9 |
| InternVL2-FT-32K (NTK [11]) | - | 63.2 | 54.2 | 44.9 | 41.0 | 40.4 | 34.3 | 45.3 |
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| InternVL2-2B | - | 71.7 | 86.9 | 74.1 | 58.9 | 94.1 | 85.2 | 36.3 | 73.4 | 70.9 | 72.4 |
| InternVL2-FT-Short | - | 76.0 | 85.7 | 74.0 | 57.1 | 94.0 | 88.9 | 34.8 | 73.0 | 66.6 | 72.2 |
| InternVL2-FT-32K | - | 75.6 | 84.8 | 73.6 | 56.5 | 94.7 | 88.7 | 35.3 | 73.8 | 65.1 | 72.0 |
| InternVL2-V2PE-32K | 1/256 | 76.2 | 81.6 | 72.3 | 51.7 | 94.3 | 88.0 | 35.7 | 73.2 | 71.0 | 71.6 |
| 1/128 | 76.5 | 82.3 | 72.6 | 52.9 | 94.2 | 88.1 | 34.7 | 73.5 | 70.9 | 71.7 |
| 1/64 | 76.4 | 83.0 | 72.6 | 53.6 | 94.4 | 88.0 | 35.4 | 73.4 | 70.8 | 72.0 |
| 1/32 | 76.9 | 83.6 | 72.6 | 54.3 | 94.3 | 88.1 | 35.7 | 73.3 | 71.0 | 72.2 |
| 1/16 | 77.2 | 84.3 | 73.0 | 55.2 | 94.5 | 88.1 | 35.7 | 73.3 | 71.0 | 72.5 |
| 1/8 | 77.0 | 84.6 | 73.1 | 55.4 | 94.6 | 88.1 | 36.0 | 72.9 | 71.0 | 72.5 |
| 1/4 | 77.3 | 84.7 | 73.3 | 56.5 | 94.6 | 88.2 | 36.0 | 73.6 | 71.0 | 72.8 |
| 1/2 | 76.8 | 84.9 | 73.5 | 56.0 | 94.9 | 88.7 | 35.8 | 73.8 | 71.2 | 72.9 |
| 1/1 | 76.6 | 84.9 | 73.7 | 55.2 | 94.8 | 88.4 | 36.1 | 73.7 | 71.1 | 72.7 |
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| InternVL2-2B | - | 23.9 | 33.7 | 28.7 | 26.0 | 17.3 | 21.8 | 5.3 | 0.0 |
| GPT-4o | - | 100.0 | 90.4 | 100.0 | 92.7 | 62.1 | 60.0 | 58.6 | NA |
| InternVL2-V2PE-32K | 1/256 | 100.0 | 84.7 | 79.3 | 81.5 | 61.2 | 56.9 | 36.7 | 6.0 |
| 1/64 | 96.0 | 83.9 | 78.1 | 79.5 | 43.6 | 39.3 | 23.4 | 3.4 |
| 1/16 | 96.0 | 82.4 | 73.1 | 65.4 | 57.6 | 41.3 | 19.8 | 0.0 |
| 1/4 | 96.0 | 84.2 | 76.2 | 57.6 | 48.9 | 21.5 | 2.8 | 0.0 |
| 1/1 | 83.0 | 61.2 | 42.0 | 27.5 | 25.5 | 1.5 | 0.0 | 0.0 |
| InternVL2-V2PE-256K | 1/256 | 96.0 | 97.1 | 96.6 | 97.1 | 99.1 | 95.7 | 95.1 | 64.5 |
| 1/64 | 96.0 | 94.7 | 96.6 | 97.1 | 97.1 | 94.1 | 94.1 | 62.8 |
| 1/16 | 96.0 | 94.7 | 93.1 | 94.2 | 100 | 96.2 | 92.9 | 45.1 |
| 1/4 | 96.0 | 94.4 | 100.0 | 97.1 | 75.5 | 75.2 | 38.3 | 2.5 |
| 1/1 | 91.0 | 92.8 | 96.6 | 93.1 | 56.1 | 3.7 | 10.8 | 0.0 |
| InternVL2-FT-32K with linear interpolation | - | 85.3 | 76.0 | 56.0 | 34.7 | 26.4 | 21.9 | 16.3 | 0.5 |
| InternVL2-FT-32K with NTK interpolation | - | 78.3 | 70.7 | 39.8 | 25.7 | 12.3 | 16.8 | 14.8 | 0.0 |
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| InternVL2-2B [20] | 2.0B | 71.7 | 86.9 | 74.1 | 58.9 | 94.1 | 85.2 | 36.3 | 73.4 | 70.9 | 72.4 |
| InternVL2-2B-FT32K | 2.0B | 75.6 | 84.9 | 73.7 | 56.5 | 94.7 | 88.5 | 35.3 | 73.4 | 70.9 | 71.1 |
| DeepSeek-VL-1.3B [71] | 2.0B | 47.4 | 36.5 | 51.5 | 20.6 | 68.4 | 85.9 | 33.8 | 66.4 | 66.0 | 52.9 |
| Qwen2-VL-2B [115] | 2.0B | 73.5 | 90.1 | 74.7 | 65.5 | 77.7 | 88.2 | 41.1 | 74.9 | 72.9 | 73.1 |
| Aquila-VL-2B [42] | 2.2B | 32.0 | 85.0 | 75.1 | 58.3 | 95.1 | 83.1 | 46.9 | 79.0 | 73.9 | 69.8 |
| MiniCPM-V-2 [135] | 2.8B | 55.6 | 71.9 | 62.9 | 36.0 | 80.7 | 86.3 | 38.2 | 64.1 | 67.1 | 62.5 |
| Vinterm-3B-beta [33] | 3.7B | 68.3 | 78.1 | 69.1 | 52.2 | 75.0 | 87.4 | 46.7 | 70.6 | 70.0 | 68.6 |
| Llama 3.2 11B [108] | 11B | 83.4 | 88.4 | 91.1 | - | - | - | 50.7 | 68.0 | - | - |
| Qwen2-VL-72B [115] | 73B | 88.3 | 96.5 | 88.1 | 84.5 | 91.2 | 87.2 | 64.5 | 86.9 | 77.9 | 85.0 |
| GPT-4o [81] | - | 85.7 | 92.8 | 84.7 | - | 90.1 | 97.2 | 69.1 | 82.1 | 76.7 | - |
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| InternVL2-2B [20] | 2.0B | 23.0 | 18.9 | 21.0 | 58.2 | 54.5 | 37.0 | 49.9 | 48.2 |
| InternVL2-2B-FT32K | 2.0B | 73.0 | 81.1 | 77.05 | 63.6 | 56.0 | 96.2 | 71.9 | 47.8 |
| Phi-3-Vision [1] | 2.7B | 24.9 | 26.3 | 25.6 | 46.9 | 50.0 | 73.8 | 56.9 | 40.7 |
| LongLLaVA [120] | 9B | 28.8 | 57.1 | 43.0 | 47.3 | 46.8 | 50.0 | 48.0 | 43.7 |
| LongLLaVA [120] | 13B | 27.7 | 55.7 | 41.7 | 52.7 | 52.1 | 50.0 | 51.6 | 51.6 |
| VILA1.5 [62] | 13B | 5.4 | 11.0 | 8.2 | 21.4 | 48.5 | 7.7 | 25.9 | 47.4 |
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| Gemini-1.5 [103] | - | 28.5 | 82.1 | 55.2 | 50.2 | 58.3 | 97.9 | 68.8 | 69.6 |
| GPT-4o [81] | - | 52.3 | 75.0 | 63.7 | 56.2 | 63.5 | 99.8 | 73.2 | 64.7 |
| Claude3-Opus [5] | - | - | - | - | 37.4 | 48.1 | 85.3 | 56.9 | 59.7 |
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diff --git a/2025/V2XPnP_ Vehicle-to-Everything Spatio-Temporal Fusion for Multi-Agent Perception and Prediction/36b3719d-faf2-4104-a9f7-9253a3958218_content_list.json b/2025/V2XPnP_ Vehicle-to-Everything Spatio-Temporal Fusion for Multi-Agent Perception and Prediction/36b3719d-faf2-4104-a9f7-9253a3958218_content_list.json
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+ "type": "text",
+ "text": "V2XPnP: Vehicle-to-Everything Spatio-Temporal Fusion for Multi-Agent Perception and Prediction",
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+ "text": "Zewei Zhou, Hao Xiang, Zhaoliang Zheng, Seth Z. Zhao, Mingyue Lei, Yun Zhang, Tianhui Cai, Xinyi Liu, Johnson Liu, Maheswari Bajji, Xin Xia, Zhiyu Huang* Bolei Zhou, Jiaqi Ma",
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+ "text": "https://mobility-lab.seas.ucla.edu/v2xpnp",
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+ "text": "Vehicle-to-everything (V2X) technologies offer a promising paradigm to mitigate the limitations of constrained observability in single-vehicle systems. Prior work primarily focuses on single-frame cooperative perception, which fuses agents' information across different spatial locations but ignores temporal cues and temporal tasks (e.g., temporal perception and prediction). In this paper, we focus on the spatio-temporal fusion in V2X scenarios and design one-step and multi-step communication strategies (when to transmit) as well as examine their integration with three fusion strategies - early, late, and intermediate (what to transmit), providing comprehensive benchmarks with 11 fusion models (how to fuse). Furthermore, we propose V2XPnP, a novel intermediate fusion framework within one-step communication for end-to-end perception and prediction. Our framework employs a unified Transformer-based architecture to effectively model complex spatio-temporal relationships across multiple agents, frames, and high-definition maps. Moreover, we introduce the V2XPnP Sequential Dataset that supports all V2X collaboration modes and addresses the limitations of existing real-world datasets, which are restricted to single-frame or single-mode cooperation. Extensive experiments demonstrate that our framework outperforms state-of-the-art methods in both perception and prediction tasks.",
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+ "text": "1. Introduction",
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+ "text": "Autonomous driving systems are required to accurately perceive surrounding road users and predict their future trajectories to ensure safe and interactive driving. Despite recent advances in perception and prediction [7, 13, 33], single-vehicle systems still struggle with limited perception range and occlusion issues [23, 41], compromising driving performance and road safety. Consequently, vehicle-to-everything",
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+ "Figure 1. Illustration of V2X temporal tasks and our V2X spatiotemporal fusion framework. By incorporating temporal information, our framework enhances V2X communication and supports end-to-end perception and prediction beyond single-frame perception."
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+ "text": "(V2X) technologies have emerged as a promising paradigm to address these challenges, which enable connected and automated vehicles (CAVs) and infrastructures to share complementary information and mitigate occlusions, thereby supporting holistic environment understanding [10, 14, 16].",
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+ "text": "Despite their potential, existing works focus on frame-by-frame cooperative detection [21, 27, 38, 52], which aggregates information from agents at different spatial locations. However, these works overlook temporal cues across sequential frames, which are important for locating previously visible but currently undetected objects [43] and predicting object future trajectories [28]. Although some work [37, 46] incorporate short-term temporal cues (0.5 s) in single-frame perception to mitigate asynchrony, the broader challenge of efficiently aggregating multi-agent and multi-frame information and supporting long-term temporal tasks, such as motion prediction, remains largely unexplored. Therefore, we aim to address critical questions in multi-agent multi-frame cooperation: (1) What information to transmit? (2) When to",
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+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "*Corresponding author. {zeweizhou, zhiyuh}@ucla.edu",
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+ "text": "transmit it? (3) How to fuse information across multi-agent spatial and temporal dimensions? To address what to transmit, we expand the three fusion strategies in single-frame cooperative perception (i.e., early, late, and intermediate) to incorporate the temporal dimension. Regarding when to transmit, we introduce one-step and multi-step communication strategies to capture multi-frame temporal information. For how to fuse, we conduct a systematic analysis across various spatio-temporal fusion strategies, providing comprehensive benchmarks for cooperative perception and prediction tasks across all V2X collaboration modes.",
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+ "text": "Among these strategies, we advocate intermediate fusion within one-step communication because it effectively balances the trade-off between accuracy and increased transmission load. Moreover, its capability to transmit intermediate spatial-temporal features makes it well-suited for end-to-end perception and prediction, allowing for feature sharing across multiple tasks, as shown in Fig. 1. Based on this strategy, we propose V2XPnP, a V2X spatio-temporal fusion framework leveraging a unified Transformer structure for effective spatial-temporal fusion, encompassing temporal attention, self-spatial attention, multi-agent spatial attention, and map attention. Each agent first extracts its inter-frame and self-spatial features, which can support single-vehicle perception and prediction while reducing the communication load, and then the multi-agent spatial attention model fuses the single-agent features across different agents.",
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+ "text": "Another challenge is the lack of real-world sequential datasets encompassing diverse V2X collaboration modes. In V2X scenarios, vehicles and infrastructures serve as primary agents, with collaboration modes that include vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I), and infrastructure-to-infrastructure (I2I), vehicle-centric (VC), and infrastructure-centric (IC) [16]. Most existing datasets [39, 44] are non-sequential, limited to single collaboration modes, and focus only on single-frame cooperative perception, lacking support for temporal tasks. To bridge this gap, we introduce the first large-scale real-world V2XPnP Sequential Dataset, featuring four agents and supporting all collaboration modes. This dataset includes temporally consistent perception and trajectory data across $49\\mathrm{~2V} + 2\\mathrm{I}$ scenarios, 38 V2V scenarios, and $9\\mathrm{~V} + 2\\mathrm{I}$ scenarios, totaling 40k frames, along with point-cloud and vector maps from 24 collected intersections. The main contributions of this paper can be summarized as follows:",
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+ "1. We present V2XPnP, a V2X spatio-temporal fusion framework with a novel intermediate fusion model within one-step communication. This framework is based on a unified Transformer architecture integrating diverse attention fusion modules for V2X spatial-temporal information.",
+ "2. We introduce the first large-scale, real-world V2X sequential dataset featuring multiple agents and all V2X collaboration modes (i.e., VC, IC, V2V, I2I), encompass-"
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+ "text": "End-to-end Perception and Prediction. Safe autonomous driving fundamentally depends on accurate perception and prediction [15, 49]. In single-agent systems, significant efforts have been dedicated to temporal perception and prediction [24], leading to the development of various end-to-end frameworks. These frameworks enhance computational efficiency by sharing information across tasks and mitigating error propagation inherent in modular architectures. FaF [28] and PnPNet [25] focus on LiDAR-based joint perception and prediction, while occupancy flow methods [2, 3] provide detailed spatial-temporal information. Recently, Bird's-Eye-View (BEV)-based approaches with camera data have gained prominence [9, 13, 18].",
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+ "text": "V2X Perception and Prediction. V2X perception has been extensively explored, with intermediate fusion emerging as a widely adopted strategy [7, 40, 41]. FFNet [46] and CoBEVFlow [37] utilize historical information (0.5s) from collaborators to mitigate asynchrony, and SCOPE integrates ego-history for detection. However, coordinating multi-agent systems for long-term temporal tasks remains an open challenge. In the prediction domain, deep learning models have been extensively studied for modeling inter-agent interactions [17, 32]. However, the limited short-term visibility of individual vehicles continues to restrict prediction accuracy. Cooperative prediction leveraging V2X has shown potential, though research remains preliminary [29, 36, 43, 48]. To integrate perception and prediction within an end-to-end framework, V2VNet [35] employs a graph neural network for spatio-temporal fusion. UniV2X [47] extended the end-to-end system to support downstream tasks, but with a simplified spatio-temporal fusion module. Despite these advancements, a comprehensive framework for V2X-based spatio-temporal fusion is still lacking.",
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+ "text": "Real-world Driving Datasets. Public datasets have been instrumental in advancing autonomous driving research. Early sequential datasets [1, 19] provided only object trajectories on highways [51], but lack perception data. The following datasets, such as nuScenes [5] and Waymo [34], introduced real-world urban data but were limited to single-agent perspectives, rendering them unsuitable for V2X research. Thus, simulated datasets like V2XSet [40] were developed. Recently, datasets including Dair-V2X [44], V2V4Real [42], RCooper [11], and V2X-Real [39] significant contributed to real-world data in the V2I, V2V, I2I and V2X modes. However, real-world sequential V2X datasets covering all",
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+ "Figure 2. Illustration of various V2X fusion strategies for perception and prediction. (a) What to Transmit: early, intermediate, and late fusion, transmitting raw sensor data, intermediate BEV features, or bounding boxes. (b) When to Transmit: multi-step and one-step communication."
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+ "text": "The cooperative temporal perception and prediction task requires the integration of temporal information across historical frames and spatial information from multiple agents. It is defined as follows: given map and historical sequences of raw perception data $\\mathbf{P}_i^t$ , $i \\in \\{1, \\dots, N\\}$ , from all $N$ agents within the communication range of the ego agent, the objective is to detect objects in the current frame and predict their future trajectories considering the map information.",
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+ "text": "This section addresses what and when to transmit for spatiotemporal fusion, and Sec. 3.2 delves into the fusion process. What to Transmit. In multi-agent spatial fusion, three fusion strategies are widely adopted in single-frame cooperative perception, i.e., early, late, and intermediate fusion [12, 44], which involve the transmission of raw perception data, bounding boxes, and intermediate features, respectively. Adopting this framework, we extend these fusion approaches to the V2X spatio-temporal fusion context, as illustrated in Fig. 2. (1) Early fusion transmits the entire raw historical perception data to retain complete feature information but imposes the highest transmission load. (2) Late fusion shares only the final detected results at each historical frame, resulting in the lowest transmission load but losing most of the feature information. (3) Intermediate fusion transmits intermediate spatio-temporal BEV features, striking a balance between information quality and transmission load.",
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+ "text": "When to Transmit. Determining when to transmit in spatiotemporal fusion is more challenging due to the inclusion of temporal data as compared to the existing spatial fusion. A straightforward approach is Multi-step Communication, where each transmission only includes the current frame's",
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+ "text": "data. However, the multiple steps cause the accumulation of delays and data loss, and obtaining complete historical data requires that neighboring agents stay within the ego agent's limited communication range throughout historical frames. In practice, the ego agent should aggregate as much data as possible from other agents within a single transmission, rather than relying on multiple exchanges to obtain complete spatio-temporal information. To address this, we propose a One-step Communication strategy, where individual agents share all their historical data within a single communication.",
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+ "text": "Intermediate Fusion with One-step Communication. Synthesizing the considerations for what to transmit and when to transmit, we adopt an intermediate fusion within the one-step communication strategy, which fuses temporal data from multiple frames before transmission, allowing each agent to share aggregated information without excessive communication overhead. In multi-step intermediate fusion, each agent transmits BEV feature maps at every timestep $\\mathbf{F}_i^t\\in \\mathbb{R}^{H\\times W\\times C}$ , which denotes agent $i$ 's BEV feature at time $t$ with height $H$ , width $W$ , and channels $C$ . The cumulative data shared across $T$ frames is a stacked sequence $\\mathbf{F}_i^{seq}\\in \\mathbb{R}^{T\\times H\\times W\\times C}$ , resulting in a significantly higher transmission load than single-frame, along with potential delays and data loss. Conversely, in our proposed strategy, each agent first fuses its historical BEV features internally, reducing the sequence from $\\mathbf{F}_i^{seq}$ to a single condensed BEV feature map $\\mathbf{F}_i'\\in \\mathbb{R}^{H\\times W\\times C}$ . This reduction allows agents to transmit a compact data packet, comparable in size to single-frame cooperative perception, thereby conserving bandwidth while preserving essential spatio-temporal information.",
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+ "text": "3.2. V2XPnP Framework",
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+ "text": "The spatio-temporal features of intermediate fusion render it a natural fit for end-to-end perception and prediction. Accordingly, we propose a unified end-to-end perception and prediction framework to perform multiple tasks across spatiotemporal dimensions. The overall V2XPnP framework is illustrated in Fig. 3, which includes six components and is",
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+ "Figure 3. The V2XPnP framework and multi-agent spatio-temporal fusion model. The framework comprises various components for feature extraction, fusion, and decoding. Within our fusion model, we introduce multiple attention mechanisms to enhance the fusion process."
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+ "text": "unfolded in this section. The detail of the spatio-temporal fusion model is provided in Sec. 3.3. Notably, each module in V2XPnP is modular, allowing for easy replacement.",
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+ "text": "V2X Metadata Sharing. Each agent in the V2X system is an observer and collaborator in the shared environment. Each agent will first determine its collaborators with its communication range, and share the metadata, such as relative poses and extrinsic, to construct a spatial V2X graph. Each node and edge in the graph represents an agent and a communication channel. All the point clouds are transformed into the ego agent's coordinate frame before feature extraction.",
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+ "text": "LiDAR Feature Extraction. We utilize the PointPillar network [20] to extract the LiDAR feature for each agent $i$ at time $t$ , which has low inference latency. The extracted features are structured into a 2D pseudo-image representation to produce salient feature maps $\\mathbf{F}_i^t$ , and the sequential feature is stacked as $\\mathbf{F}_i^{seq} \\in \\mathbb{R}^{T \\times H \\times W \\times C}$",
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+ "text": "Multi-frame Temporal Fusion. We propose a Transformer-based temporal fusion module to iteratively perform interframe and intra-agent BEV feature fusion through self-attention mechanisms. The spatio-temporal feature of each agent is extracted through the temporal dimension while minimizing communication overhead. The feature map for each agent after temporal fusion is $\\mathbf{F}_i' \\in \\mathbb{R}^{H \\times W \\times C}$ .",
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+ "text": "Compression and Sharing. To reduce the transmission load, intermediate features are compressed using a $1 \\times 1$ kernel convolution network in its channel dimension. The ego agent uses another convolution network to decompress the features, restoring them to their original dimensionality. Multi-agent Spatial Fusion. The decompressed features are passed into a Transformer-based multi-agent spatial fusion network to learn inter-agent and intra-agent spatio-temporal interaction and update the multi-agent feature map $\\mathbf{F}'$ .",
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+ "type": "text",
+ "text": "Map Feature Extraction. The HD map is directly accessed for each agent without V2X fusion. We project the vectorized HD map to BEV space by incorporating the map polylines into each BEV feature grid. We first employ a multi-layer perceptron (MLP) to encode the surrounding map polylines for each grid $\\mathbf{M} \\in \\mathbb{R}^{H \\times W \\times N_m \\times n \\times D}$ , re",
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+ "type": "text",
+ "text": "sulting in the map feature $\\mathbf{F}_m\\in \\mathbb{R}^{H\\times W\\times N_m\\times C}$ . Here, $N_{m}$ and $n$ represent the number of map polylines and the waypoints per polyline, while $D$ represents waypoint attributes (i.e., position and lane type). The map encoding is expressed as: $\\mathbf{F}_m = \\phi (\\mathrm{MLP}(\\mathbf{M}))$ , where $\\phi$ denotes max-pooling on the waypoint axis. Then, a map-BEV attention is introduced to inject the map feature into the BEV feature. We concatenate the BEV and map feature $\\mathbf{F}_{bm} = [\\mathbf{F}',\\mathbf{F}_m]\\in \\mathbb{R}^{H\\times W\\times (1 + N_m)\\times C}$ , and add the position embedding $\\mathbf{P}_m$ based on sinusoidal positional encoding. The final content feature map $\\mathbf{F}\\in \\mathbb{R}^{H\\times W\\times C}$ is updated by multi-head self-attention (MHSA) as follows:",
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+ "type": "equation",
+ "text": "\n$$\n\\mathbf {F} = \\operatorname {M H S A} \\left(\\mathrm {Q}: \\left[ \\mathbf {F} _ {b m}, \\mathbf {P} _ {m} \\right], \\mathrm {K}: \\left[ \\mathbf {F} _ {b m}, \\mathbf {P} _ {m} \\right], \\mathrm {V}: \\mathbf {F} _ {b m}\\right). \\tag {1}\n$$\n",
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+ "text": "Detection and Prediction Heads. Finally, a detection head and a prediction head are connected to the final feature $\\mathbf{F}$ to output states for each predefined anchor box: (1) The detection head contains two 2D convolution layers for bounding box regression and classification. The regression branch outputs the bounding box position $(x,y,z)$ , size $(w,l,h)$ , and yaw $\\theta$ . The classification branch outputs the confidence score of each anchor box, determining whether it corresponds to an object or background. (2) The prediction head outputs offset values for each anchor box at each future timestamp using two 2D convolution layers, and the final trajectory is generated by accumulating these offsets.",
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+ "text": "3.3. Spatio-Temporal Fusion Transformer",
+ "text_level": 1,
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+ "text": "In this section, we introduce spatio-temporal fusion with a unified Transformer architecture. The proposed model comprises three blocks: temporal attention, self-spatial attention, and multi-agent spatial attention, as shown in Fig. 3, and two core fusion modules. (1) Multi-frame temporal fusion: Each agent first extracts their spatio-temporal features through iterative temporal and self-spatial attentions. (2) Multi-agent spatial fusion: rich BEV features from multiple agents are acquired via V2X and then fused through iterative multi-agent spatial and self-spatial attentions.",
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+ "text": "Temporal Attention. This block is designed to capture the inter-frame relationship and aggregate historical BEV features $\\mathbf{F}_i^{seq}$ across the temporal dimension. The history timestamps are encoded with a learnable embedding, which is added to each BEV feature frame to form $\\mathbf{F}_i^{seq'}$ . To preserve temporal cues, this block only fuses temporal features from the same spatial positions across frames, and spatial features are further extracted by the self-spatial Transformer. Temporal fusion is expressed as:",
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+ "text": "\n$$\n\\begin{array}{l} \\mathbf {F} _ {i} ^ {t e m} = \\operatorname {M H S A} \\left(\\mathrm {Q}: \\operatorname {M L P} \\left(\\mathbf {F} _ {i} ^ {s e q ^ {\\prime}}\\right), \\mathrm {K}: \\operatorname {M L P} \\left(\\mathbf {F} _ {i} ^ {s e q ^ {\\prime}}\\right), \\right. \\\\ \\left. \\mathrm {V}: \\operatorname {M L P} \\left(\\mathbf {F} _ {i} ^ {\\text {s e q} ^ {\\prime}}\\right)\\right). \\tag {2} \\\\ \\end{array}\n$$\n",
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+ "text": "Self-spatial Attention. To capture the intra-agent spatial BEV interaction, this block employs multi-scale window attention to capture spatial features at different resolutions and ranges. A large window focuses on global features for long-term behavior, and a small window preserves local finer information. Note that this block only fuses spatial features for each agent in a frame without inter-frame and inter-agent fusion. Specifically, we utilize local, intermediate, and global windows $P_{k} \\in \\{P_{loc}, P_{inter}, P_{gl}\\}$ to partition the feature map through the $H$ and $W$ dimension, generating the self-spatial token $\\mathbf{F}^{sp} \\in \\mathbb{R}^{\\frac{H}{P_k} \\times \\frac{W}{P_k} \\times P_k^2 \\times C}$ . With an additional relative position encoding, MHSA is operated among $P_{k}^{2}$ tokens. The final output is obtained by performing split attention to fuse features from different windows.",
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+ "text": "Multi-agent Spatial Attention. This block facilitates inter-agent fusion by aggregating BEV feature maps from multiple agents. Considering the different deployment positions and capabilities of vehicle and infrastructure sensors, the multiagent spatial Transformer is heterogeneous with individual learnable weights for different interaction pairs (i.e., V-I, V-V, I-V, and I-I). The attention token of $i$ th agent $\\mathbf{F}_{i,m}^{sp}$ is modulated by its type $m$ embedding, and is weighted by the relation matrix $\\mathbf{W}_{\\mathrm{att}}^{(e_{i,j})}$ between edge $e_{i,j}$ during aggregation with agent $j$ of type $n$ :",
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+ {
+ "type": "equation",
+ "text": "\n$$\n\\begin{array}{l} \\mathbf {Q} _ {i} ^ {m} = \\operatorname {M L P} \\left(\\mathbf {F} _ {i, m}\\right), \\mathbf {K} _ {j} ^ {n} = \\operatorname {M L P} \\left(\\mathbf {F} _ {j, n}\\right), \\mathbf {V} _ {j} ^ {n} = \\operatorname {M L P} \\left(\\mathbf {F} _ {j, n}\\right), \\\\ \\mathbf {F} _ {i, m} ^ {s p} = \\sum_ {j} \\operatorname {S o f t m a x} \\left(\\mathbf {Q} _ {i} ^ {m} \\cdot \\mathbf {W} _ {\\text {a t t}} ^ {\\left(e _ {i, j}\\right)} \\cdot \\mathbf {K} _ {j} ^ {n}\\right) \\cdot \\mathbf {V} _ {j} ^ {n}. \\tag {3} \\\\ \\end{array}\n$$\n",
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+ "type": "text",
+ "text": "3.4. Learning Objective",
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+ "type": "text",
+ "text": "The learning objective is comprised of temporal perception and prediction tasks. First, we define the perception loss as the combination of regression $\\mathcal{L}_{\\mathrm{reg}}$ and classification loss $\\mathcal{L}_{\\mathrm{cla}}$ of the predefined anchor box. Specifically, the smooth $\\ell_1$ -loss is leveraged for the regression part, and the focal loss [26] is utilized for classification. Second, we define the prediction loss $\\mathcal{L}_{\\mathrm{pred}}$ as $\\ell_2$ -loss between the prediction points sequence with ground truth trajectory. The final loss function is the weighted sum of $\\mathcal{L}_{\\mathrm{reg}}$ , $\\mathcal{L}_{\\mathrm{cla}}$ , and $\\mathcal{L}_{\\mathrm{pred}}$ .",
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+ "type": "text",
+ "text": "4. V2XPnP Sequential Dataset",
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+ "text": "We introduce the V2XPnP-Sequential dataset, the first large-scale, real-world V2X sequential dataset featuring multiple agents and all collaboration modes. This dataset comprises 96 scenarios (49 2V+2I scenarios, 38 V2V scenarios, and 9 V+2I scenarios), each spanning 95 to 283 frames captured at $10\\mathrm{Hz}$ . The dataset comprises two data sequences from CAV perception (point clouds and camera images) and two data sequences from infrastructure perception, as shown in Fig. 4(b). We also provide corresponding vector maps and point-cloud maps for all collection areas, as shown in Fig. 4(c). Ten object categories are included, and the average trajectory length and frequency of each category are shown in Fig. 4(d). Further details on data visualization, annotation, trajectory and map generation are provided in the supplementary.",
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+ "text": "4.1. Data Acquisition",
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+ "text": "V2X temporal tasks require diverse time-consistent perception data and object behavior data. We choose urban arterial roads, expressways, and intersections to collect V2X data. The sensor configurations for two CAVs and two infrastructures are shown in Fig. 4(a). By permuting and combining the behavior patterns of CAVs (such as overtaking, platooning, turning, etc.), we designed a total of about 60 interaction pairs between CAVs to collect data. From more than 66h driving logs, we annotate 28 representative scenarios. We also process the non-sequential data from V2X-Real [39] with a V2X sequential data processing pipeline, detailed in Sec. 4.2. Since perception tasks do not need to consider labeling consistency, identical objects may be assigned different IDs within a sequence, leading to data fragmentation and limiting support for temporal tasks. The final dataset is yielded by processing our collected data and V2X-Real data.",
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+ "text": "4.2. Sequential Data Processing",
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+ "text": "Time-consistent data is crucial for temporal tasks, and thus we develop a V2X sequential data processing pipeline to track objects across time and different agents' views. We construct a multi-agent spatio-temporal graph, where each node $n_{it}^{k}$ represents an annotated bounding box $i$ at time $t$ from agent $k$ 's LiDAR data, and edges connect nodes that correspond to the same object. Identifying objects with the same ID then reduces to finding connected components in this graph, with each isolated component representing a unique object. Moreover, we build this graph by leveraging the temporal continuity in single-agent annotations and incorporating multi-agent data. For temporal consistency within a single agent, we add edges between $n_{it}^{k}$ and $n_{it+1}^{k}$ , although annotation errors may sometimes assign different IDs to the same object. To address this, we integrate annotations from multiple agents, transforming annotations into a global coordinate frame and connecting nodes if their Intersection-over-Union (IoU) exceeds a threshold. Once",
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+ "img_path": "images/f3e0de73232735f76fc01dc3d1e4f92423870544212136e36fac90a3c1b4a311.jpg",
+ "image_caption": [
+ "Figure 4. Illustration of the V2XPnP Sequential Dataset. (a) V2X data acquisition systems; (b) Sequential LiDAR and camera data; (c) Data collection area and vector map; (d) Total number and average tracking length of 3D tracked objects per category."
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+ "type": "text",
+ "text": "the graph is complete, we identify connected components and assign each a unique tracking ID. To mitigate annotation biases, we refine object attributes based on their consensus.",
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+ "type": "text",
+ "text": "5. Experiments",
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+ "text": "5.1. Experimental Setup",
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+ "text": "Evaluation Metrics. Following the detection evaluation protocol in [39], we measure detection performance using Average Precision (AP) at an IoU threshold of 0.5. For prediction, we provide the results of commonly used metrics [8, 30, 31], including Average Displacement Error (ADE), Final Displacement Error (FDE), and Miss Rate (MR) within a 2-meter threshold. However, prediction accuracy is influenced by false positives and missed detections from the perception module. For example, a poorly performing perception module that detects only a simple object in a straight-line trajectory can misleadingly inflate the prediction accuracy. To address this, we employ the End-to-end Perception and Prediction Accuracy (EPA) metric [9] to jointly evaluate perception and prediction performance.",
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+ {
+ "type": "equation",
+ "text": "\n$$\nE P A = \\frac {\\left| \\hat {S} _ {\\text {m a t c h , h i t}} \\right| - \\alpha N _ {\\mathrm {F P}}}{N _ {\\mathrm {G T}}}, \\tag {4}\n$$\n",
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+ "type": "text",
+ "text": "where $|\\hat{S}_{\\mathrm{match,hit}}|$ is the number of true positive objects with prediction $FDE < \\tau_{EPA}, N_{FP}, N_{GT}$ represent the number of false positive objects and ground truth objects, respectively, and $\\alpha$ is a penalty coefficient. A higher EPA value indicates superior object detection and prediction capabilities, and we set $\\tau_{EPA} = 2\\mathrm{m}$ , $\\alpha = 0.5$ following [9].",
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+ "type": "text",
+ "text": "Collaboration Modes. The V2XPnP Sequential Dataset supports various V2X collaboration modes by organizing data with specific interaction patterns. Vehicle-Centric (VC): The ego CAV is the focal agent, communicating with other CAVs and infrastructure (Infra). Infrastructure-Centric (IC): Infrastructure is the central entity, communicating with other Infras and CAVs. Vehicle-to-Vehicle (V2V): The ego CAV communicates exclusively with other CAVs without involving Infra. Infrastructure-to-Infrastructure (I2I): Infra shares data only with each other. Each VC and IC scenario includes",
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+ "type": "text",
+ "text": "2-4 agents, which is close to real-world V2X settings and can evaluate model generalization across diverse V2X scenarios, whereas each V2V and I2I scenario has two agents.",
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+ "text": "Implementation Details. During the testing stage, we select a fixed agent as the ego agent in each cooperative scenario, while the ego agent is shuffled and randomly selected during training. Following the real-time setting [50], we set the communication range to 50 meters and evaluate surrounding agents within a range of $x \\in [-70, 70] \\mathrm{m}$ and $y \\in [-40, 40] \\mathrm{m}$ . Messages beyond 50 meters are discarded. Besides, the history length is $2 \\mathrm{~s}$ ( $2 \\mathrm{~Hz}$ ), and the prediction horizon is $3 \\mathrm{~s}$ ( $2 \\mathrm{~Hz}$ ). The train/Validation/test data splits are 76/6/14 scenarios. Additional training and model details are provided in the supplementary materials.",
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+ "type": "text",
+ "text": "5.2. Benchmark Methods",
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+ "text": "End-to-end methods. Most of the single-frame perception models cannot support the prediction task, thus, we first implement a baseline end-to-end model with the same LiDAR backbone and decoding heads as V2XPnP but utilizing the temporal fusion module FaF [28] - alternating 2D and 3D convolutions - as the No fusion- $FaF^{*}$ baseline, which can extend the non-temporal model to support temporal tasks. Then, the early fusion configurations and several state-of-the-art intermediate fusion models are integrated as: Early Fusion, $FFNet^{*}$ [46], $CoBEVFlow^{*}$ [37], $V2X-ViT^{*}$ [40]). More benchmark results of $DiscoNet^{*}$ [22], $F-Cooper^{*}$ [6], and $V2VNet^{*}$ [35] are provided in the supplementary. These models marked with * are reimplemented in our framework with the same LiDAR backbone and decoding heads.",
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+ "text": "Decoupled methods. Transmitting final detection results renders late fusion incompatible with end-to-end models. Thus, we benchmark Late Fusion with a decoupled pipeline, where objects in each historical frame are detected using a single-frame perception module, and results are fused via non-maximum suppression. Assuming an ideal tracker to generate object trajectories from perception results and interpolate missing points, we implement an attention-based predictor for trajectory-level prediction tasks, following the prediction mainstream [32]. To further assess end-to-end per",
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+ "Table 1. Benchmark results of cooperative perception and prediction models on V2XPnP Sequential (V2XPnP-Seq) Dataset"
+ ],
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+ "table_body": "| Dataset | Method | E2E | Map | AP@0.5 (%) ↑ | ADE (m) ↓ | FDE (m) ↓ | MR (%) ↓ | EPA (%) ↑ |
| V2XPnP-Seq-VC(with V+2I at most) | No Fusion | | ✓ | 43.9 | 1.87 | 3.24 | 33.8 | 24.3 |
| No Fusion-FaF* [28] | ✓ | | 53.4 | 1.55 | 2.81 | 34.3 | 31.6 |
| Late Fusion | | ✓ | 58.1 | 1.59 | 2.82 | 32.4 | 33.0 |
| Early Fusion | ✓ | ✓ | 60.3 | 1.37 | 2.49 | 33.8 | 36.7 |
| CoBEVFlow* [37] | ✓ | ✓ | 63.3 | 1.36 | 2.49 | 33.0 | 41.9 |
| FFNet* [46] | ✓ | ✓ | 64.6 | 1.36 | 2.47 | 34.7 | 42.3 |
| V2X-ViT* [40] | ✓ | ✓ | 69.6 | 1.39 | 2.56 | 35.2 | 44.7 |
| V2XPnP (Ours) | ✓ | ✓ | 71.6 +2.0 | 1.35 | 2.36 | 31.7 | 48.2 +3.5 |
| V2XPnP-Seq-IC(with 2V+I at most) | No Fusion | | ✓ | 46.4 | 1.69 | 3.06 | 36.2 | 28.8 |
| No Fusion-FaF* [28] | ✓ | | 56.7 | 1.34 | 2.65 | 41.4 | 31.7 |
| Late Fusion | | ✓ | 55.9 | 1.39 | 2.44 | 30.1 | 32.9 |
| Early Fusion | ✓ | ✓ | 60.5 | 1.39 | 2.63 | 32.8 | 39.5 |
| CoBEVFlow* [37] | ✓ | ✓ | 57.6 | 1.38 | 2.58 | 31.0 | 32.5 |
| FFNet* [46] | ✓ | ✓ | 61.0 | 1.18 | 2.18 | 35.1 | 37.5 |
| V2X-ViT* [40] | ✓ | ✓ | 69.3 | 1.27 | 2.39 | 35.4 | 43.3 |
| V2XPnP (Ours) | ✓ | ✓ | 71.0 +1.7 | 1.18 | 2.16 | 34.0 | 46.0 +2.7 |
| V2XPnP-Seq-V2V | No Fusion | | ✓ | 40.8 | 1.99 | 3.38 | 34.0 | 19.8 |
| No Fusion-FaF* [28] | ✓ | | 51.9 | 1.67 | 3.12 | 39.3 | 27.5 |
| Late Fusion | | ✓ | 55.3 | 1.75 | 3.07 | 34.0 | 30.5 |
| Early Fusion | ✓ | ✓ | 53.0 | 1.64 | 3.11 | 40.2 | 26.9 |
| CoBEVFlow* [37] | ✓ | ✓ | 58.7 | 1.72 | 3.15 | 40.3 | 33.6 |
| FFNet* [46] | ✓ | ✓ | 56.5 | 1.68 | 3.12 | 39.8 | 31.2 |
| V2X-ViT* [40] | ✓ | ✓ | 64.6 | 1.68 | 3.13 | 39.8 | 36.7 |
| V2XPnP (Ours) | ✓ | ✓ | 70.5 +5.9 | 1.78 | 3.28 | 39.9 | 40.6 +3.9 |
| V2XPnP-Seq-I2I | No Fusion | | ✓ | 51.0 | 1.69 | 3.06 | 36.2 | 31.7 |
| No Fusion-FaF* [28] | ✓ | | 56.6 | 1.34 | 2.65 | 41.4 | 31.7 |
| Late Fusion | | ✓ | 61.3 | 1.41 | 2.50 | 30.0 | 41.6 |
| Early Fusion | ✓ | ✓ | 64.6 | 1.57 | 2.98 | 39.9 | 37.7 |
| CoBEVFlow* [37] | ✓ | ✓ | 58.4 | 1.31 | 2.61 | 41.5 | 33.0 |
| FFNet* [46] | ✓ | ✓ | 66.1 | 1.41 | 2.59 | 36.3 | 40.9 |
| V2X-ViT* [40] | ✓ | ✓ | 65.4 | 1.22 | 2.33 | 35.9 | 41.3 |
| V2XPnP (Ours) | ✓ | ✓ | 69.2 +3.1 | 1.26 | 2.31 | 36.5 | 42.8 +1.2 |
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+ "text": "formance, we also evaluate a decoupled No-Fusion model.",
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+ "text": "Tab. 1 presents the benchmark results across four V2X collaboration modes. Since prediction performance inherently depends on detection quality, the difficulty posed by different detected objects can significantly impact prediction accuracy. Thus, the EPA metric serves as the most appropriate indicator for assessing the overall performance. More details and baseline results are provided in the supplementary.",
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+ "text": "What to Transmit. In both end-to-end and decoupled PnP frameworks, the cooperation perception and prediction performance are consistently better than non-fusion models in all collaboration modes, especially in the primary EPA metric, which demonstrates the benefits of cooperation in temporal perception and prediction. Moreover, intermediate fusion models (e.g., V2X-ViT, FFNet, and V2XPnP) generally outperform other fusion strategies, while early fusion consistently surpasses late fusion. Our proposed V2XPnP model achieves the best performance, outperforming other competitive cooperative methods.",
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+ "text": "When to Transmit. Tab. 2 shows the performance of our model under two communication strategies. We find that the",
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+ "Table 2. Comparison of one-step and multi-step communication"
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+ "table_body": "| Strategy | AP@0.5↑ | ADE ↓ | FDE ↓ | MR ↓ | EPA ↑ |
| Multi-step | 68.2 | 1.56 | 2.84 | 31.8 | 43.0 |
| One-step | 71.6 | 1.35 | 2.36 | 31.7 | 48.2 |
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+ "Table 3. Ablation results of V2XPnP model"
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+ "table_body": "| Temp | Spatial | Map | AP@0.5↑ | ADE↓ | FDE↓ | MR↓ | EPA↑ |
| | | 43.9 | - | - | - | - |
| ✓ | | | 57.2 | 1.52 | 2.76 | 35.5 | 33.8 |
| ✓ | ✓ | | 71.3 | 1.48 | 2.70 | 36.2 | 44.4 |
| ✓ | ✓ | ✓ | 71.6 | 1.35 | 2.36 | 31.7 | 48.2 |
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+ "text": "perception and prediction performance of one-step communication is improved compared to multi-step communication by $5.0\\%$ AP and $12\\%$ in EPA. This improvement arises because each agent first directly fuses their lossless raw temporal data before sharing, avoiding error accumulation from lossy intermediate information transformed in multi-step communication across temporal dimensions. Moreover, the one-step strategy compresses spatio-temporal feature transmission (under a $32\\times$ compression rate) from $5\\times 0.269$ Mb to $0.269$ Mb compared to multi-step communication, while mitigating information loss when agents move out of com",
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+ ": detection box ground truth box"
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+ "text": "munication range in historical frames. At a typical C-V2X data transmission rate [4], the transmission delay of one-step communication is approximately $10 \\sim 20$ ms.",
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+ "text": "How to Fuse. Tab. 3 provides the ablation study of V2XPnP, showing the effectiveness of different components in V2XPnP. The temporal fusion module provides the history information for current-frame detection, while multi-agent spatial fusion alleviates occlusions and improves performance by incorporating other views. The map fusion module enhances trajectory prediction by guiding future trajectories to align with road structures. Our complete V2XPnP model with all these fusion modules performs the best.",
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+ "text": "End-to-end vs. Decoupled Frameworks. The end-to-end model consistently outperforms the decoupled framework. In no-fusion situations, the end-to-end model $\\mathrm{FaF^{*}}$ outperforms the decoupled model in detection by leveraging temporal cues. Furthermore, $\\mathrm{FaF^{*}}$ achieves performance comparable to late fusion with V2X spatial aggregation due to integrating temporal features. The intermediate fusion of spatio-temporal features in V2XPnP aligns well with the end-to-end architecture, showcasing its superior performance.",
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+ "text": "Infrastructure vs. Vehicle Centric. As shown in Tab. 1, models under VC and IC modes outperform those in V2V and I2I modes, because VC and IC can aggregate information from up to four agents rather than only two, resulting in enhanced environmental understanding. Notably, the evaluation protocol is consistent across all models within each mode. Additionally, stationary infrastructure-based agents in IC and I2I modes offer higher prediction accuracy by providing elevated sensing perspectives and less noisy data.",
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+ "text": "Transmission Data Size and Robustness Test. Results in Fig. 6 indicate that V2XPnP achieves a good balance between communication efficiency and accuracy, maintaining superior performance compared to full-size V2X-ViT* even at a $\\times 128$ compression rate. Following the setting in [40], we provide the results with 100-500 ms time delay and positional/head Gaussian noise from $(0.2\\mathrm{m}, 0.2^{\\circ})$ to $(1\\mathrm{m}, 1^{\\circ})$ . Both V2XPnP and V2X-ViT* maintain robust performance",
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+ "image_caption": [
+ "Figure 5. Qualitative results of different fusion models on the testing set. V2XPnP shows better perception and prediction results."
+ ],
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+ "image_caption": [
+ "Figure 6. Transmission data size and communication noise test results. V2XPnP shows better performance with varying data compression rates and robustness under communication noise."
+ ],
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+ "text": "due to their spatial attention fusion, and V2XPnP performs better due to its designed temporal attention.",
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+ "text": "Qualitative Results. Fig. 5 visualizes the outcomes of cooperative perception and prediction across different fusion models. The No Fusion model is constrained by its limited field of view. The FaF model, leveraging temporal information within an end-to-end pipeline, performs better under occlusion. Late and early fusion models significantly benefit from multi-agent data integration, though late fusion remains impacted by error propagation, such as detection heading errors misleading trajectory direction. Notably, the end-to-end intermediate fusion model, particularly V2XPnP, performs better in both detection and prediction tasks.",
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+ "text": "6. Conclusions",
+ "text_level": 1,
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+ "text": "We propose V2XPnP, a novel V2X spatio-temporal fusion framework for cooperative temporal perception and prediction. The core of this framework is a unified Transformer-based model for spatio-temporal fusion and map fusion. Furthermore, we examine various fusion strategies concerning what, when to transmit, and how to fuse, offering comprehensive benchmarks. Additionally, we introduce the V2X Sequential Dataset, which supports all V2X collaboration modes. Extensive experiments demonstrate the superior performance of the proposed framework, establishing its efficacy in advancing cooperative temporal tasks.",
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+ "text": "Acknowledgements",
+ "text_level": 1,
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+ "text": "This work was supported by the Federal Highway Administration Center of Excellence on New Mobility and Automated Vehicles, and by the National Science Foundation under Award No. 2346267, POSE: Phase II - DriveX: An Open Source Ecosystem for Automated Driving and Intelligent Transportation Research.",
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+ "content": "Vehicle-to-everything (V2X) technologies offer a promising paradigm to mitigate the limitations of constrained observability in single-vehicle systems. Prior work primarily focuses on single-frame cooperative perception, which fuses agents' information across different spatial locations but ignores temporal cues and temporal tasks (e.g., temporal perception and prediction). In this paper, we focus on the spatio-temporal fusion in V2X scenarios and design one-step and multi-step communication strategies (when to transmit) as well as examine their integration with three fusion strategies - early, late, and intermediate (what to transmit), providing comprehensive benchmarks with 11 fusion models (how to fuse). Furthermore, we propose V2XPnP, a novel intermediate fusion framework within one-step communication for end-to-end perception and prediction. Our framework employs a unified Transformer-based architecture to effectively model complex spatio-temporal relationships across multiple agents, frames, and high-definition maps. Moreover, we introduce the V2XPnP Sequential Dataset that supports all V2X collaboration modes and addresses the limitations of existing real-world datasets, which are restricted to single-frame or single-mode cooperation. Extensive experiments demonstrate that our framework outperforms state-of-the-art methods in both perception and prediction tasks."
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+ "content": "Figure 2. Illustration of various V2X fusion strategies for perception and prediction. (a) What to Transmit: early, intermediate, and late fusion, transmitting raw sensor data, intermediate BEV features, or bounding boxes. (b) When to Transmit: multi-step and one-step communication."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "collaboration modes remain scarce. V2X-Seq [45] is the only sequential dataset incorporated with various behavior and map data for prediction tasks; however, is limited to V2I data and has restricted accessibility with download constraints."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3. V2XPnP Fusion Framework"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "The cooperative temporal perception and prediction task requires the integration of temporal information across historical frames and spatial information from multiple agents. It is defined as follows: given map and historical sequences of raw perception data \\(\\mathbf{P}_i^t\\), \\(i \\in \\{1, \\dots, N\\}\\), from all \\(N\\) agents within the communication range of the ego agent, the objective is to detect objects in the current frame and predict their future trajectories considering the map information."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.1. V2X Spatio-Temporal Fusion Strategies"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "This section addresses what and when to transmit for spatiotemporal fusion, and Sec. 3.2 delves into the fusion process. What to Transmit. In multi-agent spatial fusion, three fusion strategies are widely adopted in single-frame cooperative perception, i.e., early, late, and intermediate fusion [12, 44], which involve the transmission of raw perception data, bounding boxes, and intermediate features, respectively. Adopting this framework, we extend these fusion approaches to the V2X spatio-temporal fusion context, as illustrated in Fig. 2. (1) Early fusion transmits the entire raw historical perception data to retain complete feature information but imposes the highest transmission load. (2) Late fusion shares only the final detected results at each historical frame, resulting in the lowest transmission load but losing most of the feature information. (3) Intermediate fusion transmits intermediate spatio-temporal BEV features, striking a balance between information quality and transmission load."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "When to Transmit. Determining when to transmit in spatiotemporal fusion is more challenging due to the inclusion of temporal data as compared to the existing spatial fusion. A straightforward approach is Multi-step Communication, where each transmission only includes the current frame's"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "data. However, the multiple steps cause the accumulation of delays and data loss, and obtaining complete historical data requires that neighboring agents stay within the ego agent's limited communication range throughout historical frames. In practice, the ego agent should aggregate as much data as possible from other agents within a single transmission, rather than relying on multiple exchanges to obtain complete spatio-temporal information. To address this, we propose a One-step Communication strategy, where individual agents share all their historical data within a single communication."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ "angle": 0,
+ "content": "Intermediate Fusion with One-step Communication. Synthesizing the considerations for what to transmit and when to transmit, we adopt an intermediate fusion within the one-step communication strategy, which fuses temporal data from multiple frames before transmission, allowing each agent to share aggregated information without excessive communication overhead. In multi-step intermediate fusion, each agent transmits BEV feature maps at every timestep \\(\\mathbf{F}_i^t\\in \\mathbb{R}^{H\\times W\\times C}\\), which denotes agent \\(i\\)'s BEV feature at time \\(t\\) with height \\(H\\), width \\(W\\), and channels \\(C\\). The cumulative data shared across \\(T\\) frames is a stacked sequence \\(\\mathbf{F}_i^{seq}\\in \\mathbb{R}^{T\\times H\\times W\\times C}\\), resulting in a significantly higher transmission load than single-frame, along with potential delays and data loss. Conversely, in our proposed strategy, each agent first fuses its historical BEV features internally, reducing the sequence from \\(\\mathbf{F}_i^{seq}\\) to a single condensed BEV feature map \\(\\mathbf{F}_i'\\in \\mathbb{R}^{H\\times W\\times C}\\). This reduction allows agents to transmit a compact data packet, comparable in size to single-frame cooperative perception, thereby conserving bandwidth while preserving essential spatio-temporal information."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.2. V2XPnP Framework"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ 0.909,
+ 0.901
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+ "angle": 0,
+ "content": "The spatio-temporal features of intermediate fusion render it a natural fit for end-to-end perception and prediction. Accordingly, we propose a unified end-to-end perception and prediction framework to perform multiple tasks across spatiotemporal dimensions. The overall V2XPnP framework is illustrated in Fig. 3, which includes six components and is"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "25401"
+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
+ 0.107,
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+ ],
+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.089,
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+ "angle": 0,
+ "content": "Figure 3. The V2XPnP framework and multi-agent spatio-temporal fusion model. The framework comprises various components for feature extraction, fusion, and decoding. Within our fusion model, we introduce multiple attention mechanisms to enhance the fusion process."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
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+ "angle": 0,
+ "content": "unfolded in this section. The detail of the spatio-temporal fusion model is provided in Sec. 3.3. Notably, each module in V2XPnP is modular, allowing for easy replacement."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "V2X Metadata Sharing. Each agent in the V2X system is an observer and collaborator in the shared environment. Each agent will first determine its collaborators with its communication range, and share the metadata, such as relative poses and extrinsic, to construct a spatial V2X graph. Each node and edge in the graph represents an agent and a communication channel. All the point clouds are transformed into the ego agent's coordinate frame before feature extraction."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "LiDAR Feature Extraction. We utilize the PointPillar network [20] to extract the LiDAR feature for each agent \\(i\\) at time \\(t\\), which has low inference latency. The extracted features are structured into a 2D pseudo-image representation to produce salient feature maps \\(\\mathbf{F}_i^t\\), and the sequential feature is stacked as \\(\\mathbf{F}_i^{seq} \\in \\mathbb{R}^{T \\times H \\times W \\times C}\\)"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Multi-frame Temporal Fusion. We propose a Transformer-based temporal fusion module to iteratively perform interframe and intra-agent BEV feature fusion through self-attention mechanisms. The spatio-temporal feature of each agent is extracted through the temporal dimension while minimizing communication overhead. The feature map for each agent after temporal fusion is \\(\\mathbf{F}_i' \\in \\mathbb{R}^{H \\times W \\times C}\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
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+ ],
+ "angle": 0,
+ "content": "Compression and Sharing. To reduce the transmission load, intermediate features are compressed using a \\(1 \\times 1\\) kernel convolution network in its channel dimension. The ego agent uses another convolution network to decompress the features, restoring them to their original dimensionality. Multi-agent Spatial Fusion. The decompressed features are passed into a Transformer-based multi-agent spatial fusion network to learn inter-agent and intra-agent spatio-temporal interaction and update the multi-agent feature map \\(\\mathbf{F}'\\)."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Map Feature Extraction. The HD map is directly accessed for each agent without V2X fusion. We project the vectorized HD map to BEV space by incorporating the map polylines into each BEV feature grid. We first employ a multi-layer perceptron (MLP) to encode the surrounding map polylines for each grid \\(\\mathbf{M} \\in \\mathbb{R}^{H \\times W \\times N_m \\times n \\times D}\\), re"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.302,
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+ ],
+ "angle": 0,
+ "content": "sulting in the map feature \\(\\mathbf{F}_m\\in \\mathbb{R}^{H\\times W\\times N_m\\times C}\\). Here, \\(N_{m}\\) and \\(n\\) represent the number of map polylines and the waypoints per polyline, while \\(D\\) represents waypoint attributes (i.e., position and lane type). The map encoding is expressed as: \\(\\mathbf{F}_m = \\phi (\\mathrm{MLP}(\\mathbf{M}))\\), where \\(\\phi\\) denotes max-pooling on the waypoint axis. Then, a map-BEV attention is introduced to inject the map feature into the BEV feature. We concatenate the BEV and map feature \\(\\mathbf{F}_{bm} = [\\mathbf{F}',\\mathbf{F}_m]\\in \\mathbb{R}^{H\\times W\\times (1 + N_m)\\times C}\\), and add the position embedding \\(\\mathbf{P}_m\\) based on sinusoidal positional encoding. The final content feature map \\(\\mathbf{F}\\in \\mathbb{R}^{H\\times W\\times C}\\) is updated by multi-head self-attention (MHSA) as follows:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.522,
+ 0.5,
+ 0.907,
+ 0.518
+ ],
+ "angle": 0,
+ "content": "\\[\n\\mathbf {F} = \\operatorname {M H S A} \\left(\\mathrm {Q}: \\left[ \\mathbf {F} _ {b m}, \\mathbf {P} _ {m} \\right], \\mathrm {K}: \\left[ \\mathbf {F} _ {b m}, \\mathbf {P} _ {m} \\right], \\mathrm {V}: \\mathbf {F} _ {b m}\\right). \\tag {1}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.532,
+ 0.907,
+ 0.713
+ ],
+ "angle": 0,
+ "content": "Detection and Prediction Heads. Finally, a detection head and a prediction head are connected to the final feature \\(\\mathbf{F}\\) to output states for each predefined anchor box: (1) The detection head contains two 2D convolution layers for bounding box regression and classification. The regression branch outputs the bounding box position \\((x,y,z)\\), size \\((w,l,h)\\), and yaw \\(\\theta\\). The classification branch outputs the confidence score of each anchor box, determining whether it corresponds to an object or background. (2) The prediction head outputs offset values for each anchor box at each future timestamp using two 2D convolution layers, and the final trajectory is generated by accumulating these offsets."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
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+ ],
+ "angle": 0,
+ "content": "3.3. Spatio-Temporal Fusion Transformer"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.75,
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+ 0.901
+ ],
+ "angle": 0,
+ "content": "In this section, we introduce spatio-temporal fusion with a unified Transformer architecture. The proposed model comprises three blocks: temporal attention, self-spatial attention, and multi-agent spatial attention, as shown in Fig. 3, and two core fusion modules. (1) Multi-frame temporal fusion: Each agent first extracts their spatio-temporal features through iterative temporal and self-spatial attentions. (2) Multi-agent spatial fusion: rich BEV features from multiple agents are acquired via V2X and then fused through iterative multi-agent spatial and self-spatial attentions."
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "angle": 0,
+ "content": "25402"
+ }
+ ],
+ [
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Temporal Attention. This block is designed to capture the inter-frame relationship and aggregate historical BEV features \\(\\mathbf{F}_i^{seq}\\) across the temporal dimension. The history timestamps are encoded with a learnable embedding, which is added to each BEV feature frame to form \\(\\mathbf{F}_i^{seq'}\\). To preserve temporal cues, this block only fuses temporal features from the same spatial positions across frames, and spatial features are further extracted by the self-spatial Transformer. Temporal fusion is expressed as:"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.113,
+ 0.242,
+ 0.482,
+ 0.284
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathbf {F} _ {i} ^ {t e m} = \\operatorname {M H S A} \\left(\\mathrm {Q}: \\operatorname {M L P} \\left(\\mathbf {F} _ {i} ^ {s e q ^ {\\prime}}\\right), \\mathrm {K}: \\operatorname {M L P} \\left(\\mathbf {F} _ {i} ^ {s e q ^ {\\prime}}\\right), \\right. \\\\ \\left. \\mathrm {V}: \\operatorname {M L P} \\left(\\mathbf {F} _ {i} ^ {\\text {s e q} ^ {\\prime}}\\right)\\right). \\tag {2} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Self-spatial Attention. To capture the intra-agent spatial BEV interaction, this block employs multi-scale window attention to capture spatial features at different resolutions and ranges. A large window focuses on global features for long-term behavior, and a small window preserves local finer information. Note that this block only fuses spatial features for each agent in a frame without inter-frame and inter-agent fusion. Specifically, we utilize local, intermediate, and global windows \\( P_{k} \\in \\{P_{loc}, P_{inter}, P_{gl}\\} \\) to partition the feature map through the \\( H \\) and \\( W \\) dimension, generating the self-spatial token \\( \\mathbf{F}^{sp} \\in \\mathbb{R}^{\\frac{H}{P_k} \\times \\frac{W}{P_k} \\times P_k^2 \\times C} \\). With an additional relative position encoding, MHSA is operated among \\( P_{k}^{2} \\) tokens. The final output is obtained by performing split attention to fuse features from different windows."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.484,
+ 0.665
+ ],
+ "angle": 0,
+ "content": "Multi-agent Spatial Attention. This block facilitates inter-agent fusion by aggregating BEV feature maps from multiple agents. Considering the different deployment positions and capabilities of vehicle and infrastructure sensors, the multiagent spatial Transformer is heterogeneous with individual learnable weights for different interaction pairs (i.e., V-I, V-V, I-V, and I-I). The attention token of \\( i \\) th agent \\( \\mathbf{F}_{i,m}^{sp} \\) is modulated by its type \\( m \\) embedding, and is weighted by the relation matrix \\( \\mathbf{W}_{\\mathrm{att}}^{(e_{i,j})} \\) between edge \\( e_{i,j} \\) during aggregation with agent \\( j \\) of type \\( n \\):"
+ },
+ {
+ "type": "equation",
+ "bbox": [
+ 0.097,
+ 0.678,
+ 0.482,
+ 0.731
+ ],
+ "angle": 0,
+ "content": "\\[\n\\begin{array}{l} \\mathbf {Q} _ {i} ^ {m} = \\operatorname {M L P} \\left(\\mathbf {F} _ {i, m}\\right), \\mathbf {K} _ {j} ^ {n} = \\operatorname {M L P} \\left(\\mathbf {F} _ {j, n}\\right), \\mathbf {V} _ {j} ^ {n} = \\operatorname {M L P} \\left(\\mathbf {F} _ {j, n}\\right), \\\\ \\mathbf {F} _ {i, m} ^ {s p} = \\sum_ {j} \\operatorname {S o f t m a x} \\left(\\mathbf {Q} _ {i} ^ {m} \\cdot \\mathbf {W} _ {\\text {a t t}} ^ {\\left(e _ {i, j}\\right)} \\cdot \\mathbf {K} _ {j} ^ {n}\\right) \\cdot \\mathbf {V} _ {j} ^ {n}. \\tag {3} \\\\ \\end{array}\n\\]"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.4. Learning Objective"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ "angle": 0,
+ "content": "The learning objective is comprised of temporal perception and prediction tasks. First, we define the perception loss as the combination of regression \\(\\mathcal{L}_{\\mathrm{reg}}\\) and classification loss \\(\\mathcal{L}_{\\mathrm{cla}}\\) of the predefined anchor box. Specifically, the smooth \\(\\ell_1\\)-loss is leveraged for the regression part, and the focal loss [26] is utilized for classification. Second, we define the prediction loss \\(\\mathcal{L}_{\\mathrm{pred}}\\) as \\(\\ell_2\\)-loss between the prediction points sequence with ground truth trajectory. The final loss function is the weighted sum of \\(\\mathcal{L}_{\\mathrm{reg}}\\), \\(\\mathcal{L}_{\\mathrm{cla}}\\), and \\(\\mathcal{L}_{\\mathrm{pred}}\\)."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4. V2XPnP Sequential Dataset"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ "angle": 0,
+ "content": "We introduce the V2XPnP-Sequential dataset, the first large-scale, real-world V2X sequential dataset featuring multiple agents and all collaboration modes. This dataset comprises 96 scenarios (49 2V+2I scenarios, 38 V2V scenarios, and 9 V+2I scenarios), each spanning 95 to 283 frames captured at \\(10\\mathrm{Hz}\\). The dataset comprises two data sequences from CAV perception (point clouds and camera images) and two data sequences from infrastructure perception, as shown in Fig. 4(b). We also provide corresponding vector maps and point-cloud maps for all collection areas, as shown in Fig. 4(c). Ten object categories are included, and the average trajectory length and frequency of each category are shown in Fig. 4(d). Further details on data visualization, annotation, trajectory and map generation are provided in the supplementary."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.513,
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+ "angle": 0,
+ "content": "4.1. Data Acquisition"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
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+ ],
+ "angle": 0,
+ "content": "V2X temporal tasks require diverse time-consistent perception data and object behavior data. We choose urban arterial roads, expressways, and intersections to collect V2X data. The sensor configurations for two CAVs and two infrastructures are shown in Fig. 4(a). By permuting and combining the behavior patterns of CAVs (such as overtaking, platooning, turning, etc.), we designed a total of about 60 interaction pairs between CAVs to collect data. From more than 66h driving logs, we annotate 28 representative scenarios. We also process the non-sequential data from V2X-Real [39] with a V2X sequential data processing pipeline, detailed in Sec. 4.2. Since perception tasks do not need to consider labeling consistency, identical objects may be assigned different IDs within a sequence, leading to data fragmentation and limiting support for temporal tasks. The final dataset is yielded by processing our collected data and V2X-Real data."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Sequential Data Processing"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.512,
+ 0.629,
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+ ],
+ "angle": 0,
+ "content": "Time-consistent data is crucial for temporal tasks, and thus we develop a V2X sequential data processing pipeline to track objects across time and different agents' views. We construct a multi-agent spatio-temporal graph, where each node \\( n_{it}^{k} \\) represents an annotated bounding box \\( i \\) at time \\( t \\) from agent \\( k \\)'s LiDAR data, and edges connect nodes that correspond to the same object. Identifying objects with the same ID then reduces to finding connected components in this graph, with each isolated component representing a unique object. Moreover, we build this graph by leveraging the temporal continuity in single-agent annotations and incorporating multi-agent data. For temporal consistency within a single agent, we add edges between \\( n_{it}^{k} \\) and \\( n_{it+1}^{k} \\), although annotation errors may sometimes assign different IDs to the same object. To address this, we integrate annotations from multiple agents, transforming annotations into a global coordinate frame and connecting nodes if their Intersection-over-Union (IoU) exceeds a threshold. Once"
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+ "type": "page_number",
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+ }
+ ],
+ [
+ {
+ "type": "image",
+ "bbox": [
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+ },
+ {
+ "type": "image",
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+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Figure 4. Illustration of the V2XPnP Sequential Dataset. (a) V2X data acquisition systems; (b) Sequential LiDAR and camera data; (c) Data collection area and vector map; (d) Total number and average tracking length of 3D tracked objects per category."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "the graph is complete, we identify connected components and assign each a unique tracking ID. To mitigate annotation biases, we refine object attributes based on their consensus."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5. Experiments"
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "5.1. Experimental Setup"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Evaluation Metrics. Following the detection evaluation protocol in [39], we measure detection performance using Average Precision (AP) at an IoU threshold of 0.5. For prediction, we provide the results of commonly used metrics [8, 30, 31], including Average Displacement Error (ADE), Final Displacement Error (FDE), and Miss Rate (MR) within a 2-meter threshold. However, prediction accuracy is influenced by false positives and missed detections from the perception module. For example, a poorly performing perception module that detects only a simple object in a straight-line trajectory can misleadingly inflate the prediction accuracy. To address this, we employ the End-to-end Perception and Prediction Accuracy (EPA) metric [9] to jointly evaluate perception and prediction performance."
+ },
+ {
+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\nE P A = \\frac {\\left| \\hat {S} _ {\\text {m a t c h , h i t}} \\right| - \\alpha N _ {\\mathrm {F P}}}{N _ {\\mathrm {G T}}}, \\tag {4}\n\\]"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "where \\( |\\hat{S}_{\\mathrm{match,hit}}| \\) is the number of true positive objects with prediction \\( FDE < \\tau_{EPA}, N_{FP}, N_{GT} \\) represent the number of false positive objects and ground truth objects, respectively, and \\( \\alpha \\) is a penalty coefficient. A higher EPA value indicates superior object detection and prediction capabilities, and we set \\( \\tau_{EPA} = 2\\mathrm{m} \\), \\( \\alpha = 0.5 \\) following [9]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Collaboration Modes. The V2XPnP Sequential Dataset supports various V2X collaboration modes by organizing data with specific interaction patterns. Vehicle-Centric (VC): The ego CAV is the focal agent, communicating with other CAVs and infrastructure (Infra). Infrastructure-Centric (IC): Infrastructure is the central entity, communicating with other Infras and CAVs. Vehicle-to-Vehicle (V2V): The ego CAV communicates exclusively with other CAVs without involving Infra. Infrastructure-to-Infrastructure (I2I): Infra shares data only with each other. Each VC and IC scenario includes"
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+ "content": "2-4 agents, which is close to real-world V2X settings and can evaluate model generalization across diverse V2X scenarios, whereas each V2V and I2I scenario has two agents."
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+ "content": "Implementation Details. During the testing stage, we select a fixed agent as the ego agent in each cooperative scenario, while the ego agent is shuffled and randomly selected during training. Following the real-time setting [50], we set the communication range to 50 meters and evaluate surrounding agents within a range of \\( x \\in [-70, 70] \\mathrm{m} \\) and \\( y \\in [-40, 40] \\mathrm{m} \\). Messages beyond 50 meters are discarded. Besides, the history length is \\( 2 \\mathrm{~s} \\) (\\( 2 \\mathrm{~Hz} \\)), and the prediction horizon is \\( 3 \\mathrm{~s} \\) (\\( 2 \\mathrm{~Hz} \\)). The train/Validation/test data splits are 76/6/14 scenarios. Additional training and model details are provided in the supplementary materials."
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+ "content": "5.2. Benchmark Methods"
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+ "content": "End-to-end methods. Most of the single-frame perception models cannot support the prediction task, thus, we first implement a baseline end-to-end model with the same LiDAR backbone and decoding heads as V2XPnP but utilizing the temporal fusion module FaF [28] - alternating 2D and 3D convolutions - as the No fusion- \\( FaF^{*} \\) baseline, which can extend the non-temporal model to support temporal tasks. Then, the early fusion configurations and several state-of-the-art intermediate fusion models are integrated as: Early Fusion, \\( FFNet^{*} \\) [46], \\( CoBEVFlow^{*} \\) [37], \\( V2X-ViT^{*} \\) [40]). More benchmark results of \\( DiscoNet^{*} \\) [22], \\( F-Cooper^{*} \\) [6], and \\( V2VNet^{*} \\) [35] are provided in the supplementary. These models marked with * are reimplemented in our framework with the same LiDAR backbone and decoding heads."
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+ "content": "Decoupled methods. Transmitting final detection results renders late fusion incompatible with end-to-end models. Thus, we benchmark Late Fusion with a decoupled pipeline, where objects in each historical frame are detected using a single-frame perception module, and results are fused via non-maximum suppression. Assuming an ideal tracker to generate object trajectories from perception results and interpolate missing points, we implement an attention-based predictor for trajectory-level prediction tasks, following the prediction mainstream [32]. To further assess end-to-end per"
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+ "content": "Table 1. Benchmark results of cooperative perception and prediction models on V2XPnP Sequential (V2XPnP-Seq) Dataset"
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+ "content": "| Dataset | Method | E2E | Map | AP@0.5 (%) ↑ | ADE (m) ↓ | FDE (m) ↓ | MR (%) ↓ | EPA (%) ↑ |
| V2XPnP-Seq-VC(with V+2I at most) | No Fusion | | ✓ | 43.9 | 1.87 | 3.24 | 33.8 | 24.3 |
| No Fusion-FaF* [28] | ✓ | | 53.4 | 1.55 | 2.81 | 34.3 | 31.6 |
| Late Fusion | | ✓ | 58.1 | 1.59 | 2.82 | 32.4 | 33.0 |
| Early Fusion | ✓ | ✓ | 60.3 | 1.37 | 2.49 | 33.8 | 36.7 |
| CoBEVFlow* [37] | ✓ | ✓ | 63.3 | 1.36 | 2.49 | 33.0 | 41.9 |
| FFNet* [46] | ✓ | ✓ | 64.6 | 1.36 | 2.47 | 34.7 | 42.3 |
| V2X-ViT* [40] | ✓ | ✓ | 69.6 | 1.39 | 2.56 | 35.2 | 44.7 |
| V2XPnP (Ours) | ✓ | ✓ | 71.6 +2.0 | 1.35 | 2.36 | 31.7 | 48.2 +3.5 |
| V2XPnP-Seq-IC(with 2V+I at most) | No Fusion | | ✓ | 46.4 | 1.69 | 3.06 | 36.2 | 28.8 |
| No Fusion-FaF* [28] | ✓ | | 56.7 | 1.34 | 2.65 | 41.4 | 31.7 |
| Late Fusion | | ✓ | 55.9 | 1.39 | 2.44 | 30.1 | 32.9 |
| Early Fusion | ✓ | ✓ | 60.5 | 1.39 | 2.63 | 32.8 | 39.5 |
| CoBEVFlow* [37] | ✓ | ✓ | 57.6 | 1.38 | 2.58 | 31.0 | 32.5 |
| FFNet* [46] | ✓ | ✓ | 61.0 | 1.18 | 2.18 | 35.1 | 37.5 |
| V2X-ViT* [40] | ✓ | ✓ | 69.3 | 1.27 | 2.39 | 35.4 | 43.3 |
| V2XPnP (Ours) | ✓ | ✓ | 71.0 +1.7 | 1.18 | 2.16 | 34.0 | 46.0 +2.7 |
| V2XPnP-Seq-V2V | No Fusion | | ✓ | 40.8 | 1.99 | 3.38 | 34.0 | 19.8 |
| No Fusion-FaF* [28] | ✓ | | 51.9 | 1.67 | 3.12 | 39.3 | 27.5 |
| Late Fusion | | ✓ | 55.3 | 1.75 | 3.07 | 34.0 | 30.5 |
| Early Fusion | ✓ | ✓ | 53.0 | 1.64 | 3.11 | 40.2 | 26.9 |
| CoBEVFlow* [37] | ✓ | ✓ | 58.7 | 1.72 | 3.15 | 40.3 | 33.6 |
| FFNet* [46] | ✓ | ✓ | 56.5 | 1.68 | 3.12 | 39.8 | 31.2 |
| V2X-ViT* [40] | ✓ | ✓ | 64.6 | 1.68 | 3.13 | 39.8 | 36.7 |
| V2XPnP (Ours) | ✓ | ✓ | 70.5 +5.9 | 1.78 | 3.28 | 39.9 | 40.6 +3.9 |
| V2XPnP-Seq-I2I | No Fusion | | ✓ | 51.0 | 1.69 | 3.06 | 36.2 | 31.7 |
| No Fusion-FaF* [28] | ✓ | | 56.6 | 1.34 | 2.65 | 41.4 | 31.7 |
| Late Fusion | | ✓ | 61.3 | 1.41 | 2.50 | 30.0 | 41.6 |
| Early Fusion | ✓ | ✓ | 64.6 | 1.57 | 2.98 | 39.9 | 37.7 |
| CoBEVFlow* [37] | ✓ | ✓ | 58.4 | 1.31 | 2.61 | 41.5 | 33.0 |
| FFNet* [46] | ✓ | ✓ | 66.1 | 1.41 | 2.59 | 36.3 | 40.9 |
| V2X-ViT* [40] | ✓ | ✓ | 65.4 | 1.22 | 2.33 | 35.9 | 41.3 |
| V2XPnP (Ours) | ✓ | ✓ | 69.2 +3.1 | 1.26 | 2.31 | 36.5 | 42.8 +1.2 |
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+ "content": "formance, we also evaluate a decoupled No-Fusion model."
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+ "content": "Tab. 1 presents the benchmark results across four V2X collaboration modes. Since prediction performance inherently depends on detection quality, the difficulty posed by different detected objects can significantly impact prediction accuracy. Thus, the EPA metric serves as the most appropriate indicator for assessing the overall performance. More details and baseline results are provided in the supplementary."
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+ "content": "What to Transmit. In both end-to-end and decoupled PnP frameworks, the cooperation perception and prediction performance are consistently better than non-fusion models in all collaboration modes, especially in the primary EPA metric, which demonstrates the benefits of cooperation in temporal perception and prediction. Moreover, intermediate fusion models (e.g., V2X-ViT, FFNet, and V2XPnP) generally outperform other fusion strategies, while early fusion consistently surpasses late fusion. Our proposed V2XPnP model achieves the best performance, outperforming other competitive cooperative methods."
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+ "content": "When to Transmit. Tab. 2 shows the performance of our model under two communication strategies. We find that the"
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+ "content": "| Strategy | AP@0.5↑ | ADE ↓ | FDE ↓ | MR ↓ | EPA ↑ |
| Multi-step | 68.2 | 1.56 | 2.84 | 31.8 | 43.0 |
| One-step | 71.6 | 1.35 | 2.36 | 31.7 | 48.2 |
"
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+ "content": "Table 3. Ablation results of V2XPnP model"
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+ "content": "| Temp | Spatial | Map | AP@0.5↑ | ADE↓ | FDE↓ | MR↓ | EPA↑ |
| | | 43.9 | - | - | - | - |
| ✓ | | | 57.2 | 1.52 | 2.76 | 35.5 | 33.8 |
| ✓ | ✓ | | 71.3 | 1.48 | 2.70 | 36.2 | 44.4 |
| ✓ | ✓ | ✓ | 71.6 | 1.35 | 2.36 | 31.7 | 48.2 |
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+ "content": "perception and prediction performance of one-step communication is improved compared to multi-step communication by \\(5.0\\%\\) AP and \\(12\\%\\) in EPA. This improvement arises because each agent first directly fuses their lossless raw temporal data before sharing, avoiding error accumulation from lossy intermediate information transformed in multi-step communication across temporal dimensions. Moreover, the one-step strategy compresses spatio-temporal feature transmission (under a \\(32\\times\\) compression rate) from \\(5\\times 0.269\\) Mb to \\(0.269\\) Mb compared to multi-step communication, while mitigating information loss when agents move out of com"
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+ "content": ": detection box ground truth box"
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+ "content": "Figure 5. Qualitative results of different fusion models on the testing set. V2XPnP shows better perception and prediction results."
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+ "content": "munication range in historical frames. At a typical C-V2X data transmission rate [4], the transmission delay of one-step communication is approximately \\(10 \\sim 20\\) ms."
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+ "bbox": [
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+ "content": "How to Fuse. Tab. 3 provides the ablation study of V2XPnP, showing the effectiveness of different components in V2XPnP. The temporal fusion module provides the history information for current-frame detection, while multi-agent spatial fusion alleviates occlusions and improves performance by incorporating other views. The map fusion module enhances trajectory prediction by guiding future trajectories to align with road structures. Our complete V2XPnP model with all these fusion modules performs the best."
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+ "content": "End-to-end vs. Decoupled Frameworks. The end-to-end model consistently outperforms the decoupled framework. In no-fusion situations, the end-to-end model \\(\\mathrm{FaF^{*}}\\) outperforms the decoupled model in detection by leveraging temporal cues. Furthermore, \\(\\mathrm{FaF^{*}}\\) achieves performance comparable to late fusion with V2X spatial aggregation due to integrating temporal features. The intermediate fusion of spatio-temporal features in V2XPnP aligns well with the end-to-end architecture, showcasing its superior performance."
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+ "content": "Infrastructure vs. Vehicle Centric. As shown in Tab. 1, models under VC and IC modes outperform those in V2V and I2I modes, because VC and IC can aggregate information from up to four agents rather than only two, resulting in enhanced environmental understanding. Notably, the evaluation protocol is consistent across all models within each mode. Additionally, stationary infrastructure-based agents in IC and I2I modes offer higher prediction accuracy by providing elevated sensing perspectives and less noisy data."
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+ "content": "Transmission Data Size and Robustness Test. Results in Fig. 6 indicate that V2XPnP achieves a good balance between communication efficiency and accuracy, maintaining superior performance compared to full-size V2X-ViT* even at a \\(\\times 128\\) compression rate. Following the setting in [40], we provide the results with 100-500 ms time delay and positional/head Gaussian noise from \\((0.2\\mathrm{m}, 0.2^{\\circ})\\) to \\((1\\mathrm{m}, 1^{\\circ})\\). Both V2XPnP and V2X-ViT* maintain robust performance"
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+ "content": "Figure 6. Transmission data size and communication noise test results. V2XPnP shows better performance with varying data compression rates and robustness under communication noise."
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+ "bbox": [
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+ "angle": 0,
+ "content": "due to their spatial attention fusion, and V2XPnP performs better due to its designed temporal attention."
+ },
+ {
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+ "bbox": [
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+ "angle": 0,
+ "content": "Qualitative Results. Fig. 5 visualizes the outcomes of cooperative perception and prediction across different fusion models. The No Fusion model is constrained by its limited field of view. The FaF model, leveraging temporal information within an end-to-end pipeline, performs better under occlusion. Late and early fusion models significantly benefit from multi-agent data integration, though late fusion remains impacted by error propagation, such as detection heading errors misleading trajectory direction. Notably, the end-to-end intermediate fusion model, particularly V2XPnP, performs better in both detection and prediction tasks."
+ },
+ {
+ "type": "title",
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+ "angle": 0,
+ "content": "6. Conclusions"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "We propose V2XPnP, a novel V2X spatio-temporal fusion framework for cooperative temporal perception and prediction. The core of this framework is a unified Transformer-based model for spatio-temporal fusion and map fusion. Furthermore, we examine various fusion strategies concerning what, when to transmit, and how to fuse, offering comprehensive benchmarks. Additionally, we introduce the V2X Sequential Dataset, which supports all V2X collaboration modes. Extensive experiments demonstrate the superior performance of the proposed framework, establishing its efficacy in advancing cooperative temporal tasks."
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+ "angle": 0,
+ "content": "Acknowledgements"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "This work was supported by the Federal Highway Administration Center of Excellence on New Mobility and Automated Vehicles, and by the National Science Foundation under Award No. 2346267, POSE: Phase II - DriveX: An Open Source Ecosystem for Automated Driving and Intelligent Transportation Research."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "References"
+ },
+ {
+ "type": "ref_text",
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+ 0.483,
+ 0.271
+ ],
+ "angle": 0,
+ "content": "[1] Next Generation Simulation (NGSIM) Vehicle Trajectories and Supporting Data | USDOT Open Data. 2"
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+# V2XPnP: Vehicle-to-Everything Spatio-Temporal Fusion for Multi-Agent Perception and Prediction
+
+Zewei Zhou, Hao Xiang, Zhaoliang Zheng, Seth Z. Zhao, Mingyue Lei, Yun Zhang, Tianhui Cai, Xinyi Liu, Johnson Liu, Maheswari Bajji, Xin Xia, Zhiyu Huang* Bolei Zhou, Jiaqi Ma
+
+University of California, Los Angeles
+
+https://mobility-lab.seas.ucla.edu/v2xpnp
+
+# Abstract
+
+Vehicle-to-everything (V2X) technologies offer a promising paradigm to mitigate the limitations of constrained observability in single-vehicle systems. Prior work primarily focuses on single-frame cooperative perception, which fuses agents' information across different spatial locations but ignores temporal cues and temporal tasks (e.g., temporal perception and prediction). In this paper, we focus on the spatio-temporal fusion in V2X scenarios and design one-step and multi-step communication strategies (when to transmit) as well as examine their integration with three fusion strategies - early, late, and intermediate (what to transmit), providing comprehensive benchmarks with 11 fusion models (how to fuse). Furthermore, we propose V2XPnP, a novel intermediate fusion framework within one-step communication for end-to-end perception and prediction. Our framework employs a unified Transformer-based architecture to effectively model complex spatio-temporal relationships across multiple agents, frames, and high-definition maps. Moreover, we introduce the V2XPnP Sequential Dataset that supports all V2X collaboration modes and addresses the limitations of existing real-world datasets, which are restricted to single-frame or single-mode cooperation. Extensive experiments demonstrate that our framework outperforms state-of-the-art methods in both perception and prediction tasks.
+
+# 1. Introduction
+
+Autonomous driving systems are required to accurately perceive surrounding road users and predict their future trajectories to ensure safe and interactive driving. Despite recent advances in perception and prediction [7, 13, 33], single-vehicle systems still struggle with limited perception range and occlusion issues [23, 41], compromising driving performance and road safety. Consequently, vehicle-to-everything
+
+
+
+
+Figure 1. Illustration of V2X temporal tasks and our V2X spatiotemporal fusion framework. By incorporating temporal information, our framework enhances V2X communication and supports end-to-end perception and prediction beyond single-frame perception.
+
+(V2X) technologies have emerged as a promising paradigm to address these challenges, which enable connected and automated vehicles (CAVs) and infrastructures to share complementary information and mitigate occlusions, thereby supporting holistic environment understanding [10, 14, 16].
+
+Despite their potential, existing works focus on frame-by-frame cooperative detection [21, 27, 38, 52], which aggregates information from agents at different spatial locations. However, these works overlook temporal cues across sequential frames, which are important for locating previously visible but currently undetected objects [43] and predicting object future trajectories [28]. Although some work [37, 46] incorporate short-term temporal cues (0.5 s) in single-frame perception to mitigate asynchrony, the broader challenge of efficiently aggregating multi-agent and multi-frame information and supporting long-term temporal tasks, such as motion prediction, remains largely unexplored. Therefore, we aim to address critical questions in multi-agent multi-frame cooperation: (1) What information to transmit? (2) When to
+
+transmit it? (3) How to fuse information across multi-agent spatial and temporal dimensions? To address what to transmit, we expand the three fusion strategies in single-frame cooperative perception (i.e., early, late, and intermediate) to incorporate the temporal dimension. Regarding when to transmit, we introduce one-step and multi-step communication strategies to capture multi-frame temporal information. For how to fuse, we conduct a systematic analysis across various spatio-temporal fusion strategies, providing comprehensive benchmarks for cooperative perception and prediction tasks across all V2X collaboration modes.
+
+Among these strategies, we advocate intermediate fusion within one-step communication because it effectively balances the trade-off between accuracy and increased transmission load. Moreover, its capability to transmit intermediate spatial-temporal features makes it well-suited for end-to-end perception and prediction, allowing for feature sharing across multiple tasks, as shown in Fig. 1. Based on this strategy, we propose V2XPnP, a V2X spatio-temporal fusion framework leveraging a unified Transformer structure for effective spatial-temporal fusion, encompassing temporal attention, self-spatial attention, multi-agent spatial attention, and map attention. Each agent first extracts its inter-frame and self-spatial features, which can support single-vehicle perception and prediction while reducing the communication load, and then the multi-agent spatial attention model fuses the single-agent features across different agents.
+
+Another challenge is the lack of real-world sequential datasets encompassing diverse V2X collaboration modes. In V2X scenarios, vehicles and infrastructures serve as primary agents, with collaboration modes that include vehicle-to-vehicle (V2V), vehicle-to-infrastructure (V2I), and infrastructure-to-infrastructure (I2I), vehicle-centric (VC), and infrastructure-centric (IC) [16]. Most existing datasets [39, 44] are non-sequential, limited to single collaboration modes, and focus only on single-frame cooperative perception, lacking support for temporal tasks. To bridge this gap, we introduce the first large-scale real-world V2XPnP Sequential Dataset, featuring four agents and supporting all collaboration modes. This dataset includes temporally consistent perception and trajectory data across $49\mathrm{~2V} + 2\mathrm{I}$ scenarios, 38 V2V scenarios, and $9\mathrm{~V} + 2\mathrm{I}$ scenarios, totaling 40k frames, along with point-cloud and vector maps from 24 collected intersections. The main contributions of this paper can be summarized as follows:
+
+1. We present V2XPnP, a V2X spatio-temporal fusion framework with a novel intermediate fusion model within one-step communication. This framework is based on a unified Transformer architecture integrating diverse attention fusion modules for V2X spatial-temporal information.
+2. We introduce the first large-scale, real-world V2X sequential dataset featuring multiple agents and all V2X collaboration modes (i.e., VC, IC, V2V, I2I), encompass-
+
+ing perception data, object trajectories, and map data.
+
+3. We conduct extensive analysis across various spatiotemporal fusion strategies and benchmarks 11 fusion models for cooperative perception and prediction in all V2X collaboration modes, demonstrating the state-of-the-art performance of the proposed model.
+
+# 2. Related Work
+
+End-to-end Perception and Prediction. Safe autonomous driving fundamentally depends on accurate perception and prediction [15, 49]. In single-agent systems, significant efforts have been dedicated to temporal perception and prediction [24], leading to the development of various end-to-end frameworks. These frameworks enhance computational efficiency by sharing information across tasks and mitigating error propagation inherent in modular architectures. FaF [28] and PnPNet [25] focus on LiDAR-based joint perception and prediction, while occupancy flow methods [2, 3] provide detailed spatial-temporal information. Recently, Bird's-Eye-View (BEV)-based approaches with camera data have gained prominence [9, 13, 18].
+
+V2X Perception and Prediction. V2X perception has been extensively explored, with intermediate fusion emerging as a widely adopted strategy [7, 40, 41]. FFNet [46] and CoBEVFlow [37] utilize historical information (0.5s) from collaborators to mitigate asynchrony, and SCOPE integrates ego-history for detection. However, coordinating multi-agent systems for long-term temporal tasks remains an open challenge. In the prediction domain, deep learning models have been extensively studied for modeling inter-agent interactions [17, 32]. However, the limited short-term visibility of individual vehicles continues to restrict prediction accuracy. Cooperative prediction leveraging V2X has shown potential, though research remains preliminary [29, 36, 43, 48]. To integrate perception and prediction within an end-to-end framework, V2VNet [35] employs a graph neural network for spatio-temporal fusion. UniV2X [47] extended the end-to-end system to support downstream tasks, but with a simplified spatio-temporal fusion module. Despite these advancements, a comprehensive framework for V2X-based spatio-temporal fusion is still lacking.
+
+Real-world Driving Datasets. Public datasets have been instrumental in advancing autonomous driving research. Early sequential datasets [1, 19] provided only object trajectories on highways [51], but lack perception data. The following datasets, such as nuScenes [5] and Waymo [34], introduced real-world urban data but were limited to single-agent perspectives, rendering them unsuitable for V2X research. Thus, simulated datasets like V2XSet [40] were developed. Recently, datasets including Dair-V2X [44], V2V4Real [42], RCooper [11], and V2X-Real [39] significant contributed to real-world data in the V2I, V2V, I2I and V2X modes. However, real-world sequential V2X datasets covering all
+
+
+Figure 2. Illustration of various V2X fusion strategies for perception and prediction. (a) What to Transmit: early, intermediate, and late fusion, transmitting raw sensor data, intermediate BEV features, or bounding boxes. (b) When to Transmit: multi-step and one-step communication.
+
+
+
+collaboration modes remain scarce. V2X-Seq [45] is the only sequential dataset incorporated with various behavior and map data for prediction tasks; however, is limited to V2I data and has restricted accessibility with download constraints.
+
+# 3. V2XPnP Fusion Framework
+
+The cooperative temporal perception and prediction task requires the integration of temporal information across historical frames and spatial information from multiple agents. It is defined as follows: given map and historical sequences of raw perception data $\mathbf{P}_i^t$ , $i \in \{1, \dots, N\}$ , from all $N$ agents within the communication range of the ego agent, the objective is to detect objects in the current frame and predict their future trajectories considering the map information.
+
+# 3.1. V2X Spatio-Temporal Fusion Strategies
+
+This section addresses what and when to transmit for spatiotemporal fusion, and Sec. 3.2 delves into the fusion process. What to Transmit. In multi-agent spatial fusion, three fusion strategies are widely adopted in single-frame cooperative perception, i.e., early, late, and intermediate fusion [12, 44], which involve the transmission of raw perception data, bounding boxes, and intermediate features, respectively. Adopting this framework, we extend these fusion approaches to the V2X spatio-temporal fusion context, as illustrated in Fig. 2. (1) Early fusion transmits the entire raw historical perception data to retain complete feature information but imposes the highest transmission load. (2) Late fusion shares only the final detected results at each historical frame, resulting in the lowest transmission load but losing most of the feature information. (3) Intermediate fusion transmits intermediate spatio-temporal BEV features, striking a balance between information quality and transmission load.
+
+When to Transmit. Determining when to transmit in spatiotemporal fusion is more challenging due to the inclusion of temporal data as compared to the existing spatial fusion. A straightforward approach is Multi-step Communication, where each transmission only includes the current frame's
+
+data. However, the multiple steps cause the accumulation of delays and data loss, and obtaining complete historical data requires that neighboring agents stay within the ego agent's limited communication range throughout historical frames. In practice, the ego agent should aggregate as much data as possible from other agents within a single transmission, rather than relying on multiple exchanges to obtain complete spatio-temporal information. To address this, we propose a One-step Communication strategy, where individual agents share all their historical data within a single communication.
+
+Intermediate Fusion with One-step Communication. Synthesizing the considerations for what to transmit and when to transmit, we adopt an intermediate fusion within the one-step communication strategy, which fuses temporal data from multiple frames before transmission, allowing each agent to share aggregated information without excessive communication overhead. In multi-step intermediate fusion, each agent transmits BEV feature maps at every timestep $\mathbf{F}_i^t\in \mathbb{R}^{H\times W\times C}$ , which denotes agent $i$ 's BEV feature at time $t$ with height $H$ , width $W$ , and channels $C$ . The cumulative data shared across $T$ frames is a stacked sequence $\mathbf{F}_i^{seq}\in \mathbb{R}^{T\times H\times W\times C}$ , resulting in a significantly higher transmission load than single-frame, along with potential delays and data loss. Conversely, in our proposed strategy, each agent first fuses its historical BEV features internally, reducing the sequence from $\mathbf{F}_i^{seq}$ to a single condensed BEV feature map $\mathbf{F}_i'\in \mathbb{R}^{H\times W\times C}$ . This reduction allows agents to transmit a compact data packet, comparable in size to single-frame cooperative perception, thereby conserving bandwidth while preserving essential spatio-temporal information.
+
+# 3.2. V2XPnP Framework
+
+The spatio-temporal features of intermediate fusion render it a natural fit for end-to-end perception and prediction. Accordingly, we propose a unified end-to-end perception and prediction framework to perform multiple tasks across spatiotemporal dimensions. The overall V2XPnP framework is illustrated in Fig. 3, which includes six components and is
+
+
+Figure 3. The V2XPnP framework and multi-agent spatio-temporal fusion model. The framework comprises various components for feature extraction, fusion, and decoding. Within our fusion model, we introduce multiple attention mechanisms to enhance the fusion process.
+
+unfolded in this section. The detail of the spatio-temporal fusion model is provided in Sec. 3.3. Notably, each module in V2XPnP is modular, allowing for easy replacement.
+
+V2X Metadata Sharing. Each agent in the V2X system is an observer and collaborator in the shared environment. Each agent will first determine its collaborators with its communication range, and share the metadata, such as relative poses and extrinsic, to construct a spatial V2X graph. Each node and edge in the graph represents an agent and a communication channel. All the point clouds are transformed into the ego agent's coordinate frame before feature extraction.
+
+LiDAR Feature Extraction. We utilize the PointPillar network [20] to extract the LiDAR feature for each agent $i$ at time $t$ , which has low inference latency. The extracted features are structured into a 2D pseudo-image representation to produce salient feature maps $\mathbf{F}_i^t$ , and the sequential feature is stacked as $\mathbf{F}_i^{seq} \in \mathbb{R}^{T \times H \times W \times C}$
+
+Multi-frame Temporal Fusion. We propose a Transformer-based temporal fusion module to iteratively perform interframe and intra-agent BEV feature fusion through self-attention mechanisms. The spatio-temporal feature of each agent is extracted through the temporal dimension while minimizing communication overhead. The feature map for each agent after temporal fusion is $\mathbf{F}_i' \in \mathbb{R}^{H \times W \times C}$ .
+
+Compression and Sharing. To reduce the transmission load, intermediate features are compressed using a $1 \times 1$ kernel convolution network in its channel dimension. The ego agent uses another convolution network to decompress the features, restoring them to their original dimensionality. Multi-agent Spatial Fusion. The decompressed features are passed into a Transformer-based multi-agent spatial fusion network to learn inter-agent and intra-agent spatio-temporal interaction and update the multi-agent feature map $\mathbf{F}'$ .
+
+Map Feature Extraction. The HD map is directly accessed for each agent without V2X fusion. We project the vectorized HD map to BEV space by incorporating the map polylines into each BEV feature grid. We first employ a multi-layer perceptron (MLP) to encode the surrounding map polylines for each grid $\mathbf{M} \in \mathbb{R}^{H \times W \times N_m \times n \times D}$ , re
+
+sulting in the map feature $\mathbf{F}_m\in \mathbb{R}^{H\times W\times N_m\times C}$ . Here, $N_{m}$ and $n$ represent the number of map polylines and the waypoints per polyline, while $D$ represents waypoint attributes (i.e., position and lane type). The map encoding is expressed as: $\mathbf{F}_m = \phi (\mathrm{MLP}(\mathbf{M}))$ , where $\phi$ denotes max-pooling on the waypoint axis. Then, a map-BEV attention is introduced to inject the map feature into the BEV feature. We concatenate the BEV and map feature $\mathbf{F}_{bm} = [\mathbf{F}',\mathbf{F}_m]\in \mathbb{R}^{H\times W\times (1 + N_m)\times C}$ , and add the position embedding $\mathbf{P}_m$ based on sinusoidal positional encoding. The final content feature map $\mathbf{F}\in \mathbb{R}^{H\times W\times C}$ is updated by multi-head self-attention (MHSA) as follows:
+
+$$
+\mathbf {F} = \operatorname {M H S A} \left(\mathrm {Q}: \left[ \mathbf {F} _ {b m}, \mathbf {P} _ {m} \right], \mathrm {K}: \left[ \mathbf {F} _ {b m}, \mathbf {P} _ {m} \right], \mathrm {V}: \mathbf {F} _ {b m}\right). \tag {1}
+$$
+
+Detection and Prediction Heads. Finally, a detection head and a prediction head are connected to the final feature $\mathbf{F}$ to output states for each predefined anchor box: (1) The detection head contains two 2D convolution layers for bounding box regression and classification. The regression branch outputs the bounding box position $(x,y,z)$ , size $(w,l,h)$ , and yaw $\theta$ . The classification branch outputs the confidence score of each anchor box, determining whether it corresponds to an object or background. (2) The prediction head outputs offset values for each anchor box at each future timestamp using two 2D convolution layers, and the final trajectory is generated by accumulating these offsets.
+
+# 3.3. Spatio-Temporal Fusion Transformer
+
+In this section, we introduce spatio-temporal fusion with a unified Transformer architecture. The proposed model comprises three blocks: temporal attention, self-spatial attention, and multi-agent spatial attention, as shown in Fig. 3, and two core fusion modules. (1) Multi-frame temporal fusion: Each agent first extracts their spatio-temporal features through iterative temporal and self-spatial attentions. (2) Multi-agent spatial fusion: rich BEV features from multiple agents are acquired via V2X and then fused through iterative multi-agent spatial and self-spatial attentions.
+
+Temporal Attention. This block is designed to capture the inter-frame relationship and aggregate historical BEV features $\mathbf{F}_i^{seq}$ across the temporal dimension. The history timestamps are encoded with a learnable embedding, which is added to each BEV feature frame to form $\mathbf{F}_i^{seq'}$ . To preserve temporal cues, this block only fuses temporal features from the same spatial positions across frames, and spatial features are further extracted by the self-spatial Transformer. Temporal fusion is expressed as:
+
+$$
+\begin{array}{l} \mathbf {F} _ {i} ^ {t e m} = \operatorname {M H S A} \left(\mathrm {Q}: \operatorname {M L P} \left(\mathbf {F} _ {i} ^ {s e q ^ {\prime}}\right), \mathrm {K}: \operatorname {M L P} \left(\mathbf {F} _ {i} ^ {s e q ^ {\prime}}\right), \right. \\ \left. \mathrm {V}: \operatorname {M L P} \left(\mathbf {F} _ {i} ^ {\text {s e q} ^ {\prime}}\right)\right). \tag {2} \\ \end{array}
+$$
+
+Self-spatial Attention. To capture the intra-agent spatial BEV interaction, this block employs multi-scale window attention to capture spatial features at different resolutions and ranges. A large window focuses on global features for long-term behavior, and a small window preserves local finer information. Note that this block only fuses spatial features for each agent in a frame without inter-frame and inter-agent fusion. Specifically, we utilize local, intermediate, and global windows $P_{k} \in \{P_{loc}, P_{inter}, P_{gl}\}$ to partition the feature map through the $H$ and $W$ dimension, generating the self-spatial token $\mathbf{F}^{sp} \in \mathbb{R}^{\frac{H}{P_k} \times \frac{W}{P_k} \times P_k^2 \times C}$ . With an additional relative position encoding, MHSA is operated among $P_{k}^{2}$ tokens. The final output is obtained by performing split attention to fuse features from different windows.
+
+Multi-agent Spatial Attention. This block facilitates inter-agent fusion by aggregating BEV feature maps from multiple agents. Considering the different deployment positions and capabilities of vehicle and infrastructure sensors, the multiagent spatial Transformer is heterogeneous with individual learnable weights for different interaction pairs (i.e., V-I, V-V, I-V, and I-I). The attention token of $i$ th agent $\mathbf{F}_{i,m}^{sp}$ is modulated by its type $m$ embedding, and is weighted by the relation matrix $\mathbf{W}_{\mathrm{att}}^{(e_{i,j})}$ between edge $e_{i,j}$ during aggregation with agent $j$ of type $n$ :
+
+$$
+\begin{array}{l} \mathbf {Q} _ {i} ^ {m} = \operatorname {M L P} \left(\mathbf {F} _ {i, m}\right), \mathbf {K} _ {j} ^ {n} = \operatorname {M L P} \left(\mathbf {F} _ {j, n}\right), \mathbf {V} _ {j} ^ {n} = \operatorname {M L P} \left(\mathbf {F} _ {j, n}\right), \\ \mathbf {F} _ {i, m} ^ {s p} = \sum_ {j} \operatorname {S o f t m a x} \left(\mathbf {Q} _ {i} ^ {m} \cdot \mathbf {W} _ {\text {a t t}} ^ {\left(e _ {i, j}\right)} \cdot \mathbf {K} _ {j} ^ {n}\right) \cdot \mathbf {V} _ {j} ^ {n}. \tag {3} \\ \end{array}
+$$
+
+# 3.4. Learning Objective
+
+The learning objective is comprised of temporal perception and prediction tasks. First, we define the perception loss as the combination of regression $\mathcal{L}_{\mathrm{reg}}$ and classification loss $\mathcal{L}_{\mathrm{cla}}$ of the predefined anchor box. Specifically, the smooth $\ell_1$ -loss is leveraged for the regression part, and the focal loss [26] is utilized for classification. Second, we define the prediction loss $\mathcal{L}_{\mathrm{pred}}$ as $\ell_2$ -loss between the prediction points sequence with ground truth trajectory. The final loss function is the weighted sum of $\mathcal{L}_{\mathrm{reg}}$ , $\mathcal{L}_{\mathrm{cla}}$ , and $\mathcal{L}_{\mathrm{pred}}$ .
+
+# 4. V2XPnP Sequential Dataset
+
+We introduce the V2XPnP-Sequential dataset, the first large-scale, real-world V2X sequential dataset featuring multiple agents and all collaboration modes. This dataset comprises 96 scenarios (49 2V+2I scenarios, 38 V2V scenarios, and 9 V+2I scenarios), each spanning 95 to 283 frames captured at $10\mathrm{Hz}$ . The dataset comprises two data sequences from CAV perception (point clouds and camera images) and two data sequences from infrastructure perception, as shown in Fig. 4(b). We also provide corresponding vector maps and point-cloud maps for all collection areas, as shown in Fig. 4(c). Ten object categories are included, and the average trajectory length and frequency of each category are shown in Fig. 4(d). Further details on data visualization, annotation, trajectory and map generation are provided in the supplementary.
+
+# 4.1. Data Acquisition
+
+V2X temporal tasks require diverse time-consistent perception data and object behavior data. We choose urban arterial roads, expressways, and intersections to collect V2X data. The sensor configurations for two CAVs and two infrastructures are shown in Fig. 4(a). By permuting and combining the behavior patterns of CAVs (such as overtaking, platooning, turning, etc.), we designed a total of about 60 interaction pairs between CAVs to collect data. From more than 66h driving logs, we annotate 28 representative scenarios. We also process the non-sequential data from V2X-Real [39] with a V2X sequential data processing pipeline, detailed in Sec. 4.2. Since perception tasks do not need to consider labeling consistency, identical objects may be assigned different IDs within a sequence, leading to data fragmentation and limiting support for temporal tasks. The final dataset is yielded by processing our collected data and V2X-Real data.
+
+# 4.2. Sequential Data Processing
+
+Time-consistent data is crucial for temporal tasks, and thus we develop a V2X sequential data processing pipeline to track objects across time and different agents' views. We construct a multi-agent spatio-temporal graph, where each node $n_{it}^{k}$ represents an annotated bounding box $i$ at time $t$ from agent $k$ 's LiDAR data, and edges connect nodes that correspond to the same object. Identifying objects with the same ID then reduces to finding connected components in this graph, with each isolated component representing a unique object. Moreover, we build this graph by leveraging the temporal continuity in single-agent annotations and incorporating multi-agent data. For temporal consistency within a single agent, we add edges between $n_{it}^{k}$ and $n_{it+1}^{k}$ , although annotation errors may sometimes assign different IDs to the same object. To address this, we integrate annotations from multiple agents, transforming annotations into a global coordinate frame and connecting nodes if their Intersection-over-Union (IoU) exceeds a threshold. Once
+
+
+Figure 4. Illustration of the V2XPnP Sequential Dataset. (a) V2X data acquisition systems; (b) Sequential LiDAR and camera data; (c) Data collection area and vector map; (d) Total number and average tracking length of 3D tracked objects per category.
+
+
+
+
+
+
+
+the graph is complete, we identify connected components and assign each a unique tracking ID. To mitigate annotation biases, we refine object attributes based on their consensus.
+
+# 5. Experiments
+
+# 5.1. Experimental Setup
+
+Evaluation Metrics. Following the detection evaluation protocol in [39], we measure detection performance using Average Precision (AP) at an IoU threshold of 0.5. For prediction, we provide the results of commonly used metrics [8, 30, 31], including Average Displacement Error (ADE), Final Displacement Error (FDE), and Miss Rate (MR) within a 2-meter threshold. However, prediction accuracy is influenced by false positives and missed detections from the perception module. For example, a poorly performing perception module that detects only a simple object in a straight-line trajectory can misleadingly inflate the prediction accuracy. To address this, we employ the End-to-end Perception and Prediction Accuracy (EPA) metric [9] to jointly evaluate perception and prediction performance.
+
+$$
+E P A = \frac {\left| \hat {S} _ {\text {m a t c h , h i t}} \right| - \alpha N _ {\mathrm {F P}}}{N _ {\mathrm {G T}}}, \tag {4}
+$$
+
+where $|\hat{S}_{\mathrm{match,hit}}|$ is the number of true positive objects with prediction $FDE < \tau_{EPA}, N_{FP}, N_{GT}$ represent the number of false positive objects and ground truth objects, respectively, and $\alpha$ is a penalty coefficient. A higher EPA value indicates superior object detection and prediction capabilities, and we set $\tau_{EPA} = 2\mathrm{m}$ , $\alpha = 0.5$ following [9].
+
+Collaboration Modes. The V2XPnP Sequential Dataset supports various V2X collaboration modes by organizing data with specific interaction patterns. Vehicle-Centric (VC): The ego CAV is the focal agent, communicating with other CAVs and infrastructure (Infra). Infrastructure-Centric (IC): Infrastructure is the central entity, communicating with other Infras and CAVs. Vehicle-to-Vehicle (V2V): The ego CAV communicates exclusively with other CAVs without involving Infra. Infrastructure-to-Infrastructure (I2I): Infra shares data only with each other. Each VC and IC scenario includes
+
+2-4 agents, which is close to real-world V2X settings and can evaluate model generalization across diverse V2X scenarios, whereas each V2V and I2I scenario has two agents.
+
+Implementation Details. During the testing stage, we select a fixed agent as the ego agent in each cooperative scenario, while the ego agent is shuffled and randomly selected during training. Following the real-time setting [50], we set the communication range to 50 meters and evaluate surrounding agents within a range of $x \in [-70, 70] \mathrm{m}$ and $y \in [-40, 40] \mathrm{m}$ . Messages beyond 50 meters are discarded. Besides, the history length is $2 \mathrm{~s}$ ( $2 \mathrm{~Hz}$ ), and the prediction horizon is $3 \mathrm{~s}$ ( $2 \mathrm{~Hz}$ ). The train/Validation/test data splits are 76/6/14 scenarios. Additional training and model details are provided in the supplementary materials.
+
+# 5.2. Benchmark Methods
+
+End-to-end methods. Most of the single-frame perception models cannot support the prediction task, thus, we first implement a baseline end-to-end model with the same LiDAR backbone and decoding heads as V2XPnP but utilizing the temporal fusion module FaF [28] - alternating 2D and 3D convolutions - as the No fusion- $FaF^{*}$ baseline, which can extend the non-temporal model to support temporal tasks. Then, the early fusion configurations and several state-of-the-art intermediate fusion models are integrated as: Early Fusion, $FFNet^{*}$ [46], $CoBEVFlow^{*}$ [37], $V2X-ViT^{*}$ [40]). More benchmark results of $DiscoNet^{*}$ [22], $F-Cooper^{*}$ [6], and $V2VNet^{*}$ [35] are provided in the supplementary. These models marked with * are reimplemented in our framework with the same LiDAR backbone and decoding heads.
+
+Decoupled methods. Transmitting final detection results renders late fusion incompatible with end-to-end models. Thus, we benchmark Late Fusion with a decoupled pipeline, where objects in each historical frame are detected using a single-frame perception module, and results are fused via non-maximum suppression. Assuming an ideal tracker to generate object trajectories from perception results and interpolate missing points, we implement an attention-based predictor for trajectory-level prediction tasks, following the prediction mainstream [32]. To further assess end-to-end per
+
+Table 1. Benchmark results of cooperative perception and prediction models on V2XPnP Sequential (V2XPnP-Seq) Dataset
+
+| Dataset | Method | E2E | Map | AP@0.5 (%) ↑ | ADE (m) ↓ | FDE (m) ↓ | MR (%) ↓ | EPA (%) ↑ |
| V2XPnP-Seq-VC(with V+2I at most) | No Fusion | | ✓ | 43.9 | 1.87 | 3.24 | 33.8 | 24.3 |
| No Fusion-FaF* [28] | ✓ | | 53.4 | 1.55 | 2.81 | 34.3 | 31.6 |
| Late Fusion | | ✓ | 58.1 | 1.59 | 2.82 | 32.4 | 33.0 |
| Early Fusion | ✓ | ✓ | 60.3 | 1.37 | 2.49 | 33.8 | 36.7 |
| CoBEVFlow* [37] | ✓ | ✓ | 63.3 | 1.36 | 2.49 | 33.0 | 41.9 |
| FFNet* [46] | ✓ | ✓ | 64.6 | 1.36 | 2.47 | 34.7 | 42.3 |
| V2X-ViT* [40] | ✓ | ✓ | 69.6 | 1.39 | 2.56 | 35.2 | 44.7 |
| V2XPnP (Ours) | ✓ | ✓ | 71.6 +2.0 | 1.35 | 2.36 | 31.7 | 48.2 +3.5 |
| V2XPnP-Seq-IC(with 2V+I at most) | No Fusion | | ✓ | 46.4 | 1.69 | 3.06 | 36.2 | 28.8 |
| No Fusion-FaF* [28] | ✓ | | 56.7 | 1.34 | 2.65 | 41.4 | 31.7 |
| Late Fusion | | ✓ | 55.9 | 1.39 | 2.44 | 30.1 | 32.9 |
| Early Fusion | ✓ | ✓ | 60.5 | 1.39 | 2.63 | 32.8 | 39.5 |
| CoBEVFlow* [37] | ✓ | ✓ | 57.6 | 1.38 | 2.58 | 31.0 | 32.5 |
| FFNet* [46] | ✓ | ✓ | 61.0 | 1.18 | 2.18 | 35.1 | 37.5 |
| V2X-ViT* [40] | ✓ | ✓ | 69.3 | 1.27 | 2.39 | 35.4 | 43.3 |
| V2XPnP (Ours) | ✓ | ✓ | 71.0 +1.7 | 1.18 | 2.16 | 34.0 | 46.0 +2.7 |
| V2XPnP-Seq-V2V | No Fusion | | ✓ | 40.8 | 1.99 | 3.38 | 34.0 | 19.8 |
| No Fusion-FaF* [28] | ✓ | | 51.9 | 1.67 | 3.12 | 39.3 | 27.5 |
| Late Fusion | | ✓ | 55.3 | 1.75 | 3.07 | 34.0 | 30.5 |
| Early Fusion | ✓ | ✓ | 53.0 | 1.64 | 3.11 | 40.2 | 26.9 |
| CoBEVFlow* [37] | ✓ | ✓ | 58.7 | 1.72 | 3.15 | 40.3 | 33.6 |
| FFNet* [46] | ✓ | ✓ | 56.5 | 1.68 | 3.12 | 39.8 | 31.2 |
| V2X-ViT* [40] | ✓ | ✓ | 64.6 | 1.68 | 3.13 | 39.8 | 36.7 |
| V2XPnP (Ours) | ✓ | ✓ | 70.5 +5.9 | 1.78 | 3.28 | 39.9 | 40.6 +3.9 |
| V2XPnP-Seq-I2I | No Fusion | | ✓ | 51.0 | 1.69 | 3.06 | 36.2 | 31.7 |
| No Fusion-FaF* [28] | ✓ | | 56.6 | 1.34 | 2.65 | 41.4 | 31.7 |
| Late Fusion | | ✓ | 61.3 | 1.41 | 2.50 | 30.0 | 41.6 |
| Early Fusion | ✓ | ✓ | 64.6 | 1.57 | 2.98 | 39.9 | 37.7 |
| CoBEVFlow* [37] | ✓ | ✓ | 58.4 | 1.31 | 2.61 | 41.5 | 33.0 |
| FFNet* [46] | ✓ | ✓ | 66.1 | 1.41 | 2.59 | 36.3 | 40.9 |
| V2X-ViT* [40] | ✓ | ✓ | 65.4 | 1.22 | 2.33 | 35.9 | 41.3 |
| V2XPnP (Ours) | ✓ | ✓ | 69.2 +3.1 | 1.26 | 2.31 | 36.5 | 42.8 +1.2 |
+
+formance, we also evaluate a decoupled No-Fusion model.
+
+# 5.3. Results
+
+Tab. 1 presents the benchmark results across four V2X collaboration modes. Since prediction performance inherently depends on detection quality, the difficulty posed by different detected objects can significantly impact prediction accuracy. Thus, the EPA metric serves as the most appropriate indicator for assessing the overall performance. More details and baseline results are provided in the supplementary.
+
+What to Transmit. In both end-to-end and decoupled PnP frameworks, the cooperation perception and prediction performance are consistently better than non-fusion models in all collaboration modes, especially in the primary EPA metric, which demonstrates the benefits of cooperation in temporal perception and prediction. Moreover, intermediate fusion models (e.g., V2X-ViT, FFNet, and V2XPnP) generally outperform other fusion strategies, while early fusion consistently surpasses late fusion. Our proposed V2XPnP model achieves the best performance, outperforming other competitive cooperative methods.
+
+When to Transmit. Tab. 2 shows the performance of our model under two communication strategies. We find that the
+
+Table 2. Comparison of one-step and multi-step communication
+
+| Strategy | AP@0.5↑ | ADE ↓ | FDE ↓ | MR ↓ | EPA ↑ |
| Multi-step | 68.2 | 1.56 | 2.84 | 31.8 | 43.0 |
| One-step | 71.6 | 1.35 | 2.36 | 31.7 | 48.2 |
+
+Table 3. Ablation results of V2XPnP model
+
+| Temp | Spatial | Map | AP@0.5↑ | ADE↓ | FDE↓ | MR↓ | EPA↑ |
| | | 43.9 | - | - | - | - |
| ✓ | | | 57.2 | 1.52 | 2.76 | 35.5 | 33.8 |
| ✓ | ✓ | | 71.3 | 1.48 | 2.70 | 36.2 | 44.4 |
| ✓ | ✓ | ✓ | 71.6 | 1.35 | 2.36 | 31.7 | 48.2 |
+
+perception and prediction performance of one-step communication is improved compared to multi-step communication by $5.0\%$ AP and $12\%$ in EPA. This improvement arises because each agent first directly fuses their lossless raw temporal data before sharing, avoiding error accumulation from lossy intermediate information transformed in multi-step communication across temporal dimensions. Moreover, the one-step strategy compresses spatio-temporal feature transmission (under a $32\times$ compression rate) from $5\times 0.269$ Mb to $0.269$ Mb compared to multi-step communication, while mitigating information loss when agents move out of com
+
+
+
+
+
+
+
+
+
+
+(a) Vehicle-centric scenario
+
+
+- : prediction trajectory
+-x : ground truth trajectory
+
+
+
+
+
+
+
+
+
+
+: detection box ground truth box
+
+
+(b) Infrastructure-centric scenario
+
+munication range in historical frames. At a typical C-V2X data transmission rate [4], the transmission delay of one-step communication is approximately $10 \sim 20$ ms.
+
+How to Fuse. Tab. 3 provides the ablation study of V2XPnP, showing the effectiveness of different components in V2XPnP. The temporal fusion module provides the history information for current-frame detection, while multi-agent spatial fusion alleviates occlusions and improves performance by incorporating other views. The map fusion module enhances trajectory prediction by guiding future trajectories to align with road structures. Our complete V2XPnP model with all these fusion modules performs the best.
+
+End-to-end vs. Decoupled Frameworks. The end-to-end model consistently outperforms the decoupled framework. In no-fusion situations, the end-to-end model $\mathrm{FaF^{*}}$ outperforms the decoupled model in detection by leveraging temporal cues. Furthermore, $\mathrm{FaF^{*}}$ achieves performance comparable to late fusion with V2X spatial aggregation due to integrating temporal features. The intermediate fusion of spatio-temporal features in V2XPnP aligns well with the end-to-end architecture, showcasing its superior performance.
+
+Infrastructure vs. Vehicle Centric. As shown in Tab. 1, models under VC and IC modes outperform those in V2V and I2I modes, because VC and IC can aggregate information from up to four agents rather than only two, resulting in enhanced environmental understanding. Notably, the evaluation protocol is consistent across all models within each mode. Additionally, stationary infrastructure-based agents in IC and I2I modes offer higher prediction accuracy by providing elevated sensing perspectives and less noisy data.
+
+Transmission Data Size and Robustness Test. Results in Fig. 6 indicate that V2XPnP achieves a good balance between communication efficiency and accuracy, maintaining superior performance compared to full-size V2X-ViT* even at a $\times 128$ compression rate. Following the setting in [40], we provide the results with 100-500 ms time delay and positional/head Gaussian noise from $(0.2\mathrm{m}, 0.2^{\circ})$ to $(1\mathrm{m}, 1^{\circ})$ . Both V2XPnP and V2X-ViT* maintain robust performance
+
+
+Figure 5. Qualitative results of different fusion models on the testing set. V2XPnP shows better perception and prediction results.
+
+
+Figure 6. Transmission data size and communication noise test results. V2XPnP shows better performance with varying data compression rates and robustness under communication noise.
+
+due to their spatial attention fusion, and V2XPnP performs better due to its designed temporal attention.
+
+Qualitative Results. Fig. 5 visualizes the outcomes of cooperative perception and prediction across different fusion models. The No Fusion model is constrained by its limited field of view. The FaF model, leveraging temporal information within an end-to-end pipeline, performs better under occlusion. Late and early fusion models significantly benefit from multi-agent data integration, though late fusion remains impacted by error propagation, such as detection heading errors misleading trajectory direction. Notably, the end-to-end intermediate fusion model, particularly V2XPnP, performs better in both detection and prediction tasks.
+
+# 6. Conclusions
+
+We propose V2XPnP, a novel V2X spatio-temporal fusion framework for cooperative temporal perception and prediction. The core of this framework is a unified Transformer-based model for spatio-temporal fusion and map fusion. Furthermore, we examine various fusion strategies concerning what, when to transmit, and how to fuse, offering comprehensive benchmarks. Additionally, we introduce the V2X Sequential Dataset, which supports all V2X collaboration modes. Extensive experiments demonstrate the superior performance of the proposed framework, establishing its efficacy in advancing cooperative temporal tasks.
+
+# Acknowledgements
+
+This work was supported by the Federal Highway Administration Center of Excellence on New Mobility and Automated Vehicles, and by the National Science Foundation under Award No. 2346267, POSE: Phase II - DriveX: An Open Source Ecosystem for Automated Driving and Intelligent Transportation Research.
+
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+ "content": "Figure 1. Illustration of V2X temporal tasks and our V2X spatiotemporal fusion framework. By incorporating temporal information, our framework enhances V2X communication and supports end-to-end perception and prediction beyond single-frame perception."
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+ "content": "(V2X) technologies have emerged as a promising paradigm to address these challenges, which enable connected and automated vehicles (CAVs) and infrastructures to share complementary information and mitigate occlusions, thereby supporting holistic environment understanding [10, 14, 16]."
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+ "content": "transmit it? (3) How to fuse information across multi-agent spatial and temporal dimensions? To address what to transmit, we expand the three fusion strategies in single-frame cooperative perception (i.e., early, late, and intermediate) to incorporate the temporal dimension. Regarding when to transmit, we introduce one-step and multi-step communication strategies to capture multi-frame temporal information. For how to fuse, we conduct a systematic analysis across various spatio-temporal fusion strategies, providing comprehensive benchmarks for cooperative perception and prediction tasks across all V2X collaboration modes."
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+ "content": ". The dataset comprises two data sequences from CAV perception (point clouds and camera images) and two data sequences from infrastructure perception, as shown in Fig. 4(b). We also provide corresponding vector maps and point-cloud maps for all collection areas, as shown in Fig. 4(c). Ten object categories are included, and the average trajectory length and frequency of each category are shown in Fig. 4(d). Further details on data visualization, annotation, trajectory and map generation are provided in the supplementary."
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+ "content": "). The train/Validation/test data splits are 76/6/14 scenarios. Additional training and model details are provided in the supplementary materials."
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| V2XPnP-Seq-VC(with V+2I at most) | No Fusion | | ✓ | 43.9 | 1.87 | 3.24 | 33.8 | 24.3 |
| No Fusion-FaF* [28] | ✓ | | 53.4 | 1.55 | 2.81 | 34.3 | 31.6 |
| Late Fusion | | ✓ | 58.1 | 1.59 | 2.82 | 32.4 | 33.0 |
| Early Fusion | ✓ | ✓ | 60.3 | 1.37 | 2.49 | 33.8 | 36.7 |
| CoBEVFlow* [37] | ✓ | ✓ | 63.3 | 1.36 | 2.49 | 33.0 | 41.9 |
| FFNet* [46] | ✓ | ✓ | 64.6 | 1.36 | 2.47 | 34.7 | 42.3 |
| V2X-ViT* [40] | ✓ | ✓ | 69.6 | 1.39 | 2.56 | 35.2 | 44.7 |
| V2XPnP (Ours) | ✓ | ✓ | 71.6 +2.0 | 1.35 | 2.36 | 31.7 | 48.2 +3.5 |
| V2XPnP-Seq-IC(with 2V+I at most) | No Fusion | | ✓ | 46.4 | 1.69 | 3.06 | 36.2 | 28.8 |
| No Fusion-FaF* [28] | ✓ | | 56.7 | 1.34 | 2.65 | 41.4 | 31.7 |
| Late Fusion | | ✓ | 55.9 | 1.39 | 2.44 | 30.1 | 32.9 |
| Early Fusion | ✓ | ✓ | 60.5 | 1.39 | 2.63 | 32.8 | 39.5 |
| CoBEVFlow* [37] | ✓ | ✓ | 57.6 | 1.38 | 2.58 | 31.0 | 32.5 |
| FFNet* [46] | ✓ | ✓ | 61.0 | 1.18 | 2.18 | 35.1 | 37.5 |
| V2X-ViT* [40] | ✓ | ✓ | 69.3 | 1.27 | 2.39 | 35.4 | 43.3 |
| V2XPnP (Ours) | ✓ | ✓ | 71.0 +1.7 | 1.18 | 2.16 | 34.0 | 46.0 +2.7 |
| V2XPnP-Seq-V2V | No Fusion | | ✓ | 40.8 | 1.99 | 3.38 | 34.0 | 19.8 |
| No Fusion-FaF* [28] | ✓ | | 51.9 | 1.67 | 3.12 | 39.3 | 27.5 |
| Late Fusion | | ✓ | 55.3 | 1.75 | 3.07 | 34.0 | 30.5 |
| Early Fusion | ✓ | ✓ | 53.0 | 1.64 | 3.11 | 40.2 | 26.9 |
| CoBEVFlow* [37] | ✓ | ✓ | 58.7 | 1.72 | 3.15 | 40.3 | 33.6 |
| FFNet* [46] | ✓ | ✓ | 56.5 | 1.68 | 3.12 | 39.8 | 31.2 |
| V2X-ViT* [40] | ✓ | ✓ | 64.6 | 1.68 | 3.13 | 39.8 | 36.7 |
| V2XPnP (Ours) | ✓ | ✓ | 70.5 +5.9 | 1.78 | 3.28 | 39.9 | 40.6 +3.9 |
| V2XPnP-Seq-I2I | No Fusion | | ✓ | 51.0 | 1.69 | 3.06 | 36.2 | 31.7 |
| No Fusion-FaF* [28] | ✓ | | 56.6 | 1.34 | 2.65 | 41.4 | 31.7 |
| Late Fusion | | ✓ | 61.3 | 1.41 | 2.50 | 30.0 | 41.6 |
| Early Fusion | ✓ | ✓ | 64.6 | 1.57 | 2.98 | 39.9 | 37.7 |
| CoBEVFlow* [37] | ✓ | ✓ | 58.4 | 1.31 | 2.61 | 41.5 | 33.0 |
| FFNet* [46] | ✓ | ✓ | 66.1 | 1.41 | 2.59 | 36.3 | 40.9 |
| V2X-ViT* [40] | ✓ | ✓ | 65.4 | 1.22 | 2.33 | 35.9 | 41.3 |
| V2XPnP (Ours) | ✓ | ✓ | 69.2 +3.1 | 1.26 | 2.31 | 36.5 | 42.8 +1.2 |
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| Multi-step | 68.2 | 1.56 | 2.84 | 31.8 | 43.0 |
| One-step | 71.6 | 1.35 | 2.36 | 31.7 | 48.2 |
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| | | 43.9 | - | - | - | - |
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| ✓ | ✓ | | 71.3 | 1.48 | 2.70 | 36.2 | 44.4 |
| ✓ | ✓ | ✓ | 71.6 | 1.35 | 2.36 | 31.7 | 48.2 |
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diff --git a/2025/V2XScenes_ A Multiple Challenging Traffic Conditions Dataset for Large-Range Vehicle-Infrastructure Collaborative Perception/e74c8f66-2f14-41e8-a64e-91a69d371436_content_list.json b/2025/V2XScenes_ A Multiple Challenging Traffic Conditions Dataset for Large-Range Vehicle-Infrastructure Collaborative Perception/e74c8f66-2f14-41e8-a64e-91a69d371436_content_list.json
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+ "type": "text",
+ "text": "V2XScenes: A Multiple Challenging Traffic Conditions Dataset for Large-Range Vehicle-Infrastructure Collaborative Perception",
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+ "text": "Bowen Wang $^{1}$ Yafei Wang $^{1*}$ Wei Gong $^{1,2}$ Siheng Chen $^{1,3}$ Genjia Liu $^{1}$ Minhao Xiong $^{1}$ Chin Long Ng $^{1}$",
+ "bbox": [
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+ "text": "$^{1}$ Shanghai Jiao Tong University $^{2}$ Shanghai Lingang Economic Development (Group) Co., Ltd. $^{3}$ Shanghai AI Laboratory $^{1}$ {98.wangbowen, wyfjlu, weigong2020, sihengc, LGJ1zed, xmh123, clong.ng}@sjtu.edu.cn https://advrc-wangbw.github.io/V2XScenes/",
+ "bbox": [
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+ "type": "text",
+ "text": "Abstract",
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+ "page_idx": 0
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+ {
+ "type": "text",
+ "text": "Whether autonomous driving can effectively handle challenging scenarios such as bad weather and complex traffic environments is still in doubt. One of the critical difficulties is that the single-view perception makes it hard to obtain the complementary perceptual information around the multi-condition scenes, such as meeting occlusion and congestion. To investigate the advantages of collaborative perception in high-risky driving scenarios, we construct a multiple challenging conditions dataset for large-range vehicle-infrastructure cooperative perception, called V2XScenes, which includes seven typical multi-modal layouts at successive road sections. Particularly, each selected scene is labeled with a specific condition description, and we provide unique object tracking numbers across the entire road section and sequential frames to ensure consistency. Comprehensive cooperative perception benchmarks of 3D object detection and tracking for large-range roadside scenes are summarized, and the quantitative results based on the state-of-the-art demonstrate the effectiveness of collaborative perception facing challenging scenes. The data and benchmark codes of V2XScenes will be released.",
+ "bbox": [
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+ "type": "text",
+ "text": "1. Introduction",
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+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "Single-vehicle perception systems often suffer from occlusion and sparse sensor observations, posing significant safety risks, especially under challenging conditions such as driving on rainy nights or in congested traffic with frequent visual occlusions. [41]. To address the issues, vehicle-to-everything (V2X) for cooperative perception is a promising solution [14, 26], which aims to mitigate the limitations of",
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+ {
+ "type": "text",
+ "text": "single-vehicle perception by facilitating effective data exchange among multiple roadside units. Recently, a series of V2X datasets have been released for the development of cooperative perception, such as [47, 54, 57, 58, 62]. Among them, DAIR-V2X [57] and V2X-seq[58] introduce the first vehicle-infrastructure cooperative perception and trajectories prediction datasets based on the real-world data. V2X-Real[47] proposes the first cooperative perception dataset that can both support Vehicle-to-Infrastructure cooperation or Vehicle-to-Vehicle cooperation. The existing solid works truly make great advancements in V2X technologies.",
+ "bbox": [
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+ "page_idx": 0
+ },
+ {
+ "type": "text",
+ "text": "However, the advantages of cooperative perception in challenging scenarios such as adverse weather remain difficult to validate due to the scarcity of real-world V2X perception data. Although some works summarize the challenging V2X driving maneuvers of traffic violations, overtaking, and U-turns [62], the cooperative perception range and sensor modalities are still remain development. Due to the uncertainty of traffic dynamics and weather condition in the real-world, it is a tough task to collect the cooperative perception data under complicated scenarios. Some researchers use the simulators such as Carla [23, 24, 40, 51, 53] and generative world models [10, 22, 42] to construct challenging driving scenarios. Nevertheless, the model trained with simulated data introduced a significant domain gap to real-world scenarios.",
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+ "text": "In this paper, we introduce a multi-condition and large-range V2X dataset, named V2XSences, which mainly focuses on complicated scenarios such as heavy rainy night, congestion and occlusion. We collect the cooperative perception data under a large-range successive road section with a range view of $600\\mathrm{m}$ . Particularly, to compare the perception capabilities of different sensors in the challenging scenario, V2XSences consists of 5 sensor categories, including 3 types of LiDAR (Mechanical LiDAR, Solid-State LiDAR, Blind Repair LiDAR), 4D High-Resolution Millimeter wave Radar and Camera. Unlike the previous",
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+ "text": "CVF",
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+ "page_idx": 0
+ },
+ {
+ "type": "header",
+ "text": "This ICCV paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+ "text": "* Corresponding author: Yafei Wang \nThis research was supported by the National Natural Science Foundation of China under Number 52372417 and Number 52072243.",
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+ "img_path": "images/66143c3ed60a8757da55cf05f30beaa305ee2354b6d9308d11dc6774d6078a85.jpg",
+ "image_caption": [
+ "Figure 1. Demonstration of proposed V2XScenes, which is the first V2X dataset considering complex and challenging traffic conditions under large-range roadside scenarios. Upper shows the large-range road section, where seven roadside cooperative perception layouts are numbered and presented with related camera views, and the fused point cloud by all LiDARs and Radar is illustrated in the middle. Lower shows the multi-condition challenging scenes with complex traffic condition, diverse weather, etc. are collected in V2XScenes."
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+ {
+ "type": "text",
+ "text": "datasets without data classification according to different driving scenarios, V2XScenes exclusively collects multi-condition vehicle-infrastructure cooperative data across different times of day, traffic congestion and diverse weather. In summary, our main contributions include:",
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+ "type": "list",
+ "sub_type": "text",
+ "list_items": [
+ "- We build V2XScenes, the first multiple challenging condition dataset for large-range V2X cooperative perception with driving scenario annotation. Our dataset includes five types of sensors: mechanical LiDAR, solid-state LiDAR, blind repair LiDAR, 4D radar, and cameras.",
+ "- We provide large-range sequential 3D bounding boxes and trajectories with unique tracking IDs. The sequential data under complex traffic condition, diverse weather are well-organized with specific scene-descriptive labels.",
+ "- Two comprehensive cooperative benchmarks of 3D object detection and tracking are developed for validating the effectiveness. Experimental results demonstrate the advantages of cooperative perception on challenging scenes."
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+ "text": "2. Related Work",
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+ "text": "In this section, we summarize existing autonomous driving datasets under different cooperative modes and highlight the key differences between V2XScenes and others in Tab. 1.",
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+ "text": "Single view datasets are obtained from individual ego-vehicle or roadside infrastructure. As for the vehicle-side perspective, a number of datasets have been released since 2012 such as KITTI [9], ApolloScape [15], nuScenes [4] and Waymo [36], et al. Among them, KITTI [9] is the first large-scale multi-modal autonomous driving dataset for stereo, object detection and tracking. In comparison, nuScenes consists of six vehicle cameras mounting with a surround view, and equips with data under special scenes, such as night scene. The six surround cameras with overlapping fields of view make nuScenes the most used dataset in bird's-eye-view (BEV) perception recently [33]. On the other hand, roadside sensors can provide data in key areas for autonomous driving [11], especially intersections. Several pioneer roadside perception methods have emerged in recent years like Rope3D [56], A9 [8] and IPS300+ [37].",
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+ "text": "2.2. Vehicle-Infrastructure Datasets",
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+ "text": "The objective of the Vehicle-Infrastructure collaboration dataset construction is to explore the beneficial effect of roadside perception for single vehicle automated driving, overcoming the limitations of single-vehicle sensing under",
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+ "Table 1. Comparison of popular datasets for cooperative perception in autonomous driving. \"C\" and \"L\" represent the camera and LiDAR respectively. \"F\" represents the fisheye camera. \"R\" is denoted as Radar. The related values indicate the number of used sensors."
+ ],
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+ "table_body": "| Dataset | Cooperative Dataset Type | Sensors Layouts and View | Ground Truth Labels | Challenging Scenarios |
| Source | Mode | Year | Vehicle view | Roadside view | Annotation range | Tracking IDs for all views | Synchronized frames | Night heavy rain | Occlusion and congestion |
| OPV2V [52] | simulated | V2V | 2022 | 4C+1L | - | 120m | - | 11k | - | - |
| V2X-Sim [23] | simulated | V2X | 2022 | 2C+1L | 4C+1L | 70m | ✓ | 10k | - | ✓ |
| V2X-Set [50] | simulated | V2X | 2022 | 4C+1L | 4C+1L | 120m | - | 11k | - | ✓ |
| DeepAccident [40] | simulated | V2X | 2022 | 2C+1L | 6C+1L | 100m | ✓ | 57k | - | ✓ |
| CARTI [2] | simulated | V2I | 2022 | 1L | 1L | - | - | 11k | - | - |
| CODD [1] | simulated | V2V | 2022 | 2L | - | 100m | - | 13.5k | - | - |
| DOLPHINS [30] | simulated | V2X | 2022 | 1C+1L | 1C+1L | 200m | - | 42.4k | ✓ | - |
| Intersection-A9 [8] | real-world | I2I | 2022 | - | 2C+2L | 70m | - | 1.1k | - | - |
| IPS300+ [37] | real-world | I2I | 2022 | - | 2C+3L | 230m | - | 14k | - | ✓ |
| DAIR-V2X [57] | real-world | V2X | 2022 | 1C+1L | 1C+1L | 280m | - | 464k | - | - |
| V2V4Real [54] | real-world | V2V | 2023 | 4C+2L | - | 200m | ✓ | 20k | - | - |
| V2X-Seq [58] | real-world | V2X | 2023 | 1C+1L | 1C+1L | 280m | ✓ | 15k | - | - |
| HoloVIC [29] | real-world | V2I | 2024 | 2C+2L | 12C+4F+2L | - | ✓ | 100k | - | - |
| TUMTraf-V2X [62] | real-world | V2I | 2024 | 1C+1L | 4C+2L | 200m | ✓ | 2k | - | ✓ |
| Rcooper [12] | real-world | I2I | 2024 | - | 2C+2L | 230m | - | 30K | ✓ | - |
| V2X-Real [47] | real-world | V2X | 2024 | 4C+1L | 2C+1L | 280m | - | 33K | - | - |
| V2XScenes (Ours) | real-world | V2X | 2025 | 6C+3L | 13C+11L+2R | 600m | ✓ | 35k | ✓ | ✓ |
",
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+ "text": "scenarios such as occlusion. DAIR-V2X [57] is the first and one of the foremost cooperative multi-modal datasets, which contains 464k 3D box labels belonging to 10 classes. The V2X-Seq [58] extends selected sequences of the DAIR-V2X dataset with track IDs and is partitioned into a sequential perception dataset (SPD) and a trajectory forecasting dataset. Unlike the most of existing V2X datasets focus on single collaboration mode, V2V4Real [54] collects the data by two connected vehicles which can achieve different types of V2X collaboration modes. Due to the difficulty of collecting traffic data for real-world scenarios, some simulated multi-agent perception datasets included V2X-Sim [23], V2XSet [50] and OPV2V [52], et al. are proposed for data supplementation and scenario customization.",
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+ "text": "2.3. Multi-condition Datasets for V2X perception",
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+ "text": "Special-scenario data plays a vital role in driving algorithmic improvements. Several cooperative perception datasets, such as V2X-Seq [58] and IPS300+ [37], have included multi-condition data including both daytime and nighttime scenes. Wang et al. [38] propose AdvSim to obtain adversarial scenarios by modifying the vehicle trajectories in a physically guided manner. Zhang et al. [59] present ChatScene which leverages the capabilities of large language model (LLM) to generate safety-critical scenarios within the CARLA simulation environment. In addition, generative world models [19, 31, 43, 46, 60] are also utilized to create challenging virtual driving scenarios. Generation-based methods can identify thousands of semantically safety-critical and challenging scenarios for autonomous driving. However, existing approaches still benefit significantly from real-world scenario data to ensure robustness and reliability.",
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+ "Figure 2. Sensors layouts of vehicle-side and roadside view. E-N-U and X-Y-Z represent the coordinates under two views. We define the virtual E-N-U coordinate as the global coordinate."
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+ "text": "To investigate the benefits of collaborative perception in challenging multi-condition scenarios, V2XScenes focuses on the acquisition of large-range vehicle-Infrastructure cooperative data under complex traffic environments, such as in bad weather, and provides ground truth of 3D bounding box and trajectory for multi-modal object targets. Especially, V2XScenes is the first one that focuses on the holistic and complete view of both vehicle-side and roadside using camera and LiDAR data. The detailed of perception layouts, calibration and data acquisition at multi-condition scenes are presented in the following.",
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+ "text": "Base Configuration. V2XScenes covers two intersections and one middle successive road corridor within a range of $600\\mathrm{m}$ , including 7 cooperative perception positions. There",
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+ "image_caption": [
+ "Figure 3. Comparison of different point-based sensors under various weather. The first and second row represent weather of sunny and rainy, respectively. The bounding boxes with red line are the traffic object in point cloud data."
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+ "text": "are total of 13 cameras, 11 LiDARs, and 2 4D millimetre wave Radars in roadside scenes, and the automated vehicle contains 6 cameras and 3 LiDARs. All LiDARs and cameras at the roadside are synchronised via the Precision Time Protocol (PTP) with the time error less than $10ms$ , and the automated vehicle uses the same satellite clock source as the roadside configuration to the simultaneous data acquisition. The overall sensor layouts of both vehicle and roadside views are illustrate in Fig. 2.",
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+ "text": "Roadside Multi-sensor Layouts. Due to the different requirements of view-range for intersections and corridor in the roadside scene, we adopt various configurations for 7 roadside perception positions as shown in Fig. 2. For $1^{\\text{st}}$ to $6^{\\text{th}}$ perception positions, 2 cameras with 2k resolution are opposite installed on the rod and 1 camera is mounted at $7^{\\text{th}}$ position. we apply at least 1 camera and LiDAR for data acquisition. To explore the effect of roadside perception based on different types of LiDARs and Radars, 6 mechanical rotating LiDAR with 128-beams, 2 solid-state LiDAR with 125-beams, 3 bind repair LiDAR with 32-beams and 2 4D millimetre-wave Radar are mounted in close proximity for comparison. Fig. 3 shows the perception results of different roadside LiDAR and 4D Radar. Since weather affects the reflection of LiDAR, the density of valid point on rainy day becomes relatively sparse compared to the sunny day. On the contrary, the point cloud of 4D millimetre wave Radar is not affected by weather and with high robustness.",
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+ "text": "Vehicle-side Multi-sensor Layouts. Perception learning in the bird's-eye view (BEV) [20, 25, 27, 55] can obtain ro",
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+ "text": "bust feature representations from multi-sensor views. To this end, we deploy 6 cameras on the automated vehicle to achieve a full visual perception, including 4 cameras with a $60^{\\circ}$ field of view at the front and rear, 2 cameras with a $120^{\\circ}$ field of view at the left and right as shown in Fig. 2. In addition, a 128-beams mechanical LiDAR is mounted at the middle top of vehicle, along with 32-beams bind repair LiDAR on the left and right. The vehicle position and attitude information are acquired by on-board IMU and GPS.",
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+ "text": "To allow all sensors collaborate in an uniform coordinates system, we employ the following two parts, i.e., Roadside LiDAR and camera extrinsic calibration and vehicleinfrastructure calibration. The overall calibration process is illustrated in Fig. 4, we define a global coordinate denoted as $P_{g} = [X_{g},Y_{g},Z_{g}]^{\\top}$ based on the East-North-Up (ENU) coordinate system.",
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+ "text": "Roadside LiDAR&Camera Calibration. We define the LiDAR and camera coordinate as $P_{\\ell} = [X_{\\ell}, Y_{\\ell}, Z_{\\ell}]^{\\top}$ and $P_{c} = [X_{c}, Y_{c}, Z_{c}]^{\\top}$ respectively. Our goal is to obtain the optimal transferring matrix $T_{LiDAR2World}$ and $T_{LiDAR2Camera}$ . First, we calculate the intrinsic of camera parameters by using a checkerboard target. Then, we obtain the calibration results based on a automatic calibration method [39] using a customized roadside planar target, where the related global position information in $P_{g}$ is obtained based on the devices with GPS/IMU. During the calculating process, we individually determine the trans",
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+ "image_caption": [
+ "Figure 4. The calibration relationships among the sensors in V2XScenes. The red part represents the 3D object annotation process. The ground truth of 3D bounding boxes are annotated in global coordinates system. To guarantee the quality of the ground truth label, we will return the results to the previous coordinate systems (e.g. camera coordinate system, original point cloud coordinate system) for checking."
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+ "text": "formation matrix $T_{\\text{LLA2ENU}}$ between ENU and Latitude-Longitude-Altitude(LLA). After obtaining the initial estimation, the algorithm of EPnP [18] and Kabsch [34] are used to optimize the final $T_{\\text{LiDAR2World}}$ and $T_{\\text{LiDAR2Camera}}$ for Li-DAR and camera, respectively.",
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+ "text": "Vehicle-Infrastructure Calibration. We regard the vehicle coordinate system as the onboard GPS/IMU coordinate system, denoted as $P_{v} = [X_{v}, Y_{v}, Z_{v}]^{\\mathrm{T}}$ . Based on the information of GPS/IMU, we can transfer the vehicle point cloud to roadside global coordinates by the same transformation matrix of $T_{\\text{LLA2ENU}}$ , and obtain the initial vehicle-infrastructure calibration matrix of $T_{\\text{Vehicle2World}}$ . In addition, a dense point cloud map covering the entire road section is constructed for pose alignment, and we apply the point-to-point Iterative Closest Point (ICP) algorithm [3] to optimize the $T_{\\text{Vehicle2World}}$ under several iterations.",
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+ "text": "3.3. Registration and Ground Truth Labels",
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+ "text": "V2XScenes contains a total of 332,596 labeled 3D bounding boxes annotated by expert annotators across various object categories, with each scene averaging around $10\\mathrm{k}$ and $3\\mathrm{k}$ 3D bounding boxes from the roadside and vehicle-side views, respectively. Fig. 4 also demonstrates the process and defines coordinates for 3D annotation. Aiming to distinguish the distribution of objects under different views, we independently employ the data annotation of vehicle-side and roadside scenes. To enhance the efficiency and accuracy of the labeling process under two views, we combine the point cloud from 11 roadside LiDARs and 2 Radar for cooperative annotation like [47], and the targets are uniformly labeled within the normalized 3D point cloud.",
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+ "text": "For each object, we provide a unified target identity (ID) across the entire large-scale perceptive road section. Following existing works [9, 57], each object is annotated with a 7-dimensional bounding box, including the cen",
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+ "text": "ter location $[x_c, y_c, z_c]$ , dimensions of height $h$ , width $w$ , length $l$ , and heading angle $\\varphi$ . We use $L_i^{\\mathrm{VEH}}, L_i^{\\mathrm{ROAD}} = \\{x_c, y_c, z_c, h, w, l, \\varphi\\}$ to denote the annotation of vehicle-side and roadside views respectively. Additionally, eight categories of Car, Motorcycle, Cyclist, Pedestrian, Truck, Bus, Trailer, and Van are divided in the proposed dataset. In particular, we add a special category of autonomous vehicle for quickly determining the cooperative vehicle in the roadside view.",
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+ "text": "3.4. Multi-condition Data Selection",
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+ "text": "Existing vehicle-infrastructure collaboration datasets lack the definition and classification of sequential data scenarios, especially missing challenging safety scenes with multi-sensors, rendering it hard to demonstrate the advantages and effectiveness by using roadside devices to enhance the autonomous driving perception. Therefore, we constructed V2XScenes and select special data under the scenes such as rainy day, night, congestion, occlusion, etc., ranging from 8 to 51 seconds in duration.",
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+ "text": "Based on the mentioned condition elements, the selected sequential data in V2XScenes are manually processed and organized with the specific scene description labels. As described in Fig. 5, we give the description for sequential data as \"Driving to the intersection on a heavy rainy Night\" and \"Facing congestion on an sunny day\". From the figure, it can be seen that collaborative sensing can effectively expand the sensing field of view of the vehicle, especially enhancing the perception ability of automated vehicles in rainy days, occlusion and other challenging scenarios.",
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+ "Figure 5. Examples of multi-condition scenes in V2XScenes. The upper orange parts denote the scene-descriptive labels for different scenes. We provide both vehicle-side and roadside views to illustrate the challenging scenes. For each scene, the lower point cloud figures in BEV view demonstrate the single vehicle-side mode (left) and cooperative mode (right), where the vehicle-side and fused roadside point cloud are marked as darkblue and gray respectively."
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+ "text": "3D object target detection and object tracking. Instead of using the global coordinate systems for perception task, we transform all the roadside sensor data into the ego vehicle-side coordinates for final data fusion based on the previous calibration results. For a sequential data with time length $T_{max}$ , the label from vehicle-side and roadside at each time $t$ can be merged into:",
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+ "text": "\n$$\n\\left[ L _ {i} ^ {\\text {F U S E}} \\right] _ {t = 0} ^ {T _ {\\max }} = F \\left(\\left[ L _ {i} ^ {\\text {V E H}} \\right] _ {t = 0} ^ {T _ {\\max }}, \\left[ L _ {i} ^ {\\text {R O A D}} \\right] _ {t = 0} ^ {T _ {\\max }}, \\mu^ {\\text {t h}}\\right) \\tag {1}\n$$\n",
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+ "text": "Where the $F$ denotes the fusion function, and $\\mu^{\\mathrm{th}}$ represents the fusion threshold to filter the repeated objects from the vehicle-side view and roadside view.",
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+ "text": "4.1. V2X Cooperative 3D Object Detection",
+ "text_level": 1,
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+ "text": "V2X Cooperative 3D Target Detection is aimed to expand and compensate the limited vehicle-side view based on data from road-side multi-view sensors. During the cooperative training process, all sensor devices are unified into the vehicle-side coordinate system. A valid communication distance $D_{c}$ between vehicle and roadside devices is defined to obtain the fused label of $[L_i^{\\mathrm{FUSE}}]_{t=0}^{T_{max}}$ based on (1). Similar as RCooper [12] and KITTI [9], Average Precision (AP) with specific Intersection-over-Union (IoU) is used as the metrics to evaluate the cooperative object detection.",
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+ "image_caption": [
+ "V2XViT [49]"
+ ],
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+ "CoBEVT [48]"
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+ "img_path": "images/5fb430156e28167c7f9a6a793ec796de1ca45f4cc939c332ff475245206f8bf9.jpg",
+ "image_caption": [
+ "AttuFuse [13]",
+ "Figure 6. Visualization of the cooperative 3D object detection. These are the comparative illustrations of results in Tab. 2. The fused point cloud is colored by black. The ground truth and predictions are represented by red and blue respectively."
+ ],
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+ "img_path": "images/388b0f9a9adf376c6ad193e9cbcde5329dbab0298862403127bce1faaf7a4896.jpg",
+ "image_caption": [
+ "F-Cooper [7]"
+ ],
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+ {
+ "type": "table",
+ "img_path": "images/88dc79115417ce0d4f61ac6b3ff5a0f53a77b309e84d2e560dd598b09e95779c.jpg",
+ "table_caption": [
+ "Table 2. Results of Cooperative 3D object detection. The 0.3, 0.5 and 0.7 represent IoU and the best results are marked by bold."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | AP3D@0.3 | AP3D@0.5 | AP3D@0.7 |
| Late Fusion | 39.97 | 36.21 | 23.72 |
| Early Fusion | 35.59 | 23.75 | 10.31 |
| AttuFuse [52] | 57.11 | 46.69 | 20.88 |
| F-Cooper [7] | 53.48 | 40.45 | 17.27 |
| V2XVIT [49] | 58.10 | 51.11 | 26.48 |
| CoBEVT [48] | 54.50 | 43.48 | 21.92 |
| CoAlign [28] | 58.41 | 50.57 | 28.20 |
| Where2Comm [13] | 52.43 | 42.90 | 17.79 |
",
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+ "text": "4.2. Large-range Roadside Tracking",
+ "text_level": 1,
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+ "text": "The roadside perspective enables robust long-term and large-scale object tracking, offering vehicles high-fidelity, temporally coherent motion representations of surrounding objects. In our benchmark, Multiple Object Tracking Accuracy (MOTA) and Multiple Object Tracking Precision (MOTP) are used as the main metrics for the tracking task. MOTA and MOTP focus on the correctness of the predictive association and position respectively among the entire tracking trajectories. Additionally, to demonstrate the tracking robustness and accuracy under different scenarios, we include the Mostly Tracked Trajectories (MT) and Mostly Lost Trajectories (ML) metrics in the evaluation.",
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+ "text": "5. Experiments",
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+ "text": "5.1. Benchmarks Setup",
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+ "text": "Fusion Strategies. Three typical fusion method are applied in the following validation:",
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+ "list_items": [
+ "- Early fusion: directly integrates the raw data of sensors and ground truth before the training.",
+ "- Late fusion: merges the final perception results using the position relationship among different sensors.",
+ "- Intermediate fusion: Extracts the encoded feature of the cooperative data to refine the ego agent training."
+ ],
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+ "table_caption": [
+ "Table 3. Evaluation for other classes. $AP_{3D}^{\\dagger}$ is the mean of $AP_{3D}^{0.3\\sim 0.7}$ , i.e., IoU = 0.3, 0.5 and 0.7. All the units are $\\%$"
+ ],
+ "table_footnote": [],
+ "table_body": "| Methods | Pedestrians | Trucks |
| AP0.33D | AP†3D | MOTA MOTP | AP0.33D | AP†3D | MOTA MOTP |
| Early | 32.42 | 18.17 | 25.30 | 46.98 | 23.78 | 14.83 | 21.37 | 52.04 |
| CoBEVT | 39.86 | 19.86 | 20.84 | 43.60 | 23.15 | 16.47 | 15.89 | 54.24 |
| V2XVIT | 43.74 | 24.16 | 24.48 | 49.08 | 16.69 | 11.11 | 12.69 | 51.92 |
",
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+ "img_path": "images/e96c6e7db8c381120f39e9f4a9f82468b55f456458c14181f383eba2e15026ce.jpg",
+ "image_caption": [
+ "Figure 7. V2X perception results under different defined transmission latency. We follow the initial settings used in Tab. 2"
+ ],
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+ "img_path": "images/9f5b6b028cba8b31edfc0bf32901f46fce94d5d60012842584ab8179369b17ef.jpg",
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+ {
+ "type": "text",
+ "text": "We select the state-of-the-art of intermediate fusion methods including AttFuse [52], CoBEVT [48], V2XVIT [49], CoAlign [28], Where2Comm [13] and F-Cooper [7].",
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+ "text": "Implementation Details. We captured over twenty distinct scenes, each lasting between 8 and 51 seconds, from both vehicle and infrastructure perspectives with 35 sensors. The V2XScenes sequences were then split into a training set $(80\\%)$ and a test set $(20\\%)$ . All the fusion method are verified based on the 3D backbone of PointPillars [17]. Our code is built based on the open source project of Open-COOD [52] for multi-view collaboration and runs on two RTX A6000 GPUs. We train the perception collaboration for 30 epochs with learning rate of 0.001 based on the Adam optimizer. We set threshold communication distance to $100m$ so as to ensure the vehicle is constantly collaborating with at least three roadside devices.",
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+ "text": "28391",
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+ "type": "table",
+ "img_path": "images/68eb44c9b13339cec9143dcc0dbaf5d784a8212b36d754dd8d488910d444bb0c.jpg",
+ "table_caption": [
+ "Table 4. Cooperative 3D object detection results under different weather conditions of sunny and rainy. The blue background represents the improvement (\\%) compared to the no fusion method."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | Car AP3D of Sunny (%) | Car AP3D of Rainy (%) |
| IoU=0.3 | IoU=0.5 | IoU=0.7 | IoU=0.3 | IoU=0.5 | IoU=0.7 |
| No Fusion | 73.30 | - | 68.89 | - | 47.15 | - | 38.72 | - | 29.82 | - | 13.15 | - |
| Late Fusion | 75.33 | +2.8↑ | 72.26 | +4.9↑ | 49.48 | +4.9↑ | 46.27 | +19.5↑ | 31.33 | +5.0↑ | 6.33 | -51.9↓ |
| Early Fusion | 82.36 | +12.4↑ | 77.69 | +12.8↑ | 59.91 | +27.1↑ | 57.14 | +47.6↑ | 44.69 | +49.9↑ | 19.47 | +48.1↑ |
| AttuFuse | 81.65 | +11.4↑ | 74.13 | +7.6↑ | 53.05 | +12.5↑ | 50.62 | +30.7↑ | 35.54 | +19.2↑ | 12.08 | -8.2↓ |
| F-Cooper | 85.58 | +16.7↑ | 79.95 | +16.0↑ | 53.41 | +13.3↑ | 68.44 | +76.7↑ | 55.68 | +86.7↑ | 21.58 | +64.1↑ |
| V2XVIT | 86.66 | +18.2↑ | 82.46 | +19.7↑ | 62.41 | +32.3↑ | 57.18 | +47.7↑ | 42.67 | +43.1↑ | 19.87 | +51.1↑ |
| CoBEVT | 86.89 | +18.5↑ | 82.40 | +19.6↑ | 54.23 | +15.0↑ | 73.33 | +89.4↑ | 63.79 | +113.9↑ | 30.64 | +133.0↑ |
| Where2Comm | 81.37 | +11.0↑ | 73.39 | +6.5↑ | 45.18 | -4.2↓ | 46.58 | +20.3↑ | 33.62 | +12.7↑ | 12.37 | -5.9↓ |
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+ "text": "5.2. V2X Cooperative Object Detection Results",
+ "text_level": 1,
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+ "text": "Performance of Cooperative V2X perception. Neighboring roadside devices provide auxiliary information to the vehicle when it passes through the cooperative area. Tab. 2 shows the results of cooperative 3D object detection task, where most of intermediate fusion-based methods outperforms the methods of early fusion and late fusion. Particularly, V2XViT and CoAlign achieve the SOTA performance for different settings. Also, we give the comparison in Fig. 6. In addition, the results for other classes are presented in Tab. 3. Following the approach in [12], we construct a pipeline by integrating the fusion-based object detection method with the AB3DMOT tracker [44] to obtain cooperative tracking results.",
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+ "text": "Ablation of Various Weather. We select 192 and 140 synchronized frames from 35 sensors for validating the performance under rainy and sunny scenes respectively. The sunny scenarios contain multiple traffic conditions like congestion. Tab. 4 demonstrates that intermediate-based fusion achieve the best effect under various weather conditions, especially for the heavy rainy scenes. CoBEVT and V2X-ViT achieve the outstanding performance in most of the evaluation metrics. Benefiting from the sparse attention module, CoBEVT effectively captures both local and global spatial interactions, thereby enhancing fusion performance under feature-sparse conditions such as rainy days.",
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+ "type": "text",
+ "text": "Effect of Latency. We present the detection results under various predefined latency using popular V2X intermediate fusion-based methods as shown in Fig. 7. The accuracy of all methods exhibits a clear downward trend as latency increases. V2XScenes provide cooperative perception data across multiple locations, sensors and large-scale road sections, offering valuable support for optimizing transmission latency algorithms under different challenging scenes.",
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+ "text": "5.3. Large-range Roadside Object Tracking Results",
+ "text_level": 1,
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+ {
+ "type": "text",
+ "text": "The results of large-range roadside cooperative tracking are summarized in Tab. 5 with special autonomous driving object tracking methods. Among them, the ISN approach",
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+ {
+ "type": "table",
+ "img_path": "images/47ad8d3d7f3561d86fd3edb0e1dba1a5571f0811164716f6391e45abdc3103c4.jpg",
+ "table_caption": [
+ "Table 5. Comparison of tracking results under large-range roadside scenario. All the units are $\\%$ where the object tracking metrics are followed in [9]."
+ ],
+ "table_footnote": [],
+ "table_body": "| Method | MOTA ↑ | MOTP ↑ | MT ↑ | ML ↓ |
| SpaRTA [5] | 49.42 | 63.42 | 42.84 | 23.46 |
| SAIKF [16] | 55.47 | 67.61 | 53.53 | 22.94 |
| PCGDA [45] | 49.38 | 55.42 | 44.51 | 20.63 |
| CMSMC [21] | 42.96 | 49.37 | 37.18 | 28.94 |
| InfraDet3D [61] | 40.34 | 54.71 | 40.54 | 26.51 |
| ISN [32] | 53.39 | 72.54 | 60.32 | 14.51 |
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+ "text": "is especially concerned with enhancing target tracking in roadside congestion and occlusion situations, where a vehicle dynamic occlusion model is established based on the improved Siamese network to achieve accurate and continuous tracking effect under the different conditions of occlusion and congestion. From the compared results of Tab. 5, ISN surpasses the comparative methods, achieving $8.0\\%$ and $14.4\\%$ gains in MOTA and MOTP, respectively.",
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diff --git a/2025/V2XScenes_ A Multiple Challenging Traffic Conditions Dataset for Large-Range Vehicle-Infrastructure Collaborative Perception/e74c8f66-2f14-41e8-a64e-91a69d371436_model.json b/2025/V2XScenes_ A Multiple Challenging Traffic Conditions Dataset for Large-Range Vehicle-Infrastructure Collaborative Perception/e74c8f66-2f14-41e8-a64e-91a69d371436_model.json
new file mode 100644
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+ "content": "In this paper, we introduce a multi-condition and large-range V2X dataset, named V2XSences, which mainly focuses on complicated scenarios such as heavy rainy night, congestion and occlusion. We collect the cooperative perception data under a large-range successive road section with a range view of \\(600\\mathrm{m}\\). Particularly, to compare the perception capabilities of different sensors in the challenging scenario, V2XSences consists of 5 sensor categories, including 3 types of LiDAR (Mechanical LiDAR, Solid-State LiDAR, Blind Repair LiDAR), 4D High-Resolution Millimeter wave Radar and Camera. Unlike the previous"
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+ "type": "page_footnote",
+ "bbox": [
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+ "content": "* Corresponding author: Yafei Wang \nThis research was supported by the National Natural Science Foundation of China under Number 52372417 and Number 52072243."
+ },
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+ "type": "page_number",
+ "bbox": [
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+ "content": "28385"
+ }
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+ [
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+ "bbox": [
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+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 1. Demonstration of proposed V2XScenes, which is the first V2X dataset considering complex and challenging traffic conditions under large-range roadside scenarios. Upper shows the large-range road section, where seven roadside cooperative perception layouts are numbered and presented with related camera views, and the fused point cloud by all LiDARs and Radar is illustrated in the middle. Lower shows the multi-condition challenging scenes with complex traffic condition, diverse weather, etc. are collected in V2XScenes."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "datasets without data classification according to different driving scenarios, V2XScenes exclusively collects multi-condition vehicle-infrastructure cooperative data across different times of day, traffic congestion and diverse weather. In summary, our main contributions include:"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We build V2XScenes, the first multiple challenging condition dataset for large-range V2X cooperative perception with driving scenario annotation. Our dataset includes five types of sensors: mechanical LiDAR, solid-state LiDAR, blind repair LiDAR, 4D radar, and cameras."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- We provide large-range sequential 3D bounding boxes and trajectories with unique tracking IDs. The sequential data under complex traffic condition, diverse weather are well-organized with specific scene-descriptive labels."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "- Two comprehensive cooperative benchmarks of 3D object detection and tracking are developed for validating the effectiveness. Experimental results demonstrate the advantages of cooperative perception on challenging scenes."
+ },
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+ "type": "list",
+ "bbox": [
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+ "content": "2. Related Work"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "In this section, we summarize existing autonomous driving datasets under different cooperative modes and highlight the key differences between V2XScenes and others in Tab. 1."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.1. Single View Datasets"
+ },
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+ "type": "text",
+ "bbox": [
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+ "content": "Single view datasets are obtained from individual ego-vehicle or roadside infrastructure. As for the vehicle-side perspective, a number of datasets have been released since 2012 such as KITTI [9], ApolloScape [15], nuScenes [4] and Waymo [36], et al. Among them, KITTI [9] is the first large-scale multi-modal autonomous driving dataset for stereo, object detection and tracking. In comparison, nuScenes consists of six vehicle cameras mounting with a surround view, and equips with data under special scenes, such as night scene. The six surround cameras with overlapping fields of view make nuScenes the most used dataset in bird's-eye-view (BEV) perception recently [33]. On the other hand, roadside sensors can provide data in key areas for autonomous driving [11], especially intersections. Several pioneer roadside perception methods have emerged in recent years like Rope3D [56], A9 [8] and IPS300+ [37]."
+ },
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+ "type": "title",
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+ "angle": 0,
+ "content": "2.2. Vehicle-Infrastructure Datasets"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The objective of the Vehicle-Infrastructure collaboration dataset construction is to explore the beneficial effect of roadside perception for single vehicle automated driving, overcoming the limitations of single-vehicle sensing under"
+ },
+ {
+ "type": "page_number",
+ "bbox": [
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+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 1. Comparison of popular datasets for cooperative perception in autonomous driving. \"C\" and \"L\" represent the camera and LiDAR respectively. \"F\" represents the fisheye camera. \"R\" is denoted as Radar. The related values indicate the number of used sensors."
+ },
+ {
+ "type": "table",
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+ "angle": 0,
+ "content": "| Dataset | Cooperative Dataset Type | Sensors Layouts and View | Ground Truth Labels | Challenging Scenarios |
| Source | Mode | Year | Vehicle view | Roadside view | Annotation range | Tracking IDs for all views | Synchronized frames | Night heavy rain | Occlusion and congestion |
| OPV2V [52] | simulated | V2V | 2022 | 4C+1L | - | 120m | - | 11k | - | - |
| V2X-Sim [23] | simulated | V2X | 2022 | 2C+1L | 4C+1L | 70m | ✓ | 10k | - | ✓ |
| V2X-Set [50] | simulated | V2X | 2022 | 4C+1L | 4C+1L | 120m | - | 11k | - | ✓ |
| DeepAccident [40] | simulated | V2X | 2022 | 2C+1L | 6C+1L | 100m | ✓ | 57k | - | ✓ |
| CARTI [2] | simulated | V2I | 2022 | 1L | 1L | - | - | 11k | - | - |
| CODD [1] | simulated | V2V | 2022 | 2L | - | 100m | - | 13.5k | - | - |
| DOLPHINS [30] | simulated | V2X | 2022 | 1C+1L | 1C+1L | 200m | - | 42.4k | ✓ | - |
| Intersection-A9 [8] | real-world | I2I | 2022 | - | 2C+2L | 70m | - | 1.1k | - | - |
| IPS300+ [37] | real-world | I2I | 2022 | - | 2C+3L | 230m | - | 14k | - | ✓ |
| DAIR-V2X [57] | real-world | V2X | 2022 | 1C+1L | 1C+1L | 280m | - | 464k | - | - |
| V2V4Real [54] | real-world | V2V | 2023 | 4C+2L | - | 200m | ✓ | 20k | - | - |
| V2X-Seq [58] | real-world | V2X | 2023 | 1C+1L | 1C+1L | 280m | ✓ | 15k | - | - |
| HoloVIC [29] | real-world | V2I | 2024 | 2C+2L | 12C+4F+2L | - | ✓ | 100k | - | - |
| TUMTraf-V2X [62] | real-world | V2I | 2024 | 1C+1L | 4C+2L | 200m | ✓ | 2k | - | ✓ |
| Rcooper [12] | real-world | I2I | 2024 | - | 2C+2L | 230m | - | 30K | ✓ | - |
| V2X-Real [47] | real-world | V2X | 2024 | 4C+1L | 2C+1L | 280m | - | 33K | - | - |
| V2XScenes (Ours) | real-world | V2X | 2025 | 6C+3L | 13C+11L+2R | 600m | ✓ | 35k | ✓ | ✓ |
"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "scenarios such as occlusion. DAIR-V2X [57] is the first and one of the foremost cooperative multi-modal datasets, which contains 464k 3D box labels belonging to 10 classes. The V2X-Seq [58] extends selected sequences of the DAIR-V2X dataset with track IDs and is partitioned into a sequential perception dataset (SPD) and a trajectory forecasting dataset. Unlike the most of existing V2X datasets focus on single collaboration mode, V2V4Real [54] collects the data by two connected vehicles which can achieve different types of V2X collaboration modes. Due to the difficulty of collecting traffic data for real-world scenarios, some simulated multi-agent perception datasets included V2X-Sim [23], V2XSet [50] and OPV2V [52], et al. are proposed for data supplementation and scenario customization."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "2.3. Multi-condition Datasets for V2X perception"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Special-scenario data plays a vital role in driving algorithmic improvements. Several cooperative perception datasets, such as V2X-Seq [58] and IPS300+ [37], have included multi-condition data including both daytime and nighttime scenes. Wang et al. [38] propose AdvSim to obtain adversarial scenarios by modifying the vehicle trajectories in a physically guided manner. Zhang et al. [59] present ChatScene which leverages the capabilities of large language model (LLM) to generate safety-critical scenarios within the CARLA simulation environment. In addition, generative world models [19, 31, 43, 46, 60] are also utilized to create challenging virtual driving scenarios. Generation-based methods can identify thousands of semantically safety-critical and challenging scenarios for autonomous driving. However, existing approaches still benefit significantly from real-world scenario data to ensure robustness and reliability."
+ },
+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 2. Sensors layouts of vehicle-side and roadside view. E-N-U and X-Y-Z represent the coordinates under two views. We define the virtual E-N-U coordinate as the global coordinate."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "content": "3. V2XScenes Dataset"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "To investigate the benefits of collaborative perception in challenging multi-condition scenarios, V2XScenes focuses on the acquisition of large-range vehicle-Infrastructure cooperative data under complex traffic environments, such as in bad weather, and provides ground truth of 3D bounding box and trajectory for multi-modal object targets. Especially, V2XScenes is the first one that focuses on the holistic and complete view of both vehicle-side and roadside using camera and LiDAR data. The detailed of perception layouts, calibration and data acquisition at multi-condition scenes are presented in the following."
+ },
+ {
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+ "angle": 0,
+ "content": "3.1. Multi-sensor setup under different view"
+ },
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Base Configuration. V2XScenes covers two intersections and one middle successive road corridor within a range of \\(600\\mathrm{m}\\), including 7 cooperative perception positions. There"
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+ {
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+ },
+ {
+ "type": "image_caption",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "Figure 3. Comparison of different point-based sensors under various weather. The first and second row represent weather of sunny and rainy, respectively. The bounding boxes with red line are the traffic object in point cloud data."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "are total of 13 cameras, 11 LiDARs, and 2 4D millimetre wave Radars in roadside scenes, and the automated vehicle contains 6 cameras and 3 LiDARs. All LiDARs and cameras at the roadside are synchronised via the Precision Time Protocol (PTP) with the time error less than \\(10ms\\), and the automated vehicle uses the same satellite clock source as the roadside configuration to the simultaneous data acquisition. The overall sensor layouts of both vehicle and roadside views are illustrate in Fig. 2."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.869
+ ],
+ "angle": 0,
+ "content": "Roadside Multi-sensor Layouts. Due to the different requirements of view-range for intersections and corridor in the roadside scene, we adopt various configurations for 7 roadside perception positions as shown in Fig. 2. For \\(1^{\\text{st}}\\) to \\(6^{\\text{th}}\\) perception positions, 2 cameras with 2k resolution are opposite installed on the rod and 1 camera is mounted at \\(7^{\\text{th}}\\) position. we apply at least 1 camera and LiDAR for data acquisition. To explore the effect of roadside perception based on different types of LiDARs and Radars, 6 mechanical rotating LiDAR with 128-beams, 2 solid-state LiDAR with 125-beams, 3 bind repair LiDAR with 32-beams and 2 4D millimetre-wave Radar are mounted in close proximity for comparison. Fig. 3 shows the perception results of different roadside LiDAR and 4D Radar. Since weather affects the reflection of LiDAR, the density of valid point on rainy day becomes relatively sparse compared to the sunny day. On the contrary, the point cloud of 4D millimetre wave Radar is not affected by weather and with high robustness."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Vehicle-side Multi-sensor Layouts. Perception learning in the bird's-eye view (BEV) [20, 25, 27, 55] can obtain ro"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "bust feature representations from multi-sensor views. To this end, we deploy 6 cameras on the automated vehicle to achieve a full visual perception, including 4 cameras with a \\(60^{\\circ}\\) field of view at the front and rear, 2 cameras with a \\(120^{\\circ}\\) field of view at the left and right as shown in Fig. 2. In addition, a 128-beams mechanical LiDAR is mounted at the middle top of vehicle, along with 32-beams bind repair LiDAR on the left and right. The vehicle position and attitude information are acquired by on-board IMU and GPS."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.2. Sensor Coordinates and Calibration"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "To allow all sensors collaborate in an uniform coordinates system, we employ the following two parts, i.e., Roadside LiDAR and camera extrinsic calibration and vehicleinfrastructure calibration. The overall calibration process is illustrated in Fig. 4, we define a global coordinate denoted as \\(P_{g} = [X_{g},Y_{g},Z_{g}]^{\\top}\\) based on the East-North-Up (ENU) coordinate system."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Roadside LiDAR&Camera Calibration. We define the LiDAR and camera coordinate as \\( P_{\\ell} = [X_{\\ell}, Y_{\\ell}, Z_{\\ell}]^{\\top} \\) and \\( P_{c} = [X_{c}, Y_{c}, Z_{c}]^{\\top} \\) respectively. Our goal is to obtain the optimal transferring matrix \\( T_{LiDAR2World} \\) and \\( T_{LiDAR2Camera} \\). First, we calculate the intrinsic of camera parameters by using a checkerboard target. Then, we obtain the calibration results based on a automatic calibration method [39] using a customized roadside planar target, where the related global position information in \\( P_{g} \\) is obtained based on the devices with GPS/IMU. During the calculating process, we individually determine the trans"
+ },
+ {
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+ "bbox": [
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+ "content": "28388"
+ }
+ ],
+ [
+ {
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+ "bbox": [
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+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 4. The calibration relationships among the sensors in V2XScenes. The red part represents the 3D object annotation process. The ground truth of 3D bounding boxes are annotated in global coordinates system. To guarantee the quality of the ground truth label, we will return the results to the previous coordinate systems (e.g. camera coordinate system, original point cloud coordinate system) for checking."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "formation matrix \\( T_{\\text{LLA2ENU}} \\) between ENU and Latitude-Longitude-Altitude(LLA). After obtaining the initial estimation, the algorithm of EPnP [18] and Kabsch [34] are used to optimize the final \\( T_{\\text{LiDAR2World}} \\) and \\( T_{\\text{LiDAR2Camera}} \\) for Li-DAR and camera, respectively."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Vehicle-Infrastructure Calibration. We regard the vehicle coordinate system as the onboard GPS/IMU coordinate system, denoted as \\( P_{v} = [X_{v}, Y_{v}, Z_{v}]^{\\mathrm{T}} \\). Based on the information of GPS/IMU, we can transfer the vehicle point cloud to roadside global coordinates by the same transformation matrix of \\( T_{\\text{LLA2ENU}} \\), and obtain the initial vehicle-infrastructure calibration matrix of \\( T_{\\text{Vehicle2World}} \\). In addition, a dense point cloud map covering the entire road section is constructed for pose alignment, and we apply the point-to-point Iterative Closest Point (ICP) algorithm [3] to optimize the \\( T_{\\text{Vehicle2World}} \\) under several iterations."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.09,
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+ ],
+ "angle": 0,
+ "content": "3.3. Registration and Ground Truth Labels"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "V2XScenes contains a total of 332,596 labeled 3D bounding boxes annotated by expert annotators across various object categories, with each scene averaging around \\(10\\mathrm{k}\\) and \\(3\\mathrm{k}\\) 3D bounding boxes from the roadside and vehicle-side views, respectively. Fig. 4 also demonstrates the process and defines coordinates for 3D annotation. Aiming to distinguish the distribution of objects under different views, we independently employ the data annotation of vehicle-side and roadside scenes. To enhance the efficiency and accuracy of the labeling process under two views, we combine the point cloud from 11 roadside LiDARs and 2 Radar for cooperative annotation like [47], and the targets are uniformly labeled within the normalized 3D point cloud."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "For each object, we provide a unified target identity (ID) across the entire large-scale perceptive road section. Following existing works [9, 57], each object is annotated with a 7-dimensional bounding box, including the cen"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ 0.371,
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+ "angle": 0,
+ "content": "ter location \\([x_c, y_c, z_c]\\), dimensions of height \\(h\\), width \\(w\\), length \\(l\\), and heading angle \\(\\varphi\\). We use \\(L_i^{\\mathrm{VEH}}, L_i^{\\mathrm{ROAD}} = \\{x_c, y_c, z_c, h, w, l, \\varphi\\}\\) to denote the annotation of vehicle-side and roadside views respectively. Additionally, eight categories of Car, Motorcycle, Cyclist, Pedestrian, Truck, Bus, Trailer, and Van are divided in the proposed dataset. In particular, we add a special category of autonomous vehicle for quickly determining the cooperative vehicle in the roadside view."
+ },
+ {
+ "type": "title",
+ "bbox": [
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+ "angle": 0,
+ "content": "3.4. Multi-condition Data Selection"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Existing vehicle-infrastructure collaboration datasets lack the definition and classification of sequential data scenarios, especially missing challenging safety scenes with multi-sensors, rendering it hard to demonstrate the advantages and effectiveness by using roadside devices to enhance the autonomous driving perception. Therefore, we constructed V2XScenes and select special data under the scenes such as rainy day, night, congestion, occlusion, etc., ranging from 8 to 51 seconds in duration."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "content": "Based on the mentioned condition elements, the selected sequential data in V2XScenes are manually processed and organized with the specific scene description labels. As described in Fig. 5, we give the description for sequential data as \"Driving to the intersection on a heavy rainy Night\" and \"Facing congestion on an sunny day\". From the figure, it can be seen that collaborative sensing can effectively expand the sensing field of view of the vehicle, especially enhancing the perception ability of automated vehicles in rainy days, occlusion and other challenging scenarios."
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+ "content": "4. Perception Tasks and Metrics"
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+ "angle": 0,
+ "content": "Figure 5. Examples of multi-condition scenes in V2XScenes. The upper orange parts denote the scene-descriptive labels for different scenes. We provide both vehicle-side and roadside views to illustrate the challenging scenes. For each scene, the lower point cloud figures in BEV view demonstrate the single vehicle-side mode (left) and cooperative mode (right), where the vehicle-side and fused roadside point cloud are marked as darkblue and gray respectively."
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+ "type": "text",
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+ "content": "3D object target detection and object tracking. Instead of using the global coordinate systems for perception task, we transform all the roadside sensor data into the ego vehicle-side coordinates for final data fusion based on the previous calibration results. For a sequential data with time length \\( T_{max} \\), the label from vehicle-side and roadside at each time \\( t \\) can be merged into:"
+ },
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+ "type": "equation",
+ "bbox": [
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+ "angle": 0,
+ "content": "\\[\n\\left[ L _ {i} ^ {\\text {F U S E}} \\right] _ {t = 0} ^ {T _ {\\max }} = F \\left(\\left[ L _ {i} ^ {\\text {V E H}} \\right] _ {t = 0} ^ {T _ {\\max }}, \\left[ L _ {i} ^ {\\text {R O A D}} \\right] _ {t = 0} ^ {T _ {\\max }}, \\mu^ {\\text {t h}}\\right) \\tag {1}\n\\]"
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+ "angle": 0,
+ "content": "Where the \\(F\\) denotes the fusion function, and \\(\\mu^{\\mathrm{th}}\\) represents the fusion threshold to filter the repeated objects from the vehicle-side view and roadside view."
+ },
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+ "content": "4.1. V2X Cooperative 3D Object Detection"
+ },
+ {
+ "type": "text",
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+ "angle": 0,
+ "content": "V2X Cooperative 3D Target Detection is aimed to expand and compensate the limited vehicle-side view based on data from road-side multi-view sensors. During the cooperative training process, all sensor devices are unified into the vehicle-side coordinate system. A valid communication distance \\( D_{c} \\) between vehicle and roadside devices is defined to obtain the fused label of \\( [L_i^{\\mathrm{FUSE}}]_{t=0}^{T_{max}} \\) based on (1). Similar as RCooper [12] and KITTI [9], Average Precision (AP) with specific Intersection-over-Union (IoU) is used as the metrics to evaluate the cooperative object detection."
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+ "bbox": [
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+ "angle": 0,
+ "content": "V2XViT [49]"
+ },
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+ "angle": 0,
+ "content": "CoBEVT [48]"
+ },
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+ "bbox": [
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+ "bbox": [
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+ "angle": 0,
+ "content": "AttuFuse [13]"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "F-Cooper [7]"
+ },
+ {
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+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Figure 6. Visualization of the cooperative 3D object detection. These are the comparative illustrations of results in Tab. 2. The fused point cloud is colored by black. The ground truth and predictions are represented by red and blue respectively."
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Table 2. Results of Cooperative 3D object detection. The 0.3, 0.5 and 0.7 represent IoU and the best results are marked by bold."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ "angle": 0,
+ "content": "| Method | AP3D@0.3 | AP3D@0.5 | AP3D@0.7 |
| Late Fusion | 39.97 | 36.21 | 23.72 |
| Early Fusion | 35.59 | 23.75 | 10.31 |
| AttuFuse [52] | 57.11 | 46.69 | 20.88 |
| F-Cooper [7] | 53.48 | 40.45 | 17.27 |
| V2XVIT [49] | 58.10 | 51.11 | 26.48 |
| CoBEVT [48] | 54.50 | 43.48 | 21.92 |
| CoAlign [28] | 58.41 | 50.57 | 28.20 |
| Where2Comm [13] | 52.43 | 42.90 | 17.79 |
"
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+ "bbox": [
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+ "angle": 0,
+ "content": "4.2. Large-range Roadside Tracking"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "The roadside perspective enables robust long-term and large-scale object tracking, offering vehicles high-fidelity, temporally coherent motion representations of surrounding objects. In our benchmark, Multiple Object Tracking Accuracy (MOTA) and Multiple Object Tracking Precision (MOTP) are used as the main metrics for the tracking task. MOTA and MOTP focus on the correctness of the predictive association and position respectively among the entire tracking trajectories. Additionally, to demonstrate the tracking robustness and accuracy under different scenarios, we include the Mostly Tracked Trajectories (MT) and Mostly Lost Trajectories (ML) metrics in the evaluation."
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+ "angle": 0,
+ "content": "5. Experiments"
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+ "angle": 0,
+ "content": "5.1. Benchmarks Setup"
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+ "angle": 0,
+ "content": "Fusion Strategies. Three typical fusion method are applied in the following validation:"
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- Early fusion: directly integrates the raw data of sensors and ground truth before the training."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- Late fusion: merges the final perception results using the position relationship among different sensors."
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+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "- Intermediate fusion: Extracts the encoded feature of the cooperative data to refine the ego agent training."
+ },
+ {
+ "type": "list",
+ "bbox": [
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+ "bbox": [
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+ "angle": 0,
+ "content": "Table 3. Evaluation for other classes. \\(AP_{3D}^{\\dagger}\\) is the mean of \\(AP_{3D}^{0.3\\sim 0.7}\\), i.e., IoU = 0.3, 0.5 and 0.7. All the units are \\(\\%\\)"
+ },
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+ "bbox": [
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+ "angle": 0,
+ "content": "| Methods | Pedestrians | Trucks |
| AP0.33D | AP†3D | MOTA MOTP | AP0.33D | AP†3D | MOTA MOTP |
| Early | 32.42 | 18.17 | 25.30 | 46.98 | 23.78 | 14.83 | 21.37 | 52.04 |
| CoBEVT | 39.86 | 19.86 | 20.84 | 43.60 | 23.15 | 16.47 | 15.89 | 54.24 |
| V2XVIT | 43.74 | 24.16 | 24.48 | 49.08 | 16.69 | 11.11 | 12.69 | 51.92 |
"
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+ "angle": 0,
+ "content": null
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+ {
+ "type": "image",
+ "bbox": [
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+ "angle": 0,
+ "content": null
+ },
+ {
+ "type": "image_caption",
+ "bbox": [
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+ "angle": 0,
+ "content": "Figure 7. V2X perception results under different defined transmission latency. We follow the initial settings used in Tab. 2"
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "We select the state-of-the-art of intermediate fusion methods including AttFuse [52], CoBEVT [48], V2XVIT [49], CoAlign [28], Where2Comm [13] and F-Cooper [7]."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Implementation Details. We captured over twenty distinct scenes, each lasting between 8 and 51 seconds, from both vehicle and infrastructure perspectives with 35 sensors. The V2XScenes sequences were then split into a training set \\((80\\%)\\) and a test set \\((20\\%)\\). All the fusion method are verified based on the 3D backbone of PointPillars [17]. Our code is built based on the open source project of Open-COOD [52] for multi-view collaboration and runs on two RTX A6000 GPUs. We train the perception collaboration for 30 epochs with learning rate of 0.001 based on the Adam optimizer. We set threshold communication distance to \\(100m\\) so as to ensure the vehicle is constantly collaborating with at least three roadside devices."
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+ "type": "page_number",
+ "bbox": [
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+ "content": "28391"
+ }
+ ],
+ [
+ {
+ "type": "table_caption",
+ "bbox": [
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+ ],
+ "angle": 0,
+ "content": "Table 4. Cooperative 3D object detection results under different weather conditions of sunny and rainy. The blue background represents the improvement (\\%) compared to the no fusion method."
+ },
+ {
+ "type": "table",
+ "bbox": [
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+ 0.875,
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+ "angle": 0,
+ "content": "| Method | Car AP3D of Sunny (%) | Car AP3D of Rainy (%) |
| IoU=0.3 | IoU=0.5 | IoU=0.7 | IoU=0.3 | IoU=0.5 | IoU=0.7 |
| No Fusion | 73.30 | - | 68.89 | - | 47.15 | - | 38.72 | - | 29.82 | - | 13.15 | - |
| Late Fusion | 75.33 | +2.8↑ | 72.26 | +4.9↑ | 49.48 | +4.9↑ | 46.27 | +19.5↑ | 31.33 | +5.0↑ | 6.33 | -51.9↓ |
| Early Fusion | 82.36 | +12.4↑ | 77.69 | +12.8↑ | 59.91 | +27.1↑ | 57.14 | +47.6↑ | 44.69 | +49.9↑ | 19.47 | +48.1↑ |
| AttuFuse | 81.65 | +11.4↑ | 74.13 | +7.6↑ | 53.05 | +12.5↑ | 50.62 | +30.7↑ | 35.54 | +19.2↑ | 12.08 | -8.2↓ |
| F-Cooper | 85.58 | +16.7↑ | 79.95 | +16.0↑ | 53.41 | +13.3↑ | 68.44 | +76.7↑ | 55.68 | +86.7↑ | 21.58 | +64.1↑ |
| V2XVIT | 86.66 | +18.2↑ | 82.46 | +19.7↑ | 62.41 | +32.3↑ | 57.18 | +47.7↑ | 42.67 | +43.1↑ | 19.87 | +51.1↑ |
| CoBEVT | 86.89 | +18.5↑ | 82.40 | +19.6↑ | 54.23 | +15.0↑ | 73.33 | +89.4↑ | 63.79 | +113.9↑ | 30.64 | +133.0↑ |
| Where2Comm | 81.37 | +11.0↑ | 73.39 | +6.5↑ | 45.18 | -4.2↓ | 46.58 | +20.3↑ | 33.62 | +12.7↑ | 12.37 | -5.9↓ |
"
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.09,
+ 0.299,
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+ "angle": 0,
+ "content": "5.2. V2X Cooperative Object Detection Results"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.322,
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+ ],
+ "angle": 0,
+ "content": "Performance of Cooperative V2X perception. Neighboring roadside devices provide auxiliary information to the vehicle when it passes through the cooperative area. Tab. 2 shows the results of cooperative 3D object detection task, where most of intermediate fusion-based methods outperforms the methods of early fusion and late fusion. Particularly, V2XViT and CoAlign achieve the SOTA performance for different settings. Also, we give the comparison in Fig. 6. In addition, the results for other classes are presented in Tab. 3. Following the approach in [12], we construct a pipeline by integrating the fusion-based object detection method with the AB3DMOT tracker [44] to obtain cooperative tracking results."
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.089,
+ 0.52,
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+ 0.7
+ ],
+ "angle": 0,
+ "content": "Ablation of Various Weather. We select 192 and 140 synchronized frames from 35 sensors for validating the performance under rainy and sunny scenes respectively. The sunny scenarios contain multiple traffic conditions like congestion. Tab. 4 demonstrates that intermediate-based fusion achieve the best effect under various weather conditions, especially for the heavy rainy scenes. CoBEVT and V2X-ViT achieve the outstanding performance in most of the evaluation metrics. Benefiting from the sparse attention module, CoBEVT effectively captures both local and global spatial interactions, thereby enhancing fusion performance under feature-sparse conditions such as rainy days."
+ },
+ {
+ "type": "text",
+ "bbox": [
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+ "angle": 0,
+ "content": "Effect of Latency. We present the detection results under various predefined latency using popular V2X intermediate fusion-based methods as shown in Fig. 7. The accuracy of all methods exhibits a clear downward trend as latency increases. V2XScenes provide cooperative perception data across multiple locations, sensors and large-scale road sections, offering valuable support for optimizing transmission latency algorithms under different challenging scenes."
+ },
+ {
+ "type": "title",
+ "bbox": [
+ 0.09,
+ 0.833,
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+ 0.85
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+ "angle": 0,
+ "content": "5.3. Large-range Roadside Object Tracking Results"
+ },
+ {
+ "type": "text",
+ "bbox": [
+ 0.09,
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+ 0.902
+ ],
+ "angle": 0,
+ "content": "The results of large-range roadside cooperative tracking are summarized in Tab. 5 with special autonomous driving object tracking methods. Among them, the ISN approach"
+ },
+ {
+ "type": "table_caption",
+ "bbox": [
+ 0.513,
+ 0.299,
+ 0.907,
+ 0.34
+ ],
+ "angle": 0,
+ "content": "Table 5. Comparison of tracking results under large-range roadside scenario. All the units are \\(\\%\\) where the object tracking metrics are followed in [9]."
+ },
+ {
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+ "content": "| Method | MOTA ↑ | MOTP ↑ | MT ↑ | ML ↓ |
| SpaRTA [5] | 49.42 | 63.42 | 42.84 | 23.46 |
| SAIKF [16] | 55.47 | 67.61 | 53.53 | 22.94 |
| PCGDA [45] | 49.38 | 55.42 | 44.51 | 20.63 |
| CMSMC [21] | 42.96 | 49.37 | 37.18 | 28.94 |
| InfraDet3D [61] | 40.34 | 54.71 | 40.54 | 26.51 |
| ISN [32] | 53.39 | 72.54 | 60.32 | 14.51 |
"
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+ "content": "is especially concerned with enhancing target tracking in roadside congestion and occlusion situations, where a vehicle dynamic occlusion model is established based on the improved Siamese network to achieve accurate and continuous tracking effect under the different conditions of occlusion and congestion. From the compared results of Tab. 5, ISN surpasses the comparative methods, achieving \\(8.0\\%\\) and \\(14.4\\%\\) gains in MOTA and MOTP, respectively."
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+ "content": "6. Conclusion"
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+ "angle": 0,
+ "content": "In this paper, we construct a challenging multi-condition dataset for long-range vehicle-infrastructure cooperative perception, named V2XScenes. Specifically, V2XScenes is the first V2X dataset that considers complex and challenging traffic scenarios over an extended road section, including pedestrians randomly crossing, occlusions by large trucks, and driving during heavy rainy nights, among others. The dataset comprises a total of 35k synchronized frames collected from five types of heterogeneous sensors on both the vehicle side and the roadside, including three types of LiDARs with different beam configurations and two high-resolution 4D millimeter-wave Radars deployed at the roadside. The dataset is organized into multiple sequences, each associated with specifically defined challenging scenarios such as adverse weather and complex traffic conditions. We establish 3D detection and tracking benchmarks, and the results demonstrate effectiveness of collaborative perception."
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+# V2XScenes: A Multiple Challenging Traffic Conditions Dataset for Large-Range Vehicle-Infrastructure Collaborative Perception
+
+Bowen Wang $^{1}$ Yafei Wang $^{1*}$ Wei Gong $^{1,2}$ Siheng Chen $^{1,3}$ Genjia Liu $^{1}$ Minhao Xiong $^{1}$ Chin Long Ng $^{1}$
+
+$^{1}$ Shanghai Jiao Tong University $^{2}$ Shanghai Lingang Economic Development (Group) Co., Ltd. $^{3}$ Shanghai AI Laboratory $^{1}$ {98.wangbowen, wyfjlu, weigong2020, sihengc, LGJ1zed, xmh123, clong.ng}@sjtu.edu.cn https://advrc-wangbw.github.io/V2XScenes/
+
+# Abstract
+
+Whether autonomous driving can effectively handle challenging scenarios such as bad weather and complex traffic environments is still in doubt. One of the critical difficulties is that the single-view perception makes it hard to obtain the complementary perceptual information around the multi-condition scenes, such as meeting occlusion and congestion. To investigate the advantages of collaborative perception in high-risky driving scenarios, we construct a multiple challenging conditions dataset for large-range vehicle-infrastructure cooperative perception, called V2XScenes, which includes seven typical multi-modal layouts at successive road sections. Particularly, each selected scene is labeled with a specific condition description, and we provide unique object tracking numbers across the entire road section and sequential frames to ensure consistency. Comprehensive cooperative perception benchmarks of 3D object detection and tracking for large-range roadside scenes are summarized, and the quantitative results based on the state-of-the-art demonstrate the effectiveness of collaborative perception facing challenging scenes. The data and benchmark codes of V2XScenes will be released.
+
+# 1. Introduction
+
+Single-vehicle perception systems often suffer from occlusion and sparse sensor observations, posing significant safety risks, especially under challenging conditions such as driving on rainy nights or in congested traffic with frequent visual occlusions. [41]. To address the issues, vehicle-to-everything (V2X) for cooperative perception is a promising solution [14, 26], which aims to mitigate the limitations of
+
+single-vehicle perception by facilitating effective data exchange among multiple roadside units. Recently, a series of V2X datasets have been released for the development of cooperative perception, such as [47, 54, 57, 58, 62]. Among them, DAIR-V2X [57] and V2X-seq[58] introduce the first vehicle-infrastructure cooperative perception and trajectories prediction datasets based on the real-world data. V2X-Real[47] proposes the first cooperative perception dataset that can both support Vehicle-to-Infrastructure cooperation or Vehicle-to-Vehicle cooperation. The existing solid works truly make great advancements in V2X technologies.
+
+However, the advantages of cooperative perception in challenging scenarios such as adverse weather remain difficult to validate due to the scarcity of real-world V2X perception data. Although some works summarize the challenging V2X driving maneuvers of traffic violations, overtaking, and U-turns [62], the cooperative perception range and sensor modalities are still remain development. Due to the uncertainty of traffic dynamics and weather condition in the real-world, it is a tough task to collect the cooperative perception data under complicated scenarios. Some researchers use the simulators such as Carla [23, 24, 40, 51, 53] and generative world models [10, 22, 42] to construct challenging driving scenarios. Nevertheless, the model trained with simulated data introduced a significant domain gap to real-world scenarios.
+
+In this paper, we introduce a multi-condition and large-range V2X dataset, named V2XSences, which mainly focuses on complicated scenarios such as heavy rainy night, congestion and occlusion. We collect the cooperative perception data under a large-range successive road section with a range view of $600\mathrm{m}$ . Particularly, to compare the perception capabilities of different sensors in the challenging scenario, V2XSences consists of 5 sensor categories, including 3 types of LiDAR (Mechanical LiDAR, Solid-State LiDAR, Blind Repair LiDAR), 4D High-Resolution Millimeter wave Radar and Camera. Unlike the previous
+
+
+Figure 1. Demonstration of proposed V2XScenes, which is the first V2X dataset considering complex and challenging traffic conditions under large-range roadside scenarios. Upper shows the large-range road section, where seven roadside cooperative perception layouts are numbered and presented with related camera views, and the fused point cloud by all LiDARs and Radar is illustrated in the middle. Lower shows the multi-condition challenging scenes with complex traffic condition, diverse weather, etc. are collected in V2XScenes.
+
+datasets without data classification according to different driving scenarios, V2XScenes exclusively collects multi-condition vehicle-infrastructure cooperative data across different times of day, traffic congestion and diverse weather. In summary, our main contributions include:
+
+- We build V2XScenes, the first multiple challenging condition dataset for large-range V2X cooperative perception with driving scenario annotation. Our dataset includes five types of sensors: mechanical LiDAR, solid-state LiDAR, blind repair LiDAR, 4D radar, and cameras.
+- We provide large-range sequential 3D bounding boxes and trajectories with unique tracking IDs. The sequential data under complex traffic condition, diverse weather are well-organized with specific scene-descriptive labels.
+- Two comprehensive cooperative benchmarks of 3D object detection and tracking are developed for validating the effectiveness. Experimental results demonstrate the advantages of cooperative perception on challenging scenes.
+
+# 2. Related Work
+
+In this section, we summarize existing autonomous driving datasets under different cooperative modes and highlight the key differences between V2XScenes and others in Tab. 1.
+
+# 2.1. Single View Datasets
+
+Single view datasets are obtained from individual ego-vehicle or roadside infrastructure. As for the vehicle-side perspective, a number of datasets have been released since 2012 such as KITTI [9], ApolloScape [15], nuScenes [4] and Waymo [36], et al. Among them, KITTI [9] is the first large-scale multi-modal autonomous driving dataset for stereo, object detection and tracking. In comparison, nuScenes consists of six vehicle cameras mounting with a surround view, and equips with data under special scenes, such as night scene. The six surround cameras with overlapping fields of view make nuScenes the most used dataset in bird's-eye-view (BEV) perception recently [33]. On the other hand, roadside sensors can provide data in key areas for autonomous driving [11], especially intersections. Several pioneer roadside perception methods have emerged in recent years like Rope3D [56], A9 [8] and IPS300+ [37].
+
+# 2.2. Vehicle-Infrastructure Datasets
+
+The objective of the Vehicle-Infrastructure collaboration dataset construction is to explore the beneficial effect of roadside perception for single vehicle automated driving, overcoming the limitations of single-vehicle sensing under
+
+Table 1. Comparison of popular datasets for cooperative perception in autonomous driving. "C" and "L" represent the camera and LiDAR respectively. "F" represents the fisheye camera. "R" is denoted as Radar. The related values indicate the number of used sensors.
+
+| Dataset | Cooperative Dataset Type | Sensors Layouts and View | Ground Truth Labels | Challenging Scenarios |
| Source | Mode | Year | Vehicle view | Roadside view | Annotation range | Tracking IDs for all views | Synchronized frames | Night heavy rain | Occlusion and congestion |
| OPV2V [52] | simulated | V2V | 2022 | 4C+1L | - | 120m | - | 11k | - | - |
| V2X-Sim [23] | simulated | V2X | 2022 | 2C+1L | 4C+1L | 70m | ✓ | 10k | - | ✓ |
| V2X-Set [50] | simulated | V2X | 2022 | 4C+1L | 4C+1L | 120m | - | 11k | - | ✓ |
| DeepAccident [40] | simulated | V2X | 2022 | 2C+1L | 6C+1L | 100m | ✓ | 57k | - | ✓ |
| CARTI [2] | simulated | V2I | 2022 | 1L | 1L | - | - | 11k | - | - |
| CODD [1] | simulated | V2V | 2022 | 2L | - | 100m | - | 13.5k | - | - |
| DOLPHINS [30] | simulated | V2X | 2022 | 1C+1L | 1C+1L | 200m | - | 42.4k | ✓ | - |
| Intersection-A9 [8] | real-world | I2I | 2022 | - | 2C+2L | 70m | - | 1.1k | - | - |
| IPS300+ [37] | real-world | I2I | 2022 | - | 2C+3L | 230m | - | 14k | - | ✓ |
| DAIR-V2X [57] | real-world | V2X | 2022 | 1C+1L | 1C+1L | 280m | - | 464k | - | - |
| V2V4Real [54] | real-world | V2V | 2023 | 4C+2L | - | 200m | ✓ | 20k | - | - |
| V2X-Seq [58] | real-world | V2X | 2023 | 1C+1L | 1C+1L | 280m | ✓ | 15k | - | - |
| HoloVIC [29] | real-world | V2I | 2024 | 2C+2L | 12C+4F+2L | - | ✓ | 100k | - | - |
| TUMTraf-V2X [62] | real-world | V2I | 2024 | 1C+1L | 4C+2L | 200m | ✓ | 2k | - | ✓ |
| Rcooper [12] | real-world | I2I | 2024 | - | 2C+2L | 230m | - | 30K | ✓ | - |
| V2X-Real [47] | real-world | V2X | 2024 | 4C+1L | 2C+1L | 280m | - | 33K | - | - |
| V2XScenes (Ours) | real-world | V2X | 2025 | 6C+3L | 13C+11L+2R | 600m | ✓ | 35k | ✓ | ✓ |
+
+scenarios such as occlusion. DAIR-V2X [57] is the first and one of the foremost cooperative multi-modal datasets, which contains 464k 3D box labels belonging to 10 classes. The V2X-Seq [58] extends selected sequences of the DAIR-V2X dataset with track IDs and is partitioned into a sequential perception dataset (SPD) and a trajectory forecasting dataset. Unlike the most of existing V2X datasets focus on single collaboration mode, V2V4Real [54] collects the data by two connected vehicles which can achieve different types of V2X collaboration modes. Due to the difficulty of collecting traffic data for real-world scenarios, some simulated multi-agent perception datasets included V2X-Sim [23], V2XSet [50] and OPV2V [52], et al. are proposed for data supplementation and scenario customization.
+
+# 2.3. Multi-condition Datasets for V2X perception
+
+Special-scenario data plays a vital role in driving algorithmic improvements. Several cooperative perception datasets, such as V2X-Seq [58] and IPS300+ [37], have included multi-condition data including both daytime and nighttime scenes. Wang et al. [38] propose AdvSim to obtain adversarial scenarios by modifying the vehicle trajectories in a physically guided manner. Zhang et al. [59] present ChatScene which leverages the capabilities of large language model (LLM) to generate safety-critical scenarios within the CARLA simulation environment. In addition, generative world models [19, 31, 43, 46, 60] are also utilized to create challenging virtual driving scenarios. Generation-based methods can identify thousands of semantically safety-critical and challenging scenarios for autonomous driving. However, existing approaches still benefit significantly from real-world scenario data to ensure robustness and reliability.
+
+
+Figure 2. Sensors layouts of vehicle-side and roadside view. E-N-U and X-Y-Z represent the coordinates under two views. We define the virtual E-N-U coordinate as the global coordinate.
+
+# 3. V2XScenes Dataset
+
+To investigate the benefits of collaborative perception in challenging multi-condition scenarios, V2XScenes focuses on the acquisition of large-range vehicle-Infrastructure cooperative data under complex traffic environments, such as in bad weather, and provides ground truth of 3D bounding box and trajectory for multi-modal object targets. Especially, V2XScenes is the first one that focuses on the holistic and complete view of both vehicle-side and roadside using camera and LiDAR data. The detailed of perception layouts, calibration and data acquisition at multi-condition scenes are presented in the following.
+
+# 3.1. Multi-sensor setup under different view
+
+Base Configuration. V2XScenes covers two intersections and one middle successive road corridor within a range of $600\mathrm{m}$ , including 7 cooperative perception positions. There
+
+
+
+
+
+
+
+
+
+
+Figure 3. Comparison of different point-based sensors under various weather. The first and second row represent weather of sunny and rainy, respectively. The bounding boxes with red line are the traffic object in point cloud data.
+
+
+
+
+
+
+
+are total of 13 cameras, 11 LiDARs, and 2 4D millimetre wave Radars in roadside scenes, and the automated vehicle contains 6 cameras and 3 LiDARs. All LiDARs and cameras at the roadside are synchronised via the Precision Time Protocol (PTP) with the time error less than $10ms$ , and the automated vehicle uses the same satellite clock source as the roadside configuration to the simultaneous data acquisition. The overall sensor layouts of both vehicle and roadside views are illustrate in Fig. 2.
+
+Roadside Multi-sensor Layouts. Due to the different requirements of view-range for intersections and corridor in the roadside scene, we adopt various configurations for 7 roadside perception positions as shown in Fig. 2. For $1^{\text{st}}$ to $6^{\text{th}}$ perception positions, 2 cameras with 2k resolution are opposite installed on the rod and 1 camera is mounted at $7^{\text{th}}$ position. we apply at least 1 camera and LiDAR for data acquisition. To explore the effect of roadside perception based on different types of LiDARs and Radars, 6 mechanical rotating LiDAR with 128-beams, 2 solid-state LiDAR with 125-beams, 3 bind repair LiDAR with 32-beams and 2 4D millimetre-wave Radar are mounted in close proximity for comparison. Fig. 3 shows the perception results of different roadside LiDAR and 4D Radar. Since weather affects the reflection of LiDAR, the density of valid point on rainy day becomes relatively sparse compared to the sunny day. On the contrary, the point cloud of 4D millimetre wave Radar is not affected by weather and with high robustness.
+
+Vehicle-side Multi-sensor Layouts. Perception learning in the bird's-eye view (BEV) [20, 25, 27, 55] can obtain ro
+
+bust feature representations from multi-sensor views. To this end, we deploy 6 cameras on the automated vehicle to achieve a full visual perception, including 4 cameras with a $60^{\circ}$ field of view at the front and rear, 2 cameras with a $120^{\circ}$ field of view at the left and right as shown in Fig. 2. In addition, a 128-beams mechanical LiDAR is mounted at the middle top of vehicle, along with 32-beams bind repair LiDAR on the left and right. The vehicle position and attitude information are acquired by on-board IMU and GPS.
+
+# 3.2. Sensor Coordinates and Calibration
+
+To allow all sensors collaborate in an uniform coordinates system, we employ the following two parts, i.e., Roadside LiDAR and camera extrinsic calibration and vehicleinfrastructure calibration. The overall calibration process is illustrated in Fig. 4, we define a global coordinate denoted as $P_{g} = [X_{g},Y_{g},Z_{g}]^{\top}$ based on the East-North-Up (ENU) coordinate system.
+
+Roadside LiDAR&Camera Calibration. We define the LiDAR and camera coordinate as $P_{\ell} = [X_{\ell}, Y_{\ell}, Z_{\ell}]^{\top}$ and $P_{c} = [X_{c}, Y_{c}, Z_{c}]^{\top}$ respectively. Our goal is to obtain the optimal transferring matrix $T_{LiDAR2World}$ and $T_{LiDAR2Camera}$ . First, we calculate the intrinsic of camera parameters by using a checkerboard target. Then, we obtain the calibration results based on a automatic calibration method [39] using a customized roadside planar target, where the related global position information in $P_{g}$ is obtained based on the devices with GPS/IMU. During the calculating process, we individually determine the trans
+
+
+Figure 4. The calibration relationships among the sensors in V2XScenes. The red part represents the 3D object annotation process. The ground truth of 3D bounding boxes are annotated in global coordinates system. To guarantee the quality of the ground truth label, we will return the results to the previous coordinate systems (e.g. camera coordinate system, original point cloud coordinate system) for checking.
+
+formation matrix $T_{\text{LLA2ENU}}$ between ENU and Latitude-Longitude-Altitude(LLA). After obtaining the initial estimation, the algorithm of EPnP [18] and Kabsch [34] are used to optimize the final $T_{\text{LiDAR2World}}$ and $T_{\text{LiDAR2Camera}}$ for Li-DAR and camera, respectively.
+
+Vehicle-Infrastructure Calibration. We regard the vehicle coordinate system as the onboard GPS/IMU coordinate system, denoted as $P_{v} = [X_{v}, Y_{v}, Z_{v}]^{\mathrm{T}}$ . Based on the information of GPS/IMU, we can transfer the vehicle point cloud to roadside global coordinates by the same transformation matrix of $T_{\text{LLA2ENU}}$ , and obtain the initial vehicle-infrastructure calibration matrix of $T_{\text{Vehicle2World}}$ . In addition, a dense point cloud map covering the entire road section is constructed for pose alignment, and we apply the point-to-point Iterative Closest Point (ICP) algorithm [3] to optimize the $T_{\text{Vehicle2World}}$ under several iterations.
+
+# 3.3. Registration and Ground Truth Labels
+
+V2XScenes contains a total of 332,596 labeled 3D bounding boxes annotated by expert annotators across various object categories, with each scene averaging around $10\mathrm{k}$ and $3\mathrm{k}$ 3D bounding boxes from the roadside and vehicle-side views, respectively. Fig. 4 also demonstrates the process and defines coordinates for 3D annotation. Aiming to distinguish the distribution of objects under different views, we independently employ the data annotation of vehicle-side and roadside scenes. To enhance the efficiency and accuracy of the labeling process under two views, we combine the point cloud from 11 roadside LiDARs and 2 Radar for cooperative annotation like [47], and the targets are uniformly labeled within the normalized 3D point cloud.
+
+For each object, we provide a unified target identity (ID) across the entire large-scale perceptive road section. Following existing works [9, 57], each object is annotated with a 7-dimensional bounding box, including the cen
+
+ter location $[x_c, y_c, z_c]$ , dimensions of height $h$ , width $w$ , length $l$ , and heading angle $\varphi$ . We use $L_i^{\mathrm{VEH}}, L_i^{\mathrm{ROAD}} = \{x_c, y_c, z_c, h, w, l, \varphi\}$ to denote the annotation of vehicle-side and roadside views respectively. Additionally, eight categories of Car, Motorcycle, Cyclist, Pedestrian, Truck, Bus, Trailer, and Van are divided in the proposed dataset. In particular, we add a special category of autonomous vehicle for quickly determining the cooperative vehicle in the roadside view.
+
+# 3.4. Multi-condition Data Selection
+
+Existing vehicle-infrastructure collaboration datasets lack the definition and classification of sequential data scenarios, especially missing challenging safety scenes with multi-sensors, rendering it hard to demonstrate the advantages and effectiveness by using roadside devices to enhance the autonomous driving perception. Therefore, we constructed V2XScenes and select special data under the scenes such as rainy day, night, congestion, occlusion, etc., ranging from 8 to 51 seconds in duration.
+
+Based on the mentioned condition elements, the selected sequential data in V2XScenes are manually processed and organized with the specific scene description labels. As described in Fig. 5, we give the description for sequential data as "Driving to the intersection on a heavy rainy Night" and "Facing congestion on an sunny day". From the figure, it can be seen that collaborative sensing can effectively expand the sensing field of view of the vehicle, especially enhancing the perception ability of automated vehicles in rainy days, occlusion and other challenging scenarios.
+
+# 4. Perception Tasks and Metrics
+
+In this section, two main cooperative perception tasks will be introduced, namely vehicle-infrastructure cooperative
+
+
+
+
+Driving to the intersection on a heavy rainy Night
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Facing occlusion on a cloudy rainy day
+
+
+
+
+Facing congestion on an sunny day
+
+
+
+
+Motorbike cut-through during vehicle U-turn
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+Figure 5. Examples of multi-condition scenes in V2XScenes. The upper orange parts denote the scene-descriptive labels for different scenes. We provide both vehicle-side and roadside views to illustrate the challenging scenes. For each scene, the lower point cloud figures in BEV view demonstrate the single vehicle-side mode (left) and cooperative mode (right), where the vehicle-side and fused roadside point cloud are marked as darkblue and gray respectively.
+
+
+
+
+
+
+
+3D object target detection and object tracking. Instead of using the global coordinate systems for perception task, we transform all the roadside sensor data into the ego vehicle-side coordinates for final data fusion based on the previous calibration results. For a sequential data with time length $T_{max}$ , the label from vehicle-side and roadside at each time $t$ can be merged into:
+
+$$
+\left[ L _ {i} ^ {\text {F U S E}} \right] _ {t = 0} ^ {T _ {\max }} = F \left(\left[ L _ {i} ^ {\text {V E H}} \right] _ {t = 0} ^ {T _ {\max }}, \left[ L _ {i} ^ {\text {R O A D}} \right] _ {t = 0} ^ {T _ {\max }}, \mu^ {\text {t h}}\right) \tag {1}
+$$
+
+Where the $F$ denotes the fusion function, and $\mu^{\mathrm{th}}$ represents the fusion threshold to filter the repeated objects from the vehicle-side view and roadside view.
+
+# 4.1. V2X Cooperative 3D Object Detection
+
+V2X Cooperative 3D Target Detection is aimed to expand and compensate the limited vehicle-side view based on data from road-side multi-view sensors. During the cooperative training process, all sensor devices are unified into the vehicle-side coordinate system. A valid communication distance $D_{c}$ between vehicle and roadside devices is defined to obtain the fused label of $[L_i^{\mathrm{FUSE}}]_{t=0}^{T_{max}}$ based on (1). Similar as RCooper [12] and KITTI [9], Average Precision (AP) with specific Intersection-over-Union (IoU) is used as the metrics to evaluate the cooperative object detection.
+
+
+V2XViT [49]
+
+
+CoBEVT [48]
+
+
+AttuFuse [13]
+Figure 6. Visualization of the cooperative 3D object detection. These are the comparative illustrations of results in Tab. 2. The fused point cloud is colored by black. The ground truth and predictions are represented by red and blue respectively.
+
+
+F-Cooper [7]
+
+Table 2. Results of Cooperative 3D object detection. The 0.3, 0.5 and 0.7 represent IoU and the best results are marked by bold.
+
+| Method | AP3D@0.3 | AP3D@0.5 | AP3D@0.7 |
| Late Fusion | 39.97 | 36.21 | 23.72 |
| Early Fusion | 35.59 | 23.75 | 10.31 |
| AttuFuse [52] | 57.11 | 46.69 | 20.88 |
| F-Cooper [7] | 53.48 | 40.45 | 17.27 |
| V2XVIT [49] | 58.10 | 51.11 | 26.48 |
| CoBEVT [48] | 54.50 | 43.48 | 21.92 |
| CoAlign [28] | 58.41 | 50.57 | 28.20 |
| Where2Comm [13] | 52.43 | 42.90 | 17.79 |
+
+# 4.2. Large-range Roadside Tracking
+
+The roadside perspective enables robust long-term and large-scale object tracking, offering vehicles high-fidelity, temporally coherent motion representations of surrounding objects. In our benchmark, Multiple Object Tracking Accuracy (MOTA) and Multiple Object Tracking Precision (MOTP) are used as the main metrics for the tracking task. MOTA and MOTP focus on the correctness of the predictive association and position respectively among the entire tracking trajectories. Additionally, to demonstrate the tracking robustness and accuracy under different scenarios, we include the Mostly Tracked Trajectories (MT) and Mostly Lost Trajectories (ML) metrics in the evaluation.
+
+# 5. Experiments
+
+# 5.1. Benchmarks Setup
+
+Fusion Strategies. Three typical fusion method are applied in the following validation:
+
+- Early fusion: directly integrates the raw data of sensors and ground truth before the training.
+- Late fusion: merges the final perception results using the position relationship among different sensors.
+- Intermediate fusion: Extracts the encoded feature of the cooperative data to refine the ego agent training.
+
+Table 3. Evaluation for other classes. $AP_{3D}^{\dagger}$ is the mean of $AP_{3D}^{0.3\sim 0.7}$ , i.e., IoU = 0.3, 0.5 and 0.7. All the units are $\%$
+
+| Methods | Pedestrians | Trucks |
| AP0.33D | AP†3D | MOTA MOTP | AP0.33D | AP†3D | MOTA MOTP |
| Early | 32.42 | 18.17 | 25.30 | 46.98 | 23.78 | 14.83 | 21.37 | 52.04 |
| CoBEVT | 39.86 | 19.86 | 20.84 | 43.60 | 23.15 | 16.47 | 15.89 | 54.24 |
| V2XVIT | 43.74 | 24.16 | 24.48 | 49.08 | 16.69 | 11.11 | 12.69 | 51.92 |
+
+
+Figure 7. V2X perception results under different defined transmission latency. We follow the initial settings used in Tab. 2
+
+
+
+We select the state-of-the-art of intermediate fusion methods including AttFuse [52], CoBEVT [48], V2XVIT [49], CoAlign [28], Where2Comm [13] and F-Cooper [7].
+
+Implementation Details. We captured over twenty distinct scenes, each lasting between 8 and 51 seconds, from both vehicle and infrastructure perspectives with 35 sensors. The V2XScenes sequences were then split into a training set $(80\%)$ and a test set $(20\%)$ . All the fusion method are verified based on the 3D backbone of PointPillars [17]. Our code is built based on the open source project of Open-COOD [52] for multi-view collaboration and runs on two RTX A6000 GPUs. We train the perception collaboration for 30 epochs with learning rate of 0.001 based on the Adam optimizer. We set threshold communication distance to $100m$ so as to ensure the vehicle is constantly collaborating with at least three roadside devices.
+
+Table 4. Cooperative 3D object detection results under different weather conditions of sunny and rainy. The blue background represents the improvement (\%) compared to the no fusion method.
+
+| Method | Car AP3D of Sunny (%) | Car AP3D of Rainy (%) |
| IoU=0.3 | IoU=0.5 | IoU=0.7 | IoU=0.3 | IoU=0.5 | IoU=0.7 |
| No Fusion | 73.30 | - | 68.89 | - | 47.15 | - | 38.72 | - | 29.82 | - | 13.15 | - |
| Late Fusion | 75.33 | +2.8↑ | 72.26 | +4.9↑ | 49.48 | +4.9↑ | 46.27 | +19.5↑ | 31.33 | +5.0↑ | 6.33 | -51.9↓ |
| Early Fusion | 82.36 | +12.4↑ | 77.69 | +12.8↑ | 59.91 | +27.1↑ | 57.14 | +47.6↑ | 44.69 | +49.9↑ | 19.47 | +48.1↑ |
| AttuFuse | 81.65 | +11.4↑ | 74.13 | +7.6↑ | 53.05 | +12.5↑ | 50.62 | +30.7↑ | 35.54 | +19.2↑ | 12.08 | -8.2↓ |
| F-Cooper | 85.58 | +16.7↑ | 79.95 | +16.0↑ | 53.41 | +13.3↑ | 68.44 | +76.7↑ | 55.68 | +86.7↑ | 21.58 | +64.1↑ |
| V2XVIT | 86.66 | +18.2↑ | 82.46 | +19.7↑ | 62.41 | +32.3↑ | 57.18 | +47.7↑ | 42.67 | +43.1↑ | 19.87 | +51.1↑ |
| CoBEVT | 86.89 | +18.5↑ | 82.40 | +19.6↑ | 54.23 | +15.0↑ | 73.33 | +89.4↑ | 63.79 | +113.9↑ | 30.64 | +133.0↑ |
| Where2Comm | 81.37 | +11.0↑ | 73.39 | +6.5↑ | 45.18 | -4.2↓ | 46.58 | +20.3↑ | 33.62 | +12.7↑ | 12.37 | -5.9↓ |
+
+# 5.2. V2X Cooperative Object Detection Results
+
+Performance of Cooperative V2X perception. Neighboring roadside devices provide auxiliary information to the vehicle when it passes through the cooperative area. Tab. 2 shows the results of cooperative 3D object detection task, where most of intermediate fusion-based methods outperforms the methods of early fusion and late fusion. Particularly, V2XViT and CoAlign achieve the SOTA performance for different settings. Also, we give the comparison in Fig. 6. In addition, the results for other classes are presented in Tab. 3. Following the approach in [12], we construct a pipeline by integrating the fusion-based object detection method with the AB3DMOT tracker [44] to obtain cooperative tracking results.
+
+Ablation of Various Weather. We select 192 and 140 synchronized frames from 35 sensors for validating the performance under rainy and sunny scenes respectively. The sunny scenarios contain multiple traffic conditions like congestion. Tab. 4 demonstrates that intermediate-based fusion achieve the best effect under various weather conditions, especially for the heavy rainy scenes. CoBEVT and V2X-ViT achieve the outstanding performance in most of the evaluation metrics. Benefiting from the sparse attention module, CoBEVT effectively captures both local and global spatial interactions, thereby enhancing fusion performance under feature-sparse conditions such as rainy days.
+
+Effect of Latency. We present the detection results under various predefined latency using popular V2X intermediate fusion-based methods as shown in Fig. 7. The accuracy of all methods exhibits a clear downward trend as latency increases. V2XScenes provide cooperative perception data across multiple locations, sensors and large-scale road sections, offering valuable support for optimizing transmission latency algorithms under different challenging scenes.
+
+# 5.3. Large-range Roadside Object Tracking Results
+
+The results of large-range roadside cooperative tracking are summarized in Tab. 5 with special autonomous driving object tracking methods. Among them, the ISN approach
+
+Table 5. Comparison of tracking results under large-range roadside scenario. All the units are $\%$ where the object tracking metrics are followed in [9].
+
+| Method | MOTA ↑ | MOTP ↑ | MT ↑ | ML ↓ |
| SpaRTA [5] | 49.42 | 63.42 | 42.84 | 23.46 |
| SAIKF [16] | 55.47 | 67.61 | 53.53 | 22.94 |
| PCGDA [45] | 49.38 | 55.42 | 44.51 | 20.63 |
| CMSMC [21] | 42.96 | 49.37 | 37.18 | 28.94 |
| InfraDet3D [61] | 40.34 | 54.71 | 40.54 | 26.51 |
| ISN [32] | 53.39 | 72.54 | 60.32 | 14.51 |
+
+is especially concerned with enhancing target tracking in roadside congestion and occlusion situations, where a vehicle dynamic occlusion model is established based on the improved Siamese network to achieve accurate and continuous tracking effect under the different conditions of occlusion and congestion. From the compared results of Tab. 5, ISN surpasses the comparative methods, achieving $8.0\%$ and $14.4\%$ gains in MOTA and MOTP, respectively.
+
+# 6. Conclusion
+
+In this paper, we construct a challenging multi-condition dataset for long-range vehicle-infrastructure cooperative perception, named V2XScenes. Specifically, V2XScenes is the first V2X dataset that considers complex and challenging traffic scenarios over an extended road section, including pedestrians randomly crossing, occlusions by large trucks, and driving during heavy rainy nights, among others. The dataset comprises a total of 35k synchronized frames collected from five types of heterogeneous sensors on both the vehicle side and the roadside, including three types of LiDARs with different beam configurations and two high-resolution 4D millimeter-wave Radars deployed at the roadside. The dataset is organized into multiple sequences, each associated with specifically defined challenging scenarios such as adverse weather and complex traffic conditions. We establish 3D detection and tracking benchmarks, and the results demonstrate effectiveness of collaborative perception.
+
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+[54] Runsheng Xu, Xin Xia, Jinlong Li, Hanzhao Li, Shuo Zhang, Zhengzhong Tu, Zonglin Meng, Hao Xiang, Xiaoyu Dong, Rui Song, et al. V2v4real: A real-world large-scale dataset for vehicle-to-vehicle cooperative perception. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13712–13722, 2023. 1, 3
+[55] Chenyu Yang, Yuntao Chen, Hao Tian, Chenxin Tao, Xizhou Zhu, Zhaoxiang Zhang, Gao Huang, Hongyang Li, Yu Qiao, Lewei Lu, et al. Bevformer v2: Adapting modern image backbones to bird's-eye-view recognition via perspective supervision. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17830-17839, 2023. 4
+[56] Xiaoqing Ye, Mao Shu, Hanyu Li, Yifeng Shi, Yingying Li, Guangjie Wang, Xiao Tan, and Errui Ding. Rope3d: The roadside perception dataset for autonomous driving and monocular 3d object detection task. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 21341-21350, 2022. 2
+[57] Haibao Yu, Yizhen Luo, Mao Shu, Yiyi Huo, Zebang Yang, Yifeng Shi, Zhenglong Guo, Hanyu Li, Xing Hu, Jirui Yuan, et al. Dair-v2x: A large-scale dataset for vehicleinfrastructure cooperative 3d object detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 21361-21370, 2022. 1, 3, 5
+[58] Haibao Yu, Wenxian Yang, Hongzhi Ruan, Zhenwei Yang, Yingjuan Tang, Xu Gao, Xin Hao, Yifeng Shi, Yifeng Pan, Ning Sun, et al. V2x-seq: A large-scale sequential dataset for vehicle-infrastructure cooperative perception and forecasting. In Proceedings of the IEEE/CVF Conference on Com
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+puter Vision and Pattern Recognition, pages 5486-5495, 2023.1,3
+[59] Jiawei Zhang, Chejian Xu, and Bo Li. Chatscene: Knowledge-enabled safety-critical scenario generation for autonomous vehicles. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15459-15469, 2024. 3
+[60] Guosheng Zhao, Xiaofeng Wang, Zheng Zhu, Xinze Chen, Guan Huang, Xiaoyi Bao, and Xingang Wang. Drivedreamer-2: Llm-enhanced world models for diverse driving video generation. arXiv preprint arXiv:2403.06845, 2024.3
+[61] Walter Zimmer, Joseph Birkner, Marcel Brucker, Huu Tung Nguyen, Stefan Petrovski, Bohan Wang, and Alois C. Knoll. Infradet3d: Multi-modal 3d object detection based on roadside infrastructure camera and lidar sensors. In 2023 IEEE Intelligent Vehicles Symposium (IV), pages 1-8, 2023. 8
+[62] Walter Zimmer, Gerhard Arya Wardana, Suren Sritharan, Xingcheng Zhou, Rui Song, and Alois C Knoll. Tumtraf v2x cooperative perception dataset. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 22668-22677, 2024. 1, 3
\ No newline at end of file
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| Source | Mode | Year | Vehicle view | Roadside view | Annotation range | Tracking IDs for all views | Synchronized frames | Night heavy rain | Occlusion and congestion |
| OPV2V [52] | simulated | V2V | 2022 | 4C+1L | - | 120m | - | 11k | - | - |
| V2X-Sim [23] | simulated | V2X | 2022 | 2C+1L | 4C+1L | 70m | ✓ | 10k | - | ✓ |
| V2X-Set [50] | simulated | V2X | 2022 | 4C+1L | 4C+1L | 120m | - | 11k | - | ✓ |
| DeepAccident [40] | simulated | V2X | 2022 | 2C+1L | 6C+1L | 100m | ✓ | 57k | - | ✓ |
| CARTI [2] | simulated | V2I | 2022 | 1L | 1L | - | - | 11k | - | - |
| CODD [1] | simulated | V2V | 2022 | 2L | - | 100m | - | 13.5k | - | - |
| DOLPHINS [30] | simulated | V2X | 2022 | 1C+1L | 1C+1L | 200m | - | 42.4k | ✓ | - |
| Intersection-A9 [8] | real-world | I2I | 2022 | - | 2C+2L | 70m | - | 1.1k | - | - |
| IPS300+ [37] | real-world | I2I | 2022 | - | 2C+3L | 230m | - | 14k | - | ✓ |
| DAIR-V2X [57] | real-world | V2X | 2022 | 1C+1L | 1C+1L | 280m | - | 464k | - | - |
| V2V4Real [54] | real-world | V2V | 2023 | 4C+2L | - | 200m | ✓ | 20k | - | - |
| V2X-Seq [58] | real-world | V2X | 2023 | 1C+1L | 1C+1L | 280m | ✓ | 15k | - | - |
| HoloVIC [29] | real-world | V2I | 2024 | 2C+2L | 12C+4F+2L | - | ✓ | 100k | - | - |
| TUMTraf-V2X [62] | real-world | V2I | 2024 | 1C+1L | 4C+2L | 200m | ✓ | 2k | - | ✓ |
| Rcooper [12] | real-world | I2I | 2024 | - | 2C+2L | 230m | - | 30K | ✓ | - |
| V2X-Real [47] | real-world | V2X | 2024 | 4C+1L | 2C+1L | 280m | - | 33K | - | - |
| V2XScenes (Ours) | real-world | V2X | 2025 | 6C+3L | 13C+11L+2R | 600m | ✓ | 35k | ✓ | ✓ |
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| Late Fusion | 39.97 | 36.21 | 23.72 |
| Early Fusion | 35.59 | 23.75 | 10.31 |
| AttuFuse [52] | 57.11 | 46.69 | 20.88 |
| F-Cooper [7] | 53.48 | 40.45 | 17.27 |
| V2XVIT [49] | 58.10 | 51.11 | 26.48 |
| CoBEVT [48] | 54.50 | 43.48 | 21.92 |
| CoAlign [28] | 58.41 | 50.57 | 28.20 |
| Where2Comm [13] | 52.43 | 42.90 | 17.79 |
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| AP0.33D | AP†3D | MOTA MOTP | AP0.33D | AP†3D | MOTA MOTP |
| Early | 32.42 | 18.17 | 25.30 | 46.98 | 23.78 | 14.83 | 21.37 | 52.04 |
| CoBEVT | 39.86 | 19.86 | 20.84 | 43.60 | 23.15 | 16.47 | 15.89 | 54.24 |
| V2XVIT | 43.74 | 24.16 | 24.48 | 49.08 | 16.69 | 11.11 | 12.69 | 51.92 |
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| IoU=0.3 | IoU=0.5 | IoU=0.7 | IoU=0.3 | IoU=0.5 | IoU=0.7 |
| No Fusion | 73.30 | - | 68.89 | - | 47.15 | - | 38.72 | - | 29.82 | - | 13.15 | - |
| Late Fusion | 75.33 | +2.8↑ | 72.26 | +4.9↑ | 49.48 | +4.9↑ | 46.27 | +19.5↑ | 31.33 | +5.0↑ | 6.33 | -51.9↓ |
| Early Fusion | 82.36 | +12.4↑ | 77.69 | +12.8↑ | 59.91 | +27.1↑ | 57.14 | +47.6↑ | 44.69 | +49.9↑ | 19.47 | +48.1↑ |
| AttuFuse | 81.65 | +11.4↑ | 74.13 | +7.6↑ | 53.05 | +12.5↑ | 50.62 | +30.7↑ | 35.54 | +19.2↑ | 12.08 | -8.2↓ |
| F-Cooper | 85.58 | +16.7↑ | 79.95 | +16.0↑ | 53.41 | +13.3↑ | 68.44 | +76.7↑ | 55.68 | +86.7↑ | 21.58 | +64.1↑ |
| V2XVIT | 86.66 | +18.2↑ | 82.46 | +19.7↑ | 62.41 | +32.3↑ | 57.18 | +47.7↑ | 42.67 | +43.1↑ | 19.87 | +51.1↑ |
| CoBEVT | 86.89 | +18.5↑ | 82.40 | +19.6↑ | 54.23 | +15.0↑ | 73.33 | +89.4↑ | 63.79 | +113.9↑ | 30.64 | +133.0↑ |
| Where2Comm | 81.37 | +11.0↑ | 73.39 | +6.5↑ | 45.18 | -4.2↓ | 46.58 | +20.3↑ | 33.62 | +12.7↑ | 12.37 | -5.9↓ |
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| SpaRTA [5] | 49.42 | 63.42 | 42.84 | 23.46 |
| SAIKF [16] | 55.47 | 67.61 | 53.53 | 22.94 |
| PCGDA [45] | 49.38 | 55.42 | 44.51 | 20.63 |
| CMSMC [21] | 42.96 | 49.37 | 37.18 | 28.94 |
| InfraDet3D [61] | 40.34 | 54.71 | 40.54 | 26.51 |
| ISN [32] | 53.39 | 72.54 | 60.32 | 14.51 |
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+ "content": "[1] Eduardo Arnold, Sajjad Mozaffari, and Mehrdad Dianati. Fast and robust registration of partially overlapping point clouds. IEEE Robotics and Automation Letters, 7(2):1502-1509, 2021. 3"
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+ "content": "[2] Zhengwei Bai, Guoyuan Wu, Matthew J Barth, Yongkang Liu, Emrah Akin Sisbot, and Kentaro Oguchi. Pillargrid: Deep learning-based cooperative perception for 3d object detection from onboard-roadside lidar. In 2022 IEEE 25th International Conference on Intelligent Transportation Systems (ITSC), pages 1743-1749. IEEE, 2022. 3"
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+ "content": "[3] Paul J Besl and Neil D McKay. Method for registration of 3-d shapes. In Sensor fusion IV: control paradigms and data structures, pages 586-606. Spie, 1992. 5"
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