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Info. Processing, School of CS, Fudan University + +$^{2}$ Shanghai Collaborative Innovation Center of Intelligent Visual Computing + +3 Microsoft Research Asia + +https://quanhaol.github.io/magicmotion-site/ + +![](images/a32a487e53822fdc24d9b084a1d24633b01dea4a261219956023352c401e2207.jpg) +Figure 1. Example videos generated by MagicMotion. MagicMotion consists of three stages, each supporting a different level of control from dense to sparse: mask, box, and sparse box. Given an input image and any form of trajectory, MagicMotion can generate high-quality videos, animating objects in the image to move along the user-specified path. + +# Abstract + +Recent advances in video generation have led to remarkable improvements in visual quality and temporal coherence. Upon this, trajectory-controllable video generation has emerged to enable precise object motion control through explicitly defined spatial paths. However, existing methods struggle with complex object movements and multi-object motion control, resulting in imprecise trajectory adherence, poor object consistency, and compromised + +visual quality. Furthermore, these methods only support trajectory control in a single format, limiting their applicability in diverse scenarios. Additionally, there is no publicly available dataset or benchmark specifically tailored for trajectory-controllable video generation, hindering robust training and systematic evaluation. To address these challenges, we introduce MagicMotion, a novel image-to-video generation framework that enables trajectory control through three levels of conditions from dense to sparse: masks, bounding boxes, and sparse boxes. Given an input image and trajectories, MagicMotion seamlessly animates objects along defined trajectories while maintaining object consistency and visual quality. Furthermore, + +we present MagicData, a large-scale trajectory-controlled video dataset, along with an automated pipeline for annotation and filtering. We also introduce MagicBench, a comprehensive benchmark that assesses both video quality and trajectory control accuracy across different numbers of objects. Extensive experiments demonstrate that MagicMotion outperforms previous methods across various metrics. + +# 1. Introduction + +With the rapid development of diffusion models, video generation has witnessed significant progress in recent years. In contrast to images, videos [53, 63, 64, 73] capture dynamic temporal changes and offer a richer representation of semantic content. Earlier video generation approaches, such as AnimateDiff [16] and SVD [3], primarily rely on the UNet [46] structure, which results in videos with limited length and quality. Sora [4] has demonstrated the powerful capabilities of the DiT [37] architecture in text-to-video (T2V) generation. Following this breakthrough, subsequent models leveraging the DiT architecture [28, 82, 93] have achieved higher quality outputs and extended video duration. + +While DiT-based models [28, 82, 93] excel at producing high-quality and longer videos, many text-to-video approaches [16, 75, 77] lack precise control over attributes like object movement and camera motion [16, 75, 82]. Fine-grained trajectory-controllable video generation emerges as a solution, which is especially critical for generating controllable videos in real-world scenarios. + +Previous trajectory-controllable video generation methods can be categorized based on the type of control signals they use. These include points-based control [14, 59, 66, 94], optical flow-based control [5, 30, 48, 84, 91], bounding boxes-based control [22, 35, 39, 60, 67, 69, 81], masks-based control [83], and 3D trajectories-based control [13, 15, 62]. However, these methods exhibit several limitations. First, the trajectory control conditions used by these methods are unitary. Each method only supports a single type of control signal. However, sparse trajectories (e.g., points and optical flow) result in imprecise control over object shape and size, while dense trajectories (e.g., masks and 3D trajectories) are challenging for users to provide. Second, a publicly available large-scale dataset for trajectory-controllable video generation is lacking. Existing VOS (Video Object Segmentation) datasets suffer from short video lengths [33, 34, 80], small scales [9, 10, 20, 38], or few foreground objects [12]. Third, a unified benchmark for evaluating different methods is absent. Besides, previous work focuses solely on video quality and trajectory accuracy while neglecting the impact of the number of moving objects. We argue that controlling fewer or more objects presents different challenges, making it essential to include + +this factor in the evaluation metrics. + +To address these issues, we propose MagicMotion, a controllable video generation framework with dense-to-sparse trajectory guidance. To inject trajectory conditions into the generation process, we utilize an architecture similar to ControlNet [89] called Trajectory ControlNet to encode the trajectory information, which is later added to the original DiT model through a zero-initialized convolution layer. MagicMotion supports three types of trajectory conditions: masks, boxes, and sparse boxes using a progressive training strategy. Experiments show that the model can leverage the knowledge learned in the previous stage to achieve better performance than training from scratch. Additionally, we propose a novel latent segment loss that helps the video generation model better understand the fine-grained shape of objects with minimal computation. + +We also construct MagicData, a high-quality public dataset comprising 23K video samples, each annotated with a triplet. We design a data pipeline that uses a large language model [52] to extract the main moving objects in the video, and Segment Anything Model (SAM2) [43, 44] to annotate the segmentation masks and bounding boxes of these objects. Furthermore, we introduce MagicBench, a large-scale comprehensive trajectory-controllable video generation benchmark. It categorizes all videos into 6 classes based on the number of foreground objects and evaluates models separately for each category in terms of both video generation quality and trajectory control accuracy. + +In conclusion, the main contributions of our work are summarized as follows: + +- We present MagicMotion, a trajectory-controllable image-to-video generation model that supports three types of control signals: masks, boxes, and sparse boxes. +- We introduce a data curation and filtering mechanism, and construct MagicData, the first public dataset for trajectory-controlled video generation. +- We propose MagicBench, a comprehensive benchmark for evaluating trajectory-controllable video generation models for both video quality and trajectory control accuracy across different numbers of controlled objects. + +# 2. Related Works + +Video Diffusion Models Diffusion models [18, 31, 49, 50] have made great progress in image generation [8, 36, 40, 41, 45, 47, 61, 85-88, 90], which has led to the rapid development of video generation [3, 11, 16, 19, 21, 25, 28, 51, 54-57, 70, 72, 74, 76, 77, 82, 93]. VDM [19] is the first to apply diffusion models to video generation. Early works likeAnimateDiff [16] and SimDA [75] attempt to insert temporal layers into pretrained T2I model for video generation. Subsequently, VideoCrafter [6] and SVD [3] use large-scale and high-quality data for training, achieving + +better performance. However, these methods have trouble on generating long videos with high quality, mainly due to the inherent limitations of the UNet architecture. The emergence of Sora [4] is a significant success, demonstrating the potential of DiT [37] models to generate high-quality videos with tens of seconds. Recent video generation methods [28, 82, 93] are mainly based on DiT architecture, and have achieved great success in the open-source community. However, these methods rely solely on text or image guidance for video generation, lacking precise control over object or camera trajectory, which is crucial for high-quality video generation. + +Trajectory Controllable Video Generation Trajectory Controllable Video Generation has recently garnered significant attention for its ability to precisely control object and camera trajectories during video synthesis. Previous methods [30, 48, 84, 91] integrate optical flow maps into video generation through a trajectory encoder. Recent works [66, 94] suggest using point maps as a form of guidance. MotionCtrl [66] processes point maps with a Gaussian filter and employs trainable encoders to encode object trajectories. Trackgo [94] represents objects using a few key points and injects this information via an encoder and a custom-designed adapter structure. Other works [22, 35, 39, 60] employ bounding box to control object trajectories. Boximator [60] employs a trainable self-attention layer to fuse box and visual tokens inspired by GLIGEN [29]. Some training-free methods [22, 35, 39] purpose to modify attention layers or initial noised video latents to inject box signals. Additionally, certain methods [13, 15, 59, 62] explore the potential of 3D trajectories to achieve more sophisticated motion control. LeViTor [59] employs keypoint trajectory maps enriched with depth information, while others [13, 15, 62] construct custom 3D trajectories to represent object movements. However, sparse trajectories lead to imprecise control on objects shape and size, while dense trajectories are difficult for users to provide. In contrast, MagicMotion can control both dense and sparse trajectories, providing users with more flexible control over video generation. + +# 3. Method + +# 3.1. Overview + +Our work mainly focuses on trajectory-controllable video generation. Given an input image $I \in R^{H \times W \times 3}$ , and several trajectory maps $C \in R^{T \times H \times W \times 3}$ , the model can generate a video $V \in R^{T \times H \times W \times 3}$ in line with the provided trajectories, where $T$ denotes the length of generated video. In the following sections, we first provide a detailed explanation of our model architecture in Section 3.2. Next, we outline our progressive training procedure in Section 3.3. In Section 3.4, we introduce the Latent Segmentation Loss and + +demonstrate how it enhances the model capabilities on fine-grained object shape. We then describe our dataset curation and filtering pipeline in Section 3.5. Finally, we present an in-depth overview of MagicBench in Section 3.6. + +# 3.2. Model Architecture + +Base I2V generation model We utilize CogVideoX-5B-I2V [82] and Wan2.1 1.3B [58] as our base image to video model. The models are built upon a DiT (Diffusion Transformer) architecture, incorporating 3D-Full Attention to generate high-quality videos. As shown in Fig. 2, the model takes an input image $I \in R^{H \times W \times 3}$ and a corresponding video $V \in R^{T \times H \times W \times 3}$ and encodes them into latent representations $Z_{image}, Z_{video} \in R^{\frac{T}{4} \times \frac{H}{8} \times \frac{W}{8} \times 16}$ using a pretrained 3D VAE [26]. Later, $Z_{image}$ is zeropadded to $T$ frames and concatenated with a noised version of $Z_{video}$ and then fed into the Diffusion Transformer, where a series of Transformer blocks iteratively denoise it over a predefined number of steps. Finally, the denoised latent is decoded by a 3D VAE decoder to get the output video $V_{out} \in R^{T \times H \times W \times 3}$ . + +Trajectory ControlNet To ensure that the generated video follows the motion patterns given by the input trajectory maps $C \in R^{T \times H \times W \times 3}$ , we adopt a design similar to ControlNet [89] to inject trajectory condition. As shown in Fig. 2, we employ the 3D VAE encoder to encode the trajectory maps into $Z_{\text{trajectory}} \in R^{\frac{T}{4} \times \frac{H}{8} \times \frac{W}{8} \times 16}$ , which is then concatenated with the encoded video $Z_{\text{video}}$ and serves as input to Trajectory ControlNet. Specifically, Trajectory ControlNet is constructed with a trainable copy of all pre-trained DiT blocks to encode the user-provided trajectory information. The output of each Trajectory ControlNet block is then processed through a zero-initialized convolution layer and added to the corresponding DiT block in the base model to provide trajectory guidance. + +# 3.3. Dense-to-Sparse Training Procedure + +Dense trajectory conditions, such as segmentation masks, offer more precise control than sparse conditions like bounding boxes but are less user-friendly. To address this, MagicMotion employs a progressive training procedure, where each stage initializes its model with the weights from the previous stage. This enables three types of trajectory control ranging from dense to sparse. We found that this progressive training strategy helps the model achieve better performance compared to training from scratch with sparse conditions. Specifically, we adopt the following trajectory conditions across stages: stage1 uses segmentation masks, stage2 uses bounding boxes, and stage3 uses sparse bounding boxes, where fewer than 10 frames have box annotations. Additionally, we always set the first frame of the trajectory condition as a segmentation mask to specify the foreground objects that should be moving. + +![](images/ce03cc00e790838b861392b345e3ba56afae65187bba3e8afbaf57d69834affc.jpg) +Figure 2. Overview of MagicMotion Architecture (text prompt and encoder are omitted for simplicity). MagicMotion employs a pretrained 3D VAE to encode the input trajectory, first-frame image, and training video into latent space. It has two separate branches: the video branch processes video and image tokens, and the trajectory branch uses Trajectory ControlNet to fuse trajectory and image tokens, which is later integrated to the video branch through a zero-initialized convolution layer. Besides, diffusion features from DiT blocks are concatenated and processed by a trainable segment head to predict latent segmentation masks, which contribute to our latent segment loss. + +Our model uses velocity prediction following [82]. Let $x_0$ be the initial video latents, $\epsilon$ be the gaussian noise, $x_t = \sqrt{\alpha_t} * x_0 + \sqrt{1 - \alpha_t} * \epsilon$ be the noised video latents, and $v_\theta$ be the model output. The diffusion loss can be written as: + +$$ +\mathcal {L} _ {\text {d i f f u s i o n}} = \mathbb {E} _ {t, \epsilon \sim \mathcal {N} (0, I), x _ {0}} \left[ \left\| x _ {0} - \left(\sqrt {\alpha_ {t}} x _ {t} - \sqrt {1 - \alpha_ {t}} v _ {\theta}\right) \right\| _ {2} ^ {2} \right] \tag {1} +$$ + +# 3.4. Latent Segmentation Loss + +Bounding box-based trajectory is able to control an object's position and size but lacks fine-grained shape perception. To address this, we propose Latent Segmentation Loss, which introduces segmentation mask information during model training and enhances the model's ability to perceive fine-grained object shapes. + +Previous works [2, 68, 79, 92] have leveraged diffusion generation models for perception tasks, demonstrating that the features extracted by diffusion models contain rich semantic information. However, these models generally operate in the pixel space, which leads to extensive computational time and substantial GPU memory. + +To incorporate dense trajectory information while keeping computational costs within a reasonable range, we propose utilizing a lightweight segmentation head to predict segmentation masks directly in the latent space, eliminating the need for decoding operations. Specifically, our segmentation head takes a list of diffusion features $Z_{\text{feature}} \in R^{\frac{T}{4} * \frac{H}{16} * \frac{W}{16} * 3072}$ from each DiT block, and outputs a latent segmentation mask $Z_{\text{segment}} \in R^{\frac{T}{4} * \frac{H}{8} * \frac{W}{8} * 16}$ . We use a light-weight architecture inspired by Panoptic FPN [27]. Each diffusion feature first passes through a convolution + +layer to extract visual features $P \in R^{\frac{T}{4} *\frac{H}{16} *\frac{W}{16} *64}$ . The resulting features are then concatenated and processed by another convolution layer followed by an upsampling layer to generate the final latent segmentation mask. We compute the latent segment loss as the Euclidean distance between $Z_{segment}$ and the ground truth mask trajectory latents $Z_{mask}$ , which can be written as, + +$$ +\mathcal {L} _ {s e g} = \mathbb {E} _ {t, \epsilon \sim \mathcal {N} (0, I), z _ {0}} [ \| Z _ {s e g m e n t} - Z _ {m a s k} \| _ {2} ^ {2} ] \quad (2) +$$ + +In practice, $\mathcal{L}_{seg}$ is only used in stage2 and stage3, providing the model with dense conditions information when trained with sparse conditions. In detail, we set the weight of $\mathcal{L}_{seg}$ as 0.5, and the original diffusion loss as 1. In total, our final loss function can be written as, + +$$ +\mathcal {L} = \mathcal {L} _ {\text {d i f f u s i o n}} + \lambda * \mathcal {L} _ {\text {s e g}} \tag {3} +$$ + +where $\lambda$ is set to 0 in stage1, and 0.5 in stage2 and stage3. + +# 3.5. Data Pipeline + +Trajectory controllable video generation requires a video dataset with trajectory annotations. However, existing large-scale video datasets [1, 7, 24] only provide text annotations and lack trajectory data. Moreover, almost all previous works [30, 66, 84, 91, 94] use privately curated datasets, which are not publicly available. + +We present a comprehensive and general data pipeline for generating high-quality video data with both dense (mask) and sparse (bounding box) annotations. As shown in Fig. 3, the pipeline consists of two main stages: the Curation Pipeline and the Filtering Pipeline. The Curation + +![](images/0f6ad988d2ad9a862d0c9f1a3099da9176ce69f632148a1fc4e59c98862af247.jpg) +Figure 3. Overview of the Dataset Pipeline. The Curation Pipeline is used to construct trajectory annotations, while the Filtering Pipeline filters out unsuitable videos for training. + +Pipeline is responsible for constructing trajectory information from a video-text dataset, while the Filtering Pipeline ensures that unsuitable videos are removed before training. + +Curation Pipeline. We begin our dataset curation process with Pexels [23], a large-scale video-text dataset containing 396K video clips with text annotations. It encompasses videos featuring diverse subjects, various scenes, and a wide range of movements. We utilize Llama3.1 [52] to extract the foreground moving objects from the textual annotations of each video. As shown in Fig. 3, we input the video's caption into the language model and prompt it to identify the main foreground objects mentioned in the sentence. If the model determines that the sentence does not contain any foreground objects, it simply returns "empty" and such videos are filtered out. Next, we utilize GroundedSAM2 [43, 44], a grounded segmentation model that takes a video along with its main objects as input and generates segmentation masks for each primary object. Each object is consistently annotated with a unique color. Finally, bounding boxes are extracted from each segmentation mask using the coordinates of the top-left and bottom-right corners to draw the corresponding boxes. The color of the bounding box for each object remains consistent with its masks. + +Filtering Pipeline. Many videos contain only static scenes, which are not beneficial for training trajectory-controlled video generation models. To address this, we use optical flow scores to filter out videos with little motion and dynamics. Specifically, we utilize UniMatch [78] to extract optical flow maps between frames and compute the mean absolute value of these flow maps as the optical flow score, representing the video's motion intensity. However, videos with background movement but static foreground can still have high motion scores. To address this, we further use UniMatch to extract optical flow scores for foreground objects based on segmentation masks and bounding boxes. + +Videos with low foreground optical flow scores are filtered out, ensuring MagicData includes only videos with moving foreground objects. + +The trajectory annotations generated by the curation pipeline require further refinement. As shown in Fig. 3, some videos contain too many foreground objects annotations, or their sizes may be too large or too small. To address this, we regulate these factors within a reasonable range and filter out videos that fall outside the acceptable range. + +Specifically, based on extensive manual evaluation, we empirically set the optical flow score threshold to 2.0, limit the number of foreground object annotations from 1 to 3, and constrain the annotated area ratio to a range of 0.008 to 0.83. The whole data curation and filtering pipeline yields us with MagicData, a high quality dataset for trajectory controllable video generation containing 23K videos with both dense and sparse trajectory annotations. + +# 3.6. MagicBench + +Previous works on trajectory-controlled video generation [30, 35, 48, 65, 71, 91, 94] have primarily been validated on DAVIS (which has a relatively small dataset size), VIPSeg (where the annotated frames per video are insufficient), or privately constructed test sets. Thus there is an urgent need for a large-scale, publicly available benchmark to enable fair comparisons across different models in this field. To merge this gap, we use the data pipeline mentioned in Sec. 3.5 to construct MagicBench, a large-scale open benchmark consisting of 600 videos with corresponding trajectory annotations. MagicBench evaluates not only video quality and trajectory accuracy but also takes the number of controlled objects as a key evaluation factor. Specifically, it is categorized into 6 groups based on the number of controlled objects, ranging from 1 to 5 objects and more than 5 objects, with each category containing 100 high-quality videos. + +Metrics. For evaluation metrics, we adopt FVD [42] to assess video quality and FID [17] to evaluate image quality, following [59, 66, 71, 94]. To quantify motion control accuracy, we use Mask_IoU and Box_IoU, which measure the accuracy of masks and bounding boxes, respectively. Specifically, given a generated video $V_{gen}$ , we use the groundtruth masks of the first frame $M_{gt}(0)$ as input to SAM2 [43] to predict the masks $M_{gen}$ of the foreground objects in $V_{gen}$ . For each foreground object, we compute the Intersection over Union (IoU) between $M_{gen}(i)$ and groundtruth masks $M_{gt}(i)$ in each frame, then average these values to obtain Mask_IoU. Similarly, we compute the IoU between the predicted and groundtruth bounding boxes for each foreground object in each frame and take the average as Box_IoU. + +
MethodMagicBenchDAVIS
FID(↓)FVD(↓)M_IoU%(↑)B_IoU%(↑)FID(↓)FVD(↓)M_IoU%(↑)B_IoU%(↑)
Motion-I2V [48]39.31354.1056.1960.6694.141558.3232.0042.61
ImageConductor [30]49.95331.7651.7652.9091.711155.0834.3943.41
DragAnything [71]31.36253.4066.3070.8570.701166.2240.1353.60
LeViTor [59]38.32194.5339.9646.3697.98922.6825.2431.42
DragNUWA [84]39.73185.5266.8869.2184.611079.8941.2252.61
SG-I2V [35]32.60168.8268.7874.3990.931170.6037.3650.96
Tora [91]26.27245.2358.9564.0351.75766.7637.9850.90
Ours (Stage1-Wan1.3B)17.74129.7983.7980.9646.65548.5642.8353.67
Ours (Stage2-Wan1.3B)19.33143.0768.8971.7448.33662.8244.7561.88
Ours (Stage1-CogVideoX)15.06112.6991.5787.7545.06579.9481.3384.97
Ours (Stage2-CogVideoX)15.17107.2176.6181.4550.36760.9553.9472.84
+ +![](images/8815955d60a7d3b3bf38a39fe165d589fd5ae5e07f9943664acd638cf0405ef3.jpg) +Table 1. Quantitative Comparison results on MagicBench and DAVIS. "M_IoU" and "B_IoU" refer to Mask_IoU and Box_IoU, respectively. +Figure 4. Comparison results of different object number on MagicBench. To present the results more clearly, we have negated the FVD and FID scores. + +# 4. Experiment + +# 4.1. Experiment Settings + +Implementation details. We employ CogVideoX 5B [82] and Wan2.1 1.3B [58] as our base image-to-video model, which is trained to generate video based on an input image. Each stage of MagicMotion was trained on MagicData for one epoch. The training process consists of three stages. stage1 trains Trajectory ControlNet from scratch. In stage2, Trajectory ControlNet is further refined using the weights from stage1, while Segment Head is trained from scratch. Finally, in stage3, both Trajectory ControlNet and Segment Head continue training initialized with the weights from stage2. All training experiments were conducted on 4 NVIDIA A100-80G GPUs. We employed AdamW [32] as the optimizer, training with a learning rate of $1e - 5$ and a batch size of 1 on each GPU. During inference, we set steps to 50, the guidance scale to 6, and the weight of Trajectory ControlNet to 1.0 by default. + +Datasets. During training, we use MagicData as our training set. MagicData is annotated with dense to sparse trajec + +tory information using the data pipeline described in Section 3.5. It comprises a total of 23K video samples, annotated with text and trajectory. For evaluation, we evaluate all methods on both MagicBench and DAVIS [38], using the comparison metrics illustrated in Sec 3.6. + +# 4.2. Comparison with Other Approaches + +For thorough and fair comparisons, we compare our methods against 7 public trajectory controllable I2V methods [30, 35, 48, 59, 71, 84, 91]. Quantitative comparison and qualitative comparison results are shown below. + +Quantitative comparison. To compare MagicMotion with previous works, we use the first 49 frames of each video from DAVIS and MagicBench as the ground truth video. Since some methods [30, 35, 48, 59, 71, 84] do not support video generation up to 49 frames in length, we uniformly sample N frames from these 49 frames for evaluation, where N represents the video length that each method supports. We leverage the mask and box annotations from these selected frames as trajectory inputs for mask or box-based methods. The center point of each frame's + +![](images/eff7090cdb7bb8d523ec884a837abcc3090f10a75e628c84db7316c41025af69.jpg) +Figure 5. MagicMotion successfully controls the main objects moving along the provided trajectory, while all other methods exhibit significant defects marked with the orange box. + +mask is extracted as input for point or flow-based methods [30, 48, 59, 71, 84, 91]. + +As shown in Table 1, our method outperforms all previous approaches across all metrics both on MagicBench and DAVIS, demonstrating its ability to produce higher-quality videos and more precise trajectory control. Additionally, we evaluate each method's performance on MagicBench based on the number of controlled objects. As shown in Fig. 4, our method achieves the best results across all object number categories, demonstrating the superiority of our approach. + +Qualitative comparison. Qualitative comparison results are shown in Fig. 5, with the input image, prompt and trajectory provided. As shown in Fig. 5, Tora [91] accurately controls the motion trajectory but struggles to maintain the shape of the objects. While DragAnything [71], ImageConductor [30], and MotionI2V [48] have difficulty preserving the consistency of the original subject, resulting in substantial deformation in subsequent frames. Meanwhile, DragNUWA [84], LeviTor [59], and SG-I2V [35] frequently produce artifacts and inconsistencies in fine details. In contrast, + +MagicMotion allows moving objects to follow the specified trajectory smoothly while preserving high video quality. + +# 4.3. Ablation Studies + +In this section, we present ablation studies to validate the effectiveness of our MagicData dataset. Additionally, we demonstrate how our progressive training procedure and latent segment loss enhance the model's understanding of precise object shapes under sparse control conditions, thereby improving trajectory control accuracy. + +Ablations on Dataset. To verify the effectiveness of MagicData, we constructed an ablation dataset by combining two public VOS datasets, MeViS [9] and MOSE [10]. For a fair comparison, we trained MagicMotion stage2 for one epoch using either MagicData or the ablation dataset as the training set, both initialized with the same stage1 weights. We then evaluated the models on both MagicBench and DAVIS. + +As shown in Table 2, the model trained on MagicData + +outperforms the one trained on the ablation dataset across all metrics. Qualitative comparisons are shown in Fig. 6. In this case, we aim to gradually move the boy in the lower right corner to the center of the image. However, not using MagicData results to an unexpected child appears next to the boy. In contrast, the model trained with MagicData performs well, moving the boy along the specified trajectory while maintaining video quality. + +
MethodMagicBench/DAVIS
FID(↓)FVD(↓)M_IoU%(↑)B_IoU%(↑)
w/o MagicData24.24/50.91125.19/768.2773.39/50.9578.66/70.05
Ours15.17/50.35107.21/760.9576.61/53.9481.45/72.84
+ +![](images/156b7312e42b51dfae7c9326a39192478870b973262fed741fc289a40668035f.jpg) +Figure 6. Ablation Study on MagicData. Not using MagicData causes the model to generate an unexpected child. + +Ablations on Progressive Training Procedure. Progressive Training Procedure allows the model to leverage the weights learned in the previous stage, incorporating dense trajectory control information when trained with sparse trajectory conditions. To validate the effectiveness of this approach, we train the model from scratch for one epoch using bounding boxes as trajectory conditions. We then compare its performance with MagicMotion stage2. + +As shown in Table 3, excluding Progressive Training Procedure weakens the model's ability to perceive object shapes, ultimately reducing the accuracy of trajectory control. Qualitative comparisons in Fig. 7 further illustrate these effects, where the model trained without Progressive Training Procedure turns the woman's head entirely into hair. + +Ablations on Latent Segment Loss. Latent Segment Loss makes the model predict dense segmentation masks while training with sparse trajectories, enhancing its ability to perceive fine-grained object shapes under sparse conditions. To evaluate the effectiveness of this technique, we train the model from stage1 for one epoch using bounding + +Table 2. Ablation Study on MagicData. The model trained with MagicData outperforms the one trained without it across all metrics. + +
MethodMagicBenchDAVIS
M_IoU%(↑)B_IoU%(↑)M_IoU%(↑)B_IoU%(↑)
w/o LSL74.6578.0249.1964.19
w/o PT74.6179.4949.2267.34
Ours76.6181.4553.9472.84
+ +Table 3. Ablation Study on Progressive Training (PT) and Latent Segment Loss (LSL). Experimental results demonstrate that these techniques enhance the model with better comprehension on fine-grained object shapes. + +![](images/27d61328ec27478b85eefd4aedf4e98232949957e706a5b7864f44b56216bddb.jpg) +Figure 7. Ablation study on the progressive training procedure. Without it, the generated head shapes become noticeably distorted. + +boxes as trajectory conditions and compare its performance with MagicMotion stage2. Table 3 shows that the absence of Latent Segment Loss reduces the model's ability on object shapes, leading to less precise trajectory control. + +# 5. Conclusion + +In this paper, we proposed MagicMotion, a trajectory-controlled image-to-video generation method that uses a ControlNet-like architecture to integrate trajectory information into the diffusion transformer. We employed a progressive training strategy, allowing MagicMotion to support three levels of trajectory control: dense masks, bounding boxes and sparse boxes. We also utilized Latent Segment Loss to enhance the ability of the model to perceive fine-grained object shapes when only provided with sparse trajectory conditions. Additionally, we presented MagicData, a high-quality annotated dataset for trajectory-controlled video generation, created through a robust data pipeline. Finally, we introduced MagicBench, a large-scale benchmark for evaluating trajectory-controlled video generation. MagicBench not only assessed video quality and trajectory accuracy but also took the number of controlled objects into account. 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The generated images evoke a sense of happiness in viewers, contrasting with the negative emotions elicited by the source images. Given a source image that triggers negative emotions (framed in green), our method (Ours) synthesizes a new image that elicits the given positive target emotions (in red), while maintaining the essential elements and structures of the scene. For instance, our method replaces the anger-inducing flames in the source image with cute-shaped lamps to evoke the target emotion of amusement. While in an outdoor setting, the raging fire is substituted with a tranquil, lush meadow to inspire a sense of awe. For comparisons, we include other competitive methods. The blue number below each image represents its CAM-based ESMI score, with higher values being better. + +![](images/60c15160c4f1851ca5a6c8be744d74c68518bcff5a1b00d81e0d2360373e9d1b.jpg) +EmoEdit 70.57 + +![](images/8438fb3df864212f985c2f69e9373a21c1660a9b951e9d0fc87dbd3c525f070f.jpg) +LMS 65.03 + +![](images/4181cc21ff8b34b6392806509c0452ffc59287bc489bf74bf8f4c1fbd44e634f.jpg) +Ours 78.45 +From anger to awe + +![](images/58a2ed4ccc5353a9ea80d4816b6baa11fb886e02a03ac4ac0885583a3f12f8a5.jpg) +Source Image + +![](images/e93f86aeaec54a154adbc0d5e76887965f2bcc89f2734dcc3bb59dc837388505.jpg) +CT 38.10 + +![](images/6484775f028078f971a5c687b4cca3f3aca77c4496caac5585bc48f3efd9a092.jpg) +NST 64.56 + +![](images/dc11b2e63630a7ab8a76667a52e0efda64848e6fa2d3ce775f84593301a45935.jpg) +AIF 32.97 + +![](images/f3d260e6d519a60f12c118573713db5d27c9ed2dbd35bc280e471747f6a4fbd4.jpg) +EmoEdit 31.25 + +![](images/4836d8eabf624ce1d9b37b008a96eb81555f2cc314ae4ca136bb5708282405a6.jpg) +LMS 10.27 + +![](images/bef723c8194101f09d92492a224b30a4725b900a022adf3989ab1cdbf0c934f6.jpg) +Ours 68.12 + +# Abstract + +Despite the rapid progress in image generation, emotional image editing remains under-explored. The semantics, context, and structure of an image can evoke emotional responses, making emotional image editing techniques valuable for various real-world applications, including treatment of psychological disorders, commercialization of products, and artistic design. First, we present a novel challenge of emotion-evoked image generation, aiming to synthesize images that evoke target emotions while retaining the semantics and structures of the original scenes. To address this challenge, we propose a diffusion model capable of effectively understanding and editing source images to convey desired emotions and sentiments. Moreover, due to the lack of emotion editing datasets, we provide a unique dataset consisting of 340,000 pairs of images and their emotion annotations. Furthermore, we conduct human psychophysics experiments and introduce a new evaluation metric to systematically benchmark all the methods. Experimental results demonstrate that our method + +surpasses all competitive baselines. Our diffusion model is capable of identifying emotional cues from original images, editing images that elicit desired emotions, and meanwhile, preserving the semantic structure of the original images. All code, model, and dataset are available at GitHub. + +# 1. Introduction + +"I am feeling down. Bring some excitement to my room." + +What we perceive not only entails useful visual information but also evokes profound emotional reactions. Incorporating visual cues that elicit emotions into images holds practical significance in various domains. In commercialization, it enhances brand impact and captures consumer attention. In augmented or virtual reality, it supports therapeutic interventions for conditions such as autism and schizophrenia. Despite recent advances in image generation [5, 27, 35], emotion conditioning remains largely underexplored. We introduce the novel task of emotion-evoked image generation: given a source image and a target emotion, the goal is to generate a new image that evokes the specified emotion while preserving the semantics and structure of the original scene. This task is + +challenging, requiring both recognition of subtle emotional cues in the source image and the ability to modify them meaningfully. For example, as shown in Figure 1, clusters of fire flames on the water intensify the emotion of anger. In the generated image, they are replaced with lamps designed in cute shapes, transforming the overall emotional response to amusement. + +Studies have shown that both global and local factors influence emotional responses in images, such as overall color tones, local facial expressions, and emotion-related objects like graveyards (sadness) or balloons (amusement) [30, 31]. As shown in Figure 2, inserting fearful elements, such as fire, into a peaceful scene can evoke negative emotions, as they trigger instinctive responses to threats. However, some elements, such as the sky and plants, remain emotionally neutral. Given that humans are generally more sensitive to negative than positive stimuli [2, 10], simply adjusting global attributes like brightness may not be enough to alter negative emotions. Traditional methods such as color transfer and style transfer [6, 20, 28] attempt to modify emotional tone through global appearance changes. However, they often fail to elicit desired emotions, as they cannot identify and edit the specific local regions responsible for emotional impact. In Figure 2, while darkening the scene may enhance fear (left panel), brightening a scene of a burning hillside does not effectively convey awe (right panel). In contrast, transforming anger into awe requires editing key emotional cues, for example, removing the fire and adding vibrant clouds to create a tranquil atmosphere. Emotion-evoked image generation thus requires not just global color or style adjustments, but also semantic understanding and purposeful local modification. + +Drawing inspiration from these emotion-associated factors, we propose our model, EmoEditor, for emotion-evoked image generation. We develop EmoEditor based on state-of-the-art stable diffusion models and introduce three technical novelties. (1) EmoEditor employs a novel dual-branch architecture in the reverse diffusion process that integrates emotion-conditioned global context and local emotional cues from the source images to ensure coherence with the original content while reflecting the desired emotional outcome. (2) During training, the network's behaviors are guided by aligning model creativity with human expectations in the neuro-symbolic space, implicitly learning the mapping from target emotions to human-annotated text instructions. (3) During inference, iterative emotion discrimination mechanisms are employed to select emotionally coherent images autonomously. + +With the rapid advancements in diffusion models, various effective image editing techniques have emerged [3, 11, 23]. However, these methods are not specifically tailored for understanding and identifying + +![](images/58a327cf3913cfc87c91f225b080b61c7d629c920d677def7dbbee6cb0f711b5.jpg) +Figure 2. Emotions are influenced by both global and local cues from the source images. We present examples of transitions from positive to negative emotions (blue shading) and from negative to positive emotions (orange shading). In each example, the target emotions are in red, and source images are framed in green. + +![](images/565c14960020b2ea3bc9d1ce8c7927000d31b12f057a5226fd2dcd4c03483f32.jpg) + +emotion-associated elements within images. To address this gap, we propose a competitive baseline called Large Model Series (LMS), concatenating multiple large language and vision models. This baseline first understands source images through image captioning, then generates emotion-prompted instructions using language models, and finally edits images prompted by these instructions with diffusion models. Upon comparison with existing methods through a series of human psychophysics experiments and a new quantitative evaluation, our end-to-end trained EmoEditor achieves outstanding image generation results. It effectively preserves the structural coherence and semantic consistency with the source images while eliciting the target emotion of human viewers. To obtain training data for this task, we establish a dataset curation pipeline and introduce the first large-scale EmoPair dataset, comprising approximately 340,000 pairs of images annotated with emotion-conditioned editing instructions. Unlike existing datasets on visual emotion analysis [17, 19, 31], which assign emotion labels to individual images for classification, our dataset provides paired images annotated with source and target emotion labels. + +The main contributions of this paper are highlighted below: (1) We study the problem of emotion-evoked image generation, which focuses on modifying visual content to trigger intended emotional responses while preserving scene structures and contextual coherence. To benchmark all methods, we establish a comprehensive framework for evaluating model performance, incorporating human psychophysics experiments and introducing a new metric. (2) We propose EmoEditor, an emotion-evoked diffusion model, which employs a novel two-branch architecture to integrate global context with local semantic regions of source images that evoke emotional responses. (3) EmoEditor learns emotional cues during end-to-end training, eliminating the need for additional emotion reference images. During inference, EmoEditor generates emotion-evoked images without hand-crafted emotion-conditioned text instructions, while preserving context and structural coherence with the source image. Its performance is superior among all the competitive methods. (4) We curate the large-scale EmoPair dataset, containing 340,000 image pairs with emotion annotations. + +# 2. Related Work + +# 2.1. Visual Emotion Analysis + +Visual Emotion Analysis (VEA) seeks to understand and predict human emotional responses from visual data. In psychology, Categorical Emotion States (CES) underpin classification models such as the 8-category Mikels model [17]. Early work relied on handcrafted features like color [15], while recent methods leverage deep learning for more accurate emotion prediction [30, 33]. However, generating images to evoke specific emotions remains underexplored. To address this, we introduce EmoEditor, a two-branch diffusion model that jointly learns emotion recognition and image generation. + +Existing VEA datasets [19, 34] focus on emotion classification, including EmoSet [31], which has 120k images with emotion labels and attributes. However, they lack image pairs with annotated emotions and text editing instructions essential for emotion-evoked image generation. Thus, we introduce the EmoPair dataset, comprising 340k image pairs with differing source and target emotions while ensuring consistent scene semantics and structure. + +# 2.2. Image Editing + +Diffusion-based Image Editing. Earlier studies used GANs [7] and CLIP models [21] for image manipulation based on detailed text descriptions [1]. Diffusion models have advanced, generating high-quality images from various prompts [8, 23]. Methods like SDEdit [16] use stochastic differential equations for editing. Ip2p [3] allows image editing based on human instructions. PnP [25] achieves fine-grained control of generated structures by manipulating spatial features and self-attention. CtrlNet [36] adds conditional control for better precision. Despite these advances, current diffusion models often overlook emotional cues needed for effective emotion editing. + +Emotion Editing. Color and style transfer methods like PDF-Transfer [20], Neural Style Transfer (NST) [6], and CLIP-Styler (Csty) [13] manipulate images using reference images but struggle with local adjustments, limiting their versatility in generating emotion-evoking images. AIF [28] reflects emotions from text to images by incorporating affective content into the image generation process. It relies heavily on detailed textual prompts and cannot edit image regions locally. EmoEdit [32] maps input images and target emotions into an embedding guided by a set of fixed learned queries, restricting emotional cues and diversity in generation to the representational capacity of these queries. In contrast, our EmoEditor uses end-to-end training to implicitly understand and edit emotional cues locally and globally without relying on external references. + +# 3. Method + +We formulate emotion-evoked image generation as a supervised learning task. First, we curate the EmoPair dataset with emotion-labeled image pairs and editing instructions. Next, EmoEditor is trained on this dataset. During inference, it takes source images and target emotions, producing generated images without the need for text instructions or emotion reference images. + +# 3.1. Curating Our EmoPair Dataset + +Given the unavailability of a paired image dataset for emotion editing, we curate EmoPair. It consists of two subsets: EmoPair-Annotated Subset (EPAS), containing 331,595 image pairs from Ip2p [3] annotated with emotion labels; and EmoPair-Generated Subset (EPGS), consisting of 6,949 pairs generated based on text instructions given target emotions. All images from EmoPair are of size $224 \times 224$ . Figure 3 illustrates the pipeline for curating our EmoPair dataset. See Sec S1 for more details. + +Emotion Predictor $\mathcal{P}$ . To construct our dataset, we use the emotion predictor $\mathcal{P}$ proposed in [31], which was trained on the largest VEA dataset, EmoSet. All images are classified into 8 emotion categories, encompassing four positive (amusement, awe, contentment, excitement) and four negative (anger, disgust, fear, sadness) emotions. + +EmoPair-Annotated Subset (EPAS). The original Ip2p dataset lacks emotion labels, consisting only of image pairs with text instructions for editing. To address this, we use $\mathcal{P}$ to classify the source and target images from the Ip2p dataset into eight distinct emotions. We augment the Ip2p dataset with emotion labels, resulting in 331,595 image pairs. Notably, the text instructions with these image pairs serve as human expectations to guide EmoEditor's training but are not utilized during inference. + +EmoPair-Generated Subset (EPGS). To address the lack of emotional cues in the Ip2p dataset, we create the EPGS subset using emotionally rich images from EmoSet [31]. However, EmoSet lacks paired images with consistent scenes and target emotions, and it does not include text editing instructions. Single-word prompts like "[Target Emotion]" prove ineffective in existing text-to-image models due to their limited emotional reasoning. Single-emotion terms lack specificity, resulting in varied interpretations depending on the context of source images. For instance, enhancing an image for excitement can vary significantly based on context, such as having a happy smile on a person or adding fireworks to the sky for a landscape. Thus, to generate accurate image pairs, we develop 50 general instructions for transitioning to desired emotions of 8 categories using GPT-3 [4]. Human annotators rank these instructions, keeping the top ten per emotion. The pre-trained Ip2p model then uses these instructions to manipulate EmoSet source images, resulting + +![](images/b09b54c7912bd4be87f7774cbd540bdaf7d046ee61f1ab1c3450c674e514261d.jpg) +Figure 3. Pipeline for Curating Our EmoPair Dataset. The dataset comprises two subsets: EmoPair-Annotated Subset (EPAS, left blue box) and EmoPair-Generated Subset (EPGS, right orange box). Each subset includes schematics depicting the creation, selection, and labeling of image pairs in the upper quadrants, with two example pairs in the lower quadrants. Each example pair comprises a source image (framed in green) and a target image. The classified source and target emotion labels (highlighted in red) and target-emotion-driven text instructions for image editing are provided. Note that these instructions are used during model training to guide the learning of rich neural-symbolic embeddings, but are not used during model inference. + +![](images/8621c88c28144a44983dc37d3b253d2cfda61d182e27bb5d48576a14199c82d4.jpg) + +![](images/ce8c7bfbd7922a448e04208d3c234a5e0dbf26382d6f45e1a8743fd759843a0b.jpg) +Figure 4. Architecture of Our Proposed EmoEditor. EmoEditor is an image diffusion model with local (shaded in green) and global (shaded in blue) branches. The pre-trained VAE's encoder $\mathcal{E}$ and decoder $\mathcal{D}$ are fixed during training and inference. Exclusively employed during inference, the fixed emotion predictor $\mathcal{P}$ predicts emotions on generated images for iterative emotion inference. + +in 6,949 high-quality image pairs after quality control measures. To ensure the quality of the generated images, we have human annotators providing corrections for some results (see Sec S1). + +# 3.2. Our Diffusion Model - EmoEditor + +Our EmoEditor, in Figure 4, takes a source image $I_{s}$ and a target emotion $y$ to generate an image evoking the desired emotion. It employs the latent diffusion model (LDM) [22] with three key novelties. + +Integration of Global and Local Emotion Cues. In the global branch of our EmoEditor, we convert the target emotion $y$ into a binary one-hot vector $e_{oh}$ , where the corresponding entry to $y$ in $e_{oh}$ is set to 1 and the rest are set to 0. This simplifies model design, enhancing comprehension and generation of complex emotional + +images, as one-hot encoding can capture intricate emotion combinations through a multi-label representation. We use the pre-trained emotion predictor $\mathcal{P}$ to predict the source image's emotional state $e_s$ , representing the probability distribution of emotions for each category. EmoEditor avoids using emotion labels for $I_s$ for two reasons: (1) Obtaining emotion labels for source images is often impractical in real-world scenarios. (2) Source images can be complex, conveying multiple emotions simultaneously. Utilizing a stereotypical source emotion as input potentially introduces biases and limits the model's ability to generate diverse outputs. + +Next, we compute the emotion editing direction $e_{dir}$ using the target emotion code $e_{oh}$ and the source emotional state $e_s$ : $e_{dir} = e_{oh} - e_s$ . This allows the model to adaptively adjust the editing direction based on the initial state of different source images. To map the emotion editing direction into the latent space, we introduce an emotion encoder $\tau_{\theta}$ , trained from scratch to learn neural-symbolic embeddings. It first encodes $e_{dir}$ into an emotion embedding $e$ through fully connected layers: $e = \tau_{\theta}(e_{dir})$ (See Sec S2.1 for details). Later on, we introduce novel losses to regularize the behaviors of $\tau_{\theta}$ . Notably, we intentionally avoid using explicit text editing instructions as conditional inputs to the model due to the varied interpretations of target emotions, where multiple solutions can elicit the same emotions. Including explicit text instructions may hinder the model's creativity, restricting its capacity to produce diverse sets of images conveying the same emotions. + +In the local branch of our EmoEditor, we introduce an image encoder $\mathcal{E}$ to extract visual features of the source image, acquiring $z$ for $I_{s}$ : $z = \mathcal{E}(I_s)$ . Similar to the LDM [22], $\mathcal{E}$ is based on a pre-trained VAE [12]. The forward diffusion process gradually adds noise to $z$ , generating a noisy latent $z_{t}$ , where the noise level increases over $t$ time steps $(t\in T)$ . Specifically, we expressed $z_{t} = \sqrt{\alpha_{t}}\cdot z_{t - 1} + \sqrt{1 - \alpha_{t}}\cdot \epsilon$ , where $\alpha_{t}$ is the diffusion coefficient controlling the rate of noise increase, and $\epsilon$ is a random noise sampled from a normal distribution. + +In the reverse diffusion process, the denoising network $\epsilon_{\theta}$ predicts noise added to the noisy latent $z_{t}$ using cross-attention with the target emotion condition $e$ and source image condition $z$ . The features in $z$ and $z_{t}$ enhance understanding of intrinsic information in the image, leading to emotion-specific content for $I_{s}$ . After $T - 1$ denoising steps, decoder $\mathcal{D}$ produces an emotion-evoked image. We minimize the latent diffusion loss, which is the expected error between the predicted noise by $\epsilon_{\theta}$ and the actual noise $\epsilon$ sampled during training: $L_{noise} = E_{t,y,z,\epsilon (z_t),\epsilon \sim N(0,1)}\| \epsilon -\epsilon_{\theta}(z_t,t,z,\tau_{\theta}(y))\|^2$ . + +Alignment Loss between Model and Human Judgements. A single emotion term lacks the depth to convey the nuanced causes underlying emotions, posing a challenge for diffusion models to grasp the diagnostic information triggering emotions. In contrast to existing text-to-image models, EmoEditor emulates human reasoning by aligning its thought process with text instructions in our EmoPair dataset, which leads the transition from the source emotion to the target emotion. To achieve this, we introduce an alignment loss in a neuro-symbolic space, between emotion embeddings $e$ from $\tau_{\theta}$ and text embeddings $c$ of instructions in each image pair of our EmoPair dataset with pre-trained CLIP. Specifically, the alignment loss is formulated as the inverse of cosine similarity between $e$ and $c$ : $L_{emb} = 1 - \cos(e, c)$ . Overall, we conduct joint training of $\tau_{\theta}$ and $\epsilon_{\theta}$ with the following loss: $L_{total} = L_{noise} + \lambda L_{emb}$ , where $\lambda = 0.5$ represents the weight for balancing different losses. + +Importantly, we differentiate our alignment loss from the losses typically employed in classical language models, which focus on predicting specific word tokens. Our approach loosens the constraint of precisely predicting the exact text instructions. This flexibility empowers our model to explore a wider array of editing solutions, that can augment the source emotions of human viewers to target emotions. Consequently, our model learns to reason in a neuro-symbolic manner akin to humans and preserves its creativity and capacity for exploring novel editing solutions. + +Iterative Emotion Inference (IEI). Editing emotions is a complex process often requiring iterative image edits. To address this, we introduce a recurrent emotion critic process during inference. This critic iteratively infers the evoked + +emotions from generated images while assessing their structural coherence and semantic consistency. Specifically, we employ the emotion predictor $\mathcal{P}$ as the critic. + +In the first iteration of image generation, the source image $I_{s}$ serves as both the input and condition image, producing latent variables $z$ and $z_{t}$ . These, along with the emotion vector $e$ , are fed to the EmoEditor to obtain the generated image $\hat{I}$ . The critic evaluates the generated image quality based on two criteria: (1) the structural similarity (SSIM) between $\hat{I}$ and $I_{s}$ falls within 0.5-0.8, and (2) the predicted emotion by $\mathcal{P}$ on $\hat{I}$ matches the target emotion, with a confidence level exceeding 0.6. If both criteria are met, EmoEditor ceases image generation; otherwise, it continues to generate new images. In subsequent iterations, we use $\hat{I}$ as the input image, generating its noisy latent variable $\hat{z}_{t}$ , with $I_{s}$ remaining as the condition. We use $\mathcal{P}$ to predict the emotional state of $\hat{I}$ as the new source emotional state and calculate the new emotion editing direction to update the emotion embedding $e$ . Based on these new inputs, EmoEditor generates a new edited image for the critic. This process iterates until both criteria are satisfied, or the number of critic iterations exceeds a predefined limit of 30. In the latter case, we select the generated result with the highest confidence level predicted by $\mathcal{P}$ given the target emotion among all past iterations. See Sec S2.5 for more implementation details. + +# 4. Experiment + +Ideally, with source images and their classified emotions, our goal is to generate images evoking the other 7 target emotions. Considering emotional valence, we propose two tasks: within-valence emotion editing and cross-valence emotion editing. This division serves two purposes. Firstly, cross-valence emotion editing is more common in real-world scenarios, like enhancing positive emotions in stressful environments or creating fear in lively settings during Halloween. Secondly, images of the same valence may contain subtle differences challenging for humans to discern. For instance, an amusement park scene might evoke a mixture of excitement and amusement. We randomly select test images from EmoSet [31], ensuring they differ from those in our EmoPair dataset and that each source emotion category is evenly distributed. We then evaluate the competitive baselines and our EmoEditor on the cross-valence emotion editing task, with a total of 2,016 test images. We also present the results of applying our EmoEditor to more challenging emotion editing scenarios. To ensure a fair comparison, the input image size is standardized to $224 \times 224$ across all methods. + +Baselines. We compare our EmoEditor with nine methods: (1) Color-Transfer (CT) [20]; (2) Neural-Style-Transfer (NST) [6]. Both methods require an additional reference image from the target emotion category as input. We randomly select these reference images from the EmoSet + +dataset. We also include representative text-driven image editing models (3) Csty [13]; (4) CtrlNet [36] (5) SDEdit [16]; (6) Ip2p [3] and (7) AIF [28]. We provide these models with the target emotion category as a one-word text prompt, such as "excitement". We also compare with (8) EmoEdit [32], which performs emotion-driven image editing by retrieving semantically similar examples from an emotion dictionary. In addition, we concatenate existing large language and vision models and introduce the baseline (9) "Large Model Series" (LMS). This includes GPT-4o [9] for image captioning, followed by GPT-o4 [18] for generating reasoning-based text instructions, and Ip2p for image editing based on the instructions (See Sec S2.2). + +Human Psychophysics Experiment. We evaluate the generated results of all methods on Amazon Mechanical Turk (MTurk) [26]. We recruit 136 participants, with each participant undergoing 180 trials, yielding a total of 24,480 trials. All the experiments are conducted with the subjects' informed consent and according to protocols approved by the Institutional Review Board of our institution. All participants are properly compensated. In each trial, participants engage in a "two-alternative forced choice" task. They are presented with two image stimuli and must select the one that most strongly evokes the target emotion in them. The two image stimuli consist of a result generated by our EmoEditor and a randomly sampled result from the baselines introduced above. The trial presentation order and the binary choices for each trial are randomized. To assess the quality of data collection, we introduce control trials and use them as filtering criteria. We discard the data from those people who fail the control trials at least $17\%$ of the time. See Sec S2.3 for more details. + +Evaluation Metrics. While CLIP [21] assesses text-image consistency, it does not fully capture emotional complexity [29]. Thus, we introduce Emotional Structure Matching Index (ESMI): $E S M I = \alpha \times S _ { s t r } + ( 1 - \alpha ) \times S _ { e m o }$ where $\alpha$ is a weighting coefficient and set to 0.5. ESMI evaluates emotion-evoked image generation from two aspects: evoking specific emotions and maintaining structural and semantic consistency between the source and generated images. Evoking Targeted Emotions. To assess how well the generated image expresses the target emotion, we use $\mathcal{P}$ to extract emotional distributions $e_{s}$ and $e_{g}$ from the source and generated images respectively. Next, we calculate the Kullback-Leibler Divergence between these distributions and the target emotion's one-hot encoding $e_{oh}$ we get $D_{src} = KLD(e_s,e_{oh})$ and $D_{gen} = KLD(e_g,e_{oh})$ . Ideally, the generated image should emotionally be closer to the target, that is, $D_{gen} < D_{src}$ . To avoid the influence of outliers or extreme values, we define the raw emotional improvement as $\Delta D = \max (0,D_{src} - D_{gen})$ . To further normalize this improvement relative to the original emotional distance, we compute the emotional evocation + +![](images/ce2eb3a86734ca24a5ed2eac42a55759c893b7bca4ad049126b8ef0dd4b0f2df.jpg) +Figure 5. Results from Human Psychophysics Experiments. The proportions of images that human participants prefer our EmoEditor over all other methods on the x-axis are presented. Chance is $50\%$ (red dotted line). Error bars are standard errors. + +score: $S_{emo} = \Delta D / (D_{src} + \epsilon)$ where $\epsilon$ is a small constant to prevent division by zero. This score ranges from 0 to 1, with higher values indicating a greater emotional shift toward the target emotion relative to the source. Preserving Original Structures. We define two regions: the Emotion-Evoking Region ( $R_{emo}$ ), which is responsible for triggering the source emotion (e.g. fire for anger) and is expected to be altered, and the Emotion-Neutral Region ( $R_{neu}$ ), which should remain unchanged. We measure structural consistency by computing the pixel-level L1 differences between the source and generated images in these regions, denoted as $L_{emo}$ and $L_{neu}$ . The structural preservation score is calculated as: $S_{str} = L_{emo} / (L_{emo} + L_{neu} + \epsilon)$ where $\epsilon$ is a small constant to avoid division by zero. This score reflects the proportion of changes in $R_{emo}$ relative to all changed pixels, with higher values indicating better preservation of neutral areas. We adopt two strategies to define $R_{emo}$ : (1) CAM-based: $R_{emo}$ is obtained by applying Grad-CAM [24] to $\mathcal{P}$ and binarizing the resulting heatmap. (2) HA-based: $R_{emo}$ is derived by averaging manually annotated emotional regions of human annotators. See Sec S2.4 for more details. + +# 5. Results + +# 5.1. Evaluation in Cross-Valence Scenarios + +Quantitative Evaluation with SOTA. Figure 5 shows human psychophysics experimental results (see Sec S3.1 for more results). If all methods generate images that elicit target emotions equally effectively, human participants would make random choices, with a $50\%$ chance in the "two-alternative forced choice" tasks. Observing Figure 5, we see that human participants consistently prefer the generated results of our EmoEditor over all competitive baselines, indicating its proficiency in evoking target emotions. Complimentary to psychophysics experiments, Table 1 presents quantitative results in CAM-based and HA-based ESMI, with our EmoEditor achieving the highest scores in both metrics. Notably, for each method, the scores remain consistent across the two evaluation metrics, indicating that the emotion predictor $\mathcal{P}$ + +
ESMI(%) ↑CTNSTCstyCtrlNetSDEditIp2pAIFEmoEditLMSOurs
CAM-based28.3347.4834.3332.9435.9127.3729.7132.9435.4051.56
HA-based26.6846.0032.7731.5334.2725.7228.3137.5333.7649.99
+ +Table 1. Quantitative Evaluation of Generated Images for All Competitive Methods. The CAM-based metric computes ESMI using $R_{\mathrm{emo}}$ , derived by binarizing the Grad-CAM output from the Emo Predictor. The HA-based metric computes ESMI using $R_{\mathrm{emo}}$ , defined as the average of human-annotated regions. Best is in bold. Larger (↑) is better. + +
VariantInput of τθIEILembESMI(%)↑
texteohedir
1✓5.85
2✓✓50.24
3✓✓7.36
4✓✓8.51
5✓✓47.36
6✓✓✓49.80
7 (ours)✓✓✓51.56
+ +Table 2. Quantitative Evaluation in CAM-based ESMI for Model Variants of our EmoEditor. A tick indicates the inclusion of a component in the corresponding model variant, while a blank cell indicates its absence. The last row represents our full EmoEditor model. Best results are in bold. Larger $(\uparrow)$ is better. + +identifies emotion-evoking regions in a manner aligned with human annotations. This consistency further supports the reliability and validity of the CAM-based ESMI metric. + +Our EmoEditor significantly outperforms CT, demonstrating that emotion-evoked image generation requires more than global color adjustments. While NST and Csty can induce negative emotions through distortions and irregular textures, they often reduce image interpretability (see Fig S10). CtrlNet and SDEdit produce abstract textures that may evoke emotion but often fail to preserve the source image's semantics. Human evaluations also prefer EmoEditor over Ip2p, underscoring the limitations of current diffusion models trained for general image generation when applied to emotion-driven tasks. Although both AIF and EmoEdit are designed for emotional editing, our EmoEditor achieves higher human preference and ESMI scores. AIF applies global filters, resulting in less targeted changes. EmoEdit maps image-emotion pairs into an embedding, but the limited and biased emotion dictionary leads to repetitive edits and poor performance on strongly emotional inputs. Finally, our EmoEditor outperforms LMS in both human preference and ESMI, suggesting that simply chaining large models may amplify biases and errors. Emotion-evoked generation demands a nuanced understanding of both the source image and target emotion, making end-to-end learning crucial. + +Model Analysis. We conduct the model analysis and present the results in Table 2. In Row 1, the model variant takes only text as input and follows the structure of Ip2p. Although it is fine-tuned on our EmoPair dataset with the pre-trained CLIP model as $\tau_{\theta}$ , the performance is the lowest among all variants, indicating that text + +![](images/4eab6517d062dbbe2191dae89d89de038ebfe726f067c96fdd88bf969a85058b.jpg) +Source Image + +![](images/64ba54abdaa3dea165f21b7ff8e8a1471c13feea2f291acc53910a68a2ea11c6.jpg) +(a) From anger to excitement + +![](images/002d1165eba1f35b9e722943340cead9a0f2fe01a08e03be2377dc44727117cc.jpg) +NST 11.49 + +![](images/a9858bf75b1484cb483e3255921d6ae6a23aef2c38f749564b53c8120dbb1318.jpg) +AIF 17.39 + +![](images/20fcd4101d3903a894195a7063dc51847f19772070ad3f14383a497cdb2223f1.jpg) +CT 39.16 +EmoEdit 18.79 + +![](images/aad545f1ea01e394ab3d98afaa9235939e24297a59a542a92997bf68ccab1b1d.jpg) +LMS 13.80 + +![](images/98fd5ff487bac8354328b7984fd6c00349ce36bc06fc279859a5fb02b614ece1.jpg) +Ours 61.67 + +![](images/155347737e0c81606d24bbb64151ede91c54bdba996958c01bef316ae8ff2465.jpg) +(b) From amusement to sadness + +![](images/37b5eaa969f12fa3ebccef57ffb84ebd47041d92e73413fb14e565dc62a55731.jpg) + +![](images/9a448c275ac9a90a985cea19fdc442b716a6755ed6c9a30fac77cdb87e4ebba9.jpg) +Figure 6. Visualization of Generated Images from Different Methods. Target emotion is highlighted in red and source image is framed in green. The blue number below each image is its CAM-based ESMI score, with higher values being better. More examples in Sec S3.2. + +![](images/eeea2faee1dd02a34851128fd2b9e84d39f65eaecfe4b2c0484d7a8a6f1a8617.jpg) + +![](images/fabb851e7ae562aa5719040cb0f6fc75a7bc49d31be8bc55fdb39497d8b79f49.jpg) + +guidance is insufficient. Adding IEI (Row 2) results in notable improvements over the version without IEI (Row 1), confirming its contribution to enhancing emotional consistency. Next, replacing the text input with a one-hot encoding of the target emotion $e_{oh}$ (Row 3) leads to a better result, highlighting the advantage of structured emotion encoding over text. Further improvement is observed when replacing $e_{oh}$ with an emotion editing direction $e_{dir}$ (Row 4), suggesting that incorporating information about the source emotion enables more precise and effective editing. Adding the alignment loss $L_{emb}$ (Row 6) improves performance over the variant without it (Row 5), confirming its complementary role in promoting emotionally consistent generation. Our final model (Row 7) integrates $e_{dir}$ , IEI, and $L_{emb}$ , enabling emotion-aware editing based on the source-target gap. This configuration achieves the highest score, demonstrating its superior emotional precision and generative diversity. + +Visualization of Emotional Image Generation across Valence. Figure 1 and 6 present visualizations of generated images in cross-valence scenarios. CT primarily replicates tonal characteristics from a reference image, often failing to significantly enhance emotions. NST relies on randomly + +![](images/737cc292247f91ad9a88d4629879f94b36bd80223f54db03f4eb72e84e3843d4.jpg) +(a) Same-Valence Editing + +![](images/1029588a6f97cafa863c3cc2dd02faccddd419e359be98524c3d78c71e5a814a.jpg) +Figure 7. Our EmoEditor can generalize to more challenging emotion editing scenarios. (a) Same-Valence Editing highlights our EmoEditor's ability to produce images evoking emotions of the same positive valence as the source images. (b) Neutral-Valence Editing demonstrates how our EmoEditor can transform neutral real-world images to evoke positive or negative emotions. (c) Multi-Emotion Editing demonstrates its capability to generate images that evoke a wider range of emotions, providing more nuanced and diverse visual outputs. Source images are framed in green. Target emotions are in red. + +![](images/6bf4c96cf1be5da2de35a9dbf73017f30c2383342746f984b92db958f1052bc3.jpg) +(b) Neutral-Valence Editing + +![](images/bb881074e29968a8e1bfe684196d36642ed4c2fdf1d98c93ad5e780825aef1b1.jpg) + +![](images/45726848c751ce13ef10bbc23e06b5fb48a81d4127f72d05e8897980fe6cc456.jpg) + +![](images/64e0cdd71f16e83b69d20e62454cc772392ae2d6f9ba22319688f4e89990e7e2.jpg) +(c) Multi-Emotion Editing + +![](images/06efc67a56383ca5e7259f460b1f3ee3a3cd97281293e7755bf766633f39d8dd.jpg) + +selected references, producing artistic textures aligned with target emotions but losing essential semantic content. AIF, dependent on emotional text descriptions, applies a global filter effect but struggles with localized editing. EmoEdit relies on fixed learned queries, leading to limited, context-incongruent edits (e.g., always adding balloons for amusement; Figure 1) and failing to edit local emotional cues such as fire flames or fireworks (Figure 6). Even with a richer vocabulary, such as LMS, which integrates three large models, it still struggles to generate desirable outputs. In contrast, our EmoEditor takes only a source image and target emotion as input, yet generates creative and emotionally aligned results while preserving structural and semantic coherence. By learning an emotion editing direction, it understands the source-target gap and applies precise edits. In Figure 6, where fire and fireworks dominate the original emotion, EmoEditor adapts its edits to the target: extinguishing flames and adding mountains to evoke excitement (a), or removing fireworks and darkening tones to convey sadness (b). In Figure 1, it replaces fire flames with lamps to elicit amusement. Notably, even when handling similar anger-inducing elements like fire, our EmoEditor produces diverse, context-aware edits tailored to the source image without any manual design, demonstrating a nuanced understanding of emotional cues. We also show CAM-based ESMI scores (in blue) for each result. Our EmoEditor achieves the highest scores, demonstrating its ability to accurately identify and effectively modify emotion-evoking regions in source images, striking a balance between evoking the target emotion and preserving the original structure. + +# 5.2. Generalization to Real-world Scenarios + +Editing images with the same emotional valence is more challenging due to subtle emotional cues. Figure 7a demonstrates EmoEditor's ability to handle such tasks, as it removes a parachutist to reveal a breathtaking landscape, shifting excitement to awe. In real-world scenarios, some naturalistic images may evoke mixed emotions or no strong emotional responses at all. We challenge our EmoEditor to generate emotion-evoked images using neutral-valence + +source images randomly selected from the MSCOCO dataset [14]. These images depict scenes of everyday life with neutral emotions. EmoEditor applies positive and negative emotion transformations to these source images. It enhances the lushness of a forest to evoke contentment and transforms it into a barren landscape for disgust (Figure 7b). Notably, EmoEditor generates these results purely from its creativity, without any human-annotated editing instructions or scene interpretations. + +Furthermore, EmoEditor can manage multi-emotion editing with the use of emotion encoding as input. We extend the single-target emotion scenario by randomly adding one additional emotion of the same valence as the target and then use EmoEditor for image generation. In Figure 7c, EmoEditor generates a majestic mountain in the flame area of the source image to evoke awe. After adding contentment, it enriches the area with dense forests. + +# 6. Discussion + +We introduce the challenging problem of emotion-evoked image generation and propose EmoEditor, an image diffusion model that understands emotional cues, creates implicit editing instructions aligned with human decisions, and manipulates image regions to evoke emotions, while maintaining coherent scene structures and semantics. Moreover, we contribute EmoPair dataset for model training. To benchmark all methods, we introduce a new evaluation metric that effectively measures the balance between evoking target emotions and maintaining the structural and semantic integrity of the source image. + +While EmoEditor excels in quantitative performance and visual results, it struggles with fine details on faces (See Sec S3.4). While we adopt the 8-category Mikels model, real-world emotions are far more nuanced and complex. In particular, differentiating between positive emotions tends to be more challenging than distinguishing negative ones. 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This rigidity constrains high-performance models trained in resource-rich environments from being efficiently deployed on resource-constrained devices. We hence introduce a novel paradigm for lossless adaptation across scenarios, enabling models to maintain optimal performance under high-resource conditions while seamlessly transferring to low-resource environments. Central to this is Token Optimization (TO), an adaptive inference framework that dynamically samples and selects input token set to optimize input information under varied computational constraints. To support this, we propose Flux, an augmentation tool that enables flexible sampling grids and token selection. It integrates seamlessly into popular video training frameworks, significantly enhancing model robustness and adaptability with negligible additional cost. Applied to large-scale video pretraining, our method produces FluxViT, which achieves state-of-the-art performance across multiple tasks under standard costs. Remarkably, with only 1/4 of the tokens, FluxViT matches prior state-of-the-art models under TO across tasks, achieving nearly $90\%$ computational savings. Code and models are available at https://github.com/OpenGVLab/FluxViT. + +# 1. Introduction + +Video representation learning [20, 45, 71] is a fundamental task in computer vision, as it is critical in developing spatiotemporal perception and procedural reasoning in multimodal large language models [38, 41, 54, 77] and embodied AI systems [24, 78]. However, the deployment of video models is computationally intensive due to the high volume + +![](images/1c0853aa42a0303919f4fbc44443d4798a8228c20d8d20032bd87a5e320ef25a.jpg) +Figure 1. Flux (right) employs flexible sampling and token selection to achieve Token Optimization. Common methods(left) use rigid sampling(and use token reduction for applications directly). + +of video tokens compared to image tokens. Popular video training methods work on fixed-count patched tokens sampled from a predefined spatiotemporal grid (e.g., $8 \times 224^2$ ), leading to considerable redundancy in training and deployment, especially for long, high-resolution videos. Moreover, this inflexible and fixed training achieves sub-optimal results for tasks that require dynamic resolution settings, including restricted computation or emphasizing frame counts rather than frame resolution. Researchers have developed different approaches for better trade-offs. + +First, to fit a limited computation budget in inference, many works [15, 31, 59] use token reduction on the same densely sampled tokens as in training, showing sub-optimal performance. For one thing, there is a trade-off between the complexity (cost) and performance of the token reduction strategy. Current strategies can not perform well with a significant reduction rate. For another, the inflexibly trained models can not generalize with the sparse, masked tokens. + +Second, existing methods for flexible network training, such as Resformer [65] and FFN [88], have demonstrated the efficacy of flexible networks operating at different spatial or temporal resolutions but not both simultaneously. Al- + +though these approaches achieve robust performance across diverse settings, we contend that merely reducing frame counts or resolution under computational constraints fails to optimize token capacity utilization and remains susceptible to redundancy. Notably, FFN exhibits substantial performance degradation when operating with only two frames in their research. We argue that the input token set with a size equal to 2 frames can be optimized. Also, they are not validated in large-scale pre-training to achieve competitive results for real-world applications, and the performance gain with larger resolution input comes with quadratic computation cost increase, which is also insufficient. + +We propose a new perspective of the desired optimal computation-and-accuracy and spatial-and-temporal trade-offs across various settings, termed 'Token Optimization' (TO in short), as shown in Figure 1. It involves selecting an optimized set of input tokens based on budget from more properly sampled videos for information maximization. Since there is no perfect token selector for all settings, we promote a better solution of using flexible sampling, with more densely and finely sampled videos for higher computation and more sparsely sampled videos for lower budget. Spatial and temporal trade-offs are also achieved. + +To better achieve TO, we propose a new data augmentation tool for training flexible video models, termed Flux for Flexibility in universal contexts, by utilizing the combination of flexible sampling and token selector to make training flexible while not introducing costs. We integrate it with the Unmasked Teacher [42] pre-training, supervised-training, multi-modal contrastive training, and chat-centric training to validate its efficiency. Our new recipe brings more robustness caused by Flux augmentation both in standard settings and our TO setting. Two plug-in modules are used for better feature extraction regarding the reduced token set with flexible reduction rates and input spatiotemporal resolutions. We build bottom-up ablation studies in turning the model flexible. The resulting model FluxViT achieves supreme improvements regarding the currently state-of-the-art InternVideo2-Dist series models in fair settings across budgets and across tasks, as in Figure 2. + +Our FluxViT-S outperforms the previous state-of-the-art small-scale model, InternVideo2-S [77], by $2.2\%$ on K400 under standard computation constraints. Moreover, it achieves comparable performance to InternVideo2-S while utilizing only about $10\%$ of inference cost. FluxViTB achieves competitive results with state-of-the-art much larger scale models on various tasks, including scene-based action recognition task [34] $(90.0\%)$ top-1 accuracy on K400), motion-intensive [23] $(75.8\%)$ top-1 accuracy on SSv2), long-term task [64] $(94.1\%)$ top-1 accuracy on COIN), zero-shot text-to-video retrieval [1, 12, 28, 61, 81] $(49.9\%)$ R@1 on MSRVTT, $53.5\%$ R@1 on DiDeMo and $56.7\%$ R@1 on ActivityNet). Notably, it maintains state + +![](images/b7c292fdbdf379deeb3f34615f76f85e135099d17283a572ae582d37a25c38f0.jpg) + +![](images/a4e9a73fb1dc10a5f53b56f8d0aa05453293e4673b3d11228638b812cacb5acc.jpg) +Figure 2. Overview of our Flux method. The same-scaled FluxViT and InternVideo2 [77] series models are both pre-trained with the InternVideo2-1b model as the teacher using the same dataset. The "FluxViT+" refers to the results using Token Optimization at test time with the same GFLOPS. + +![](images/0ce28d2e99d9e6bc1ff2d764b966fe23c04afb46aecc44d4e43b497b8d905120.jpg) + +of-the-art performance among the similar scaled models while using only 1/4 to 1/2 of their tokens, resulting in $70\%$ to $95\%$ savings in computation. On chat centric tasks including MVbench [41] for general perception and Dream-1k [70] for fine-grained caption, our model surpasses widely used SigLIP, CLIP and UMT in 'linear prob' setting across computation budgets, where only the projector between the ViT and LLM is trained for comparability regarding the ViT's capability as the common stage-1 training in chat models. This highlights Flux's strong effect across computation constraints and tasks and underscores the robustness afforded by such flexibility. + +# 2. Related Work + +Flexible Model Training. Many recent studies focus on developing a method to train a single model that performs well across various settings, facilitating seamless adaptation to diverse downstream deployment scenarios. These methods include training a model as a set of shared weights to be pruned for specific tasks [7, 84], as well as optimizing models for varied spatial resolutions [65], frame counts [88], spatiotemporal resolutions [48, 51, 73, 80], patch sizes [6], and representation dimensions [8, 36]. The Resformer [65] and FFN [88] methods propose co-training with three different resolution settings in a single batch, uti + +![](images/102e5ce7acdd753e8603a9a396abb300de00927594960668459d79922bd3acb0.jpg) +Figure 3. Our proposed Flux method with UMT framework. We show that our proposed Flux training is easy to integrate with mainstream video training frameworks. + +lizing self-distillation mechanisms to enhance performance under limited input resolutions for spatial and temporal dimensions, although separately. We argue that they can't achieve optimal performance within constrained computational budgets. Simply reducing frame counts and resolutions is suboptimal. Further, performance gains brought by high-resolution inputs lead to significant cost increases, a challenge also noted in Oryx [51]. Token Optimization addresses this by optimizing the set of input tokens anytime. + +Masked Vision Modeling. Mask has always been seen as a critical method in training and utilizing scaled vision models, especially in the video domain. Previous methods can be mainly divided into two categories. First, drawing insights from the masked language modeling [16, 17, 52], researchers use masks in vision transformer [18] pre-training as a data augmentation strategy, as seen in masked autoencoder frameworks [21, 27, 66, 72] and BERT-like mask-then-predict frameworks [4, 58, 74, 90]. Works like UMT [42], MVP [79], and Milan [29] further utilize such augmentation strategy to predict the CLIP [60] model's feature instead of native pixels as a Teacher-Student pretraining method. Second, methods like MAR [59] and MCM [31] apply masking techniques during the fine-tuning stage and inference to save computation with minimal performance loss. We here propose that mask can be used as novel data-augmentation tool with our flexible sampling to boost performance with our Token Optimization idea. + +# 3. Method + +In this section, we introduce our Flux for effectively pretraining video models that represent videos at varying resolution scales using tokens with flexible quantities robustly. + +# 3.1. Flux-Pretraining + +We begin with a widely adopted pre-training paradigm in which the representations of a teacher model are employed as soft labels for a student model. Popular approaches following this typically rely on fixed sampling grids and utilize all extracted visual tokens for both the teacher and student + +![](images/7695ba9da52af9f9433e6b6696158d750d5a1e5ac767d8069290bba1391b694b.jpg) +Figure 4. Our proposed essential modules for Flux. From the model side, Flux modules include Group-dynamic token selector, dual patch norm, and Global-Local positional embedding. + +models. However, this methodology suffers from substantial redundancy, particularly in video data at finer resolutions. To address this, Unmasked Teacher (UMT) [42] proposes using only a subset of the visual tokens for the student while retaining the full input for the teacher. This masked alignment strategy enhances both efficiency and robustness for the student model. We propose a further examination of the input tokens for the teacher and leverage flexible sampling grids combined with a group-dynamic token selection mechanism. This enables us to select the same number of tokens as the original setting but from a larger pool extracted at flexibly higher spatiotemporal resolutions that are more informative, thus harvesting more diversified and meaningful representations from the teacher without cost, as shown in Figure 3. The other settings, like alignment losses, are the same as the original UMT, which trains the competitive InternVideo2-Series models [77]. + +Flexi-Sampling. For each video in a batch, we randomly select a frame count ranging from $F_{min}$ to $F_{max}$ with a temporal stride $t_s$ and select a spatial resolution between $R_{min}$ and $R_{max}$ with a spatial stride $r_s$ and enforce a threshold $T_{thres}$ in keeping a reasonable size of visual token pool. + +Double Mask Module. To make the training flexible while not introducing new costs, we leverage token selection in the teacher input side. We propose a simple but effective method that prioritizes tokens exhibiting significant changes between frames. We use additional sparse groups for this selection to ensure coverage of the full video and resist several rapid changes in videos, termed Group-Dynamic Selector. Formally, with a pre-defined token count $K$ , which is set to keep unchanged teacher forward cost, and a given tokenized frame sequence $\{F_1, F_2, \dots, F_T\}$ by teacher's patch embedding layer, we uniformly sample it into $N$ sparse groups where $B_i = \{F_t \mid t \in [iB, (i + 1)B - 1)\}, i \in [0, N)$ . In each group, we compute the dynamic value as $\mathrm{D}(F_{t + 1,i}) = ||F_{t + 1,i} - F_{t,i}||_p$ , where $F_{t,i}$ means the value of $i_{th}$ spatial token in the $t_{th}$ frame and $p$ means the $p$ -dim distance. Then we take the top $\left(\frac{K}{N}\right)$ tokens with the highest dynamic values in each group to + +form $K$ visible tokens in total. This selector, along with flexible sampling, is utilized for the teacher model. We also employ another student mask based on the teacher's attention score of CLS token adopted in Unmasked Teacher. The usage of the two masks is referred to as the Double Mask Module. Such a module greatly boosts the student model's performance and brings no additional cost, showing a natural integration of Flux in the UMT framework. + +# 3.2. Flux-Tuning + +For the stage of supervised tuning, we keep the flex-sampling method and group-dynamic selector for the trained student model. Table 1 shows such a method's gain even on a competitive model pre-trained with standard setting, showing Flux as a general augmentation tool. + +Token Optimization As proposed in the introduction, we hope to maximize token information under any given budget, termed as Token Optimization at downstream tasks. Thus, during evaluation, we use a subset of the train-set to find optimized sampling under a given token count for the task. We provide a heuristic searching method in the Appendix, which takes acceptable overhead. + +# 3.3. FluxViT + +Conventional ViT architecture struggles with the variable token numbers, flexible spatiotemporal resolution, and sparsity patterns inherent in Flux training. Thus, we propose two useful plug-in augmentation modules: Global-Local Positional Embedding (GLPE) and Dual Patch Normalization (DPN), as shown in Figure 4. + +Global-Local Positional Embedding. As we utilize flexible sampling with various spatiotemporal resolutions and token reduction rates, it is important to encode the position information of the selected input tokens about where they are from and how they are related. Thus, Global-Local Positional Embedding (GLPE) is utilized. We enhance the global learnable positional embedding, initialized using the sine-cosine method for the maximum possible input size, by applying a Depth-Wise Convolution [30]. Then, to encode local positional information at a finer granularity in the position-invariant attention mechanism, we apply a Linear Projection function (LPE) to the value vector $\mathbf{V}$ . The modified attention is formulated as: + +$$ +\mathbf {Z} = \left(\operatorname {S o f t m a x} \left(\frac {\mathbf {Q K} ^ {T}}{\sqrt {D}}\right) + L P E\right) \mathbf {V}. \tag {1} +$$ + +Such LPE can be generated regardless of the input token number by adding a bias term for the permutation-invariant attention. This is vital in Flux to encode the discrete position information. The Value-dependent nature of LPE is more robust in Flux than others, like RoPE, in that the un-masked tokens are from different places from the source. + +The encoding of the relative relations between them is naturally Value-dependent. RoPE is more useful in scenarios without token selection for length extension. + +Dual Patch Normalization. The Patch Embedding layer plays a crucial role in dynamics estimation and it must be robust to various spatiotemporal resolution distributions. We observed that an additional Layer Normalization after the standard Patch Embedding improves the accuracy of dynamic estimation, leading to more effective token selection. Furthermore, the flexible sampling strategy leads to a varied distribution of input tokens. Consequently, we find the gradient norm of the Patch Embedding layer can become excessively large, as shown in the Appendix. To stabilize training, we introduce a second Layer-Normalization layer before the Patch Embedding operation. + +# 3.4. Train with Varied Input Lengths + +As we aim to train a flexible video model that can seamlessly adjust to varied token numbers according to budgets, we propose to use a multi-number co-training approach. For Flux-UMT frameworks, we suggest utilizing three distinct input numbers within a single batch for the student model. This strategy maximizes the benefits of the extensive teacher-forward computation while enhancing robustness under varying conditions. Specifically, we forward the student three times using three different token numbers and compute the teacher-student alignment loss for each. In standard training frameworks without a pre-trained teacher, we incorporate additional self-distillation, using the final aggregated features with the largest input as the teacher for the intermediate and the intermediate as the teacher for the smallest. We include training efficiency in the ablation. + +# 4. Experiments + +We leverage InternVideo2-1B [77] as the teacher in Flux-UMT due to its strong performance in general video understanding tasks. We use the same data-decomposition and similar training recipe as the currently most competitive InternVideo2-series distilled models as baselines. Note that they are also built using the Unmasked Teacher framework under the supervision of InternVideo2-1B. For notation simplification, we use Flux-Single for Flux training with a single token count and Flux-Multi for Flux training with multi token counts, while Flux-PT is for Flux with UMT pretraining and Flux-FT for supervised tuning. + +# 4.1. Ablation Study + +In the ablation study, we ablate the effect of our Flux through a systematic approach, progressively transforming the original UMT framework into our Flux-UMT and getting our competitive FluxViT. We utilize K710 for pretraining, which integrates the K400 [34], K600 [9], and + +
MethodInput SizeTest Token NumberAvg
307220481024512
\( 8\times 224^2 \)Direct Tuned\( 2\times 224^2 \)∅∅∅69.569.5
\( 4\times 224^2 \)∅∅80.573.677.1
\( 8\times 224^2 \)∅83.981.972.779.5
\( 12\times 224^2 \)84.684.280.969.879.9
\( 16\times 224^2 \)84.583.579.167.078.5
\( 20\times 224^2 \)84.182.777.764.377.2
\( 24\times 224^2 \)83.682.176.462.376.1
Avg84.283.379.468.5-
Max84.684.381.973.6-
2048 fixed countFlux-Single Tuned\( 2\times 224^2 \)∅∅∅68.168.1
\( 4\times 224^2 \)∅∅79.974.777.3
\( 8\times 224^2 \)∅84.382.776.781.2
\( 12\times 224^2 \)85.185.182.875.882.2
\( 16\times 224^2 \)85.485.282.675.382.1
\( 20\times 224^2 \)85.685.182.274.681.9
\( 24\times 224^2 \)85.484.882.074.181.6
Avg85.484.982.074.2-
Max85.6↑1.085.2↑0.982.8↑0.976.7↑3.1-
\( 12\times 224^2 \)Direct Tuned\( 2\times 224^2 \)∅∅∅69.369.3
\( 4\times 224^2 \)∅∅80.572.876.7
\( 8\times 224^2 \)∅83.981.972.779.5
\( 12\times 224^2 \)85.084.380.967.879.4
\( 16\times 224^2 \)84.983.978.965.278.2
\( 20\times 224^2 \)84.783.477.662.477.0
\( 24\times 224^2 \)84.382.676.460.475.9
Avg84.783.679.467.2-
Max85.084.381.972.8-
(3072, 2048, 1024)Flux-Multi Tuned\( 2\times 224^2 \)∅∅∅72.272.2
\( 4\times 224^2 \)∅∅81.079.380.2
\( 8\times 224^2 \)∅84.482.880.382.5
\( 12\times 224^2 \)85.485.283.379.983.5
\( 16\times 224^2 \)85.785.183.579.283.4
\( 20\times 224^2 \)85.785.383.078.983.2
\( 24\times 224^2 \)85.685.082.778.282.9
Avg85.685.082.778.3-
Max85.7↑0.785.3↑1.083.5↑1.680.3↑7.5-
+ +Table 1. Directly use Flux-Tuning with the previsou SOTA InternVideo2-S on K400. Results are reported on K400 using 1clip $\times$ 1crop. It shows that Flux can be used as an advanced augmentation tool directly in supervised tuning scenario. + +K700 [10] datasets with duplicates removed. Performance is evaluated using scene-based K400 and motion-intensive SSv2 [23]. We use 1 clip $\times$ 1 crop for test configurations. For flexible sampling, we set the parameters as follows: $F_{min} = 4$ , $F_{max} = 24$ , $t_s = 2$ , $R_{min} = 168$ , $R_{max} = 252$ , $r_s = 28$ and $T_{thres} = (2048, 4096)$ by default. + +Flux-Single Pre-training and Tuning. Figure 5 illustrates the performance of three models differing in their pretraining and tuning approaches. The first model, termed the FixRes Distilled FixRes Tuned model, employs a fixed resolution of $8 \times 224^2$ during both the pre-training stage and fine-tuning stage, the same as the original setting to get InternVideo2-S. We evaluate this tuned model using a fixed input token count of 2048 by our token selector on + +![](images/488e7e274f11ec5e5ce53767c52d7ad8096e169d076a1e4cdddf7b6cebbecbf7.jpg) +Figure 5. Comparison between different training methods on K400 using a fixed number of 2048 tokens. Note the three lines and all the points share similar training and inference costs. The shaded part shows results for the AnyRes Distilled AnyRes Tuned model with spatial resolution in range (196, 252), while others use a fixed spatial resolution at 224. + +
Mask TypeK400w/ TOSSv2w/ TO
∅ (single res)78.478.465.465.4
Random78.679.0 (↑0.6)65.365.9 (↑0.5)
Tube78.880.0 (↑1.6)65.766.7 (↑1.3)
Dynamic(L1)78.779.8 (↑1.4)65.766.6 (↑1.2)
Dynamic(L2)78.880.0 (↑1.6)65.866.7 (↑1.3)
Group-Dynamic(L2)-278.880.2 (↑1.8)66.067.0 (↑1.6)
Group-Dynamic(L2)-479.280.3 (↑1.9)66.367.3 (↑1.9)
+ +Table 2. Ablation on using token selection strategies We validate the effect of different token selection methods on Flux-Single-Pre-training and Tuning on ViT. A group size of 4 works well. + +the K400 dataset, which corresponds to the number of input tokens in the standard $8 \times 224^{2}$ configuration, but with varied frame counts to assess the model's capability to leverage additional temporal information in fixed-number tokens for enhanced performance. Thus, models trained and tuned with fixed sampling grid can hardly harvest costless performance gain with Token Optimization. + +In contrast, the AnyRes Distilled FixRes Tuned model utilizes Flux-UMT-Single upon the original setting. Through Flux token selection, we maintain consistent pretraining computational costs by regulating a fixed quota of 2048 input tokens. The tuning method also remains unchanged. The diversified features from the teacher by the flexible sampling accumulate more valued representations for the student, gaining a $+0.7\%$ improvement at the original $8 \times 224^2$ test setting. Notably, the new model exhibits greater robustness in processing a fixed number of tokens from larger spatiotemporal resolution, achieving another $+0.3\%$ gain with Token Optimization costlessly. + +We further test tuning the any-res trained model using Flux-FT with a fixed input token number of 2048 on K400, as termed AnyRes Distilled AnyRes Tuned in the figure. As + +
Method & ArchK400w/ TOSSv2w/ TO
Vanilla + ViT78.478.465.465.4
Vanilla + FluxViT79.379.6 (↑1.2)66.066.4 (↑1.0)
Flux-Single + ViT79.280.3 (↑1.9)66.367.3 (↑1.9)
With new positional embeddings
w/ RoPE79.580.7 (↑0.4)66.567.5 (↑0.2)
w/ GPE79.480.5 (↑0.2)66.467.4 (↑0.1)
w/ LPE79.781.0 (↑0.7)66.868.3 (↑1.0)
w/ GLPE79.981.3 (↑1.0)67.068.6 (↑1.3)
With DPN
w/ DPN79.881.2 (↑0.9)66.968.4 (↑1.1)
+ +Combining the two modules + +
Flux-Single + FluxViT80.581.7 (↑3.3)67.669.3 (↑3.9)
Flux-Multi + FluxViT81.482.4 (↑4.0)68.470.0 (↑4.6)
+ +Table 3. Results with $8 \times 224^2$ (and TO w/ 2048 tokens, which is the same token count as in $8 \times 224^2$ ) on K400 and SSv2. ( $\uparrow$ ) for absolute improvement and ( $\uparrow$ ) for relative gain. Vanilla means PT and FT without Flux augmentation. + +
Settings8×22422048 + TO
K400SSv2K400SSv2
Baseline80.567.681.769.3
Change Thres to (2048, 6144)80.167.281.268.7
w/o varied spatial resolution80.567.781.469.1
enlarge Fmax to 3280.467.481.669.1
enlarge Resmax to 33680.267.381.469.0
+ +Table 4. Ablations on hyper-parameter on sampling designs for Flux-Single training with FluxViT. Most settings regarding flexible sampling cause only minor influences except $T_{thres}$ . + +
Pre-training LengthFine-tuning LengthTest Length
20481024512
∅(w/o Flux)∅79.374.762.1
SingleSingle80.577.465.8
SingleMulti(w/ align)80.379.075.0
MultiSingle81.078.870.2
MultiMulti80.979.173.3
MultiMulti(w/ align)81.480.376.6
+ +shown, this tuning method can harvest a $+1.9\%$ top-1 accuracy gain on K400 compared with the normal distilled and normal tuned method while nearly bringing no computation increment throughout pre-training and fine-tuning. + +Table 1 further shows that only combining Flux-Tuning and Token Optimization on a competitive model pre-trained with standard setting can achieve non-trivial gain, highlighting that the sampling and selection module in Flux can effectively serve as novel augmentation tools. + +Token Selection Module. We test four token selection methods for Flux-Single, including random, tube, dynamic + +Table 5. Ablation on using varied input lengths in training FluxViT on K400. Results are tested with fixed $8 \times 224^2$ input but varied test token lengths based on our selector. + +
ModelExtra Data#P(M)GFLOPsTop-1
TimeSformer-L [5]-1212380×380.7
VideoSwin-L [50]IN-21K197604×1283.1
VideoMAE-L [66]-3053958×2186.1
CoVeR-L [87]JFT-3B+SMI4315860×387.1
UniFormerV2-L [39]CLIP-400M+K71035412550×690.0
UMT-L [42]K7104315860×390.6
VideoMAE2-H [72]UnlabeledHybrid6331192×1588.6
ViViT-H [2]JFT-300M6543981×1284.9
MTV-H [82]IN-21K+WTS-60M1000+6130×1289.9
CoCa-G [85]JFT-3B+ALIGN-1.8B1000+N/A×1288.9
MViTv1-B [19]-3770×580.2
MViTv2-B [44]-37255×581.2
ST-MAE-B [21]K60087180×2181.3
VideoMAE-B [66]-87180×1581.5
VideoSwin-B [50]IN-21k88282×1282.7
UniFormer-B [40]IN-1k50259×1283.0
UMT-B [42]K71087180×1287.4
InternVideo2-B [77]K710+MASH96440×1288.4
FluxViT-Be200-97440×1288.7 89.4
49×1284.0 86.7
FluxViT-Be100K710+MASH97440×1289.6 90.0
255×1289.3 89.7
108×1287.3 88.9
49×1284.7 87.4
UniFormer-S [40]IN-1k2142×480.8
MViTv2-S [44]-3564×581.0
VideoMAE-S [66]-2257×1579.0
VideoMAE2-S [72]-2257×1583.7
InternVideo2-S [77]K710+MASH23154×1285.8
FluxViT-Se200-24154×1286.4 87.3
13×1279.7 84.0
FluxViT-Se100K710+MASH24154×1287.7 88.0
83×1287.3 87.7
32×1284.7 86.6
13×1280.1 84.7
+ +Table 6. Comparison with the state-of-the-art methods with on scene-related Kinetics-400. #P is short for the number of parameters. The blue values of FluxViT show results using larger spatiotemporal resolutions but keeping fixed input token count to 3072, 2048, 1024, and 512 respectively, corresponding to the four GFLOPs listed. SMI is short for the train set of SSv2, MiT and ImageNet and MASH for MiT, ANet, SSv2 and HACS. + +(as also directly used in [31]) and our group-dynamic method. We further ablate the token dynamics measurement and the sparse group size. Table 2 shows that our group-dynamic strategy with token dynamics measured by L2-distance of tokens within adjacent frames in sparsely divided four groups is the most robust among the token-selection methods. More advanced token selectors can be utilized for better results but with increased complexity, cost, and tedious hyperparameters. + +FluxViT Modules. Table 3 analyzes the impact of our proposed plug-in modules. The inclusion of Global-Local positional embedding can strengthen the model's robustness when processing sparse tokens derived from larger spatiotemporal resolutions. We compare our GLPE with ROPE [63] within our Flux scheme and show better results + +
ModelExtra DataGFLOPsTop-1Top-5
TimeSformer-L [5]IN-21k2380×362.3-
MViTv1-B [19]K400455×367.770.9
MViTv2-B [44]K400255×370.592.7
VideoMAE-B [66]K400180×669.792.3
VideoMAE-L [66]K400596×674.094.6
UniFormerV2-B [39]CLIP-400M375×370.793.2
UniFormerV2-L [39]CLIP-400M1718×373.094.5
UMT-B [42]K710180×670.892.4
InternVideo2-B [77]K710+MASH253×673.594.4
FluxViT-B440×675.3 75.695.1 95.1
255×675.1 75.594.9 95.1
108×672.0 75.193.3 94.8
49×656.8 73.984.8 94.4
UniFormer-S [40]IN-1K42×367.791.4
VideoMAE-S [66]K60057×666.890.3
InternVideo2-S [77]K710+MASH83×671.593.4
FluxViT-S154×673.4 73.894.1 94.1
83×672.9 73.494.0 94.1
32×670.0 72.593.4 93.8
13×655.3 70.983.7 93.1
+ +with LPE illustrated in the Method section. Furthermore, adding a dual patch norm module optimizes the performance gains in TO. Combining the two modules achieves $+3.3\%$ and $+3.9\%$ on K400 and SSv2 respectively with TO. + +Hyper-parameters of flexi-sampling Table 4 gives ablation studies on the results of different hyper-parameters regarding sampling. Most settings regarding flexible sampling cause only minor influences except $T_{thres}$ . A proper scale of the flexible space is the most powerful. + +Flux-Multi training. We compare our proposed method of co-training with three input numbers(2048, 1024, 512) in both pretraining and tuning in Table 5 and also validate the tuning effects on well-pretrained InternVideo2-S in table 1(3072, 2048, 1024). As shown, pre-training with multiple token numbers can not only boost performance under standard settings but also increase model consistency in input token sparsity. Tuning with different token numbers with a smoothed-L1-loss based self-distillation mechanism can further enhance such alignment consistently. + +# 4.2. Single Modality Results + +We scale up the training data using the K-MASH[77] dataset of 1.1 million samples, aligning with the data employed in the Internvideo2-Distilled series models, including K710, SSv2[23], ANet[28], HACS[89], and MiT[56]. We train the FluxViT model using a total batch size of 2048 for 100 epochs. FluxViT's performance is validated using scene-based K400, motion-intensive SSv2, and long-term COIN with Token Optimization. + +K400. Table 6 reports our results compared with the previous solutions on K400. We set 3072, 2048, and 1024 + +Table 7. Comparison with the state-of-the-art methods with on motion-intensive SSv2. Our model achieves far better results. + +
Modele2eBackBoneTop-1
Distant Supervision [47]XTimeSformer90.0
ViS4mer [32]XSwin-B88.4
Turbof32 [25]✓VideoMAE-B87.5
VideoMamba64 [43]✓VideoMamba-S88.7
VideoMamba64 [43]✓VideoMamba-M90.4
InternVideo2f12 [77]✓InternVideo2-S90.0
MA-LMM [26]✓MLLM93.2
HERMES [33]✓MLLM93.5
FluxViT3072✓FluxViT-S91.8 92.1
FluxViT2048✓FluxViT-S91.5 91.9
FluxViT1024✓FluxViT-S89.8 91.0
FluxViT3072✓FluxViT-B93.9 94.1
FluxViT2048✓FluxViT-B93.7 93.9
FluxViT1024✓FluxViT-B92.5 93.2
+ +Table 8. Comparison with the state-of-the-art on long-form video classification COIN dataset. We report the results based on our preset token number, with the left line using unmasked 12, 8, 4 frames, and 224 spatial resolution while the blue values show results that can be achieved using more informative tokens. + +as our token numbers in Flux-Multi-Tuning. For our FluxViT-S, we report $88.0\% (+2.2\%)$ on K400 compared with InternVideo2-S, which is the previous SOTA solution, while still achieving $84.7\%$ with nearly the same computation as the lightweight network UniFormer [40] but with competitive accuracy. For fair comparison without K-MASH, we pretrain FluxViT using only K400 in Flux-UMT, which also shows much better results. + +SSv2. Table 7 shows our model's performance in dealing with motion-intensive video understanding tasks. Our FluxViT-S and FluxViT-B models set new state-of-the-art performance on SSv2 with either standard or limited computation cost. For FluxViT-B, we achieve $75.6\%$ with standard computation while still achieving $75.1\%$ with only $25\%$ cost of the standard setting. Previous work [88] instead gets a huge performance drop using 2 frames, which corresponds to the least computation listed. + +COIN. Table 8 shows our model's performance in dealing with long-form video understanding tasks. Our FluxViT-S and FluxViT-B models set new state-of-the-art performance on COIN with either standard or limited computation cost. + +# 4.3. Multi Modality Retrieval Results + +We use the pre-trained FluxViT with the CLIP [60] framework and our Flux method to train a video clip model using 27M corpus, far lower than most baseline models, including 25M coarse level caption data: Webvid10M [3], CC3M [62], COCO [46], VG [35], SBU [57], CC12M [11] and 2M high-quality data: S-MiT [55], InternVid-2M-Recap [76]. We leverage MobileClip-B [67] as the text encoder and only use the vanilla VTC loss, which is short for Video-Text Contrastive loss in training. We only unfreeze the ViT projector for the first stage using the 25M coarse + +
ModelMSRDDMANetLSMDCMSVD
Internvideo2-S2048 [77]35.633.734.514.741.8
Frozen-B [3]18.720.2---
VIOLET-B [22]25.923.5---
Singularity-B [37]34.037.130.6--
OmniVL-B [69]34.633.3---
CLIP4Clip-B [53]30.6--13.636.2
UMT-B [42]35.241.235.519.142.3
Internvideo2-B2048 [77]40.340.341.518.749.1
VINDLU-L [14]32.036.930.9--
InternVideo-L [75]40.731.530.717.643.4
UMT-L [42]40.748.641.924.949.0
ViClip-L [76]42.418.415.120.149.1
InternVideo2-L [77]42.142.843.621.4-
LanguageBind-L [91]42.839.738.4-54.1
LanguageBind-H [91]44.839.941.0-53.9
VideoCoCa-G [83]34.3-34.5--
VideoPrism-G [83]39.7-52.7--
VAST-G [13]49.355.5---
FluxViT-S204844.448.352.420.849.4
45.049.352.422.449.7
FluxViT-S102442.245.447.218.748.1
44.549.050.320.548.5
FluxViT-S51236.838.538.217.745.5
40.545.844.719.046.9
FluxViT-B204849.852.256.623.753.8
49.953.556.725.454.2
FluxViT-B102448.048.851.822.652.8
49.153.054.824.153.4
FluxViT-B51242.642.942.820.150.7
47.249.850.322.852.1
+ +caption data for 3 epochs. Then we unfreeze all the modules for the second stage using the 2M high-quality data for one epoch to fully boost the ViT's capacity. By default, we train the clip model with a batch size of 4096. Also, we train the clip model with three input token numbers, 2048, 1024, and 512, and utilize smoothed-L1-loss on the final aggregated vision features to perform self-distillation and compute contrastive loss for each vision feature of the three numbers. Table 9 indicates that the clip model trained with our FluxViT method outperforms the Intervideo2-Series model with a large margin and further surpasses most of the top-performing models in Large or even Giant scale. Results on zero-shot action recognition results are included in Appendix for full validation of FluxViT-CLIP. + +Table 9. Zero-shot text-to-video retrieval on MSRVTT ("MSR"), DiDeMo ("DDM"), AcitivityNet ("ANet"), LSMDC, and MSVD. We only report the R@1 accuracy. The upper line regarding FluxViT shows results with non-masked $8 \times 224^2$ , $4 \times 224^2$ and $2 \times 224^2$ input setting as indicated by the token count while each lower bold line shows results further using more informative tokens. We employ Dual Softmax Loss for the results. + +
Encoder#Tokensw/ TOMVbenchDream1k-F1
Clip-L [60]8×256X45.628.4
SigLIP336-L [86]8×576X46.729.2
InternVideo2-L [77]8×224X47.028.7
SigLIP336-L [86]4×576X44.525.4
UMT-L [42]4×256X45.024.6
FluxViT-L8×25648.329.0
4×256X46.927.9
2×25646.025.6
FluxViT-L204849.0 (↑0.7)29.5 (↑0.5)
1024✓47.7 (↑0.8)28.5 (↑0.6)
51247.6 (↑1.6)27.5 (↑1.9)
+ +Table 10. Results on Chat-Centric benchmarks MVbench (General perception) and Dream1k(Fine-grained caption). Models are trained in a multimodal 'linear prob' setting where both the Encoder and the LLM are frozen. #Tokens for the number of visual tokens by the vision encoder. + +# 4.4. Chat-Centric Evaluation Results + +We scale the pre-trained model size to FluxViT-Large and evaluate its performance under the VideoChat framework. We employ a single-layer MLP projector between ViT and an LLM(Qwen2-7B[73]) and train only the projector to ensure an unbiased evaluation of the ViT's performance, termed 'linear probe' setting in multimodal scenarios. Such a probing strategy is widely used in the Stage-1 training of multi-modal chat models. We utilize a large-scaled trainset including Llava-558K[49], S-MiT, 700k filtered subset of WebVid-10M, VidLN[68], and SSv2-open-ended. We then compare the models' performance on two benchmarks: MVbench, which assesses general spatiotemporal perception capabilities, and Dream1k, which evaluates the model's fine-grained ability to generate detailed captions. The other models tested include CLIP-L, SigLIP-L, and UMT-L, which are widely used in Video MLLMs. Given that ViT and LLM remain frozen, we maintain the original input settings as their pretraining phases to ensure comparability. We will scale the corpus size and fully tune the chat model for full performance in future work. + +# 5. Conclusion and Future work + +We present a token optimization process to maximize information in limited tokens within any budget. It integrates seamlessly with mainstream frameworks, offering a simple and scalable method to enhance real-world applications and facilitate future video foundation models. 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To address this challenge, we propose MamTiff-CAD, a novel CAD parametric command sequences generation framework that leverages a Transformer-based diffusion model for multi-scale latent representations. Specifically, we design a novel autoencoder that integrates Mamba+ and Transformer, to transfer parameterized CAD sequences into latent representations. The Mamba+ block incorporates a forget gate mechanism to effectively capture long-range dependencies. The non-autoregressive Transformer decoder reconstructs the latent representations. A diffusion model based on multi-scale Transformer is then trained on these latent embeddings to learn the distribution of long sequence commands. In addition, we also construct a dataset that consists of long parametric sequences, which is up to 256 commands for a single CAD model. Experiments demonstrate that MamTiff-CAD achieves state-of-the-art performance on both reconstruction and generation tasks, confirming its effectiveness for long sequence (60-256) CAD model generation. + +# 1. Introduction + +Computer-Aided Design (CAD) is a core tool in modern industrial product manufacturing, constructing complex 3D models through parametric command sequences (such as Sketch, Extrusion, and Boolean operations). It not only defines geometric shapes but also thoroughly records design logic and engineering intentions. With the growing demand + +![](images/4cf82f70895fc1e97da4bb4dce3bc3090ea0d629067a0d4ef92bb6929d2d3716.jpg) +Figure 1. Gallery of Generated CAD Designs. Our generative model infers parametric CAD command sequences, enabling the creation of diverse and structurally valid CAD models. The resulting 3D shapes exhibit clean geometry, well-defined features, and full editability, allowing users to modify designs seamlessly. + +for highly complex and long sequence CAD models in industrial design, existing generation methods are limited by computational efficiency and sequence modeling capabilities, making it difficult to effectively handle industrial-grade design processes that contain hundreds of commands. + +The key challenges lie in overcoming the bottleneck of long sequence modeling and enabling the automated generation of complex CAD models. Significant progress has been made in deep learning-based parametric CAD modeling, with Transformer architectures being employed to generate parametric CAD models [42, 45, 46]. While these approaches achieve strong performance in short-sequence command generation, the inherent quadratic complexity of the Transformer's self-attention mechanism limits its scalability to longer sequences [37]. This constraint makes it difficult to model intricate CAD structures, significantly restricting the applicability of existing methods for generating complex CAD models. + +To address these challenges, we propose MamTiff- + +CAD, a novel CAD command sequence generation framework that integrates Mamba+ and Transformer autoencoder with a multi-scale diffusion model. In the autoencoding stage, the Mamba+ encoder optimizes state transitions through a gating mechanism, improving its ability to model long-range dependencies. It works with a non-autoregressive Transformer decoder to reconstruct latent representations of CAD command sequences. Once trained, the encoder maps parametric CAD data into a compact, low-dimensional latent space. In the generation stage, a multi-scale Transformer-driven diffusion model is employed. Through hierarchical denoising, it synchronizes local geometric details with global topological constraints, generating logically coherent latent vectors from Gaussian noise. These vectors are then decoded into executable parametric CAD command sequences. We make following contributions in this paper: + +- proposing a novel autoencoder architecture that combines Mamba+ and Transformer to model long sequence parametric CAD commands. +- proposing a multi-scale diffusion-based CAD sequence generator to fuse local and global topology, improving both generation quality and +- evaluations showing that our approach achieving state-of-the-art (SOTA) performance on a long sequence CAD dataset containing 13,705 samples with sequence lengths ranging from 60 to 256. + +# 2. Related Work + +# 2.1. CAD Model Generation + +Parametric CAD generation has recently shifted from traditional geometric representations to deep learning approaches emphasizing sequence modeling. DeepCAD [42] pioneered the use of a Transformer architecture for autoregressive CAD command generation, but it was constrained to short sequences (length $< 60$ ), limiting its ability to capture hierarchical structures in complex models. Follow-up efforts introduced hierarchical representations to improve generation accuracy. SkexGen [45] proposed a decoupled approach for sketching and extrusion operations, facilitating geometric-topological separation, while HNC-CAD [46] built independent codebooks for rings, sketches, and extrusions via a VQ-VAE [36] framework, enabling multi-granularity control. Nevertheless, these methods still grapple with the quadratic computational overhead of Transformer-based architectures, hindering their ability to generate complex, long-sequence CAD models. + +The rise of multimodal generation techniques has opened new pathways for CAD generation. CAD-MLLM [44] constructed the first multimodal dataset supporting text, image, and point cloud inputs. However, its generative model still faces topological rupture issues in complex geometric over + +lapping regions. FlexCAD [49], by fine-tuning LLMs[13], has achieved controllable CAD generation, but the generated models are relatively simple and do not meet the complex design demands of industrial-grade applications. + +# 2.2. Long-Sequence Modeling Techniques + +A key challenge in long-sequence modeling is balancing computational efficiency with long-term dependency capture. Traditional methods [5, 12] suffer from the problem of vanishing gradients, making it difficult to effectively capture long-term dependencies. While Transformers address this via self-attention, their quadratic complexity in sequence length drives up memory and training costs. To address this issue, sparse attention mechanisms [2, 14, 29, 38] and local window strategies [22, 32, 33] have been proposed. These methods can alleviate computational bottlenecks to some extent. However, they sacrifice global context awareness, which can lead to design logic breakdowns and information loss when processing CAD sequence generation. + +State Space Models [10] offer a novel approach for long-sequence modeling. Mamba [8] incorporates a selective scanning mechanism to achieve long-sequence modeling with linear complexity, demonstrating significant advancements in fields such as audio [3, 16, 40], vision [4, 17, 20, 21], and 3D [19, 39]. However, Mamba's application in the CAD domain remains underexplored. In this work, we adapt Mamba for CAD sequence modeling and refine its structure to better capture long-range dependencies. + +# 2.3. 3D Generation with Diffusion Models + +Diffusion models, as an advanced generative approach, achieve high-quality generation through the process of gradually adding Gaussian noise to the data and then performing denoising in reverse [11]. In the field of 3D generation, diffusion models have been widely applied to tasks such as point cloud to mesh [9, 26] image to 3D reconstruction [23, 28, 34, 43] and CAD model generation [7, 47]. + +Recent studies have made significant progress in combining diffusion models with 3D generation. Generating 3D models through point clouds remains the mainstream method [25, 35, 50]. For example, 3DShape2VecSet[48] proposed a latent set diffusion framework, achieving 3D shape generation and point cloud completion through multiscale feature fusion. DiT-3D[30] is the first Diffusion Transformer architecture designed for 3D shape generation, leveraging the denoising process of DDPM on voxelized point clouds to efficiently generate high-fidelity 3D models. DiffCAD [7] employs diffusion models to learn the probabilistic model of CAD generation and alignment. GetMesh [27] uses a latent set diffusion model to generate meshes from point clouds, while Polydiff [1] uses a discrete denoising diffusion model to process mesh data, generating 3D triangular mesh structures. Diffusion-SDF [18] generates + +![](images/faf100c8a13f3b8ffba6570328d32abd812522bf2cfec80de483dd5d2d61496b.jpg) +Figure 2. The framework of MamTiff-CAD consists of two main steps. In Step 1, an autoencoder integrating Mamba and Transformer architectures is used to learn the latent representation of CAD command sequences. In Step 2, a diffusion-based module is employed to model the generative distribution of the learned latent representations. During inference, the model directly generates latent variables, which are subsequently decoded to reconstruct the CAD command sequences. + +3D shapes via diffusion models, offering flexibility in generating diverse shapes that match textual descriptions. + +Although these methods have shown potential in generating complex 3D structures, they still face challenges when dealing with parametric CAD sequences. Existing methods primarily focus on generating geometric shapes, neglecting the design logic and parametric constraints of CAD models, which makes the generated results difficult to directly apply to industrial design. The MamTiff-CAD framework proposed in this paper is the first to introduce diffusion models into the field of parametric CAD sequence generation. By learning in latent space vectors and combining Mamba's efficient long-sequence modeling capabilities, it significantly enhances the stability of long-sequence generation. + +# 3. Method + +# 3.1. Architecture Overview + +As shown in Figure 2, our MamTiff-CAD architecture consists of two steps. In the first step, we train a autoencoder to encode CAD command sequences into latent representation. The input CAD command sequences is represented as a set of parameterized commands $M = \{m_i\}_{i=1}^{N_c}$ , where $N_c$ is the fixed sequence length set to 256. This CAD first passes through an embedding layer and is then fed into Mamba+ blocks. Afterwards, it undergoes compression via a Compress Block for the convenience of following training, generating a latent vector $Z$ . The Transformer-based decoder takes both a learnable embedding and $Z$ as inputs and subsequently outputs the predicted command sequence $\hat{M} = \{\hat{m}_i\}_{i=1}^{N_c}$ . In the second step, we use diffusion-based + +networks to learn the generation of encoded latent representation $Z$ . During inference, MamTiff-CAD uses the trained diffusion network to generate the latent representation $\hat{Z}$ , which is then decoded into a command sequence using the frozen decoder. + +# 3.2. AutoEncoder for Latent Representation + +Parametric CAD Representation. We follow Deep-CAD [42] to represent each CAD model as a sequence of parametric commands $M = \{(C_1, p_1), \ldots, (C_n, p_n)\}$ , where $C_i$ is a command type and $p_i$ is its associated parameter set. For neural network input, we set the sequence length to 256 and end with the special token $\langle \mathrm{EOS} \rangle$ . For sequences less than 256, we pad the length to 256. Each command's parameters $p_i$ are encoded as a 16-dimensional vector: $\mathbf{p}_i = [x, y, \alpha, f, r, \theta, \phi, \gamma, p_x, p_y, p_z, s, e_1, e_2, b, u] \in \mathbb{R}^{16}$ , where unused entries are padded with -1. Continuous parameters are normalized to a $2 \times 2 \times 2$ cube and quantized into 256 discrete levels to preserve geometric consistency. All parameters are eventually converted to discrete tokens for learning. + +Forget Gate Encoder. To encode CAD commands into the latent space $Z$ , we employ a Forget Gate Encoder. We first embed the parametric representation by considering the command type $C_i$ , parameters $p_i$ , and the command's position within the sequence $pos_i$ . The embedding of each CAD command, $\mathrm{Emb}(m_i)$ , is defined as follows: + +$$ +\operatorname {E m b} \left(m _ {i}\right) = W _ {\mathrm {c m d}} \delta_ {C _ {i}} + W _ {\mathrm {p a}} \cdot \text {f l a t t e n} \left(W _ {\mathrm {p b}} \delta_ {p _ {i}}\right) + W _ {\mathrm {p o s}} \delta_ {i} \tag {1} +$$ + +![](images/de3d4c72fa8f416287c0c280e7bb95e02efa21ce46f28200d1cd27e442cb64e4.jpg) +Figure 3. An overview of our autoencoder architecture. The input CAD command sequence is first parameterized and fused with command, parameter, and positional embeddings. It is then processed through four Mamba+ blocks and mapped to the latent representation $Z$ via a compression bolck. Finally, the Transformer decoder reconstructs the CAD sequence, predicting command types and their corresponding parameters. + +Here, $W_{\mathrm{cmd}} \in \mathbb{R}^{d_E \times 6}$ is a learnable matrix and $\delta_{C_i} \in \mathbb{R}^6$ is a one-hot vector indicating the command type. The system defines six command types. Each CAD command comprises 16 parameters, each quantized into an 8-bit integer. We convert each integer into a one-hot vector of dimension 257, where 256 dimensions correspond to the quantized values and the remaining one dimension indicates that the parameter is unused. Stacking these 16 one-hot vectors forms a matrix $\delta_{p_i} \in \mathbb{R}^{257 \times 16}$ . Then, using the learnable matrix $W_{\mathrm{pb}} \in \mathbb{R}^{d_E \times 257}$ , we embed each parameter individually, flatten the resulting embeddings, and apply a linear transformation via $W_{\mathrm{pa}} \in \mathbb{R}^{d_E \times 16d_E}$ . Finally, $W_{\mathrm{pos}} \in \mathbb{R}^{d_E \times N_c}$ is another learnable matrix, and $\delta_i \in \mathbb{R}^{N_c}$ is a one-hot vector that marks the command's position within the sequence, with $N_c = 256$ being the maximum sequence length. + +We then use four Mamba+ blocks, i.e. optimized SSM-based modules integrated with a forget gate mechanism, as our main encoder block. Specifically, the Mamba+ block employs a dual-branch structure for information processing. The feature transformation branch (b1) extracts sequence features using 1D convolution and SSM blocks, while the gating mechanism branch (b2) generates control signals for information flow using the SiLU activation function. To further enhance the retention of historical information, we introduce a forget gate $\mathbf{G}_f$ as: + +$$ +\mathbf {G} _ {f} = 1 - \mathbf {G} _ {b 2} \tag {2} +$$ + +$\mathrm{G}_{b2}$ is calculated using the Sigmoid function, controlling the flow of current input information. The forget gate $\mathrm{G}_f$ , modulates the output $x^{\prime}$ from $b1$ , ensuring that some historical information is not completely discarded. The updated historical information is given by $x^{\prime \prime} = \mathrm{G}_f\cdot x^{\prime}$ . The final output of Mamba+ blocks integrates the SSM computation result with the feature adjusted by the forget gate $h_\mathrm{out} = x'' + h_{\mathrm{SSM}}$ . This design enables the Mamba+ block to effectively extract new features while preserving long-term dependencies, enhancing its ability to process complex CAD command sequences efficiently. + +To efficiently encode long sequence CAD commands, we construct the Mamba+ block by stacking four layers of Mamba+ blocks, capable of modeling CAD command sequences ranging from 60 to 256 in length. The encoder first converts the input command sequence $M = \{m_{1}, m_{2}, \ldots, m_{256}\}$ into continuous representations through an embedding layer, then progressively captures local and global dependencies through hierarchical processing in the Mamba+ blocks. + +Decoder. We employ a Transformer-based decoder, which consists of four blocks, to reconstruct parametric CAD command sequences. The decoder's input comprises two parts: 1) a latent vector $Z$ , and 2) a set of learnable embedding vectors produced by a learnable embedding layer, which provides a representation for each position in the sequence. In our model, the maximum sequence length is set to $N_{c} = 256$ . The decoder processes these inputs layer by layer to capture global dependencies among commands in long sequences and ultimately generates the predicted CAD command sequence $\hat{M} = \{\hat{m}_1, \hat{m}_2, \dots, \hat{m}_{256}\}$ , where each command $\hat{m}_i$ consists of a command type $\hat{C}_i$ and parameters $\hat{\mathbf{p}}_i$ . Our objective is to maximize the generation probability: + +$$ +p (\hat {M} \mid z, \Theta) = \prod_ {i = 1} ^ {N _ {c}} p \left(\hat {C} _ {i}, \hat {\mathbf {p}} _ {i} \mid z, \Theta\right) \tag {3} +$$ + +Here, $\Theta$ denotes the decoder's network parameters. Finally, the decoder's output hidden states are mapped through a linear transformation layer into the specific command type and parameter space, thereby completing the generation of the entire CAD command sequence. + +Training of the Autoencoder. We train our autoencoder by reconstructing parameterized CAD command sequences to learn the latent representation $Z$ of CAD models. The training objective is to minimize the discrepancy between the predicted outputs and the ground truth, ensuring that the model accurately captures the structural information of the parameterized CAD sequences. We employ a cross-entropy loss function to supervise the learning of both CAD command types and parameters. + +Our output sequence is fixed to $N_{c} = 256$ commands, each with $N_{p} = 16$ parameters. For the $i$ -th command, the + +ground truth command type is denoted by $t_i$ (derived from the true command $C_i$ ), and the corresponding ground truth parameters are represented as $\{a_{i,j}\}_{j=1}^{N_p}$ (where each $a_{i,j}$ is an element of the previously defined parameter vector). The model predicts a probability distribution over command types $p_i$ such that $p_i(t_i)$ represents the probability assigned to the true command type, and for each parameter $a_{i,j}$ , it predicts a probability distribution $q_{i,j}$ over quantized parameter values. The total loss is defined as: + +$$ +L = \sum_ {i = 1} ^ {N _ {c}} \ell \left(p _ {i} \left(t _ {i}\right)\right) + \beta \sum_ {i = 1} ^ {N _ {c}} \sum_ {j = 1} ^ {N _ {p}} \ell \left(q _ {i, j} \left(a _ {i, j}\right)\right) \tag {4} +$$ + +where $\beta$ is set to 2 to balance the parameter loss against the command type loss. Contributions from padding commands, such as the $\langle \mathrm{EOS} \rangle$ token, and unused parameters labeled as $-1$ are ignored during loss computation. For further details on the experimental configurations, please refer to the Appendix. + +# 3.3. Diffusion Generator + +The above frozen autoencoder encodes the command sequences into a compact latent variable $Z \in \mathbb{R}^{N \times 256 \times 64}$ . In the forward process, we employ a linear variance schedule $\{\beta_t\}$ to add noise into the latent space, while the denoising process is guided by a Multi-Scale Transformer-based Diffusion Generator (MST-D), as shown in Figure 4. + +Multi-Scale Transformer Denoiser. The denoising network is composed of stacked multi-scale Transformer layers, each following a three-stage pipeline: Hierarchical Attention: Each layer contains three parallel attention branches with window sizes of 64, 128 and 256 to capture local geometric constraints, medium-range topological dependencies, and global semantic coherence respectively, processing the latent sequence at three different scales. Adaptive Fusion: The outputs of these attention branches are concatenated and fused via a learnable gating mechanism: + +$$ +\mathbf {H} = \operatorname {M L P} \left(\sigma \left(\mathbf {W} _ {g} \left[ \mathbf {H} _ {l} \| \mathbf {H} _ {m} \| \mathbf {H} _ {g} \right]\right) \odot \left[ \mathbf {H} _ {l} \| \mathbf {H} _ {m} \| \mathbf {H} _ {g} \right]\right) \tag {5} +$$ + +where $\sigma(\cdot)$ is the sigmoid function, and $\parallel$ denotes concatenation. Time-Step Embedding: This module inputs temporal information into each Transformer block by transforming the diffusion time step $t$ into an embedding vector. The embedding is then processed through an MLP to generate two sets of scale and shift parameters $\{\xi_i, \psi_i, \omega_i\}$ . Here, $\xi_i$ and $\psi_i$ modulate the layer-normalized activations, while $\omega_i$ adjusts the strength of the residual connections. Together, these parameters enable the Transformer to adapt its behavior in a time-aware manner. + +Sequence-Aware Positional Encoding. To preserve the sequential logic of CAD commands, we employ a scalable si + +![](images/75f5e5c4338b6976733c73cf42388d79c4f147affc4a779f125b0ab176c2663a.jpg) +Figure 4. Our denoising diffusion model. The input noise undergoes linear projection with positional and timestep embeddings, followed by feature extraction through encoder blocks $(\times 6)$ . The core denoising structure, MST with Adaptive Fusion, integrates multi-scale attention and adaptive fusion to dynamically adjust feature distributions. Finally, the MLP Head reconstructs the denoised output features. + +nusoidal positional encoding $PE$ , defined as + +$$ +P E (Z) = Z + \eta \cdot \operatorname {P E} (\operatorname {p o s}, D) \tag {6} +$$ + +where $\eta \in \mathbb{R}$ is a trainable scalar that adaptively adjusts the positional weighting. Instead of writing the full vector in one long equation, we define the positional encoding function piecewise as follows: + +$$ +\mathrm {P E} _ {2 i} (\text {p o s}, D) = \sin \left(\frac {\text {p o s}}{1 0 0 0 0 ^ {2 i / D}}\right) \tag {7} +$$ + +$$ +\mathrm {P E} _ {2 i + 1} (\operatorname {p o s}, D) = \cos \left(\frac {\operatorname {p o s}}{1 0 0 0 0 ^ {2 i / D}}\right) +$$ + +for $i = 0,1,\dots ,\frac{D}{2} -1$ . Here, pos denotes the sequence position, and $D$ is the embedding dimension. This encoding scheme provides both absolute and relative position information, enabling the model to capture the sequential dependencies of CAD commands more effectively. + +Training and Generation. The denoising network learns to predict the noise injected at each timestep, modeling the distribution of the target latent space. Given a clean latent vector $Z_{0}$ from the frozen encoder, we first sample a timestep $t \sim U(1,T)$ and add noise according to the linear variance schedule $\{\beta_t\}$ : + +$$ +Z _ {t} = \alpha_ {t} Z _ {0} + \sqrt {1 - \alpha_ {t}} \epsilon \tag {8} +$$ + +where $\epsilon \sim \mathcal{N}(0,I)$ , $\alpha_{t} = \prod_{s=1}^{t}(1 - \beta_{s})$ controls the rate of noise accumulation. The network $\epsilon_{\theta}$ is then trained to predict $\epsilon$ by minimizing the mean squared error: + +$$ +L _ {\text {d i f f}} = \mathbb {E} _ {t, Z _ {0}, \epsilon} \left[ \| \epsilon - \epsilon_ {\theta} (Z _ {t}, t) \| _ {2} ^ {2} \right] \tag {9} +$$ + +Table 1. Statistical comparison between the DeepCAD dataset and our ABC-256 dataset, including the total number, the average length of parametric CAD sequences, and the length distribution. + +
DatasetTotalAverage Length1-1011-6061-128129-256
DeepCAD178,2381544.5855.42--
ABC-25613,70599--82.8917.11
+ +Sampling Process: Starting from Gaussian noise $Z_{T}$ , the latent vector is iteratively denoised using: + +$$ +Z _ {t - 1} = \frac {1}{\alpha_ {t}} \left(Z _ {t} - \beta_ {t} \frac {1}{\sqrt {1 - \alpha_ {t}}} \epsilon_ {\theta} \left(Z _ {t}, t\right)\right) + \beta_ {t} z \tag {10} +$$ + +where $z \sim \mathcal{N}(0, I)$ . Here, $\alpha_{t}$ and $\beta_{t}$ denote the attenuation factor and variance schedule parameter at timestep $t$ , respectively. Through this process, our diffusion generator progressively removes noise in the latent space to yield CAD command sequences with global consistency and rich structural information. + +# 4. ABC-256 Dataset + +Although several publicly available CAD datasets exist, such as ABC [15], DeepCAD [42], Fusion 360 Gallery [41], and CAD as Language [6], datasets that fully capture the CAD design process remain scarce. The ABC dataset contains 1 million B-rep models from Onshape [31], but lacks design operation sequences, making full process reconstruction difficult. The Fusion 360 Gallery dataset provides CAD command sequences based on sketch profile extrusions, but these sequences are short, limiting their suitability for long sequence CAD generation. DeepCAD includes 178,238 CAD models with parameterized sequences, but its maximum sequence length of 60 constrains its ability to model complex, long sequence CAD designs. + +To address this, we constructed and publicly released a complex CAD command sequence dataset to advance research in this field. Using ABC dataset model links, we leveraged the Onshape API and FeatureScript to extract CAD commands from CSG representations and convert them into parameterized sequences. We then filtered models to retain only those with complete operations, excluding simpler cases with only sketching and extrusion, ensuring sequence lengths between 60 and 256. The final dataset includes 13,705 CAD models, split into 10,964 for training, 1,370 for validation, and 1,371 for testing. Compared to DeepCAD, our dataset has a $6.6 \times$ longer average sequence length (Table 1), offering greater complexity in both length and distribution, making it more suitable for long sequence CAD model generation. + +# 5. Experiment + +# 5.1. Implementation details + +We implemented the MamTiff-CAD model based on the PyTorch framework and completed the training of the model on an NVIDIA RTX 4090 GPU. During training, we adopted the AdamW optimizer [24] with an initial learning rate of 0.001, applying linear warmup for the first 2000 steps. Additionally, we introduced gradient clipping to prevent gradient explosion issues. The training of MamTiff-CAD is divided into two stages. The first stage involves training for 300 epochs with a batch size of 32. In the second stage, training for 200,000 epochs with a batch size of 64 to ensure the model has enough time to fully learn and reach convergence. + +# 5.2. Evaluation Metrics + +We comprehensively evaluate the performance of the autoencoder using five metrics, including Command Accuracy, Parameter Accuracy, Median Chamfer Distance, Invalid Ratio, and Step Ratio. + +Command Accuracy $(\mathrm{ACC_c})$ : the match between the predicted CAD command type and the ground truth. +- Parameter Accuracy $(\mathrm{ACC_p})$ : the match of command parameters under the condition that the command type is correctly predicted. +- Median Chamfer Distance (MCD): the geometric error between the reconstructed 3D shape and the reference shape, computed as the median distance between corresponding points. +- Invalid Ratio (IR): the proportion of CAD models that cannot be converted into point clouds. +- Step Ratio (SR): the proportion of generated CAD sequences successfully converted to the STEP format. + +For the performance evaluation of the generator, we adopt six metrics, including Coverage (COV), Jensen-Shannon Divergence (JSD), Minimum Matching Distance (MMD), Novelty, Uniqueness, and Step Ratio. The specific metric descriptions are as follows: + +- Coverage (COV): whether the generated data covers the distribution of real data. +- Jensen-Shannon Divergence (JSD): the difference between the generated data distribution and the real data distribution. +- Minimum Matching Distance (MMD): the minimum average distance between generated and real samples. +- Unique: the proportion of non-duplicate samples in the generated dataset. +- Novel: the proportion of samples in the generated dataset that do not appear in the training set. + +![](images/e84d3b4b318b40340d01c889094e33aa7b491693eb80674b13d822dedf0693ac.jpg) +Figure 5. This figure compares the CAD models generated by DeepCAD, SkexGen, HNC-CAD, and MamTiff-CAD, highlighting differences in shape complexity and geometric details among the methods. It can be observed that MamTiff-CAD produces models with higher structural integrity and greater complexity. + +# 5.3. Autoencoding Parametric CAD + +To comprehensively evaluate the effectiveness of our proposed MamTiff-CAD framework, we conducted a comparative analysis across multiple models, including DeepCAD, MT-CAD, MLSTM-CAD, and our own model. Among them, MT-CAD integrates Mamba with Transformer, while MLSTM-CAD combines Mamba with LSTM. Experimental results confirm that our framework offers significant advantages in long sequence parametric CAD modeling, further reinforcing the rationale behind our design decisions. + +Results. The experimental results are presented in Table 2. Overall, our model achieves SOTA performance across all evaluation metrics. Specifically, our proposed MamTiff-CAD attains a command accuracy of $99.99\%$ and a parameter accuracy of $99.93\%$ , demonstrating superior capability in long command sequence prediction. In terms of Median Chamfer Distance (MCD), MamTiff-CAD outperforms other baseline models, indicating that the reconstructed 3D shapes are geometrically closer to the reference data. Invalid Ratio and Step Ratio, our model achieves an IR of $8.50\%$ and a Step Ratio of $93.93\%$ , indicating a higher proportion of valid command sequences, thereby demonstrating the reliability of MamTiff-CAD. Furthermore, Figure 6 provides a visual comparison of CAD sequence re + +Table 2. Autoencoding performance on ABC-256 dataset. Comparison of MamTiff-CAD and other models in CAD sequence reconstruction. MCD is multiplied by $10^{3}$ , and $\mathrm{ACC}_c$ , $\mathrm{ACC}_p$ , and IR are multiplied by $100\%$ . + +
MethodACCc↑ACCp↑MCD↓IR↓SR↑
DeepCAD92.2475.9341.0233.11%70.46%
MT-CAD89.7266.87121.3539.89%63.97%
MLSTM-CAD86.0965.55112.8942.53%59.85%
OURS99.9999.930.758.50%93.93%
+ +Table 3. Quantitative evaluation of generalization ability on the Fusion360 reconstruction dataset. + +
MethodACCc↑ACCp↑MCD↓IR↓SR↑
DeepCAD93.3577.99104.7619.41%82.57%
MT-CAD91.8560.18300.2111.81%90.17%
MLSTM-CAD88.4262.13261.8023.39%80.97%
OURS99.9997.991.445.70%95.16%
+ +construction results across different models. MamTiff-CAD produces CAD models with better structural integrity and geometric accuracy, making them closer to the ground truth. This further validates the superior performance of MamTiff-CAD in long sequence parametric CAD prediction. + +Generalization Performance. To evaluate the generalization capability of MamTiff-CAD, we trained the model on the ABC-256 dataset and directly tested it on the Fusion360 dataset, which was not used during training. The Fusion360 dataset consists of approximately 8,000 parametric CAD sequences derived from Autodesk Fusion 360 designs. Although the CAD models in the Fusion360 dataset exhibit simpler structures, which narrows the performance gap between MamTiff-CAD and the baseline models in certain metrics, MamTiff-CAD still consistently outperforms all other models across all evaluation metrics, achieving the best overall performance (see Table 3). + +# 5.4. Unconditional Generation + +We comprehensively evaluated latent vector-based CAD generation across several models, including DeepCAD, SkexGen, HNC-CAD, and our MamTiff-CAD. Each method randomly generated 10,000 samples, which were converted to point clouds for metric-based evaluation. The experimental results in Table 4 indicate that our method achieves state-of-the-art (SOTA) performance in all metrics, particularly excelling in JSD (3.19) and Step Ratio + +![](images/398ad3a7a21a1d26e0404eb7e920ffe6ecbf54a9ecc5462db3698a82691ec98c.jpg) +Figure 6. Visual illustrations of CAD sequence reconstruction. GT represents Ground Truth, and Ours refers to MamTiff-CAD. The symbol $\emptyset$ indicates an invalid CAD sequence, resulting in the failure of 3D shape construction. + +Table 4. The unconditional generation result compared with Deep-CAD, SkexGen, HNC-CAD and ours. + +
MethodMMD ↓JSD ↓COV ↑Unique ↑Novel ↑SR ↑
DeepCAD2.666.4956.66%75.888.023.96%
SkexGen2.314.5357.76%80.596.975.26%
HNC-CAD1.634.2562.03%89.291.880.86%
OURS1.323.1965.31%99.699.485.38%
+ +(85.38%), demonstrating the higher quality and effectiveness of the generated sequences. Furthermore, as shown in Figure 5, MamTiff-CAD generates more complex CAD models compared to other methods, further validating its advantage in long sequence CAD generation tasks. + +# 5.5. Ablation Studies + +We conducted two ablation studies to systematically assess the impact of the two key techniques, Mamba+ and MultiScale Transformer (MST), on our model's performance. + +Mamba+ Block. To investigate the role of the Mamba+ block in reconstructing long sequence parametric CAD commands, we conducted two ablation experiments: (1) replacing the Mamba+ block with Transformer block, and (2) replacing the Mamba+ block with the standard Mamba block. The experimental results (see Table 5) indicate that, compared to the standard Mamba block, the Mamba+ block achieves improvements across most evaluation metrics. This confirms that the incorporation of the forget gate mechanism enhances the model's ability to capture long-range dependencies in CAD command sequences, with particularly notable improvements in common CAD sequence tasks over the Transformer-based approach. + +MST or Non-MST. To assess the impact of MST on our generative model, we conducted an ablation study by randomly generating 10,000 models and comparing the generation capabilities with and without the MST module. The experimental results in Table 6 demonstrate that incorporating MST significantly improves model performance, partic + +Table 5. Comparison of reconstruction performance between Mamba and Mamba+ block for parametric CAD sequences. + +
MethodACCc↑ACCp↑MCD ↓IR ↓SR ↑
Transformer77.2963.6264.3067.46%34.28%
Mamba99.9899.900.7610.35%92.01%
Mamba+99.9999.930.758.50%93.93%
+ +Table 6. The unconditional generation result compared between w/o MST and MST. + +
MethodMMD ↓JSD ↓COV ↑Unique ↑Novel ↑SR ↑
w/o MST1.474.9261.69%99.599.677.05%
w/ MST1.323.1965.31%99.699.485.38%
+ +ularly in terms of generation quality and validity, confirming the critical role of MST in the diffusion process. + +# 6. Discussion and Conclusion + +Although MamTiff-CAD has demonstrated exceptional performance in long-sequence parameterized CAD modeling tasks, several limitations remain that warrant further investigation. Firstly, the dataset used in this study does not cover all CAD command types in industrial design, which somewhat limits the model's ability to handle more complex topological structures. Secondly, this research primarily focuses on the generation and parsing of CAD command sequences and does not directly extract features from Boundary Representation (Brep). Therefore, future research is required to address how to effectively integrate CSG (Constructive Solid Geometry) and Brep representations to enhance the model's generalization ability and applicability. This remains a challenging but promising direction. + +In conclusion, this paper presents MamTiff-CAD, a novel framework that integrates an improved Mamba module with a diffusion model to efficiently model long parameterized CAD command sequences and generate complex 3D shapes. We also introduce a dataset of 13,705 CAD models with sequence lengths of 60 to 256, significantly surpassing existing datasets. Experimental results validate MamTiff-CAD's superiority in sequence reconstruction and generation. Future work will focus on refining the model and exploring its integration with advanced design processes and interactive methods to enhance intelligent CAD design. + +# Acknowledgments + +This research was funded by the Fundamental Research Funds for the Central Universities, the Natural Science Basic Research Program of Shaanxi Province under Grant 2024JC-YBQN-0702 and NUS Research Scholarship. 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Traditional manual calibration methods are often time-consuming, labor-intensive, and may require road closures. This paper proposes MamV2XCalib, the first V2X-based infrastructure camera calibration method with the assistance of vehicle-side LiDAR. MamV2XCalib only requires autonomous vehicles equipped with LiDAR to drive near the cameras to be calibrated in the infrastructure, without the need for specific reference objects or manual intervention. We also introduce a new targetless LiDAR-camera calibration method, which combines multi-scale features and a 4D correlation volume to estimate the correlation between vehicle-side point clouds and roadside images. We model the temporal information and estimate the rotation angles with Mamba, effectively addressing calibration failures in V2X scenarios caused by defects in the vehicle-side data (such as occlusions) and large differences in viewpoint. We evaluate MamV2XCalib on the V2X-Seq and TUMTraf-V2X real-world datasets, demonstrating the effectiveness and robustness of our V2X-based automatic calibration approach. Compared to previous LiDAR-camera methods designed for calibration on one car, our approach achieves better and more stable calibration performance in V2X scenarios with fewer parameters. The code is available at https://github.com/zhuyaoye/MamV2XCalib. + +# 1. Introduction + +In recent years, due to the inherent limitations of on-board perception systems, many researchers have started focusing on utilizing external sensor information to assist autonomous vehicles [5, 10]. Among these external sources, infrastructure cameras are widely used in V2X systems + +![](images/b05421792a77790f1c70539ea64d72b7db36d7e6ebe29ab416da0cdaecae6fae.jpg) +(a) Calibration with targets in ing trajectory or vehicle itself + +![](images/913811fe8bb880274fa7c2e77220d2609418b4dd60954033040cfce9ef0dff25.jpg) + +![](images/0ee347861dcef5dde3174568b8f9ebce7e48cabf92219ecaec9e9972267f47f3.jpg) +(b) Calibration with reference images prepared before calibration +(c) Ours: V2X-based target-less camera calibration method +Figure 1. Comparison of roadside camera calibration methods. + +for their wide deployment, broader field of view, and reduced occlusion [24]. However, outdoor deployment exposes roadside cameras to extreme weather and vibrations from large vehicles, causing shifts from their initial positions. If not recalibrated, such shifts can significantly degrade the accuracy of data fusion between road and vehicle sensors. In cases of large deviations, they may even result in a complete loss of monitoring over the intended area [38]. Therefore, efficient, scalable calibration methods are essential for stable intelligent transportation systems in outdoor environments. + +Traditional calibration methods [32, 39] primarily rely on manual targets, but unlike vehicle sensors that can be calibrated indoors, fixed roadside cameras cannot be relocated. As the demand for camera calibration increases, these manual methods become time-consuming and labor-intensive and may cause disruptions to regular traffic operations. Re- + +cent efforts focus on automated calibration [7, 30, 40]. Some methods use autonomous vehicle trajectories or vehicle detection targets. However, these approaches heavily depend on the accuracy of trajectory prediction and object detection, while overlooking rich background data. Other methods require the preparation of reference images or use real-world map images, employing virtual cameras aligned with these images as reference objects [6]. Preparing a series of reference images for each camera is both inconvenient and lacks real-time adaptability. + +Whether traditional or modern methods, determining the position of a sensor in the world coordinate system requires two key conditions: known reference objects and the sensor's perception of these objects. In road scenarios, autonomous vehicles, being high-quality intelligent agents, possess real-time, robust capabilities to collect environmental data and accurately localize themselves. Given this, can we invert the typical V2X process, using a vehicle's perception data to treat the entire environment as a reference, thereby calibrating multiple roadside cameras as the vehicle moves? + +We propose a novel V2X-based calibration algorithm that fuses vehicle-mounted LiDAR point clouds with roadside camera images. A neural network is then used to regress the camera's rotation deviation relative to its initial position. Unlike vehicle cameras, roadside cameras are typically hinge-mounted on infrastructure, limiting significant translational shifts. Minor deviations (centimeterscale) have negligible impact on perception in V2X scenario [26, 35], whereas small rotational shifts, given the wider field of view, greatly degrade image quality (see Sec. 4.5). Thus, our primary focus is on the rotational deviation relative to the initial setup. + +Inspired by the optical flow estimation [29, 33] and lidar-camera calibration task [17, 21], we project vehicle LiDAR point clouds onto roadside camera images to generate a depth map. Then, using a ResNet + FPN (Feature Pyramid Networks) [18], we extract multi-scale features to form a 4D correlation volume. We iteratively update a $2 \times H \times W$ feature matrix representing pixel-level correspondences between the depth map and the RGB image, using this matrix to associate new features from the 4D correlation volume. Our Mamba architecture further integrates spatial and temporal data, combining time-series information with feature matrices from prior iterations to overcome single-frame perception limitations. We divide the training process into two stages which will be explained in Sec. 4.2. + +Compared to traditional roadside camera calibration methods, our approach fully utilizes environmental data, including but not limited to the vehicle itself. Meanwhile, it allows calibration at any road location as needed, without any pre-prepared reference equipment or images for these cameras, making it highly deployable. Compared to the ex + +isting LiDAR-camera calibration algorithms used on a single vehicle, our carefully designed network mitigates the issue of point clouds collected by vehicles in different frames occupying a relatively small and uncertain area in the roadside camera's view, delivering robust calibration results in V2X scenarios with fewer parameters. + +Our main contributions are summarized as follows: + +- To the best of our knowledge, we are the first to propose a target-less V2X-based roadside camera calibration solution. +- We designed a novel calibration network that combines multi-scale processing, iterative updates, and the mamba architecture to address the instability issues encountered when directly applying traditional LiDAR-camera calibration methods to V2X scenarios, while also improving calibration efficiency. +- We validated the effectiveness and robustness of our method on the V2X-Seq [37] and TUMTraf-V2X [43] datasets. + +# 2. Related Works + +Roadside camera calibration: A classic approach to roadside camera calibration is target-based calibration, typically using checkerboard patterns or other reference objects [39]. However, this method demands extensive manual effort and is impractical in busy traffic scenarios. To address this, some studies leverage vehicle-provided positioning or motion trajectories, aligning them with detection boxes [28, 30] or estimated trajectories [40] from roadside cameras. While eliminating the need for placing specific targets, these approaches depend heavily on detection accuracy, leading to error accumulation. Other methods exploit road geometry, such as vanishing points [12], or match perspective features like parallel curves [4], but suffer from limited accuracy in complex scenes. More recent work utilizes prepared reference images or 3D reconstructions of road environments [2, 6, 31], which are labor-intensive to collect and unsuitable for real-time deployment. Co-CalibNet [36] introduces additional roadside sensors, but this increases roadside deployment costs and calibration workload. To overcome these limitations, we propose a fundamentally different, target-less calibration framework that utilizes vehicle sensor data to assist roadside camera calibration without relying on physical targets, vision-based detection, or pre-built scene representations. + +LiDAR-camera calibration: LiDAR-camera calibration methods can be broadly categorized into target-based and target-less methods [17]. Traditional methods typically rely on specific calibration targets, such as checkerboards, spherical markers, or custom boards, transforming the calibration problem into an optimization problem. Recent research has shifted towards target-less methods, primarily applied to extrinsic parameter estimation for monoc + +ular camera and LiDAR systems on a single car. Li et al. [16] categorizes target-less calibration methods into four types: information-theoretic, feature-based, ego-motion-based, and learning-based approaches. Among these, deep learning methods have garnered widespread attention due to their promising results. RegNet [25] was the first to adopt a deep learning-based approach, using a network to extract features and then regress the parameters. CalibNet [11] introduced a geometry-supervised deep network to perform real-time calibration by maximizing geometric and photometric consistency. LCCNet [21] and CaLiCaNet [23] utilized cost volume to establish correspondences between features, which significantly improved upon previous deep learning-based calibration methods. Zhu et al. [41] use depth estimation to mitigate the modal differences. The latest researches [14, 34] attempt to enhance the form of cost volume using new architectures like Transformer. However, these deep learning-based methods perform poorly in V2X scenarios. That's because vehicle-mounted LiDAR often covers only a small portion, posing higher demands for cross-modal feature matching. Moreover, the covered area of depth maps remains nearly constant in the single vehicle's view, while the point clouds collected by the vehicle occupy different regions over time from a roadside perspective. Our method aims to address these problems by using temporal information and a better cost volume update mechanism. + +State Space Models: Recently, State-Space Models (SSMs) have excelled in modeling long sequences, particularly in capturing long-range dependencies. The Structured State-Space Sequence (S4) [9] has been proposed as an alternative to Convolutional Neural Networks (CNNs) and Transformers, offering the advantage of linear complexity for efficient handling of long sequences. As research on S4 continues to deepen, various improved models have emerged, such as the S5 layer [27] which introduces MIMO SSMs and efficient parallel scanning and the Gated State-Space layer (GSS) [22]. These models have shown promising performance in language modeling tasks. Excitingly, the recent introduction of the data-dependent SSM layer has led to the development of Mamba [8], which outperforms Transformers of various sizes on large-scale real-world data and achieves linear scaling in sequence length. Recent studies have attempted to bring Mamba model into the visual domain. Vision Mamba [42] borrows the concept from Vision Transformers [19] by marking image sequences with position embeddings and compressing the visual representation using bidirectional state space models. Furthermore, Video Mamba [15] offers a linear-complexity approach for modeling dynamic spatiotemporal contexts, making it ideal for high-resolution long videos. Research indicates that the Mamba architecture has advantages over LSTM and Transformer architectures in video processing tasks. Building on + +Mamba, our work aims to achieve more efficient temporal modeling with reduced computational cost. We draw on visual-domain Mamba applications to integrate LiDAR and roadside camera temporal features at the representation level, thereby mitigating calibration failures caused by poor single-frame data quality. + +# 3. Method + +In this section, we present MamV2XCalib, a novel roadside camera calibration method. The framework of our approach is shown in Fig. 2. In the first stage, we review the mathematical definition of the roadside camera calibration problem (Sec. 3.1) so as to better understand our newly proposed calibration strategy. Next, we provide a detailed explanation of our network design, loss function, and inference process. + +# 3.1. Problem Formulation and Input Processing + +The modeling of a standard perspective camera can be described by the correspondence between 3D spatial points and pixels. + +$$ +d _ {i} \left[ \begin{array}{l} u _ {i} \\ v _ {i} \\ 1 \end{array} \right] = \mathbf {K T} \left[ \begin{array}{l} x _ {i} \\ y _ {i} \\ z _ {i} \\ 1 \end{array} \right] = \mathbf {K} \left[ \begin{array}{l l} \mathbf {R} & \mathbf {t} \\ \mathbf {0} & 1 \end{array} \right] \left[ \begin{array}{l} x _ {i} \\ y _ {i} \\ z _ {i} \\ 1 \end{array} \right] \tag {1} +$$ + +where $\left[x_i\quad y_i\quad z_i\quad 1\right]^T$ represents the homogeneous coordinates of a 3D point in an arbitrary known coordinate system $A$ and $\left[u_i\quad v_i\quad 1\right]^T$ denotes a homogeneous camera image coordinates of a picture. $\mathbf{K}$ denotes the camera's intrinsic parameters, while $\mathbf{R}$ and $\mathbf{t}$ represent the rotation and translation matrices, which transform the coordinates from system $A$ to the camera coordinate system. $d_{i}$ represents the projection depth of the 3D point. Specifically, in our method, $A$ is set as the vehicle LiDAR coordinate system. Correspondingly, $\mathbf{R}$ and $\mathbf{t}$ represent the transformation from the onboard lidar coordinate system to the camera coordinate system. According to the description in the introduction, we assume that these parameters' initial values are given according to the expected calibration values, denoted as $K_{init}$ , $R_{init}$ , $t_{init}$ , where $K_{init}$ and $t_{init}$ are stable and easy to deal with, and changes mainly occur in $R_{init}$ : + +$$ +T _ {i n i t} = \Delta T \cdot T _ {L C} \tag {2} +$$ + +$$ +\Delta T = \left[ \begin{array}{c c} \mathbf {R} _ {\text {e r r o r}} & \mathbf {0} \\ \mathbf {0} & 1 \end{array} \right] \tag {3} +$$ + +where $T_{LC}$ represents the transformation from the current LiDAR coordinate system to the camera coordinate system. $\mathbf{R}_{\mathrm{error}}$ is the rotational deviation. $T_{init}$ is artificially set and our goal is to automatically obtain the value of $\Delta T$ through sensor data, which can determine the current position of the + +![](images/9e6939c2882ff616e531e7389130c15e8e555599d8970c71081ba51480216bb2.jpg) +Figure 2. The overall framework of MamV2XCalib. Initially, the point clouds are projected into the camera view using inaccurate initial extrinsic parameters. The network input consists of multiple frames of erroneous depth maps and roadside camera images. Multi-scale features are extracted from the images and depth maps through three channels, forming 4D correlation volumes. A GRU block is utilized to recurrently update the pixel-level correspondences between the images and depth maps (calibration flow) by retrieving features from the volume based on existing estimates. A series of calibration flows generated from multiple frames and iterations is divided into patches and fed into the Mamba model, with temporal and spatial embeddings. An additional token summarizes the features to regress the rotation deviation value. + +roadside camera in the world coordinate system. Before being fed into the network, the sensor data needs to be aligned to a unified coordinate system. The vehicle's point cloud is projected onto the roadside camera plane using the initial parameters $T_{init}$ and Eq. 1. + +# 3.2. Multi-scale feature extraction + +Our method employs three feature extraction branches to separately extract image information, depth map information, and image context. The two branches processing camera images both use a pre-trained ResNet-18 as the backbone. To obtain richer multi-scale features, and considering that highly abstract feature maps are not conducive to the subsequent search for pixel-level relationships, we fuse the upsampled feature map of latter layers with the former layers to obtain the final feature map. Finally, the output of image encoder $F_{1}$ and $F_{\text{context}}$ is $\mathbb{R}\frac{H}{8}\times \frac{W}{8}\times D$ where we set $D = 256$ . The depth map branch architecture $F'$ is similar to the image branch, except that the input channel is modified to one dimension, and pre-trained parameters are not loaded. Due to the unique nature of depth maps, the three branches do not share parameters. + +# 3.3. Feature Matching and Iterative refinement + +We directly associate the correspondences between roadside images $I_{1} \in \mathcal{I}$ and depth maps $I_{2} \in \mathcal{D}$ with the deviation of the roadside camera's extrinsic parameters. This + +pixel-level correspondence can be regarded as a special type of flow field, which we refer to as the calibration flow in this paper. Inspired by the RAFT [29] model used for optical flow estimation, we construct a multi-scale 4D correlation volume as follows: + +$$ +I n n \left(F _ {1} \left(I _ {1}\right), F ^ {\prime} \left(I _ {2}\right)\right) \in \mathbb {R} ^ {h \times w \times h \times w} \tag {4} +$$ + +$$ +U _ {k} = \operatorname {P o o l} (I n n) \in \mathbb {R} ^ {h \times w \times \frac {h}{2 ^ {k}} \times \frac {w}{2 ^ {k}}} \tag {5} +$$ + +where $Inn$ is calculated through inner product and Pool is designed to get multi-scale 4D correlation volume. Through these operations, the similarity between any two pixels is stored in this volume. Next, we repeatedly query features from the 4D dictionary to estimate pixel correspondences based on the former correspondences. We initialize the flow field (pixel correspondences) to zeros. In each iteration, given the feature flow map, we take each pixel's corresponding point as the center and get the similarity of all pixels within a distance of $r$ . We call this operation LookUp. + +$$ +h ^ {\prime \prime} = \operatorname {G R U} (\text {L o o k U p} \{U _ {k}, f, r \}, h ^ {\prime}, F _ {\text {c o n t e x t}} (I _ {1})) \tag {6} +$$ + +$$ +d f = \operatorname {F l o w} \left(h ^ {\prime \prime}\right) \tag {7} +$$ + +We then input the features we just looked up, hidden states from last iteration, and context features together into the GRU module, obtaining new hidden states. The flow residuals $df$ is predicted by layer Flow consisting of two convolutional layers. The residual $df$ is added to the previous + +flow field to update it. In this way, we obtain a series of flow field estimates $f_{i} \in \mathcal{F}$ equal to the number of iterations. + +To ensure that the model can get calibration flow fields, in the first stage of training, we directly regress the extrinsic parameters from each flow field obtained at every step using two fully connected layers. + +# 3.4. Global Aggregation with Mamba + +While our 4D correlation volume effectively captures global correlations between inaccurate depth maps and images, the unique V2X scenario poses additional challenges. The already sparse point clouds become even sparser due to viewpoint disparities between roadside and vehicle perspectives. Moreover, the effective regions of depth maps shift over time, making it inherently difficult to derive accurate calibration flow fields in uncertain, data-scarce regions using single-frame data alone. Directly regressing extrinsics from all correspondences would inevitably introduce bias. + +Fortunately, although the vehicle is in motion, the roadside camera's deviation from its initial position remains fixed over a calibration period. This stability allows us to perform temporal fusion, integrating data across frames to overcome the limitations described above. We select Mamba because our sequence of calibration flow fields has dimensions akin to video data, where Transformers excel in fusion tasks. However, our iterative process produces a large number of tokens, prompting us to adopt the latest Mamba [15, 42] for its superior efficiency in handling such data. + +Specifically, we extend the input from a single frame to a sequence. According to the method in Sec. 3.3, we can obtain a calibration flow field of size $\mathbb{R}^{T\times i\times h\times w}$ . We treat the iterative process and temporal dimension as two separate axes. First, we concatenate the flow field maps obtained from each frame into an overall map of size $\mathbb{R}^{T\times h\times (w\times i)}$ . Then we divide it into a series of patches $x_{n}^{t}$ instead of flattening them simply and project them into a hidden space through convolutional layers. The patches of the frames are arranged as shown in Fig. 2. Similar to [1, 15], we add positional and temporal embeddings $p_{s}$ and $p_t$ to retain the spatiotemporal distinctions and insert an additional token $z_{add}$ into the entire sequence to summarize the information. + +$$ +Z = \left[ z _ {a d d}, \mathbf {E} x _ {1} ^ {1}, \mathbf {E} x _ {2} ^ {1}, \dots , \mathbf {E} x _ {N} ^ {T} \right] + p _ {s} + p _ {t} \tag {8} +$$ + +$$ +z _ {a d d} = \operatorname {M a m} (Z) \tag {9} +$$ + +where the projection by $\mathbf{E}$ is equivalent to 3D convolution and Mam is the bidirectional mamba block. Through the Mamba model, we construct state space and scan it as illustrated, enabling the model to selectively model different regions of each flow field map from a spatial perspective. Additionally, this allows the model to automatically associate features generated from data with varying quality at different timestamps. The added token summarizes the series of + +lengthy calibration flow maps generated through iterations and temporal processes. + +After obtaining the refined summarized features $z_{add}$ , we use two fully connected layers to regress the quaternion, achieving the desired estimation of the rotational error. + +# 3.5. Loss Function + +For each obtained rotation prediction, our loss has the following form: + +$$ +L _ {i} = \lambda_ {r} L _ {r} + \lambda_ {p} L _ {p} \tag {10} +$$ + +where $\lambda_r$ and $\lambda_p$ denote respective loss weights. $L_r$ is the rotation loss and we use angular distance to represent the difference between quaternions. Considering that our method utilizes coordinate transformations of point clouds $P_i$ , we calculate the distance between the two point clouds after the actual transformation and the predicted transformation to obtain $L_p$ : + +$$ +L _ {p} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left\| T _ {L C} ^ {- 1} \cdot T _ {p r e d} ^ {- 1} \cdot T _ {i n i t} \cdot P _ {i} - P _ {i} \right\| _ {2} \tag {11} +$$ + +where $T_{LC}$ is the ground truth LiDAR-Camera extrinsic matrix and $T_{pred}$ is the output of the calibration network. + +In the first training stage, we iteratively obtain $n$ estimates per frame, with the loss as a weighted sum of their individual losses using exponentially increasing factors. + +$$ +L = \sum_ {i = 1} ^ {n} \gamma^ {n - i} L _ {i} \tag {12} +$$ + +In the second stage, multi-frame data is input, with each frame producing a single estimate, and the loss is defined as in Eq. 10. + +# 3.6. Calibration Inference + +One of our inputs, the depth map, is influenced not only by the quality of the point cloud itself but also by the initially given extrinsic parameters. To address significant deviations and maintain consistency with LCCNet [21], we concatenate multiple networks that have the same architecture but are trained under different noise conditions. We then reproject the depth maps based on the predictions $T_{i}$ from the previous network to obtain higher-quality input data. Therefore, during the final inference, we have: + +$$ +\tilde {T} _ {L C} = \left(T _ {0} \cdot T _ {1} \dots T _ {n}\right) ^ {- 1} T _ {\text {i n i t}} \tag {13} +$$ + +# 4. Experiment + +We conduct extensive experiments on two real-world datasets, V2X-Seq [37] and TUMTraf-V2X [43]. In this section, we will specifically introduce the training details and present the experimental results. + +
DeviationMethodMean (°)Std (°)
TotalRollPitchYawTotalRollPitchYaw
(−20°, +20°)LCCNet [21]1.07410.17880.60560.64552.53360.15372.46240.7920
(−20°, +20°)Calib-anything [20]--------
(−20°, +20°)Ours0.63130.18670.24090.47800.32110.14890.18600.3500
(−10°, +10°)LCCNet [21]0.79090.17920.34400.55481.68250.11111.61470.5985
(−10°, +10°)Calib-anything [20]--------
(−10°, +10°)Ours0.58580.22600.24410.40010.24280.15250.17450.2776
+ +Table 1. Comparison results with other calibration methods on V2X-Seq dataset [37]. Calib-anything [20] fails. (See Fig. 4) + +![](images/6c8fb4a0b52e64dd5f8bf0c7c042c056f42f7d5f29f2b39d1485266be55259cd.jpg) +(a) Ground Truth + +![](images/c874a75bcb8b45df15c36d3d4d9d363317fd753c6e86f7c574208ef894751ea7.jpg) +(b) Before Calibration + +![](images/0ea1d89586b946c68c096a6ddfac7f2a39cb05cb50aaa1a46b53d2d154e49788.jpg) +(c) LCCNet +Figure 3. Qualitative reprojection results. First row: On V2X-Seq dataset, within the initial large deflection range of $(-20^{\circ}, +20^{\circ})$ , LCCNet [21] shows significant deviation in some scenes, while our method remains accurate. Second row: TUMTraf-V2X (daytime). Third row: TUMTraf-V2X (nighttime). The initial deflections are within a small range of $(-5^{\circ}, +5^{\circ})$ and our method outperforms better. + +![](images/a69110ba1f4d78e45ac9d7a68dec1f01d00174726fd5403f12782d65f71b764d.jpg) +(d) MamV2XCalib + +# 4.1. Dataset + +V2X-Seq: Yu et al. [37] introduce a large-scale real-world cooperative vehicle-infrastructure dataset. It contains a large amount of time-synchronized data from vehicle-side and roadside sensors, as well as transformations between multiple coordinate systems. + +TUMTraf-V2X: There is another V2X dataset named TUMTraf-V2X [43]. It focuses on challenging traffic scenarios and various day and nighttime scenes. We utilize vehicle-side LiDAR data and roadside camera data. + +Similar to single-vehicle LiDAR-camera calibration tasks, we add random noise within a specified range to the extrinsic parameters to generate abundant training data. Specifically, after applying a random perturbation $\Delta T$ to $T_{LC}$ , we obtain the initial extrinsic parameter $T_{init} = \Delta T \cdot T_{LC}$ . By randomly changing the deviation value, we can acquire a large amount of training data. + +# 4.2. Training Details + +We train our network on a single A100 GPU, with the training process divided into two stages. Next, I will elaborate on the training process and use the hyperparameter settings on V2X-Seq [37] as an example. + +In the first stage, we perform calibration using only single-frame data. Specifically, we exclude the Mamba module and directly regress the extrinsic parameters from the calibration flow map. This approach allows the network to focus on accurately predicting the calibration flow map. We set the initial learning rate to 0.00003 and train for 70 epochs, after which the learning rate is reduced until convergence. All available paired data is utilized in this stage. + +In the second stage, we train the Mamba module based on the first stage, enabling the network to fuse multiple calibration flow maps generated over time. The initial learning rate is set to 0.0001 and decays during training. We begin + +
ExperimentTemporalIteration4D Correlation VolumeMean (○)Std (○)Param (M)
OursMamba[8]✓✓0.63130.321147
w/o Mamba (+Trans)Timesformer[3]✓✓0.66830.380855
w/o Temporal-✓✓0.97422.001341
w/o IterationMamba[8]-✓0.70361.616247
w/o Temporal and Iteration--✓1.10252.917847
3D feature matching [21]---1.07412.533670
+ +by freezing the network components preceding the Mamba module and then jointly update all network parameters. To enhance training data quality, we use data where the horizontal distance between vehicles and infrastructure is less than 50 meters. + +# 4.3. Evaluation + +During evaluation, we performed distance filtering before inputting the data into the network. The calibration system is activated only when the vehicle is within certain distance. We will explain the benefits of this operation in Sec. 4.5. + +On V2X-Seq Dataset [37]: Tab. 1 highlights the effectiveness of our method in roadside camera calibration tasks. For a mis-calibration range of $(-20^{\circ}, +20^{\circ})$ , our approach achieves a mean calibration error of $0.6313^{\circ}$ , with mean Euler angle errors of $[0.1867^{\circ}, 0.2409^{\circ}, 0.4780^{\circ}]$ . We compare our method to a high-performing single-vehicle LiDAR-camera calibration technique [21], demonstrating that our approach offers superior accuracy in V2X scenarios over directly applying the single-vehicle method. Furthermore, we assess its robustness. Our method significantly reduces the likelihood of extreme calibration failures, lowering the standard deviation of the angle-error from $2.5336^{\circ}$ to $0.3211^{\circ}$ —a reduction by an order of magnitude. The deviations within this range are manageable by existing perception methods [35]. When the initial error is reduced to $(-10^{\circ}, +10^{\circ})$ , our method yields even better results while maintaining greater robustness and a lower risk of severe errors. Additionally, we present a qualitative comparison with the latest train-free LiDAR-camera calibration method [20] in Fig. 4. In V2X scenarios with substantial camera deflection, the competing method fails, whereas our approach consistently succeeds. We also compared with a traditional LiDAR-camera calibration method [13] (see Appendix 4.3 for details). + +On TUMTraf-V2X Dataset [43]: Tab. 3 presents comparative results on the TUMTraf-V2X dataset, where our method remains competitive. For a mis-calibration range of $(-5^{\circ}, +5^{\circ})$ , our approach achieves a mean calibration error of $0.267^{\circ}$ . Remarkably, our calibration strategy proves effective even in nighttime scenarios (see Fig. 3). + +To ensure a fair comparison, we retrained LCCNet [21] + +on the same dataset and modified its output to predict only rotational errors, aligning it with our network's configuration. Fig. 3 shows that after passing through our calibration network, effective calibration can still be achieved despite significant initial extrinsic parameter deviations. Based on the calibrated position of the roadside camera, the vehicle point clouds can be well-matched with the images from the perspective of the roadside camera. + +![](images/c75b3a106571c9351b554798066458306d6c85791fc01bd92e43432f93fe1b35.jpg) +Figure 4. Ground Truth (Left). Calib-Anything [20] (Middle) fails to calibrate within $(-20^{\circ}, +20^{\circ})$ , while ours (Right) succeeds. + +![](images/cd90a9f39e21523bd7d723f89c57c8d8ff2a363c8c42e8033600a4f5e1cf0151.jpg) + +![](images/307e722c8844b8c66b250cb1465377282930b5309e9eb9a390fb20ee1cbfae71.jpg) + +Table 2. Ablation study on the effect of different components of our model. + +
DeviationMethodMean (°)Std (°)
(−5°, +5°)LCCNet [21]0.3890.608
(−5°, +5°)Ours0.2670.280
+ +Table 3. Comparison results on TUMTraf-V2X dataset [43]. + +# 4.4. Ablations and Analysis + +We conducted a series of ablation experiments to demonstrate the importance of each component. + +Mamba: First, we removed the Mamba component used for spatiotemporal fusion while retaining feature flow estimation for direct regression. Results are shown in Tab. 2. It can be observed that the Mamba module significantly improves calibration stability, greatly reducing the standard deviation of the estimated values, which indicates the necessity of this module. Additionally, we attempted to replace it with a Transformer-based Timesformer [3] module. It can be seen that the Mamba-based method achieves relatively better results with a smaller number of parameters. + +Iteration: Our method refines the calibration flow progressively through iteration. During inference, we iterate 10 times to generate 10 calibration flow maps, which together provide spatial dimensional information. We verified + +that using only a single iteration to produce the calibration flow during inference significantly weakens the network's capability, indicating that generating calibration flow maps through multiple iterations is essential. + +Multi-scale 4D Correlation Volume: We replace the 4D correlation volume with the 3D feature matching layer in LCCNet [21], and find it costs much more parameters and perform worse than 4D correlation volume with iteration (marked by w/o Temporal). + +# 4.5. Other experiments about V2X Calibration + +Why Ignore Translation Noise: Fig. 5 shows the point cloud projection deviations caused by translational and rotational errors in a V2X scenario. It is evident that minor translational have a negligible impact on the perception system and can be disregarded. In contrast, rotational errors often lead to significant matching discrepancies in vehicle-road data. The experiment in the appendix demonstrate that such slight deviations do not significantly affect rotational calibration. We attribute this to the fact that, in V2X scenarios, the absolute distance between the vehicle and the road typically far exceeds the potential translational offset of roadside cameras due to environmental factors. Therefore, it is reasonable to simplify the calibration problem of roadside cameras by focusing on rotation. + +Necessity of the Mamba Module: To further substantiate the importance of the Mamba module, we expanded our ablation study by comparing pre-fusion and post-fusion approaches. As shown in Tab. 4, on the V2X-Seq dataset [37], our method markedly outperforms two alternatives: directly stacking multi-frame point clouds or applying post-processing to the frames using a single-frame technique. + +Distance Filtering: By utilizing vehicle mobility, we can easily choose data with shorter distances between vehicles and infrastructure for calibration. This distance can be calculated before feeding it into the neural network, allowing us to initially evaluate data quality based on distance to boost calibration accuracy. This is an advantage that earlier methods lack. In Fig. 6, we show the mean error and standard deviation of calibration using vehicle point clouds across various distance ranges. Experiments demonstrate that filtering data by distance improves data quality and strengthens the method's robustness. + +Migration to single car calibration: Although our method was originally designed for V2X, it can naturally be extended to single car where translation errors must be considered. The results are shown in the attachment. + +# 4.6. Limitation + +Our method relies on vehicle-side LiDAR perception data, which places certain demands on the quality of vehicle-side sensors. Additionally, although the V2X-based calibration strategy offers benefits such as target-free operation, high + +![](images/215ae92200735965a91400cb53e70059d21beb028568d52309e91f9acc900b34.jpg) +Figure 5. The impact of extrinsic noise. Ground Truth (Left). Translated within $10\mathrm{cm}$ (Middle). Rotated within $20^{\circ}$ (Right). + +![](images/2673a0e6f523f29e3912ed984fa9de56e19c09e038326e89cbed574ea2319f9a.jpg) + +![](images/41d28ffc49762b2da5baa91c5b2a7d7203306ad276513104974007bf8f401746.jpg) + +
Fusion MethodsMean (°)Std (°)
stacking points0.9522.184
average0.9742.001
least square fitting0.8201.254
ours0.6310.321
+ +Table 4. Comparison with other fusion methods on the V2X-Seq dataset [37] (initial deviation $(-20^{\circ}, +20^{\circ})$ ). + +![](images/ba56af16ec2d01fb54ff7431a0b283bf62d006c180d5990ec4126c7107bc734a.jpg) +Figure 6. Calibration result on V2X-Seq dataset [37] after filtering vehicle point cloud data with a horizontal distance between the vehicle and roadside camera of distance $< d$ . + +![](images/dda8659ef8ece9e23f7464d480527f5fa0a3cf7a4ccc78e2a5ecb01368ead7a1.jpg) + +flexibility, and large-scale deployment, it also introduces vehicle-to-infrastructure information interaction, which imposes higher requirements on time synchronization. Besides, similar to other deep learning-based calibration methods, fine-tuning is necessary to achieve good results when transferring to entirely different datasets. + +# 5. Conclusion + +This paper proposes a target-less infrastructure camera calibration strategy based on vehicle-road collaboration and introduces a novel method designed specifically for V2X scenarios. Compare to existing approaches, our strategy makes full use of environmental information and is suited for busy road scenarios. We present an iterative method that establishes pixel-level correspondences between depth maps and images. By incorporating the Mamba model's strengths in temporal modeling, we overcome instability challenges in single-vehicle calibration applied to V2X contexts with fewer parameters. Our method proves effective and robust on two datasets. 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State Space Model for 3D Vision Language Learning + +# Yuan Wang $^{1,2}$ Yuxin Chen $^{2}$ Zhongang Qi $^{2}$ Lijun Liu $^{3}$ Jile Jiao $^{1,4}$ Xuetao Feng $^{1,4}$ Yujia Liang $^{5}$ Ying Shan $^{2}$ Zhipeng Zhang $^{6,7‡}$ + +$^{1}$ Tsinghua University $^{2}$ ARC Lab, Tencent PCG $^{3}$ UCAS $^{4}$ Deepeleph $^{5}$ HUST + +$^{6}$ School of Artificial Intelligence, SJTU $^{7}$ Anyverse Intelligence $\ddagger$ Corresponding Author + +# Interactive 3D Referring Segmentation + +# Single-target Referring Segmentation + +![](images/6734a2408b4128529f23c60d77c1f53ef2c6bd269e6e41afb47ce12f9988da2a.jpg) + +A black sofa behind the fan and a black backpack is lying on the top of it. + +![](images/ed0d66e10bb4e49e7cf0555cefc2a42d17a849de05c8cf7ecb3758bb9188f8b4.jpg) + +A circular end table can be found adjacent to a teal couch and an brown arm chair. + +# Box-guided Referring Segmentation + +![](images/8b06577565eab7fffd10fd590459107b8e8c0426c961f3c43a5c2783c3b8140f.jpg) +[-0.07 0.45 0.54] + +![](images/c5dbe8f794e5c82321b35983dcf634c8135f94e45d12d68c7d014821955884c7.jpg) +[-1.48 -0.41 0.41] + +# Interactive Embodied AI Tasks + +# Task Planning + +![](images/f20ffc303a94a224288b9c73e92e42e42dde2e1b220c8265a7708d25632a42c5.jpg) + +# 3D Dialog + +![](images/a36817c85aa6a2db9a32e44ca3f8e94e36cac3dfb138ea85bff4db958ec4e23b.jpg) + +# Robot Manipulation + +![](images/76a07e9726b23381e71c032c843a3a74e95bc2d631ec0d0e8fe906bc5ce89cee.jpg) + +# Embodied Navigation + +![](images/09e807708c5ac74523936c53ce33eb3d488b3066bd631c5e46d6cb247046a213.jpg) + +Human: Please arrange a space for eating. +Robot: 1. arrange chairs and ensure them face table. +2. Place any objects or decorations on the table. +3. Clean the table and chairs, wiping away any dust. +4. Check the lighting and temperature in the area. + +Q: Hello, could you describe the furniture in the living room? +A: Sure! there has a wooden table, two big wooden chair, and a gray upholstered sofa. +Q: Thanks for your help! It's I want to know + +Human User: pack all the blue andblack sneakers in the brown box + +![](images/aacb17d1112341f1efe3d8b889da2757eb9a7f7a4a67dd42b26ffd4447ab6579.jpg) + +![](images/2826334a34deb1727795f9e83efb2b260cd9eb2756b6e65ebcbe243403ae4830.jpg) + +Find the seating + +1. Turn right +2. Stop +3. Move forward +4. Turn left + +# Interactive 3D Visual Grounding + +# Single-target Grounding + +![](images/9f3d03e908fe3ea03a2a01cf39c3cbca327a290c51db158467edd278a38e5dfa.jpg) +It is a rectangular bed, with a white mattress and a yellow pillow on top. +Figure 1. Mamba-3VL serves as an interactive and general-purpose interface for 3D vision-language tasks, including Referring Segmentation, Visual Grounding, Question Answering, Dense Captioning, while generalizing well on Embodied AI tasks. + +![](images/eaf58d2d1587518e1c2360ac2bf5eb1cf5a86b6a3a6a60cd24ac78883c2a2861.jpg) +White washing machines are positioned in front of dryers + +# Interactive 3D Question Answering & Dense Captioning + +# Question Answering + +![](images/eda6e270b0ad5e37153a6f560574595f0441e99787ebaba83411614b2675ecc0.jpg) +What's black television above? Response: on the nightstand + +# Situated Reasoning + +![](images/26512d80d7ae7d7aa8c41a7d851e8eca36fbb9d362c1c5d050939c11180a647c.jpg) +Standing in front of the coffee table with the window on my left. How many chairs are behind me? + +# Dense Captioning + +![](images/39a35e8298a990d1e6105083fab72a7af01f4180f8d64d142c572fb68f1b4aaf.jpg) +A desk sits behind the brown chairs to both it's left and right. it's to the right of a bookshelf. + +# Abstract + +3D vision-language (3D-VL) reasoning, connecting natural language with 3D physical world, represents a milestone in advancing spatial intelligence. While transformer-based methods dominate 3D-VL research, their quadratic complexity and simplistic positional embedding mechanisms severely limits effective modeling of long-range 3D-VL dependencies and spatial relationships in 3D-VL tasks. State Space Models (SSM) have emerged as promising linear-complexity alternatives for sequential data processing, while inherent selection mechanism offers notable capability for spatial modeling. Despite its potential, straightforward adoption of Mamba to 3D-VL tasks encounters two obstacles: (1) how to perceive the position of 3D objects and understand complex spatial relationships, and (2) how to achieve thorough synergies of + +multi-modal features. In this paper, we propose Mamba-3VL, a pioneering 3D-VL framework to model complex intra- and inter-modality correlations and enhance spatial relation reasoning, while guaranteeing top-tier performance, high efficiency, and generalization potential for 3D-VL tasks. Specifically, Mamba Mixer explicitly models 3D-VL interaction via channel twisting and relation-prioritized spatial scanning policy. It maximally retain spatial relation of object-centric features. To further provide precise spatial encoding for mamba, we develop Instance-aware Dynamic Position Adapter (IDPA) to dynamically adjust instance-specific positional embeddings and enhance local spatial relation of 3D objects. Extensive results validate Mamba-3VL trumps other competitors on seven 3D-VL benchmarks and showcases versatile potentials for challenging Embodied AI tasks. + +# 1. Introduction + +Spatial Intelligence [31] aims to develop general-purpose assistants to understand the 3D physical world and execute + +![](images/1812a76ad0f42ed2baf55803153c399653d49215c670fa7fb7e08f8f616704de.jpg) +Figure 2. Comparison of grounding accuracy and model efficiency. + +human commands in real scenarios. Towards this goal, numerous datasets and 3D foundation models for benchmarking 3D multi-modal understanding have been proposed, e.g., visual grounding [6, 59, 69], dense captioning [4, 11], and question answering [2, 42]. The primary challenge of these tasks lies in comprehending spatial relationships between 3D objects and effectively modeling 3D-VL interactions. + +Drawing inspiration from 2D vision-language (2D-VL) models [10, 14, 28, 33, 34], contemporary 3D-VL models rely heavily on transformer-based cross-modality interaction to fuse 3D scene and linguistic features. Representative works, e.g., 3D-VisTA [73], SceneVerse [25], UniT3D [12], explore pre-trained transformers and contrastive alignment to seek mutual benefits from related 3D-VL tasks. Despite remarkable progress, quadratic complexity of full attention imposes prohibitive overhead. When handling massive points or lengthy texts, it struggles to capture long-range 3D-VL dependencies due to entropy maximization of attention weights. Instead, recent studies [20, 39, 55] develop linear attention mechanism as a scalable alternative. But in fact, their simplistic positional embedding limits performance on 3D-VL tasks. Leveraging State Space Models (SSMs) as its core, a flux of mamba proposes a selection scanning mechanism, enabling it to handle long-range sequences and spatial modeling in near-linear complexity. However, the unmodified utilization of mamba does not yield satisfactory performance on 3D-VL tasks due to the following challenges: (1) 3D point clouds are sparse, unordered and encode rich spatial information. When converting 3D data into 1D format, such dimensional reduction causes mamba to struggle to capturing spatial relationships and preserving geometric structures of 3D scene due to inherent sequential dependencies induced by its recurrent-based processing. (2) Mamba's vanilla framework lacks native cross-modal interaction mechanisms necessary to seamlessly align semantics with 3D geometries. + +Towards the dilemma, we develop the first mamba-based framework Mamba-3VL for 3D-VL understanding. Departing from transformer-based works, Mamba-3VL with linear complexity explicitly models spatial relation of 3D objects and enhances intra- & inter-modality interactions. As illustrated in Fig. 2, Mamba-3VL achieves top-tier performance on 3D-VG benchmarks compared with other query-based decoding procedures, while maintaining its high efficiency. + +To capture spatial relationships of 3D object sequences while enhancing fine-grained interactions of 3D-VL interaction, we develop a Mamba Mixer module, which consists of a + +relation-prioritized spatial scanning and a channel twisting. The relation-prioritized spatial scanning is an effective 3D-to-1D reordering policy to better model spatial relations of 3D objects. It combines the Nearest Instance Scanning (NIS) and the Furthest Instance Scanning (FIS), where the former captures local spatial information and the latter strengthens long-range dependency understanding from a global perspective. A hybrid feature chain then combines 3D object queries and multi-modal features. The channel twisting enables inter-modal semantic fusion via channel-wise traversal of this feature chain, ensuring 3D objects contextualized awareness of task-specific features across spatial positions. + +Although the spatial scanning demonstrates ability for spatial relationships modeling, the reliance on global positional embeddings to capture fine-grained instance-level features remains constrained. In fact, instance-specific positional embeddings are indispensable in 3D-VL tasks as they offer accurate spatial context and geometric attributes (e.g., color and shape). Motivated by this, we propose an Instance-aware Dynamic Position Adapter (IDPA) with intercalated EdgeConv [56-58] and Language-modulated Instance Adapter (LISA) layers. The essence of IDPA lies in its capacity to deliver fine-grained, instance-specific positional embeddings, which further enhance Mamba Mixer's spatial relationship modeling. EdgeConv enhances spatial relationships by integrating neighborhood features and embedding geometric priors of 3D objects as positional embedding. Further, LISA dynamically modulates instance-specific positional embeddings via a geometric-semantic warping mechanism, to align with contexts provided by promptable features. + +We evaluate Mamba-3VL on seven established 3D-VL datasets: ScanNet200 [51] for instance segmentation, ScanRefer [6], ReferIt3D [1], Multi3DRef [67] for visual grounding, ScanQA [2] and SQA3D [42] for question answering, and Scan2Cap [11] for dense captioning. Mamba-3VL surpasses state-of-the-arts by a clear margin. Remarkably, only fine-tuning $1\%$ LLM parameters, it exhibits impressive generalization to Embodied AI tasks, e.g., robotic manipulation. + +- We pioneer Mamba-3VL, marking the first exploration of mamba in 3D-VL tasks, achieving top performance, efficient linear complexity and generalization potential. +- To calibrate mamba with 3D-VL tasks, a Mamba Mixer models spatial relationship and enhance its 3D-VL interaction abilities. IDPA further dynamically adjust instance-aware positional embeddings to improve spatial reasoning. +- Experiments validate Mamba-3VL achieves SOTA results on all canonical benchmarks, marking mamba as a promising foundational architecture for future 3D-VL research. + +# 2. Related Works + +# 2.1. 3D Vision-language (3D-VL) Learning + +Recently, the AI community has witnessed rising interests in 3D-VL learning, driven by its potential to bridge physical + +![](images/15f077204a541a4cd9b638e99eae5e8039a964d546ff9331b25ea77cc03da314.jpg) +Figure 3. Preliminaries on pipeline of the proposed Mamba-3VL. (a) Our Mamba-3VL is a query-based decoding framework composed of stacked Mamba Mixer and IDPA layers. (b) Mamba Mixer with the interleaved (d) channel twisting mechanism and (e) relation-prioritized spatial scanning policy. (c) IDPA dynamically adjusts instance-aware positional embeddings via a geometric-semantic warping. + +world with natural language—a cornerstone for advancing spatial intelligence. During this carnival, a bunch of 3D-VL tasks, e.g., visual grounding [22, 24, 59–61, 69], dense captioning [4, 9, 11, 27], question answering [2, 42], situated reasoning [37] are proposed to evaluate capabilities to interpret human instructions in relation to object properties and spatial relationships. Embodied navigation [43, 50, 70, 71] and robotic manipulation [5, 29, 53, 62] tasks further probe the embodied perception and interacting capacity in physical environments. Despite this burst, initial efforts focus on developing task-specific models, restricting flexibility towards universal user-assistant interactions. Recent researches have pivoted towards building unified models capable of managing multiple 3D-VL tasks. [4, 7, 12] capitalize on multi-task synergies. Methods like [25, 28, 73, 74] develop pre-trained transformers and unified representations to facilitate cross-modal alignment. However, their reliance on full attention struggle to capture long-range 3D-VL dependencies. Departing from transformer-centric paradigm, our Mamba-3VL marks the first mamba-based foundation model with top-tier performance and high efficiency for 3D-VL reasoning. + +# 2.2. State Space Models and Visual Applications + +State Space Models (SSMs) [15, 17-19] excel at capturing complex correlations in the language sequence. Mamba, as a prominent SSM, has been rapidly transitioned to multiple vision tasks [36, 41, 68, 72]. Vim [72] presents the first pure SSM-based model that efficiently compress the vision representation for intensive prediction tasks. VideoMamba [35] introduces self-distillation into the non-hierarchical Vim to address the temporal redundancy in video understanding. Recent studies [32, 36, 65, 66] investigate the applicability of mamba on 3D tasks by employing distinct point cloud order + +ing policy. Despite impressive success achieved, mamba in 3D-VL tasks remains under-explored. We propose Mamba-3VL with designs like relation-prioritized scanning, which paves the road to spearhead new avenues in 3D-VL research. + +# 3. Methods + +# 3.1. Overall Framework + +In Fig. 3 (a), we formulate multiple 3D-VL tasks in a generalized query-based decoding procedure following [74-77]. We extract point cloud, multi-scale voxel, and multi-view image features with a point encoder, a voxel encoder, and an image encoder. We first group the dense 3D points into $S$ segments. For the point cloud, we use the pre-trained PointNet++ [47] to obtain point features $\mathbf{P} = \{\mathbf{p}_0,\mathbf{p}_1,\dots,\mathbf{p}_{\mathrm{S}}\}$ of the segments. For the multi-view images, the pre-trained OpenSeg [16] model is utilized to compute per-pixel embeddings, which are back-projected to 3D space and aggregated into segment-level image features $\mathbf{I} = \{\mathbf{i}_0,\mathbf{i}_1,\dots,\mathbf{i}_{\mathrm{S}}\}$ . For the voxel, we discretize the 3D scene with Mask3D [52] and leverage a sparse convolutional U-Net to extract voxel representations $\mathbf{V} = \{\mathbf{v}_0,\mathbf{v}_1,\dots,\mathbf{v}_{\mathrm{S}}\}$ of the pre-generated segments. Similar to PQ3D, these three segment-level features are aligned within a shared 3D coordinate space, yielding the final 3D scene representation, denoted as $\mathbf{X} = \{\mathbf{V},\mathbf{I},\mathbf{P}\}$ . Further, a mamba-based query decoder is introduced with the multi-modal Mamba-Mixer module (Sec. 3.2) and Instance-aware Dynamic Position Adapter (Sec. 3.3). Forming the foundation of Mamba-3VL, it couples task-specific prompts (e.g., texts and bounding boxes) with the 3D scene features to enhance the cross-modal interaction while preserving spatial relationships among 3D objects. Each query is ultimately routed through three universal output heads to predict the instance mask, task-related score, and scene-grounded texts. + +![](images/28b51ad8d8db17b90b0683d42b40edbb17efc0ec2e3062d36a72a14adf4dc278.jpg) +A toilet bowl under tissue holder + +![](images/56a919199830a7e4975aedbd9eccb77ec355c1dc1b223e6a9d6d181608dcbb58.jpg) +Brown couch faces coffee table + +![](images/f170f5a37a808489e9d22a9f2b2f755679b6b5d82e07320583f925ca0564c693.jpg) + +![](images/57cdc1341dd16ed1819517878ea3ae231e26bde410f3c1d3d869817496ceb17a.jpg) +A black sofa behind the fan. + +![](images/dd76e893829af9ad6d59604d5e29165621bf4f8537a15ab395a594a139685a01.jpg) +a circular end table can be found next to a teal couch and an arm chair. + +![](images/69b198c11426c8dc9253c25b52ce037722428839bc6a4a7d8a509e1673a54cb3.jpg) + +![](images/6be4d79d4916f45fc21923fd6dc7325a36a81d50168f65310e4aaff7ef51df16.jpg) +a dark monitor sits on a wood desk against the wall, its screen flickering with activity. +an office chair, streamlined and professional in appearance, is sitting around a large table. + +![](images/2847b06e30e0d64a4b601a5f8d23711c999fed65fbf81c67b90ba59bc8f4de9f.jpg) + +![](images/3fd37afc964b8e6ede64eb4f018010648861b0bf5d1b995e95163cb50ccde186.jpg) +Figure 4. Visualized examples for promptable segmentation tasks. + +# 3.2. Multi-Modal Mamba Mixer Block + +To better adapt mamba to 3D-VL tasks, we introduce Mamba Mixer, which interprets spatial relationships of 3D objects and achieves holistic inter-modality and intra-modality interactions. In Fig. 3 (b), Mamba Mixer consists of relation-prioritized spatial scanning (e) and channel twisting (d). + +Following PQ3D [74], a zero-initialized query $\mathbf{Q}_0$ centered on 3D object centroids, is inputted into the mamba-based decoder, which guides instance queries to incorporate scene representations $\mathbf{X}$ and promptable features $\mathbf{T}$ . In each decoder layer $l$ , instance queries $\mathbf{Q}_l$ sequentially retrieve scene-relevant features and prompt-encoded knowledge with two successive Mamba Mixer modules, severally. Consider the prompt-based Mamba Mixer as an exemplar: + +(1) Intra-modality interactions. Before feeding instance queries $\mathbf{Q}_l \in \mathcal{R}^{N \times d}$ into the mamba block, a critical step involves reordering them into 1D sequences. While previous endeavors [36, 65, 66] employ canonical mamba for 3D representations, they fail to capture intrinsic spatial relationship among 3D objects in irregular 3D point clouds. To address this limitation, we design a relation-prioritized spatial scanning policy, which integrates the Nearest Instance Scanning (NIS) and Furthest Instance Scanning (FIS) to ensure the spatial dependencies of instance query sequence. In detail, we sort $\mathbf{Q}_l$ based on spatial proximity into two sequences: farthest and nearest neighbor orders. For FIS, we randomly select an initial target instance, then iteratively choose the one with the furthest spatial proximity from the selected set and vice versa. Before entering the SSM layer, each branch undergoes a series of normalization, linear projection, and 1D convolution operations. In theory, NIS more effectively captures spatial relationships among local objects corresponding to semantic concepts, e.g., "adjacent" and "contact". In contrast, FIS strengthens the understanding of long-range dependency, e.g., instantiated by "the farthest". + +(2) Inter-modality interactions. The spatial scanning exhibits channel independence, failing to capture multi-modal + +interactions. To establish the correspondence between 3D vision and task prompts, we first construct a hybrid feature chain by channel-wisely concatenating 3D instance queries and prompt embeddings, bridging 3D representations with task-specific contexts. The channel twisting enables intermodality fusion through channel-wise scanning of hybrid feature chains, thereby injecting task conditions into 3D instances. We organize channels as an ordered sequence, and presents selective scanning that allows mamba to be "aware" of the task prompts at every spatial location and dynamically adapt spatial reasoning based on task-related conditions. + +Formally, the total process of Mamba Mixer is written as: + +$$ +\mathbf {Q} _ {l + 1} = \operatorname {S S M} _ {\text {c h a n n e l}} \left[ \operatorname {S S M} _ {\text {s p a t i a l}} \left(\mathbf {Q} _ {l}\right), \mathbf {T} \right], \tag {1} +$$ + +$\mathrm{SSM}_{\mathrm{spatial}}$ models relation-prioritized spatial dependencies in 3D instance queries, while $\mathrm{SSM}_{\mathrm{channel}}$ treats hybrid feature chain as an ordered sequence along the channel axis. + +# 3.3. Instance-aware Dynamic Position Adapter + +While Mamba Mixer's relation-prioritized reordering policy does model spatial relationship of 3D objects, it is, however, still relies on global positional embeddings. They exhibit limited dynamic adaptability to instance-wise object features, essential for 3D-VL tasks. Inspired by this, we introduce an Instance-aware Dynamic Position Adapter (IDPA) to provide fine-grained, instance-specific positional embeddings for Mamba Mixer with enhanced spatial relation modeling. + +As depicted in Fig. 3 (c), we derive local object proxies for 3D objects using KNN algorithm based on their spatial positions: $\mathcal{Q}_i = \mathrm{KNN}(\mathbf{Q},\mathbf{q}_i)$ ( $i\in [1,|\mathbf{Q}|]$ ). $\mathcal{Q}_i,|\mathbf{Q}|$ denote object proxy of $\mathbf{q}_i$ and total number of query instances. Each $\mathcal{Q}_i$ includes $K$ closest object queries $\{\mathbf{q}_{i_j}|j\in [1,K]\}$ of $\mathbf{q}_i$ . This local proxy effectively captures geometric structure and spatial layout of objects in 3D scene. The predefined spatial geometric priors are then formulated as: + +$$ +\mathbf {q} _ {i _ {j}} ^ {\prime} = \operatorname {c o n c a t} \left(\mathbf {q} _ {i} - \mathbf {q} _ {i _ {j}}, \mathbf {q} _ {i}, \| \mathbf {q} _ {i} - \mathbf {q} _ {i _ {j}} \|\right), j \in [ 1, K ] \tag {2} +$$ + +$\mathbf{q}_i^{\prime}$ embeds relative orientation and distance of 3D objects. + +Further, the low-level geometric priors are embedded as positional embedding $h_{i_j}$ with an EdgeConv layer $\mathcal{E}[\cdot]$ : + +$$ +\mathbf {h} _ {i _ {j}} = \mathbf {q} _ {i _ {j}} ^ {\prime} + \mathcal {E} [ \mathbf {q} _ {i _ {j}} ^ {\prime} ], \forall j \in \mathcal {Q} _ {i}. \tag {3} +$$ + +In each layer of IDPA, we regenerate the object proxy using nearest neighbors. In this manner, EdgeConv dynamically captures local geometric relationships among 3D objects and their high-level dependencies in the feature space. + +Beyond refining spatial relationships, our LISA serves to further modulate instance-specific positional embeddings via a geometric-semantic warping mechanism. Specifically, it adjusts spatial features of each 3D object instance to align with contexts provided by promptable features $\mathbf{T}$ : + +$$ +\mathbf {r} _ {i} = \left\{\mathbf {r} _ {i _ {j}} \mid j \in [ 1, K ] \right\} = \alpha (\mathbf {T}) \odot \frac {\left\{\mathbf {h} _ {i _ {j}} \right\} - \mathbf {h} _ {i}}{\Omega + \varepsilon} + \beta (\mathbf {T}) \tag {4} +$$ + +
MethodScanReferNr3DSr3DMulti3DRefer
UniqueMultipleAverageEasyHardVDVIDAverageEasyHardVDVIDAverageZTSTMTAverage
3DVG [69]60.628.434.748.534.834.843.740.854.244.944.651.751.445.816.726.525.5
M3DRef-CLIP [67]77.236.844.755.643.4——49.4—————39.430.637.938.4
BUTD-DETR [24]65.034.038.660.748.446.058.054.668.663.253.067.667.0————
EDA [61]68.637.642.358.246.150.253.152.170.362.954.168.768.1————
G3-LQ [59]72.740.845.662.050.753.857.157.074.766.357.274.073.1————
LIBA [60]74.344.149.072.457.260.366.664.578.970.261.777.375.8————
ViL3DRel [8]68.630.737.770.257.462.064.564.474.967.963.873.272.8————
3DJCG [4]64.330.837.3——————————66.916.726.226.6
UniT3D [12]73.131.139.1——————————————
3D-VisTA [73]75.139.145.872.156.761.565.164.278.871.358.977.376.4————
PQ3D [74]78.246.251.275.058.762.868.666.782.772.862.980.579.757.743.640.950.1
Mamba-3VL (Ours)79.948.953.577.862.966.771.569.784.475.869.181.881.769.545.743.553.2
+ +Table 1. Grounding accuracy (%) on 3D-VG benchmarks. Results on ScanRefer and Multi3DRefer are reported under IoU@0.5. The ZT and ST results from Multi3DRefer are with distractors of the same class. "VD" and "VID" means "View-Dependent" and "View-Independent". + +
ModelAP\( AP_{50} \)\( AP_{25} \)headcommontail
Closed-Vocabulary
Mask3D [52]26.936.241.439.821.717.9
PQ3D (w/cls) [74]27.038.946.335.824.220.0
Mamba-3VL (w/cls)27.939.648.237.526.423.3
Open-Vocabulary
OpenScene [46]11.715.217.813.411.69.9
SAM3D [63]6.114.221.37.06.24.6
OVIR-3D [40]13.024.932.314.412.711.7
OpenMask3D [54]15.419.923.117.114.114.9
OpenIns3D [23]8.810.314.416.06.54.2
PQ3D [74]20.228.032.530.917.011.3
OV-3DIS [44]23.729.432.827.821.221.8
Mamba-3VL (Ours)22.430.534.733.620.413.8
+ +Table 2. Instance segmentation results on ScanNet200 [51], with w/cls indicating the closed-vocabulary classification head. + +
MethodTest Dataset
WhatIsHowCanWhichOtherOverall
ClipBERT [30]30.260.138.763.342.542.743.3
SQA3D [42]31.663.846.069.543.945.346.6
3D-VisTA [73]34.863.345.469.847.248.148.5
PQ3D [74]37.161.344.560.947.045.147.1
Mamba-3VL44.565.748.368.448.952.852.4
+ +$\varepsilon$ is a small constant for numerical stability. $\alpha (\mathbf{T})$ and $\beta (\mathbf{T})$ are learnable factors modulated by promptable features $\mathbf{T}$ (e.g., texts). $\Omega$ is standard deviation across all object proxies. + +Further, instance features $\mathbf{x}_i$ are semantically "warped" according to their prompt-modulated spatial features $\mathbf{r}_i$ : + +$$ +\mathbf {x} _ {i} ^ {\prime} = \operatorname {W a r p i n g} \left(\mathbf {r} _ {i}, \mathbf {x} _ {i}\right) = \operatorname {L i n e a r} \left(\operatorname {c o n c a t} \left(\mathbf {r} _ {i}, \mathbf {x} _ {i}\right)\right), \tag {5} +$$ + +The instance-specific positional embeddings $\mathbf{x}_i^{\prime}$ encodes rich object-centric attributes. Finally, $\mathbf{x}_i^{\prime}$ is updated by aggregating the neighboring queries with softmax-based weights: + +$$ +\bar {\mathbf {x}} _ {i} = \sum \operatorname {s o f t m a x} \left(\mathbf {x} _ {i j} ^ {\prime}\right) \cdot \mathbf {x} _ {i j} ^ {\prime} \in \mathcal {R} ^ {d}, \forall j \in [ 1, K ], \tag {6} +$$ + +Table 3. Answer accuracy on the SQA3D [42] by question types. + +
MethodC@25C@50B-4@50M@50R@50Avg.
Scan2Cap [11]53.735.222.421.443.630.7
3DJCG [4]60.847.731.524.351.138.7
3D-VisTA [73]71.066.934.027.154.345.6
X-Trans2Cap [64]61.843.825.122.545.334.2
MORE [26]58.938.923.021.744.332.0
PQ3D [74]87.180.336.029.157.950.8
3D-VLP [28]64.150.031.824.551.239.4
Mamba-3VL (Ours)91.284.039.530.859.853.5
+ +Table 4. Results of 3D dense captioning on Scan2Cap [11] under IoU@50, evaluated by text similarity scores. + +The output $\bar{\mathbf{x}}_i$ of IDPA is incorporated into the mamba-based query decoder branch via a residual connection. IDPA supplements instance-specific positional embeddings to Mamba Mixer for precise spatial relationship modeling of objects. + +# 3.4. Output Heads and Losses + +As shown in Fig. 3, our Mamba-3VL utilizes three output heads to support 3D-VL tasks. We compute the cross entropy loss $\mathcal{L}_{\mathrm{grd}}$ and $\mathcal{L}_{\mathrm{gen}}$ for both grounding and generation heads, while the dice loss $\mathcal{L}_{\mathrm{mask}}$ is applied to the mask head. The model is optimized through multi-task learning with combined losses. Further details are provided in Appendix C.1. + +# 4. Experimental Results + +# 4.1. Implementation Details + +We evaluate the Mamba-3VL on multiple 3D-VL datasets, i.e., ScanNet200 [51], Multi3DRefer [67], ScanRefer [6], Sr3D/Nr3D [1], SQA3D [42], ScanQA [2], Scan2Cap [11]. We utilize AdamW [38] optimizer with a base learning rate of 1e-4 and a warm-up cosine scheduler. Our method implements two-stage optimization: (1) 800-epoch ScanNet200-based initialization through instance segmentation training with a classification head. (2) 80-epoch full-task training on all benchmark datasets with promptable queries. The hidden dimension and query decoder layer is set to $d = 768$ , $L = 4$ . + +![](images/caad829e6cb1e0532a107f838ec95d16a5e1dd09fe7fe8c24ba38b23b8e34099.jpg) +you are looking for the chair closest to the front. it is on the right side, right behind the chair leg. + +![](images/8cdb664c6782826f007a2f360eff805300e25bd81b5312794edb41667e98450c.jpg) +The bookshelf you want to pick is on the end of middle bookshelves, next to the shorter strip of orange carpet. + +![](images/8d5f6c17942754c1377a975f276472dfa9907f1f983f32328ea29cbd8e45e4cb.jpg) +the floral printed chair is in front of glass double doors. the floral printed chair is to the left of grey desk. + +![](images/a85ba4a21789b09b3f9b2ba264e731076211ba80840c07ff265536f6ac5bfb3b.jpg) +this desk is longer and located at the foot of the bed. It is located on the opposite wall from the door. + +![](images/e790c9d765916202ba290ee23a97577161f2d82e0580ef43f0b386203cdeedad.jpg) +(a) Visual Grounding (ScanRefer, Nr3D, and Multi3DRefer) +it is a dark colored two-sealer futon located by the door. it is located underneath a whiteboard. + +![](images/ebd8165e08ba42145a3c22a9fa051fbf7360f02be2f5b44296f936c124d82d44.jpg) +the chair is part of a row of chairs and is surrounded by one on its left and one on its right. + +![](images/acbecf840f3a14a8f3d0f4b4822aa345ec67ee365a3161fdf1a511cb6b76ac31.jpg) +the towel is hanging on the bar of shower door, and it is the left most towel. The one closest to the door. + +![](images/d4aa38e578299918561bd94488cc45fc3d32417a21f2544af0e7c0bd0c224381.jpg) +a library boasts a pristine white window. The windows located on the wall above the bookshelf. + +![](images/6e5f947da6c056b12a81af8ecc960fd92ec0358ea9f9f7ce0bd166d9725baade.jpg) +the chair the closes to the bed in the northeast corner from entrance the chair has a curved backside. + +![](images/d4f31e6fcc0b948b3af07b8b39f9940c9ba3e7898b9b3a76b48bc502b8c84739.jpg) +the back of the room holds a chair, with another chair in front of this one. + +![](images/eb31e8ebefda8cd91d876933bcaea512c2f6b5924e650cdd4b1a2f7cf84c2dca.jpg) +the window is the leftmost placed on the side of the wall. The window is rectangular as a clear middle area. + +![](images/a843e691a44d2dcdc6f331d5245d77cb2542c34f760992c9e0eeed1cadd26d25.jpg) +a blue armchair is perpendicular to blue-green couch on right, opposite the rectangular white coffee table. + +![](images/c0a485ff36e6292e243efafbb21108dd416701791bd10feeed8095379ad75e65.jpg) +Where is the red pillow located? GT on bed +Ours: on top of the bed + +![](images/a1497fd3d0ffacdb45afaa93f05f744e3a3efb0ec5a3f7e19568951eb8ef13f2.jpg) +What color is trash can near printer? GT: black trash can +Ours: black + +![](images/1b786349fd1ba060d4248649c777267609179d23df74bf3c18a1fd3d875c8e6a.jpg) +(b) Question Answering (ScanQA and SQA) +How many chairs surround the table? GT: two chairs. +Ours: two + +![](images/50d845b54b17ac8c10195fd17e59d1a6b20f3ecebca7174105328d84cc39b253.jpg) +red backpack is on right side, an d I am facing wall. Are all the chairs in the room the same color? + +![](images/12844b9aa0b6644a2817255ade68c69f5d69ccf459917becf9bd9b7bd999c31c.jpg) +I am facing the table. There is no more chair on my left. Is the amount of oven I am facing odd or even? + +![](images/f2edd2b98d6a8ce15a671a7f8d8373b4f42f595d41541752c1061ef802875d59.jpg) +I am facing a whiteboard and there are thrash cans on my right. Which wall has a clock hanging on it? + +![](images/ed3cc3e89fff24dfcdf0913d2a18bc4c581d90b5a92dbe30e0f221e625189a7a.jpg) +this is a long white tablethe right of another table . itin the middle of the room +Figure 5. Visualizations on several 3D-VL tasks. (a) Visual grounding on ScanRefer [6] and Multi3DRefer [67]. (b) Question answering on ScanQA [2] and SQA [42]. (c) Dense captioning on Scan2Cap [11]. Comparisons with PQ3D shows our Mamba-3VL's superior ability. + +![](images/275862b23894af54fe127a1c664e038bdb1ce5b90ea2bd4809fc0c37115f57e3.jpg) +the table is in center of the room. the table is a brown rectangle and surrounded by chairs + +![](images/64f4ad75da2830ba0870b34aad5118883c4d51eb4cadf8677a71274c4b981d49.jpg) +(c) Dense Captioning (Scan2Cap) +It is a white shower curtain on top of the bathtub. it is to the right of toilet when you walk in. + +![](images/9eefed52115d72427a9369b28a8fb0865c2af8f1be3229f182be157402af8193.jpg) +this is a desk covered with itemsIt is a light brown rectangle. It isin front of the bed . + +![](images/0ddcce705a9de502a866a4484a51bb5c6756bc04d17b97b26341c24a019ebd9f.jpg) +this is a bookshelf. it is rectangular with many items. It is to the left of the blue chair. + +![](images/2781b2f149fcf487580bcb463a364d8b2f9ce8ee3259543f680004bdad634508.jpg) +this is a bed with a white matted . It is sitting on the left ofanother bed + +
MethodEM@1EM@10BLEU-1BLEU-2BLEU-4ROUGEMETEORCIDErSPICE
ScanQA [2]23.5/20.956.5/54.131.6/30.721.4/21.212.0/10.834.3/31.113.6/12.667.3/60.212.0/11.3
3D-VisTA [73]27.0/23.057.9/53.534.4/30.2——38.6/32.815.2/12.976.6/62.6—
Image+MCAN [42]22.3/20.853.1/51.226.7/26.318.5/17.914.3/9.731.3/29.212.1/11.560.4/55.69.1/8.9
VoteNet+MCAN [42]19.7/18.150.7/48.629.5/29.617.2/17.86.1/7.130.9/29.112.1/11.758.2/53.310.4/10.3
ScanRefer+MCAN [42]20.6/19.052.4/49.727.9/27.017.3/16.27.5/7.830.7/28.612.0/11.457.4/53.410.6/10.6
PQ3D [74]26.1/20.0—43.0/36.1——42.9/34.017.8/13.987.8/65.2—
3D-VLP [28]24.6/21.655.9/53.933.2/31.522.7/23.611.2/15.836.0/31.814.2/13.170.2/63.412.7/12.5
Mamba-3VL (Ours)27.6/23.458.2/54.145.8/38.424.7/26.414.8/16.244.6/36.719.2/15.889.3/67.913.8/13.7
+ +Table 5. Answer accuracy on the ScanQA [2] benchmark, with separate evaluations for "test w/ object" and "test w/o object". Metrics include top-1/top-10 exact match (EM@1, EM@10) and text similarity scores (BLEU, METEOR, CIDEr, SPICE) for predicted answers. + +The neighbor size of object proxy is configured to $K = 10$ . For embodied AI tasks, we replace the T5-small [49] model of generation head with Vicuna-7B [13] using the instruction-following dataset [21]. See Appendix C.3 for more details. + +# 4.2. Results on 3D Vision-Language Tasks + +3D Visual Grounding. As outlined in Tab. 1, our Mamba-3VL dominates 3D visual grounding benchmarks, surpassing state-of-the-arts by significant margins. The model achieves landmark accuracies of $79.9\%$ (Unique) and $48.9\%$ (Multiple) on the ScanRefer [6], outperforming PQ3D [74] by $1.7\%$ and $2.7\%$ , respectively. The Mamba Mixer's unique relation-prioritized spatial scanning policy effectively models spatial dependencies, which excels in handling cluttered 3D + +scenes. Our method exhibits view-invariant robustness with $3.9\%$ and $6.2\%$ improvements over PQ3D on VD subsets of $\mathrm{Nr3D / Sr3D}$ benchmarks. On Multi3DRefer [67], Mamba-3VL attains $69.5\%$ , $45.7\%$ , and $43.5\%$ scores, showing a substantial improvement in different object referencing levels. To explain, IDPA provides instance-specific positional embeddings and refines spatial relationships among different object instances, showing superiority in multi-object scenarios. Visual comparisons in Fig. 5 (a) intuitively confirms our remarkable results across visual grounding benchmarks. In the challenging MT referencing task of Multi3DRefer [67], we conclude Mamba-3VL's exceptional ability to align texts with 3D referrals in complex scenes, even amidst distractors. + +Instance Segmentation on ScanNet200. As evidenced + +
Methodsseparatingpack-googleput-blocks
-piles-objects-seq-in-bowls
seenunseenseenunseenseenunseen
Transporter48.452.346.337.364.718.7
CLIP-only90.271.095.857.897.744.5
RN50-BERT46.544.994.056.191.823.8
CLIPort89.062.884.470.310045.8
LEO98.875.276.679.886.235.2
Mamba-3VL98.881.580.183.988.341.7
+ +Table 7. Results on the object navigation task in the Habitat-web [50] and CortexBench [43]. + +
MethodsMP3D-valHD3M-val
SuccessSPLSuccessSPL
Habitat (shortest)4.42.2——
Habitat (70k demo)35.410.4——
VC-1 (ViT-B)——57.131.4
LEO23.115.223.119.1
PQ3D——80.050.0
Mamba-3VL24.519.783.953.4
+ +Table 8. Comparison with other linear-complexity works on 3D-VL datasets. + +![](images/9d00f978d9c853f699b30b077ab90e270f9f3f229ffa9b1aee3fed334b745413.jpg) + +Table 6. Results on CLIPort robot manipulation. + +
IDSpatial.Channel.IDPAScanRef.Multi3D.Scan2C.SQA3D
(a)✓X50.150.450.747.5
(b)X✓49.249.750.147.0
(c)XX49.550.150.547.2
(d)✓✓52.452.052.651.0
(e)✓X52.151.951.850.6
(f)X✓51.851.651.150.1
(g)✓✓53.553.253.552.4
+ +Table 9. Ablation study of proposed modules' effectiveness, with average performance evaluated under IoU@0.5. + +in Tab. 2, Mamba-3VL establishes new competitive benchmarks for 3D instance segmentation on ScanNet200 [51]. In open-vocabulary setting, we integrate CLIP [48] text embeddings in a promptable way and compute class logits from the grounding head after full-category prompting. Impressively, Mamba-3VL achieves comparable performance, recording an AP of $22.4\%$ , showcasing its potential as a versatile interface for 3D open-vocabulary instance segmentation. When incorporating the classification head, Mamba-3VL mitigates the class imbalance issue inherent in the feature space of CLIP and outperforms PQ3D by $3.3\%$ on tail classes. Fig. 4 vividly demonstrates that our Mamba-3VL accommodates a variety of prompts as inputs, e.g., texts or visual interactions to facilitate single-target and multiple-target referring segmentation. These findings also highlight the Mamba-3VL's flexibility in advancing interactive 3D scene understanding. + +3D Dense Captioning. As evidenced in Tab. 4, the results underscore Mamba-3VL's notable superiority on the 3D dense captioning task, securing a top position on the leaderboard. Mamba-3VL achieves Cider scores of 91.2 (IoU@25) and 84.0 (IoU@50), significantly outperforming PQ3D (87.1 and 80.3), which demonstrates its superior capacity to generate contextually accurate captions. Further, our method surpasses other leading approaches in both Bleu-4 and Meteor scores, reflecting improved fluency and better semantic alignment with contextual details of 3D scenes. Such performance gain is attributed to the channel twisting, which enriches the cross-modality interaction by preserving crucial spatial context and integrating task-relevant cues. In the last row of Fig. 5, the captions generated by our method are not only rich in detail and contextually appropriate but accurately convey colors (white table), geometric shape (rectangular), and spatial relations (on top of, the right of) of 3D objects. + +
Spatial +ScanningChannel +ScanningNr3DScan2CapScanQA (EM@1)
EasyHardCiderBleuw/ obj.w/o. obj.
RandomTwisting74.658.380.835.724.120.5
w/o. FISTwisting75.360.582.636.926.421.9
w/o. NISTwisting76.961.783.438.127.022.8
RelationAdaIN77.662.483.139.026.822.4
RelationAttention77.161.282.838.726.522.1
RelationTwisting77.862.984.039.527.623.4
+ +Table 10. Ablations of the selection of scanning mechanism. + +3D Question Answering. For the SQA3D [42], Mamba-3VL outperforms all existing state-of-the-arts across different challenging question types as illustrated in Tab. 3. Our Mamba-3VL excels with $48.3\%$ accuracy on "How" and $48.9\%$ on "Which" questions, demonstrating its profound capability in commonsense and multi-hop reasoning. To explain, the FIS mechanism enhances Mamba-3VL's ability to capture long-range dependencies and interpret multi-hop relationships. On ScanQA [2] benchmark in Tab. 5, Mamba-3VL also sets a new standard for performance, demonstrating improvements of $2.8\% / 2.3\%$ in BLEU-1, $1.7\% / 2.7\%$ in ROUGE, and $1.5\% / 2.7\%$ in CIDEr on the "w/ object" and "w/o object" sub-sets. It validates Mamba-3VL's exceptional ability to generate semantically rich and contextually coherent responses for question answering. Mamba-3VL delivers distinguished EM@1/10 scores without conventional QA classification heads, attributed to the NIS policy and the IDPA module that model spatial relation via proximity-based spatial scanning and the instance-aware positional encoding. + +Task Planning and 3D Dialog. In this part, we fine-tune the pre-trained Mamba-3VL to complete dialogue and planning tasks on 3RPlan [21] and 3RDialog [21]. Qualitative examples in Fig. 6 indicate Mamba-3VL's abilities in generating well-structured task planning and scene-grounded dialogue. Mamba-3VL's response incorporates rich informative spatial relations and concrete 3D objects, performing admirably in multi-step reasoning and contextual dialogue. + +Embodied Navigation and Robotic Manipulation. We benchmark Mamba-3VL's generalizability of embodied acting and interacting in 3D physical world. We present results of CLIPort [53] manipulation and 3D object navigation in Tab. 6 and 7. Our findings are as follows: (1) For robotic manipulation, Mamba-3VL consistently outperforms com + +![](images/fa5b5e866f5402a394b11867550677462a3af29e83b0093587e3bae269a6e002.jpg) + +![](images/3e775418a3cdba20bef4f0ef50188d2427d6f0569e5cb9b5744aee59fc056c66.jpg) + +# Tidy up and arrange the kitchen. + +![](images/bbad80e68ca3052a66d19ab7f528d05d80d50c95fab1ba3f3c9ba031aec70d4c.jpg) + +![](images/0b0bc748fddad10f2f184e6453e5eadf4fcea9557335b32f4031348b5d084d33.jpg) + +# Arrange and adorn the living room. + +![](images/59d4377ee4f635eb5d28027f6e4a630e2debda8bf2f431ce94b75640ec0b4ef2.jpg) + +![](images/27b57c284f5857a0f4b96918fd9ef90f4b09763be48ed685fc854b9d38e23b27.jpg) + +![](images/3cc45c0f0af212101f665d374c9d587f6c8d578f9f293bb172404ae8a76b576e.jpg) + +# I want to add some decorations to my bedroom. What do you suggest? + +![](images/9f1ee6e1a01b266fb4f98053b7a638a167231516bc32e0a563fc9122db963858.jpg) + +How about adding some artwork to the wall? It can bring color and personality to the room. You can consider hanging a picture or two on the wall. + +![](images/c978928b7e6f57f21ef54a7668e8f6b681c89b9c1d51a7439c2de895bc2fda8c.jpg) + +# Can you describe the objects in the bedroom? + +![](images/eecf178b970caac22683bcfeb7059bc9e7721a37d4f4bede08e57a5a9fd7352d.jpg) + +Sure! The bedroom contains a bed, an ottoman, a picture on the wall, two lamp, two nightstand, a commode, some clothes, a window with blinds, a shelf and a bin + +![](images/3797c6d7ed490aa54b6005eb0b95089c3f20fa2813e147f58381e73656d2be1d.jpg) + +# Thank you for the information. + +![](images/83751c9e33a5be56265e0fa2171d988ada00792688afd1387c78aba9145d059c.jpg) +Figure 6. Visualization results of the scene-aware task planning and embodied conversation on the 3RPlan [21] and 3RDialog [21] datasets. + +You're welcome! Let me know if you need any further assistance. + +1. Clean the kitchen counter by wiping it down with a cleaning solution + +2. Clear the clutter by removing any items lying on the kitchen counter +3. Clean the stove by wiping off any grease or food residue. +4. Clean the windows by spraying a glass cleaner and a cloth. +5. Clean the heater by dusting it off + +![](images/0cfc6256a8a43cc6b56a017593a7b01256f18dbc52c591ef637724c4901caf3f.jpg) + +1. Arrange the pillows on the sofa and making sure they are spaced evenly. +2. Dust and wipe down the surfaces of the TV stand, shelves, and chest. +3. Switch on the TV and set the volume or change the channel as desired. +4. Tidy up the items on the shelves, making sure they are organized. +5. Take blanket off sofa and fold neatly + +petitors on challenging unseen tasks, while achieving seen performance on par with SOTA baselines. (2) On object navigation task, Mamba-3VL attains remarkable success rate and SPL [50] on MP3Dval and HD3M-val compared with transformer-based generalists LEO and PQ3D, suggesting Mamba-3VL prioritizes spatial-semantic relationships, e.g., obstacle avoidance and long-range path planning. Mamba-3VL excels in delivering generalized object-centric representations to LLMs, which is conceptualized as a mamba-based visual policy analogous to RT-series models [3, 45]. + +# 4.3. Ablation Study and In-depth Analysis + +Compared with Linear-complexity Methods. We substitute the Mamba Mixer block with alternative linear attention approaches, i.e., Linformer [55], SOFT [39], and Focused-Linear [20] to highlight the superiority of Mamba-3VL in 3D-VL tasks. Tab. 8 demonstrates that the synergistic integration of explicit relation-prioritized scanning policy and dynamic cross-modality interaction positions Mamba-3VL as an adaptable solution for 3D-VL tasks, achieving SOTA performance while maintaining computational efficiency. + +Component-wise Ablation. We herein present several alternative designs to highlight advantages yielded by various modules as shown in Tab. 9. When comparing (b) and (d), the relation-prioritized spatial scanning brings substantial gains on the SQA3D [42] $(2.3\%)$ and Multi3DRefer [67] $(1.6\%)$ datasets, underscoring capabilities to explicitly capture intricate spatial relationships. The transition of (a) to (d) reveals a marked improvement when integrating spatial scanning with channel twisting. To explain, it propagates task-related cues across channels which facilitates multi-modality interaction. Comparing (d) and (g), IDPA with enhanced spatial relationship modeling and instance-specific positional embedding solidifies Mamba-3VL's performance in 3D-VL reasoning. As shown in Tab. 8, linear positional encoding substitutions for IDPA (Ours w/ Linear PE) produce performance degeneration, proving IDPA's superiority. Combining all modules, + +synergistic benefits yield a significant uplift, achieving an accuracy of 53.5 in ScanRefer [6] and 52.4 in SQA3D [42]. + +Selection of the Scanning Mechanism. In Tab. 10, we further offer a detailed analysis to investigate the effectiveness of Mamba Mixer's scanning mechanism. Compared to random-ordering scanning, our relation-prioritized spatial scanning policy achieves significant gains across all tasks. This highlights the necessity of explicitly modeling hierarchical (local&global) relation for 3D-VL reasoning. Removing either component (i.e., w/o. FIS/NIS) results in performance degradation, suggesting their complementary roles. Moreover, channel twisting mechanism outperforms alternative fusion methods in cross-modal features interaction. Cross-attention treats all tokens within a sequence equally, failing to capture the hierarchical dependencies within 3D scenes. While AdaIN provides global feature normalization, it is not explicitly designed for task-oriented 3D spatial reasoning. + +We detail hyper-parameter selection (Tab. A), more framework ablations of Mamba-3VL (Tab. B, F, H), holistic results (Tab. C-E, G), and visualizations (Fig. A-D) in Appendix. + +# 5. Conclusion + +In this paper, we first investigate capabilities of State Space Model (SSM) in 3D-VL tasks. We present Mamba-3VL, a lightweight yet powerful method to perform spatial reasoning with enhanced multi-modal interaction to tackle 3D-VL tasks. Compared with transformer-based models, Mamba-3VL attains linear complexity, guaranteeing top-tier performance and generalization potential. At its core, multi-modal Mamba Mixer explicitly formulates 3D vision-language interaction via a tailored channel twisting mechanism and a spatial relation-prioritized scanning policy to model spatial relationships of 3D objects. The IDPA is proposed to capture instance-specific features and further strengthen local relation of 3D objects. Extensive experiments and visualizations demonstrate the superiority of Mamba-3VL, performing admirably on multiple 3D-VL and Embodied AI benchmarks. + +# References + +[1] Panos Achlioptas, Ahmed Abdelreheem, Fei Xia, Mohamed Elhoseiny, and Leonidas Guibas. Referit3d: Neural listeners for fine-grained 3d object identification in real-world scenes. In European Conference on Computer Vision, pages 422-440. Springer, 2020. 2, 5 +[2] Daichi Azuma, Taiki Miyanishi, Shuhei Kurita, and Motoaki Kawanabe. Scanqa: 3d question answering for spatial scene understanding. 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While promising results have been demonstrated in image classification, its potential in multi-label image classification remains underexplored. To bridge this gap, we propose a novel Mamba-based decoder, which utilizes the intrinsic attention of Mamba to aggregate visual information from image features into label embeddings, yielding label-specific visual representations. Building upon this, a MambaML framework is developed for multi-label image classification, which models the self-correlations of image features and label embeddings with bi-directional Mamba, as well as their cross-correlations with the Mamba-based decoder, allowing visual spatial relationships, label semantic dependencies, and cross-modal associations to be explored in a unified system. In this way, robust label-specific visual representations are acquired, facilitating the training of binary classifiers towards accurate label recognition. Experiments on public benchmarks suggest that our MambaML achieves performance comparable to state-of-the-art methods in multi-label image classification, while requiring fewer parameters and computational overhead. + +# 1. Introduction + +Multi-label image classification is one of the fundamental tasks in computer vision, which requires identifying multiple objects from a input image. Unlike single-label classification, where only one salient object is identified, multi-label classification faces the challenge of dealing with images containing various objects and combinations. This complexity makes the task more intractable. Multi-label image classification has garnered sustained research enthusiasm for many years due to its importance in a wide range of downstream applications, such as scene understanding [44] and human attribute recognition [35]. + +![](images/b98fa60b0ab7d35139391003f07d910225260934c381a3ea0dcca22fa80ff6f9.jpg) +Figure 1. A brief illustration of the proposed MambaML framework. It incorporates a bi-directional Mamba to enhance the convolutional feature maps with the global context of the input image, and a Mamba-based decoder to acquire label-specific visual representations for classification. The decoder is instantiated by stacking multiple layers of Mamba-based cross-attention module and bidirectional Mamba module. The former aggregates visual information from the feature maps into the query tokens, while the latter captures semantic dependencies among these tokens. + +One of the central challenges in multi-label image classification is effectively modeling the complex correlations among labels. Existing approaches can be broadly divided into three categories: those based on recurrent neural networks (RNNs) [4, 49, 58], those utilizing graph networks [6, 8, 51, 59, 67], and those employing multi-head self-attention (MHA) [9, 33, 37, 66, 68]. While promising performance has been achieved, these studies face substantial challenges in terms of time and computational efficiency. In particular, RNN-based and graph network-based methods suffer from the time-consuming process of iterative propagation, whereas MHA-based approaches are burdened by quadratic complexity concerning image size. These inherent limitations motivate the development of an innovative architecture that offers linear computational complexity and parallel acceleration capability, thereby enhancing the efficiency of multi-label image classification. + +In light of the above issue, we focus on Mamba [20], renowned for its exceptional ability to capture long-range dependencies in sequential data across various natural language processing tasks. Mamba enhances state space models (SSMs) [22, 46] with a selective mechanism that retains or discards information from each sequential token based on its significance. Coupled with hardware-aware optimizations for parallel computing, Mamba generates robust representations with linear computational complexity, encouraging extensive exploration for image classification. Existing methods [32, 39, 55, 57, 65] divide input images into a set of non-overlapping patches, which are then linearly projected into vector sequence and processed using vanilla Mamba to capture contextual dependencies through linear scanning. Additionally, diverse scanning strategies, such as multi-directional raster scan [39, 65], local scan [32], continuous scan [57] and tree topology scan [55], are explored to enhance Mamba's ability to model spatial relationships among image patches. Despite achieving impressive performance, these architectures fail to process sequences of differing lengths, such as label embeddings and patch features. Consequently, the potential of Mamba for multi-label image classification remains unexplored. + +In this study, we begin by introducing the intrinsic attention mechanism of Mamba during linear scanning, providing intuition for the design of Mamba-based cross-attention. Next, we present a novel MambaML framework, which takes label embeddings as learnable query tokens to acquire label-specific visual representations for multi-label image classification. As illustrated in Figure 1, MambaML initially incorporates a bi-directional Mamba to enhance visual features with global image context. Subsequently, a Mamba-based decoder is developed, with each layer consisting of a Mamba-based cross-attention module and a bidirectional Mamba module. The former aggregates visual information from image features into query tokens, while the latter explores semantic dependencies between these tokens. Specifically, we propose state space sharing and label-wise pooling strategies for Mamba-based cross-attention, addressing the challenge posed by sequences of different lengths. Consequently, each decoder layer effectively captures self-correlations among query tokens and their cross-correlations with image features. After multiple layers of updating, the output query tokens adeptly extract essential information from the input image, producing robust visual representations for multi-label classification. Overall, our main contributions are summarized as follows: + +- We introduce a Mamba-based cross-attention mechanism, which endows Mamba with the ability to capture cross-correlations between label embeddings and image features. To the best of our knowledge, this work represents the first exploration of the Mamba architecture for multi-label image classification. + +- We develop an advanced MambaML framework, which is capable of jointly modeling spatial relationships between image features, semantic dependencies among label embeddings, as well as their cross-correlations, thereby producing robust label-specific visual representations. +- We conduct extensive experiments on public benchmarks to show the superiority of our MambaML framework in multi-label image classification, which achieves comparable performance to state-of-the-art methods while requiring fewer parameters and FLOPs. + +# 2. Related Work + +# 2.1. Multi-label Image Classification + +Multi-label image classification has garnered increasing attention over the years in computer vision and supports many downstream applications [18, 19]. To capture label correlations, existing studies can be categorized into sequence-based and graph-based methods. Sequence-based methods [4, 49, 58] aim to exploit semantic correlations of label representations by sequential models, while graph-based methods model label dependencies through graph message propagation. For example, Chen et al. [8] employed graph convolutional networks to map label graphs into separate label classifiers for prediction. Wang et al. [51], Chen et al. [6] and Zhu et al. [67] constructed directed label graphs using data co-occurrence statistics to guide interactions among label representations. Ye et al. [59] modeled instance-level label graphs as a parameterized module, incorporating them into end-to-end training within the overall framework. + +On the other hand, spatial dependencies among objects within images are critical in multi-label image classification. Wang et al. [52] used a spatial transformation layer to pinpoint target regions and LSTM units [29] to capture global dependencies among these regions, sequentially predicting label confidences. Chen et al. [5] proposed a recurrent attention reinforcement learning framework that detects informative regions iteratively and explicitly models their long-term dependencies, using these attention regions for label prediction. Wu et al. [53] introduced a graph matching mechanism to explore potential instance-label matches for multi-label classification. However, the iterative processes inherent in sequential models and graph models cannot be parallelized, resulting in significant time overhead. + +Recently, Vision Transformer (ViT) [14] has fueled research in multi-label image classification. Cheng et al. [9] developed a multi-label Transformer that utilizes window partitioning, intra-window pixel attention, and cross-window attention for label recognition. Lanchantin et al. [33] designed a framework based on the Transformer encoder to effectively model the complex dependencies between visual features and labels. Zhu et al. [66] proposed a dual-stream Transformer network to simultaneously ex + +plore label correlations and cross-modal textual-visual interactions. Liu et al. [37] employed label embeddings as queries, using the Transformer decoder to selectively extract class-related features from visual feature maps. Zhu et al. [68] extracted pixel-level representations using multihead self-attention for enhanced classification. + +Although current methods have achieved considerable performance gains in multi-label image classification, they either suffer from iterative propagation latency of sequential models and graph networks or face challenges of quadratic computational complexity in multi-head attention. These limitations motivate the development of a novel architecture capable of modeling label correlations, while providing linear computational complexity and parallel acceleration. + +# 2.2. State Space Models + +As pioneers in this domain, Gu et al. [23] were the first to integrate the linear state space layer into the HiPPO framework [21], addressing the challenge of modeling long-range dependencies in an efficient way. Building on this foundation, Gu et al. [22] further improved the efficiency of SSMs by parameterizing them as a diagonal plus low-rank matrix. The breakthrough success of the so-called S4 model has since spurred significant interest and ushered in a new era for SSMs [16, 25, 30]. To achieve Transformer-like modeling capabilities with linear complexity, Gu & Dao [20] introduced Mamba, which integrates a data-dependent selection mechanism into the S4 layer, streamlining both computation and architecture in a hardware-friendly manner. Further simplifying the parameter matrix into a scalar representation, Dao & Gu [12] developed Mamba2, revealing intrinsic connections between SSMs and attention mechanisms through a specific structured matrix. This innovation enables the exploration of larger, more expressive state spaces without compromising efficiency. + +However, challenges persist when processing visual data due to its inherent complexity and multi-dimensional spatial structures, which have hindered the progress of visual SSMs. One of the pioneering approaches was S4ND [42], which applied independent 1D SSMs to each dimension of multi-dimensional data. Inspired by this, Baron et al. [2] later extended the idea into a discrete multi-axial framework by introducing the 2D-SSM spatial layer, effectively adapting 1D SSMs for two-dimensional operation. To date, visual SSMs have explored various scanning orders and patterns to preserve spatial consistency, including bidirectional scanning [39], four-way scanning [65], continuous scanning [45], zigzag scanning [31], window-based methods [32], and topology-based scanning [26]. Such diverse approaches reveal the promising potential of SSMs in enhancing visual understanding, as evidenced by their successful application in multimodal foundation models [41], image restoration [24], and various other visual tasks [3, 34]. + +Existing Mamba-based architectures are limited to processing a single sequence of image patches, concentrating mainly on modeling relationships among these patches for image classification. They struggle to manage multiple sequences of varying lengths, highlighting the need for an extended Mamba architecture that can effectively capture cross-correlations between label embeddings and image features for multi-label image classification. + +# 3. Methodology + +In this section, we present details of the proposed method, covering background of Mamba in Sec. 3.1, Mamba attention in Sec. 3.2, and the MambaML framework in Sec. 3.3. + +# 3.1. Background + +SSMs in continuous systems map a input signal $x_{t} \in \mathbb{R}^{D}$ into the output $y_{t} \in \mathbb{R}^{D}$ by a hidden state vector $h_t \in \mathbb{R}^N$ , where $t, D$ and $N$ are the time step, channel number and state size, respectively. The procedure is formulated as: + +$$ +h _ {t} ^ {\prime} = \mathbf {A} h _ {t} + \mathbf {B} x _ {t}, \quad y _ {t} = \mathbf {C} h _ {t}, \tag {1} +$$ + +where $\mathbf{A} \in \mathbb{R}^{N \times N}$ , $\mathbf{B} \in \mathbb{R}^{N \times D}$ , $\mathbf{C} \in \mathbb{R}^{D \times N}$ . Structured state space sequence models (S4) integrate such continuous-time SSMs into deep learning community by the technique discretization based on Zero-Order Hold (ZOH) rule. Given a timescale parameter $\Delta \in \mathbb{R}^D$ , the discretization process is formulated as: + +$$ +\begin{array}{l} \overline {{\mathbf {A}}} = \exp (\boldsymbol {\Delta} \mathbf {A}), \\ - \end{array} \tag {2} +$$ + +$$ +\overline {{\mathbf {B}}} = (\boldsymbol {\Delta} \mathbf {A}) ^ {- 1} (\exp (\boldsymbol {\Delta} \mathbf {A}) - \mathbf {I}) \cdot \boldsymbol {\Delta} \mathbf {B}. +$$ + +Mamba [20] is developed to address the limitation of linear time invariance in SSMs. With this purpose, it obtains input-conditioned parameters $(\Delta, \mathbf{B}, \mathbf{C})$ by mapping linearly from the input sequence, allowing a time-varying system to focus more on relevant inputs for yielding more accurate representations. Providing the whole input sequence $\{x_i\}_{i=1}^L$ with $L$ being the sequence length, the per-time mapping process is denoted as follows: + +$$ +\mathbf {B} _ {i} = f _ {B} \left(x _ {i}\right), +$$ + +$$ +\mathbf {C} _ {i} = f _ {C} \left(x _ {i}\right), \tag {3} +$$ + +$$ +\boldsymbol {\Delta} _ {i} = \operatorname {s o f t p l u s} (f _ {\Delta} (x _ {i})), +$$ + +where $f_{B}(\cdot), f_{C}(\cdot)$ and $f_{\Delta}(\cdot)$ are linear layers; softplus $(\cdot)$ is an element-wise function that smoothly approximates the ReLU activation. Then, following the ZOH-based discretization rule in Eq. (2), the parameters $\overline{\mathbf{A}}_i, \overline{\mathbf{B}}_i$ can be obtained, leading to the discretized version of the Eq. (1): + +$$ +h _ {i} = \overline {{\mathbf {A}}} _ {i} h _ {i - 1} + \overline {{\mathbf {B}}} _ {i} x _ {i}, \quad y _ {i} = \mathbf {C} _ {i} h _ {i}. \tag {4} +$$ + +Mamba has been demonstrated to offer performance comparable to Transformer while requiring significantly lower computational and memory complexity. + +# 3.2. Attention in Mamba + +By rolling out the recurrent procedure in Eq. (4) within Mamba, we are able to obtain the following matrix multiplication form: + +$$ +\left[ y _ {1}, y _ {2}, \dots , y _ {L} \right] ^ {\top} = \boldsymbol {\alpha} \left[ x _ {1}, x _ {2}, \dots , x _ {L} \right] ^ {\top}, \tag {5} +$$ + +where $\alpha \in \mathbb{R}^{L\times L}$ is a lower triangular attention matrix. Each entity $\alpha_{i,j}$ is computed as follows: + +$$ +\alpha_ {i, j} = \left\{ \begin{array}{l l} 0, & \text {i f} i < j, \\ \mathbf {C} _ {i} \prod_ {k = j + 1} ^ {i} \overline {{\mathbf {A}}} _ {k} \overline {{\mathbf {B}}} _ {j}, & \text {i f} i \geq j. \end{array} \right. \tag {6} +$$ + +Then, following previous methods [39, 55], we use an approximation of $\overline{\mathbf{B}}_j$ based on the first-order Taylor Series: + +$$ +\begin{array}{l} \overline {{\mathbf {B}}} _ {j} = (\pmb {\Delta} _ {j} \mathbf {A}) ^ {- 1} (\exp (\pmb {\Delta} _ {j} \mathbf {A}) - \mathbf {I}) \cdot \pmb {\Delta} _ {j} \mathbf {B} _ {j} \\ \approx (\boldsymbol {\Delta} _ {j} \mathbf {A}) (\boldsymbol {\Delta} _ {j} \mathbf {A}) ^ {- 1} \boldsymbol {\Delta} _ {j} \mathbf {B} _ {j} \tag {7} \\ = \boldsymbol {\Delta} _ {j} \mathbf {B} _ {j}. \\ \end{array} +$$ + +Hence, by substituting the Eq. (2), Eq. (3) and Eq. (7) into the Eq. (6), the $\alpha_{i,j}$ ( $i \geq j$ ) can be reformulated as follows: + +$$ +\alpha_ {i, j} \approx Q _ {i} H _ {i, j} K _ {j}, \tag {8} +$$ + +where $Q_{i},H_{i,j}$ and $K_{j}$ are defined as: + +$$ +\begin{array}{l} Q _ {i} = f _ {C} \left(x _ {i}\right), \\ H _ {i, j} = \prod_ {k = j + 1} ^ {i} \exp (\operatorname {s o f t p l u s} \left(f _ {\Delta} \left(x _ {k}\right)\right) \mathbf {A}), \tag {9} \\ K _ {j} \approx \mathrm {s o f t p l u s} (f _ {\Delta} (x _ {j})) f _ {B} (x _ {j}). \\ \end{array} +$$ + +Specifically, $H_{i,j}$ underscores the significance of the consecutive input tokens from $x_i$ to $x_j$ , which is similar to the discussion in [1]. The above formulation inspires us that the attention in Mamba measures the correlation between $x_i$ and $x_j$ by mapping them into query and key vectors respectively, exhibiting similar behavior to the self-attention mechanism in Transformer [14, 48]. Notably, when both $x_i$ and $x_j$ originate from the same sequence, Mamba captures the self-correlations within the sequence. Conversely, when $x_i$ and $x_j$ are from different sequences, Mamba models the cross-correlations between two sequences. + +# 3.3. The MambaML Framework + +Based on the discussion in Sec. 3.2, we present the details of the MambaML framework developed for multi-label image classification. For convenience, we denote the candidate label set as $\{l_1, l_2, \dots, l_N\}$ , where $N$ is the total number of labels. Image features extracted by visual backbones are denoted as $\mathcal{F} \in \mathbb{R}^{M \times D}$ with $D$ being the channel dimension. $M$ represents the number of patches for ViT [14] and Mamba-based backbones [65] while the flattened convolutional regions for CNN-based backbones [27]. + +![](images/0f8bd6cbbd04e53110a596dcfa7c04d9d50c6672e7e8accaea43740f65e00530.jpg) +Figure 2. A detailed illustration of the proposed Mamba-based decoder. The set $\{f_1, f_2, \dots, f_M\}$ results from unpacking the image feature maps $F$ . Similarly, $\{q_1^l, q_2^l, \dots, q_N^l\}$ is derived by unpacking the query matrix $Q_l$ , where each $q_i^l$ represents the visual representation of the label $l_i$ at the $l$ -th layer of the decoder. + +Mamba-based Context Modeling. It is well known that, due to the limited size of convolutional kernels, the convolutional feature maps lack the ability to perceive the global image context. Therefore, MambaML first incorporates a bi-directional Mamba for data-dependent global visual context modeling, formulated as: + +$$ +F = \operatorname {M a m b a} _ {f w d} (\mathcal {F}) + \operatorname {M a m b a} _ {b w d} (\mathcal {F}), \tag {10} +$$ + +where $\mathrm{Mamba}_{\mathrm{fwd}}(\cdot)$ and $\mathrm{Mamba}_{\mathrm{bwd}}(\cdot)$ represent the Mamba-based sequence modeling processes for forward scanning and backward scanning, respectively. + +Mamba-based Decoder. Once the global context-aware image features are encoded, we further develop a Mamba-based decoder for label-specific visual representation learning. As illustrated in Figure 2, label embeddings act as queries to probe and gather visual information of interest from the feature maps $F$ , yielding precise representations for subsequent binary classification. Specifically, candidate labels are embedded by $N$ randomly initialized $D$ -dimensional vectors, which are packed into a query matrix $Q_0 \in \mathbb{R}^{N \times D}$ for joint learning with the entire framework in an end-to-end manner. Then, the query matrix $Q_0$ and feature maps $F$ are input into the Mamba-based decoder for acquiring label-specific visual representations. + +The decoding process for the $l$ -th layer of the Mamba-based decoder is detailed in Algo. 1. Concretely, in the Mamba-based decoder, the input control matrix $\mathbf{B}$ and the output control matrix $\mathbf{C}$ are linearly mapped from the image features and label embeddings, respectively, as shown in line 3 and line 7 of Algo. 1. Recalling the attention mechanism in Mamba discussed in Eq. (8) and Eq. (9), this decoding process is essentially a cross-attention between the label embeddings $Q_{l - 1}$ and image features $F$ , where the former acts as the query and the latter serves as the key. Consequently, label embeddings and image features are cor + +Algorithm 1 Mamba-based Decoder +Input: label embedding matrix $Q_{l-1}$ : (B, N, D) image feature matrix $F$ : (B, M, D) +Output: updated label embedding matrix $Q_l$ : (B, N, D) +1: $F': (B, M, D) \gets f_{in}(F)$ +2: A: (D, E) $\leftarrow$ Parameter $\triangleright$ Represents structured E × E matrix +3: B: (B, M, E) $\leftarrow$ $f_B(F')$ +4: $\Delta$ : (B, M, D) $\leftarrow$ softmax $(f_{\Delta}(F'))$ +5: $\overline{A}, \overline{B}$ : (B, M, D, E) $\leftarrow$ discretize $(\Delta, A, B)$ +6: h: (B, D, E, M) $\leftarrow$ SSM $(\overline{A}, \overline{B}, \text{None})(F)$ +7: C: (B, N, E) $\leftarrow$ $f_C(Q_{l-1})$ +8: h': (B, D, E, M, 1) $\leftarrow$ reshape(h) +9: C': (B, 1, E, 1, N) $\leftarrow$ reshape(C) +10: $Q_l': (B, D, E, M, N) \gets C' \cdot h'$ +11: $Q_l''': (B, D, M, N) \gets \text{sum}(Q_l', \dim = 2)$ $\triangleright$ Summation along the third (hidden state) dimension +12: $Q_l'''': (B, D, N) \gets \max(Q_l'', \dim = 2)$ $\triangleright$ Max-pooling along the third (spatial) dimension +13: $Q_l'''': (B, N, D) \gets f_{out}(Q_{l-1} + \text{Norm}(Q_l'')')$ +14: Ql: (B, N, D) $\leftarrow$ Mamba_fdw(Ql'') + Mamba_bwd(Ql''') +15: return Ql + +related in a linear scanning manner, allowing the visual information of the input image to flow into the label embeddings via Mamba's state space. Additionally, the semantic dependencies among label embeddings are further explored through a bi-directional Mamba, as shown in line 14 of Algo. 1. In this way, self-correlations among label embeddings and their cross-correlations with image features are both explored in a purely Mamba-based architecture with linear complexity. Through iterative updates across layers, label-specific visual representations are finally obtained for subsequent training of binary classifiers. + +Specifically, line 8 in Algo. 1 replicates the hidden states $N$ times to align with the length of label embedding sequence1. The intuition behind this is that all labels share the same state space, thus obviating the need of linear scanning for each label, which significantly improves model's efficiency. Similarly, line 9 in Algo. 1 replicates the control vector of each label $M$ times. This aligns them with the length of the image feature sequence, allowing the linear scanning in Mamba to proceed smoothly and aggregate the visual information into the replicas of each label embedding. Owing to the Mamba-based context modeling in Eq. (10), each token in the image feature sequence $F$ is rich in global information of the input image, thus enabling each label embedding replica to aggregate meaningful visual information fully. Naturally, as seen in line 12 of Algo. 1, we further apply a max pooling operation to those replicas, cap + +turing essential features and yielding robust label-specific visual representations. Finally, a bi-directional Mamba is applied to these label representations to model their semantic dependencies, as shown in line 14 of Algo. 1. + +Consequently, by integrating the Mamba-based context modeling module and Mamba-based decoder, the comprehensive MambaML framework is constructed for multi-label image classification. With this framework, the spatial relationships among image features, the semantic dependencies among label representations, as well as their cross-correlations are simultaneously explored, thereby producing robust label-specific visual representations and facilitating subsequent multi-label image classification. + +Classification. Following scanning and modeling by the Mamba-based decoder across $L$ layers, we derive a label embedding matrix $Q_{L}\in \mathbb{R}^{N\times D}$ . This matrix is then unpacked into a sequence of vectors $\{q_i\}_{i = 1}^N$ , where each vector $q_{i}$ encapsulates the visual representation of the label $l_{i}$ with respect to the input image. Subsequently, a linear classifier is used to compute the probability: + +$$ +p _ {i} = \sigma \left(w _ {i} ^ {\top} q _ {i}\right), \tag {11} +$$ + +where $\sigma (\cdot)$ is sigmoid function; $w_{i}\in \mathbb{R}^{D}$ is a learnable vector. Following previous approaches [6, 37], we employ the asymmetric loss [43] to train binary classifiers for each label for prediction, formulated as: + +$$ +\mathcal {L} = - \frac {1}{N} \sum_ {i = 0} ^ {N - 1} \left\{ \begin{array}{l l} (1 - p _ {i}) ^ {\gamma^ {+}} \log p _ {i}, & y _ {i} = 1, \\ p _ {i} ^ {\gamma^ {-}} \log (1 - p _ {i}), & y _ {i} = 0, \end{array} \right. \tag {12} +$$ + +where $y_{i}$ is a binary indicator; $y_{i} = 1$ if the label $l_{i}$ appears in the input image and 0 otherwise. The hyper-parameters $\gamma^{+}$ and $\gamma^{-}$ regulate the weights of positive and negative labels, respectively. + +# 4. Experiments + +# 4.1. Implementation Details + +In our experiments, we choose the widely used ResNet-101 [27] as vision backbone network for multi-label image classification. Unless otherwise specified, the resolution of input images is resized into $448 \times 448$ in both the training and testing phases throughout all experiments. The whole framework is trained for 80 epochs using AdamW [40] optimizer with a batch size of 128 and 1-cycle policy [47] with a maximum learning rate of 0.0001. Following the previous works [37, 43], we adopt the RandAugment [11] and Cutout [13] for data augmentation, and apply exponential moving average to model parameters with a default decay of 0.9997. The hyper-parameters $\gamma^{+}$ and $\gamma^{-}$ of the asymmetric loss [43] are set to 0 and 1, respectively. All experiments are conducted on a server with 8 NVIDIA A800 GPUs. + +
MethodResolution#param. (M)FLOPs (G)mAPAllTop-3
CPCRCF1OPOROF1CPCRCF1OPOROF1
ML-GCN [8]448×44842.531.583.085.172.078.085.875.480.389.264.174.690.566.576.7
CMA [60]448×448--83.482.173.177.383.776.379.987.264.674.289.166.776.3
TSGCN [56]448×448--83.581.572.376.784.975.379.884.167.174.689.569.369.3
MCAR [17]448×448--83.885.072.178.088.073.980.388.165.575.191.066.376.7
CSRA [64]448×44843.231.683.584.172.577.985.675.780.388.564.274.490.466.476.5
ASL [43]448×44842.731.585.0--80.3--82.3------
Q2L-R101 [37]448×448143.143.184.984.874.579.386.676.981.578.069.173.380.770.675.4
DATran [62]448×448133.048.084.984.874.979.686.077.681.688.866.275.890.767.777.5
C-TMS [54]448×448217.031.485.187.274.279.188.776.581.490.167.576.092.371.278.3
MambaML448×44885.036.985.786.175.180.387.777.682.389.466.576.391.568.278.1
SSGRL [6]576×57687.968.783.689.568.376.991.270.779.391.962.173.093.664.276.0
C-Tran [33]576×57667.962.285.186.374.379.987.776.581.790.165.776.092.171.477.6
ADD-GCN [59]576×57648.253.085.284.775.980.184.979.482.088.866.275.890.368.577.9
Q2L-R101 [37]576×576143.167.886.585.876.781.087.078.982.890.466.376.592.467.978.3
C-TMS [54]576×576217.0-86.288.275.380.489.677.282.591.168.777.093.372.579.4
DATran [62]576×576133.0-86.386.676.181.087.278.982.890.266.976.891.668.578.4
MambaML576×57685.059.686.786.976.481.388.079.083.290.067.176.991.968.878.7
+ +# 4.2. Comparisons with State-of-the-Arts + +In this subsection, we compare the performance of our proposed MambaML framework with its counterparts on the Microsoft COCO 2014 [36], NUS-WIDE [10] and Pascal VOC 2007 [15] datasets. + +Comparison on Microsoft COCO. As another prevalent benchmark in the multi-label image classification task, Microsoft COCO 2014 [36] (MS-COCO) has 82,081 images for training set and 40,137 images for validation set, covering 80 labels with almost 2.9 labels per image. Similar to previous approaches [37, 43, 64], Table 1 presents the precision, recall and F1-measure under the settings of all and top-3 labels of the listed models. Specifically, the upper part compares the performance of the proposed MambaML framework with other competitors using the standard input resolution of $448 \times 448$ . Our MambaML framework achieves $85.7\%$ in mAP, leading C-TMS [54] by $0.6\%$ in mAP, a considerable improvement in multi-label image classification. When using larger input resolution of $576 \times 576$ , MambaML also implements best performance in mAP, suggesting its robustness and scalability in terms of the input image size. In addition, The efficiencies of all models are also reported in Table 1. As shown, our MambaML outperforms several recent models—including DATran [62] and C-TMS [54]—by achieving higher mAP scores while simultaneously requiring fewer parameters (#param.) and computation (FLOPs) across both input resolutions. Overall, our MambaML framework strikes an excellent balance between performance and efficiency in multi-label image classification. We leave the comparisons with more recent methods to be discussed in Appendix B. + +Table 1. Experimental results on the Microsoft COCO dataset under the settings of all and top-3 labels (mAP in %). The optimal scores are highlighted in bold. + +
MethodmAPAllTop-3
CF1OF1CF1OF1
CNN-RNN [49]56.1--34.755.2
SRN [63]62.058.573.448.962.2
S-CLs [38]60.158.773.753.871.1
CMA [60]61.460.573.755.570.0
GM-MLIC [53]62.261.074.155.372.5
ICME [7]62.860.774.156.370.6
ASL [43]63.962.774.6--
Q2L [37]65.063.175.0--
C-TMS [54]62.861.474.655.272.8
MambaML65.963.775.059.870.7
+ +Table 2. Experimental results on the NUS-WIDE dataset under the settings of all and top-3 labels (mAP in%). The optimal scores are highlighted in bold. + +Comparison on NUS-WIDE. As a web dataset from the Flickr, the original NUS-WIDE [10] dataset contains a training set of 125,449 images and a testing set of 83,898 images. We follow the official split and that use 150,000 images for training and the remaining 59,347 images for testing. Experimental results are presented in Table 2. Compared with the Q2L model [37], our proposed MambaML framework achieves pronounced performance gain, improving mAP score from $65.0\%$ to $65.9\%$ , a total of $0.9\%$ improvement. On other significant metrics, such as CF1 and OF1, our MambaML framework also achieves best scores in most cases. The remarkable merits suggest the superior capacity of our MambaML in learning from the large-scale image dataset for multi-label image classification. + +
MethodplanebikebirdboatbottlebuscarcatchaircowtabledoghorsemotorpersnplantsheepsofatraintvmAP
RMIC [28]97.191.394.257.186.790.793.163.383.376.492.894.491.695.192.359.786.069.596.479.084.5
RLSD [61]96.492.793.894.171.292.594.295.774.390.074.295.496.292.197.966.993.573.797.587.688.5
RDAR [52]98.697.496.396.275.292.496.597.176.592.087.796.897.593.898.581.693.782.898.689.391.9
RARL [5]98.697.197.195.575.692.896.897.378.392.287.696.996.593.698.581.693.183.298.589.392.0
RCP [50]99.397.698.096.479.393.896.697.178.088.787.197.196.395.499.182.193.682.298.492.892.5
SSGRL†[6]99.597.197.697.882.694.896.798.178.097.085.697.898.396.498.884.996.579.898.492.893.4
ML-GCN [8]99.598.598.698.180.894.697.298.282.395.786.498.298.496.799.084.796.784.398.993.794.0
TSGCN [56]98.998.596.897.387.594.297.497.784.192.689.398.498.096.198.784.996.687.298.493.794.3
ASL [43]--------------------94.4
CSRA [64]99.998.498.198.982.295.397.897.984.694.890.898.197.696.299.186.495.988.398.994.494.7
DATran [62]99.998.798.698.482.696.097.798.685.096.284.798.598.296.998.885.097.986.799.295.294.6
C-TMS [54]99.596.297.696.586.495.895.298.988.797.587.699.299.297.399.085.098.186.199.194.294.8
MambaML99.898.697.898.082.896.398.198.384.096.788.398.298.696.899.087.596.889.899.295.195.0
+ +Comparison on Pascal VOC 2007. Pascal VOC 2007 [15] is one of the most widely used datasets in multi-label image classification task. It contains 20 labels and a total of 9,963 images, in which 5,011 images form train-val set and remaining 4,952 images constitute test set for model evaluation. Following the setting of existing works [37, 43, 66], our MambaML framework is trained on the train-val set and evaluated on the test set. Experimental results including the average precision (AP) of each label and mAP over all labels are reported in Table 3. Notably, our MambaML framework achieves state-of-the-art performance on both pre-training settings. Specifically, our MambaML shows prominent merits in recognizing potted plant and sofa, outperforming the sub-optimal results by $1.1\%$ and $1.5\%$ in AP. Overall, our MambaML framework implements the highest AP on nearly quarter of the label categories. + +# 4.3. Ablation Study + +In this subsection, we explore the effectiveness of key components within the MambaML framework. + +Effect of Key Components. We begin by examining the effectiveness of key components within the MambaML framework, specifically the Mamba-based context modeling (MCM) module and the Mamba-based semantic dependency modeling (MSDM) module in the decoder. The MCM module is designed to capture global visual contexts for each image feature, while the MSDM module focuses on modeling semantic dependencies among label representations. Both modules utilize architectures of bidirectional Mamba to achieve these objectives in a linear scanning manner. Experimental results are reported in Table 4. Clearly, both MCM and MSDM substantially improve the performance of the MambaML framework in multi-label image classification task. Absence of these modules results in a decline in mAP scores by $0.4\%$ , $0.5\%$ , and $0.7\%$ on the Pascal VOC 2007, MS-COCO, and NUS-WIDE + +Table 3. Experiments results on the Pascal VOC 2007 dataset in terms of class-wise precision (AP in %) and mean average precision (mAP in %). The symbol † denotes using a large input resolution (576×576). + +
MCMMSDMVOC 2007MS-COCONUS-WIDE
××94.685.265.2
✓×94.885.465.5
×✓94.885.565.6
✓✓95.085.765.9
+ +Table 4. The effects of key modules on the performance of the proposed MambaML framework (mAP in %). + +datasets, respectively, highlighting their crucial role in enhancing the performance of the framework on multi-label image classification. Moreover, the findings demonstrate the effectiveness of the bi-directional Mamba architecture in modeling correlations in sequence data. + +Effect of Mamba-based Decoder. We further investigate the effectiveness of the Mamba-based decoder, whose performance is susceptible to the number of decoder layers and hidden states within Mamba. Ablation studies on these two critical factors are illustrated in Figure 3, respectively. It is worth noting that when the number of hidden states or layers is zero, we present the performance of the backbone network. Interestingly, the performance of the MambaML framework in multi-label image classification does not benefit much from an increased number of hidden states and even deteriorate as the number of layers in the decoder grows. Nonetheless, in the initial stages, all performance curves show a marked increase, underscoring the importance of the Mamba-based decoder to the performance of the while MambaML framework in multi-label image classification. Benefiting from the exceptional capability of the Mamba-based decoder in aggregating pertinent visual information from input images to label embeddings, the MambaML framework is capable of acquiring robust label-specific visual representations, thereby achieving impressive performance in multi-label image classification. + +![](images/2127b46595d86a797fe866c389e90654a77cbd56ffd0951861dbae7e4ffbc580.jpg) + +![](images/4fd83b3c552c57e013922029b38416cff8ebe00a4931b6a7ceef7423778e555d.jpg) + +![](images/e24937f6ba0037ab384fd27863891f83ffdeab39f49332d45c97b6dee561867d.jpg) + +![](images/4c275448e9b986a7716b755eb2df485d3edc02d32fc8fe8394ede5ab64124117.jpg) +Figure 3. The impact of the number of hidden states and decoder layers on the performance of the MambaML framework on the Pascal VOC 2007, Microsoft COCO and NUS-WIDE datasets, respectively. + +![](images/1765a858527a35b6b8e228d84caeb37d3bf5cd3171a5d4e407f3208376fce8a0.jpg) + +![](images/f8ea325e08b245cf4d39efbe1f96486309614baf5328d106af3b8a0a3bf89a53.jpg) + +# 4.4. Visualization and Analysis + +In this subsection, we present a visualization of the attention maps within the MambaML framework to provide an in-depth analysis of its functionality in multi-label image classification. To achieve this, we randomly select several images from the MS-COCO testing set and depict their attention maps generated by MambaML using heatmaps. The visualization results are exhibited in Figure 4. It can be observed that most labels highlighted in blue, such as bed, book, chair, cat, cup person and truck, effectively concentrate on their semantically related image regions, thereby providing precise visual cues for classification and resulting in high prediction accuracies. Nevertheless, our MambaML framework also encounters challenges when dealing with small, occluded, or hidden objects of labels marked in red, such as bottle and backpack, motivating areas for potential improvement. Overall, our MambaML demonstrates proficiency in localizing and recognizing labels in most scenarios, achieving performance comparable to the state-of-the-art methods in multi-label image classification. + +# 5. Conclusion + +In this work, we propose an advanced MambaML framework for multi-label image classification. In this framework, the Mamba-based decoder leverages Mamba's inherent attention mechanism to implement cross-attention between image features and label embeddings. Together with bi-directional Mamba for scanning image features and label representations, the spatial relationships of image features, semantic dependencies among label embeddings, as well + +![](images/01e178ba2ef8df87e022c12982a0acb80563dbedcb15a560fc74e55edf526e70.jpg) +Figure 4. Visualization of attention maps in the MambaML framework on several examples from the MS-COCO testing set. + +as their cross-correlations are jointly explored in a unified Mamba-based architecture, producing robust label-specific visual representations for classification. Extensive experiments have demonstrated the effectiveness of our MambaML framework in multi-label image classification. + +Beyond a simple endeavor, we anticipate that our pioneering exploration on Mamba-based multi-label classification framework will encourage the research community to develop more effective Mamba architectures, which are expected to deliver superior classification performance while preserving commendable computational efficiency in terms of the multi-label image classification task. + +# Acknowledgments + +We thank Jiawei Ge for his insightful discussions and suggestions. This work was jointly supported by the Young Scientists Fund of the National Natural Science Foundation of China (42301520), the Research Grants Council of Hong Kong (25206524). + +# References + +[1] Ameen Ali, Itamar Zimerman, and Lior Wolf. The hidden attention of mamba models. arXiv preprint arXiv:2403.01590, 2024. 4 +[2] Ethan Baron, Itamar Zimerman, and Lior Wolf. 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The problem is hampered by its combinatorially large yet sparse solution space thus making learning to assemble a challenging task for current machine learning models. In this paper, we attempt to solve this task by leveraging the assembly instructions provided in diagrammatic manuals that typically accompany the furniture parts. Our key insight is to use the cues in these diagrams to split the problem into discrete and continuous phases. Specifically, we present Manual-PA, a transformer-based instruction Manual-guided 3D Part Assembly framework that learns to semantically align 3D parts with their illustrations in the manuals using a contrastive learning backbone towards predicting the assembly order and infers the 6D pose of each part via relating it to the final furniture depicted in the manual. To validate the efficacy of our method, we conduct experiments on the benchmark PartNet dataset. Our results show that using the diagrams and the order of the parts lead to significant improvements in assembly performance against the state of the art. Further, Manual-PA demonstrates strong generalization to real-world IKEA furniture assembly on the IKEA-Manual dataset. + +# 1. Introduction + +With the rise of the DIY trend, nowadays it is the consumers who are increasingly assembling products like IKEA furniture [2, 3, 21, 57, 58], LEGO structures [47, 49], and exercise equipments [45, 61]. This paradigm shift can reduce the product cost, but often poses challenges for untrained consumers, as an incorrect assembly in any step may lead to irreparable outcomes. Thus, automating the assembly or providing active help in the process is often desired. + +Automated assembly faces the dual challenge of large combinatorial solution space, parameterized by the number of discrete parts in the assembly, and the need for a precise 6D pose estimation that correctly connects parts between + +![](images/c46dd605da9836f4abcdb5ad77eda97ba6cb4ac33d7b23009f2c84c2b253fd1d.jpg) +(a) + +![](images/1ee31adc01153b10617b0df4629a028eac2b1bba3a690de82b47ac33f648ae19.jpg) +(b) +(c) +Figure 1. An illustration of the manual-guided 3D part assembly task. Given (a) a diagrammatic manual book demonstrating the step-by-step assembly process and (b) a set of texture-less furniture parts, the goal is to (c) infer the order of parts for the assembly from the manual sequence and predict the 6DoF pose for each part such that the spatially transformed parts assemble the furniture described in the manual. + +each other. The limited number of feasible, stable assembly sequences makes this discrete-continuous optimization problem extremely challenging, even for advanced neural networks, especially as the number of parts increases [54]. Fortunately, most assembly tasks include language-agnostic instruction manuals, such as diagrams, delineating the assembly. While such manuals help shrink the solution search space, the problem of correctly matching the 2D manual diagrams with their corresponding 3D object parts and inferring their assembly pose and order remains a significant challenge for automated systems. + +This paper introduces a method to enable machines to learn how to assemble shapes by following a visual instruction manual, a task we call manual-guided 3D part assembly. As illustrated in Fig. 1, given a set of parts and a manual, our approach interprets the manual's step-by-step diagrams to predict the precise 6D pose of each part, assembling them into the target shape. There are two lines of prior approaches that have similarities to our proposed task, namely methods that focus on the geometry of individual parts and inter-part relationships [8, 9, 23, 56, 59, 60], + +and methods such as MEPNet [49] that learns the assembly in specific conditions, such as LEGO shapes. The former rely on priors like peg-hole joints [25] or sequence generation [54] to reduce search complexity but are generative and may yield unstable assemblies due to occlusions [23]. The latter often simplifies the task by assuming that parts are provided step-by-step, e.g., LEGO manuals. However, furniture manuals, such as IKEA, may not have such information, and it is necessary to determine which parts are used at each step before assembly. Additionally, while LEGO tasks feature standardized "stud" joints, general furniture assembly is more complex and lacks such constraints. + +Based on the above observations, we identify two key challenges in our task. First, how to detect which part or parts are added at each step in the assembly diagrams. Given that these diagrams depict incremental assembly stages, the core challenge is to recognize newly added parts at each step. This requires aligning 2D assembly diagrams with the 3D parts to establish a correct assembly sequence. Second, how to effectively align the assembly process with the learned order. A straightforward approach is to directly use the learned sequence as the order for predicting poses, e.g., by adopting an auto-regressive prediction method similar to MEPNet [49]. However, this approach carries the risk of accumulating errors—if a mistake occurs in an earlier step, subsequent steps are likely to fail as well. On the other hand, completely disregarding the sequence forces the assembly model to implicitly find correspondences, which makes both learning and prediction significantly more difficult. Therefore, the inferred sequence should serve as a soft guidance for the assembly process, helping each part focus more on the relevant step diagram. + +To address these challenges, we present Manual-guided Part Assembly (Manual-PA), a novel transformer-based neural network that predicts correspondences between step diagrams and parts by computing their semantic similarity, which is learned using contrastive learning. Using this similarity matrix, we establish an assembly order via solving an optimal assignment problem between the aligned features of the 3D object parts and the ordered manual diagram steps, followed by permuting each part's positional encoding according to the learned order. Finally, a transformer decoder fuses the two feature modalities to predict the final 6DoF pose for each part. Notably, the cross-attention between step diagrams and parts is guided by the positional encoding, ensuring that each step diagram receives a higher attention score for its corresponding part. + +To empirically validate the effectiveness of Manual-PA, we conduct experiments on the standard PartNet benchmark dataset [27], on the categories of assembling the chair, table and storage classes. Our experiments and ablation studies clearly show that Manual-PA leads to state-of-the-art results on multiple metrics, including success rate, outper + +forming prior methods by a significant margin. Results further showcase the strong generalizability of our approach to real-world IKEA furniture assembly through experiments using the IKEA-Manual dataset [50]. + +We summarize our key contributions below: + +1. We introduce a new problem setup of assembling 3D parts using diagrammatic manuals for guidance. +2. We present a novel framework, Manual-PA, for solving this task that learns the assembly order of the 3D parts, which is then used as soft guidance for the assembly. +3. We present experiments on the benchmark PartNet and IKEA-Manual datasets demonstrating state-of-the-art performances and cross-category generalization. + +# 2. Related Works + +3D Part Assembly involves reconstructing complete shapes from sets of 3D parts, a task originally assisted by leveraging semantic part information [6, 11, 15, 43, 52, 55]. With the introduction of the PartNet dataset [27], recent works [8, 9, 28, 56, 59, 60] leverage geometric features. For instance, 3DHPA [9] uses part symmetry for a hierarchical assembly, SPAFormer [54] circumvents combinatorial explosion by generating a part order, and Joint-PA [25] introduces a peg-hole constraint to facilitate assembly. However, these methods are generative towards producing plausible final shapes without aiming for preciseness. Approaches like GPAT [24] and Image-PA [23] add guidance from point clouds or rendered images, respectively. Our work extends this direction by introducing guidance through instruction manuals, similar to how humans would do. + +Permutation Learning is often used in self-supervised methods for learning image representations [4, 16, 31, 35, 40]. However, in this work, we seek to align the 3D parts to instruction steps, for which we adopt a contrastive learning [14, 17, 22, 39] using a novel cross-modal alignment setup. 6DoF Object Pose Estimation methods can be classified into instance-level [36, 38, 53], category-level [44, 48], and unseen [20, 51]. Our approach relates to the unseen object category as furniture typically comprises novel parts. When the 3D models of these parts are available, many methods [7, 13, 26, 30, 34] rely on feature matching followed by the PnP algorithm to infer pose. However, IKEA-style manuals are represented as line drawings making accurate feature extraction for matching to 3D parts challenging. Alternatively, some approaches [20, 51] use end-to-end models to directly predict the 6D pose. A common approach is to use CNOS [29] for object segmentation. However, in assembly diagrams, where multiple parts are connected and depicted together, SAM-based methods [18] often struggle with accurate segmentation. Our approach addresses these challenges using an end-to-end framework that uses a cross-attention scheme to enable each part to attend to its relevant region in the step diagram. + +![](images/d0e8f5448eca3a7e4fa28f985b4f2c072c18d2a4cf46675a96be002251ebcbd2.jpg) +Figure 2. Overview of our proposed method Manual-PA. (a) Feature extraction (Sec. 3.2): we extract semantic and geometrical features from both the step diagrams of the assembly manual and the corresponding part point clouds using the image encoder and point encoder, respectively. (b) Manual-guided part permutation learning (Sec. 3.3): we compute a similarity matrix $\mathbf{S}$ between the two modalities, and subsequently apply the Hungarian algorithm to obtain the permutation matrix $\mathbf{P}$ for the parts. (c) Manual-guided part pose estimation (Sec. 3.4): we add positional encodings (PE) $\Phi$ to both the step diagrams and parts, where the PE order for parts is determined by the order predictions from (b). This is followed by a transformer decoder to enable multimodal feature fusion and interaction, along with a pose prediction head to determine the rotation $R_{i}$ and translation $t_i$ of each part. The predicted poses are then applied to the corresponding parts to obtain the final assembled shape $\mathbf{S}$ . + +# 3. Manual-Guided Part Assembly + +In this section, we first provide a concrete formal definition of the manual-based 3D part assembly task in Sec. 3.1. We then present a detailed explanation in Secs. 3.2 to 3.4 of the proposed learning pipeline as depicted in Fig. 2, followed by a description of the training process and the loss functions used for each stage in Sec. 3.5. + +# 3.1. Problem Formulation + +Our task involves two different input modalities: a set of 3D parts and a corresponding instruction manual. The 3D parts are represented as a multiset1 of unordered point clouds, denoted by $\{\mathcal{P}_i\}_{i=1}^N$ . Note that the number of parts $N$ may differ from furniture to furniture. The manual consists of an ordered sequence of $N$ step diagram images, denoted by $(\mathcal{I}_1, \mathcal{I}_2, \ldots, \mathcal{I}_N)$ ; each diagram depicting an incremental step in the assembly process of a 3D furniture shape $S$ . These step diagrams are 2D line drawings, which are 2D projections of textureless 3D CAD models of these parts captured from a camera $\mathcal{C}$ , and we assume for each step, only one additional part is attached to the furniture assembled thus far. Our goal is to align the 3D parts with their + +delineations in the respective manual steps towards predicting the assembly order of the parts and the part poses $\{(R_i,t_i)\in SE(3)\}_{i = 1}^N$ for the final assembled furniture, where $R_{i},t_{i}$ represent the $3\times 3$ rotation matrix and the three-dimensional translation vector respectively for the $i$ -th part in the SE(3) transformation space. That is, these parts undergo rigid transformations such that their combination constructs the complete 3D furniture shape $\mathcal{S}$ as seen from the viewpoint of camera $\mathcal{C}$ . + +# 3.2. Feature Extraction + +We first use off-the-shelf encoders to extract semantic latent features from the inputs. For the 3D part point clouds $\{\mathcal{P}_i\}_{i = 1}^N$ , we utilize a lightweight version of PointNet [37], similar to the one used in Image-PA [23], followed by a linear layer to map the features to a common dimension $D$ , resulting in geometric part features $\mathbf{f}^{\mathrm{P}}\in \mathbb{R}^{N\times D}$ . For sequences of step diagrams $(\mathcal{I}_j)_{j = 1}^N$ , given that the assembly instructions are provided step-by-step in an incremental manner, our primary focus is on the differences between consecutive steps. For any two consecutive diagram images $\mathcal{I}_j$ and $\mathcal{I}_{j + 1}$ , for $j = 1,2,\ldots ,N - 1$ , we compute the difference image given by $|\mathcal{I}_j - \mathcal{I}_{j + 1}|$ that shows which new part is added to the thus-far assembled furniture. Next, this + +difference image is patched into $K$ image patches, that are then fed to DINOv2 image encoder [5, 33] to extract features, followed by a linear layer to map these features to the same dimensionality $D$ , resulting in semantic image features $\mathbf{f}^{\mathrm{I}} \in \mathbb{R}^{N \times K \times D}$ . + +# 3.3. Manual-Guided Part Permutation Learning + +In our task, we seek to learn the order of a set of parts conditioned on an ordered sequence of step diagrams. This problem is similar to learning the feature correspondences between two modalities in order to align them, with an ideal alignment corresponding to a permutation matrix. Specifically, our objective is to derive a similarity matrix between the two modalities such that each modality feature is unambiguously assigned to its corresponding feature in the other modality and we desire this assignment matches with the ground truth order in the step sequence in the manual. Formally, we construct the similarity matrix $\mathbf{S} \in \mathbb{R}^{N \times N}$ as: + +$$ +\mathbf {S} _ {i j} = \operatorname {s i m} \left(\mathbf {f} _ {i} ^ {\mathrm {P}}, \mathbf {g} _ {j} ^ {\mathrm {I}}\right), \tag {1} +$$ + +where $\mathbf{g}^{\mathrm{I}}\in \mathbb{R}^{N\times D}$ is derived from the $N\times K\times D$ dimensional step-diagram features $\mathbf{f}^{\mathrm{I}}$ by performing a max-pooling operation on the patch dimension $K$ . We measure the similarity in the feature space using the dot product as $\operatorname {sim}(\mathbf{a},\mathbf{b}) = \mathbf{a}\cdot \mathbf{b}$ + +Next, we obtain the permutation matrix $\mathbf{P} \in \{0,1\}^{N \times N}$ by solving a bipartite matching optimization problem using the Hungarian matching algorithm [19] with cost $\mathbf{C} = -\mathbf{S}$ : + +$$ +\text {m i n i m i z e} \quad \sum_ {i = 1} ^ {N} \sum_ {j = 1} ^ {N} \mathbf {C} _ {i j} \mathbf {P} _ {i j} +$$ + +$$ +\text {s u b j e c t} \quad \sum_ {j = 1} ^ {N} P _ {i j} = 1, \quad \forall i \in \{1, \dots , N \} \tag {2} +$$ + +$$ +\sum_ {i = 1} ^ {N} P _ {i j} = 1, \quad \forall j \in \{1, \dots , N \} +$$ + +$$ +P _ {i j} \in \{0, 1 \}, \quad \forall i, j \in \{1, \dots , N \}, +$$ + +where we minimize the cost, subject to constraints ensuring $\mathbf{P}$ is a permutation matrix, i.e., each row and column of $\mathbf{P}$ contains exactly one entry equal to 1, with all other entries being 0. The final part order can be obtained by $\sigma = \operatorname{argmax}(\mathbf{P})$ where $\operatorname{argmax}$ is applied columnwise. + +# 3.4. Manual-Guided Part Pose Estimation + +Positional Encoding. Since the attention mechanism in the transformer is permutation-invariant, we follow Vaswani et al. [46] in using positional encoding to convey the order of both step diagrams and parts to the model. Formally, the positional encoding is defined as a function that maps a scalar to a sinusoidal encoding, $\phi : \mathbb{N} \to \mathbb{R}^D$ : + +$$ +\phi (x) _ {2 i} = \sin \left(\frac {x}{\tau_ {p} ^ {2 i / d}}\right), \phi (x) _ {2 i - 1} = \cos \left(\frac {x}{\tau_ {p} ^ {2 i / d}}\right), \tag {3} +$$ + +where $i = 1,\dots ,d / 2$ indexes the dimension and $\tau_{p}$ is a temperature hyperparameter. By applying $\phi$ to encode the sequential order of step diagrams as they appear in the manual (i.e., using $x$ as a simple increasing sequence $1,2,\ldots ,N$ ), we obtain a positional encoding $\Phi \in \mathbb{R}^{N\times D}$ , where $\mathbf{p}^{\mathrm{I}}\coloneqq \Phi$ . Given the permutation matrix $\mathbf{P}$ that corresponds to the order of the parts, we can compute the positional encoding for the parts as $\mathbf{p}^{\mathrm{P}} = \mathbf{P}^{T}\Phi$ . During training, we use the ground truth part order, whereas at inference time, we replace it with the predicted permutation matrix $\hat{\mathbf{P}}$ , yielding $\hat{\mathbf{p}}^{\mathrm{P}} = \hat{\mathbf{P}}^{T}\Phi$ . These positional encodings are then added to the respective features before being fed into the transformer decoder and provide soft guidance on the sequence order. We adopt RoPE [42] for better performance. + +Transformer Decoder. The modality interaction and fusion between step diagrams and parts occur through a stack of $L$ transformer [46] decoder layers. In each layer, the self-attention module receives the output from the previous layer (initially, the part features $\mathbf{f}^{\mathrm{P}} + \mathbf{p}^{\mathrm{P}}$ in the first layer) to perform part-to-part interactions. This is followed by a cross-attention module that injects and fuses the step diagram features $\mathbf{f}^{\mathrm{I}} + \mathbf{p}^{\mathrm{I}}$ with the part features processed by the self-attention module, enabling step-to-part interactions. Notably, for the step diagram features, we concatenate the features from all diagrams from the same manual along the patch dimension, resulting in a tensor of shape $\mathbb{R}^{NK\times D}$ . + +Pose Prediction Head. Finally, the output $O_{\mathrm{Dec}}$ from the transformer decoder is fed into a pose prediction head, which predicts the translation and rotation for each part, denoted as $(\hat{R}_i,\hat{t}_i)$ . In our implementation, the rotation matrix $\hat{R}_i$ is represented as a unit quaternion $\hat{q}_i\in \mathbb{R}^4$ . We initialize its bias to an identity quaternion $(1,0,0,0)$ and normalize the prediction to ensure a unit norm. + +# 3.5. Training and Losses + +First, we train the manual-guided part order learning model until it successfully aligns the two modalities and provides an optimal permutation for the parts. Subsequently, we train the transformer decoder-based part pose estimation model using the predicted order from the first model to infer the part poses. Our empirical results indicate that having an accurate part order is crucial for enhancing the inference performance of the pose estimation network. + +Loss for Permutation Learning. Borrowing the notation from Secs. 3.2 and 3.3, we define the contrastive-based order loss as: + +$$ +\mathcal {L} _ {\text {o r d e r}} = - \frac {1}{B} \sum_ {i = 1} ^ {B} \log \frac {\exp \left(\sin \left(\mathbf {f} _ {\sigma (i)} ^ {\mathrm {P}}, \mathbf {g} _ {i} ^ {\mathrm {I}}\right) / \tau\right)}{\sum_ {j = 1} ^ {B} \exp \left(\sin \left(\mathbf {f} _ {\sigma (i)} ^ {\mathrm {P}}, \mathbf {g} _ {j} ^ {\mathrm {I}}\right) / \tau\right)}, \tag {4} +$$ + +where $B$ is the mini-batch size, $\tau$ is the temperature, and $\sigma(i)$ denotes the index for the $\sigma(i)$ -th part that corresponds to the $j$ -th step according to the ground truth part order $\sigma$ . Here, mini-batches are constructed by sampling pairs + +of step-diagram and part features, $(\mathbf{f}_{\sigma(i)}^{\mathrm{P}}, \mathbf{g}_j^{\mathrm{I}})$ for optimizing the InfoNCE loss [12, 32]. Note that we randomly sample one part from their geometric-equivalent group. In this setup, pairs $(\mathbf{f}_{\sigma(i)}^{\mathrm{P}}, \mathbf{g}_i^{\mathrm{I}})$ are considered as positive, otherwise negative. This loss encourages positive pairs to have higher similarity while negative pairs have lower similarity, allowing the similarity matrix to be used for generating the permutation matrix via Hungarian matching, as discussed in Sec. 3.3. + +Losses for Pose Estimation. Given a set of furniture parts, there may be subsets of parts that are geometrically identical to each other, such as the four legs of a table, the armrests on both sides of an armchair, or the support rods on the back of a chair. We denote geometrically equivalent parts as a part group $\mathcal{G}$ . Within each group, we calculate the chamfer distance between these parts and the ground truth. Then, we apply Hungarian Matching (see Sec. 3.3) again with cost: + +$$ +\mathbf {C} _ {i j} = \mathrm {C D} \left(\hat {R} _ {i} \mathcal {P} _ {i} + \hat {t} _ {i}, R _ {j} \mathcal {P} _ {j} + t _ {j}\right), \tag {5} +$$ + +where CD denotes the chamfer distance measuring the similarity between unordered two point clouds [10], $i$ and $j$ index the parts within $\mathcal{G}$ , and $\hat{R}$ and $\hat{t}$ denote the respective predicted rotation and translation. The optimal matching sequence is denoted as $\mathcal{M}$ . + +For the 3D part assembly task, following Li et al. [23], we supervise translation and rotation separately. We compute the $\ell_2$ -distance for translation as follows: + +$$ +\mathcal {L} _ {T} = \frac {1}{N} \sum_ {i = 1} ^ {N} \| \hat {t} _ {[ i ]} - t _ {i} \| _ {2}, \tag {6} +$$ + +where $[i]$ denotes the index of the matched part corresponding to the $i$ -th part under optimal matching $\mathcal{M}$ . + +In addition to the geometric similarity between the parts mentioned above, each part itself may also have intrinsic symmetries. For instance, a cylindrical table leg has axial symmetry. Thus, we cannot simply use the absolute distance $(e.g., \ell_2)$ on rotation as a supervision signal. Instead we use chamfer distance to supervise the rotation per part: + +$$ +\mathcal {L} _ {C} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mathrm {C D} \left(\hat {R} _ {[ i ]} \mathcal {P} _ {i}, R _ {i} \mathcal {P} _ {i}\right). \tag {7} +$$ + +However, some parts may not be perfectly symmetric, e.g., due to small holes in different locations. To address these cases, we still encourage the model to penalize the $\ell_2$ distance for the rotation as a regularization term, formally expressed as: + +$$ +\mathcal {L} _ {E} = \frac {1}{N} \sum_ {i = 1} ^ {N} \| \hat {R} _ {[ i ]} \mathcal {P} _ {i} - R _ {i} \mathcal {P} _ {i} \| _ {2}. \tag {8} +$$ + +Additionally, to ensure that the predicted assembled shape closely matches the ground truth, we compute the + +chamfer distance between the predicted and ground truth assembled shapes: + +$$ +\mathcal {L} _ {S} = \mathrm {C D} \left(\bigcup_ {i = 1} ^ {N} \left(\hat {R} _ {[ i ]} \mathcal {P} _ {i} + \hat {t} _ {[ i ]}\right), \bigcup_ {i = 1} ^ {N} \left(R _ {i} \mathcal {P} _ {i} + t _ {i}\right)\right), \tag {9} +$$ + +where $\cup_{i=1}^{N}$ indicates the union of $N$ parts to form the assembled shape. + +Finally, the overall loss for pose estimation is computed as a weighted sum of the aforementioned losses: + +$$ +\mathcal {L} _ {\text {p o s e}} = \lambda_ {T} \mathcal {L} _ {T} + \lambda_ {C} \mathcal {L} _ {C} + \lambda_ {E} \mathcal {L} _ {E} + \lambda_ {S} \mathcal {L} _ {S}. \tag {10} +$$ + +# 4. Experiments + +# 4.1. Datasets + +Following [8, 9, 23, 28, 54, 56, 59, 60], we use PartNet [27], a comprehensive 3D shape dataset with fine-grained, hierarchical part segmentation, for both training and evaluation. In our work, we adopt the train/validation/test split used by Li et al. [23], where shapes with more than 20 parts are filtered out, and we use the finest granularity, Level-3, of PartNet. We focus on the three largest furniture categories: chair, table and storage, containing 40,148, 21,517 and 9,258 parts, respectively. Besides that, to demonstrate the generalizability of our method, we also evaluate its zero-shot capabilities on the IKEA-Manual [50] dataset, which features real-world IKEA furniture at the part level that are aligned with IKEA manuals. For consistency with PartNet, we evaluate both chair category with 351 parts, and table, with 143 parts. Storage is excluded due to only 3 samples. + +For each individual part, we sample 1,000 points from its CAD model and normalize them to a canonical space. Geometrically-equivalent part groups are identified based on the size of their Axis-Aligned Bounding Box (AABB). To generate the assembly manual, we render diagrammatic images of parts using Blender's Freestyle functionality. More details of the preprocessing and rendering process are provided in the supplementary material. + +# 4.2. Evaluation Metrics + +To evaluate the effectiveness of 3D part assembly of different models, we employ three key metrics: Shape Chamfer Distance (SCD) [23], Part Accuracy (PA) [23], and Success Rate (SR) [24]. SCD quantifies the overall chamfer distance between predicted and ground truth shapes, providing a direct measure of assembly quality, scaled by a factor of $10^{3}$ for interpretability. PA assesses the correctness of individual part poses by determining whether the chamfer distance for a part falls below a threshold of 0.01, reflecting the accuracy of each part's alignment. Finally, SR evaluates whether all parts in an assembled shape are accurately predicted, offering a strict criterion for complete assembly success. + +Table 1. 3D part assembly results on the PartNet test split and Ikea-Manual. $\dagger$ : We re-trained the Image-PA model using diagrams (2D line drawing images) as the conditioning input instead of the original RGB images. The values in bold represent the best results, while underlined indicate the second. $\ddagger$ : Average over five runs. + +
MethodConditionSCD↓PA↑SR↑
ChairTableStorageChairTableStorageChairTableStorage
Fully-Supervised on PartNet [27]
DGLNIPS'20 [56]-9.15.0-39.0049.51----
IETRA-L'22 [59]-5.43.5-62.8061.67---
Score-PABMVC'23 [8]-7.44.5-42.1151.55-8.32011.23-
CCSAAAI'24 [60]-7.0--53.59-----
3DHPACVPR'24 [9]-5.12.8-64.1364.83----
RGLWACV'22 [28]Sequence8.74.8-49.0654.16----
SPAFormerArXiv'24 [54]Sequence6.73.84.555.8864.3856.1116.4033.507.850
Joint-PACVPR'24 [25]Joint6.07.0-72.8067.40----
Image-PAECCV'20 [23]Image6.73.75.045.4071.6040.20---
Image-PA†ECCV'20Diagram5.93.93.762.6770.1047.7919.9732.834.730
Manual-PA w/o OrderManual3.03.64.279.0774.0348.5434.1337.714.054
Manual-PA (Ours)Manual1.71.82.989.0687.4156.5158.0356.664.730
Manual-PA (Ours)Multi-Part3.43.53.384.6378.9553.4138.3140.155.405
Manual-PA (Ours)Multi-View‡3.63.23.082.0475.4954.3738.3139.964.054
Zero-Shot on IKEA-Manual [50]
3DHPACVPR'24-34.337.8-1.9144.027-0.0000.000-
Image-PA†ECCV'20Diagram17.314.7-19.0736.74-0.00010.53-
Manual-PA w/o OrderManual12.88.9-38.3642.01-1.75410.53-
Manual-PA (Ours)Manual11.44.8-42.5149.72-3.50915.79-
+ +# 4.3. Main Results + +Fully Supervised on PartNet. In this setting, we train our model on PartNet for each category and test it on unseen shapes in the test split, which share similar patterns with the training set. As shown in Tab. 1, our method, Manual-PA, significantly outperforms all previous approaches in all three categories. Specifically, Manual-PA achieves superior performance compared to all other conditioned methods. Notably, when compared to Image-PA, we observe improvements of 26, 17 and 8 part accuracy for the chair, table and storage categories, respectively. This shows that for the 3D Part Assembly task, instruction manuals provide far better guidance than a single image or other conditioning inputs. "Manual-PA w/o Order" refers to our model without access to the part assembly order information, requiring it to learn this implicitly. Although the instruction manual provides strong visual guidance, performance improvements remain limited in this case, highlighting the challenges of implicit learning. By explicitly learning the correspondences between step diagrams and parts and applying positional encoding as soft guidance, we achieve PA improvements of approximately 10, 13 and 8 in the chair, table and storage categories, respectively. Note that all other methods, except for Image-PA and ours, are generative and follow the setting proposed by [56], where multiple assembly results are generated with varying Gaussian noise for the + +same set of parts. Only the most faithful assembly (based on Minimum Matching Distance [1]) is evaluated. + +Extension to More Realistic Assembly Settings. Our problem setting arises from the lack of a standardized format in real-world instruction manuals, which makes it difficult to define a universal learning framework. Our model is designed with scalability and generalizability in mind, allowing it to be extended to more realistic assembly scenarios. To demonstrate this, we implement and evaluate our framework under two challenging settings: 1) Multi-Part Assembly, where multiple new parts are introduced in a single step. In this scenario, parts are grouped based on their geometric similarity, and their positional encodings are adjusted accordingly to reflect their associations. 2) Multi-View, where each step diagram is captured from a randomly chosen viewpoint among eight predefined angles, simulating the viewpoint variations commonly observed in real manuals. To handle these variations, we modify the vision encoder to encode consecutive step diagrams separately before concatenating their features as input. As shown in Tab. 1, while these more complex settings introduce additional challenges and result in some performance degradation compared to the original setup, our method still significantly outperforms baseline approaches. These results highlight the robustness and versatility of our framework, demonstrating its ability to generalize beyond the + +![](images/6021ebf01050470f1082bf9b9ded031293f318874da6eb8811c4487718f495cd.jpg) +Figure 3. Results trained on chair and tested table and storage. Solid bars: cross-category; lighter bars: same-category. Arrows show performance drop with percentages above. + +single-part-per-step assumption and handle more practical assembly tasks. Further details on these experiments are provided in the supplementary material. + +Cross-Category Generalization. We evaluate cross-category generalization by training both Manual-PA and Image-PA on the chair category and testing on chair, table, and storage. As shown in Fig. 3, the performance drop of Manual-PA when tested on unseen categories is minimal compared to that of Image-PA, indicating stronger cross-category generalization. This result suggests that Manual-PA does not solely rely on shape priors but effectively extracts assembly-relevant information from manuals, enabling strong performance even on unseen shapes. These findings reinforce the advantage of using stepwise instruction diagrams as guidance for 3D part assembly. + +Zero-shot on IKEA-Manual. We use the same model, pretrained on PartNet, to directly estimate the poses of furniture in IKEA-Manual, where all shapes are 3D models of real-world IKEA furniture, and each part corresponds to illustrations in their official assembly manuals. As shown in Tab. 1, our method, significantly outperforms strong competitors such as 3DHPA and Image-PA, demonstrating the strong generalizability of our approach to real world. + +# 4.4. Ablation Studies + +Effect of the Order for 3D Part Assembly. We conduct experiments to explore various methods for incorporating order information in a 3D part assembly model, as shown in Tab. 2. First, by comparing lines 1 and 2, we observe that adding sequential information solely to part features improves assembly performance. We attribute this improvement to two factors: (1) distinguishing geometrically equivalent components, and (2) mitigating the combinato + +Table 2. Ablation results for various order designs on the PartNet chair test split. We use GT order for both training and inference. + +
#TypeStepPartsSCD↓PA↑SR↑
1PE4.372.2222.50
2PE✓3.079.3133.88
3OneHot✓3.079.0734.13
4OneHot✓✓2.781.2236.92
5PE (Ours)✓✓1.795.3873.07
+ +Table 3. Ablation results for various component designs in permutation learning on the PartNet chair test split. KT denotes the Kendall-tau coefficient that measure the ordinal correlation between predicted and GT order. + +
VariantsKT↑SCD↓PA↑SR↑
Manual-PA (Ours)0.7891.789.0658.03
w/o batch-level sampling0.4102.356.9315.68
w/ Sinkhorn0.7741.788.2556.26
w/ GT Order1.0001.795.3873.07
+ +rial explosion problem, as claimed in SPAFormer [54]. Second, by comparing lines 2 and 5, where the latter provides both the step diagram and part features with correct correspondence, we achieve a significant performance boost. This indicates that explicitly establishing correspondence between steps and parts is beneficial, as learning these correspondences implicitly remains challenging for the model. Last, our empirical results show that, when position information is solely relevant to self-attention (lines 2 and 3), both PE and OneHot encodings yield similar performance. This observation aligns with prior transformer-based studies, which also utilize OneHot encodings [9, 54, 59]. However, in cases requiring cross-attention (line 4 and 5), PE outperforms OneHot encodings, highlighting its advantages in cross-attentive contexts. + +Analysis of Permutation Learning Choices. We conduct an ablation study for permutation learning, as shown in Tab. 3. First, we find that batch-level sampling is essential compared to applying contrastive learning individually within each manual book. This is primarily because contrastive learning benefits from a larger pool of negative samples. Second, while we employ the Sinkhorn [41] algorithm on the similarity matrix to enforce that rows and columns sum to one, empirical results indicate limited performance improvement. Last, by providing the model with the ground truth assembly order, we establish an upper performance bound for our assembly model. + +# 4.5. Visualization and Analysis + +Demonstration of Soft Guidance. We manually add different positional encodings to the feature of chair's back, as shown in Fig. 5. With PE(5), the model focuses on the final position, aligning well with the correct step diagram. + +![](images/d1012fae2f211719a7a5e12dad7e6eaf22b6d3345f52a182560e40f55cdb5236.jpg) +Figure 4. Qualitative comparison of various 3D part assembly methods. Four examples are shown: chair (a) and table (b) from the PartNet dataset, and chair (c) and table (d) from the IKEA-Manual dataset. + +![](images/92abb7530521214acb3eceaf903a17bfdbbd508c2fa627ef8ea52fdbd860142b.jpg) +Figure 5. Visualization of the cross attention scores between step diagrams (top) and a part (left, chair's back) with PE at different positions. The final assembly results are displayed on the right. + +However, when PE(2) is applied, drawing the model's attention to the second step diagram, the model struggles to accurately predict the chair's back pose. Notably, even with PE(0), the model manages to shift its attention toward the correct final step, demonstrating the fault tolerance and robustness of soft guidance: the model can still identify the correct match even when given an incorrect sequence. + +Qualitative Comparison. As shown in Fig. 4, our proposed Manual-PA produces the most faithful part pose prediction for the shapes illustrated in the step diagrams. For "Manual-PA w/o Order", some parts do not align well with the assembly instructions, indicating the importance of providing precise correspondences between the step diagram and the parts for accurate assembly. In the case of Image + +PA, the input consists only of the final image, making it challenging to locate the poses of parts that are occluded, such as the supporting rods beneath the table top in (b). 3DHPA lacks visual input and operates in a generative mode, relying solely on shape priors. Consequently, it generates shapes that are reasonable, as seen in (a), but there are noticeable discrepancies between its output and the ground truth shapes. For zero-shot results on the IKEA-Manual dataset, both 3DHPA and Image-PA exhibit degraded performance, while Manual-PA still produces faithful assembly results, demonstrating its superior generalization ability. + +# 5. Conclusions and Future Work + +We introduce a novel 3D part assembly framework that leverages diagrammatic manuals for guidance. Our proposed approach, Manual-PA, learns the sequential order of part assembly and uses it as a form of soft guidance for 3D part assembly. Manual-PA achieves superior performance on the PartNet dataset compared to existing methods and demonstrates strong generalizability to real-world IKEA furniture, as validated on the IKEA-Manual dataset. + +Future work could aim to bridge the gap between synthetic and real-world IKEA manuals. Although we have addressed adaptability in detecting a varying number of new parts introduced in each step and robust handling of differing perspectives, other visual elements such as arrows, detailed close-ups, and part labels remain challenging. 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Marigold-DC is a zero-shot, generative method for depth completion. It leverages a pretrained, diffusion-based monocular depth estimator as scene understanding prior and integrates sparse depth guidance into the denoising process. No fine-tuning is required, as the method utilizes test-time optimization to update the latent representation. Compared to existing methods, Marigold-DC recovers plausible depth maps even from very sparse depth observations and excels at zero-shot generalization across a broad range of scenes. + +# Abstract + +Depth completion upgrades sparse depth measurements into dense depth maps, guided by a conventional image. Existing methods for this highly ill-posed task operate in tightly constrained settings, and tend to struggle when applied to images outside the training domain, as well as when the available depth measurements are sparse, irregularly distributed, or of varying density. Inspired by recent advances in monocular depth estimation, we reframe depth completion as image-conditional depth map generation, guided by a sparse set of measurements. Our method, Marigold-DC, builds on a pretrained latent diffusion model (LDM) for depth estimation and injects the depth observations as test-time guidance, via an optimization scheme that runs in tandem with the + +iterative inference of denoising diffusion. The method exhibits excellent zero-shot generalization across a diverse range of environments and handles even extremely sparse guidance effectively. Our results suggest that contemporary monodepth priors greatly robustify depth completion: it may be better to view the task as recovering dense depth from (dense) image pixels, guided by sparse depth; rather than as inpainting (sparse) depth, guided by an image. Project website: https://MarigoldDepthCompletion.github.io/ + +# 1. Introduction + +Depth completion aims to convert sparse depth measurements into a dense depth map, using an image – typically standard RGB or grayscale – as guidance (Fig. 1). It is + +useful across a range of computer vision applications that combine conventional cameras with sparser range sensors, e.g., robotics, autonomous driving, and 3D city modeling. Traditional approaches predominantly rely on convolutional neural networks (CNNs) [6, 7, 47, 54] or transformer models [58, 85, 88] and achieve satisfactory results within their particular problem setting. However, they do not generalize well and fail, often catastrophically, when transferred to new domains (Fig. 1). This is all the more concerning because depth sensors are barely standardized and each system comes with its own sampling pattern, data gaps, and noise characteristics. + +In contrast, depth estimation only from a single view, without depth guidance, has progressed to a point where it generalizes remarkably well and can handle a broad range of images "in the wild" [3, 57, 81, 83], which begs the question: why does depth completion not generalize at least as well? + +The answer, we claim, lies in the much more powerful visual prior. Modern monodepth estimators build on top of foundation models like DINOv2 [53] or Stable Diffusion [60] and inherit their rich knowledge about the structure of the visual world. We therefore bridge the gap between depth completion and monocular depth and adapt Marigold [33], a latent diffusion model (LDM) for monodepth estimation, to the depth completion task. Marigold casts depth estimation from a single image as generating a depth map, conditioned on the input image. Marigold-DC uses this capability as a basis and adds sparse depth observations as a further guidance signal. Importantly, our proposed scheme is based on test-time optimization and does not alter the Marigold model; thus avoiding the risk of degrading the prior, as well as the effort of collecting or generating suitable training data. + +Our proposed guidance scheme exploits the iterative nature of Denoising Diffusion Probabilistic Models (DDPMs) [28, 72]. This class of models has revolutionized image generation. They are capable of synthesizing photorealistic images from pure noise, and by appropriate training, the generative process can be conditioned on various inputs, including text [60, 65] but also images and depth maps [86]. What is more, also fully trained DDPMs can, at test time, be guided towards specific outputs by injecting suitable signals into the inference process [1, 15], which opens up the possibility to repurpose them for certain applications without having to retrain them. + +In this paper, we leverage such test-time guidance for depth completion, by guiding the inference loop of a pretrained monodepth estimator with additional depth input. Our contributions are: + +- We rethink depth completion from the perspective of monocular depth prediction, such that it can benefit from the comprehensive visual knowledge baked into state-of-the-art monodepth estimators, and the associated ability to + +generalize. + +- We introduce a computational scheme that seamlessly integrates sparse depth cues into the diffusion process of a pretrained LDM, and thus achieves depth completion without any architectural modifications or retraining of that base model. +- We design a strategy to anchor affine-invariant predictions in latent space on sparse depth cues in metric space. By dynamically adjusting the corresponding scale and shift parameters during inference, our method effectively aligns model predictions with the available depth measurements. In experiments on several datasets, we demonstrate that Marigold-DC sets a new state of the art for the depth completion task, especially in the desirable but challenging zero-shot setting. With our take on depth completion as a constrained form of monocular depth estimation, we hope to close the widening performance gap between those two closely related computer vision problems and inspire further research towards depth completion methods that generalize to unseen images, environments, and sensor setups. + +# 2. Related Work + +# 2.1. Depth Completion + +Early depth completion methods rely solely on sparse depth inputs and employ classical interpolation techniques or sparsity-invariant convolutional neural networks (CNNs) [8, 36, 75]. These approaches often produce blurred predictions lacking fine structural details, especially around object boundaries. To address this, it has become common to incorporate an RGB image as guidance, enabling sharper transitions and improved extrapolation in regions without depth information. Other works [30, 47, 48, 73] leverage both sparse depth and RGB inputs using encoder-decoder multi-modal fusion networks with a ResNet [26] backbone. + +Advancements include multi-scale prediction objectives [31, 37], intermediate representations such as surface normals [55, 79, 87] or coarse depth estimates [42], and graph-based approaches for modeling neighborhood relations [78, 89]. Post-processing refinement methods, mostly following the spatial propagation network (SPN) mechanism [43], have been proposed to enhance output quality. Notable examples include CSPN [6] and its successor $\mathrm{CSPN}++$ [7], which introduce convolutions with fixed and adaptive kernels, respectively, improving efficiency. Further improvements involve non-local neighborhoods in NL-SPN [54], adaptive affinity matrices in DySPN [40], and varying kernel scopes in LRRU [76]. This paradigm has been extended to a three-stage method in BP-Net [74]. + +While most architectures process features in 2D, some methods [5, 69, 80, 85] leverage 3D geometry information, though this requires knowledge of camera intrinsics, limiting generalization. The vision transformer (ViT) [16], + +widely successful in computer vision, has also been explored for depth completion in works like GuideFormer [58], PointDC [85], and CompletionFormer [88]. To handle sparse and irregular patterns, SpAgNet [12] proposes a sparsity-agnostic framework and obtains reasonable predictions even with $< 10$ guidance points. For robust generalization, VPP4DC [2] revisits depth completion from a fictitious stereo-matching perspective, OGNI-DC [92] iteratively optimizes a depth gradient field, and Prompt Depth Anything [39] fine-tunes a feedforward depth foundation model [82] for sparse depth prompting. + +Generative approaches have also been explored: DepthFM [24] employs flow matching [41, 44] conditioned on the RGB image and the sparse depth, densified with distance functions, to implement refinement. Similarly, DepthLab [46] embeds the interpolated sparse depth in latent space to condition a diffusion model alongside the RGB. Such densification before or during processing is a viable strategy, as also seen in concurrent work [29] leveraging depth priors and [23], which encodes a blend of sparse guidance and intermediate predictions back into the latent space. The drawback of intermediate densification is that it introduces high-frequency variations around sparse guidance points, resulting in corruption of the latent codes. This requires spatial smoothing to manage artifacts, adding further design choices and complexity to the guidance framework. In contrast, our guidance approach integrates observations via test-time optimization, penalizes decoded predictions in the pixel space, and can accommodate varying sparsity levels, cf. Fig. 1. + +# 2.2. Diffusion Models + +Denoising Diffusion Probabilistic Models (DDPMs) [28] generate high-quality samples by reversing a Gaussian noise diffusion process. Their enhanced sample quality [15] and computational efficiency [51] have been well documented. Denoising Diffusion Implicit Models (DDIMs) [70] offer speedups with non-Markovian inference. Conditional diffusion models allow controlled generation by incorporating inputs like text [65], images [64], and semantic maps [86]. Stable Diffusion (SD) [60] exemplifies text-based image generation, using an LDM trained on the large-scale LAION-5B dataset [68]. By performing denoising in compressed latent space via a U-Net [61], it reduces complexity, making the model more scalable and easier to fine-tune. A separately trained variational autoencoder (VAE) maps images to and from latent space, thus embedding extensive image knowledge into the model weights, which has been utilized for various downstream tasks. + +# 2.3. Diffusion Guidance + +To allow fine-grained control over the output, guidance-based diffusion [14] incorporates external supervision alongside the original conditioning, using a guidance function that + +measures whether certain criteria are met. In guided image generation, classifier guidance [15] enables class-conditional outputs from a pretrained, unconditional diffusion model, via gradients from a classifier trained on ImageNet [63] images at different noise scales. Similarly, gradients from a CLIP model [56] trained on noisy images can guide generation toward a user-defined text caption [52]. An alternative, classifier-free guidance [27, 52], achieves similar control without training a separate classifier, by parameterizing both conditional and unconditional diffusion models within the same network. The approach is further extended to handle general nonlinear inverse problems [9, 10], using gradients calculated on the expected denoised images. Alternatively, one can optimize the constraints on the clean signal [91] and then reintroduce noise. Guidance is commonly framed from a score-based perspective on denoising diffusion [71, 72], where an unconditional model approximates the time-dependent score function of the log data distribution. Finally, a variety of universal constraints, such as segmentation masks, image style, and object location, have been applied with SD under a single framework [1], fully exploiting the flexibility and control of diffusion-based image generation. + +# 2.4. Diffusion for Monocular Depth Estimation + +Monocular depth estimation predicts per-pixel depth from a single RGB image, a challenging and ill-posed problem due to the absence of definitive depth information. Deep learning approaches leverage features learned from large datasets to tackle this. More recently, several methods have employed DDPMs for generative depth estimation. DDP [32] conditions diffusion on image features for dense visual prediction. DiffusionDepth [17] performs latent space diffusion conditioned on features from a Swin Transformer [45]. DepthGen [67] and its successor DDVM [66] extend multi-task diffusion models for depth estimation, addressing noisy ground truth and emphasizing pretraining on synthetic and real data for improved quality. VPD [90] utilizes a pretrained SD with text input as its image feature extractor for various visual perception tasks, highlighting the semantic knowledge embedded in these models. + +Marigold [33] repurposes Stable Diffusion to denoise depth maps conditioned on an input image, achieving impressive zero-shot monocular depth estimation with fine details across diverse datasets. Trained purely on synthetic data and relying on the foundational knowledge of Stable Diffusion, this affine-invariant model outputs depth predictions in a fixed $[0,1]$ range. Motivated by our view that depth completion is essentially monocular depth estimation anchored at sparse points, we develop a plug-and-play optimization framework around Marigold by lifting its output to metric space, enabling effective depth completion without fine-tuning or architectural changes. + +# 3. Method + +# 3.1. Guided Diffusion Formulation + +We formulate depth completion as a guided monocular depth estimation task and use Marigold, the pretrained, affine-invariant, diffusion-based model, as our prior. At inference time, we dynamically refine its predictions by incorporating a penalizing loss $\mathcal{L}$ at sparse point measurements in metric space. Marigold generates a linearly normalized depth map $\hat{\mathbf{d}}\in \mathbb{R}^{W\times H}$ within the range [0, 1] by sampling from the conditional distribution $D(\mathbf{d}\mid \mathbf{x})$ , where $\mathbf{x}\in \mathbb{R}^{W\times H\times 3}$ is an RGB image, and $\mathbf{d}$ is a pixel-wise corresponding depth map. Let $\mathbf{c}\in \mathbb{R}^{W\times H}$ denote a sparse metric depth map in the same image space, where only a limited subset of pixels contains valid depth values. Let further $\hat{a}$ and $\hat{b}$ represent the scale and shift coefficients for linear prediction scaling, maintained as additional parameterized variables throughout the process and initialized as in Sec. 3.2. + +The proposed modified inference pipeline for depth completion is presented in Fig. 2. We start by encoding the input image $\mathbf{x}$ into latent space, using the SD encoder $\mathcal{E}$ to obtain the latent code $\mathbf{z}^{(\mathbf{x})} \coloneqq \mathcal{E}(\mathbf{x})$ . We also sample a random noise tensor $\mathbf{z}_T^{(\mathbf{d})} \sim \mathcal{N}(0, I)$ as the initial depth latent, which we also treat as an estimable parameter. We employ the DDIM scheduler [70] for accelerated inference with $T = 50$ steps, adopting the fix for trailing timesteps [20]. Then, at every denoising iteration $t$ , we feed the image latent concatenated with the depth latent $\mathbf{z}_t^{(\mathbf{d})}$ into the U-Net to obtain a noise estimate $\hat{\pmb{\epsilon}}_t \coloneqq \pmb{\epsilon}_{\theta}(\mathbf{z}_t^{(\mathbf{d})}, \mathbf{z}^{(\mathbf{x})}, t)$ . Instead of immediately completing the current iteration and continuing with timestep $t - 1$ , we "preview" the final, denoised depth latent $\mathbf{z}_{0|t}^{(\mathbf{d})}$ by computing a posterior mean estimate using Tweedie's formula [18]: + +$$ +\mathbf {z} _ {0 | t} ^ {(\mathbf {d})} = \frac {\mathbf {z} _ {t} ^ {(\mathbf {d})} - \sqrt {1 - \bar {\alpha} _ {t}} \hat {\boldsymbol {\epsilon}} _ {t}}{\sqrt {\bar {\alpha} _ {t}}}, \tag {1} +$$ + +where $\bar{\alpha}_t$ is defined by the noise schedule. After obtaining $\mathbf{z}_{0|t}^{(\mathbf{d})}$ , we decode it through the SD decoder $\mathcal{D}$ to produce a predicted clean depth sample $\hat{\mathbf{d}}_t$ in pixel space. This affine-invariant depth is then scaled and shifted using our parameterized coefficients to render it in metric units as $\hat{\mathbf{d}}_t^{(\mathfrak{m})} \coloneqq \hat{\mathbf{d}}_t \cdot \hat{a} + \hat{b}$ . We then compute the loss function $\mathcal{L}$ between the sparse depth $\mathbf{c}$ and the metric estimate $\hat{\mathbf{d}}_{\mathrm{m}}$ at the pixels where $\mathbf{c}$ is valid, resizing the prediction as needed if processing at an intermediate resolution (which is possible in Marigold). For $\mathcal{L}$ , we use an equally weighted sum of mean absolute error and mean squared error. Intuitively, this combination penalizes large geometric errors while also encouraging fine-scale adjustments. Given the loss, we compute gradients for both scale and shift coefficients, as well as the latent depth variable $\mathbf{z}_t^{(\mathbf{d})}$ , by backpropagating through the decoder $\mathcal{D}$ , the Eq. (1), and the U-Net prediction. + +![](images/79fef7c3abae7eda08acdf5b29f1a90cbbdcd2721f5767fea9a96d69a9f3298e.jpg) +Figure 2. Overview of Marigold-DC inference scheme for depth completion. Our method extends the existing Marigold architecture (above the dashed line) by incorporating task-specific guidance (below the line). Starting from the current depth latent variable $\mathbf{z}_t^{(\mathbf{d})}$ , our method calculates a "preview" of the final denoised depth map via the Tweedie formula. This preview is then decoded and scaled using the learnable scale parameter $\hat{a}$ and shift $\hat{b}$ . We backpropagate the loss (red arrows) between the "preview" and sparse depth and adjust the latent simultaneously with the scale and shift. Finally, we execute a scheduler step to proceed to the next denoising iteration. + +We found that scaling the gradient w.r.t. the depth latent proves effective in practice, such that its $L_{2}$ norm is proportional to that of the predicted score gradient [84]. We update $\hat{a}, \hat{b}$ , and $\mathbf{z}_t^{(\mathbf{d})}$ based on their respective gradients using the Adam [34] optimizer, with a learning rate of 0.005 for the affine parameters and 0.05 for the depth latent. The former two always remain positive thanks to the parametrization described in Sec. 3.2. + +After this, we perform a scheduler step with the previously computed noise estimate $\hat{\epsilon}$ and proceed to the next denoising iteration. Once the process is completed and the final denoising iteration has been reached, we decode the optimized affine-invariant depth map, apply the scale and shift coefficients, and return a depth map in metric units. + +The optimization loop is repeated at each timestep for a total of $T$ iterations, similarly to [9, 19, 22, 38], but with additional variables included in the loop. This proposed update encourages affine-invariant predictions to align with both the image conditioning and sparse depth measurements, as a standard depth completion architecture would, but with the added benefit of a comprehensive representation of the visual world inherited from Stable Diffusion. This knowledge prevents overfitting to noisy depth measurements because the image prior serves as a strong regularizer. + +Our end-to-end optimization approach is a variant of guid- + +ance methods that use Bayes' rule to adjust the score function with a conditional term [1, 15, 84]. This often involves the diffusion posterior sampling (DPS) [9] approximation of the likelihood, calculated on the expected clean samples. Our choice of a simpler yet effective variant is motivated by three factors: (i) For latent inverse problems, a straightforward extension of DPS lacks the theoretical guarantees of its pixel-space counterpart [62] due to extra nonlinearity introduced by $\mathcal{D}$ and the absence of a one-to-one mapping from latent to pixel space [14]; (ii) We introduce additional variables that require optimization, as the mapping from the base model output to sparse depth is linear but unknown, unlike traditional inverse approaches, which keep the mapping function between prediction and the condition fixed. (iii) Modifying the score gradient during our experiments led to less stable optimization and reduced overall performance. In this way, our streamlined guidance approach is able to handle varying levels of sparsity in the depth guidance. + +# 3.2. Scale and Shift Parameterization + +Proper parameterization of scale and shift is crucial to achieve high-quality results. Notably, expressing metric depth through an affine-invariant prediction does not yield a unique decomposition, as multiple affine transformations can represent the same depth structure. However, since Marigold outputs are in the unit interval, given affine parameters $\hat{a}$ and $\hat{b}$ , only metric values within the range $[\hat{b}, \hat{a} + \hat{b}]$ can be predicted. If this interval is not expressive enough, the loss will push points in the affine-invariant space toward its boundaries, leading to irrecoverable saturation. + +We observe that a least squares fit to the condition c often produces a range notably smaller than the full set of available depth values, mainly because the initial geometry is not fully accurate, especially at the far plane. The opposite is also true: overshooting the range forces optimization towards a prediction with a distribution of values concentrated in a sub-range, even though Marigold has been trained to utilize the entire range of the decoder. To enable meaningful, non-saturating updates to all optimized components, we parameterize the scale and shift as follows (min-max initialization): + +$$ +\hat {a} = \alpha^ {2} \cdot \left(\mathbf {c} _ {\max } - \mathbf {c} _ {\min }\right) \quad \hat {b} = \beta^ {2} \cdot \mathbf {c} _ {\min } \tag {2} +$$ + +where $\mathbf{c}_{\mathrm{max}}$ and $\mathbf{c}_{\mathrm{min}}$ are the maximum and minimum depth available as sparse conditioning, and $\alpha$ and $\beta$ , initialized to one, are the parameters that receive the actual gradient updates. We ablate other initialization methods in Sec. 4.4. + +# 3.3. Ensembling Procedure + +Even with anchoring at guidance points, inherent variability in the final depth maps persists with a generative method, depending on the initial noise - similar to the unguided setting. This variability is particularly pronounced in challenging areas, such as reflective surfaces, edges, and distant planes, + +where depth points are often missing due to sensor limitations or range constraints. We leverage the variability via a simple ensemble method in metric space: after linearly scaling the predictions from multiple individual inferences, we compute the pixel-wise median to produce the final result. This gives us more robust estimates and, as an added benefit, generates an uncertainty map based on the median absolute deviation (MAD) between predictions. We use 10 separate predictions for evaluation, as suggested for Marigold. + +# 4. Experiments + +# 4.1. Evaluation Datasets + +We evaluate Marigold-DC in a zero-shot setting on 6 real-world datasets unseen by the base model [33], which was trained exclusively on synthetic data from Hypersim [59] and Virtual KITTI [4]. The evaluation datasets span both indoor and outdoor scenes, covering various image resolutions, sparse depth densities, acquisition devices, and noise levels. NYU-Depth V2 [50] consists of indoor scenes captured with an RGB-D Kinect sensor. We use the original test split of 654 samples. Images are downsampled to $320 \times 240$ and then center-cropped to $304 \times 228$ , following established practice [6, 47, 54]. The sparse depth input is generated by sampling 500 random points from the ground truth depth map. ScanNet [13] contains room scans collected with a commodity RGB-D sensor. Following the filtering in [69], we select 745 samples from the official 100 scenes for testing. Images are resized to $640 \times 480$ to align with the depth resolution, and 500 random points are sampled as sparse guidance. The VOID [77] dataset includes synchronized RGB and depth streams of indoor and outdoor scenes at a resolution of $640 \times 480$ , acquired via active stereo. We utilize all 800 frames from the 8 designated test sequences, and their provided sparse depth maps with three density levels of 150, 500, and 1500 points. iBims-1 [35] is a high-quality indoor RGB-D dataset captured with a laser scanner, characterized by its low noise level, sharp depth transitions, precise details, and extended depth range up to 50 meters. We employ all 100 available images at $640 \times 480$ resolution and sample 1000 random depth points from the intersection of valid pixel masks (invalid, transparent, missing) as per the official evaluation protocol. The KITTI DC [75] dataset comprises driving scenes with paired RGB images and sparse LiDAR depth measurements captured at a resolution of $1216 \times 352$ . The semi-dense ground truth is obtained by temporally accumulating multiple consecutive LiDAR frames with error filtering [21, 75]. We use the original validation split of 1000 samples and remove outliers [11] from the guidance points based on distance from the minimum depth within a local $7 \times 7$ patch, as in [2]. DDAD [25] is an autonomous driving dataset featuring a $360^{\circ}$ multi-camera setup, capturing long-range LiDAR depth up to 250 meters. The official validation + +set includes 3950 samples for each camera at $1936 \times 1216$ resolution. Following [2, 92], we use only the front-facing view and sample approximately $20\%$ of the available depth measurements as sparse input, applying the same filtering as done for KITTI DC raw LiDAR [11]. + +# 4.2. Evaluation Protocol + +As mentioned, Marigold-DC is a zero-shot approach that requires no task-specific training, unlike most baselines, which rely on depth-completion checkpoints trained specifically for indoor (NYU-Depth V2) or outdoor (KITTI DC) environments. Our proposition for fair evaluation is to transfer the indoor checkpoints to the indoor benchmarks (ScanNet, iBims-1, and Void) and the outdoor checkpoints to the outdoor benchmark (DDAD). For evaluation on NYU-Depth V2 and KITTI DC, we avoid expensive retraining of baselines on other datasets and instead reuse the available zero-shot results from the VPP4DC [2] paper, reporting the best of all examined training configurations and leaving the rest blank. + +We run inference on each dataset at its original resolution, except for NYU and DDAD, where we resize the images to a 768-pixel longer side while preserving the aspect ratio. This is done for our method and Marigold, due to the image sizes being too small and too large, respectively. In these cases, we resize the output to the original resolution for guidance, enabling processing at the finest level. + +Following recent work [2, 69, 92], we report Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE) as performance metrics. + +# 4.3. Comparison with Other Methods + +We compare Marigold-DC to 8 baselines that have achieved strong results in standard evaluation settings on NYU-Depth V2 and KITTI DC, with some also claiming good generalization. NLSPN [54], SpAgNet [12], CompletionFormer [88] and BP-Net [74] are variants of the multi-modal fusion with depth refinement strategy. VPP4DC [2] reformulates the problem as fictitious stereo matching and OGNI-DC [92] optimizes a depth gradient field. DepthLab [46] uses latent diffusion for densification and Prompt Depth Anything [39] adapts the depth foundation model from [82] for completion tasks. To show the effectiveness of our guidance framework, we also compare to vanilla Marigold [33] using only the RGB input with ensemble size 10, followed by (i) a least-squares estimate and (ii) a L1 + L2 optimization for scale and shift based on the sparse depth. These methods are referred to as "Marigold + LS" and "Marigold + optim" below. + +As shown in Tab. 1, Marigold-DC outperforms the baselines in most cases and secures the highest overall ranking by a significant margin. Notably, this is achieved despite relying on a frozen base model trained on synthetic datasets for a different task, offering a true plug-and-play solution largely independent of guidance patterns. We argue that the crucial + +![](images/f397d63912a61cd2d1bcc460ea3c45fd70f4836719140bbbcdd5612ad2cddc88.jpg) +Figure 3. Qualitative comparison of benchmarked methods on samples from four datasets. Non-generative methods struggle with dataset-specific biases, such as input resolution lock or variations in guidance sparsity. Marigold-DC demonstrates high-quality metric depth densification with strong generalization. Sampling patterns and noise characteristics vary across datasets. Black regions indicate missing depth values. Arrows suggest key areas of interest. + +factor is to exploit the rich monocular depth estimation prior provided by the base model, while simultaneously supplying it with sparse evidence. This is in line with our hypothesis that depth completion benefits more from a strong visual prior than from task-specific training. + +In Fig. 3, we present a qualitative comparison of samples from several evaluation datasets. In these examples, although the depths predicted with "Marigold + LS" are rich in de + +Table 1. Quantitative comparison of Marigold-DC with state-of-the-art depth completion methods on several zero-shot benchmarks. All metrics† are presented in absolute terms; bold numbers are best, underscored second best. In most cases, our method outperforms other approaches in both indoor and outdoor scenes, despite not having seen a real depth sample nor being trained for the depth completion task. + +
MethodScanNetIBims-1VOID 150VOID 500VOID 1500NYU-Depth V2KITTI DCDDAD
MAE↓RMSE↓MAE↓RMSE↓MAE↓RMSE↓MAE↓RMSE↓MAE↓RMSE↓MAE↓RMSE↓MAE↓RMSE↓MAE↓RMSE↓
NLSPN [54] (ECCV '20)0.0360.1270.0490.1910.4920.9630.3010.7830.2100.6680.4400.7161.3352.0762.4989.231
SpAgNet [12] (WACC '23)∅∅∅∅0.4080.8660.3260.7520.2440.7060.1580.2920.5181.7884.57813.236
CompletionFormer [88] (CVPR '23)0.1200.2320.0580.2060.4870.9560.3850.8210.2610.7260.1860.3740.9521.9352.5189.471
VPP4DC [2] (3DV '24)0.0230.0760.0620.2280.2450.6900.1870.5820.1480.5430.0770.2470.4131.6091.3446.781
BP-Net [74] (CVPR '24)0.1220.2120.0780.2890.4710.9360.3700.7930.2700.742○○○○2.2708.344
OGNI-DC [92] (ECCV '24)0.0290.0940.0590.1860.2610.6930.1980.5890.1750.593○○○○1.8676.876
DepthLab [46] (arXiv preprint '24)0.0510.0810.0980.1980.2680.6890.2230.5900.2140.6020.1840.2760.9212.1714.4988.379
Prompt Depth Anything [39] (CVPR '25)0.0420.0790.0880.1960.2480.6810.2020.5890.1910.6050.1100.2330.9342.8032.1077.494
Marigold + optim [33] (CVPR '24)0.0910.1410.1670.3000.2790.6870.2610.6250.2610.6520.1940.3091.7653.36122.87232.661
Marigold + LS [33] (CVPR '24)0.0830.1290.1540.2860.2660.6700.2430.6060.2380.6280.1900.2941.7093.3058.21714.728
Ours (w/o ensemble)0.0200.0630.0620.2050.2010.6290.1670.5460.1570.5570.0570.1420.5581.6762.9857.905
Ours (w/ ensemble)0.0170.0570.0450.1660.1940.6220.1580.5350.1520.5510.0480.1240.4341.4652.3646.449
+ +$\dagger$ Metrics highlighted in gray are sourced from OGNI-DC [92] and VPP4DC [2], reported with the best training setup. For the others, we evaluated all baselines in zero-shot settings (cf. Sec. 4.2). $\bigcirc$ indicates that generating zero-shot results would require retraining on an unidentified set of datasets, as the available checkpoints were trained on these benchmarks. $\varnothing$ denotes cases where neither training code nor checkpoints are available, making evaluation impossible. + +![](images/54cfb633e3bef341064231b6cb60fe363a80c1252a017a3428d08dd970e98564.jpg) +Figure 4. Comparison between vanilla Marigold and guided predictions on iBims-1 [35] samples. With guidance from sparse points, the scene geometry is correctly adjusted (first row) and the depth of challenging protruding text can be recovered (second row). + +tail, they frequently exhibit layout distortions (Fig. 4) and struggle to position the far plane accurately. In such cases, merely achieving correct depth ordering is insufficient, and the overall scene layout becomes critical. + +Performance degradation occurs rapidly in methods that rely on spatial propagation, leading to visible artifacts in the predictions. We hypothesize that this is primarily due to their inability to handle inputs that are sparser than those encountered during training. + +Our depth completion approach produces realistic results in regions lacking depth measurements and preserves fine details where other methods resort to coarse interpolation. This makes our method particularly effective in sparse settings with only a few hundred or even a few dozen points. + +# 4.4. Ablation Studies + +We analyze the impact of some key design choices on overall performance. Aspects not targeted in each respective experiment are fixed to our reference settings: a learning rate of 0.05 for the depth latent and 0.005 for affine parameters and min-max initialization for scale and shift. We re-use some of the default settings of Marigold [33], namely 50 DDIM denoising steps and an ensemble size of 10. All studies are + +conducted on a randomly selected subset of 100 samples from the training split of NYU-Depth V2. + +Learning rates. Since our method involves test-time optimization, we evaluate the impact of different learning rates used to update the depth latent and affine parameters. For the study, we vary the value of $\lambda_{\mathrm{base}}$ on a log-scale from 0.005 to 0.5, setting the learning rate for the depth latent to this value and the learning rate for scale and shift to $\lambda_{\mathrm{base}} / 10$ . The results are shown in Fig. 5: we observe a sweet spot around $\lambda_{\mathrm{base}} = 0.05$ , with performance degrading in both directions. Lower values result in weak guidance, whereas higher values lead to instability in the optimization process. + +Number of denoising steps. We vary the number of denoising steps of the DDIM scheduler [70] and show results in Fig. 5. Unsurprisingly, increasing the number of denoising steps improves the results, though the relative gain diminishes between 25 and 50 steps, with performance saturating beyond that. Inference with less than 25 steps comes at the cost of reduced accuracy and geometric distortions. We anticipate greater speed improvements by having the base model trained on more complex, deeper scenes with enhanced far-plane supervision, since the discrepancy between the initial prediction and the true linear scaling heavily influences convergence speed. Additional speedup by an order of magnitude can be achieved with a TinyVAE [49], using mixed precision and enabling model compilation. + +Test-time ensembling. We assess the effectiveness of the proposed test-time ensembling scheme by comparing different ensemble sizes. As shown in Tab. 1 and Fig. 5, a single prediction already yields competitive, often state-of-the-art results. Consistent with standard Marigold, we observe a performance boost through ensembling, with errors generally decreasing as ensemble size increases, albeit with a linear increase in runtime. The relative improvement diminishes for ensemble sizes $>10$ . This is a hyper-parameter that can be easily adjusted to balance between runtime and performance. + +![](images/e446556d02e5bdd2d7ed752f51230bc49df0a7ed52dbb829dfb794fdada8c6b4.jpg) +Figure 5. Ablation of learning rate, number of inference steps, and ensemble size. Left: Empirically, we identify an optimal learning rate that balances the trade-off between guidance strength and optimization stability. Middle: Performance consistently improves with more denoising iterations, showing saturation beyond 50 steps. Right: A monotonic improvement is seen with increasing ensemble size, diminishing after 10 predictions per sample. + +![](images/a1848d4188bb912900614fe95d59b36634b7aed7fa5beefe78cd0ed3fa52255e.jpg) + +![](images/122c0d5c5b6c385ca9547433dae389bb2e622bcc8873e1dd9614cf201efe8191.jpg) + +
InitializationNYU-Depth V2
MAE ↓RMSE ↓
Least Squares0.0650.165
Oracle0.0580.153
Extended Min-Max0.0570.148
Min-Max0.0550.147
+ +Scale and shift initialization. Proper initialization of scale and shift is crucial to converge to a solution that aligns well with the sparse depth conditioning, especially when significant adjustments to the initial prediction are necessary. We compare four initialization methods, each derived from the affine-invariant depth map estimate obtained after the first denoising iteration: (1) least-squares fit to align with sparse depth; (2) min-max scaling to match the minimum and maximum values of the sparse input; (3) extended min-max scaling, adjusting the range by $5\%$ beyond the far plane and $5\%$ closer to the near plane, assuming the sparse points provide only a lower bound on scene depth; (4) an oracle using the union of sparse conditioning and ground truth, unavailable in practice but serving as a near-perfect baseline. + +As shown in Tab. 2, (extended) min-max and oracle initialization achieve similar performance. Least-squares, however, performs noticeably worse. We acknowledge that the min-max method may struggle when the point distribution is not fully representative of the actual range (e.g. the degenerate case of guidance only in a narrow range). However, we are not aware of any depth completion method that does not suffer from this issue. Within our framework, the most robust solution would be an improved model-based initialization or a switch between min-max and least squares whenever the point distribution is considered unrepresentative. + +Guidance method. We compare our fully end-to-end opti + +Table 2. Ablation of scale and shift initialization. Min-max methods perform similarly to the oracle initialization, whereas least squares performs significantly worse. + +
Depth LatentScale & ShiftNYU-Depth V2
Score FunctionDirect Optim.Direct Optim.MAE ↓RMSE ↓
✓✗✓0.0580.150
✗✓✓0.0550.147
+ +Table 3. Ablation of guidance method. Direct optimization of the depth latent proves more effective than modifying the score function. Affine parameters are optimized separately in both cases. + +mization framework to an alternative guidance approach that adjusts the score function with a conditional term [1, 15, 84] (i.e., adding the gradient of the likelihood to the predicted noise) while optimizing scale and shift separately. Both approaches are evaluated at their optimal settings, with results reported in Tab. 3. Our optimization-based method outperforms the mixed variant, demonstrating both higher performance and greater stability. + +# 5. Conclusion + +We have introduced Marigold-DC, which effectively combines monocular depth estimators' generalization and robustness with the anchoring needed to solve depth completion tasks. By leveraging a pretrained, affine-invariant diffusion-based model and dynamically incorporating sparse depth measurements during inference, Marigold-DC merges rich monocular depth priors with reliable sensor data. Without task-specific training, the method achieves state-of-the-art performance across six zero-shot benchmarks spanning both indoor and outdoor environments. With our work, we aim to inspire further research on methods that prioritize generalization and robustness, to extend depth completion beyond specific training domains and make it more applicable in real-world settings. Our diffusion-based backbone introduces computational overhead due to the iterative nature of denoising diffusion models and its ensembling process. Future research directions include reducing inference time and supporting alternative guidance cues. + +# References + +[1] Arpit Bansal, Hong-Min Chu, Avi Schwarzschild, Soumyadip Sengupta, Micah Goldblum, Jonas Geiping, and Tom Goldstein. 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MaskControl enables a wide range of applications in text-to-motion generation with high quality and precision. (a) Any-Joint Any-Frame Control: Controls specific joints at designated frames. (b) Body-Part Timeline Control: Generates motion from multiple text prompts, each corresponding to different body parts. (c) Arbitrary Objective Control: Supports any control function at inference time. + +![](images/7594407ca0d8d28c700a170687bbc60444ae3c9603a34747a156c4317a30a141.jpg) +(c) Zero-shot Objective Control + +# Abstract + +Recent advances in motion diffusion models have enabled spatially controllable text-to-motion generation. However, these models struggle to achieve high-precision control while maintaining high-quality motion generation. To address these challenges, we propose MaskControl, the first approach to introduce controllability to the generative masked motion model. Our approach introduces two key innovations. First, Logits Regularizer implicitly perturbs logits at training time to align the distribution of motion tokens with the controlled joint positions, while regularizing the categorical token prediction to ensure high-fidelity generation. Second, Logit Optimization explicitly optimizes the predicted logits during inference time, directly reshaping the token distribution that forces the generated motion to accurately align with the controlled joint positions. Moreover, we introduce Differentiable Expectation Sampling (DES) to combat the non-differential distribution sampling process encountered by logits regularizer and optimization. Extensive experiments demonstrate that MaskControl outperforms state-of-the-art methods, achieving superior motion quality (FID decreases by $77\%$ ) and higher control precision (average error 0.91 vs. 1.08). Additionally, MaskControl enables diverse applications, including any-joint-any-frame control, body-part timeline + +control, and zero-shot objective control. Video visualization can be found at https://www.ekkasit.com/ControlMM-page/ + +# 1. Introduction + +Text-driven human motion generation has recently gained significant attention due to the semantic richness and intuitive nature of natural language descriptions. This approach has broad applications in animation, film, virtual/augmented reality (VR/AR), and robotics. While text descriptions offer a wealth of semantic guidance for motion generation, they often fall short in providing precise joint control over specific human joints, such as the pelvis and hands. As a result, achieving natural interaction with the environment and fluid navigation through 3D space remains a challenge. + +To tackle this challenge, a few controllable motion generation models have been developed recently to synthesize realistic human movements that align with both text prompts and joint control signals [42, 43, 51, 55]. However, existing solutions face significant difficulties in generating high-fidelity motion with precise and flexible joint control. In particular, current models struggle to support both sparse and dense joint control signals simultaneously. For instance, some models excel at generating natural human movements that traverse sparse waypoints [21, 42], while + +others are more effective at synthesizing motions that follow detailed trajectories specifying human positions at each time point [51]. Recent attempts to support both sparse and dense joint inputs encounter issues with control precision; the generated motion often is not aligned well with the control conditions [55]. Besides unsatisfied joint flexibility and accuracy, the quality of motion generation in controllable models remains suboptimal, as evidenced by much worse FID scores compared to models that rely solely on text inputs. Moreover, most current methods utilize motion-space diffusion models, applying diffusion processes directly to raw motion sequences. While this design facilitates the incorporation of joint control signals, the redundancy in raw data introduces computational overhead, resulting in slower motion generation speeds. + +Current controllable motion generation methods mostly rely on diffusion model [7, 21, 55, 55]. However, these methods exhibit lower control precision and less generation quality. The current SOTA method, TLControl, [51] achieves high-precision control through test-time optimization with a simple feedforward transformer, but this comes at the cost of lower generation quality, as shown in Tab. 1. Moreover, these methods cannot adapt to arbitrary objective functions at inference time in a zero-shot manner. + +To address these challenges, we introduce the first method that integrates joint control into generative masked motion models, enabling simultaneous high-fidelity motion generation and precise control across a broad range of tasks, as illustrated in Fig. 1. In contrast to diffusion-based approaches, masked models generate motion sequences by training a multi-category token classifier and subsequently sampling from the learned categorical distributions conditioned on input signals, such as text and joint trajectories. Building upon this insight, we propose MaskControl—a straightforward yet powerful control mechanism for generative masked motion models—that implicitly and explicitly manipulates the logits of the token classifier to align token distributions closely with input control signals. + +Our contributions can be summarized as follows. + +- We propose MaskControl, the first approach to introduce controllability to generative masked motion models. +- We introduce two novel control components of MaskControl: (1) Logits Regularizer that implicitly perturbs logits at training time to align the distribution of motion tokens with the controlled joint positions. (2) Logits Optimization explicitly optimizes the predicted logits during inference time, directly reshaping the token distribution to minimize the residual errors between the generated motion and the target joint position. Moreover, we propose Differentiable Expectation Sampling (DES) to overcome the challenge of non-differentiable probabilistic token selection in logits regularization and optimization. +- We show that Logits Optimization can be generalized to + +solve unseen control tasks in a zero-shot manner. + +- We conduct extensive qualitative and quantitative evaluations on multiple tasks, demonstrating that our approach outperforms current SOTA in both motion generation quality and control precision while supporting multiple applications i.e. any-joint-any-frame control, body part timeline control, and zero-shot objective control. + +Table 1. Comparison of text-conditioned motion generation with joint control signals. Our MaskControl SOTA achieves performance by leveraging Masked Motion Model, demonstrating high-precision control (low Average Error) while maintaining high generation quality (low FID). Previous SOTA methods utilize diffusion in motion space, latent space, or simple feed-forward models. $\checkmark$ indicates the ability to control motion using zero-shot objective functions, while $\mathcal{X}$ denotes the lack of this capability. $-\cdot$ signifies control limited to the pelvis. + +
MethodFID ↓Average Error (cm) ↓Base ModelZero-shot Objective
GMD [21]0.57614.39Motion Diffusion-
OmniControl [55]0.2183.38Motion DiffusionX
MotionLCM [7]0.53118.97Latent DiffusionX
TLControl [51]0.2711.08Feed ForwardX
Ours0.0610.98Masked Model✓
+ +# 2. Related Work + +Text-driven Motion Generation. Early methods for text-to-motion generation primarily focus on aligning the latent distributions of motion and language, typically by employing loss functions such as Kullback-Leibler (KL) divergence and contrastive losses. Representative works in this domain include Language2Pose [1], TEMOS [37], T2M [15], MotionCLIP [47], and DropTriple [56]. However, the inherent discrepancy between the distribution of text and motion often results in suboptimal generation quality when using these latent space alignment techniques. + +Recently, diffusion models have become a widespread choice for text-to-motion generation, operating directly in the motion space [23, 48, 60], VAE latent space [5], or quantized space [24, 31]. In these works, the model gradually denoises the whole motion sequence to generate the output in the reverse diffusion process. Another line of work explores the token-based models in the human motion domain, for example, autoregressive GPTs [14, 20, 58, 61] and masked motion modeling [16, 39, 40]. These methods learn to generate discrete motion token sequences that are obtained from a pretrained motion VQVAE [12, 53]. While GPT models usually predict the next token from history tokens, masked motion models utilize the bidirectional context to decode the masked motion tokens. By predicting multiple tokens at once, the masked modeling methods can generate motion sequences in as few as 10 steps, achieving state-of-the-art performance on generation quality and efficiency. Despite the performance gains of masked motion + +models, supporting spatial controllability in these models remains unexploited. This paper is the first work that proposes controllable masked motion model to simultaneously achieve high-quality motion generation with high-precision spatial control. + +Controllable Motion Synthesis. In addition to text prompts, synthesizing motion based on other control signals has also been a topic of interest. Example control modalities include music [26, 27, 29, 44, 45, 49], interacting object [2, 9, 25, 28], tracking sensors [11], scene [17, 52] programmable motion [30], style [62], goal-reaching task [10], and multi-track timeline control [38]. [32, 33, 35, 36, 46, 54, 57] incorporate physics into motion generation. To control the trajectory, PriorMDM [43] finetunes MDM to enable control over the locations of end effectors. ConMDI [6] generates motion in-between using arbitrarily placed dense or sparse keyframes. GMD [21] and Trace and Pace [42] incorporates spatial control into the diffusion process by guiding the root joint location. OmniControl [55] extends the control framework to any joint, while MotionLCM [7] applies this control in the latent space, both leveraging ControlNet [59]. DNO [22] introduces an optimization process on the diffusion noise to generate motion that minimizes a differentiable objective function. Recent approaches [18, 51] model each body part separately to achieve fine-grained control but are limited to dense trajectory objectives. The existing frameworks for controllable motion generation predominantly rely on diffusion models; however, these models typically suffer from low-quality motion generation. + +# 3. MaskControl + +The objective of MaskControl is to enable controllable text-to-motion generation based on a masked motion model that generates high-precision and high-quality motion. In particular, given a text prompt and an additional joint control signal, our goal is to generate a physically plausible human motion sequence that closely aligns with the textual descriptions, while following the joint control conditions, i.e., $(x,y,z)$ positions of each human joint at each frame in the motion sequence. Towards this goal, in Sec. 3.1, we first introduce the background of conditional motion synthesis based on the generative masked motion model. We then describe two key components of MaskControl, including Logits Regularizer in Sec. 3.2 and inference-time Logits Optimization in Sec. 3.3. The first component aims to learn the categorical distribution of motion tokens, conditioned on joint control signals during training time. The second component aims to improve control precision by optimally modifying learned motion distribution via Logits Optimization during inference time. Lastly, we introduce Differentiable Expectation Sampling to overcome non-differentiability of categorical sampling during Logits Regularizer and Opti + +mization. + +# 3.1. Preliminary: Masked Motion Model + +Generative masked motion models [16, 39, 40] generally consist of two stages: Motion Tokenizer and Text-conditioned Masked Transformer. The objective of the Motion Tokenizer is to learn a discrete representation of motion by quantizing the encoder's output embedding $z$ into a codebook $\mathcal{C}$ . For a given motion sequence $\mathcal{P} = [p_1, p_2, \dots, p_F]$ , where each frame $p$ represents a 3D pose, Motion Tokenizer outputs a discrete motion tokens $X = [x_1, x_2, \dots, x_L]$ . Specifically, the encoder compresses $\mathcal{P}$ into a latent embedding $z \in \mathbb{R}^{t \times d}$ with a downsampling rate of $F / L$ . The embedding $z$ is quantized into codes $c \in \mathcal{C}$ from the codebook $\mathcal{C} = \{c_k\}_{k=1}^K$ , which contains $K$ codes. The nearest code is selected by minimizing the Euclidean distance between $z$ and the codebook entries, computed as $\hat{z} = \mathrm{argmin}_j \| \mathbf{z} - c_j \|_2^2$ . The vector quantization loss $L_{VQ}$ is defined as: + +$$ +L _ {V Q} = \left\| \operatorname {s g} (\mathbf {z}) - \mathbf {c} _ {\mathbf {j}} \right\| _ {2} ^ {2} + \beta \| \mathbf {z} - \operatorname {s g} (\mathbf {c} _ {\mathbf {j}}) \| _ {2} ^ {2}, \tag {1} +$$ + +where $\mathrm{sg}(\cdot)$ is the stop-gradient operator and $\beta$ is a hyperparameter for commitment loss. + +During the second stage, the quantized motion token sequence $X = [x_{1}, x_{2}, \ldots, x_{L}]$ is updated with [MASK] tokens to form the corrupted motion sequence $X_{\overline{\mathbf{M}}}$ . This corrupted sequence along with text embedding $W$ are fed into a text-conditioned masked transformer parameterized by $\theta$ to reconstruct input motion token sequence with reconstruction probability equal to $p_{\theta}(x_i \mid X_{\overline{\mathbf{M}}}, W)$ , which is obtained by the motion token classifier. The objective is to minimize the negative log-likelihood of the predicted masked tokens conditioned on text: + +$$ +\mathcal {L} _ {\text {m a s k}} = - \underset {\mathbf {X} \in \mathcal {D}} {\mathbb {E}} \left[ \sum_ {\forall i \in [ 1, L ]} \log p \left(x _ {i} \mid X _ {\overline {{\mathbf {M}}}}, W\right) \right]. \tag {2} +$$ + +During inference, the transformer masks out the tokens with the least confidence and re-samples these tokens according to their respective distributions $p_{\theta}(x_i \mid X_{\overline{\mathbf{M}}}, W)$ in the subsequent step. The number of masked tokens $n_M$ is controlled by a masking schedule, a decaying function of the step $t$ . Early steps use a large masking ratio due to high uncertainty, and as the process continues, the ratio decreases as more context is available from previous predictions. + +# 3.2. Logits Regularizer + +MaskControl aims to generate a human motion sequence based on the text prompt $W$ and joint control signals $S$ . Towards this goal, we introduce Logits Regularizer to conditioned masked transformer, which aims to learn the motion token distribution jointly conditioned both on $W$ and $S$ . + +![](images/45e9434a2d9dee60c4902b840b58693076413c562cf78e63abcdef54592f1639.jpg) +(a) Pretrained Motion Tokenizer + +![](images/4480364764843385b5595dc4df067d717fd69b5825ac270191d2bff7c33ab8c9.jpg) +(b) Differentiable Expectation Sampling (DES) + +![](images/631ffc7542f61d8b7e472761b7e680f8a3ae46580128ca7a13f8c9016af48921.jpg) +(c) Train: Logits Regularizer +Figure 2. Overall architecture of MaskControl. (a) Motion Tokenizer transforms the motion sequence into discrete motion tokens. (b) Differentiable Expectation Sampling (DES) is a differentiable sampling from logits enabling differentiable conversion between discrete tokens in codebook space and transformer token space. (c) Training: Logits Regularizer ensures high-quality motion by generating embedding closely aligns with joint control signals during an unmasking process. (d) Inference: Logits Optimization guides logits during the unmasking process at inference time based on the objective function. + +![](images/83eca107b96699d06e6832f26629d0a91c8eab73c8fe4cc98388e9d391a48884.jpg) +(d) Inference: Logits Optimization + +Logits Regularizer implicitly alters the output logits of pretrained text-to-motion model, thus changing the distribution of motion tokens, toward joint control positions. + +Model Architecture. Diffusion ControlNet has shown its excellence in adding additional control signals to pretrained image diffusion model [59]. We demonstrate for the first time that similar design principle can be applied to introduce controllability to generative masked models [3, 4, 8, 50]. Our architecture consists of a pre-trained text-conditioned masked motion model and a Logits Regularizer. The pre-trained model provides a strong motion prior based on text prompts, while the Logits Regularizer introduces additional joint control signals. Specifically, the Logits Regularizer is a trainable replica of the pre-trained masked motion model, as shown in Fig 2. Each Transformer layer in the original model is paired with a corresponding layer in the trainable copy, connected via a zero-initialized linear layer. This initialization ensures that the layers have no effect at the start of training. Unlike the original masked motion model, the Logits Regularizer incorporates two conditions: the text prompt $W$ from the pre-trained CLIP model [41] and the joint control signals $S$ . The text prompt $W$ influences the motion tokens through attention, while the joint control signal $S$ is directly added to the motion token + +sequence via a projection layer. + +Joint Control Signal. The conditioned masked transformer is trained to learn the conditional distribution $p_{\theta}\left(x_{k} \mid X, X_{\overline{\mathbf{M}}}, W, S\right)$ by reconstructing the masked motion tokens $X_{\overline{\mathbf{M}}}$ , conditioned on the unmasked tokens $X$ , text prompt $\mathbf{W}$ , and joint control signals $\mathbf{S}$ . The joint control condition is a sequence of joint control signals $S = [s_{1}, s_{2}, \dots, s_{F}]$ with $s_{i} \in \mathbb{R}^{j \times 3}$ . Each control signal $s_{i}$ specifies the targeted 3D coordinates of the joints to be controlled, among the total $j$ joints, while joints that are not controlled are zeroed out. Since the semantics of the generated motion are primarily influenced by the textual description, to guarantee the controllability of joint control signals, we extract the joint control signals from the generated motion sequence and directly optimize the consistency loss between input control signals and those extracted from the output. Note that zero-valued in 3D joint coordinates can be ambiguous. Please refer to Sec. A.11 for more details. + +Motion Consistency Loss evaluates the alignment between the generated motion and the input joint control signals $s$ : + +$$ +L _ {s} \left(e _ {c}, s\right) = \frac {\sum_ {n} \sum_ {j} \sigma_ {n j} \odot \left\| s _ {n j} - R \left(D \left(e _ {c}\right)\right) \right\|}{\sum_ {n} \sum_ {j} \sigma_ {n j}}, \tag {3} +$$ + +where $\sigma_{nj}$ is a binary value indicating whether the joint + +control signals $s$ contains a control value at frame $n$ for joint $j$ . The motion tokenizer decoder $D(\cdot)$ converts motion embedding into relative position in local coordinate system and $R(\cdot)$ further transforms the joint's local positions to global absolute locations. The global location of the pelvis at a specific frame can be calculated from the cumulative aggregation of rotations and translations from all previous frames. The locations of the other joints can also be computed by the aggregation of the relative positions of the other joints to the pelvis position. + +Logits Consistency Loss extends the objective function of masked motion model in Eq. 2 by applying negative log-likelihood to all positions, including unmasked ones, conditioned on both the text $W$ and joint control signals $S$ . + +$$ +\mathcal {L} _ {\text {l o g i t s}} = - \sum_ {\forall i \in [ 1, L ]} \log p (x _ {i} \mid X _ {\overline {{\mathbf {M}}}}, W, S). \tag {4} +$$ + +The final loss is the weighted combination Logits Consistency Loss and Motion Consistency Loss: + +$$ +\mathcal {L} = \alpha \mathcal {L} _ {\text {l o g i t s}} + (1 - \alpha) L _ {s} \left(e _ {c}, s\right). \tag {5} +$$ + +# 3.3. Logits Optimization + +The goal of inference-time Logits Optimization is to enhance control precision by further reducing the discrepancy between the generated motion and the desired control objectives. This approach does not require pretraining on specific tasks, allowing the model to handle arbitrary objective functions during inference, enabling new control tasks in a zero-shot manner. + +The core idea behind Logits Optimization is to update the learned logits through gradient-guided optimization during inference, perturbing the motion token distribution. Optimizing logits makes optimization during unmasking process possible since the process requires conversion between transformer token for unmask sampling and codebook embedding for motion reconstruction, as shown in Fig. 2. The optimization process is initialized with the logits obtained from conditioned masked transformer with Logits Regularizer, and these logits are iteratively updated to minimize the motion consistency loss $L_{s}$ . + +$$ +l ^ {+} = \arg \min _ {l} \left(L _ {s} \left(e _ {c}, s\right)\right). \tag {6} +$$ + +At each iteration $m$ , the logits $l_{m}$ are updated using the following gradient-based approach: + +$$ +l _ {m + 1} = l _ {m} - \eta \nabla_ {l _ {m}} L _ {s} (l _ {m}, s), \tag {7} +$$ + +where $\eta$ controls the magnitude of the updates to the logits, while $L_{s}(l_{m}, s)$ represents the gradient of the objective function w.r.t. the logits $l_{m}$ . This refinement process continues over $I$ iterations. Similarly, in the last unmask step, + +optimizing embeddings from the codebook space directly is possible. We can directly optimize the embedding: + +$$ +e _ {m + 1} = e _ {m} - \eta \nabla_ {e _ {m}} L _ {s} \left(e _ {m}, s\right), \tag {8} +$$ + +where $e$ represents the embedding in the codebook space. For zero-shot objective control, loss function $L_{s}$ can be replaced with any arbitrary objective function. + +# 3.4. Differentiable Expectation Sampling (DES) + +Differentiable Sampling. Both logits regularizer and optimization update the logits by computing the gradient of the disparity between spatial-temporal control signals and generated motion sequence defined in eq. 3. This requires sampling motion tokens according to the categorical token distribution during training/optimization time, which is inherently non-differentiable. To address this, we apply StraightThrough Gumbel-Softmax Estimator [19], a reparameterization trick that allows differentiable sampling from a categorical distribution, i.e., + +$$ +p _ {\theta} \left(x _ {k} \mid X _ {\overline {{\mathbf {M}}}}, W, S\right) = \frac {\exp \left(\left(\ell_ {k} + g _ {k}\right) / \tau\right)}{\sum_ {j = 1} ^ {K} \exp \left(\ell_ {j} + g _ {j} / \tau\right)}, \tag {9} +$$ + +where $l$ is logits, $\tau$ refers to temperature, and $g$ represents Gumbel noise with $g_{1},\ldots ,g_{K}$ being independent and identically distributed (i.i.d.) samples from a Gumbel(0,1) distribution. The Gumbel(0,1) distribution can be sampled via inverse transform sampling by first drawing $u\sim \mathrm{Uniform}(0,1)$ and then computing $g = -\log (-\log (u))$ . + +Token Expectation. Masked models reconstruct an embedding from the reconstruction probability $p_{\theta}(x_k \mid \cdot)$ by querying the discrete token embedding using the index with the highest probability, $\operatorname{argmax}_k p_{\theta}(x_k \mid \cdot)$ . However, argmax is non-differentiable, and cannot be controlled by perturbation from a control signal. To address this, we relax the quantization constraint by utilizing the weighted average of the codebooks (or transformer tokens) w.r.t. the reconstruction probability $p_{\theta}(x_k \mid \cdot)$ to approximate continuous tokens. This can be expressed as the expectation of the reconstructed embedding $X_{recon}$ : + +$$ +\mathbb {E} \left[ X _ {\text {r e c o n}} \right] = \sum_ {k = 1} ^ {K} p _ {\theta} \left(x _ {k} \mid X _ {\overline {{\mathbf {M}}}}, W, S\right) \cdot c _ {k}. \tag {10} +$$ + +# 4. Applications + +Any-Joints-Any-Frame Control. To control specific joints at particular frames, the joint control signal can be directly applied to the desired joint and frame in the global position, as the loss function during training is specifically designed for this task. + +Body-Part Timeline Control. MaskControl supports motion generation conditioned on multiple joints, enabling + +![](images/d867354b9665b4e6ef6ad70eeed53b4cccec250d9850ffa98a7251fa6e41013b.jpg) +Figure 3. Visualization comparisons to state-of-the-art methods for any-joint any-frame control. The plots on the top display the top view of pelvis control (root trajectory), while the bottom plot shows the side view of the right wrist. Red represents the control signal, and Blue represents the generated joint motion. + +![](images/879e5a5c9fee5be79e9786a249ffde091bbe934f77fdcd61001a0d4d247d4d9a.jpg) +Text: a man slowly leaps forward, turns around and leaps again and then repeats the forward leap. +Figure 4. Visualization comparisons to state-of-the-art methods for zero-shot objective control. Objective: constrain a human to walk inside a square area. + +control over body parts. To handle multiple prompts corresponding to various body parts and timelines, MaskControl processes each prompt sequentially. Initially, it generates motion without any body part control, then iteratively refines the motion by incorporating prompts conditioned on the specified body parts and timeline constraints from the prior generation. Since MaskControl allows joint control signals to target any joint and frame, partial body or temporal frame control is applicable within this framework. The detail of this process is described in A.12. + +Zero-shot Objective Control. In many human motion generation tasks, motion generation requires adaptation to dynamic constraints at inference time, such as human-scene interaction, human-object interaction, or human self-contact. Logits Optimization allows optimization with arbitrary loss functions that take joints and frames as inputs, enabling zero-shot adaptation at inference time. However, direct optimization to satisfy arbitrary objective functions can often lead to unrealistic motion. To mitigate this, Logits Optimization perturbs the logits during the unmasking process, allowing the masked transformer to re-predict them. By doing so, it ensures that the generated motion remains close to the learned distribution while still achieving the desired control. + +# 5. Experiment + +Datasets. We conduct comprehensive experiments on the HumanML3D dataset [15] HumanML3D covers a wide va + +riety motions. It includes 14,616 motion sequences accompanied by 44,970 text descriptions. The textual data contains 5,371 unique words. The motion sequences are sourced from AMASS [34] and HumanAct12 [13]. + +Evaluation. We follow the evaluation protocol from OmniControl [55] which combines evaluation of quality from HumanML3D[15] and trajectory error from GMD [21]. + +# 5.1. Quantitative Comparison to State-of-the-art + +GMD [21] only addresses the pelvis location on the ground plane (xz coordinates). To ensure a fair comparison, we follow OmniControl [55] and compare GMD in managing the full 3D position of the pelvis (xyz coordinates). The first section of Tab. 2 resents results for models trained on the pelvis alone to ensure a fair comparison with previous state-of-the-art methods on the HumanML3D [15] dataset. $\rightarrow$ means closer to real data is better. Our model demonstrates significant improvements across all evaluation metrics. When compare to TLControl, the FID score notably decreased from 0.271 to 0.061, the R-Precision increased from 0.779 to 0.809, indicating superior generation quality. In terms of joint control accuracy, both Trajectory Error and Location Error dropped to zero, while the average error decreased to $0.91~\mathrm{cm}$ , indicating highly precise joint control. Furthermore, our model outperforms existing methods in both Diversity and Foot Skating Ratio metrics. In the second section, Train on All Joints, we follow the evaluation from OmniControl [55], as our model supports control of any joint, not just the root (pelvis). We train the model to control multiple joints, specifically the pelvis, left foot, right foot, head, left wrist, and right wrist. Our model constantly outperform SOTA in all metrics. + +# 5.2. Qualitative Comparison to State-of-the-art + +Any-joint-Any-Frame. We visualize the generated motion using GMD [21], MotionLCM [7] and OmniControl [55] in Fig. 3. The motion is generated based on the prompt "a person walks forward and waves his hands," with the pelvis and right wrist controlled in a zigzag pattern. Since GMD can only control the pelvis, we apply control only to the pelvis + +Table 2. Comparison of text-condition motion generation with joint control signal on the HumanML3D. The first section, "Train on Pelvis Only," evaluates our model that was trained solely on the pelvis. The last section, "Train on All Joints", is trained on all joints and reports the average evaluation for each joint. $\rightarrow$ indicates the closer to the real value, the better. + +
MethodJointR-Precision Top-3↑FID ↓Diversity →Foot Skating Ratio ↓Trajectory Error (>50 cm) (%) ↓Location Error (>50 cm) (%) ↓Average Error (cm) ↓
Real-0.7970.0029.503-0.000.000.00
Train on Pelvis Only
MDM0.6020.6989.1970.101940.2230.7659.59
PriorMDM0.5830.4759.1560.089734.5721.3244.17
GMD0.6650.5769.2060.10099.313.2114.39
OmniControl (on pelvis)Pelvis0.6870.2189.4220.05473.870.963.38
MotionLCM0.7520.5319.253-18.877.6918.97
TLControl0.7790.2719.569-0.000.001.08
Ours (on pelvis)0.8090.061 (-77%)9.4960.05470.000.000.98
Train on All Random Joints
OmniControl0.6930.3109.5020.06086.171.074.04
TLControlAverage0.7820.2569.719-0.000.001.11
Ours0.8050.083 (-68%)9.3950.05450.000.000.72
+ +for GMD. However, it fails to follow the zigzag pattern, tending instead to move in a straight line. OmniControl receives control signals for both the pelvis and right wrist. Yet, it not only fails to follow the root trajectory (pelvis) but also does not adhere to the zigzag pattern for the right wrist. In contrast, our MaskControl demonstrates realistic motion with precise joint control for both the pelvis and the right wrist, accurately following the intended zigzag pattern. + +Zero-shot Objective Control. Fig. 4 shows the visualization results with the unseen objective function, 'Constrain a human to walk inside a square area,' compared to ProgMoGen [30]. ProgMoGen not only violates the constraint but also generates motion unrelated to the text, as it lacks any 'turns around' motion. + +# 5.3. Body Part Editing + +Table 3. Quantitative result of upper body editing task on HumanML3D dataset. + +
MethodR-precision ↑FID ↓MM-Dist ↓Diversity →
Top1Top2Top3
MDM [48]0.2980.4620.5714.8274.5987.010
OmniControl [55]0.3740.5500.6561.2135.2289.258
MMM [40]0.5000.6940.7980.1032.9729.254
MotionLCM [7]0.5120.6850.7980.3112.9489.736
Ours0.5170.7080.8040.0742.9459.380
+ +With joint signal controls, our model is capable of conditioning on multiple joints, which can be treated as distinct body parts, while generating the remaining body parts based on text input. In Tab. 3 We quantitatively compare our approach to existing methods designed for this task, including MDM [48] and MMM [40]. Additionally, we compare it with OmniControl [55] and MotionLCM [7], which also supports joint signal control. However, our evaluation demonstrates that OmniControl performs poorly in this task. Following the evaluation protocol from [40], we condition the lower body parts on ground truth for all frames and generate the upper body based on text descriptions us + +ing the HumanML3D dataset [15]. Our model is evaluated without retraining, using the same model as in the Train on All Joints setup, ensuring a fair comparison with OmniControl, which is trained on a subset of joints. Specifically, we condition only on the pelvis, left foot, and right foot as the lower body signals. + +The results show that MDM struggles significantly when conditioned on multiple joints, with the FID score increasing to 4.827. Although OmniControl supports multiple joint control, our experiments reveal that it also suffers under these conditions, with its FID score rising to 1.213. This is consistent with the Cross-Joint evaluation in Tab. 7, which evaluate on multiple joint combination, where OmniControl's FID score deteriorates considerably. MMM performs well in this task but requires retraining with separate codebooks for upper and lower body parts. In contrast, our model outperforms all other methods across all metrics without any retraining. When comparing to the 'Train on Pelvis Only' setup in Tab. 2, our model achieves similar FID and R-Precision scores, highlighting its robustness in handling multiple joint control signals. + +# 5.4. Zero-shot Objective Control + +We evaluate three zero-shot objective control tasks using three Human-Scene Interaction evaluations from ProgMoGen [30], a programmable motion control model, i.e. 'Head Height Constraint', 'Avoiding Barrier', and 'Walking Inside a Square'. MDM [48] and MoMask [16] serve as baselines without any control mechanisms. Since ProgMoGen builds on MDM as its base model. Similarly MoMask is shown as a baseline for the unconstrained Mask Motion Model. Tab. 4 shows that our MaskControl outperform ProgMoGen in all metrics. Max Acc. represents the maximum acceleration of joints which indicates the amount of joint jittering. Constraint Error measures how much the head height exceeds the specified constraint. Unsucc. Rate represents the rate of motion sequences that violate the height constraint. + +Table 4. Comparison of zero-shot objective control. Three Human-Scene Interaction objectives are adopted from the programmable motion model (ProgMoGen [30]). Both ProgMoGen and MaskControl are able to control motion during inference by arbitrary loss functions, while MDM and MoMask serve as uncontrollable baseline models. +Task HSI-1: Head Height Constraint + +
MethodFoot Skate ↓Max Acc. ↓Constraint Error ↓Unsucc. Rate ↓FID ↓Diversity →R-prec. (Top3) ↑
MDM [48] (Unconstrained)0.0860.0970.1180.7180.5459.6560.610
MoMask [16] (Unconstrained)0.0670.0720.0920.6010.3549.5050.683
ProgMoGen [30]0.0750.0940.0120.0880.5569.6110.597
Ours0.0660.0740.0000.0000.2469.3930.695
+ +Task HSI-2: Avoiding Barrier +Task HSI-3: Walking Inside a Square + +
MethodFoot Skate ↓Max Acceleration ↓Constraint Error ↓Foot Skate ↓Max Acceleration ↓Constraint Error ↓
MDM [48] (Unconstrained)0.0960.1260.4540.0960.1260.301
MoMask [16] (Unconstrained)0.0720.1170.4640.0720.1170.270
ProgMoGen [30]0.1890.1500.0970.1250.0930.012
Ours0.1460.1260.0000.0920.0780.000
+ +# 6. Ablation Study + +# 6.1. Component Analysis + +Table 5. Ablation results of components analysis and different densities of joint control signal. + +
MethodR-Prec. Top-3↑FID ↓Foot Skat. ↓Traj. Err. ↓Loc. Err. ↓Avg. Err. ↓
Component Analysis
No Control0.8070.0950.052750.6635.1163.18
w/o Logits Regularizer0.7950.1420.05770.320.022.18
w/o Logits Optimization0.8020.1280.059439.1424.0040.41
Full model0.8090.0610.05470.000.000.98
Density of Spatial Control Signal
Density: 10.8040.0770.05510.000.000.10
Density: 20.8060.0870.05530.000.000.34
Density: 50.8110.0780.05530.000.000.98
Density: 25%0.8120.0550.05360.010.001.68
Density: 100%0.8140.0540.05430.020.001.64
+ +To understand how each component impacts the quality and joint control error. We conduct an ablation study on each component in sec. Component Analysis of Tab. 5, using same evaluation as Tab. 2. Without any control, No Control, the model achieves the highest diversity and the lowest Foot Skating Ratio, indicating strong realism in the generated motion. The FID score is also on par. However, all spatial errors are poor due to the absence of joint control components in the model. Without the Logits Regularizer, the average error remains relatively low, but the FID score is the worst, highlighting the importance of the Logits Regularizer for generation quality. Without Logits Optimization, the average error significantly worsens, although the FID remains acceptable, suggesting that the Logits Regularizer helps maintain generation quality. In the Full model, both the Logits Regularizer and Logits Optimization complement each other, improving both generation quality (FID) and control accuracy (Average Error). + +# 6.2. Density of Joint Control Signal + +In second part of table 5, we provide a detailed analysis of MaskControl's performance across five different joint control density levels, where the model is trained for pelvis control using the HumanML3D dataset. The values 1, 2, and 5 refer to controlling the motion using exactly 1, 2, or 5 frames. The values $25\%$ and $100\%$ indicate the percentage of the total ground-truth motion length for each sample, which can range from 40 to 196 frames depending on the sample. The results show that increasing the joint control improves the quality: the FID score decreases from 0.077 with 1-frame control to 0.054 with full 196-frame $(100\%)$ control. Similarly, R-Precision improves from 0.804 at 1-frame density to 0.814 at 196-frame $(100\%)$ density. However, the Average Error shows the opposite trend—more joint control leads to higher error, as the model is required to target more specific points. + +# 7. Conclusion + +MaskControl is the first model to introduce controllability to the generative masked motion model, enabling precise control while maintaining high-quality motion generation, consistently outperforming diffusion-based controllable frameworks. MaskControl introduces Differentiable Expectation Sampling (DES) to relax the quantization constraint, enabling two key innovations: Logits Regularizer uses random masking and reconstruction to ensure that the generated motions are of high fidelity, while also reducing inconsistencies between the input control signals and the motions produced. Inference-Time Logit Optimization fine-tunes the predicted motion distribution during the unmasking process to the input control signals, enhancing precision and making MaskControl adaptable for unseen tasks. 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MaskHand: a novel generative masked model for accurate and robust 3D hand mesh recovery from single RGB images, excelling in diverse scenarios like occlusions, hand-object interactions, and varied appearances. Watch our Supplemental Video to see it in action! + +![](images/afba1b56a04c3b5529d3332f4cde3a82debf87be868dc1888ceaaf76e303adc8.jpg) + +![](images/707f38d4a9e86ddbaf1ac741621fc30ffdb4f2df88505acf8cf2c75a721d60a6.jpg) + +![](images/694f22594ec01e6efb68d2c634685c202008844954a5c4e7965fd35e1e2759bb.jpg) + +![](images/2708ed33ad527357ec7d30dce8477d683fa4b02bfad66196f3891ab87d02c4da.jpg) + +![](images/d27628c19aff719243856f3d0343a4e92b79ad444558ae69292e85559a821a9b.jpg) + +![](images/9b6d7b7d426207eae00bfc55d03f72f88b72a6732975056b3b160d1ed60b6c60.jpg) + +# Abstract + +Reconstructing a 3D hand mesh from a single RGB image is challenging due to complex articulations, self-occlusions, and depth ambiguities. Traditional discriminative methods, which learn a deterministic mapping from a 2D image to a single 3D mesh, often struggle with the inherent ambiguities in 2D-to-3D mapping. To address this challenge, we propose MaskHand, a novel generative masked model for hand mesh recovery that synthesizes plausible 3D hand meshes by learning and sampling from the probabilistic distribution of the ambiguous 2D-to-3D mapping process. MaskHand consists of two key components: (1) a VQ-MANO, which encodes 3D hand articulations as discrete pose tokens in a latent space, and (2) a Context-Guided Masked Transformer that randomly masks out pose tokens and learns their joint distribution, conditioned on corrupted token sequence, image context, and 2D pose cues. This learned distribution facilitates confidence-guided sampling during inference, producing mesh reconstructions with low uncertainty and high precision. Extensive evaluations on benchmark and real-world datasets demonstrate that MaskHand achieves state-of-the-art accuracy, robust + +ness, and realism in 3D hand mesh reconstruction. Project website: https://m-usamasaleem.github.io/publication/MaskHand/MaskHand.html. + +# 1. Introduction + +Hand mesh recovery has gained significant interest in computer vision due to its broad applications in fields such as robotics, human-computer interaction [43, 57], animation, and AR/VR [12, 31]. While previous methods have explored markerless, image-based hand understanding, most depend on depth cameras [3, 24, 44, 50, 58] or multi-view images [5, 25, 54, 56]. Consequently, most of these methods are not feasible for real-world applications where only monocular RGB images are accessible. On the other hand, monocular hand mesh recovery from a single RGB image, especially without body context or explicit camera parameters, is highly challenging due to substantial variations in hand appearance in 3D space, frequent self-occlusions, and complex articulations. + +Recent advances, especially in transformer-based methods, have shown significant promise in monocular hand mesh recovery (HMR) by capturing intricate hand struc + +tures and spatial relationships. For instance, METRO [15] and MeshGraphormer [40] utilize multi-layer attention mechanisms to model both vertex-vertex and vertex-joint interactions, thereby enhancing mesh fidelity. Later, HaMeR [48] illustrated the scaling benefits of large vision transformers and extensive datasets for HMR, achieving improved reconstruction accuracy. However, these methods are inherently discriminative, producing deterministic outputs for each image. Consequently, they face limitations in complex, real-world scenes where ambiguities arise due to occlusions, hand-object interactions, and challenging viewpoints are prevalent. + +![](images/67eb8ddddb2576e2bf8f079fb951b7795d22240da083c7d711ba79707d030f07.jpg) +Multiple Reconstruction Hypotheses with Explicit Confidence Levels +Figure 2. MaskHand is a quantifiable probabilistic HMR method that can learn 2D-to-3D mapping distributions and explicitly estimate confidence levels or prediction probabilities for all mesh reconstruction hypotheses + +To overcome these limitations, we introduce MaskHand, a novel generative masked model designed for accurate 3D hand mesh recovery. By learning and sampling from the underlying joint distribution of hand articulations and image features, our model synthesizes most probable 3D hand meshes, mitigating ambiguities inherent in single-view reconstruction as shown in Figure 2. MaskHand consists of two main components: a VQ-MANO and a context-guided masked transformer, which are trained in two consecutive stages. In the first stage, VQ-MANO is trained with Vector Quantized Variational Autoencoders (VQ-VAE) [60] to encode continuous hand poses (e.g., joint rotations) of the MONO parametric hand model into a sequence of discrete pose tokens. The discretization in VQ-MANO is crucial for generative masked modeling, allowing the model to learn per-token probabilities conditioned on the input image. In the second stage, the token sequence is partially masked and the context-guided masked transformer is trained to reconstruct the masked tokens by learning token conditional distribution, based on multiple contextual clues, including corrupted token sequence, image features, and 2D pose structures. The learned distribution enables uncertainty quantification at each prediction step, facilitating confidence-guided sampling to iteratively refine mesh reconstructions. By selectively retaining high-confidence tokens during inference, MaskHand minimizes uncertainty in the 2D-to-3D mapping, enabling high-precision hand mesh recovery, even + +in occluded and ambiguous scenarios. + +- MaskHand is the first to leverage generative masked modeling for reconstructing robust 3D hand mesh. The main idea is to explicitly learn the 2D-to-3D probabilistic mapping and synthesize high-confidence, plausible 3D meshes by sampling from learned distribution. +- We design context-guided masked transformer that effectively fuses multiple contextual clues, including 2D pose, image features, and unmasked 3D pose tokens. +- We propose differential masked training to learn hand pose token distribution, conditioned on all contextual clues. This learned distribution facilitates confidence-guided sampling during inference, producing mesh reconstructions with low uncertainty and high precision. +- We show that MaskHand is a generic framework that unifies hand-mesh estimation and hand-mesh generation. +- We demonstrate through extensive experiments that MaskHand outperforms SOTA methods on standard datasets. + +# 2. Related Work + +# 2.1. Discriminative Methods + +Human hand recovery has been developed in recent years, with early approaches [23, 29, 59, 62, 71, 73] leveraging optimization techniques to estimate hand poses based on 2D skeleton detections. Later, MANO [52] introduced a differentiable parametric mesh model that capture hand shape and articulation, allowing the model to provide a plausible mesh with end-to-end estimation of model parameters directly from a single-view image. Boukhayma et al. [6] presented the first fully learnable framework to directly predict the MANO hand model parameters [52] from RGB images. Similarly, several subsequent methods have leveraged heatmaps [70] and iterative refinement techniques [4] to ensure 2D alignment. Kulon et al. [35, 36] proposed a different regression approach that predicts 3D vertices instead of MANO pose parameters, achieving notable improvements over prior methods. Recent methods, such as METRO [49], MeshGraphormer [40], HaMeR [48] achieve the SOTA performance by modeling both vertex-vertex and vertex-joint interactions. These existing methods, based on discriminative regression, learn a deterministic mapping from the input image to the output mesh. This deterministic approach struggles to capture the uncertainties and ambiguities caused by hand self-occlusions, interactions with objects, and extreme poses or camera angles, resulting in unrealistic hand mesh reconstructions. + +# 2.2. Generative Methods + +Our MaskHand employs a generative method that learns a probabilistic mapping from the input image to the output mesh. It utilizes this learned distribution to synthesize high-confidence, plausible 3D hand meshes based on + +2D visual contexts. HHMR [37] is the only other generative hand mesh recovery method in the literature. Unlike HHMR [37] that utilizes diffusion models, MaskHand is inspired by the success of masked image and language models for image and text generation tasks [8, 9, 18, 19, 72]. This fundamental difference allows MaskHand to explicitly and quantitatively estimate confidence levels or prediction probabilities for all mesh reconstruction hypotheses, enabling confidence-guided hypothesis selection for accurate reconstruction, as shown in Fig. 2. In contrast, HHMR's denoising diffusion process synthesizes multiple mesh hypotheses without associating a confidence level with each hypothesis. Thus, it only reports the theoretically best mesh reconstruction by finding the hypothesis with minimal reconstruction errors under the assumption that ground-truth meshes are available. + +# 3. Proposed Method: MaskHand + +Problem Formulation. Given a single-hand image $I$ , we aim to learn a mapping function $f(I) = \{\theta, \beta, \pi\}$ that output the MANO [52] model parameters from the input image. This mapping function encompasses three key components: the hand pose parameters $\theta \in \mathbb{R}^{48}$ , shape parameters $\beta \in \mathbb{R}^{10}$ , and camera parameters $\pi \in \mathbb{R}^3$ , enabling comprehensive 3D hand reconstruction. + +Overview of Proposed Method. As shown in Figure 3, MaskHand consists of two primary modules: VQ-MANO and the Context-Guided Masked Transformer. Initially, VQ-MANO discretizes 3D MANO pose parameters $(\theta)$ into discrete tokens, enabling generative masked modeling and uncertainty quantification. Next, the Context-Guided Masked Transformer leverages an encoder-decoder structure: the encoder extracts multi-scale image features, which, combined with 2D pose cues and unmasked tokens, are processed by the masked decoder. The decoder employs Graph-based Anatomical Pose Refinement to capture joint dependencies and a Context-Infused Masked Synthesizer to fuse visual features and token interactions, learning the probabilistic reconstruction via differential masked modeling. During inference, pose predictions are iteratively refined by selectively retaining high-confidence tokens and re-masking uncertain ones, progressively improving accuracy. Finally, the reconstruction is completed as the predicted pose $(\theta)$ , shape $(\beta)$ and camera parameters $(\pi)$ are feed into the MANO hand model. + +# 3.1. Hand Model and VQ-MANO + +Our approach employs the MANO model [52], which maps pose $\theta \in \mathbb{R}^{48}$ and shape $\beta \in \mathbb{R}^{10}$ to a 3D hand mesh $M \in \mathbb{R}^{778 \times 3}$ and joint locations $X \in \mathbb{R}^{21 \times 3}$ , representing both hand surface and pose. + +VQ-MANO is a MANO hand tokenizer that employs a 1D convolutional autoencoder to learn a discrete latent space for 3D pose parameters $\theta \in \mathbb{R}^{48}$ by quantizing the + +continuous pose embeddings into a learned codebook $C$ with discrete code entries, as depicted in Figure 3(a). A key feature is its upsampling mechanism, expanding 16 MANO poses into 64 discrete pose tokens, which enhances spatial detail and improves mesh recovery accuracy (Supplementary Section C). To this end, we employ a Vector Quantized Variational Autoencoder (VQ-VAE) [60] for pretraining the tokenizer. Specifically, we input the MANO pose parameters $\theta$ into a convolutional encoder $E$ , which maps them to a latent embedding $z$ . Each embedding $z_{i}$ is then quantized to its nearest codebook entry $c_{k} \in C$ based on Euclidean distance, defined as + +$$ +\hat {z} _ {i} = \arg \min _ {c _ {k} \in C} \| z _ {i} - c _ {k} \| _ {2}. +$$ + +The total loss function of VQ-MANO is formulated as: + +$$ +\mathcal {L} _ {\mathrm {v q - m a n o}} = \lambda_ {\mathrm {r e}} \mathcal {L} _ {\mathrm {r e c o n}} + \lambda_ {\mathrm {E}} \| \operatorname {s g} [ z ] - c \| _ {2} + \lambda_ {\alpha} \| z - \operatorname {s g} [ c ] \| _ {2}, +$$ + +where $\mathcal{L}_{\mathrm{vq - nano}}$ consists of a MANO reconstruction loss $\mathcal{L}_{\mathrm{recon}}$ , a latent embedding loss, and a commitment loss, weighted by hyperparameters $\lambda_{\mathrm{re}}$ , $\lambda_{\mathrm{E}}$ , and $\lambda_{\alpha}$ , respectively. Here, $\mathrm{sg}[\cdot]$ denotes the stop-gradient operator, which prevents gradients from flowing through its argument during backpropagation. To further enhance reconstruction quality, we incorporate an additional L1 loss: + +$$ +\mathcal {L} _ {\text {r e c o n}} = \lambda_ {\theta} \mathcal {L} _ {\theta} + \lambda_ {\mathrm {V}} \mathcal {L} _ {\mathrm {V}} + \lambda_ {\mathrm {J}} \mathcal {L} _ {\mathrm {J}}, +$$ + +which aims to minimize the discrepancies between the predicted and ground-truth MANO parameters, including the pose parameters $\theta$ , mesh vertices $V$ , and hand joints $J$ . The tokenizer is optimized using a straight-through gradient estimator to facilitate gradient propagation through the nondifferentiable quantization step. Additionally, the codebook entries $C$ are updated via exponential moving averages and periodic codebook resets, as described in [21, 64]. + +# 3.2. Context-Guided Masked Transformer + +The context-guided masked transformer comprises two main components: the multi-scale image encoder and the masked graph transformer decoder. + +# 3.2.1. Multi-scale Image Encoder + +Our encoder uses a vision transformer (ViT-H/16) [2] to extract image features [48], processing 16x16 pixel patches into feature tokens. Following ViTDet [38], we adopt a multi-scale feature approach by upsampling the initial feature map to produce feature maps at varying resolutions. This multi-scale representation is critical for handling complex articulations and self-occlusions in hand poses. High-resolution maps provide fine-grained joint details, while low-resolution maps capture global hand structure, balancing precision in joint positioning with overall anatomical coherence. Moreover, we utilize cross-attention with low-resolution feature maps in the x-Attention head to regress + +![](images/8fb2e77fff9a9de1831f900a4890275f9fc5a0f0f917a42d6c9758acf20cd953.jpg) +Figure 3. MaskHand Training Phase. MaskHand consists of two key components: (1) VQ-MANO, which encodes 3D hand poses into a sequence of discrete tokens within a latent space, and (2) a Context-Guided Masked Transformer that models the probabilistic distributions of these tokens, conditioned on the input image, 2D pose cues, and a partially masked token sequence. + +![](images/2ac1de63cfd7f05db7ca03ab22b1c54cdae71d5e96a379faed355fa4265f05c6.jpg) +Figure 4. Architecture of Graph-based Anatomical Pose Refinement (GAPR) and Context-Infused Masked Synthesizer, illustrating fusion of anatomical pose dependencies and contextual cues for precise mesh reconstruction. + +stable shape parameters $(\beta)$ and camera orientation $(\pi)$ , making the process computationally efficient. This approach decouples shape estimation from pose modeling, preserving morphological stability and spatial alignment, and enhancing robustness and anatomical accuracy in 3D hand reconstruction. + +# 3.2.2. Masked Graph Transformer Decoder + +The Masked Transformer Decoder is composed of two key components (Figure 3 and 4): Graph-based Anatomical Pose Refinement (GAPR) and the Context-Infused Masked Synthesizer Module. + +Graph-based Anatomical Pose Refinement (GAPR). Our decoder employs two blocks of a lightweight graph transformer that process pose tokens generated by VQ-MANO, enriched with 2D pose guidance, ensuring anatomically coherent hand reconstructions as shown in Figure 4. To construct a hand-kinematic aware 2D pose token, we first process OpenPose 2D keypoints [7] through a Graph Convolutional Network (GCN) with a fixed hand skeleton adjacency matrix, capturing explicit kinematic structures. Simultaneously, VQ-MANO pose tokens, which inherently + +encode implicit and non-linear joint dependencies, are extracted. These two representations are then fused and refined through two graph transformer block, where learnable adjacency matrices adaptively model complex joint relationships, ensuring robust spatial and structural consistency. To further enhance stability and anatomical accuracy, we integrate a transformer encoder with a Squeeze-and-Excitation (SE) block [30], which emphasizes joint orientations and angles while ensuring spatial alignment through a 1x1 convolution layer. Within the transformer encoder, Multi-Head Attention (MHA) and pointwise convolution layers refine high-resolution dependencies between joints, producing a cohesive and anatomically aligned 3D pose representation, denoted as $Q_{\mathrm{GAPR}}$ . The output $Q_{\mathrm{GAPR}}$ is formulated as: + +$$ +Q ^ {\prime} = \mathrm {M H A} \left(\operatorname {N o r m} \left(Q _ {\mathrm {C}}\right)\right) + \operatorname {C o n v} \left(\operatorname {N o r m} \left(Q _ {\mathrm {C}}\right)\right) + Q _ {\mathrm {C}} \tag {1} +$$ + +$$ +Q _ {\mathrm {G A P R}} = \operatorname {S E} \left(\operatorname {N o r m} \left(Q ^ {\prime}\right)\right) \tag {2} +$$ + +where $Q_{\mathrm{C}} \in \mathbb{R}^{K \times D}$ represents MANO pose tokens and 2D pose context queries, and $Q_{\mathrm{GAPR}}$ is the stabilized, anatomically consistent pose representation. These refined tokens $Q_{\mathrm{GAPR}}$ are then processed by the Context-Infused Masked Synthesizer to generate precise 3D hand meshes. + +Context-Infused Masked Synthesizer. We leverage a multi-layer transformer (as shown in Figure 4) whose inputs are refined pose tokens $Q_{\mathrm{GAPR}}$ and cross-attends them with multi-scale feature maps generated by the image encoder. To enhance computational efficiency with high-resolution feature maps, a deformable cross-attention mechanism is employed [75]. This allows each pose token to focus on a selected set of sampling points around a learnable reference point, rather than the entire feature map. By concentrating attention on relevant areas, the model achieves a + +balance between computational efficiency and spatial precision, preserving essential information for accurate 3D hand modeling. The deformable cross-attention is defined as: + +$$ +\operatorname {M C D A} \left(Q _ {\text {G A P R}}, \hat {p} _ {y}, \left\{x ^ {l} \right\}\right) = \sum_ {l, k} A _ {l y k} \cdot \mathbf {W} x ^ {l} \left(\hat {p} _ {y} + \Delta p _ {l y k}\right) +$$ + +where $Q_{\mathrm{GAPR}}$ are refined manifold query queries, $\hat{p}_y$ are learnable reference points, $\Delta p_{lyk}$ are sampling offsets, $\{x^l\}$ are multi-scale features, $A_{lyk}$ are attention weights, and $\mathbf{W}$ is a learnable weight matrix. With the inclusion of a [MASK] token in the masked transformer decoder, the module can predict masked pose tokens during training, while also facilitating token generation during inference. This approach uses the [MASK] token as a placeholder for pose predictions, enabling robust synthesis of occluded or unobserved hand parts for coherent 3D hand reconstruction. + +# 3.3. Training: Differential Masked Modeling + +Context-conditioned Masked Modeling. We employ masked modeling to train our model that learns the probabilistic distribution of 3D hand poses, conditioned on multiple contextual cues. Given a sequence of discrete pose tokens $Y = [y_i]_{i=1}^L$ from the pose tokenizer, where $L$ is the sequence length, we randomly mask out a subset of $m$ tokens with $m = \lceil \gamma(\tau) \cdot L \rceil$ , where $\gamma(\tau)$ is a cosine-based masking ratio function. Here, $\tau$ is drawn from a uniform distribution $U(0,1)$ , and we adopt the masking function $\gamma(\tau) = \cos\left(\frac{\pi\tau}{2}\right)$ , inspired by generative text-to-image modeling strategies [8]. Masked tokens are replaced with learnable [MASK] tokens, forming a corrupted sequence $Y_{\overline{\mathbf{M}}}$ that the model must reconstruct. Each token $y_i$ is predicted based on the probabilistic distribution $p(y_i | Y_{\overline{\mathbf{M}}}, X_{2D}, X_{img})$ , conditioned on corrupted token sequence $Y_{\overline{\mathbf{M}}}$ , 2D pose embedding $X_{2D}$ , and image prompt $X_{img}$ . This approach enables the model to explicitly account for the uncertainty inherent in mapping 2D observations to a coherent 3D hand mesh. The training objective is to minimize the negative log-likelihood of correctly predicting each pose token in the sequence, formulated as follows: + +$$ +\mathcal {L} _ {\mathrm {m a s k}} = - \mathbb {E} _ {Y \in \mathcal {D}} \left[ \sum_ {\forall i \in [ 1, L ]} \log p (y _ {i} | Y _ {\overline {{\mathbf {M}}}}, X _ {2 D}, X _ {i m g}) \right]. +$$ + +Expectation-Approximated Differential Sampling. The training objective $\mathcal{L}_{\mathrm{mask}}$ captures stochastic uncertainty in hand mesh reconstruction, enabling precise estimation of pose parameters $\theta$ within a structured latent space. Recent studies [48] show that auxiliary 3D and 2D joint losses improve pose recovery by aligning predicted and ground-truth 2D/3D joints. Integrating these losses requires transforming latent pose tokens into $\theta$ , a process involving non-differentiable probabilistic sampling. To address this, instead of sampling the distribution $p(y_i|Y_{\overline{\mathbf{M}}},X_{2D},X_{img})$ to + +![](images/42aca582118b758d2b91a914b3898c30b581d1ae94177c52fe3bf9056a41ef86.jpg) +Figure 5. MaskHand Inference Phase: Confidence-Guided Iterative Sampling — a step-by-step refinement of pose selection by probabilistically sampling high-confidence tokens. + +obtain the most probable token from codebook, we implement an expectation-based differential relaxation: instead of directly estimating discrete code indices, the model outputs logits $L$ for each token. These logits undergo a softmax operation, producing the token distribution, which are multiplied by the pretrained codebook, resulting in the mean quantized feature representations $\bar{z} = [\bar{z}_1, \bar{z}_2, \dots, \bar{z}_M]$ : + +$$ +\bar {z} = \operatorname {s o f t m a x} \left(L _ {M \times K}\right) \times \mathbf {C B} _ {K \times D} +$$ + +where $L$ represents the logits matrix, CB denotes the codebook, $M$ is the token count, $K$ specifies the codebook size, and $D$ defines the dimensionality of each codebook entry. This mean token embeddings $\bar{z}$ are feed into the decoder to reconstruct the pose parameter $\theta'$ . Combined with shape parameters $\beta$ and camera parameters $\pi$ , this process reconstructs the 3D hand mesh, enabling the computation of both 3D joint loss and 2D projection loss. Since obtaining $\bar{z}$ is differential, the model can be trained end-to-end using the overall loss function. + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {m a s k}} + \mathcal {L} _ {\text {M A N O}} + \mathcal {L} _ {\text {3 D}} + \mathcal {L} _ {\text {2 D}} +$$ + +which combines the masked token prediction loss $(\mathcal{L}_{\mathrm{mask}})$ , 3D joint loss $(\mathcal{L}_{\mathrm{3D}})$ , 2D projection loss $(\mathcal{L}_{\mathrm{2D}})$ , and MANO parameter loss $\mathcal{L}_{\mathrm{MANO}}$ . Together, these terms collectively minimize discrepancies within MANO space, enabling precise 3D hand reconstruction. + +# 3.4. Inference: Confidence-Guided Sampling + +Our model leverages confidence-guided sampling to achieve precise and stable 3D hand pose predictions as shown in Figure 5. This process begins with a fully masked sequence $Y_{1}$ of length $L$ , with each token initialized as [MASK]. Over $T$ decoding iterations, each iteration $t$ applies stochastic sampling to predict masked tokens based on their distributions $p(y_{i}|Y_{\overline{\mathbf{M}}},X_{2D},X_{img})$ . Following each sampling step, tokens with the lowest prediction confidences are re-masked to be re-predicted in subsequent iterations. The number of tokens re-masked is determined by a + +![](images/3caed67dc525058d963a583092005a1481ac941fd01eb71cef3ca1d5c8a4f111.jpg) +Figure 6. Comparison of SOTA methods: MaskHand synthesizes unobserved parts for accurate 3D reconstructions in occluded scenarios. + +masking schedule $\lceil \gamma \left(\frac{t}{T}\right)\cdot L\rceil$ , where $\gamma$ is a decaying function of $t$ . This schedule dynamically adjusts masking intensity based on confidence, using a higher masking ratio in earlier iterations when prediction confidence is lower. Consequently, the model iteratively refines ambiguous regions, progressively improving prediction confidence as context builds. The masking ratio decreases with each step, stabilized by the cosine decay function $\gamma$ . + +# 4. Experiments + +
MethodPA-MPJEMm(↓)PA-MPVEMm(↓)F@5(↑)F@15(↑)AUCJ(↑)AUCV(↑)
S2HAND [13]11.511.10.4480.9320.7690.778
KPT-Transf. [28]10.9---0.785-
ArtiBoost [67]10.810.40.5070.9460.7850.792
Yu et al. [69]10.810.4----
HandGCAT [63]9.39.10.5520.9560.8140.818
AMVUR [32]8.78.30.5930.9640.8260.834
HMP [20]10.1-----
SPMHand [42]8.88.60.5740.962--
MaskHand7.07.00.6630.9840.8600.860
+ +Training Datasets. To train the hand pose tokenizer, we employed a diverse set of datasets to capture a wide range of hand poses and interactions. This includes DexYCB [10], InterHand2.6M [45], MTC [65], and RHD [76]. For training MaskHand, we constructed a comprehensive dataset following a similar setup as [48] to ensure fair comparison. Specifically, for evaluations on HO3Dv3 [28] and HInt [48], MaskHand was trained on a diverse mix of datasets, including FreiHAND [77], HODv2 [27], MTC [65], RHD [76], InterHand2.6M [45], H2O3D [27], DexYCB [10], COCO-Wholebody [33], Halpe [22], and MPII NZSL [54]. However, for FreiHAND and DexYCB, MaskHand was trained specifically on their respective training datasets. + +Table 1. Zero-Shot 3D Mesh Reconstruction Evaluation on HO3Dv3 [28] Benchmark: SOTA Comparison. "-" indicates unreported metrics. + +
MethodsPA-MPJEMm (↓)PA-MPVEMm (↓)F@5 (↑)F@15 (↑)
MeshGraphormer† [40]5.96.00.7640.986
FastMETRO [16]6.57.10.6870.983
FastViT [61]6.66.70.7220.981
AMVUR [32]6.26.10.7670.987
Deformer [68]6.26.40.7430.984
PointHMR [34]6.16.60.7200.984
Zhou et al. [74]5.76.00.7720.986
HaMeR [48]6.05.70.7850.990
HHMR§ [37]5.85.8--
MaskHand‡5.55.40.8010.991
+ +$\ddagger$ MaskHand produces confident mesh reconstruction, guided by the learned 2D-to-3D distribution without assuming GT meshes. +§ HHMR reports best hypothesis mesh reconstruction with minimum MPJPE and MPVPE, with the assumption of available GT meshes. + +Table 2. 3D Mesh Reconstruction Accuracy on FreiHAND [77]: SOTA Comparison. $\dagger$ Denotes Test-Time Augmentation. PA-MPJPE/PA-MPVPE in mm. "-" indicates unreported metrics. + +
MethodPA-MPJPE(↓)PA-MPVPE(↓)MPJPE(↓)MPVPE(↓)
METRO [70]7.0---
Spurr et al. [55]6.8---
Liu et al. [41]6.6---
HandOccNet [46]5.85.514.013.1
MobRecon [11]6.45.614.213.1
H2ONet [66]5.75.514.013.0
Zhou et al. [74]5.55.512.412.1
Ours5.04.911.711.2
+ +Table 3. 3D Mesh Reconstruction Accuracy on DexYCB [10]: SOTA Comparison. " -" indicates unreported metrics. + +Evaluation Metrics. We follow standard protocols [48] to assess 3D joint reconstruction using PA-MPJPE and $\mathrm{AUC}_J$ . For 3D mesh evaluation, we use PA-MPVPE, $\mathrm{AUC}_V$ , and F@5mm/F@15mm to measure vertex precision. Moreover, PCK evaluates 2D reconstruction by reprojecting 3D joints into 2D space. The computational efficiency is measured by Average Inference Time per Image (AITI) in seconds [7], where lower values indicate better performance. + +
MethodVenueNewDaysVISOREgo4D
@0.05 (↑)@0.1 (↑)@0.15 (↑)@0.05 (↑)@0.1 (↑)@0.15 (↑)@0.05 (↑)@0.1 (↑)@0.15 (↑)
Occluded Joints Evaluation
FrankMocap [53]ICCVW 20219.228.046.911.033.055.08.426.945.1
METRO [39]CVPR 20217.023.642.410.232.453.98.026.244.7
MeshGraphormer [40]ICCV 20217.925.744.310.933.354.19.332.651.7
HandOccNet (param) [47]CVPR 20227.223.542.47.426.146.77.226.145.7
HandOccNet (no param) [47]CVPR 20229.831.250.89.933.755.49.631.152.7
HaMeR [48]CVPR 202427.260.878.925.960.880.723.056.976.3
MaskHandOurs29.464.180.331.464.283.629.465.380.1
Occluded Joints Evaluation with 80% Masked Hand
HaMeR [48]CVPR 20248.728.448.97.124.441.77.123.440.2
MaskHandOurs10.531.652.08.225.041.98.226.244.1
Occluded Joints Evaluation with 90% Masked Hand
HaMeR [48]CVPR 20248.727.448.17.124.342.27.123.440.2
MaskHandOurs10.431.051.19.127.344.38.025.143.2
+ +Table 4. Zero-shot evaluation on the HInt Benchmark [48] for occluded joint reconstruction using the PCK metric, comparing MaskHand to SOTA methods. MaskHand demonstrates superior robustness and resilience to missing hand structures under severe occlusions, maintaining strong performance even with $80\%$ and $90\%$ masked hand regions. None of the models were trained on the HInt dataset. + +Reconstruction Evaluation. We evaluate MaskHand's joint and mesh reconstruction on HO3Dv3 [28], DexYCB [10], FreiHAND [77], and HInt [48] benchmarks. + +Zero-Shot Generalization Evaluation: The HO3Dv3 dataset, with 20K annotated images, serves as a benchmark for evaluating generalization in complex hand-object interactions. MaskHand is tested on HO3Dv3 without prior training to assess its capability in handling unseen data, occlusions, dataset biases, and diverse hand articulations in real-world scenarios. Additionally, we evaluate MaskHand's zero-shot performance on the HInt benchmark [48], which presents challenges such as varied lighting, extreme viewpoints, and complex hand-object interactions. Using the PCK metric, MaskHand is tested on HInt-NewDays [14], HInt-EpicKitchens VISOR [17], and HInt-Ego4D [26], demonstrating its ability to operate in diverse and occlusion-heavy environments. + +Supervised Evaluation: We evaluated MaskHand on FreiHAND [77], which consists of 4K images captured in controlled environments, and DexYCB [10], a large-scale dataset containing 78K images of hands interacting with objects. For a fair comparison, we trained MaskHand exclusively on FreiHAND, following the evaluation protocols of MeshGraphormer [40] and HHMR [37]. Similarly, aligning with recent work [74], we trained MaskHand on DexYCB and conducted evaluations under the same conditions, ensuring a direct and consistent comparison. + +# 4.1. Comparison to State-of-the-art Approaches + +We evaluate MaskHand on HO3Dv3, FreiHAND, DexYCB, and HInt (Tables 1-4), where it outperforms SOTA methods, demonstrating strong zero-shot generalization and in-the-wild robustness. Unlike prior approaches, MaskHand leverages confidence-aware masked modeling to effectively handle uncertainty, occlusions, and complex hand poses. In zero-shot evaluation on HO3Dv3 (Table 1), + +MaskHand reduces PA-MPJPE by $19.5\%$ and PA-MPVPE by $15.7\%$ , demonstrating superior dataset-agnostic reconstruction. On FreiHAND (Table 2), it achieves $3.5\%$ lower PA-MPJPE and $5.3\%$ lower PA-MPVPE, with the highest F@5mm (0.801) and F@15mm (0.991), ensuring precise, high-fidelity hand recovery. In DexYCB (Table 3), MaskHand reduces MPJPE by $9.1\%$ and MPVPE by $10.9\%$ , confirming its robustness in real-world hand-object interactions. In zero-shot evaluation on HInt (Table 4), which includes challenging egocentric, heavily occluded hand poses, MaskHand achieves state-of-the-art occluded joint reconstruction, improving PCK@0.05 by $8.1\%$ on HInt-NewDays, $21.2\%$ on HInt-VISOR, and $27.8\%$ on HInt-Ego4D. Qualitatively, Figure 6 shows MaskHand's superior synthesis of occluded regions compared to prior methods, while Figure 7 demonstrates its robustness under extreme masking. These results highlight MaskHand's strong generalization and practical effectiveness in challenging real-world conditions. + +# 4.2. Ablation Study + +The key to MaskHand's effectiveness lies in its generative masked modeling and uncertainty quantification, enabling robust reconstruction in occluded regions. Its iterative decoding strategy refines predictions, progressively enhancing accuracy in challenging scenarios. This ablation study explores iterative refinement and MaskHand's versatility in text-conditioned 3D hand synthesis. + +Further analyses, experimental details, and qualitative visualizations in the Supplementary Material explore key aspects, including the influence of architectural choices (e.g., VQ-MANO tokenizer, proposed modules, multi-scale feature resolutions, deformable attention layers), training strategies (masking ratios, regularization losses via differential sampling), and advanced MaskHand capabilities such as unconditional mesh generation and robust recon + +![](images/719789e51fa6628442858312ef351ed5c7e4bb2199833af551acc7b56c0891e4.jpg) +Figure 7. SOTA Comparison: Qualitative zero-shot evaluation on HInt Benchmark [48] for heavily masked hand images. MaskHand reconstructs occluded hand poses, demonstrating robustness to severe occlusions and generalizability to unseen masked regions. + +struction under severe real-world occlusions. + +Impact of Iterative Confidence-Guided Sampling. In confidence-guided sampling, we iteratively refines predictions by retaining high-confidence tokens and re-masking low-confidence ones, progressively enhancing stability and accuracy. As shown in Table 5, increasing iterations from 1 to 5 reduces PA-MPVPE (7.2 → 7.0 on HO3Dv3, 5.6 → 5.4 on FreiHAND). These improvements result from confidence-guided masking of uncertain regions during decoding, enhancing reconstruction accuracy. + +
# of iter.HO3Dv3FreiHANDAITI (s)
PA-MPJPEPA-MPVPEPA-MPJPEPA-MPVPE(↓)
17.27.25.65.60.04
37.17.15.65.50.08
57.07.05.55.40.12
+ +# 4.3. Application: Text-to-Mesh Generation + +MaskHand's modular design extends beyond hand mesh reconstruction to text-conditioned 3D hand synthesis. By replacing the image encoder with a CLIP-based text encoder [51], MaskHand can generate 3D hand meshes from text inputs, as shown in Figure 8. Using the ASL dataset [1], we trained MaskHand with pseudo-ground-truth annotations generated by MaskHand. During testing, a top-5% probabilistic sampling strategy ensured diverse yet plausible mesh outputs, evaluated using Hausdorff Distance, Chamfer Distance, and PA-MPVPE. Results (Table 6) demonstrate high fidelity and consistency in text-driven reconstruction, with qualitative examples shown in Figure 9. More details are provided in Supplementary Section B. + +Table 5. Iterations in Iterative Confidence-Guided Sampling. AITI is obtained on a single mid-grade GPU (NVIDIA RTX A5000). + +
MetricMeanStandard Deviation
Hausdorff Distance0.02210.0073
Chamfer Distance9.73 × 10-55.47 × 10-5
PA-MPVPE (mm)12.23.1
+ +Table 6. Quantitative evaluation of text-to-mesh generation using MaskHand's Masked Synthesizer, reporting mean and standard deviation across all generated meshes per text prompt. + +![](images/56656b979deaba19dc7796f745bed40129d82bdedac211ad0ea29423b27f3979.jpg) +Figure 8. Repurposed MaskHand for Text-to-Mesh Generation + +![](images/7496f76d3c24f5517497a457f58e4d900698bdef6cee54981f6bd853d458d4a8.jpg) +Figure 9. Text-to-mesh generation results on the ASL dataset, demonstrating MaskHand's Masked Synthesizer's ability to generate structurally accurate and diverse meshes from text inputs. + +# 5. Conclusion + +We introduced MaskHand, a generative masked model for accurate and robust 3D hand mesh reconstruction, particularly in occluded and ambiguous regions. By explicitly learning and sampling from the probabilistic 2D-to-3D mapping, MaskHand effectively handles self-occlusions, depth ambiguities, and missing hand parts. 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However, SAM is not directly applicable to medical image segmentation due to its inability to predict semantic labels, reliance on additional prompts, and suboptimal performance in this domain. To address these limitations, we propose MaskSAM, a novel prompt-free SAM adaptation framework for medical image segmentation based on mask classification. + +MaskSAM introduces a prompt generator integrated with SAM's image encoder to produce auxiliary classifier tokens, binary masks, and bounding boxes. Each pair of auxiliary mask and box prompts eliminates the need for user-provided prompts. Semantic label prediction is enabled by summing the auxiliary classifier tokens with learnable global classifier tokens in SAM's mask decoder. Additionally, we design a 3D depth-convolution adapter for image embeddings and a 3D depth-MLP adapter for prompt embeddings, which are injected into each transformer block in the image encoder and mask decoder to efficiently fine-tune SAM for volumetric medical imaging. Our method achieves state-of-the-art performance, with a Dice score of $90.52\%$ on AMOS2022, outperforming nnUNet by $2.7\%$ . MaskSAM also surpasses nnUNet by $1.8\%$ on ACDC and $1.0\%$ on the Synapse dataset, demonstrating its effectiveness in medical image segmentation. We release our code at https://github.com/bxie9/MaskSAM. + +# 1. Introduction + +Foundation models [14, 21] trained on large datasets have significantly advanced artificial intelligence [39, 41]. + +![](images/74baef9701fb9cb7b45b3dafc803355352cbd3556f6a5f7bb16537e406092b50.jpg) +Figure 1. Visualization of auxiliary box prompts, which generate multiple prompts to enhance mask prediction, on Synapse dataset. + +Their strong zero-shot and few-shot generalization capabilities have driven broad adoption across downstream tasks. Unlike traditional task-specific training, the "pre-training then fine-tuning" paradigm has become essential, particularly in computer vision. The Segment Anything Model (SAM) [30], pre-trained on over 1 billion masks from 11 million natural images, has gained attention for its prompt-driven segmentation capabilities. + +Medical image segmentation, a crucial subfield, has been dominated by deep learning methods [1, 2, 44]. These models, tailored for specific tasks, benefit from strong inductive biases but lack generalization. This raises an important question: Can SAM be adapted for medical image segmentation while leveraging its zero-shot capabilities? + +Several studies have attempted to adapt SAM to medical segmentation, but few have successfully addressed key challenges, such as those in AMOS22 [29], a benchmark for medical segmentation. The limitations of SAM-based adaptations stem from three factors: + +1) Lack of semantic label prediction. SAM generates binary masks per prompt but does not associate them with semantic labels. Medical segmentation requires multiple labeled structures. Existing SAM-based approaches either require external prompts [33, 35, 47] or disrupt SAM's zero-shot capability, limiting them to one-class datasets [16, 46]. + +![](images/0a2f7268b44b33443a998d313ea94c2504f4ec323732c966eb64eac1d6a251d5.jpg) +Figure 2. Overview of the MaskSAM architecture. + +2) Dependence on user-provided prompts. SAM requires precise prompts, posing challenges for automated segmentation. Some methods generate prompts from ground truth (GT) [12, 17, 53], but since medical challenges do not provide GT prompts, these models cannot be fairly evaluated. To ensure fair comparison, we fine-tune our model using GT-generated prompts, achieving $94.70\%$ Dice on Synapse and $94.30\%$ on ACDC, surpassing nnUNet by $8.5\%$ and $2.7\%$ . +3) Suboptimal performance. Even with appropriate prompts, SAM does not consistently perform well in medical segmentation. Some adaptations [6, 52] integrate prompt generation and semantic labels but still underperform. The challenge lies in effectively adapting SAM from natural to medical image segmentation, leading to limited participation in medical segmentation challenges. + +To address these limitations, we propose MaskSAM, a SAM-based framework for medical image segmentation. MaskSAM eliminates manual prompts through a prompt-free architecture. By leveraging SAM's Vision Transformer (ViT) [15], pre-trained with masked autoencoders [21], our approach extracts robust feature representations. We introduce a prompt generator that utilizes multi-level feature maps from the image encoder to generate auxiliary binary masks and bounding boxes as prompts, removing external input requirements. + +For semantic label prediction, the prompt generator produces auxiliary classifier tokens. Since SAM's mask decoder lacks class prediction functionality, we incorporate global learnable classifier tokens, inspired by Mask-Former [10], to assign class labels to predicted masks. + +We design a dataset mapping pipeline (Figure 2) that converts multi-class masks into binary masks with semantic labels, accommodating variable numbers of binary masks. Inspired by DETR [8] and MaskFormer [10], the prompt generator produces more prompts than the maximum number of class-level binary masks in the dataset. Predictions are matched to ground truth using bipartite matching. + +SAM does not consistently perform well in medical segmentation, even with appropriate prompts. Studies [13, 22, 24, 37, 45, 48, 55] highlight its challenges with weak boundaries, low contrast, and irregular shapes. These findings align with broader assessments [27, 28], reinforcing the need for fine-tuning. + +Fine-tuning SAM is computationally expensive. Efficient fine-tuning strategies [17, 32, 34, 50] demonstrate that lightweight adapters [23] can effectively adapt SAM while minimizing computational costs. Unlike prior approaches that discard SAM's prompt encoder or mask decoder, we retain the full architecture. Removing these components would disrupt SAM's structure and compromise its pre-trained capabilities. Instead, we leverage SAM's zero-shot properties by freezing its weights and inserting adapter modules for efficient adaptation. + +Medical images, unlike standard 2D natural images, often contain volumetric data (e.g., MRI, CT) with an additional depth dimension. To effectively process this information, we introduce learnable layers that extract depth features within lightweight adapters. + +In SAM, both the image encoder and mask decoder use transformer blocks, where we insert adapters. The mask decoder contains attention mechanisms for prompt and image embeddings. Conventional adapters process only the last dimension (channels), limiting spatial learning. Since image embeddings encode spatial structure, we design a 3D depth-convolution adapter (DConvAdapter) that integrates a depth-wise convolution layer within the adapter, with a skip connection for attention blocks processing image embeddings. For prompt embeddings, which lack spatial relationships, we introduce a 3D depth-MLP adapter (DMLPAdapter), following an inverted bottleneck structure with fully connected layers and an activation layer to process depth information. + +These adapter designs are illustrated in Figure 4. Since the image encoder consists only of attention blocks for image embeddings, we insert a DConvAdapter into each trans + +![](images/afc772058651ce2c4a83243ff2f75092e8412c07aa87330816c480fed0a43238.jpg) +Figure 3. Overview of (a) redesigned image encoder, (b) proposed prompt generator, and (c) redesigned mask decoder. Blue and white boxes are frozen; the rest are fine-tuned. + +![](images/4cd932bb56f8ecb32f66906da83138c70036872f68d59a1060a0ca6bb4856676.jpg) + +![](images/03c477801ad6f992d90f36da3d37a8ca1c5cf9ae7d33869348e498947b26daea.jpg) + +![](images/d5c5f02ac76bc932c16b634e50b8baf5d3145a3a2dd2f17b4151bb5acc99e4f2.jpg) +Figure 4. The proposed adapters. + +former block, enabling effective adaptation of 2D SAM models to 3D medical segmentation. + +In summary, our contributions are as follows: + +- We propose MaskSAM, a mask classification prompt-free SAM framework that retains SAM's full structure and pre-trained weights while adapting it for medical image segmentation; +- We introduce a prompt generator that utilizes multi-level feature maps from the image encoder to generate auxiliary masks and bounding boxes as prompts, eliminating the need for external inputs. Additionally, the prompt generator produces auxiliary classifier tokens, which are summed with learnable global classifier tokens in the mask decoder to enable semantic label prediction for each binary mask; +- We design a 3D depth-convolution adapter (DConvAdapter) for image embeddings and a 3D depth-MLP adapter (DMLPAdapter) for prompt embeddings. These adapters are inserted into each transformer block in the image encoder and mask decoder, allowing pre-trained 2D SAM models to capture 3D spatial information and adapt to medical image segmentation; +- We conduct experiments on three medical segmentation datasets—AMOS2022 [29], ACDC [3], and + +Synapse [31]—showing that MaskSAM achieves state-of-the-art performance, surpassing nnUNet by $2.7\%$ , $1.8\%$ , and $1.0\%$ on AMOS2022, ACDC, and Synapse, respectively. + +# 2. Related Works + +Deep Learning Methods for Medical Image Segmentation. Deep learning has become the dominant approach in medical image segmentation. The main categories of methods include convolution-based models [11, 26, 36, 44, 56], transformer-based models [54], and hybrid models [7, 9] that combine convolutional and transformer architectures. Encoder-decoder networks, particularly U-shaped networks, have been widely adopted. These architectures are explicitly designed for medical image segmentation and are typically trained from scratch. However, they often exhibit a strong inductive bias, which can limit their adaptability and generalization. + +Foundation Models and Parameter-efficient Finetuning. Foundation models [4, 38] are large-scale, general-purpose models trained on diverse datasets and have demonstrated strong performance across a range of applications. These models follow a pre-training and fine-tuning paradigm [20, 25], allowing them to generalize well to various tasks. Parameter-efficient finetuning [23, 25, 40, 51] reduces the number of trainable parameters and computational cost while maintaining or exceeding the performance of full finetuning. Recently, the Segment Anything Model (SAM) [30], trained on 1 billion masks from 11 million natural images, has been introduced as a foundation model for image segmentation. In this work, we adopt parameter-efficient finetuning strategies to adapt SAM from 2D natural image segmentation to 3D medical image segmentation. + +SAM-based Medical Image Segmentation. Research on SAM-based medical image segmentation falls into two main categories. The first category [13, 22, 24, 37, 45, 48, 55] evaluates SAM's performance across different medical imaging tasks using manually provided prompts. These + +![](images/2ac56a88a8b1af4ff7ca9a5f84983e677560f4a14e855e5bbfabba26064307f1.jpg) +Figure 5. (a) A prompt generator with learnable masks. (b) A prompt generator with learnable boxes. (c) A prompt generator with learnable masks and learnable boxes. (d) A prompt generator with learnable masks and averaged boxes. + +![](images/ef0ab01bdd59ec2e8be61918e21f07ed0b624dd054deb24ae22582f3ca327f55.jpg) + +![](images/efe23f9a3ef377a4485d848184fb405986cd0b86a06b5c0322cace496c8a3c12.jpg) + +![](images/7c71a7d915eb92cdfd920a7c5d7c1e144039ae1850fc2e600a7aee57c2710e32.jpg) + +studies highlight variations in SAM's performance across datasets, showing strong results for specific objects and modalities but struggling in cases with weak boundaries, low contrast, or irregular shapes, leading to suboptimal segmentation performance. The second category [17, 32, 34, 50] explores ways to adapt SAM more effectively to medical image segmentation. One of the primary challenges is the need for prompts. Some studies attempt to bypass this requirement by modifying or removing the prompt encoder or mask decoder, but this can compromise SAM's consistency and effectiveness. To address this, we propose a prompt-free adaptation of SAM that generates auxiliary masks and bounding boxes directly from the image encoder using a designed prompt generator. This approach leverages SAM's zero-shot capabilities while eliminating the need for manually provided prompts, providing a more comprehensive and efficient solution. + +# 3. The Proposed Approach + +SAM is a prompt-driven foundation model for natural image segmentation, trained on the large-scale SA-1B dataset consisting of 1 billion masks and 11 million images. The architecture of SAM comprises three main components: an image encoder based on a Vision Transformer backbone, a prompt encoder that processes various types of prompts such as points, boxes, and texts, and a lightweight mask decoder that generates masks using image embeddings, prompt embeddings, image positional embeddings, and output tokens. To segment a 2D image, SAM requires prompts such as points or boxes and produces a binary mask for each prompt. However, it does not associate semantic labels with the generated masks, making it unsuitable for medical image segmentation tasks where multiple objects with distinct semantic labels may be present within a single image. + +MaskSAM retains the structure of SAM while incorporating modifications to adapt it from 2D natural images to 3D medical images. It introduces additional components while keeping the original SAM architecture intact. + +MaskSAM includes a modified image encoder, a designed prompt generator, the original prompt encoder, and a modified mask decoder. Additionally, a dataset mapping mechanism is introduced to convert multi-class labels into binary masks for each class with corresponding semantic labels, ensuring that each predicted binary mask corresponds to a single class. + +# 3.1. Proposed Dataset Mapping + +SAM generates a single binary mask without an associated semantic label for each prompt, whereas the ground truth for medical images typically consists of multiple classes. Each cropped patch input may contain different classes, presenting the challenge of handling binary masks of varying lengths in the ground truth. To address this, inspired by DETR [8] and MaskFormer [10], our model generates a sufficiently large number of binary masks, each dedicated to predicting a single class. Bipartite matching is then used to align predicted masks with ground truth segments. To facilitate this process, we design a dataset mapping pipeline, shown at the bottom of Figure 2, that converts a multi-class mask into a set of binary masks, each associated with a semantic label. + +# 3.2. Proposed Prompt Generator + +To address the need for additional prompts, we propose a prompt generator, shown in Figure 3(b), which generates a set of auxiliary binary masks and bounding boxes as prompts instead of relying on manual input. We adopt a combination of box and mask prompts, as point prompts can introduce instabilities detrimental to medical segmentation tasks. Leveraging ViT's strong representation capabilities, we extract multi-level feature maps from the image encoder as input to the prompt generator. The feature maps from the final output of the image encoder are processed through convolutional layers, upsampled, and concatenated with lower-level feature maps. This approach produces feature maps with the same resolution as the ground truth. A final convolutional layer adjusts the channel size to a fixed + +
Semantic labelsPromptsMethodSpl.R.KdL.KdGBEso.LiverStom.AortaIVCPanc.RAGLAGDuo.Blad.Pros.DSC
✓-TransBTS [49]0.8850.9310.9160.8170.7440.9690.8370.9140.8550.7240.6300.5660.7040.7410.6500.792
UNETR [19]0.9260.9360.9180.7850.7020.9690.7880.8930.8280.7320.7170.5540.6580.6830.7220.762
nnFormer [54]0.9350.9040.8870.8360.7120.9640.7980.9010.8210.7340.6650.5870.6410.7440.7140.790
SwinUNETR [18]0.9590.9600.9490.8940.8270.9790.8990.9440.8990.8280.7910.7450.8170.8750.8410.880
nn-UNet [26]0.9650.9590.9510.8890.8200.9800.8900.9480.9010.8210.7850.7390.8060.8690.8390.878
XnnUNetSAM [30] bbox0.6790.7410.6400.1680.4430.7730.6710.6510.5540.4340.2320.3240.4440.6980.6020.538
XnnUNetSAM 2 [42] bbox0.7840.8170.8190.6640.7340.7800.6970.7930.7390.5360.4570.6040.5630.7440.6910.695
XnnUNetMedSAM [35] bbox0.7140.8110.7020.1930.4690.7590.7250.7010.6810.4340.3650.4120.4620.7830.7580.600
✓No needsSAMed [52]0.8490.8570.8300.5730.7330.8940.8160.8550.7840.7270.6220.6830.7010.8440.8190.772
✓No needsSAM3D [6]0.7960.8630.8710.4280.7110.9080.8330.8780.7490.6990.5640.6070.6350.8840.8400.751
✓No needsMaskSAM (Ours)0.9630.9730.9690.8720.8760.9820.9400.9620.9220.8880.7940.8130.8510.9200.8540.905
+ +Table 1. Comparison of MaskSAM with state-of-the-art methods on the AMOS testing dataset, evaluated using the Dice Score. For a fair comparison, all results are obtained through 5-fold cross-validation without any ensembles. "Semantic labels" denote the model's capability to assign semantic labels, while "Prompt" indicates the source of the prompt. The best results are shown in bold. + +number $N$ , which is set larger than the maximum number of object-level binary masks in the dataset. + +Simultaneously, the last convolutional layer outputs features at each level, which are processed through adaptive average pooling layers to adjust the spatial dimension to (2,2) for box queries. The box queries are concatenated and passed through an MLP layer to match the $N$ channel dimension, resulting in $N$ learnable binary masks and bounding boxes. + +Different configurations of learnable binary masks and bounding boxes are illustrated in Figure 5(a)-(d). In Figure 5(a), the prompt generator produces only learnable binary masks, with bounding boxes computed from them. Figure 5(b) depicts a generator that produces only box prompts. Figure 5(c) generates both learnable binary masks and bounding boxes as prompts. Figure 5(d) produces learnable binary masks and combines bounding boxes computed from masks with learnable bounding boxes by averaging them to form the final box prompts. Empirical results indicate that the configuration in Figure 5(d) achieves the best performance by incorporating more information and improving robustness. + +To enable semantic label prediction, the prompt generator also produces a set of auxiliary classifier tokens, following a similar process as for auxiliary box prompts, except that adaptive average pooling layers adjust the spatial dimension to $(1,1)$ for classifier tokens. These auxiliary classifier tokens are summed with learnable global classifier tokens within the mask decoder. + +# 3.3. Proposed Adapters + +We adopt the lightweight adapter [23], a bottleneck architecture composed of two fully connected layers with an activation layer in between, which is inserted into each transformer block for fine-tuning. Unlike 2D natural images, medical scans such as MRI and CT volumes include an additional depth dimension. To capture depth information, we introduce learnable layers for the extra dimension within the adapters. + +In SAM, both the image encoder and mask decoder contain transformer blocks where adapters can be inserted. The mask decoder includes two types of attention blocks, one for prompt embeddings and another for image embeddings. Standard adapters only process the last dimension (the channel dimension), limiting their ability to capture relationships between tokens. However, since image embeddings contain spatial information crucial for understanding spatial relationships, we design a 3D depth-convolution adapter (DConvAdapter), shown in Figure 4(b). This adapter incorporates a 3D depth-wise convolution layer in the middle of the original adapter, with a skip connection, to enhance processing within attention blocks handling image embeddings in the mask decoder. + +For attention blocks processing prompt embeddings, spatial relationships are not relevant. Thus, we design a 3D depth-MLP adapter (DMLPADapter), shown in Figure 4(a), which employs an inverted bottleneck architecture with two fully connected layers and an activation layer applied along the depth dimension. This allows the model to capture additional depth information. Since the image encoder contains only attention blocks for image embeddings, we insert a DConvAdapter into each transformer block of the image encoder. + +Figure 4(c) illustrates how adapters are integrated into vision transformers. Each transformer block is modified by inserting an adapter after the multi-head attention block and in parallel with the MLP block. + +# 3.4. Modified Image Encoder + +Figure 3(a) illustrates the modified image encoder. i) SAM is designed for natural images with three RGB channels, whereas medical images have varied modalities as input channels. The differences between these modalities and RGB channels introduce a domain gap. To address this, we introduce a sequence of convolutional layers with an inverted bottleneck architecture to adapt medical image modalities to a standardized three-channel input. ii) The image encoder includes positional embeddings. To incorpo + +![](images/ee4a8075828261fcb9bc90d817273657159f97f399de1dd371e1c179e82aacc3.jpg) +Figure 6. Qualitative comparison on the Synapse dataset. MaskSAM provides the most precise segmentation for each class. + +rate depth information, we add a learnable depth positional embedding alongside the original positional embedding. iii) The base ViT backbone in SAM consists of 12 attention blocks. We insert the proposed DConvAdapter into each attention block and extract feature maps from every three attention blocks, as well as the final output of the image encoder, to be used by the prompt generator. + +# 3.5. Modified Mask Decoder + +Figure 3(c) illustrates the modified mask decoder. i) We introduce learnable global classifier tokens, which are summed with auxiliary classifier tokens generated by the prompt generator. These are concatenated with sparse prompt embeddings and the original mask tokens, enabling the model to predict semantic labels for each binary mask. ii) The mask decoder also includes positional embeddings. To improve depth-awareness, we incorporate a learnable depth positional embedding alongside the original image positional embedding. iii) The mask decoder consists of two sequential transformer blocks. Each block first applies self-attention to prompt embeddings, where we insert a DMLPAdapter after self-attention. Then, a cross-attention block allows tokens to attend to image embeddings, where we insert a DMLPAdapter after the cross-attention. Next, we insert a DMLPAdapter in parallel with an MLP block. Finally, the last cross-attention block enables image embeddings to attend to tokens, where we insert a DConvAdapter after the cross-attention. This approach allows the model to learn spatial relationships while incorporating depth information for image embeddings and enhancing depth-awareness for prompt embeddings. + +# 3.6. Losses and Matching + +Following [8, 10], we define an auxiliary loss consisting of a combination of binary cross-entropy and Dice loss for auxiliary binary mask predictions $(\mathcal{L}_{mask}^{\mathrm{aux}})$ , along with an $L_{1}$ + +
Sem. Lab.PromptsMethodAortaGBL.KdR.KdLiv.Panc.Spl.Stom.DSC
✓-TransUNet [9]87.2363.1681.8777.0294.0855.8685.0875.6277.48
SwinUNet [7]85.4766.5383.2879.6194.2956.5890.6676.679.13
UNETR [19]89.9960.5685.6684.8094.4659.2587.8173.9979.56
nnUNet [26]92.3971.7186.0791.4695.8482.9290.3179.0186.21
nnFormer [54]92.4070.1786.5786.2596.8483.3590.5186.8386.57
XGTSAM [30] bbox60.0524.9068.8754.2276.9145.3669.2067.9358.43
XGTMedSAM [35] bbox70.1622.4479.0864.6376.3852.3173.0779.1064.65
XGTMaskSAM (Ours) bbox96.2293.3194.7594.2597.6989.1396.6895.5894.70
✓No needSAMed [52]87.7769.1180.4579.9594.8072.1788.7282.0681.88
✓No needSAMed_s [52]83.6257.1179.6378.9293.9865.6685.8177.4977.78
✓No needSAM3D [6]89.5749.8186.3185.6495.4269.3284.2976.1179.56
✓No needMaskSAM (Ours)93.3271.7587.2887.3097.0780.9992.0688.6087.30
+ +Table 2. Comparisons with SOTA methods on Synapse. + +loss and generalized IoU loss [43] for bounding box predictions $(\mathcal{L}_{box})$ . Additionally, a main loss is defined for the final MaskSAM output, which includes a standard classification cross-entropy loss and a combination of binary cross-entropy and Dice loss for the final binary mask predictions $(\mathcal{L}_{mask}^{\mathrm{final}})$ . + +To find the optimal assignment, we employ bipartite matching [8, 10] between the ground truth segments and the combination of auxiliary and final predictions. The model selects the corresponding indices from the $N$ auxiliary binary masks and $N$ final binary masks using bipartite matching and uses these indices to compute losses with the ground truth. + +Specifically, the desired final output is represented as $z = \{(p_i, m_i)\}_{i=1}^N$ , where $N$ pairs of binary masks $\{m_i^{\mathrm{final}} | m_i^{\mathrm{final}} \in [0,1]^{H \times W}\}_{i=1}^N$ are associated with class probability distributions $p_i \in \Delta^{K+1}$ . The distribution includes $K$ category labels and an auxiliary "no object" label $(\varnothing)$ . Similarly, the model produces $N$ auxiliary boxes and masks, denoted as $z_{\mathrm{aux}} = \{(b_i^{\mathrm{aux}}, m_i^{\mathrm{aux}}) | b_i^{\mathrm{aux}} \in [0,1]^4, m_i^{\mathrm{aux}} \in \{0,1\}^{H \times W}\}_{i=1}^N$ . The set of $N^{gt}$ ground truth segments is represented as $z^{gt} = \{(c_i^{gt}, b_i^{gt}, m_i^{gt}) | c_i^{gt} \in \{1, ..., K\}, b_i^{gt} \in [0,1]^4, m_i^{gt} \in \{0,1\}^{H \times W}\}_{i=1}^{N^{gt}}$ . Since we set $N \geq N^{gt}$ , the ground truth set is padded with "no object" tokens $(\varnothing)$ to enable one-to-one matching. + +To train the model parameters, given a matching $\sigma$ , the + +![](images/444541b3c48a612c094a09424c6c24aa1bd0b9c6355cc482c93fcec2324f19ed.jpg) +Figure 7. Qualitative comparison on the ACDC dataset. MaskSAM provides the most precise segmentation for each class and reduces segmentation outliers. + +main loss $\mathcal{L}_{\mathrm{mask - box -cls}}$ is formulated as: + +$$ +\begin{array}{l} \sum_ {j = 1} ^ {N} \left[ - \log p _ {\sigma (j)} \left(c _ {j} ^ {g t}\right) + \mathbb {1} _ {c _ {j} ^ {g t} \neq \emptyset} \mathcal {L} _ {m a s k} ^ {\text {a u x}} \left(m _ {\sigma (j)} ^ {\text {a u x}}, m _ {j} ^ {g t}\right) \right. \\ + \mathbb {1} _ {c _ {j} ^ {g t} \neq \emptyset} \mathcal {L} _ {\text {b o x}} \left(b _ {\sigma (j)}, b _ {j} ^ {g t}\right) + \mathbb {1} _ {c _ {j} ^ {g t} \neq \emptyset} \mathcal {L} _ {\text {m a s k}} ^ {\text {f i n a l}} \left(m _ {\sigma (j)} ^ {\text {f i n a l}}, m _ {j} ^ {g t}\right) ]. \tag {1} \\ \end{array} +$$ + +# 4. Experimental Evaluation + +# 4.1. Datasets and Evaluation Metrics. + +We use three publicly available datasets: AMOS22 Abdominal CT Organ Segmentation [29], Synapse Multiorgan Segmentation [31], and the Automatic Cardiac Diagnosis Challenge (ACDC) [3]. (i) The AMOS22 dataset consists of 200 abdominal CT cases with 16 manually annotated anatomical structures for multi-organ segmentation. There are 200 testing images, and we evaluate our model using the AMOS22 leaderboard. (ii) The Synapse dataset contains 30 abdominal CT cases. Following the split strategy from [9], we randomly split the dataset into 18 training cases and 12 validation cases. Model performance is evaluated using the average Dice score (DSC) across 8 abdominal organs. (iii) The ACDC dataset consists of 100 patient cases with labels for the right ventricle (RV), myocardium (MYO), and left ventricle (LV). We randomly split the dataset into 70 training cases, 10 validation cases, and 20 testing cases, evaluating performance using the average DSC. + +In Tab. 1, 2, and 3, "Semantic labels" indicate whether the model can predict semantic labels, while "Prompt" specifies the source of the prompts. Since SAM and MedSAM do not inherently predict semantic labels and require additional prompts, we use ground truth (GT) or inferred predictions from a pre-trained nnUNet to generate prompts, assigning semantic labels based on the same predictions. + +# 4.2. Results on the AMOS 2022 Dataset. + +We present the quantitative results of our experiments on the AMOS 2022 dataset in Tab. 1, comparing MaskSAM with + +
Semantic labelsPromptsMethodRV ↑Myo ↑LV ↑DSC ↑
✓UNETR [19]85.2986.5294.0288.61
TransUNet [9]88.8684.5495.7389.71
-SwinUNet [7]88.5585.6295.8390.00
nnUNet [26]90.2489.2495.3691.61
nnFormer [54]90.9489.5895.6592.06
XGTSAM [30]bbox70.9533.3381.3162.53
XGTMedSAM [35]bbox85.8680.3192.3386.17
XGTMaskSAMbbox94.2791.6996.9294.30
✓No needsSAM3D [6]89.4487.1294.6790.41
✓No needsMaskSAM (Ours)92.6491.2096.4093.41
+ +Table 3. The comparison of MaskSAM with SOTA methods on ACDC dataset (DSC in %). The best are in bold. + +widely used segmentation methods, including convolution-based approaches (nnUNet [26]), transformer-based methods (UNETR [19], SwinUNETR [18], and nnFormer [54]), and SAM-based approaches (SAM [30], MedSAM [35], SAMed [52], and SAM3D [6]). To ensure a fair comparison, all methods are evaluated using 5-fold cross-validation without any ensemble techniques. + +MaskSAM outperforms existing methods on most organs, achieving state-of-the-art DSC performance. Additionally, models using point-based prompts show lower performance compared to those using bounding box prompts. When using bounding box prompts generated from nnUNet predictions, SAM and MedSAM experience accuracy drops of $34\%$ and $27\%$ , respectively, compared to nnUNet's baseline accuracy of $87.8\%$ . These reductions indicate the impact of prompt dependency on segmentation performance. Specifically, MaskSAM surpasses nnUNet and Swi-nUNETR by $2.7\%$ and $2.5\%$ in DSC, respectively. Furthermore, MaskSAM outperforms SAMed and SAM3D by $13\%$ and $15\%$ in DSC, respectively. On the challenging AMOS 2022 dataset, MaskSAM achieves state-of-the-art performance, demonstrating the effectiveness of the proposed method. + +# 4.3. Results on ACDC Dataset. + +In Tab. 3, we present the quantitative experimental results on the ACDC dataset. We compare MaskSAM with several leading approaches, including SAM-based methods (i.e., SAM3D [5]), convolution-based methods (i.e., nnUNet [26]), and transformer-based methods (i.e., UN-ETR [19] and nnFormer [54]). The results demonstrate that MaskSAM outperforms state-of-the-art methods, surpassing nnFormer by $1.3\%$ , $1.7\%$ , $1.6\%$ , and $0.8\%$ in DSC, RV dice, Myo dice, and LV dice, respectively. Furthermore, MaskSAM outperforms SAM-based methods, including SAM (1bbox), MedSAM (1bbox), and SAM3D, by $31\%$ , $7\%$ , $6\%$ , and $3\%$ , respectively, highlighting the effectiveness of our approach. + +In Fig. 7, we provide qualitative comparisons with state-of-the-art methods. The visual results further demonstrate the model's accuracy across all labels, achieving near-perfect predictions in this challenging and highly satu + +rated dataset. These findings validate the effectiveness of MaskSAM, showing that our proposed modules successfully address the limitations of SAM in medical image segmentation. + +# 4.4. Results on Synapse Dataset. + +We present the quantitative results on the Synapse dataset in Tab. 2, comparing MaskSAM with leading SAM-based methods (i.e., SAMed [52] and SAM3D [5]), convolution-based methods (VNet [44] and nnUNet [26]), and transformer-based methods (TransUNet [9], SwinUNet [7], and nnFormer [54]). MaskSAM achieves state-of-the-art performance, surpassing nnFormer by $0.7\%$ in DSC. Additionally, our method outperforms SAM-based models, including SAM (1bbox), MedSAM (1bbox), SAMed, and SAM3D, by $29\%$ , $23\%$ , $6\%$ , and $8\%$ , respectively, further demonstrating its effectiveness. + +Notably, our model excels in predicting large anatomical structures such as the 'Liver,' 'Spleen,' and 'Stomach,' which can be attributed to the integration of our DConvAdapter and DMLPAdapter. These adapters enhance the ability to capture complex 3D spatial information, allowing the adaptation of 2D SAM models for medical image segmentation. In Fig. 6, we present qualitative comparisons with representative methods, further illustrating that MaskSAM produces more accurate predictions for the 'Liver,' 'Spleen,' and 'Stomach' labels. The robustness of our method is clearly demonstrated through both quantitative and qualitative results. + +# 4.5. Ablation Study + +MaskSAM has nine baseline models (i.e., B1-B9) as shown in Tab. 4. All baselines retain the full SAM architecture, a prompt generator, and a learnable class token. (i) B1 employs a prompt generator that produces only learnable binary masks, using them as mask prompts to compute bounding boxes, as shown in Fig. 5(a). (ii) B2 uses a prompt generator that generates only learnable bounding boxes, as shown in Fig. 5(b). (iii) B3 generates both learnable binary masks as mask prompts and learnable bounding boxes as box prompts, as shown in Fig. 5(c). (iv) B4 enhances B3 by averaging bounding boxes computed from binary masks with learnable bounding boxes to form the final box prompts, as shown in Fig. 5(d). (v) B5 builds on B4 by incorporating depth positional embedding (DPosEmbed) in the image encoder and mask decoder. (vi) B6 modifies the vanilla adapter by inserting an invert-bottleneck depth MLP with a skip connection after the fully connected layers for upsampling, based on B5. (vii) B7 modifies the vanilla adapter by inserting the invert-bottleneck depth MLP before the fully connected layers for downsampling, based on B5. (viii) B8 replaces the vanilla adapter with the proposed DMLPAdapter, based on B5. (ix) B9, the full model, + +
MethodDSC ↑
B1SAM + MaskPG + vAdapter89.53
B2SAM + BBoxPG + vAdapter88.78
B3SAM + MaskBBoxPG + vAdapter90.08
B4SAM + MaskAvgBBoxPG + vAdapter91.45
B5SAM + MaskAvgBBoxPG + vAdapter + DPosEmbed91.61
B6SAM + MaskAvgBBoxPG + vAdapter w/ D-MLP after FC-Up + DPosEmbed92.88
B7SAM + MaskAvgBBoxPG + vAdapter w/ D-MLP before FC-Down + DPosEmbed92.93
B8SAM + MaskAvgBBoxPG + DMLPAdapter + DPosEmbed93.10
B9Our Full Model (B8 + DConvAdapter)93.41
+ +Table 4. Ablation study on ACDC. $\{^{*}\} \mathrm{PG}$ indicates different prompt generators. vAdapter refers to the vanilla adapter. D-MLP represents MLP layers on the depth dimension. DPosEmbed denotes depth positional embedding. + +MaskSAM, employs the DMLPAdapter for prompt embeddings and the DConvAdapter for image embeddings, based on B8, as illustrated in Fig. 2. + +The ablation study results in Tab. 4 highlight the impact of each proposed component. Using MaskAvgBBoxPG to generate auxiliary binary masks and auxiliary boxes, followed by averaging the bounding boxes computed from binary masks and learnable auxiliary boxes, improves performance. This approach outperforms B1, B2, and B3 by $1.9\%$ , $2.6\%$ , and $1.3\%$ , respectively, confirming the effectiveness of the prompt generator. + +Inserting depth positional embedding (DPosEmbed) into the image encoder and mask decoder improves B5's performance by $0.15\%$ over B4, demonstrating its effectiveness. The DMLPAdapter (B8), which incorporates depth MLPs with a skip connection in the middle of the vanilla adapter, further enhances performance, surpassing B6 and B7 by $0.2\%$ and $0.1\%$ , respectively. The full model, MaskSAM (B9), replaces the depth MLP in the DMLPAdapter with a 3D depth-wise convolution layer (DConvAdapter) for image embeddings, improving performance by $0.3\%$ over B8. These results confirm the effectiveness of MaskSAM. + +# 4.6. Model Analysis + +Fig. 1 illustrates the generated box prompts. For complex objects and images containing a few objects, the model generates multiple prompts to assist in mask prediction, as object queries outnumber objects in 2D images. Additionally, generated bounding boxes tend to be slightly larger than the objects themselves, helping to account for adjacent structures. This approach results in precise and meaningful auxiliary box prompts. + +# 5. Conclusion + +We propose MaskSAM, a mask classification prompt-free adaptation framework for medical image segmentation based on SAM. By integrating a prompt generator with SAM's image encoder, our method produces auxiliary classifier tokens, binary masks, and bounding boxes, removing the need for external prompts and enabling semantic label prediction. We design 3D depth-convolution and 3D depth-MLP adapters to efficiently adapt 2D SAM to 3D images. + +# References + +[1] Zeynettin Akkus, Alfia Galimzianova, Assaf Hoogi, Daniel L Rubin, and Bradley J Erickson. Deep learning for brain mri segmentation: state of the art and future directions. Journal of digital imaging, 30(4):449-459, 2017. 1 +[2] MR Avendi, Arash Kheradvar, and Hamid Jafarkhani. A combined deep-learning and deformable-model approach to fully automatic segmentation of the left ventricle in cardiac mri. 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However, the rapid expansion of visual instruction datasets introduces data redundancy, leading to excessive computational costs. We propose a collaborative framework, DataTailor, which leverages three key principles—informativeness, uniqueness, and representativeness—for effective data selection. We argue that a valuable sample should be informative of the task, non-redundant, and represent the sample distribution (i.e., not an outlier). We further propose practical ways to score against each principle, which automatically adapts to a given dataset without tedious hyperparameter tuning. Comprehensive experiments on various benchmarks demonstrate that DataTailor achieves $101.3\%$ of the performance of full-data fine-tuning with only $15\%$ of the data, significantly reducing computational costs while maintaining superior results. This exemplifies the "Less is More" philosophy in MLLM development. The code and data is available in this URL. + +# 1. Introduction + +The rapid development of Multi-modal Large Language Models (MLLMs) has made promising progress on various multi-modal tasks [2, 55, 61]. A typical MLLM is developed through two main training stages: pre-training on vast image-text pairs and fine-tuning on task-specific multimodal instructions. Notably, the fine-tuning stage is critical for enhancing the instruction-following capabilities of MLLMs. Yet, this stage can become exceedingly time-consuming due to the large-scale but low-quality instruction data. Hence, the community is interested in fine-tuning data + +![](images/5f5f7013056115503443257ccd97716c170efc3cdc25c4ea22a7eb7ea291964a.jpg) +(a) Performance v.s. Selected Data Ratio on LLaVA-mix-665k + +![](images/2d8c8e3ae8790ca233d64382f96d034d3b3b70ddc898235ed202895890d6ab1c.jpg) +(b) Metric triangle among informativeness, uniqueness, and representativeness +Figure 1. (a) The Performance v.s. Selected Data Ratio on LLaVA-mix-665k of DataTailor compared with SOTA data selection methods. (b) Metric triangle among informativeness, uniqueness, and representativeness when applying IFD [28] (data-specific methods), InsTag [36] (human-reward methods), LESS [51] (gradient-based methods), and DataTailor. (c) The corresponding MLLM performance on LLaVA-mix-665k [33] of different methods. + +![](images/0b06dba929762b05c10cf973f6d0c257918db3c84aef39bd834a18ba2443b7b3.jpg) +(c) MLLM relative performance of DataTailer compared with other data selection methods + +selection methods, such that an MLLM trained on the selected subset yields comparable or even better performance. + +Existing MLLM data selection methods [9, 19, 35, 49] largely follow similar ideas from the NLP community [28, 36, 45, 51, 60]. They can be divided into three main categories: (1) Data-specific methods [6, 10, 28] leverage vast hand-designed rules to select data in specific datasets, which are not flexible and robust for diverse tasks. (2) Human-reward methods [36, 60] utilize human feedback to select data, which are both time-consuming and expensive. (3) Gradient-based methods [31, 45, 51] select sam + +![](images/7901a4d4265389cce3216df24b327cb60b51e06af39388fc9220939b29003aed.jpg) +Figure 2. Illustration of the proposed method based on informativeness, uniqueness, and representativeness, where the x and y axes show information dimensions in latent space. The red star denotes a high-quality sample that satisfies the three principles. + +plies whose gradients are similar to the average training gradient of the dataset. However, they require additional training on downstream tasks, making total computation costly. + +To address these deficiencies, we build a systematic data selection method for MLLM called DataTailor. We evaluate each sample with three principles and select the most valuable samples, leading to state-of-the-art MLLM performance with a fraction of data (c.f. Fig. 1). The three principles are: (1) Informativeness: a valuable sample should be informative of the hard task, e.g., If the task is reasoning, describing the movement differences between skiing and ice skating is more informative and complex than simply describing someone skiing. In Fig. 2 where each axis (heuristically) represents an orthogonal dimension of task information, points along the diagonal carry more information about the task. (2) Uniqueness: A valuable sample should be distinct from others, offering unique insights rather than prevalent commonsense knowledge (c.f. Fig. 2 near the blue dashed region in the intra-cluster space demonstrates high uniqueness). (3) Representativeness: it should be a typical sample in the data distribution. This prevents selecting noisy outliers or mislabeled samples (c.f. Fig. 2 the clusters connected by blue lines in the inter-cluster space exhibit high representativeness for the overall dataset). + +We further propose a practical method to measure the value of each sample against each principle. For informativeness, we take motivations from information theory [7, 8]. For each sample, we analyze the singular value distribution of its features and use the entropy of the singular values to determine if it is informative of the task. To compute uniqueness and representativeness, we first cluster the samples based on their visual and textual features. This allows efficient calculation for uniqueness, as we can simply measure the average distances of a sample to its neighbors in the same cluster, and mark those with a large dis + +tance as unique. Then we find connected clusters and mark samples in those clusters as representative. Hence, noisy or mislabeled data from a far-away cluster can be filtered. + +Moreover, as multi-modal samples exhibit varying structures and complexities across diverse tasks, we propose an adaptive weight to combine the values, which removes the need for expensive hyper-parameter tuning. We also adaptively determine the proportion of selected data for each task by using the average largest singular value of samples in the task, which empirically reflects task difficulty and correlates with training robustness. Combining these techniques, DataTailor synergizes the three principles for data selection and achieves an optimal balance between data volume and model performance (as shown Fig. 1(a) red line). + +To our knowledge, we are the first to explore sample relationships between multi-modal instructions systematically. Through extensive experiments, we demonstrate that DataTailor exhibits significant effectiveness in data selection for MLLMs (with less than $5\%$ data but achieving over $95\%$ performance). This effectiveness is further demonstrated through quantitative metrics designed for the three principles (c.f. Fig. 1(b)), proving that DataTailor improves data selection by addressing the essential aspects of each principle (detailed analyses is in Sec. 4.4 and Appendix D.1 & D.2). In contrast, other methods lack a systematic evaluation, particularly of sample relationships, leading to weaknesses in uniqueness and representativeness and resulting in suboptimal MLLM performance (c.f. Fig. 1(c)). Remarkably, when DataTailor increases the data selection ratio, multi-modal data selection can even outperform full data fine-tuning (achieve $101.3\%$ performance with $15\%$ data), truly exemplifying the concept of "Less is More". Overall, our main contributions are summarized as follows: + +- We identify three key principles (i.e., informativeness, uniqueness, and representativeness) from a systematic perspective to master multi-modal data selection. +- We propose a unified framework, DataTailor, to adaptively integrate these principles for value evaluation to optimize multi-modal data selection in a collaborative way. +- Extensive results show DataTailor's effectiveness in optimizing all three principles during selection and achieving new SOTA performance on various benchmarks. + +# 2. Related Work + +# 2.1. Multi-modal Large Language Model + +With the outstanding performance of LLMs in zero-shot settings, early work combining LLMs with visual modalities has demonstrated impressive visual language comprehension abilities [9, 15, 23, 25-27, 55]. Recently, more powerful MLLMs have emerged [5, 17, 33, 38, 39, 53, 54, 57, 61], which possess perceptual abilities for visual-language tasks and excellent reasoning abilities. Generally, the training + +process of MLLMs primarily includes two stages: the pretraining stage and the instruction tuning stage. Recent studies [13, 14, 32, 42, 48, 56] have focused on the second stage to enhance instruction-following abilities. However, this stage is gradually facing inevitable computational overhead due to the growing volume of multi-modal data [35, 41]. It is critical to identify a small subset of high-quality instructions to improve MLLM fine-tuning efficiency. + +# 2.2. Instruction-based Data Selection + +Although MLLMs have demonstrated remarkable performance, data redundancy is becoming apparent with the rapid growth of visual instruction datasets, similar to challenges in LLMs [6, 11, 60]. Previous LLM-based works mainly focus on using pre-defined specific rules [6, 28], human feedback [36], or gradient-based approximation [3, 51] to select high-quality data. INSTRUCTMINING [6] uses 9 indicators to fit specific rules for data selection. In contrast, DataTailor automatically assesses values without hand-designed rules, offering greater robustness and flexibility. Moreover, these methods only focus on individual sample values while neglecting similar or noisy data when applied to more complex multi-modal instructions. For MLLM-based data selection, TIVE [35] identifies redundancy in multi-modal instructions and selects valuable data at the task and instance level through gradient similarity, while ICONS [50] extends this by integrating specialist influence estimation. However, they both require extra training on downstream tasks for data selection. SELF-FILTER [49] attaches evaluation models and updates its parameters during training to select high-value samples. InstructionGPT-4 [47] selects 200 instructions for MiniGPT4 [61], but it is unscalable for other settings. COINCIDE [22] roughly clusters data by conceptual representations, while overlooking the value differences between clusters. These methods largely follow prior approaches and overlook the complex relationships between samples, which limits their generalization. To mitigate these limitations, we are the first to adopt a collaborative perspective for multi-modal data selection, focusing on three core principles: informativeness, uniqueness, and representativeness. + +# 3. Method + +As illustrated in Figure 3, our DataTailor framework consists of four primary steps: (1) The informative value captures the information density in latent space, directly reflecting informativeness to enhance MLLM generalization. (2) The unique value identifies distinct samples within the intra-cluster space, reflecting the uniqueness of sample relationships to reduce redundancy effectively. (3) The representative value captures samples that align closely with the overall dataset distribution in the inter-cluster space, ensuring representativeness and preventing compromise by noisy + +outliers. (4) Finally, DataTailor adaptively integrates these three values to enable collaborative multi-modal data selection. Next, we will elaborate on the details of each step. + +# 3.1. Problem Formulation + +Given a visual input $X_{v}$ and a textual query $X_{q}$ , the objective of the MLLM is to predict the correct answer $X_{a}$ for downstream tasks. We formulate multi-modal data selection as selecting fewest samples $S^{*} = \{s_{1},\dots,s_{k}\}$ from the candidate dataset $S$ for MLLM training that achieves the best inference performance, where $s_i = (X_v,X_q,X_a)$ and $k$ is the total data selection proportion for $S$ . Typically, the sample value is measured by the performance perturbations to the MLLM when removing the sample [21], but this is not practical for large-scale datasets. Therefore, we propose three core principles (i.e., informativeness, uniqueness, and representativeness) that practically identify the most valuable samples to improve MLLM's performance on downstream tasks. More concrete instantiations of each principle are in Appendix D.2. Then, we introduce each principle. + +# 3.2. Informative Value Estimation in Latent Space + +Although several approaches have been proposed for multi-modal data selection [35, 47, 49, 50], they are either infeasible at scale due to computational overhead or are limited in generalizability by pre-defined evaluation rules. Previous studies [30, 34, 51] have shown that difficult samples contribute more to improving the performance of downstream tasks in MLLMs. Thus, DataTailor directly estimates samples' essential difficulty for multi-modal data selection. + +However, it is non-trivial to quantify sample difficulty for multi-modal instructions due to varying information representations in different modalities. Drawing upon previous spectral analysis [7, 8, 52], we perform singular value decomposition (SVD) on the unified feature matrix at the token level for image and text modalities to reflect the difficulty of samples, as it consists of the variations across different tokens in latent space. Formally, given a multi-modal sample $s_i$ , we obtain its unified feature matrix $\mathbf{M}_{\mathrm{i}} \in \mathbb{R}^{L_i * d}$ from the penultimate layer, where $L_{i}$ is the token length and $d$ is the feature dimension. We adopt this layer as the lower layers struggle to capture complex features, while the final layer suffers biases of pre-training datasets [34]. Besides, the penultimate layer retains earlier layer information, providing richer features. Subsequently, we perform SVD on the matrix in latent space $\mathbf{M}_{\mathrm{i}} = \mathbf{U}_{\mathrm{i}} \hat{\boldsymbol{\Sigma}}_{\mathrm{i}} \mathbf{V}_{\mathrm{i}}^{\top}$ and its corresponding diagonal singular matrix is defined as follows: + +$$ +\hat {\Sigma} _ {\mathbf {i}} = \left\{\sigma_ {1}, \dots , \sigma_ {L _ {i}} \right\} \tag {1} +$$ + +where we assume $L_{i} \leq d$ [33] and all singular values $\{\sigma_j\}_{j=1}^{L_i}$ are listed in order. Building on this, we compute the entropy of normalized singular values as the informative + +![](images/094f391f70cc31254035ef2675ad76e5db4b30d297a5224ecc997ec5b84afb5a.jpg) +Figure 3. Overview of our proposed DataTailor for automatically selecting high-quality multi-modal data through the collaboration of three principled values (i.e., informative value, unique value, and representative value) from a systematic perspective. + +value to assess the information density of each data: + +$$ +V _ {i} ^ {I n f} = - \sum_ {j = 1} ^ {L _ {i}} \frac {\sigma_ {j}}{\sum_ {k = 1} ^ {L _ {i}} \sigma_ {k}} \log \frac {\sigma_ {j}}{\sum_ {k = 1} ^ {L _ {i}} \sigma_ {k}} \tag {2} +$$ + +Intuitively, simple samples contain redundant information in images or text, and only part of information is necessary to answer the query (see Appendix D.2 for examples). As a result, the columns of their feature matrices exhibit strong linear dependence, which drive down the smaller singular values, causing the top ones to be much bigger by comparison, leading lower singular value entropy. In contrast, more challenging samples are richer in information, with feature matrices that are closer to full rank, resulting in more uniform singular values and higher entropy. In this way, SVE can as a practical approximation to measure the difficulty of samples, enabling the selection of hard samples to enhance the performance of MLLM in downstream tasks. + +# 3.3. Unique Value in Intra-cluster Space + +To enrich the value of samples for multi-modal data selection, it is crucial to emphasize the unique values of samples to select unique samples from similar clusters. The unique value estimation in the intra-cluster space consists of two steps: cross-modal domain clustering and unique value calculation. Next, we introduce each step in detail. + +Cross-modal Domain Clustering. To efficiently distinguish unique samples, we propose an optimized Cross-modal Domain Clustering that aggregate sufficiently similar samples into cluster in each task. This process begins with quantifying the $\ell_2$ -norm distance between samples for cluster variance computation. It then utilizes the Ward criterion [37] to merge clusters with the minimum increase in sum of squared errors (SSE) progressively, computed as: + +$$ +\Delta \mathrm {S S E} = \frac {n _ {A} \cdot n _ {B}}{n _ {A} + n _ {B}} \cdot \| \boldsymbol {\mu} _ {A} - \boldsymbol {\mu} _ {B} \| _ {2} \tag {3} +$$ + +where $n_A, n_B$ denote cluster cardinalities and $\pmb{\mu}_A, \pmb{\mu}_B$ represent cluster centroids. The clustering terminates when the $\Delta \mathrm{SSE}$ exceeds the threshold $\lambda \Delta \mathrm{SSE}_{\mathrm{max}}$ , where $\Delta \mathrm{SSE}_{\mathrm{max}}$ denotes the maximum increase in SSE. Here, $\lambda$ controls + +the number of clusters and is set to 0.1 by default to match the total data selection proportion for capturing sample relationships. Moreover, we use parallel computation and memory optimization for efficiency. More implementation details and analyses are shown in Appendix B.3. + +Unique Value Calculation. To quantify the uniqueness of samples, we focus on identifying discriminative samples in the intra-cluster space that contribute uniquely to training. The key intuition is that unique samples exhibit larger distance from similar samples (as shown in Fig. 2) to contain more information in the cluster for generalization. Therefore, we introduce a distance coefficient to assign high unique values to these distinctive instructions based on their distance from surrounding samples as follows: + +$$ +V _ {i} ^ {U n i} = \sum_ {s _ {j} \in \mathbf {C}, j \neq i} \| \mathbf {p} _ {\mathbf {j}} - \mathbf {p} _ {\mathbf {i}} \| _ {2} \cdot \frac {V _ {j} ^ {I n f}}{\sum_ {k \in \mathbf {C}} V _ {k} ^ {I n f}} \tag {4} +$$ + +where $\| \mathbf{p_j} - \mathbf{p_i}\| _2$ is the Euclidean distance of two samples $s_i,s_j$ in the cluster $\mathbf{C}$ in latent space. We assign higher reference weights to samples with greater informative value when computing their unique and representative values, reflecting their stronger influence on other samples. In this manner, these challenging instructions are more likely to be selected due to their enhanced unique values. + +# 3.4. Representative Value in Inter-cluster Space + +Empirically, evaluating samples solely with their informativeness and uniqueness within clusters may introduce outlier noisy or mislabeled data. These samples, despite higher uniqueness, have weaker associations with other clusters, limiting their ability to represent the overall dataset. Therefore, we introduce an inter-cluster representative coefficient to measure relationships across clusters, ensuring that selected samples capture representative features from the overall dataset, thereby avoiding the selection of noisy data: + +$$ +\tau_ {i} ^ {c} = \frac {1}{K - 1} \sum_ {k \neq c} ^ {K} \exp (\sin (\overline {{\mathbf {p _ {k}}}}, \overline {{\mathbf {p _ {c}}}})) \tag {5} +$$ + +where $\overline{\mathbf{p_c}}$ is the average sample feature in the target cluster $\mathbf{C}$ that contains sample $s_i$ , $\{\overline{\mathbf{p_k}}\}_{k\neq c}^K$ is the average sample + +feature of other clusters and $K$ is the number of clusters in each task. We use the feature of the last token to represent the sample feature as it aggregates all visual and textual features by cross-attention. Here, $\mathrm{sim}(\cdot ,\cdot)$ is the cosine similarity and $\exp (\cdot)$ is used to amplify the effect of clusters. Based on this coefficient, we then assign the weighted representative value to the instruction $s_i$ as follows: + +$$ +V _ {i} ^ {R e p} = \tau_ {i} ^ {c} \cdot \frac {V _ {i} ^ {I n f}}{\sum_ {k \in \mathbf {C}} V _ {k} ^ {I n f}} \tag {6} +$$ + +In this way, the representative value uses the association coefficient to ensure that selected samples align with the overall distribution. When the value is high, it indicates that the selected samples can effectively represent other samples, reducing the impact of noisy data and enhancing the overall representativeness in conjunction with uniqueness. More implementation details are shown in Appendix C.1. + +# 3.5. Adaptively Collaborative Data Selection + +Although we obtain multi-scale values from three complementary perspectives, combining them to select ideal samples is challenging since these multi-modal samples exhibit varying instruction rounds. Multi-IF [18] points out that multi-turn instructions prioritize informative value due to their weak interrelationships while single-turn ones emphasize unique and representative value due to their limited information. Inspired by this, we introduce an influence factor based on the number of response rounds of each multimodal instruction for adaptively collaborative data selection to enable adaptive, collaborative data selection, enhancing the synergy among these three values as follows: + +$$ +V _ {i} = \frac {r _ {i}}{r _ {i} + 2} \cdot V _ {i} ^ {\text {I n f}} + \frac {1}{r _ {i} + 2} \cdot \left(V _ {i} ^ {\text {U n i}} + V _ {i} ^ {\text {R e p}}\right) \tag {7} +$$ + +where $r_i$ denotes the conversation round of each multimodal instruction. We employ a 1:1 ratio to simplify the balance between uniqueness and representativeness values, as their trade-off remains stable. With this synergistic value for data selection, we can identify informative and unique instructions while adequately representative (c.f., Fig. 4). We also show detailed demonstration of DataTailor addressing each of three principles in Sec. 4.4 and Appendix D.1. + +In addition, we observe that standardizing the data selection proportion across all tasks limits selection diversity due to differences in task difficulty. Since spectral analysis shows that samples with the higher largest singular value exhibit less directional diversity for generalization, they require more selected data to improve the model's training robustness. Thus, we propose adaptive data selection proportion $k_{p}$ for each task $S_{p}$ based on largest singular values, which is computed as follows: + +$$ +k _ {p} = \frac {x _ {p} ^ {2} \cdot | S _ {p} |}{\sum_ {q} x _ {q} ^ {2} \cdot | S _ {q} |} \cdot k, \quad x _ {p} = a v g \left(\frac {\sigma_ {\max}}{\sum_ {j = 1} ^ {L _ {i}} \sigma_ {j}}\right) \tag {8} +$$ + +![](images/5b142766267cbdfe4ce89b7022168c0d5dcd12f897aaa6784fd41e3ebb6fb1de.jpg) +Figure 4. Visualization of the collaboration among informativeness, uniqueness, and representativeness for data selection, where each bar represents a subset defined by a specific value interval. + +where $x_{q}$ is the average ratio of the largest singular value $\sigma_{\mathrm{max}}$ to the sum of all singular values for all samples in the task $S_{q}$ , $|S_{q}|$ is the number of samples in the task, and $k$ is the whole data selection proportion. Through collaborative value assessment with task-adaptive proportions, DataTailor promotes more diversity during MLLM data selection. More details and analyses are shown in Appendix B.2. + +# 4. Experiments + +We first evaluate DataTailor on the standard data selection of MLLM on various benchmarks (§ 4.2). Additionally, we examine its transferability to other datasets (§ 4.3) and conduct an in-depth analysis (§ 4.4) for further evaluation. + +# 4.1. Experimental Setup + +Multi-modal Instruction Data & Backbone. As ideal data selections should be adaptable to diverse MLLM instruction datasets, we integrate DataTailor with two widely-used datasets to conduct experiments for its effectiveness evaluation: 1) MiniGPT4-Instruction [61] includes about $3.5\mathrm{K}$ instances refined by ChatGPT from detailed descriptions. 2) LLaVA-1.5-mix-665k [33] is a wider collection with 665K instructions, which encompass a wide range of task categories, including dialogue-based Q&A pairs, multiple-choice short Q&A, detailed descriptions, and text-only reasoning tasks. For the general setting, we conduct experiments on MiniGPT-4-7B and LLaVA-v1.5-7B. + +**Benchmarks.** We assess our methods using a mix of MLLM-specific benchmarks and more general downstream tasks. Aligned with SOTA MLLM methods, we include MLLM benchmarks for comprehensiveness: MME [12] is used to evaluate MLLM's ability of perception and cognition; SEED-Bench [24] involves multi-modal tasks across 12 perspectives with the assistance of GPT-4; POPE [29] + +
MethodsValid DataMLLM BenchmarksVQA BenchmarksCaptioning
MME-P ↑MME-C ↑SEED-I ↑POPE ↑MM-Vet ↑LLaVA-Wild ↑MMMU(val) ↑VizWiz ↑SciQA ↑GQA ↑VQA-v2↑TextVQA ↑NoCaps (val) ↑Rel.
MiniGPT4-InstructionMiniGPT4-7B
MiniGPT4-7B3.4k717.4259.623.868.319.025.123.436.036.332.232.121.4111.5100.0%
Random0.2k698.4227.725.169.717.227.919.118.334.019.233.217.2105.189.1%
Length0.2k683.4209.626.769.818.326.717.429.935.632.533.717.4106.594.7%
EL2N [40]0.2k668.6207.626.572.017.427.323.141.936.132.936.323.7108.3102.2%
IFD [28]0.2k678.6213.829.147.418.928.420.642.738.128.336.023.4106.699.8%
InsTag [36]0.2k715.6237.926.870.415.828.121.740.038.130.134.522.2105.9100.8%
LESS [51]0.2k698.5191.422.471.819.825.822.238.435.426.034.416.6109.795.4%
InstructionGPT-4 [47]0.2k716.9229.617.471.621.325.314.929.935.126.834.822.1106.893.3%
SELF-FILTER [49]0.5k438.7128.621.771.419.424.320.441.335.730.435.022.0105.692.8%
TIVE [35]0.2k707.0200.923.672.317.525.818.231.433.826.435.117.5108.992.7%
DataTailor (Ours)0.2k720.6263.927.369.821.428.423.640.837.730.734.721.0106.9104.6%
LLaVA-1.5-mix-665kLLaVA-7B
LLaVA-v1.5-7B (LoRA)665k1476.9267.967.486.430.967.932.847.870.063.079.158.2106.5100.0%
Random50k1387.5287.559.785.729.564.532.242.370.055.073.753.1107.795.3%
Length50k1357.0265.747.082.629.767.633.949.260.955.570.745.288.291.0%
EL2N [40]50k1077.3252.559.380.821.140.133.644.471.041.761.041.786.982.3%
GradN [40]50k1275.4303.658.375.724.868.232.437.870.944.964.046.0101.989.3%
IFD [28]50k1113.4301.855.176.727.663.133.048.748.241.964.243.6106.887.3%
InsTag [36]50k1317.1345.057.482.129.668.134.047.469.352.563.253.3108.396.4%
LESS [51]50k1344.8281.861.279.428.365.533.044.471.053.471.852.0106.294.3%
SELF-FILTER [49]25k955.7262.547.576.026.660.330.640.859.43.62.15.682.365.8%
TIVE [35]50k1334.8248.662.285.930.267.933.145.171.456.273.851.196.094.6%
COINCIDE [22]133k1495.6--86.1-67.3-46.869.259.876.555.6-98.0%
ICONS [50]133k1485.7--87.529.766.1-50.170.860.776.355.6-98.8%
DataTailor (Ours)50k1461.2362.561.782.130.469.333.946.370.957.775.053.1107.2100.1%
DataTailor (Ours)100k1476.2319.363.685.331.871.133.249.571.060.576.755.7108.7101.3%
+ +Table 1. Comprehensive comparison between DataTailor and other baselines for multi-modal data selection on MLLM and downstream general benchmarks. Our results are shown in the gray block. Due to limited resources, we all use the LoRA model for fair comparisons. + +mainly evaluates the MLLM's hallucination problems; MM-Vet [58] and LLaVA-Wild [34] assess the model's open-ended conversational capabilities; The MMMU [59] consists of more challenging scientific problems to assess reasoning ability. For general VQA tasks, VizWiz [16] and ScienceQA [43] contain unseen visual queries and multiple-choice questions to evaluate the zero-shot generalization of MLLMs. VQA-v2 [4] and GQA [20] access the model's visual perception abilities with open-ended questions while TextVQA [44] focuses on text-rich questions. For captioning, we transfer MLLMs to the NoCaps [1] validation set. We also show the amount of valid data selected to demonstrate the effectiveness of data selection. Note that Rel. in all tables represents the relative boost on all benchmarks + +Baselines. We use the following baselines: 1) Traditional data selection: it includes traditional random selection; length-based selection; GradN [40] and EL2N [40] use the L2-norm of the gradient and the error vector for selection, respectively. 2) LLM data selection: it directly transfers the selection methods from LLMs to MLLMs, including data-specific methods [6], human-reward methods [36], and gradient-based method [51]. 3) MLLM-specialized selection: it involves methods specifically designed for data selection in MLLM, including InstructionGPT-4 [47], SELF-FILTER [49], TIVE [35], COINCIDE [22], ICONS [50]. + +# 4.2. Main Results on Multi-modal Data Selection + +We report the results of our DataTailor and other diverse data selection methods for the MiniGPT4 and LLaVA shown in Table 1. Based on the observation of experimental results, we have summarized the following conclusions: + +Multi-modal instruction data suffers from serious redundancy, resulting in overall poor data quality. We can observe that in most benchmarks, even randomly selecting a + +small amount of instruction data does not result in a performance drop. Moreover, in some cases, simply selecting part of the data outperforms utilizing the entire dataset (33.2 v.s. 32.1 of VQA-v2 on MiniGPT-4), suggesting that excessive low-quality data hinder several MLLMs' capabilities on the contrary. Qualitatively, as shown in Fig. 1, most methods achieve $80\%$ performance with less than $20\%$ of the data. This confirms our analysis of the data redundancy in multimodal datasets and the necessity of data selection. + +For LLM data selection approaches (i.e., IFD [28], InsTag [36], and LESS [51]), the performances across several benchmarks overall remain unsatisfactory. Although these baselines explicitly distinguish tasks and features, they still underperform DataTailor by $12.8\%$ , $3.7\%$ , and $5.8\%$ on overall relative performance due to their rough information modeling and disregard for sample relationships. Moreover, all LLM data selection methods demonstrate severe shortcomings in representativeness, which leads to a decline in the performance of general VQA tasks (average 49.6 in TextVQA and 49.3 in GQA). In contrast, we observe that DataTailor obtains overall improvement on various tasks. For an intuitive illustration, we visually compare the metrics of three principles of DataTailor and those LLM data selection methods, as shown in Figure 1(b). Similarly, those LLM data selection methods exhibit deficiencies in at least one dimension, whereas DataTailor consistently achieves promising results. This result demonstrates DataTailor's capability to effectively promote these principles for multi-modal data selection, rather than roughly selecting samples based on individual values. + +Our DataTailor can be flexibly applied to different MLLMs. We incorporate our DataTailor into the two most popular MLLMs for evaluation. Despite the diversity in data and model structures, our DataTailor consistently im + +
MethodsFeature BackboneMME↑SEED-I ↑MMMU(val)↑SciQA ↑Rel.
mPLUG-264k [54]
Full Data (100%)-1243.434.326.941.1100.0%
Random (5%)-1183.233.926.640.697.9%
TIVE [35] (5%)LLaVA-vicuna-7B1177.134.026.940.297.9%
DataTailor (5%)LLaVA-vicuna-7B1260.034.527.841.9101.8%
mPLUG-OWL-7B1217.234.328.041.3100.6%
Bunny-695k [17]
Full Data (100%)-1778.170.738.770.9100.0%
Random (5%)-1578.864.436.770.193.4%
TIVE [35] (5%)LLaVA-vicuna-7B1542.461.734.768.490.0%
DataTailor (5%)LLaVA-vicuna-7B1582.865.337.175.896.0%
Bunny-Phi-3B1599.863.337.374.495.2%
+ +proves relative performance of data selection across all benchmarks compared to random selection (e.g., $+15.5\%$ on MiniGPT4-7B and $+4.8\%$ on LLaVA-v1.5-7B). Notably, despite comprising only $7.5\%$ data, DataTailor consistently outperforms full fine-tuning on the challenging MMMU benchmark (23.6 v.s. 23.4 on MiniGPT4-7B and 33.9 v.s. 32.8 on LLaVA-7B). These results indicate that our proposed method consistently addresses data redundancy across different datasets and architectures. + +Compared with MLLM-specialized selection methods, DataTailor exceeds SOTA for overall benchmarks. Specifically, DataTailor achieves an average of $100.1\%$ relative performance, outperforming TIVE [35] $(94.6\%)$ and the latest ICONS [50] $(98.8\%)$ . Notably, when increasing data selection ratio to $15\%$ , DataTailor surpasses the performance of the full tuning of LLaVA-v1.5-7B $(103.0\%)$ for MLLM benchmarks and $101.3\%$ for total benchmarks. This indicates that a small amount of high-quality data is more crucial than a large volume of low-quality data for enhancing MLLMs, which truly exemplifies "Less is More". + +# 4.3. Transferability of Multi-modal Data Selection + +Previous MLLM-specialized methods [35, 51] relied on the same MLLMs as in the training phase for data selection. The transferability analysis aims to investigate whether multi-modal data selected by surrogate models can be efficiently transferred into the target MLLM. Here, we use LLaVA-v1.5-7B as the surrogate model to select valuable data for the target MLLMs mPLUG-Owl-7B [54] and Bunny-3B [17], whose corresponding target datasets are mPLUG-264k and Bunny-695k, respectively. Moreover, we explore DataTailor's robustness among other feature backbones with different structures and parameters. Table 2 presents the results of our DataTailor and other baselines + +We observe that, (a) despite inconsistencies between the data selection model and the target MLLMs, DataTailor still consistently achieves over $95\%$ relative performance of full fine-tuning with only $5\%$ data (101.8% in mPLUG-264k and 96.0% in Bunny-695k). This demonstrates the powerful transferability of DataTailor and its potential for surrogate data selection. In contrast, TIVE [35] performs similarly to or worse than random selection (e.g., 90.0% vs. 93.4% in Bunny-695k) though it outperforms it in Tab. 1. This discrepancy may stem from TIVE's strong correlation with + +Table 2. Transferability analysis of multi-modal data selection. + +
MethodsPrincipled ValuesBenchmarks
\( V_{i}^{Inf} \)\( V_{i}^{ini} \)\( V_{i}^{Rep} \)MME ↑MMMU(val) ↑SciQA ↑Rel.
1Full Data1744.832.870.0100.0%
2Random✘✘✘1675.032.270.095.3%
3\( +V_{i}^{Inf} \)✓✘✘1759.334.970.298.0%
4\( +V_{i}^{Uusi} \)✘✓✘1716.233.569.897.3%
5\( +V_{i}^{Rep} \)✘✘✓1771.433.868.597.5%
6DataTailor✓✓✓1823.733.970.9100.1%
7w/o adaptive collaboration✓✓✓1770.234.070.298.8%
8w/o adaptive proportion✓✓✓1753.433.370.197.7%
9w/o adaptive collaboration & proportion✓✓✓1730.032.469.397.2%
+ +Table 3. Ablation study of each module in DataDailor. All experiments are with $7.5\%$ selection proportion on LLaVA-mix-665k and Rel. denotes the average boost on all 13 benchmarks. + +training gradients of the specific model. (b) The stable performance transition (nearly $1\%$ ) indicates that DataTailor emphasizes the inherent value of samples rather than relying on the model features as in previous feature-based baselines, which highlights its transferability for data selection. + +# 4.4. In-depth Analysis + +Analysis of Instruction Selection Factors. To investigate our DataTailor deeply, we study the ablation variants of different factors in Table 3. Specifically, we analyze their independence using the following ablation strategy: $1) + V_{i}^{Inf}$ : we only use the informative value. $2) + V_{i}^{Uni}$ : we only include the unique value. $3) + V_{i}^{Rep}$ : we only consider the representative value. $4) w/o$ adaptive collaboration & proportion: we gradually remove adaptive weights for collaboration and adaptive proportions for selection. Note that we adopt adaptive proportion in all Row 2-5 for fair comparison. The results of Row 3 indicate that informative value is the most crucial principle. Also, Row 4 and 5 suggest the importance of unique and representative values, as unique values support MLLMs' discriminative capabilities, while representative values enhance their generative capabilities. Furthermore, decreasing performance in rows 7-9 suggests that the adaptively collaborative strategy effectively ensures diversity between tasks in multi-modal data selection. + +Instantiation of Three Principles. To explore DataTailor addressing three principles for data selection, we clarify three principles based on the following insights: (a) informativeness is crucial for generalization when initializing MLLMs; (b) uniqueness is guaranteed to promote MLLMs after partial training by novel contributions; (c) representativeness improves relevant samples' performance during training. Specifically, we instantiate three settings to evaluate each of them essentially: (a) the improvement with $1\%$ data added to initial MLLMs reflects informativeness; (b) the improvement with extra $1\%$ data added to MLLMs based on $15\%$ random data training reflects uniqueness; (c) the average reduced loss of relevant samples with $1\%$ data added reflects representativeness. We normalize each metric and compare it to three types of baselines in Fig. 1(b). The selected data from baselines show limitations in at least one principle. In contrast, DataTailor effectively selects valuable data for all three aspects of MLLM. Please refer to Appendix D.1 for more details of instantiation analysis. + +Robustness Analysis of DataTailor. (a) Model scale ro + +
MethodsMMMU(val)LLaVA-WildSciQAGQARel.
LLaVA-v1.5-13B
Full Data (100%)35.269.572.663.3100.0%
Random (15%)33.067.371.860.796.3%
DataTailor (15%)36.475.073.961.2102.4%
+ +Table 4. Model scale robustness analysis of DataTailor. + +
MethodsRedundancy PerturbationNoise Perturbation
POPESciQAGQAPOPESciQAGQA
LLaVA-v1.5-7B
Full Data (100%)84.768.256.183.065.351.2
Random (5%)82.164.040.781.563.943.2
TIVE (5%)81.154.142.580.962.445.4
DataTailor (5%)81.465.946.984.263.748.5
+ +bustness. In Table 4, we verify the robustness of DataTailor with larger model scales. When keeping the same architecture and using LLaVA-v1.5-13B with higher parameters, our method demonstrates enhanced performance with larger scale MLLMs, especially +5.5 points on the LLaVA-Wild benchmark. This shows the stability of DataTailor at model scales. (b) Dataset robustness. In Table 5, we explore the dataset robustness of DataTailor with two challenging perturbations of candidate datasets: redundancy perturbation and noise perturbation. Specifically, we construct these perturbations with 50k redundant data and 50k noisy data by resampling and wrong answer combination. Note that we also sample 50k normal data from LLaVA-665k for balance. With redundancy and noise perturbations, we notice that DataTailor consistently demonstrates superior performance with limited data, whereas TIVE experiences a significant performance drop (65.9 v.s. 54.1 of SciQA on redundancy disturbance and 48.5 v.s. 45.4 of GQA on noise disturbance). It indicates DataTailor can bring out more distinctive and representative samples to identify the truly valuable samples from the redundant and noisy data for better robustness, which is crucial for discrimination tasks. + +Influence of Selection Proportion $\mathbf{k}\%$ in DataTailor. As shown in Figure 5 (a), when the selected data volume is relatively small, the model's performance improves as the data scale increases. However, due to the limited valuable data, further increasing the data volume introduces redundancy and noise, which degrades data-sensitive visual recognition performance (i.e. MM-Vet). This reveals the necessity of selecting data to ensure efficiency and maintain performance. Moreover, DataTailor quickly obtains over $100\%$ overall performance ( $100.1\%$ with only $7.5\%$ data) while TIVE exhibits only limited performance while growing slowly, as shown in Figure 5 (b). It indicates that DataTailor considers the uniqueness of the selected samples to avoid repetition and achieve continuous improvement. + +Computation Cost Analysis. Since the overhead of data selection is crucial for effective pruning methods, we analyze the computational cost of DataTailor when selecting $7.5\%$ data. We find that TIVE even exceeds the original training cost, which has certain limitations. In contrast, + +Table 5. Dataset robustness analysis of DataTailor with redundancy perturbation and noise perturbation. + +
WarmupData Selection (7.5%)Training
ComplexityActualComplexityActualComplexityActual
Full Model----O(|D| · |S|)100 H
TIVE [35]O(|D| · |Swarmup|)8 HO(|D| · |S|)100 HO(|D| · |S*|)7.5 H
DataTailor (Ours)--O(|S|)15 HO(|D| · |S*|)7.5 H
+ +Table 6. Asymptotic complexity and wall-clock runtime (measured with $4^{*}3090$ for LLaVA-v1.5-7B experiments on LLaVAMix-665k dataset). $|D|$ is the complexity of gradient computation. + +![](images/1f4e6b3eb36ca5d347723121000e7238643f2d7d1acc2057606ea3d66881e56c.jpg) +(a) Data Scaling in LLaVA-1.5-mix-665k + +![](images/27a74be973391f7484b482d67c696ff5a1bb8f45c440dd670e3c7fddb3a355b2.jpg) +(b) Data Scaling Comparison + +![](images/31ecdf5757ff619d2575973fe06f28508047f5943cad69c7d9ec510622b83786.jpg) +Figure 5. Ablation study of selection ratio $k\%$ in DataTailor. +(a) TIVE +Figure 6. Visualization using t-SNE on feature space. + +![](images/879273476d3f2e1aee91061f6baf15a2fa3a732e092907958e6113e1ab791c07.jpg) +(b) DataTailor + +DataTailor saves nearly $80\%$ of the overall time while outperforming the full model's performance. This confirms the efficiency of data selection with DataTailor for MLLMs. + +Distribution of Selected Data. To give an intuitive perspective on the selected data, we employ t-SNE [46] on the feature space of data chosen by DataTailor in Fig. 6. Notably, DataTailor selects informative samples without redundancy or deviation, while TIVE, despite high informativeness, focuses solely on gradient similarity, leading to redundancy and outlier noise. This visualization confirms the effectiveness of our method adhering to three principles. + +# 5. Conclusion and Future Work + +In this paper, we reveal the drawbacks of existing data selection methods and identify three systematic principles of informativeness, uniqueness, and representativeness as fundamental to optimizing multi-modal data selection. Building on this, we propose a unified framework, DataTailor, to synergistically integrate these principles for value evaluation and adaptively address the varying structure and complexity of samples across diverse tasks, thereby mastering collaborative multi-modal data selection. Comprehensive experiments on the challenging MLLM and general VQA benchmarks show that DataTailor significantly improves the performance of MLLM data selection. In the future, we aim to extend DataTailor to more challenging interleaved datasets with extra modalities such as video and audio. + +Acknowledgment. This work was supported by the National Natural Science Foundation of China (62436007), the Key R&D Projects in Zhejiang Province (No. 2024C01106, 2025C01030), the Zhejiang NSF (LRG25F020001) and Wallenberg-NTU Presidential Postdoctoral Fellowship. We thank all the reviewers for their valuable comments. + +# References + +[1] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. Nocaps: Novel object captioning at scale. 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Automatic match-cut generation with MatchDiffusion. In the history of cinema, there is prevalent use of match-cut transitions, i.e. semantic shifts in the content of two scenes that share the same structure, as exemplified by Stanley Kubrick's iconic transition from a bone to a spaceship (bottom left). However, obtaining visually appealing match-cuts requires sophisticated planning and multiple shots, due to the complexity of the transition. Our proposed MatchDiffusion approach is able to automatically generate match-cuts following textual prompts (right), thanks to a training-free inference technique composed of Joint and Disjoint Diffusion mechanisms (top left). + +![](images/aaec9c667f652bcfc309e810fcbae4c8c1ec642fd72962f7918e4193cb9cb29a.jpg) +Text-based automatic Match-Cut generation + +# Abstract + +Match-cuts are powerful cinematic tools that create seamless transitions between scenes, delivering strong visual and metaphorical connections. However, crafting match-cuts is a challenging, resource-intensive process requiring deliberate artistic planning. In MatchDiffusion, we present the first training-free method for match-cut generation using text-to-video diffusion models. MatchDiffusion leverages a key property of diffusion models: early denoising steps define the scene's broad structure, while later steps add details. Guided by this insight, MatchDiffusion employs "Joint Diffusion" to initialize generation for two prompts from shared + +noise, aligning structure and motion. It then applies "Disjoint Diffusion", allowing the videos to diverge and introduce unique details. This approach produces visually coherent videos suited for match-cuts. User studies and metrics demonstrate MatchDiffusion's effectiveness and potential to democratize match-cut creation. Visit our website for video results. Our code is open source. + +# 1. Introduction + +"The art challenges the technology, and the technology inspires the art." + +John Lasseter + +Cinematic transitions are powerful storytelling tools that evoke emotions, suggest the passage of time, or visually connect themes [28]. Among transitions, match-cuts are defined as "Two successive shots joined to create a strong similarity of compositional elements" [34]. They are particularly effective in bridging two scenes with strikingly different content but similar composition, creating a strong sense of visual continuity. For instance, in Kubrick's "2001: A Space Odyssey", a match-cut is used to transition from a bone thrown by an ape into a satellite orbiting Earth—conveying Humanity's evolutionary leap, from primitive tools to space technology, without a single word. + +Despite their visual elegance and narrative power, match-cuts are notoriously difficult to create. They require careful planning and precise visual alignment, often shaping the entire production process to ensure a cohesive transition [1, 29, 33, 42, 44]. This complexity limits match-cuts to experienced filmmakers with substantial resources, making them rare cinematic gems. Our aim is to democratize this powerful tool by providing a simple method that allows creators of various skill levels to experiment with match-cuts, helping amateurs and experienced filmmakers to quickly iterate and refine ideas before full-scale production. + +While many video editing tasks—such as scene interpolation [11], video morphing [27], and multi-text generation [36]—create continuity by generating intermediate frames, gradually deforming visuals, or extending narratives across prompts, match cuts operate differently. Rather than blending scenes, they establish a direct visual connection between two distinct yet compositionally aligned shots. Leveraging this principle, we formulate match-cut generation as synthesizing a pair of videos that share structural coherence while differing in semantics, further post-processed into a match-cut. To achieve this, we exploit an empirical property of text-to-video diffusion models, extending prior diffusion analyses [8, 23, 35]. We introduce MatchDiffusion, a training-free approach that generates match-cuts from two prompts by guiding the diffusion process. + +Our method first performs "Joint Diffusion", by initializing the synthesis for both prompts from a single noise sample and then guiding both along a common denoising path for the first denoising steps. This process translates into a cohesive layout and structure being shared between the two videos. After this stage, we then perform "Disjoint Diffusion", where we allow the videos' diffusion paths to diverge, as guided by their corresponding prompts. With these processes, MatchDiffusion generates videos that independently exhibit unique content while jointly displaying visual coherence established in the early stages—resulting in distinct yet harmonized scenes suitable for a match-cut. Please refer to Fig. 1 for an overview of our approach. + +To evaluate our diffusion-based approach to synthesizing match-cuts, we implement intuitive baselines using existing + +methods (e.g. [27, 50, 54]). We selected each of these methods for its potential to effectively assess aspects of the generation of match-cuts. Alongside these baselines, we propose metrics to quantify match-cut quality, and allow comparing synthesis methods. Together, these elements establish an evaluation framework that demonstrates our method's effectiveness and adaptability. + +In summary, our contributions are three-fold: (i) We formalize the task of creating match-cuts as synthesizing video pairs that are structurally coherent yet semantically divergent. (ii) We introduce MatchDiffusion, a training-free method that leverages pre-trained diffusion models to automate the generation of match-cuts. (iii) We implement robust baselines and propose metrics for evaluating match-cut quality, establishing a benchmark for synthesis methods. + +# 2. Related works + +Noise manipulation in diffusion models Early works showed that manipulating noise in diffusion models can yield desirable outputs. In images, fusing noise estimates from multiple prompts enables composition [5, 57], while Visual Anagrams [13] and Factorized Diffusion [12] reveal how summing noise can produce optical illusions. SyncDiffusion [20] applies similar ideas to generate panoramic images. SyncTweedies [18] unifies such strategies, including MultiDiffusion [5], under a general framework. In videos, noise is often fused across all iterations to ensure long-term consistency [36, 45, 46] or enable scene interpolation [11], with emerging properties over time also explored [7]. Crucially, these methods combine noise across all steps to produce a single scene. In contrast, we formulate match cuts as a distinct problem, exploiting diffusion's emerging properties in a novel way to generate coherent video pairs. + +Match-cut synthesis. Cutting in video editing has been widely explored. Some focus on detecting cut points in untrimmed videos using audio-visual cues [30], audio-beat alignment [32], or transitions for dialogue scenes [19], without differentiating types of transitions. Shen et al. [40] propose smooth transitions such as fades and panes, excluding straight cuts. Pardo et al. [31] offer a dataset for straight-cut classification, with match-cuts as one category, though underrepresented. Recently, retrieval-based approaches addressed match-cut creation: one curating candidates via audio-visual features [9], the other focusing on audio-based match-cuts [10]. These studies tackle match-cut synthesis through retrieval, whereas we propose a generative approach to synthesize video pairs that form a match-cut. + +Multi-scene video generation. Recent work has explored multi-shot video generation. Several works [22, 25, 26] generate multi-scene layouts from scripts derived by large language models (LLMs), while others [14, 51, 56] focus on ensuring temporal coherence and reducing hallucinations between frames. TALC [4] improves temporal alignment + +![](images/0c3b8a850a07ae8dc4b9942bb8a285e76dc92dcc66521d5837ae828ae9c6abec.jpg) +Timesteps + +![](images/e651e2f5bfb88ccb2f92b4fd4cc78fdd77fd2229c0a32e71512c0909b44165e9.jpg) + +![](images/93ee601978dfeed742ec9412e031997ef8d1ed1ffecac861e40c520c8036d654.jpg) + +![](images/4a830a89381af94fc33a16d7d1db9c1021795ec656a211e0ad2d87cdae36c96d.jpg) + +![](images/87ba11b1de748ea59c17bff039e526f188ff3eadd2d361d0ddd1cf8125c9981c.jpg) + +![](images/76b35b4d3b7c4884dde3c7dd0df1e3ff6b8fd2e3b48c4bf055d46e64cdba2ebb.jpg) + +![](images/ba0d2d70f80689d5dee07955dc7de2ccdbbeda9ff614683030ed8284fe1091b7.jpg) + +![](images/b73f436223a6310cfbec4dc9a72e6d6155ed6861e68e4b00fe09568817a43e3d.jpg) + +![](images/ad96110fc4ee0bdabadec03a7386d8239024604af47e836b55d10544eb19c72d.jpg) +Figure 2. Feature emergence during denoising. While the first iterations (top) yield ambiguous outputs displaying colors and basic structure, further iterations inject semantics (middle), until the final output is generated (bottom). + +![](images/a798894470620a6f2f53e164e7c761e05f481c955821cf31633f33ab184e8d5c.jpg) + +![](images/cfb8f24b81af8cfb12e59c4ccc31317bca7b171b6f7281f99afbdcb31cc2532f.jpg) + +![](images/f52cd3916c54dc15fed405b55cc42c699a9fc22b651ab112ea65f83b75e72c86.jpg) + +with aligned captions, while Contrastive-Sequential Diffusion [37] enhances visual coherence in multi-scene videos. MiNT [49] allows for cut synthesis, but maintains high semantic consistency. Unlike these, which focus on ensuring consistency within a single narrative, our method prioritizes structural coherence across two distinct prompts, optimizing for structure and motion consistency suited for match-cut transitions rather than narrative flow. + +# 3. MatchDiffusion + +Given two prompts $(\rho', \rho'')$ describing different scenes, our goal is to generate a pair of videos $(x', x'')$ that align with their respective prompts while remaining visually cohesive for match-cut transitions. Each video is generated separately, allowing them to be seamlessly post-processed into a match-cut. For example, this can be done by joining the first half of $x'$ with the second half of $x''$ . This setup enables multiple cut styles from a single video pair. On our website, we showcase three such styles: straight cuts, alpha blending, and flickering. While these are just a few editorial options, the synchronized outputs open the door to many other creative possibilities. We rely on a key property of diffusion models to achieve paired video synthesis: as highlighted in prior works [8, 23, 35] and illustrated in Figure 2, diffusion models establish broad structural patterns in the early denoising stages, while finer details and prompt-specific textures emerge later. By leveraging this progression, we design MatchDiffusion, a two-stage training-free pipeline tailored for match-cut generation. MatchDiffusion comprises: (1) Joint Diffusion (Section 3.2), where we set up a shared visual structure based on both prompts, followed by (2) Disjoint Diffusion (Section 3.3), where each video independently develops the semantics corresponding to its prompt. In the following sections, we introduce preliminaries, then go into detail into each stage of MatchDiffusion, elaborating on how the joint and disjoint diffusion stages provide the balance needed for match-cut generation. + +# 3.1. Preliminaries + +We first introduce the working mechanism of diffusion models for text-to-video (T2V) synthesis. T2V models operate by iteratively denoising Gaussian noise, with the goal of producing a fully denoised video that aligns with a conditioning textual prompt. Recent methods [53] execute this process in a latent space established by a pretrained autoencoder, mitigating computational costs [39]. The autoencoder comprises an encoder $\mathcal{E}$ and a decoder $\mathcal{D}$ . The latent space of this autoencoder is then iteratively denoised by a noise estimation network $\epsilon_{\theta}$ over $T$ steps, starting from sampled Gaussian noise $z_{T} \sim \mathcal{N}(0, I)$ . We denote the latent video representation at the $t$ -th iteration as $z_{t}$ , where $t \in \{0, \dots, T\}$ . That is, the network $\epsilon_{\theta}$ predicts the noise $\epsilon_{t}$ for $z_{t}$ . The network's prediction is conditioned on both the input textual prompt $\rho$ and the timestep $t$ : $\epsilon_{t} = \epsilon_{\theta}(z_{t}, \rho, t)$ . + +This noise prediction is then used to update the noisy latent representation, following scheduling strategies such as DDPM [16] or DDIM [41]. Namely, at step $t$ , the noisy representation $z_{t}$ is denoised into $z_0^{(t)}$ by combining the estimated noise with the latent representation: $z_0^{(t)} = z_t - \gamma_t\epsilon_t$ where $\gamma_{t}$ is a scaling factor function of $t$ . Then, another Gaussian noise $\epsilon \sim \mathcal{N}(0,I)$ sample is used to noise $z_0^{(t)}$ again, following a noise schedule whose intensity decreases over timesteps. Formally: $z_{t-1} = \eta_tz_0^{(t)} + \sigma_t\epsilon$ , where $\eta_t$ and $\sigma_t$ regulate the noise intensity, which decreases with increasing $t$ [16, 41]. After $T$ timesteps, $z_0$ is decoded via $x = \mathcal{D}(z_0)$ into the output video $x$ . + +For creating a match-cut, we generate two videos simultaneously by breaking the diffusion process into two stages: a joint stage where the latent representation of the videos is shared, and a disjoint one where representations are allowed to diverge. We now elaborate on each. + +# 3.2. Joint Diffusion + +The first stage of MatchDiffusion is Joint Diffusion. During this stage, we simultaneously generate both videos by forcing the synthesis to incorporate both input prompts for the first $K$ denoising iterations, where $K \in \{0, \dots, T\}$ . After these $K$ iterations, the result is a single latent displaying an abstract structure that broadly satisfies both prompts. Our intuition behind this design builds on previous work on hybrid images [6, 12, 13], showing that the diffusion process can be manipulated to produce images displaying different scenes depending on viewing conditions. However, our scenario is unique, since we require each output, $x'$ and $x''$ , to clearly and independently comply with its own prompt, sharing only selected appearance-related traits. As illustrated in Figure 2, the intermediate denoising outputs $z_0^{(t)}$ reveal motion patterns and the scene layout—the essential elements for match-cuts—emerge in early stages, while later refinement steps focus on details related to semantic + +![](images/eab18067fcd8f21b0134e8ffbb5be78d6b8f382c66dcf899d77e3ed655b203d6.jpg) +Figure 3. MatchDiffusion. We formulate the task of creating match-cuts as generating a pair of videos sharing a general appearance while having different in semantics. A portion of the frames of these videos can then be combined to enable match-cut transitions. To generate these videos, MatchDiffusion first performs a Joint Diffusion process for $K$ steps (left) by combining the noise predictions from the two prompts via a function $f$ . Then, a Disjoint Diffusion process is executed to obtain the final outputs $x'$ and $x''$ , i.e. denoising separately for the remaining $T - K$ iterations with one prompt per path. Optionally, MatchDiffusion also supports manual user intervention by allowing the integration of generated video tone and structural edits. + +content. As shown in Figure 3 (left), for the first $K$ iterations, we combine noise predictions from each prompt using a function $f$ , ensuring shared foundational characteristics early in synthesis. The joint diffusion process is defined by modifying noise estimate to: + +$$ +\epsilon_ {t} = f \left(\epsilon_ {\theta} \left(z _ {t}, \rho^ {\prime}, t\right), \epsilon_ {\theta} \left(z _ {t}, \rho^ {\prime \prime}, t\right)\right), \tag {1} +$$ + +while keeping the computation of $z_{t-1}$ unchanged, as described in Section 3.1. Although this formulation supports different expressions for $f$ , we choose it to simply be the averaging function, i.e. $f(a,b) = (a + b)/2$ . + +# 3.3. Disjoint Diffusion + +After $K$ iterations of Joint Diffusion, we obtain a noisy latent $z_{T - K}$ encoding characteristics that are desirable to preserve in both $x^{\prime}$ and $x''$ . This second stage of Disjoint Diffusion allows the remaining $T - K$ steps of the diffusion process to start from this latent but depart from the shared path to introduce the characteristics that are specific to the individual prompts. In particular, Disjoint Diffusion starts from $z_{T - K}$ and finishes denoising via $T - K$ evaluations of $\epsilon_{\theta}$ , conditioned on one prompt at a time. As such, Disjoint Diffusion produces separate noise predictions $\epsilon_t^\prime$ and $\epsilon_t^{\prime \prime}$ , as shown in Figure 3 (right). This procedure ensures that the emergence of semantics and details specific to each prompt occurs while maintaining the structure encoded in the initial $K$ steps. For $t\in \{0,\dots,T - K\}$ , this becomes: + +$$ +\epsilon_ {t} ^ {\prime} = \epsilon_ {\theta} \left(z _ {t} ^ {\prime}, \rho^ {\prime}, t\right), \quad \epsilon_ {t} ^ {\prime \prime} = \epsilon_ {\theta} \left(z _ {t} ^ {\prime \prime}, \rho^ {\prime \prime}, t\right). \tag {2} +$$ + +When $t = T - K$ , both $z_{t}^{\prime}$ and $z_{t}^{\prime \prime}$ are set to $z_{T - K}$ . After Disjoint Diffusion, we obtain two videos, $x^{\prime} = \mathcal{D}(z_{0}^{\prime})$ and $x^{\prime \prime} = \mathcal{D}(z_0^{\prime \prime})$ , which can be combined into a match-cut. + +One might assume that results of MatchDiffusion resemble those of video-to-video translation based on SDEdit [27], which perform prompt-based editing by injecting noise into an existing video $x_{\mathrm{init}}$ from step $K$ onward. However, our approach is fundamentally different, as we jointly synthesize the two scenes, rather than modifying an initial video. That is, MatchDiffusion generates outputs that satisfy both prompts from scratch, effectively narrowing the range of possible appearances to those that align with the shared structure and characteristics specified by both prompts. This process enables the synthesis of match-cuts for semantically uncorrelated scenes, as shown in Fig. 6, where the video-to-video translation approach fails. + +User intervention. To allow for iterative user editing, we propose a human-in-the-loop strategy for a finer customization of the generated videos. Namely, a user may wish to depart from the strict color adherence of the match-cut to better align with the tone of a preceding sequence, or to modify the background. While this could be achieved with post-processing, we propose a more natural mechanism that integrates user interventions directly into the diffusion process. + +We define $\tau$ as a generic user-driven modification, which may be automatic (e.g., a color look-up table) or manual (e.g., adding scene elements). We incorporate $\tau$ in the denoised video at the start of a disjoint diffusion path, e.g. $x_0^{(K)} = \mathcal{D}(z_0^{(K)})$ , as shown in Fig. 4. By doing so, we + +![](images/d4a3ac993e4c87f6855965bde4856fcaaf653c4eb570c7e068ebbc18c9b9aa8d.jpg) +Figure 4. User intervention. For reproducing the match-cut in the teaser, we apply a background mask to the denoised output generated by joint diffusion. After the remaining denoising iterations, the output is refined to integrate the new background. + +obtain an updated video i.e. $\tilde{x}_0^{(K)} = \tau (x_0^{(K)})$ . We then encode this video into its corresponding $\tilde{z}_0^{(K)}$ and proceed with disjoint diffusion. Hence, we integrate $\tau$ seamlessly into the synthesized video by leveraging the diffusion process itself to achieving realistic modifications. Although some [52] have proposed similar intervention mechanisms for some $\tau$ such as background editing, our novel integration with Disjoint Diffusion allows us to preserve a coherent match-cut. Importantly, since the diffusion process continues for $T - K$ steps after $\tau$ 's application, even modifications that would otherwise compromise scene realism in post-processing will be inherently refined, as shown in Fig. 4. + +# 4. Experiments + +We provide our experimental setup in Section 4.1, then show results of the match-cuts generated by MatchDiffusion in Section 4.2. Later, we compare against baselines, using qualitative and quantitative evaluations as well as user studies, in Section 4.3. We further report results with potential user interventions in Section 4.4. We conclude with a sensitivity analysis of MatchDiffusion to $K$ in Section 4.5. + +# 4.1. Setup + +MatchDiffusion settings. For the backbone of MatchDiffusion, we choose the open-source text-to-video (T2V) diffusion model CogVideoX-5B [53]. For sampling, we use a DDIM scheduler [41] with $T = 50$ steps. For baselines and ours, we generate videos with 40 frames, and form a match-cut by concatenating the first 20 frames of $x'$ with the last 20 of $x''$ . We tune $K$ for each pair of prompts. Our method's computational cost is the same as the backbone (i.e. CogVideoX-5B) since it does not add any extra computational cost. We report results on 50 prompt pairs. + +Baselines. To the best of our knowledge, we are the first to synthesize match-cuts from scratch. Hence, the definition of suitable baselines is challenging. We define here three strong baselines in our best efforts to define different strategies for training-free match-cut synthesis: + +Video-to-video. We define a video-to-video (V2V) translation baseline, and note that these approaches are designed for structural consistency. We first use $\rho'$ to generate $x'$ with the T2V version of CogVideoX-5B. Then, we use the V2V version of the same model (based on SDEdit [27]) to inject noise at step $K$ in $x'$ , and denoise using $\rho''$ , obtaining $x''$ . + +Motion Transfer. Recent literature has highlighted the possibility of conditioning the generation of new videos with the motion of an existing video. These motion transfer approaches allow for disentangling the motion from the reference scene content. Compared to V2V, this approach increases the flexibility in the outputs, allowing to significantly depart from the appearance of the reference video. We use a T2V model to generate $x'$ from $\rho'$ , then we use either SMM [54] or MOFT [50] to synthesize a new video with $\rho''$ as input, and $x'$ as guidance. For a fair comparison, we reimplemented SMM and MOFT on top of CogVideoX-5B. Hence, all our baselines use the same backbone. In supplementary, we include extra analysis on the suitability of these baselines for match-cuts, along with experiments using alternative backbones and V2V methods. + +Metrics. The evaluation of a match-cut is highly subjective. However, we propose different metrics to quantify desirable aspects of a match-cut. First, we use a frame-wise CLIPScore [15] to assess prompt adherence of the generated video. We average the CLIPScore of $x'$ and $\rho'$ , and $x''$ and $\rho''$ for each frame. This ensures that each video respects its prompt. To evaluate motion agreement between $x'$ and $x''$ , we use the Motion Consistency metric of SMM [54], evaluating the motion consistency of tracklets extracted by a pre-trained tracking model [17]. Finally, we use LPIPS [55] to quantify frame-wise perceptual similarity across $x'$ and $x''$ . Intuitively, a low LPIPS should indicate structurally-consistent outputs, i.e. suitable for match-cuts. In Supp., we measure the video quality of our method's results and show that it does not yield to any quality degradation. + +# 4.2. Results + +We report outputs of MatchDiffusion in Figs. 1, 5, and 6. In Fig. 5, we show a variety of match-cuts generated by our method, highlighting its ability to connect diverse concepts across different scenes. In the first two rows, MatchDiffusion demonstrates capacity to bridge unrelated scenes through background elements. For example, in the lighthouse scene, the beam of light seamlessly transitions into the fog of the adjacent scene, creating a cohesive visual connection. The third row illustrates a color-based match: transitioning from a spice market to a painter's palette by + +"waves lapping at the shore, foam fizzing at the water." + +"alineofantsmarchingalongaforestfloor." + +![](images/55da46815045391031a384f4749c74ba3f50b9441428b6418d3747ec915985e6.jpg) + +![](images/8306b1a1f9e2a526d0034f6f86e85156d07ccffcf3ed04ccd34623dfaa38ab6e.jpg) + +![](images/2edf06a52be1c6d02e561424b2b647d582073df8605f83f240e284935666eae2.jpg) + +![](images/9d7cd61f8218b224cb7e39b8e4aa56467ba74e828127043f4a7715aec5c12231.jpg) + +![](images/ed6be476dcb017c7f777549f5289f256ea0b0d81431203a165823cfad6590e4f.jpg) + +"a lighthouse beam sweeping across a dark ocean." + +"acar'sheadlightscuttingthroughthefog." + +![](images/4016f045329823b6e74cf9937f47b9fc2c57dd478bc7ea6318aa59198e108346.jpg) + +![](images/74de81b8a4b881a2d05612f42f8647c131b05bf5091df4599dcf8f204eb6a551.jpg) + +![](images/96fdd45df707349642a3a18955a677433a87a8f6a5d4d5af02fbebf7aeb84d31.jpg) + +![](images/a0f0fb08b2cc2828558b0a094e4cf0a48d868651e2548b7bb52e1565ab53585e.jpg) + +![](images/412dd2cb52acdbe0cf1efbdce0c5b3db866702935cb29ebe610c41db0eb2e931.jpg) + +"acolorful market stall filled with spices in glass jars" + +"a painter mixing oil colors on a palette" + +![](images/af990291db42c25110d75c10a8cc4b0b0c4cc3f644bcd63a6b8c415526cab950.jpg) + +![](images/b6ee32b827339bbeab808bb626d64bde1c218f54eb0c03767be36ead3b4ecbff.jpg) + +![](images/9f3a73745e592294cb153e7012c815102beeafa9baf86f734e51c453c4acfbe3.jpg) + +![](images/852c0f9d77c3ce887e9f02e599ba4c6e387df56688d4cfff2e2dda08afb26f08.jpg) + +![](images/69ade5538bc1adafdd44d7ad429a3c591a6f311c35ff4e288c1ea5ab9823023e.jpg) + +"a whiskey bottle on a rustic wooden table" + +"acozy wooden cabin among snow." + +![](images/37c154ba076fb25865fc9cf1057a77993092a1c1cdd02ddce03b44cb86782c3e.jpg) + +![](images/4ce73575573cd866d1acca7c645783ece22b5c831d50441309e423bce5022f51.jpg) + +![](images/d44c23e8461ace1d7f2d0c28a53f48e6ad49faca348be8ae27527eb77f165eff.jpg) + +![](images/db36142d4c6a0733a0ec64b4852de243b702693556f6b1356ec53cc798ffa2a8.jpg) + +![](images/d1518248640167fb29196bd87911147ecf7d9d504bd7aab3648249b1dea19445.jpg) + +"an aerial view of a busy, circular highway." + +"an aerial view of a person ice skating" + +![](images/39b67473ff1aac6c70ad8db42c72bafc877c5fb2515cb56f096826a9cfbc12cb.jpg) +Figure 5. Generated match-cuts. MatchDiffusion can automatically synthesize match-cuts based on the prompts in green and red. Note how the cuts enjoy highly consistent appearance while preserving each prompt's semantics. Please see the website for more samples. + +![](images/1a9acc61b2ad9b1be2cca8875c9a89470bbc2069c77c4007ec07e23169b487a5.jpg) + +![](images/c041a4c93755dd34044263d069db8a3591f315053a7f2b6cbb684876af385af1.jpg) + +![](images/5f73606bc12e58fb448734dd033c397362e4ebce7b14c628dd7c99532bcc094e.jpg) + +![](images/74c33445da7524727590910825e49a40f0a420dc189db15751c0d5c6252b584c.jpg) + +aligning the colors in each scene. The last two rows highlight structural alignment across scenes. In the fourth row, the shape of a bottle transitions into a wooden cabin, exploiting how the liquid's color mirrors the hues of the cabin. The final row connects a highway with an ice-skating scene, aligning the circular highway shape with the ice ring's structure. These examples demonstrate the ability of MatchDiffusion to generate creative match-cuts that would otherwise be challenging to envision. + +# 4.3. Comparison with baselines + +Qualitative comparison. Fig. 6 displays frames before and after the transition for three different prompts, comparing MatchDiffusion with our proposed baselines. This figure illustrates how each approach handles various cases of match-cuts. As seen in the first column, V2V tends to + +produce similar-looking scenes across prompts. This result is expected, as these methods are primarily designed to translate features within scenes that already share visual similarities (e.g., changing the season from summer to winter). When faced with highly dissimilar prompts, V2V typically alters minor aspects of the scene, which fall short of achieving the strong semantic shifts needed for a high-quality match-cut. For example, in the first row, the burning parchment merely becomes more rounded in the subsequent frame. Instead, motion transfer methods, such as SMM and MOFT, yield results aligned with the prompts, preserving movement across frames. However, in the same example, we observe that SMM and MOFT depart significantly from the appearance of the original image, preventing the structural alignment present in match-cuts. Finally, MatchDiffusion achieves smoother and cohesive transitions by aligning + +V2V +![](images/8b64aeaea7e4b09bad26d1d3bf109a087a4e5c1e3ecc52df8823982b2e613306.jpg) +"A parchment catching fire" "A sunset at the ocean" + +SMM +![](images/1e5a5944336bf0a5cccf5f17958afff81411e08fdd200f66b1de80280fb6dd37.jpg) +"A metro speeding through a station" "A conveyor belt carrying boxes" + +![](images/07bfb11098fa650762c20b4d8d53507185c9c1827a0e16ff7187cf4cf2871d0c.jpg) + +MOFT +![](images/a8e690642942ff85978df712b4f9aa101c3810676b9af75122860275f3ad51dc.jpg) +"A crescent moon rising over a desert" "A lantern being lit in a campsite" + +![](images/97dc0eab862c93392addf6682385608fb5b04cc087994a0abc0cb49c67ad0ef3.jpg) + +![](images/2c390f2793a67648c486a632a686503b004f90992a9b74229e7cf51edbba88d7.jpg) +MatchDiffusion + +![](images/933f7b5c74fe3db95318e66ea12eadc68f19aba2623f76fe8f8aa670e1a4fa1f.jpg) + +
MethodCLIPScore ↑Motion ↑LPIPS ↓
T2V (Lower Bound)0.330.400.74
V2V0.310.670.31
SMM0.340.640.74
MOFT0.330.660.56
MatchDiffusion0.340.700.32
+ +Table 1. Metrics comparison. Aligned with qualitative results (Fig. 6), we report that V2V is mostly impacted in CLIP-Score, due to many translations not being able to follow the prompts. On the other hand, SMM and MOFT excessively modify the scene, resulting in a high LPIPS. Only MatchDiffusion allows for high performance in all metrics. Best results are boldfaced, second best are underlined. Red cells show the worst performing scores. Our method (gray) strikes the best balance among all. + +both structure and motion across scenes. In the first row, the burning flame transitions into the sunrise reflection, creating a transition that aligns well with the match-cut effect. + +Metrics evaluation. Note that match-cut synthesis is a novel task, making quantitative evaluation inherently challenging. Nonetheless, we present quantitative results in Table 1. We start from a lower-bound baseline (T2V), defined as prompting CogVideoX-5B independently for $(\rho', \rho'')$ . The lower bound achieves a moderate CLIPScore due to its performance as a T2V method, but fails to capture continuity across scenes, as reflected by its low Motion Consistency (0.40) and high LPIPS (0.74). In contrast, V2V achieves the lowest LPIPS (0.31) and the highest Motion Consistency (0.71), indicating strong structural alignment across frames as expected. However, its CLIPScore is significantly lower than that of all other methods, suggesting the difficulty to adhere to highly distinct prompts, as seen in Fig. 6. Conversely, motion transfer methods introduce too much free + +![](images/751fca3184d5df59411d75ecaed99408b4a73d8eccd0ed89cfa08789068cc85a.jpg) +Figure 6. Qualitative comparison with baselines. Overall, we notice that V2V does not allow for drastic modifications of the scene in presence of prompts with strong semantic differences (e.g., first row). On the contrary, motion transfer baselines (SMM and MOFT) depart significantly from the content of the scene, prohibiting for a visuallyappealing match-cut. Only MatchDiffusion achieves a satisfying balance between semantic changes and prompt consistency. +Figure 7. User study. We evaluate users' agreement with a statement describing match cuts, to assess how much our generated videos align with the requirements in terms of visual consistency and prompt adherence. We significantly outperform all baselines. + +dom in the scene structure, as confirmed by the considerably higher LPIPS (0.73 for SMM, 0.53 for MOFT). Finally, MatchDiffusion enjoys a well-balanced performance. With a CLIPScore of 0.33, it matches the prompt adherence of SMM, MOFT and the vanilla model (T2V), while still achieving a Motion Consistency (0.69) and LPIPS (0.32) score that matches the V2V baseline. + +User study. Match-cuts target human audiences, and thus we conduct an evaluation against baselines based on user quality assessment. In this evaluation, we aim to quantify the smoothness of our transitions, while respecting different prompts. To do so, we show users both prompts, $(\rho', \rho'')$ , along with the match-cuts generated by MatchDiffusion and baselines. We then ask users to evaluate their agreement in a Likert-5 [21] scale with: "This video accurately reflects the scenes described by the text and smoothly transitions between them, maintaining consistent colors, structure, movement, and appearance from one scene to the next one". This question assesses if the videos align with the expected consistency, while preserving different semantics. We query 35 users (average age $30.11 \pm 7.29$ years old). We + +![](images/db6a11526005a2009bd6a5aa0ce06f7b9db023d25abfcb085bc6c55626ebd6b8.jpg) +(a) Qualitative samples + +![](images/9831ba7df9af556fcd44b0401c1d118e21a3e596f15aa1c256ee67d1a8f91c00.jpg) +(b) Impact on CLIPScore +Figure 8. Intervention effects. In (a), we verify that our user intervention strategy allows to depart from the original image following $\tau$ with no detrimental impact to realism. We quantify this effect in (b): although our SSIM with reference frames is lower, we maintain very similar CLIPScore. We plot results as mean and std. + +test against MOFT only for motion transfer, to maximize the questions per method presented to users. Results are reported in Fig. 7, showing that users significantly prefer MatchDiffusion over the baselines. In particular, we highlight that $39.44\%$ of them strongly agree with our statement, against $12.36\%$ for the best baseline (MOFT). This evidence suggests superior quality of our match-cuts. + +# 4.4. Evaluating user interventions + +We evaluate our optional user intervention strategy (Section 3.3) to test whether MatchDiffusion can relax strict color/structure adherence while still generating match-cuts. We apply three $\tau$ functions to $x_0^{(K)}$ : (1) color jittering, (2) histogram matching with random COCO [24] images, and (3) gamma correction. Ideally, $\tau$ should integrate with Disjoint Diffusion, preserving realism and scene structure. Fig. 8a shows results: applying $\tau$ post-generation exaggerates colors, reducing realism, while applying it to $x_K^{(0)}$ ("Ours") preserves realism despite minor structure shifts (e.g., leaf shape). This allows transformations that maintain scene composition, making them suitable for match-cuts. + +To assess the quality of these interventions, we randomize the parameters of $\tau$ five times and apply it to 36 synthesized video pairs, $x^{\prime}$ and $x''$ , generating a total of 180 for each of the two strategies. We then compute SSIM [48] between + +![](images/ac6e6756f54ac54ed1d248b9bab497f4fc808c2201ed33c1b6c9c3730a525f85.jpg) +Figure 9. Effects of $K$ . Increasing $K$ to the maximum produces a hybrid video between prompts, maximizing motion fidelity and bringing LPIPS to zero. CLIPScore is slightly impacted since hybrid videos present traits of both prompts. + +![](images/5c45b227e98769f31a2db53f7ad0cf2b8ee0094ec401ba7f5385efc353549c75.jpg) + +![](images/eb4728c20beb9019c87108adcc0ae762a926ae7e1251e1ad59f367bc9559792b.jpg) + +the videos and their post-processed counterparts to quantify visual modifications, along with CLIPScore of $\tau(x)$ with the corresponding $\rho$ . Fig. 8b shows that our method maintains the same CLIPScore while achieving a greater reduction in SSIM compared to the post-processing alternative. This suggests that our approach alters the video's appearance more significantly while still adhering to the prompt. In Fig. 8b histogram matching shows lower SSIM due to structural changes (e.g., the leaf in Fig. 8a). Our experiments show that our pipeline produces diverse videos, smoothly integrating $\tau$ and enabling varied match-cuts. + +# 4.5.Impact of $K$ + +We investigate the impact of the number of Joint Diffusion steps $(K)$ on MatchDiffusion. Fig. 9 shows the impact of $K$ on metrics. While most results presented in Figure 5 have $K$ between 10 and 15, we notice that although CLIPScore decreases, Motion Fidelity and LPIPS monotonically improve. This fact deserves ad hoc considerations. The case of $K = 0$ is equivalent to the lower bound (i.e. no shared structure), while $K = 50$ means that $x'$ and $x''$ share all the diffusion process (similar to Factorized Diffusion [12]), hence $x' = x''$ . In this case, MatchDiffusion produces a hybrid video (shown in supplementary). This property is not useful for match-cuts but might enable other applications. For the purpose of match-cut generation, the user's needs play a central role; $K$ serves as a tunable parameter to adjust the results according to artistic preferences. + +# 5. Conclusions + +We presented MatchDiffusion, the first method for the synthesis of match-cuts. We formalized the match-cut generation problem as a synthesis of two videos, and proposed a method for exploiting emerging characteristics of diffusion models. MatchDiffusion has limitations, opening future research directions. Effective prompting requires creativity, and automated prompt engineering could make the method more accessible to a broader audience. Finally, refining conditioning mechanisms to give users control over specific aspects of the match-cut could simplify interaction and reduce reliance on precise prompts. + +Acknowledgements The research reported in this publication was supported by funding from King Abdullah University of Science and Technology (KAUST) - Center of Excellence for Generative AI, under award number 5940. We thank the reviewers for their constructive feedback, in particular for suggesting alternative transition strategies between the two videos. + +# References + +[1] Adobe Creative Cloud. What is a match cut?, n.d. Accessed: 2024-11-14. 2 +[2] S Alireza Golestaneh and Lina J Karam. Spatially-varying blur detection based on multiscale fused and sorted transform coefficients of gradient magnitudes. In CVPR, 2017. 3 +[3] Jianhong Bai, Tianyu He, Yuchi Wang, Junliang Guo, Haoji Hu, Zuozhu Liu, and Jiang Bian. 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A series of textured meshes with PBR material generated by MaterialMVP, showcasing exceptional texture generation and realistic physical behavior under environmental illumination. More results and code can be found on https://github.com/ZebinHe/MaterialMVP. + +# Abstract + +Physically-based rendering (PBR) has become a cornerstone in modern computer graphics, enabling realistic material representation and lighting interactions in 3D scenes. In this paper, we present MaterialMVP, a novel end-to-end + +model for generating PBR textures from 3D meshes and image prompts, addressing key challenges in multi-view material synthesis. Our approach leverages Reference Attention to extract and encode informative latent from the input reference images, enabling intuitive and controllable texture generation. We also introduce a Consistency-Regularized Training strategy to enforce stability across varying viewpoints and illumination conditions, ensuring illumination- + +invariant and geometrically consistent results. Additionally, we propose Dual-Channel Material Generation, which separately optimizes albedo and metallic-roughness (MR) textures while maintaining precise spatial alignment with the input images through Multi-Channel Aligned Attention. Learnable material embeddings are further integrated to capture the distinct properties of albedo and MR. Experimental results demonstrate that our model generates PBR textures with realistic behavior across diverse lighting scenarios, outperforming existing methods in both consistency and quality for scalable 3D asset creation. + +# 1. Introduction + +Generating textures for 3D models is a crucial task in creating visually compelling and realistic digital assets, with numerous studies dedicated to advancing this field [1, 3-5, 20, 21, 23, 37, 40, 47, 57, 66, 68, 71, 76]. While traditional RGB textures focus on color representation, Physically Based Rendering (PBR) textures take a step further by simulating real-world material properties such as reflectivity, roughness, and light interaction, resulting in more immersive and physically plausible visual experiences. + +Some methods tackle the task of PBR texture generation through an optimization-based approach guided by text [6, 35, 59, 65, 75]. These techniques typically rely on pretrained 2D diffusion models to provide image priors, employing mechanisms like score distillation sampling [39]. By iteratively optimizing the textured mesh to align with the textual description, they achieve high-quality results. However, the iterative nature of this process makes it computationally expensive and time-consuming. + +Image-conditioned approaches are often more intuitive and user-friendly, by providing more direct guidance. Texturedreamer [64] and Hyperdreamer [56] extend the optimization-based framework to image-conditioned generation by leveraging DreamBooth [42], yet they are still bottlenecked by the lengthy inference time. On the other hand, generative approaches like SuperMat [16], RGB $\leftrightarrow$ X [69], and IntrinsicAnything [7] utilize diffusion priors to achieve faster generation. However, these methods are limited to single-view generation. TexGen [67] takes the images in the form of UV maps and demonstrates reasonable results, but struggles to handle the backside of the model and the seams correctly. CLAY [72] proposes to generate multi-view PBR textures from 3D models, leveraging IP-Adapter [63] to introduce reference images and achieving impressive results, though it often struggles with precise alignment between the generated textures and the input images. + +We introduce MaterialMVP, a one-stage model designed to generate PBR textures for 3D meshes. Our model produces multi-view, high-quality PBR textures, including albedo, metallic, and roughness maps. These textures not + +only highly follow the input reference images but also ensure precise alignment between different texture maps. + +To be specific, we employ a Multiview Diffusion Model framework designed to generate multiple view-consistent PBR maps from image prompts. To simultaneously produce albedo, metallic, and roughness maps, we introduce a Dual-Channel Material Generation framework, which extends the original diffusion model by adding an extra channel to generate metallic-roughness (MR) alongside the existing albedo channel. For the input reference image, we utilize Reference Attention, leveraging a reference branch to extract detailed information from the input. This ensures the generated textures retain fine details and remain faithful to the reference. To address issues such as unwanted lighting artifacts in diffusion-generated outputs and improve the model's robustness to input viewpoint perturbations, we introduce Consistency-Regularized Training. This strategy trains the model on pairs of reference images with subtle variations in camera pose and lighting but requires the model to produce identical, lighting-invariant results. This forces the model to learn lighting-invariant and accurate PBR maps across diverse conditions. Additionally, to tackle the misalignment problem in PBR material generation tasks, we design a Multi-Channel Aligned Attention module to synchronize information between the albedo and MR channels, ensuring the output materials are well-aligned and do not produce unexpected shadows or artifacts on textured meshes. At the same time, we incorporate Learnable Material Embeddings for each channel, providing additional context to help each channel learn its unique distribution, resulting in artifact-free and coherent textures. + +In summary, our contributions are as follows. 1) We propose MaterialMVP, an end-to-end multi-view PBR material generation model that produces high-quality, multichannel-aligned, and view-consistent textures. 2) We introduce Consistency-Regularized Training to improve model robustness to viewpoint perturbations and effectively disentangle lighting effects from material properties, producing lighting-invariant and accurate PBR maps. 3) We develop a Dual-Channel Material Generation framework, which processes albedo and metallic-roughness maps in separate channels. Leveraging Multi-Channel Aligned Attention and enhanced by Learnable Material Embeddings, it produces high-quality, coherent, and artifact-free textures. + +# 2. Related Work + +Texture Generation. The development of 3D generation has significantly advanced the creation of high-quality textures for 3D meshes [1, 3-5, 23, 37, 40, 47, 57, 66-68, 71, 76]. Extending text-to-image diffusion models[14, 29, 38, 41, 46] provides a foundation for generating detailed and semantically coherent textures from textual descriptions [1, 3-5, 23, 34, 37, 40, 47, 70]. Building upon this, us + +![](images/b4185cff3b96014457d24192050f71f32f9da27d3aa49e164cf74ea0b3d766db.jpg) +Figure 2. Overview of MaterialMVP, which takes a 3D mesh and a reference image as input and generates high-quality PBR textures through multi-view PBR diffusion. The albedo and MR channels are aligned via MCAA, effectively reducing artifacts. And Consistency-Regularized Training effectively eliminates illumination and addresses material inconsistency across multi-view PBR textures. + +ing image prompts as input enables textures to closely align with specific visual references [67, 68, 71, 72, 76]. Advancing further, 3D priors, such as depth maps [23, 47, 57, 71], normal maps [1, 37, 76], and position maps [1, 68, 76], ensures that the textures are not only visually realistic but also geometrically consistent with the underlying 3D structure. + +PBR Generation. PBR simulates light-surface interactions with physically accurate material properties, driving extensive research into PBR information estimation [6, 7, 13, 35, 43, 50, 51, 56-59, 64, 65, 74, 75] for high-quality 3D texture generation. Generation-based approaches [7, 43, 50, 51, 69] leverage diffusion models to learn material priors and recover PBR properties through physical rendering; retrieval-based techniques [13, 74] adapt pre-built material graphs from libraries to ensure visual consistency and editability; optimization-based methods [6, 35, 56, 59, 64, 65, 75] first generate initial textures and then refine them through techniques like Score-Distillation Sampling [39]. + +Multi-view Generation. Multi-view generation [12, 17, 25-28, 31, 32, 36, 44, 45, 48, 52-54, 61] has been adopted in texture generation [1, 11, 34, 37, 70, 72, 76] to address issues such as blurring or artifacts. Some methods integrate viewpoint information or 3D priors [8, 15, 19, 33, 60, 62]. Other approaches utilize epipolar geometry to improve consistency between views or reduce memory overhead [18, 22, 26], while another technique tiles multiple view images into a single layer, treating them as a unified input during the dif + +fusion model's denoising process [24, 44, 45, 55]. + +# 3. Method + +As shown in Fig. 2, our MaterialMVP generates PBR textures conditioned on a 3D mesh and an image prompt. The 3D mesh is input in the form of normal maps and position maps, which are encoded into latent space and concatenated channel-wise with noise latent as U-Net input. The generated albedo map is expected to be free from lighting information, while the metallic and roughness maps should be both accurate and precisely aligned. In this section, we first review the multi-view image generation diffusion model and the principles of PBR-based material modeling, which form the foundation of our approach. Then, we introduce the Consistency-Regularized Training method, designed to disentangle residual lighting information from the albedo map while improving robustness against input variations. Finally, we present our dual-channel material generation framework, which ensures the precise alignment and fidelity of the generated texture maps. + +# 3.1. Preliminary + +Multi-view Diffusion. The Latent Diffusion Model (LDM) [41] is a generative framework that operates in a compressed latent space, combining the principles of diffusion processes with VAEs to generate high-quality images efficiently. Building upon LDM, existing meth + +![](images/68cae627e2028934f7372697eb741b87587e577d18e30cb6f7d438fe3998b20f.jpg) +Figure 3. Reference Image Pair Selection. The selected image pair exhibits perturbations in camera pose and/or lighting. The solid box indicates the chosen reference image, and the dashed box indicates the perturbed reference image. + +ods [36, 48, 52] propose multi-view diffusion models that extends the latent space $z$ to multi-view representations $Z = \{z_{1},\ldots ,z_{n}\}$ via multi-view attention as + +$$ +z _ {i} ^ {\text {n e w}} = \sum_ {j = 1} ^ {n} \operatorname {S o f t m a x} \left(\frac {Q _ {i} K _ {j} ^ {T}}{\sqrt {d}}\right) \cdot V _ {j}, \tag {1} +$$ + +where $Q$ , $K$ , and $V$ are the projected features of Query, Key, and Value, enabling synchronized denoising of geometrically consistent multi-view outputs. + +PBR Material. Our material representation employs the Disney Principled Bidirectional Reflectance Distribution Function (BRDF) framework [2], defining surfaces through three parameters: albedo, metallic, and roughness. These parameters are stored in two separate textures: a combined MR map storing metallic and roughness data, while albedo remains in an RGB texture map. + +# 3.2. Consistency-Regularized Training + +We observe two key limitations in multi-view PBR synthesis with image prompts: (1) view sensitivity, where slight perturbations in camera pose can lead to dramatically different material outputs, and (2) illumination entanglement, where lighting from the reference images is incorrectly baked into the output, or the pretrained diffusion model generates unintended lighting effects. + +To address these issues, we propose a consistency-regularized training strategy that trains the model on pairs of reference images rather than individual samples. At each training step, the diffusion model is jointly conditioned on two reference images. This dual-prompt mechanism introduces implicit geometric consistency constraints to stabilize multi-view generation while encouraging the model to disentangle lighting variations from material features. + +# 3.2.1. Reference Pair Selection + +For each object, we construct a candidate set $\mathcal{I}$ of 312 images rendered in various camera poses and lighting condi + +tions at elevation angles $\theta_c \in \{-20^\circ, 0^\circ, 20^\circ\}$ , random\}, with 24 azimuth angles $\phi_c$ uniformly sampled per elevation. For $\theta_c \in \{-20^\circ, 0^\circ, 20^\circ\}$ , each pose is rendered under three random HDR lighting conditions; for $\theta_c = \text{random}$ , each pose is rendered under a single point light with random light elevation $\theta_l \in \{-30^\circ, 0^\circ, 30^\circ\}$ and light azimuth $\phi_l \in \{-45^\circ, 0^\circ, 45^\circ\}$ . As shown in Fig. 3, to select a reference pair $(I_1, I_2)$ , we first choose $I_1$ from $\mathcal{T}$ with probability $p$ favoring point light images (in practice, we set $p = 0.4$ ), and then select $I_2$ from the subset $S(I_1)$ defined as + +$$ +\mathcal {S} \left(I _ {1}\right) = \left\{I \in \mathcal {I} \mid \phi_ {c} (I) \in \left\{\phi_ {c} \left(I _ {1}\right), \phi_ {c} \left(I _ {1}\right) \pm 1 5 ^ {\circ} \right\} \right\}, +$$ + +where $\phi_c(I)$ denotes the camera azimuth angle of image $I$ . The selection process can be compactly expressed as + +$$ +\left(I _ {1}, I _ {2}\right) = \left(\operatorname {S a m p l e} (\mathcal {I}, p), \operatorname {S a m p l e} (\mathcal {S} (I _ {1}))\right), +$$ + +where $\operatorname{Sample}(\mathcal{I}, p)$ samples $I_1$ with probability $p$ for point light images, and $\operatorname{Sample}(S(I_1))$ uniformly selects $I_2$ from $S(I_1)$ . In this way, we obtain a reference image pair with subtle differences in viewpoint and lighting. + +# 3.2.2. Training Strategy + +Following the input of reference image pair $(I_1, I_2)$ , the network processes each image sequentially while enforcing output equivalence through consistency regularization. Specifically, at each training timestep $t$ the model $\epsilon_{\theta}$ generates diffusion noises $\epsilon_t^1$ and $\epsilon_t^2$ by conditioning on $I_1$ and $I_2$ respectively. We arbitrarily select one of them to compute the PBR loss, using $\epsilon_t^1$ as an example + +$$ +\epsilon_ {t} ^ {1} = \epsilon_ {\theta} (z _ {t}, t, c (I _ {1})), \quad \epsilon_ {t} ^ {2} = \epsilon_ {\theta} (z _ {t}, t, c (I _ {2})), +$$ + +$$ +\mathcal {L} _ {\mathrm {p b r}} = \mathbb {E} _ {\epsilon \sim \mathcal {N} (0, 1), t} [ \| \epsilon - \epsilon_ {t} ^ {1} \| _ {2} ^ {2} ]. +$$ + +To achieve consistency under varying camera poses and lighting conditions, we enforce $\epsilon_t^1\approx \epsilon_t^2$ . This is formulated through an $L_{2}$ consistency loss as + +$$ +\mathcal {L} _ {\text {c o n s}} = \mathbb {E} _ {t} \left[ \left\| \epsilon_ {t} ^ {1} - \epsilon_ {t} ^ {2} \right\| _ {2} ^ {2} \right], +$$ + +which is combined with the PBR loss via a weighting parameter $\lambda = 0.1$ as + +$$ +\mathcal {L} = (1 - \lambda) \mathcal {L} _ {\mathrm {p b r}} + \lambda \mathcal {L} _ {\mathrm {c o n s}}. \tag {2} +$$ + +# 3.3. Dual-Channel Material Generation + +Albedo and MR textures serve distinct roles in PBR material synthesis. However, existing approaches are not designed to handle the unique requirements of PBR material generation, particularly the need to address the inherent differences between albedo and MR. To bridge this gap, we propose strategies that independently optimize albedo and MR generation, ensuring not only precise alignment but also high-quality texture synthesis. + +Table 1. Quantitative comparison with state-of-the-art methods. We compare with two classes of methods, one conditioned on text only, and the other one based on image. Our method achieves the best performance compared with both classes. + +
MethodConditionCLIP-FID↓FID↓CMMD↓CLIP-I↑LPIPS↓
Text2Tex [4] ICCV'23Text31.83187.72.738-0.1448
SyncMVD [34] SIGGRAPH Asia'24Text29.93189.22.584-0.1411
Paint-it [65] CVPR'24Text33.54179.12.629-0.1538
Paint3D [68] CVPR'24Text30.17185.72.755-0.1388
Paint3D [68] CVPR'24Image26.86176.92.4000.88710.1261
TexGen [67] TOG'24Text + Image28.23178.62.4470.88180.1331
OursImage24.78168.52.1910.92070.1211
+ +# 3.3.1. Multi-Channel Aligned Attention + +Some approaches guide diffusion generation by incorporating conditional image prompts through a reference diffusion branch, where the latent representation $z_{ref}$ is injected into the generation branch via cross-attention. However, when applied to PBR material generation, it is unsuitable due to the distributional gap between the reference image and the MR texture. Specifically, attention mechanisms struggle to align these mismatched latent features, leading to inconsistent material synthesis and texture degradation, particularly in geometrically flat regions of 3D meshes where subtle material variations are critical. + +To resolve these issues, as illustrated in Fig. 2, we propose Multi-Channel Aligned Attention that independently optimizes the albedo and MR channels while maintaining their material consistency. Specifically, the albedo channel retains the conventional reference-guided cross-attention + +$$ +\operatorname {A t t n} _ {\text {a l b e d o}} = \operatorname {S o f t m a x} \left(\frac {Q _ {\text {a l b e d o}} K _ {\text {r e f}} ^ {T}}{\sqrt {d}}\right) \cdot V _ {\text {r e f}}, \tag {3} +$$ + +ensuring that the generated albedo correctly follows the reference image. In contrast, the MR latent $z_{MR}$ discards direct reference conditioning and instead leverages residual connections from the albedo channel + +$$ +z _ {M R} ^ {\text {n e w}} = z _ {M R} + \operatorname {A t t n} _ {\text {a l b e d o}}, \tag {4} +$$ + +allowing it to inherit spatial coherence and geometric priors from the albedo features. + +This design addresses the unalignment between different domains of PBR material, and maintains generation diversity without increasing parameter complexity, as no additional trainable parameters are introduced beyond the baseline cross-attention framework. + +# 3.3.2. Learnable Material Embeddings + +Inspired by IC-Light [73], we introduce learnable embeddings for both the albedo and MR channels to explicitly model their differences. Specifically, we initialize two independent $16 \times 1024$ embeddings, which are injected into the respective channels via cross-attention layers as shown in Fig. 2. Both the embeddings and the attention modules are trainable, enabling the model to effectively capture the distinct characteristics of albedo and MR textures. + +# 4. Experiment + +Dataset. Our training dataset consists of 70,000 high-quality 3D assets selected from Objaverse [10] and Objaverse-XL [9]. For each 3D object, we rendered data from four elevation angles: $-20^{\circ}$ , $0^{\circ}$ , $20^{\circ}$ , and a randomly sampled angle. At each elevation, we captured 24 uniformly distributed views, generating corresponding albedo, metallic, roughness maps, and HDR/Point-light images of $512 \times 512$ resolution. During each training step, we selected 6 sets of uniformly distributed PBR maps from the same elevation and 2 HDR/Point-light images as reference data (see Sec. 3.2.1 for the selection methodology). + +Evaluation Metrics. We use Fréchet Inception Distance (FID), CLIP-based FID (CLIP-FID), and Learned Perceptual Image Patch Similarity (LPIPS) to measure the similarity between the generated textures and the ground truth. CLIP Maximum-Mean Discrepancy (CMMD) is used to assess the diversity and richness of the generated texture details. And CLIP-Image Similarity (CLIP-I) is employed to evaluate how well the generated textures semantically align with the input images (for image prompt methods). + +Experimental Setup. Our model is initialized from the ZSNR checkpoint [30] of Stable Diffusion 2.1 and trained using the AdamW optimizer with a learning rate of $5 \times 10^{-5}$ . The training process includes 2000 warm-up steps and requires approximately 180 GPU days. + +Compared Methods. We compare with text- and image-conditioned methods, including Text2Tex [4], Paint3D [68], Paint-it [65], SyncMVD [34], and TexGen [67]. + +# 4.1. Quantitative Comparison + +We at first conduct a quantitative evaluation to assess the performance of our proposed method, focusing on its ability to generate high-quality textures and maintain image alignment capabilities. We utilize a subset of Objaverse containing 176 objects as the evaluation set. The evaluation results are presented in Tab. 1, showcasing that our method demonstrates superior texture generation quality and semantic alignment capabilities. As the table reports, the leading performance in FID and LPIPS metrics indicates a high similarity between our model's outputs and the ground truth images, demonstrating our model's ability to effectively fol + +![](images/9919cf326befaec0a71c48caf8fd5488744b79a1ce8bddf83e33baeb942b4e80.jpg) +A cheeseburger. + +![](images/8d24461d179205b2f18bd074bd5b0f8c65113e8677e4b733e91b0e586d0c43e1.jpg) + +![](images/8b912f74db4885b7c5e22fe2baa61a8d2fe364fe3a70108c5651626c20ed403e.jpg) + +![](images/7aa8e684fb8577000d66ee113e6eb35255a594d9ad02fd4a71865eb6e7bdb242.jpg) + +![](images/6a8de04bc17afea61b0e2bcd6445d7351c8ea1f9513576df97fe60c1b89c32e2.jpg) + +![](images/d93d53e210463752554421cd2d02d99d5423efadc9965a36629cc8a3a1fff5c8.jpg) +A mechanical nightingale. + +![](images/8eb3db5d705c389be5316156d918ab279ea83dbc8a98fc6f19ee3ccb196069c2.jpg) +A floral-patterned wall lamp. + +![](images/577fa28b2f3c96d795be707d55acd72f25b99a70b2f5b4ad1ee476d14bb83d9e.jpg) + +![](images/a2f9232365488843ab749a66cdd492651369c1d567a78d0feb20ae921bba491f.jpg) + +![](images/febff7cbdf2042bc7a892f90bbdaab46682a5a8d6b7450f3dedb1790a2f31959.jpg) + +![](images/9510a14e1a63e3fe7587c3b2c3136509671b6674320f27a24fb2d46267a60705.jpg) +Text2Tex + +![](images/5ec988bf0a0699300277ab7f58a821d43712deeccebb93ba84f6f840486fc799.jpg) +SyncMVD + +![](images/da91974e371fd02b32b89109c0d30099a2b692a4434ce64622a5182800383cd0.jpg) +Paint-it + +![](images/dad4b161ffb6ffc34e8905574bc2a54a3be6868c63a3e5f41b766d833671bb6a.jpg) +Paint3D + +![](images/505ded986d3e4f3bbc1f011c944928fc5a70e87d38b61f62faab0a176d9d70c0.jpg) +Ours + +![](images/4dc6c20b48ac82c01e6c9e67d9513df251270356ddd3f0e76d714b2b7ef6d9eb.jpg) + +![](images/f32c94aa1352b5080addc882eb344a2ce8c8ab384d321963f67eaf0aa7bc3c59.jpg) +Figure 4. Qualitative comparison of text-conditioned 3D generation methods and our approach. Our method achieves superior fidelity in texture and pattern coherence, avoiding blur, inconsistent lighting, and misaligned patterns found in other approaches. + +![](images/77e9e141394fa3eb742d22bf8cb098d0cb4d0f4256ae8efb3ad83a6de6ae01db.jpg) + +![](images/48cc8bf4de1115f2abddfd0e56fd19b3dc2dcb0a0d7480a875727fa24e600197.jpg) + +![](images/1310fe71ef95660144fc12bb9ecc72071d35ec92ebf87935b4fa6da6c55600f5.jpg) + +![](images/a7f5932e8d0728cc7f28265ca0069a9328590022156212da351c21c0211935fa.jpg) + +![](images/d51edc4a82713df7c1db268c774b0daaf479f4e782995cf2861a32f8e6ef40fc.jpg) + +![](images/240cf48d9e8f330d9192836e15d5e08cbc49defb58229f97708f573663fe5970.jpg) + +![](images/310bcdb953dbf8b553bc331046bd42795112295ff2dd5ab181cc8bbfe9b0e933.jpg) + +![](images/aa96209d468d86110f664829b2a8fdc3786181cb0df5e10d30c1fea24bf2e74c.jpg) + +![](images/454d356da258f96964e6fe4229ea17a93f2ffac727b479f27c3480f0e7a2fb9c.jpg) + +![](images/6c0062221521048f5079cfcb88edf9f0b46ca07f4345f2a873066a58588199d3.jpg) + +![](images/107ecf37d4559bb73d800f42de544560b964efb4a8f3335d617355f6ffc37491.jpg) + +![](images/4ed0cd28f5107ab216e046e13f842d281ff56528609d28b4b32433ddc6344f0e.jpg) + +![](images/13164ff81b9f4cea25bee42c27f2deaa1942c91fc58f053e34090e84f3c36bc5.jpg) +Image Prompt + +![](images/e8ce04088e75c7d2912b2e741e5d3af0f4a6b241fa981b7995e5c7b954b7c9ec.jpg) +Paint3D + +![](images/2e77b27dac5abc38954ac0d2835b072f058d4bebc859271216ef667220f9a79d.jpg) +Figure 5. Qualitative comparison of image-conditioned 3D texture generation methods. It demonstrates that our method outperforms other methods in terms of faithfully following the image and its semantics, as well as generating textures with superior coherence. + +![](images/1f6c2b93bbd29b5ab6aa1aa9c375a63a24dee9d743817f7a76312178c5d7b1df.jpg) +TexGen + +![](images/132d7b3b2819874c5dfcab59e79b472415fc7a210eb11556b3772263a5eedf2c.jpg) + +![](images/6fffb3b33f29e9eb201c6a75d24e2778513587547d41c65b5f52552a28b61d20.jpg) +Ours + +![](images/4621b63ced1b5915a524247201c78702679c40b4b330f9cd27a4cf82c0b6a180.jpg) + +low the input reference images. The superior performance in the CMMD metric suggests that the textures generated by our model are rich in details. Additionally, the leading scores in CLIP-I and CLIP-FID metrics reveal that the gen- + +erated textures are semantically well-aligned with the reference images, further validating the semantic consistency of our model's outputs. + +![](images/622aaae6605115a2b30bc8cb0adf4251e85decc3a694fbab81e87698678684c7.jpg) +A bunny statue made of ... +Figure 6. We show a variety of PBR textures for two different 3D assets, demonstrating the diversity and semantic alignment capabilities of our model. (Better viewed by zooming in) + +![](images/5ad7abbf0f7ac722c8bea3405369eae9febe3056f2eee4a272601eddfc766b79.jpg) +A teapot in style of ... + +![](images/e4e025d528ed683f3e5de97b20226e105338121acdd2daf50ed7b5405fd9e1d6.jpg) +Figure 7. We show PBR textures for two meshes with image prompts and display them under various environmental illuminations. The results demonstrate high accuracy in our PBR textures and the ability to remain unaffected by the input image's lighting. + +# 4.2. Qualitative Comparison + +For image-conditioned models, we use JimengAI [49] to generate reference images as prompts. Qualitative results are presented in Fig. 4 and Fig. 5. Our model demonstrates superior performance compared to other methods in terms of: 1) Realism. Our model exhibits astonishingly realistic effect, especially under various environmental illumination. Also, the consistency between multi-view PBR materials effectively avoids artifacts such as blurring, texture seams, and the Janus Effect. 2) Illumination invariance. Results in Fig. 5 show that our method has successfully eliminated the illumination present in the input image while accurately reflecting the environmental lighting through the generated PBR materials. In contrast, other methods presented in Fig. 4 and Fig. 5, although capable of generating some illumination effects, fail to adhere to physical principles, resulting in visually unappealing outcomes. 3) Global + +consistency. Some methods achieve accurate alignment with the reference image on the front view (see Fig. 5), while exhibiting poor consistency on the back views. This inconsistency manifests itself as chaotic patterns, unwanted shadows, or even illogical textures. The inconsistency is also observed in Fig. 4. In contrast, our method generates seamless and consistent textures, reasonably extending the content beyond the reference image and maintaining global coherence. Furthermore, our method achieves precise alignment with the input image both at the pixel level and semantically. + +# 4.3. Ablation Study + +One Stage Generation Strategy. To demonstrate the superiority of the end-to-end generation of multi-view PBR maps over the two-stage approach, which first generates multi-view images and subsequently converts them into PBR maps, we replicate a representative work of this + +![](images/abb785cfa55eef7b22c8909170199e55e3f58d6517e3c3f2e9c234b2729d39fc.jpg) +(c) Multi-Channel Aligned Attention +Figure 8. We ablate the one-stage generation scheme, the consistency loss, and the MCAA, validating the effectiveness of our method in generating high-quality and semantically accurate textures, as well as eliminating blurring artifacts caused by PBR misalignment. + +method, SuperMat [16]. It can be observed in Fig. 8 (a) that SuperMat is not able to accurately estimate materials, often rendering glass or metal with a plastic-like appearance, which is likely due to the accumulated errors during the process of generating multi-view images from a single RGB image. Therefore, the end-to-end generation method is better suited to handle this task. + +Consistency Loss. To show the importance of the consistency loss in improving PBR map accuracy during training, we set the weighting parameter $\lambda$ to zero and trained the model till convergence. The results in Fig. 8 (b) indicate that, without the consistency loss, the model frequently mispredicts materials with excessively high metallic properties, assigning a metallic appearance to various materials. + +MCAA. To verify the effectiveness of MCAA, we train a variant where MCAA is replaced with standard weight sharing between dual channels. As Fig. 8 (c) shows, we predict the albedo and MR maps for the same mesh, and subsequently generate the final textured mesh. The variant without MCAA produces misaligned albedo and MR maps in detailed regions, ultimately leading to blurred textures. It is worth noting that generating an MR map that is perfectly aligned with the albedo or generating a blank MR map can both achieve artifact-free results in the final output. + +# 4.4. Application + +Our model shows promising capability in generating high-quality textures. As illustrated in Fig. 6, it enables the creation of textures with realistic material properties using different prompts. Moreover, as shown in Fig. 7, we generate two objects and render them under five distinct environmental illuminations. The textures generated by our model exhibit exceptional fidelity and physical accuracy under various lighting conditions. + +# 5. Conclusion + +We present MaterialMVP, a novel one-stage framework that generates high-quality PBR textures for 3D meshes from image prompts. We extend the conventional multi-view diffusion to a multi-view PBR diffusion process, generating consistent albedo, metallic, and roughness maps across multiple views. We also incorporate an additional perturbed reference image during training, ensuring stable texture generation in varying lighting conditions or unstable viewpoints. Experiments demonstrate MaterialMVP's superior performance in both text-to-texture and image-to-texture generation tasks. + +# Acknowledgment + +This work was supported in part by the National Natural Science Foundation of China (Grant No. 62372480), in part by the Guangdong Basic and Applied Basic Research Foundation (No. 2023A1515012839), in part by 2025 Tencent AI Lab Rhino-Bird Focused Research Program, in part by Huawei (No. HUWEI25IS02 and No. 25260020L082), in part by gift fund from Wiener Intelligence (No. HKWITL25IS01), and in part by HKUST-MetaX Joint Lab Fund (No. METAX24EG01-D). + +# References + +[1] Raphael Bensadoun, Yanir Kleiman, Idan Azuri, Omri Harosh, Andrea Vedaldi, Natalia Neverova, and Oran Gafni. 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a/ICCV/2025/MeasureXpert_ Automatic Anthropometric Measurement Extraction from Two Unregistered, Partial, Posed, and Dressed Body Scans/full.md b/ICCV/2025/MeasureXpert_ Automatic Anthropometric Measurement Extraction from Two Unregistered, Partial, Posed, and Dressed Body Scans/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d3bedfcac825d5e803fe57878ecc51edcfbc87b6 --- /dev/null +++ b/ICCV/2025/MeasureXpert_ Automatic Anthropometric Measurement Extraction from Two Unregistered, Partial, Posed, and Dressed Body Scans/full.md @@ -0,0 +1,323 @@ +# MeasureXpert: Automatic Anthropometric Measurement Extraction from Two Unregistered, Partial, Posed, and Dressed Body Scans + +Ran Zhao $^{1}$ Xinxin Dai $^{1}$ $^{1}$ Vrije Universiteit Brussel + +Pengpeng Hu $^{2*}$ Vasile Palade $^{3}$ $^{2}$ The University of Manchester + +Adrian Munteanu1 +3Coxentry University + +# Abstract + +While automatic anthropometric measurement extraction has witnessed growth in recent years, effective, non-contact, and precise measurement methods for dressed humans in arbitrary poses are still lacking, limiting the widespread application of this technology. The occlusion caused by clothing and the adverse influence of posture on body shape significantly increase the complexity of this task. Additionally, current methods often assume the availability of a complete 3D body mesh in a canonical pose (e.g., "A" or "T" pose), which is not always the case in practice. To address these challenges, we propose MeasureXpert, a novel learning-based model that requires only two unregistered, partial, and dressed body scans as input, and accommodates entirely independent and arbitrary poses for each scan. MeasureXpert computes a comprehensive representation of the naked body shape by synergistically fusing features from the front- and back-view partial point clouds. The comprehensive representation obtained is mapped onto a 3D undressed body shape space, assuming a canonical posture and incorporating predefined measurement landmarks. A point-based offset optimization is also developed to refine the reconstructed complete body shape, enabling accurate regression of measurement values. To train the proposed model, a new large-scale dataset, consisting of 300K samples, was synthesized. The proposed model was validated using two publicly available real-world datasets and was compared with different relevant methods. Extensive experimental results demonstrate that MeasureXpert achieves superior performance compared to the reference methods. The code and dataset are available at: MeasureXpertProject. + +# 1. Introduction + +Accurate body measurement values are essential in various fields such as personalized medicine [42, 50], sports assessment [10, 40], and bespoke clothing design [43], to name a few. Traditionally, the extraction of anthropometric values + +is performed by technical experts, such as doctors or tailors, who use measuring tools to make contact measurements on a naked or tight-fitting human body in canonical posture [36]. However, this method is costly, time-consuming, and highly dependent on expert's skill. + +With advances in computer vision, non-contact measurement techniques are increasingly developed for automatic and precise anthropometric measurement. Current vision-based methods fall into two categories: image-based [24, 32, 48] and 3D model-based approaches [13, 28, 29, 52, 55]. Image-based methods use single [24], multiple RGB images [48], or video sequences [32] to define measurement landmarks and extract body dimensions. These methods are accessible, cost-effective, and convenient, making them ideal for consumer applications such as virtual fitting rooms, fitness tracking, and basic health assessments. However, 2D-based approaches face several limitations: (i) Lack of inherent 3D information: while multi-view images improve depth estimation, they increase computational complexity and require robust algorithms for large-scale data processing; (ii) Environmental sensitivity: performance is affected by lighting conditions, camera resolution, and lens distortion [62]; (iii) Clothing interference: loose or thick garments obscure body contours, leading to inaccurate measurements. Due to these limitations, image-based methods are unsuitable for applications requiring high precision, such as bespoke clothing design, custom prosthetics, and ergonomic equipment development. + +3D scans provide precise geometric information, enabling more accurate and intuitive anthropometric measurements. However, existing scan-based methods typically require a complete 3D body scan with the subject undressed or minimally clothed in a canonical standing posture (e.g., A-pose or T-pose) [13, 52], which is often impractical. Additionally, these methods are sensitive to scan impairments, such as noise and missing regions [39]. The introduction of parametric human models, such as SCAPE [1] and SMPL [37], has led to an alternative approach: fitting parametric models to raw body scans in a canonical posture instead of measuring the subject directly. This approach offers a more efficient and scalable solution. However, parametric + +model fitting is inherently complex, computationally expensive, and sensitive to initialization and noise. Recent efforts have focused on refining parametric human models to enhance fitting efficiency and reduce discrepancies between real and modeled human bodies by incorporating various input signals. For instance, some methods regress shape and pose parameters from RGB images [12, 55], relying on 2D key points or silhouette detection to estimate body shape. However, this approach suffers from scale ambiguity, an inherent limitation of 2D images. While multi-view images [47, 54] help mitigate this issue, they introduce higher computational and data processing complexity. With the advancement of commodity depth cameras, researchers have increasingly focused on fitting parametric body models to complete or partial 3D point clouds [28, 29]. However, obtaining a complete body scan from a single depth camera is often infeasible, and fitting a parametric model to a single partial scan remains challenging and less accurate. + +To overcome the above limitations, we develop a novel method for precisely measuring the human body using only two partial body scans. Our proposed algorithm offers robust operability as it is insensitive to the pose and pose variations between the two partial scans. Additionally, we allow users to wear loose clothing and do not require prior registration of the partial scans. The proposed algorithm has the potential to advance the field of body scanning and analysis, providing significant advantages in terms of cost-effectiveness and user convenience. The main contributions of this paper are: + +- We propose MeasureXpert, which, to the best of our knowledge, is the first deep learning-based measurement method that accurately measures the human body using solely two partial scans from the front and back of a clothed individual, even when the postures differ between views. + +- MeasureXpert, in addition to providing precise body measurements, offers a novel approach to the estimation of body shape and posture. This dual reconstruction capability could enhance the framework's utility for detailed body morphology analysis and applications sensitive to pose variations. + +- A novel synthetic dataset consisting of 300k data entries, with equal representation of males and females (150k each). Each entry includes three unclothed body meshes for the same subject: one T-posed, and two arbitrary posed bodies, two dressed bodies corresponding to the unclothed two posed bodies with their front and back view partial scans, and measurement landmarks and values on the T-posed body. + +- A comprehensive evaluation of the proposed methods, utilizing partial scans from open-access real-world datasets demonstrates that MeasureXpert has the capability to handle unclothed, clothed, and unseen clothing + +styles bodies, enabling it to handle various body measurement tasks efficiently. + +# 2. Related Works + +# 2.1. Vision-based anthropometric measurement + +Non-contact anthropometric measurements can be obtained via image-based or 3D scan-based methods, each addressing specific challenges. Image-based methods exploit the accessibility of images for convenience and cost-effectiveness but usually face scalability issues due to the lack of depth information. To mitigate this, methods like [24] use a frontal image of a body along with height and weight to improve measurements via neural networks. Alternatively, methods such as [2, 14, 17, 41] require both front and side images, imposing constraints on camera pose, body pose, and clothing to estimate 3D information. Enhancements include additional images [32] or personal data like sex, height, and weight [14] to improve accuracy. Despite these efforts, precision remains limited, making them suitable for applications where ease of use outweighs exactness. Conversely, 3D scan-based methods offer higher accuracy by analyzing the 3D human body geometry. Early approaches utilized expensive, bulky scanners [13] requiring minimal clothing and standard standing poses, extracting measurements manually [38] or automatically [9, 39, 60, 68]. Modern methods employ low-cost sensors and template fitting to reconstruct shapes from incomplete [29] or low-quality data [30, 56], yet still need specific poses and struggle with data quality issues. More recent studies allow measuring dressed bodies [44, 61, 67], but often require standard scanning postures [61] and assistive devices [44], or can only output specific measurements, such as waist-to-hip ratios [67]. In summary, while image-based methods prioritize accessibility, they have limitations in accuracy, whereas 3D methods improve accuracy and demand more resources and controlled conditions. + +# 2.2. Estimation of body shape under clothing + +Unclothed body shape estimation mainly relies on parametric human models, such as SCAPE [1] and SMPL [37]. Depending on the type of input, techniques of estimation of body shape under clothing can be classified into two categories: image-based approach and 3D scan-based approach. Early image-based work, such as [19], used the SCAPE model and required manual interaction to identify height and key points. The fully automatic approach, SMPLify [7], is based on the SMPL model and employs DeepCut [46] to predict key points instead of manual labeling, optimizing the SMPL model parameters to fit these predictions. Subsequent image-based methods, such as SMPL-X [45] and SMPL-H [51], all build upon SMPL. Recent algorithms have improved template parameter prediction + +by integrating additional data sources, including 2D key points [5, 31, 35], body segmentation [63], pixel information [64, 65], per-sample variance [15], and semantic attributes [11]. However, traditional PCA-derived shape parameters remain limited in capturing local shape variations. ShapeBoost [4] addresses this issue by redefining shape representation through local part parameterization, allowing for more precise shape estimation via parameter regression. Instead of predicting template parameters, some approaches directly regress body mesh vertices [12, 27, 34, 58]. Varol et al. [58] employ a volumetric reconstruction method with voxel-based output, while Jackson et al. [27] extend their face reconstruction network [26] to full-body images. Kolotouros et al. [34] and Chun et al. [12] introduce a standard template and regress 3D vertex coordinates to obtain a deformed mesh. NLF [53] builds on the neural localization field method, learning continuous point locators within the human body volume to estimate 3D human pose and shape from a single RGB image. 3D-based approaches typically estimate the gap between body skin and clothing before deforming a template or a parametric body model to fit the skin surface [3]. These methods are formulated as a complex optimization problem, which is computationally expensive and sensitive to correspondences. To accelerate body fitting, deep learning-based methods [20, 21] have been proposed by regression of the vertices of SMPL models to obtain body under clothes. ArtEq [16] simplifies template fitting by approximating human body deformation as part-based, articulated, rigid $SE(3)$ transformations and leveraging $SE(3)$ invariant properties to regress SMPL shape and posture parameters from point clouds. GALA [33], on the other hand, adopts a different strategy by progressively removing clothing layers to isolate the underlying human body shape. Despite these advancements, existing methods usually still require a complete body scan as input and often struggle with shape accuracy, limiting their practicality in scenarios where only partial scans are available. + +# 3. Method + +# 3.1. Problem statement + +Similar to the definitions in SMPL [37], we define the body shape and pose features as follows: + +Definition 1. Unadulterated Shape Vector (USV) $\mathcal{F}_s\in$ $\mathbb{R}^n$ represents the human body shape features in a $n$ dimensional space. This vector encodes the intrinsic geometric properties of a complete human body, which are generally static and define the individual's inherent shape, independent of postures. In contrast, the shape influenced by postures is a pose-conditional shape vector. + +Definition 2. Pose Vector (PV) $\mathcal{F}_p\in \mathbb{R}^n$ represents pose information specific to one posed human body. This vector + +captures dynamic factors that affect the appearance of the body shape based on postures. + +Besides, we also define a pose-independent function to remove the pose influence from the pose-conditional shape vector to extract USV. + +Definition 3. Pose-Independent Function (PIF) $\mathcal{G}$ : $\mathbb{R}^n\to \mathbb{R}_{\geq 0}^n$ , which maps the PV to a non-negative vector, dubbed Pose-Independent Vector (PIV), representing the influence of posture on the shape. + +Our task is described below. The goal is to predict an accurate unclothed body in a canonical posture with precise measurements from two partial point clouds. These point clouds are captured from the front and back views of a clothed individual in arbitrary postures using a single depth camera, ensuring a low-cost, flexible, and user-friendly capture process. + +In this study, we face the key challenge: depth sensor-captured partial point clouds contain only incomplete 3D information, are unordered and discrete, and suffer from occlusions, noise, and missing points due to camera limitations. Additionally, posture variations influence body shape [37], making it difficult to extract reliable shape features. These shape features are pose-conditioned vectors rather than USVs, making accurate USV estimation the core objective of our method. + +The task is defined more formally: Start with two partial point clouds. These two point clouds, containing $M^f$ and $M^b$ points respectively, are captured from the front and back views of an individual wearing the same clothing in either different or identical postures. They are denoted as $S^f = \{s_i^f | i = 1,2,\dots,M^f\}$ and $S^b = \{s_i^b | i = 1,2,\dots,M^b\}$ , respectively. Our goal is to learn four main functions: i) The shared encoder $\mathcal{E}$ (Eq. 1), which uses different parameter sets, $\omega_{\varepsilon}^{f}$ for $S^f$ and $\omega_{\varepsilon}^{b}$ for $S^b$ , + +$$ +\mathcal {E} \left(\mathcal {S} ^ {i} \mid \omega_ {\mathcal {E}} ^ {i}\right) = \mathcal {F} ^ {i} = \left[ \mathcal {F} _ {s} ^ {i}, \mathcal {F} _ {p} ^ {i} \right], (i \in \{f, b \}) \tag {1} +$$ + +to extract global features from $S^f$ and $S^b$ . Specifically, from $S^f$ , we aim to obtain the pose-conditional shape vector $\mathcal{F}_s^f$ and the PV $\mathcal{F}_p^f$ , collectively forming the global feature set $\mathcal{F}^f$ . Similarly, from $S^b$ , we aim to extract the pose-conditional shape vector $\mathcal{F}_s^b$ and PV $\mathcal{F}_p^b$ , collectively forming $\mathcal{F}^b$ . ii) Determine the USV extraction function $\mathcal{C}$ (Eq. 2) + +$$ +\mathcal {C} \left(\mathcal {F} ^ {f}, \mathcal {F} ^ {b}\right) = \mathcal {F} _ {s} \tag {2} +$$ + +to combine vectors $\mathcal{F}^f$ and $\mathcal{F}^b$ , and extract USV $\mathcal{F}_s$ ; iii) Determine the decoder function $\mathcal{D}$ (Eq. 3) + +$$ +\mathcal {D}: \mathbb {R} ^ {n} \rightarrow \mathbb {R} ^ {3 \times M} \tag {3} +$$ + +to recover the unclothed body with measurement landmarks from $n$ -dimensional vector USV. The landmarks consist of $n'$ points, divided into $m'$ subsets, each representing a distinct measurement level; iv) The last regression function $\Phi$ + +![](images/75429f9e0fe991fdb7ac35e4cc74e9b66a6457e2cf720062102e53883c5794ef.jpg) +Figure 1. MeasureXpert Pipeline: MeasureXpert processes point cloud pairs of an individual in the same clothing but different postures. It uses self-supervised learning to extract shape features, integrates them to predict posed and T-posed bodies with landmarks. Optimization refines the T-posed body, and regression extracts body measurements. + +(Eq. 4) maps these $n'$ points to $m'$ output values corresponding to these measurement levels. + +$$ +\Phi : \mathbb {R} ^ {3 \times n ^ {\prime}} \rightarrow \mathbb {R} ^ {m ^ {\prime}} \tag {4} +$$ + +# 3.2. Proposed Neural Network Architecture + +MeasureXpert comprises two principal components: i) TrioNet: Two partial point clouds of a human body in three postures. Specifically, it takes two partial point clouds as input and outputs three body meshes for the same subject, each in a distinct posture: front, back, and canonical; ii) OR-Net: Optimization and Regression Network. Taking the T-posed body with landmarks from TrioNet as input, this component is dedicated to optimizing the body shape and extracting anthropometric values. It utilizes an offset learning algorithm in conjunction with the regression technique to refine the T-posed model and landmark points, thereby enhancing the reconstruction and improving the body measurement accuracy. Implementation details are also provided in the Appendix Section 6. + +QuadNet. QuadNet is a novel neural network architecture that integrates two partial point clouds from a dressed individual to generate three body meshes of the same person in different poses. Specifically, it produces two meshes corresponding to the poses of the partial point clouds and one mesh in the canonical "T" pose. + +TrioNet's architecture is inspired by PoseNormNet [66] and employs two multilayer perceptrons (MLPs), each coupled with a max pooling layer, to extract global features from the front- and back-view point clouds. These MLPs learn a shared encoder function (Eq. 1) that outputs the global features $\mathcal{F}^f$ and $\mathcal{F}^b$ for the front- and back-view, respectively. + +Diverging from PoseNormNet [66], TrioNet adopts a more sophisticated decoder structure comprising three branches: + +the front-input branch, the back-input branch, and the shape branch. + +For the two input branches (the front-input branch and the back-input branch), instead of the "one-to-one" single decoder employed by PoseNormNet, we have developed a "one-to-N" multi-decoder architecture to simplify the learning complexity and enhance efficiency. Specifically, inspired by the work [23], we have partitioned the human body into six segments: the torso, the head, the left arm and hand, the right arm and hand, the left leg and foot, and the right leg and foot. The extracted global feature is fed into six sub-decoders. Each sub-decoder consists of three fully connected layers with an identical structure but unique learned weights, designed to output the 3D coordinates of the corresponding body segment. By decoding body segments separately, the model can capture finer details and variations in each segment, enhancing its ability to reconstruct complex human poses accurately. + +In the shape branch, the decoder aims to learn the mappings specified in Eq. 2 and Eq. 3. Specifically, Eq. 2 merged USV $\mathcal{F}_s$ from the global features $\mathcal{F}^f$ and $\mathcal{F}^b$ through a procedure outlined in Algorithm 1. Eq. 3 is learned by three fully connected layers to map $\mathcal{F}_s$ to the coordinates of the body points with landmarks. Therefore, the output for the shape branch consists of two main components: 21 groups of coarse landmarks on different measurement levels (due to page limitations, these definitions are provided in the Appendix), denoted as $\mathcal{L}mk_c = \{l_i'\}_{i=1}^{21}$ and a coarse T-posed mesh with a vertex set $\mathcal{T}_c = \{v_1', v_2', \dots, v_{6890}'\}$ , $v_i' \in \mathbb{R}^3$ . + +OR-Net. Despite TrioNet's capability to extract USV from two partial point clouds to predict an unclothed, complete body mesh in a "T" pose, its performance can be inconsistent due to the complexity of shape information + +![](images/541e8ac72e2d829c3ccebe28ed6931dee635fa05e9a7a609be13891f6c31b6ba.jpg) +Figure 2. Synthetic Data Generation Process. Yellow sections show the front-view process, and green sections the back-view. The rectangle in the right corner displays 21 landmarks, illustrating a convex hull at one level. Each level's measurement is the perimeter of its convex hull. + +affected by the postures in two partial scans and clothes occlusions. To overcome this limitation, we have developed an offset learning with regression optimization called the Offset with a Regression neural Network (OR-Net). + +The OR-Net consists of two components. The first component extracts the global feature of the point set obtained from TrioNet. This point set, denoted as $\mathcal{T}\mathcal{L}_c$ , consists of the vertices of coarse T-posed mesh $\mathcal{T}_c$ and coarse landmark points $\mathcal{L}mk_c$ . This global feature is then passed through a sequence of fully connected layers with dimensions of 1024, 1024, and $3\times N$ , where $N$ is the number of points in $\mathcal{T}\mathcal{L}_c$ . The outputs from these layers are reshaped to create offsets, which are then added to corresponding point coordinates in $\mathcal{T}\mathcal{L}_c$ to produce a refined point set $\mathcal{T}\mathcal{L}$ consisting of vertices set $\mathcal{T}$ of refined T-posed mesh $\mathcal{G}$ and landmarks $\mathcal{L}mk$ . These refined landmarks are then fed into the second component, a regression module with encoder and decoder blocks, designed to predict anthropometric measurements $V_{i}$ . Each $V_{i}$ in the set $V$ represents one of the 21 measurement values. + +# Algorithm 1 USV extraction function $\mathcal{C}$ + +Input: Two global features $\mathcal{F}^f$ and $\mathcal{F}^b$ + +Output: USV $\mathcal{F}_s$ + +Split global features into PV $\mathcal{F}_p^i$ and pose-conditional shape features $\mathcal{F}_s^i$ + +$\mathcal{F}_p^i,\mathcal{F}_s^i\gets \mathrm{Split}(\mathcal{F}^i),i\in \{f,b\}$ + +# PIV $\vec{\omega}^i$ extraction by PIF $\mathcal{G}$ with weights $g^{i}$ + +$$ +\vec {\omega} ^ {i} \leftarrow \mathcal {G} \left(\mathcal {F} _ {p} ^ {i} | g ^ {i}\right), i \in \{f, b \} +$$ + +$$ +\mathcal {F} _ {s} \gets \sum_ {i \in \{f, b \}} \frac {\vec {\omega} ^ {i}}{\vec {\omega} ^ {f} + \vec {\omega} ^ {b}} \mathcal {F} _ {s} ^ {i} +$$ + +Loss Functions. We employ the L2 loss (L2) and Chamfer Distance (CD) to supervise point prediction and the L1 loss (L1) to supervise value prediction. Due to page limitations, the formulations in this section can be found in the Appendix Section 6.6. + +For the two input branches with multi-decoder, the effectiveness of this "one-to-N" approach is enhanced by a comprehensive supervision strategy that encompasses local loss $\mathcal{L}_{part}^{i}$ ensures accurate reconstruction of individual body parts via L2 loss between different body segments with their corresponding ground truths, global loss $\mathcal{L}_{global}^{i}$ maintains consistency in the overall body shape via the CD between predicted posed body points and ground-truth points, and the inter-connective loss $\mathcal{L}_{boundary}^{i}$ promotes seamless integration between adjacent body segments via the L2 loss among connected points within two connected body segments. The loss function (Eq. 5) for the one input branch is the sum of all local loss, global loss, and boundary loss. + +$$ +\mathcal {L} _ {p o s e} ^ {i} = \mathcal {L} _ {p a r t} ^ {i} + \mathcal {L} _ {g l o b a l} ^ {i} + \mathcal {L} _ {b o u n d a r y} ^ {i}, i \in \{f, b \}. (5) +$$ + +For the shape branch, the loss function is tailored based on landmarks and T-posed body mesh. For landmarks, we are not concerned with the order of points, so we choose CD, denoted as $\mathcal{L}_{lmk}^{c}$ , to supervise them. However, for mesh, it is essential to maintain the order of vertices. Therefore, we use L2, denoted as $\mathcal{L}_{tpose}^{c}$ , to supervise the predicted vertices. + +In addition, the shape branch incorporates a shape loss function that is crucial for accurately modeling human shapes, which is defined as the L2 loss between two shape features extracted from front- and back-views (Eq. 6). This loss function helps to divide the global features into two distinct components: a pose-conditional shape vector and a PV. This separation allows the network to focus on aligning similar shapes, effectively differentiating them from variations in pose. + +$$ +\mathcal {L} _ {s h a p e} = \left\| \mathcal {F} _ {s} ^ {f} - \mathcal {F} _ {s} ^ {b} \right\| ^ {2} \tag {6} +$$ + +Therefore, the loss function for the shape branch is: + +$$ +\mathcal {L} _ {t} ^ {c} = \mathcal {L} _ {l m k} ^ {c} + \mathcal {L} _ {t p o s e} ^ {c} + \mathcal {L} _ {s h a p e}, \tag {7} +$$ + +and the total loss function for TrioNet is: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {p o s e}} ^ {f} + \mathcal {L} _ {\text {p o s e}} ^ {b} + \mathcal {L} _ {t} ^ {c}. \tag {8} +$$ + +The OR-Net is trained by supervising both point positions, as well as the measurement values. Specifically, the loss functions for the refined landmarks and T-posed mesh are defined as the same as the shape branch, which uses CD, denoted as $\mathcal{L}_{lmk}$ , to supervise landmarks and L2, denoted as $\mathcal{L}_{tpose}$ , to constrain mesh vertices. For measurement value prediction, we use L1, denoted as $\mathcal{L}_{value}$ , to supervise 1D data learning. Therefore, the total loss function used to train the OR-Net is: + +$$ +\mathcal {L} _ {o p} = \mathcal {L} _ {\text {v a l u e}} + \mathcal {L} _ {\text {l m k}} + \mathcal {L} _ {\text {t p o s e}}. \tag {9} +$$ + +This combined supervision ensures that the OR-Net not only refines the mesh geometry effectively but also produces reliable measurement regression predictions, thereby enhancing the overall performance of the model in tasks of body reconstruction and anthropometric values prediction. + +# 4. Experiments + +In this section, we outline our experiment configurations and compare our method with state-of-the-art methods. We also conduct ablation studies to assess our architecture's design. + +# 4.1. Environment setting + +Implementation details. The training is operated on a desktop PC with Intel(R) Core i9-9900 CPU @ 3.10GHz × 16 as the processor, GeForce RTX 2080 Ti/PCIe/SSE2 as graphics, 62.7 GiB memory, and Ubuntu 16.04 LTS as the operating system. All training and tests are operated under CUDA 9.0, cudnn 7.0.5, python 3.6, and Tensorflow-GPU 1.0.5. The proposed MeasureXpert was trained by the Adam optimizer with an initial learning rate of 0.0001 for $300K$ iterations and a batch size of 16. The learning rate was decayed by 0.7 every $50K$ iterations. The training time is 34 hours in total. During testing, the average processing time for input point clouds, with points ranging from several thousand to tens of thousands, was about 2 seconds. + +Datasets. To train, validate, and test the proposed model, we require a large-scale dataset containing front- and back-view partial scans of a subject in two distinct postures (front and back), along with corresponding posed SMPL models. Here, "corresponding" means the SMPL models are perfectly aligned with the partial scans in position, pose, and shape. Additionally, we need the T-posed SMPL model, which shares the same shape as the subject in the T-pose, along with anthropometric measurement values. Since no existing dataset meets these criteria, we develop the synthetic dataset BWM (Bodies With Measurements). Figure 2 illustrates the BWM synthesis process, with Section 7.1 in the Appendix detailing the methodology. + +We also utilize two open-access real-world datasets, FAUST and 4D-Dress, extending them for comparisons with state-of-the-art methods. Each sample in the extended datasets includes three unclothed body models: two in different poses and one in a canonical pose, along with two clothed body meshes captured from front and back views, corresponding to the posed unclothed bodies. We employ the RealPartialScan [22] to extract front and back partial scans directly from complete real-world meshes, ensuring the use of real-world data instead of synthetic scans. Additionally, it provides measurement landmarks with ground-truth values, maintaining the same data structure as BWM. Further details on dataset extension are provided in + +![](images/e1726eccf07223b74f07e49e7ad700174bfc65f454e78ef6f0699677536ddefa.jpg) +Figure 3. We compare our method against reference approaches using FAUST and 4D-Dress datasets, presenting five key cases, arranged from top to bottom: (i) unclothed body, same pose; (ii) unclothed body, different poses; (iii) clothed body, same pose (single-layer); (iv) clothed body, different poses (loose coat); (v) body, varied poses and clothes. + +Section 7.2 in the Appendix. + +Evaluation Metrics. Since measurement values are 1D data, we assess prediction accuracy using absolute error between predicted and ground-truth values. Additionally, in ablation studies, we employ CD to evaluate the accuracy of the predicted by-products: posed and T-posed body meshes. + +# 4.2. Results + +In this section, we compared the proposed method against current state-of-the-art methodologies via the extended FAUST [6] and 4D-Dress [59] datasets mentioned above and described in the Appendix. These include image-based methods such as POCO [15], NLF [53], and PyMAF-X [65], which take a single image as input and output the shape and pose parameters of the SMPL model, as well as point cloud-based methods, including ArtEq [16] and 3DBodyNet [21]. ArtEq requires a complete human point cloud to predict SMPL parameters, while 3DBodyNet, similar to MeasureXpert, processes two partial, dressed human point clouds from the front and back views in arbitrary postures, directly outputting the unposed (T-posed) SMPL model. For readers seeking a deeper understanding of our work, the Appendix includes additional method comparisons as well as extended quantitative and qualitative analyses. + +To systematically evaluate MeasureXpert's measurement extraction performance, we design experiments in three phases: unclothed bodies, clothed bodies, and unseen clothing styles, each assessing a specific aspect of the model's capability. To visualize error distributions across measurement dimensions, we use boxplots (Figure 4), which effectively highlight discreteness, stability, and outliers, making them ideal for large-scale comparative analysis. + +![](images/29d260fde3e83e7720fd92c9aad27270cec85ec275f292eb07fc8bed4b1d8f0b.jpg) +Measurement errors On FAUST(unclothing) Across Different Methods + +![](images/307ea9600c4c6f5b999d1abea3309cfeca5cb21d4fd911310503230392e50202.jpg) +Measurement errors On 4D-Dress(same clothing) Across Different Methods + +![](images/5478e3d4f8218f1a5e0f09f46a464701f6002b696ad726b13881f6ff74c43a60.jpg) +Measurement errors On 4D-Dress(unseen styles) Across Different Methods +Figure 4. This figure shows box plots of absolute errors (in cm) for body measurements on the FAUST and 4D-Dress datasets across different methods: POCO [15], NLF [53], PyMAF-X [65], ArtEq [16] and 3DBodyNet [21]. + +Unclothed bodies. This experiment evaluates the proposed method on unclothed human body point clouds captured from front and back views in identical and varying postures. Using the FAUST dataset, which provides complete human meshes in multiple postures, we assess its ability to generalize to unseen unclothed body configurations. The first plot in Figure 4 presents measurement error distributions for unclothed body inputs. While our method does not always achieve the lowest absolute error, it consistently maintains a lower overall error across all dimensions. For torso measurements (bust, underbust, waist, and hip), it achieves a mean error of $2.44\mathrm{cm}$ , significantly lower than ArtEq $(4.20\mathrm{cm})$ . Additionally, it demonstrates superior consistency, with a standard deviation of $1.44\mathrm{cm}$ , outperforming 3DBodyNet $(3.01\mathrm{cm})$ , the second most stable method. For limb measurements, our method achieves the lowest standard deviation $(0.52\mathrm{cm})$ , surpassing 3DBodyNet $(0.85\mathrm{cm})$ , confirming higher stability. Although its mean error $(1.04\mathrm{cm})$ is slightly higher than NLF $(0.87\mathrm{cm})$ , the best-performing image-based method, it maintains the highest overall stability while ensuring high measurement accuracy across both body and limb dimensions. + +Clothed bodies. In this phase, we evaluate the method on point clouds of clothed human bodies captured from front and back views, using the 4D-Dress dataset, which includes clothed subjects in both identical and varied poses. This evaluation tests the model's accuracy and reliability in conditions that closely resemble both the synthetic dataset used for training and real-world scenarios involving clothing. The middle plot in Figure 4 presents the comparisons of MeasureXpert on clothed bodies. Unlike its performance on unclothed bodies, where it did not always achieve the lowest absolute error, our method demonstrates significantly higher accuracy and stability in clothed body measurements. This advantage is expected, as the model is trained on clothed subjects, enabling better generalization to real-world conditions. Across all dimensions, our approach consistently outperforms existing methods, as evidenced by the box plots, which exhibit the shortest interquartile ranges and the lowest overall error, indicating superior measurement consistency. For torso measurements, our method achieves a mean absolute error of $0.98\text{cm}$ with a standard deviation of $0.62\text{cm}$ , significantly improving upon the second-best method, POCO, which records a mean error of $4.94\text{cm}$ and a standard deviation of $1.92\text{cm}$ . For limb measurements, our approach attains an exceptionally low mean error of $0.49\text{cm}$ with a standard deviation of $0.3\text{cm}$ , outperforming all competing methods. It reduces the mean error compared to the second-best method, POCO (mean = $1.66\text{cm}$ ), while exhibiting greater measurement stability than ArtEq, the second most stable method (STD = $0.67\text{cm}$ ). + +Unseen clothing styles bodies. In this phase, we evaluate point clouds of human bodies wearing unseen clothing styles, rendered from the 4D-Dress dataset in front and back views. As these clothing styles are not included in the training set, this experiment assesses the model's ability to generalize to unseen garment configurations. When front and back scans are captured at different times, variations in clothing introduce additional challenges for accurate anthropometric measurement. Despite these complexities, the last figure in Figure 4 demonstrates that our method consistently maintains high measurement accuracy and robustness, outperforming all competing approaches even under varying clothing conditions. For torso measurements, our method achieves a mean absolute error of $1.43\mathrm{cm}$ with a standard deviation of $0.68\mathrm{cm}$ , significantly surpassing all other methods. The second-best approach, POCO, reports a much higher mean error of $4.61\mathrm{cm}$ with a standard deviation of $2.48\mathrm{cm}$ . For limb measurements, our method attains an exceptionally low mean error of $0.68\mathrm{cm}$ with a standard deviation of $0.31\mathrm{cm}$ , again outperforming all competing techniques. The second-lowest mean error is + +![](images/cc128695e9bfc51c2aa5f99577d9a005e709cf6326c1078d7644fe454cae7aca.jpg) +Figure 5. Ablation studies results. From left to right is: i) the grouped bar charts (display the average values for each method) with error bars (represent the variability in the results for each method) to show the performance on T-posed, front-posed and back-posed meshes prediction across TSD, TNS and TrioNet; ii) the boxplots to establish absolute errors of anthropometric values prediction within MeasureXpert and TrioNet; and iii) the boxplots to showcase the vertex-to-vertex errors across MeasureXpert and TrioNet. + +![](images/446c97911004aa9bca1777dc8249fc826005f289186a923880292b2a5dcc4418.jpg) + +![](images/edb297b5953f208ebeb6ff8421f724f8e5b81dcf83c1e0489b8eea492a946237.jpg) + +observed in POCO (1.51cm), while ArtEq demonstrates the second-highest stability with the lowest standard deviation (0.63cm). These results confirm that even with inconsistent clothing between front and back scans, our method remains the most accurate and stable across all measurement categories. This robustness highlights the adaptability of our approach, making it particularly well-suited for real-world applications where scan conditions may vary. + +Beyond the key measurement error comparison, Figure. 3 also illustrates the performance of the T-posed mesh as a byproduct under different conditions. The color mapping visually represents the error distribution across the entire body, with lower errors appearing in blue. Our method demonstrates superior stability and accuracy in T-posed mesh prediction, further outperforming other approaches in preserving body shape consistency. + +Remarkably, MeasureXpert demonstrates comparable performance on samples with different types of clothing (unseen styles) to those with identical clothing. This consistency is attributed to our innovative design, which effectively extracts shape-related information from the input point cloud while condensing other extraneous information into posed branches. This unique design endows MeasureXpert with the capability to handle unseen clothing styles bodies, allowing it to accurately predict body measurements and shapes without prior exposure to specific clothing variations. By isolating and processing shape-related features independently of other factors, MeasureXpert maintains high accuracy and stability in its predictions. This capability is especially valuable in scenarios where the input data vary significantly in terms of clothing and posture, ensuring reliable performance and precise measurement outputs. + +# 4.3. Ablation study + +To validate the fundamental design of the MeasureXpert, we conducted comprehensive ablation studies experiments based on 450 unseen samples from our synthetic dataset BWM. In order to assess the impact of multi-decoder and shape loss, we design two more TrioNet variants: TrioNet with Single Decoder in two input branches (TSD) and TNS + +TrioNet with No Shape loss in the shape branch (TNS). We further present results comparing TrioNet and MeasureXpert to prove the necessity of OR-Net. All the results are shown in Figure 5. The first plot in Figure 5 shows that without shape loss, the CD errors for the three mesh predictions are high with significant variability. Adding shape loss greatly improves mesh prediction performance. Moreover, the multi-decoder (TrioNet) outperforms the single-decoder (TSD) in predicting two posed bodies, resulting in more accurate T-pose mesh predictions. Additionally, another two figures show that the OR-Net further enhances the performance of value and T-pose body predictions based on TrioNet. + +# 5. Conclusion + +This paper presented MeasureXpert, the first deep learning-based measurement method that accurately measures the human body using just two partial scans, from the front and the back of a clothed individual in various postures. The two partial point scans do not need to be registered and can contain some occlusion. Our framework introduces a novel self-supervised loss function to extract shape information while mitigating the impact of posture to enhance accuracy. We also have proposed a novel large-scale synthetic dataset with diverse human bodies, including complete meshes and partial scans with ground truth measurements. Experimental results demonstrate that our method surpasses existing techniques in terms of the accuracy of both shape estimation and anthropometric measurement extraction. + +However, MeasureXpert is not without limitations. The proposed training dataset does not include representations of hair, such as Afro hairstyles, which could affect performance with such inputs. Additionally, large occlusion leads to loss of information on large body parts, which will influence our poses and shape estimation. Future work will aim to address these limitations by incorporating additional more varied data, including different hairstyles, in order to enhance robustness. 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However, recent studies on rotation-equivariant aerial object detection remain scarce. Most detectors rely on data augmentation to enable models to learn approximately rotation-equivariant features. A few detectors have constructed rotation-equivariant networks, but due to the breaking of strict rotation equivariance by typical downsampling processes, these networks only achieve approximately rotation-equivariant backbones. Whether strict rotation equivariance is necessary for aerial image object detection remains an open question. In this paper, we implement a strictly rotation-equivariant backbone and neck network with a more advanced network structure and compare it with approximately rotation-equivariant networks to quantitatively measure the impact of rotation equivariance on the performance of aerial image detectors. Additionally, leveraging the inherently grouped nature of rotation-equivariant features, we propose a multi-branch head network that reduces the parameter count while improving detection accuracy. Based on the aforementioned improvements, this study proposes the Multi-branch head rotation-equivariant single-stage Detector (MessDet), which achieves state-of-the-art performance on the challenging aerial image datasets DOTA-v1.0, DOTA-v1.5 and DIOR-R with an exceptionally low parameter count. + +# 1. Introduction + +The primary difference between aerial object detection [3, 7, 65] and general object detection [18, 39, 66] lies in the bird's-eye view perspective of aerial images, which causes objects to appear in arbitrary orientations. If horizontal bounding boxes (commonly used in general object detection) are applied to aerial images, they may encom + +![](images/20a9097e9fff46afc7664022bf35c94000e6e263da0367ed25204910be8a572a.jpg) +Figure 1. Visualization of features extracted by different methods. When the input is rotated, features extracted by conventional CNNs are easily affected, leading to degraded detection performance. In contrast, our MessDet framework includes both approximately rotation-equivariant (Appr. MessDet) and strictly rotation-equivariant (Str. MessDet) variants. While Appr. MessDet reduces rotation error during training, Str. MessDet eliminates such errors entirely, resulting in more robust detection performance. + +pass excessive background and make it difficult to localize the target objects accurately. In recent years, several datasets [27, 33, 42, 50] have been introduced that utilize oriented bounding boxes (OBB) for annotating aerial images, which can more tightly enclose the target objects. However, bounding boxes now include angle information, increasing the data dimensionality from 4 to 5 when this approach is applied, which makes detection more challenging. When objects appear in arbitrary orientations, the detector should produce consistent outputs for classification tasks, regardless of orientation, requiring rotation invariance. In contrast, the detector needs to correctly adjust the output angles, necessitating rotation equivariance for bounding box regression. Most aerial object detectors implicitly learn rotation equivariance by increasing model parameters [12, 37, 44], enhancing data augmentation [5, 6, 14, 21, 51, 56, 57], proposing new bounding box representation methods [19, 24, 28, 45, 54, 55] or introduc + +ing customized loss functions [4, 58, 59, 61]. + +Cohen et al. [8] explicitly implement group-equivariant neural networks using group theory, which is further advanced in subsequent works such as [9, 46]. These developments lead to the creation of rotation-equivariant networks (RE-Nets) that are particularly well-suited for aerial object detection tasks. Some previous studies have applied RE-Nets to aerial object detection. ReDet [20] is the first to adopt a RE-Net as a backbone and neck. FRED [26] combines the anchor-free point-set representation from RepPoints [62] with RE-Nets to achieve a fully rotation-equivariant detector. Both ReDet and FRED achieved state-of-the-art performance at the time and have demonstrated the effectiveness of RE-Nets in aerial object detection. + +However, most object detectors use typical downsampling as a trade-off between computational efficiency and accuracy, performing $2\mathrm{x}$ downsampling with stride-2 convolutional kernels during forward propagation. Additionally, the object detection pipeline often resizes image dimensions to multiples of two to facilitate mapping predicted bounding box coordinates back to the original image. Mohamed et al. [36] has shown that applying stride-2 convolutional kernels to feature maps with even spatial dimensions breaks strict rotation equivariance. Previous research on RE-Nets in aerial object detection has not explored how strict rotation equivariance impacts model performance. For instance, ReDet only achieves approximate rotation equivariance. FRED ensures strict rotation equivariance by padding even-dimensional feature maps with zeros to make them odd-dimensional before downsampling. However, this approach may introduce misalignment issues. + +This study proposes a new downsampling process that avoids single-sided padding. Instead, an additional tuning layer is introduced before the stride-2 downsampling layer to convert even-dimensional feature maps to odd dimensions to ensure strict rotation equivariance (see Fig. 1). Additionally, Edixhoven et al. [16] have shown that approximately rotation-equivariant models may relax strict equivariance constraints during training in image classification tasks. In certain scenarios, both strict and approximate rotation equivariance have their advantages and disadvantages. However, the impact of strict versus approximate rotation equivariance on model performance in aerial detection tasks remains an open question. This study will control the strictness of rotation equivariance by determining whether to include tuning layers in the network, thus comparing the effects of strict and approximate rotation equivariance on model performance. And we track the rotation equivariance error during training of the approximately rotation-equivariant model on the aerial object detection dataset to assess the importance of rotation equivariance. + +Among the state-of-the-art CNN-based object detectors [48, 53] that have emerged in recent years, the channel + +attention mechanism proposed by SENet [25] is a commonly used component. However, applying channel attention mechanisms in RE-Nets can break rotation equivariance. In this study, we implement a rotation-equivariant channel attention mechanism and develop a more advanced backbone and neck network based on RTMDet [35]. Due to the inherent grouping properties of rotation-equivariant features, the proposed model inputs feature maps from different orientation dimensions into separate branches of the head network, which are then combined for output. Thanks to the higher degree of weight sharing in RE-Nets and the multi-branch head network, the model proposed in this paper has an exceptionally low number of parameters. To our knowledge, it is currently the model with the fewest parameters while maintaining state-of-the-art performance. The multi-branch head rotation-equivariant single-stage object detector (MessDet) we propose achieves advanced performance on DOTA-v1.0 [15], DOTA-v1.5 [15] and DIOR-R [27]. + +In summary, the contributions of this study are as follows: + +- A novel downsampling process is proposed and integrated with RE-Nets, enabling control over whether the network exhibits strict or approximate rotation equivariance. +- A rotation-equivariant channel attention mechanism is proposed to enable the implementation of rotation-equivariant backbone and neck networks with more advanced architectures. A multi-branch head network is introduced to make more efficient use of rotation-equivariant features. +- The variation of rotation equivariance error during training is quantitatively analyzed in the aerial detection task, highlighting the importance of rotation equivariance for aerial detection performance. + +# 2. Related Work + +This section briefly reviews the most pertinent studies and methodologies that have shaped the field with the aim of providing a foundation for the contributions of this work. + +# 2.1. Aerial Object Detection + +Due to the potential for objects in aerial images to appear at arbitrary angles, the detector's output must include not only the bounding box position, width, height, and class as in general object detection but also the angle information of the bounding box. This distinction allows research on aerial image object detectors to be roughly divided into the following categories. First, some studies focus on improving network structures or adding specialized modules to enable the model to better learn features related to orientation and enhance rotation equivariance. $\mathbf{R}^3\mathrm{Det}$ [57] and DRN [37] improve feature accuracy by adding feature re + +finement modules. SCRDet [56] and SCRDet++ [60] introduce instance-level denoising modules to reduce interference from cluttered background regions. RoI Transformer [14] transforms the feature regions corresponding to horizontal anchor boxes into those corresponding to oriented boxes. Oriented R-CNN [51] generates OBB with lower computational cost. S $^2$ ANet [21] introduces AlignConv, which shifts convolutional kernels, and constructs a feature alignment network using AlignConv. ReDet [20] is the first to introduce RE-Nets into aerial object detection tasks and improved RoI Align [22] by interpolating along the orientation dimension to align rotation-equivariant features, resulting in RiRoI Align. ARC [38] proposes an adaptive rotation convolutional module that allows filters to rotate for objects at different orientations. FRED [26] re-applies RE-Nets and combines them with point-set representation and deformable convolutions. All of the above studies can be viewed as methods to make networks more robust to rotational changes. In addition, LSKNet [29], PKINet [1], and Strip R-CNN [63] tackle challenges such as background noise and extreme aspect ratios in aerial images by employing large kernel and strip convolutions. This approach significantly reduces the parameter count while greatly enhancing detection performance. + +Other studies use alternative representations for oriented boxes. CenterMap OBB [45] and Oriented RepPoints [28] use point-set representations for oriented boxes. Gliding Vertex [54] represents oriented boxes based on horizontal boxes by regressing four length ratios. CFA [19] uses convex hulls to represent oriented boxes. GWD [58] transforms the box representation into a two-dimensional Gaussian distribution, using Wasserstein Distance as the loss function. KLD [59] is similar to GWD but uses Kullback-Leibler Divergence as the loss function, addressing the issue of scale invariance that GWD lacks. These representations eliminate the need to predict extra rotation angles, preventing training instability caused by drastic regression loss changes when large objects with small angular shifts alter their aspect ratios. Additionally, Cheng et al. [4] add an extra regularization term in the loss function to enforce the model's output features approximately equivariant to changes in image angles. + +Similar to ReDet and FRED, this study aims to explicitly endow the model with rotation equivariance through RE-Nets, rather than enhancing the model's robustness to angular variations by designing additional feature alignment methods or bounding box representation techniques. + +# 2.2. Rotation-equivariant Networks + +Cohen et al. [8] first introduce group-equivariant neural networks and have achieved equivariance for the discrete rotation group. Harmonic Networks [49] achieves 360-degree rotation equivariance by replacing conventional CNN fil + +![](images/be236634f041d87a71d2309813795349b1a9ca5fa0ee177ae141dbac9993699b.jpg) +Figure 2. Rotation-equivariant feature. The upper half illustrates an input image processed by a RE-Net, which generates rotation-equivariant features. In the channel dimension, feature maps are shown in different colors, each representing a different kernel, such as $\mathrm{K}_1$ (Kernel 1). The RE-Net applies $\mathrm{K}_1$ at multiple orientations (four orientations are shown for illustration) and performs convolutions with the input feature maps to obtain different output feature maps, such as $\mathrm{F}_1$ and $\mathrm{F}_2$ . The lower half illustrates the resulting feature map when the input image is first rotated $90^\circ$ clockwise before being processed by the RE-Net. The convolutional kernels and their orientations remain unchanged, but $\mathrm{F}_1$ shifts in the channel dimension and rotates $90^\circ$ clockwise in the spatial dimension. + +ters with circular harmonics. Subsequent works [9, 47] achieve better performance with convolutional kernels having fewer parameters. Spherical CNNs [10] accelerates the group-equivariant convolution process using generalized fast Fourier transform, while E2CNN [46] extends group-equivariant convolutional neural networks to the broader Euclidean group $\mathrm{E}(2)$ and experimentally demonstrate the performance advantages of $\mathrm{E}(2)$ convolutional kernels on multiple classification datasets. ReDet [20] is the first to apply RE-Nets to aerial object detection tasks, and FRED [26] implements a fully rotation-equivariant network, both achieving state-of-the-art performance at the time, highlighting the effectiveness of RE-Nets in aerial object detection. + +# 3. Preliminaries + +This section introduces concepts related to rotation equivariance in this study. + +# 3.1. Rotation Equivariance + +Let the signal be $x$ , and after applying a certain transformation, it becomes $Tx$ . If the output when $Tx$ is input into the + +network $\Phi$ should be the same as the output when $x$ is input directly into the network, after applying a certain transformation $T^{\prime}$ , that is, + +$$ +\Phi (T x) = T ^ {\prime} \Phi (x), \tag {1} +$$ + +the network $\Phi$ is equivariant to the transformation $T$ where $T$ and $T'$ do not need to be the same. In rotation-equivariant convolutional neural networks, $T$ is defined as a transformation on the group $G$ . If $T' = 1$ , the network $\Phi$ is said to be invariant to the transformation $T$ , so invariance is a special case of equivariance. Ordinary convolutional neural networks exhibit equivariance to translation but not to rotation [8]. Rotation-equivariant convolutional neural networks (hereafter referred to as RE-Nets) achieve rotation equivariance by constructing cyclic groups, as shown in Fig. 2. + +In Fig. 2, it can be observed that when the input image is rotated, the feature maps simultaneously shift within the cyclic group included in the channel dimension and undergo the corresponding rotation in the spatial dimension. So, $\Phi (T_{g}x) = T_{g}^{\prime}\Phi (x)$ , where $g$ represents an element of the group $G$ . When the input is a rotation-equivariant feature, the convolutional kernel's rotation involves both spatial rotations and translations within the cyclic group in the channel dimension. + +# 3.2. Breaking Rotation Equivariance + +In object detection tasks, it is common practice to repeatedly perform downsampling by a factor of 2, such as achieving $32 \times$ downsampling, to provide the network with a larger receptive field. Additionally, when mapping a certain region of the feature map back to the original image or converting coordinates on the feature map to original image coordinates, the image is often resized to a size that is a multiple of two to ensure feature alignment and precise boundary box localization. A typical downsampling method involves using a convolutional kernel with a stride of 2 on the feature map of even dimensions. However, Mohamed et al. [36] points out that doing this can result in different sampling points for the convolutional kernel before and after rotation, which leads to breaking the rotation equivariance. A specific example can be found in Sec. 7 of the supplementary material. + +In classification tasks, Edixhoven et al. [16] experimentally demonstrated that for models that break rotation equivariance, the rotation equivariance error of shallow convolutional layers gradually decreases during the training process, resulting in approximate rotation equivariance. In some cases, the rotation equivariance error of deeper convolutional layers may even increase during training. Romero et al. [41] use $2 \times 2$ pooling for $2 \times$ downsampling to ensure rotation equivariance. However, this approach is not suitable for aerial object detection tasks, as $2 \times 2$ pooling + +![](images/5dd97fd1351af550254edb4b11dbebbbd9fd4270af759d993426423b140d3a00.jpg) +Figure 3. MessDet architecture. "Str." and "Appr." refer to strict rotation equivariance and approximate rotation equivariance, respectively. "N" denotes the number of orientation dimensions. + +causes significant loss of information for small objects. In detection tasks, FRED [26] uses padding to ensure that convolution with a stride of 2 always encounters odd-sized dimensions. However, single-side padding can also lead to misalignment of features, which may reduce the precision of the detector. + +# 4. The Design of MessDet + +This study uses RTMDet [35] as the baseline and reimplements its backbone network CSPNeXt (an improved version of CSPNet [43]) and neck network CSPNeXtPAFPN (an improved version of PANet [32] and FPN [30]), incorporating the E2CNN [46]. Three improvements are made to handle rotation-equivariant features. These lead to the construction of a new aerial image object detector, MessDet. The network structure diagram is shown in Fig. 3. The following subsections will detail the design of MessDet. + +# 4.1. Downsampling While Keeping Rotation Equiv-ariance + +If a RE-Net directly uses a convolutional layer with a stride of 2 for downsampling on feature maps with even spatial dimensions, it will lead to different sampling points. As a result, the rotation equivariance is broken and only achieves approximate rotation equivariance, as shown in Fig. 4a. This study proposes a novel downsampling process that maintains strict rotation equivariance, as shown in Fig. 4b. Assuming that the width and height of the input feature map are the same, $S_{in} = H_{in} = W_{in}$ , the relationship between the spatial dimensions of the output feature map from the convolutional layer and the input feature map is given by: + +$$ +S _ {o u t} = \left\lfloor \frac {S _ {i n} + 2 p - d \cdot (k - 1) - 1}{s} \right\rfloor + 1. \tag {2} +$$ + +In the Formula 2, $S_{out}$ and $S_{in}$ represent the output size and input size, respectively, $p$ is the padding size, $d$ is the dilation (which is set to 1 in this study as dilation convolutions + +![](images/49caa939f84fd15313138355274e5b9cae9258f9ab567d337939d7c13dcf79d2.jpg) +(a) Common downsampling process. + +![](images/bfa2cc5414a3f87f467b65775c896a9184fe24d9bafae9dc647d2c4023d7d31e.jpg) +(b) Strictly rotation-equivariant downsampling process. +Figure 4. Comparison of different downsampling processes, where RE-Conv represents the rotation-equivariant convolutional module. + +are not involved), $k$ is the kernel size, and $s$ is the stride of the convolutional kernel. To maintain strict rotation equivariance, feature maps with even spatial dimensions $2n$ are first passed through a convolutional layer with $k = 4$ , $p = 1$ and $s = 1$ , referred to as the tuning layer. The output size of the tuning layer, calculated by Formula 2, is $2n - 1$ . Then, it is passed through a downsampling convolutional layer with $k = 3$ , $p = 1$ , and $s = 2$ , and the output feature map size is given by: $S_{out} = \left\lfloor ((2n - 1) - 1) / 2 \right\rfloor + 1 = n$ . It can be seen that the inclusion of the tuning layer does not change the output size of the downsampling layer, but it ensures that the input feature map size for the $2x$ downsampling convolutional layer is odd, thereby guaranteeing strict rotation equivariance. + +Users can easily alter whether the model exhibits strict rotation equivariance by adding a tuning layer before the two-times downsampling convolutional layer. + +# 4.2. Rotation-Equivariant Channel Attention and Multi-branch Head + +The channel attention mechanism introduced in SENet [25] is used in many state-of-the-art object detectors [35, 48, 53]. However, directly applying channel attention to rotation-equivariant features would break rotation equivariance. Therefore, this study proposes a rotation-equivariant channel attention (RE-CA) mechanism. Channel attention re-weights convolutional kernels, suppressing unimportant channels and enhancing important ones. The rotation-equivariant convolutional layer generates $N$ convolutional kernels by rotating a single kernel in $N$ orientations. Only $C / N$ convolutional kernels are needed to generate a feature map with $C$ channels. Thus, the RE-CA only needs to produce $C / N$ weights, each of which is repeated $N$ times, to weight the channels of the feature map. This ensures the + +preservation of rotation equivariance. + +For a rotation-equivariant feature $\mathbf{X} \in \mathbb{R}^{C \times H \times W}$ , it can also be written as $\mathbf{X} \in \mathbb{R}_{N}^{\frac{C}{N} \times N \times H \times W}$ . The process of RE-CA is as follows: the spatial information of the $c$ -th channel of + +$$ +\mathbf {X} = [ \mathbf {x} _ {1}, \mathbf {x} _ {2}, \dots , \mathbf {x} _ {C} ] +$$ + +is compressed into a scalar $z_{c}$ using global average pooling, $c \in [1, C]$ , resulting in the vector $\mathbf{z} = [z_{1}, z_{2}, \dots, z_{C}]$ , + +$$ +z _ {c} = \frac {1}{H \times W} \sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} \mathbf {x} _ {c} (i, j). \tag {3} +$$ + +Then, $z$ is passed through a fully connected layer $\mathbf{W} \in \mathbb{R}_{N}^{C \times C}$ and an activation function $\sigma$ , + +$$ +\boldsymbol {s} = \sigma (\mathbf {W} \cdot \boldsymbol {z}), \tag {4} +$$ + +in the weight vector $s \in \mathbb{R}^{\frac{C}{N}}$ . Each element of the weight vector is repeated $N$ times to obtain $s' \in \mathbb{R}^{C}$ , which is then multiplied with $\mathbf{X}$ channel-wise, $\tilde{\mathbf{x}}_c = s'_c \cdot \mathbf{x}_c$ , to obtain the weighted rotation-equivariant feature $\tilde{\mathbf{X}} = [\tilde{\mathbf{x}}_1, \tilde{\mathbf{x}}_2, \dots, \tilde{\mathbf{x}}_C]$ . + +The rotation-equivariant features $\mathbf{X} \in \mathbb{R}^{C \times H \times W}$ consist of feature maps generated by $N$ convolutional kernels in different orientations, inherently exhibiting a grouping property. These features can be rearranged into $N$ groups based on the orientation of the convolutional kernels that generate them, $\mathbf{X} \in \mathbb{R}^{N \times \frac{C}{N} \times H \times W}$ , with each group having $C / N$ channels. These groups are then fed into different branches of the head network, and the $N$ feature maps are concatenated for the final output. Thanks to the multibranch design, the parameter count of the head network is significantly reduced. Further details of rotation-equivariant channel attention and feature rearrangement can be found in Sec. 8 of the supplementary material. + +# 5. Experiments + +# 5.1. Datasets and Experiments Settings + +We evaluate models on DOTA-v1.0 [15, 50], DOTA-v1.5 and DIOR-R [27]. DOTA-v1.0 contains 2,806 aerial images with OBB annotations. The resolutions of these images range from $800 \times 800$ to $4000 \times 4000$ . It includes 188,282 instances across 15 categories: Plane (PL), Baseball diamond (BD), Bridge (BR), Ground track field (GTF), Small vehicle (SV), Large vehicle (LV), Ship (SH), Tennis court (TC), Basketball court (BC), Storage tank (ST), Soccer-ball field (SBF), Roundabout (RA), Harbor (HA), Swimming pool (SP), and Helicopter (HC). The image data in DOTA-v1.5 is the same as that in DOTA-v1.0, but it includes instances smaller than 10 pixels and a new category, Container Crane (CC). DOTA-v1.5 contains 402,089 instances. DIOR-R [27] includes 23,463 aerial images and 192,518 annotations across 20 categories. + +
Method#P↓mAP↑PLBDBRGTFSVLVSHTCBCSTSBFRAHASPHC
Two-stage
CenterMap[45]41.1M71.5989.0280.5649.4161.9877.9974.1983.7489.4478.0183.5247.6465.9363.6867.0761.59
SCRDet[56]41.9M72.6189.9880.6552.0968.3668.3660.3272.4190.8587.9486.8665.0266.6866.2568.2465.21
RoI Trans.[14]55.1M74.0589.0177.4851.6472.0774.4377.5587.7690.8179.7185.2758.3664.1176.5071.9954.06
FR-Est[17]-74.2089.6381.1750.4470.1973.5277.9886.4490.8284.1383.5660.6466.5970.5966.7260.55
G. Vertex[54]41.1M75.0289.6485.0052.2677.3473.0173.1486.8290.7479.0286.8159.5570.9172.9470.8657.32
O-RCNN[51]41.1M75.8789.4682.1254.7870.8678.9383.0088.2090.9087.5084.6863.9767.6974.9468.8452.28
ReDet[20]31.6M76.2588.7982.6453.9774.0078.1384.0688.0490.8987.7885.7561.7660.3975.9668.0763.59
ARC[38]74.4M77.3589.4082.4855.3373.8879.3784.0588.0690.9086.4484.8363.6370.3274.2971.9165.43
LSKNet[29]31.0M77.4989.6685.5257.7275.7074.9578.6988.2490.8886.7986.3866.9263.7777.7774.4764.82
PKINet[1]30.8M78.3989.7284.2055.8177.6380.2584.4588.1290.8887.5786.0766.8670.2377.4773.6262.94
Single-stage
R³Det[57]41.9M69.7089.0075.6046.6467.0976.1873.4079.0290.8878.6284.8859.0061.1663.6562.3937.94
DRN[37]-70.7088.9180.2243.5263.3573.4870.6984.9490.1483.8584.1150.1258.4167.6268.6052.50
S²ANet[21]38.5M74.1289.1182.8448.3771.1178.1178.3987.2590.8384.9085.6460.3662.6065.2669.1357.94
SASM[23]36.6M74.9286.4278.9752.4769.8477.3075.9986.7290.8982.6385.6660.1368.2573.9872.2262.37
FRED[26]-75.5689.3782.1250.8473.8977.5877.3887.5190.8286.3084.2562.5465.1072.6569.5563.41
G-Rep[24]36.6M75.5687.7681.2952.6470.5380.3480.5687.4790.7482.9185.0161.4868.5167.5373.0263.54
O-RepPoints[28]36.6M75.9787.0283.1754.1371.1680.1878.4087.2890.9085.9786.2559.9070.4973.5372.2758.97
R3Det-GWD[58]41.9M76.3488.8282.9455.6372.7578.5283.1087.4690.2186.3685.4464.7061.4173.4676.9457.38
R3Det-KLD[59]41.9M77.3688.9084.1755.8069.3578.7284.0887.0089.7584.3285.7364.7461.8076.6278.4970.89
RTMDet[35]52.3M78.8589.4384.2155.2075.0680.8184.5388.9790.9087.3887.2563.0967.8778.0980.7869.13
Appr. MessDet15.3M78.4589.2884.6956.2066.1881.3785.3388.8690.7888.2887.6264.4765.5978.1882.1067.82
Str. MessDet18.1M79.1288.0885.1555.8172.0981.5485.8588.9890.8488.3688.7068.7866.8578.8482.6664.26
+ +Table 1. Comparison with state-of-the-art methods on the DOTA-v1.0 dataset [50] with single-scale training and testing. The MessDet backbones are pretrained on ImageNet-1K [13] for 300 epochs, similar to other methods [1, 29, 57]. + +
MethodStrictly#P↓mAP↑
MessDet✓19.0M78.51
(Without head)X16.2M78.15
RTMDet✓74.9M77.10
(Without EMA)X52.3M77.34
+ +Table 2. Performance comparison of RTMDet and MessDet with two downsampling methods. + +For a fair comparison, we follow the approach of major methods [21, 51], training models on both the training and validation sets and evaluating them on the test set. We adopt single-scale training and testing, using $1024 \times 1024$ patches for DOTA and $800 \times 800$ resized images for DIOR-R. Similar to mainstream methods [29, 57], we pretrain the strictly and approximately rotation-equivariant backbone networks used in the main results on ImageNet-1K [13] for 300 epochs, while the backbones in the ablation studies are pretrained for 100 epochs. Our model is implemented using the MMYOLO [11] and MMRotate [64] frameworks and trained for 36 epochs on DOTA-v1.0, DOTA-v1.5 and DIOR-R using the AdamW [34] optimizer. The experiments are conducted on 4 GPUs with a batch size of 8. Following the exploration of ReDet [20], this study set $N$ , the number of orientation dimensions for the rotation-equivariant features in MessDet, to 8. More detailed experimental settings can be found in Sec. 9 of the supplementary + +material. + +# 5.2. Ablation Studies + +This section presents ablation experiments to validate the effectiveness of the newly proposed downsampling process, rotation-equivariant channel attention (RE-CA) mechanism, and multi-branch head network. Unless otherwise stated, the reported results are based on the DOTA-v1.0 test set. + +Strictly Rotation-Equivariant Downsampling. We have implemented rotation-equivariant backbone and neck networks with both approximately and strictly rotation-equivariant downsampling. To compare the impact of the new downsampling process on conventional convolutional networks, we re-implement RTMDet [35] with both approximately and strictly equivariant downsampling processes. For a fair comparison, MessDet uses the same head network as RTMDet, and RTMDet does not employ the Exponential Moving Average (EMA) strategy. Note that we only pretrain RTMDet's two backbones for 100 epochs instead of the 600 epochs as in the original paper. The new downsampling process has little impact on conventional CNN but improves MessDet implemented with RE-Nets, as shown in Tab. 2. + +Rotation-Equivariant Channel Attention. To demonstrate the effectiveness of the proposed RE-CA mechanism, we implement strictly and approximately rotation-equivariant backbones without the RE-CA, and the head + +
Method#P↓mAP↑PLBDBRGTFSVLVSHTCBCSTSBFRAHASPHCCC
Two-stage
FR-O[40]41.1M62.0071.8974.4744.4559.8751.2868.9879.3790.7877.3867.5047.7569.7261.2265.2860.471.54
Mask R-CNN[22]44.4M62.6776.8473.5149.9057.8051.3171.3479.7590.4674.2166.0746.2170.6163.0764.4657.819.42
HTC[2]77.5M63.4077.8073.6751.4063.9951.5473.3180.3190.4875.1267.3448.5170.6364.8464.4855.875.15
Roi Trans.[14]55.1M65.5071.7082.7053.0071.5051.3074.6080.6090.4078.0068.3053.1073.4073.9065.6056.903.00
ReDet[20]31.6M66.8679.2082.8151.9271.4152.3875.7380.9290.8375.8168.6449.2972.0373.3670.5563.3311.53
LSKNet[29]31.0M70.2672.0584.9455.4174.9352.4277.4581.1790.8579.4469.0062.1073.7277.4975.2955.8142.19
PKINet[1]30.8M71.4780.3185.0055.6174.3852.4176.8588.3890.8779.0468.7867.4772.4576.2474.5364.0737.13
Single-stage
RetinaNet-O[31]36.4M59.1671.4377.6442.1264.6544.5356.7973.3190.8476.0259.9646.9569.2459.6564.5248.060.83
O-RepPoints[28]36.6M66.9075.5282.6051.2470.2157.8173.8286.2590.8678.3076.4753.6172.7866.6869.4853.6611.09
FRED[26]-68.3079.6081.4452.6072.5758.0774.8286.1290.8182.1374.8453.3772.9369.5169.9154.8219.27
RTMDet[35]52.3M71.8080.0080.7551.8271.6567.1280.6989.4890.7681.4381.0760.8770.4174.8773.2970.9023.65
Appr. MessDet15.3M72.3880.6184.9954.5665.3673.6082.6989.7390.8382.4682.0359.3572.9677.6675.1465.0921.12
Str. MessDet18.1M73.1480.8386.1755.5863.2874.2482.7389.7990.8583.4782.4563.9771.6577.4476.0666.1725.54
+ +Table 3. Comparison with state-of-the-art methods on the DOTA-v1.5 dataset [15] with single-scale training and testing. The MessDet backbones are pretrained on ImageNet-1K [13] for 300 epochs, similar to other methods [1, 20]. + +
StrictlyRE-CA#P↓mAP↑
✓✓19.0M78.51
X18.8M76.91
X✓16.2M78.15
X16.0M77.47
+ +network without the multi-branch structure. The experimental results are shown in Tab. 4. The results indicate that the model with RE-CA performs significantly better than the model without it. Furthermore, due to the maintenance of rotation equivariance, the output dimension of the fully connected layer is reduced to $1 / N$ of the original. Hence, the parameter count required by the new channel attention mechanism is lower than that of conventional channel attention. + +Multi-branch Head. We conduct a series of experiments to demonstrate that the multi-branch head network not only reduces the number of parameters but also improves model performance. To achieve the best possible performance, this study explores the impact of the number of convolutional modules in the multi-branch network on performance, using the Appr. MessDet as an example, as shown in Tab. 5. The number of convolutional modules includes the number of convolutional modules in each individual branch plus one convolutional module for the output aggregation. This shows that when the number of convolutional modules in the multi-branch head is set to 3, a balance between performance and parameter count is achieved. + +# 5.3. Main Results + +On DOTA-v1.0 [15], the performance comparison between MessDet and other state-of-the-art methods is re + +Table 4. Performance comparison of MessDet with and without rotation-equivariant channel attention. + +
Num.#P(head only)↓mAP↑
RTMDet Head22.4M78.15
Multi-branch Head92.4M78.19
72.1M77.97
51.8M77.62
31.5M78.45
21.4M77.46
+ +Table 5. The impact of different head network designs on the performance of Appr. MessDet. + +
Method#P↓mAP↑
RetinaNet OBB[31]36.4M57.55
Faster R-CNN OBB[40]41.1M59.54
RoI Transformer[14]55.1M63.87
LSKNet[29]31.0M65.90
Oriented Reppoints[28]36.6M66.71
DCFL[52]-66.80
RTMDet[35]52.3M66.86
PKINet[1]30.8M67.03
Appr. MessDet15.3M67.42
Str. MessDet18.1M68.19
+ +Table 6. Comparison with state-of-the-art methods on the DIOR-R dataset [27]. The MessDet backbones are pretrained on ImageNet-1K [13] for 300 epochs, similar to other methods [1, 28, 52]. + +ported in Tab. 1. The approximately rotation-equivariant MessDet (Appr. MessDet) achieves $78.45\%$ mAP, while the strictly rotation-equivariant MessDet (Str. MessDet) achieves $79.12\%$ mAP. However, compared to other state-of-the-art models, MessDet has nearly half the parameter count of the lowest among them. + +On DOTA-v1.5 [15], Tab. 3 presents the results, showing that Appr. MessDet attains $72.38\%$ mAP, while Str. Mess + +![](images/cf18427763d83081e01df1d033346c0b293798e31e46f9338ba06ec5ced4221b.jpg) +Figure 5. The variation of equivariance error across the five stages of the MessDet backbone network, where "Appr." and "Str." denote approximately and strictly rotation-equivariant MessDet respectively, and S0 denotes the stem, S1 denotes stage 1, and so on. mAP represents the model's performance on the DOTA-v1.0 validation set. + +Det achieves $73.14\%$ mAP. + +On DIOR-R [27], as detailed in Tab. 6, Appr. MessDet records an mAP of $67.03\%$ , whereas Str. MessDet improves upon this with $68.19\%$ mAP. + +# 5.4. Analysis + +This section will analyze the behavior of rotation-equivariant networks in aerial object detection tasks, aiming to demonstrate the importance of rotation equivariance in such tasks. + +Equivariance Error Reduction in Detectors. Edixhoven et al. [16] point out that in classification tasks, approximate rotation-equivariant models relax the rotation equivariance constraint, gradually increasing the rotation equivariance error during training to improve performance. Following this paper, we define the rotation equivariance error as follows: + +$$ +\varepsilon = \frac {1}{i j k} \sqrt {\sum_ {i , j , k} ([ f (T (x)) ] _ {i j k} - [ T ^ {\prime} (f (x)) ] _ {i j k}) ^ {2}}. \tag {5} +$$ + +In Eq.(5), $i$ and $j$ are indices in the spatial dimensions, and $k$ is the index in the channel dimension. To eliminate possible extraneous interference, we separately test the Appr. and Str. MessDet models without the multi-branch head network. The variation in rotation equivariance error across the five stages of the backbone network is shown in Fig. 5, based on the DOTA-v1.0 dataset. + +As shown in Fig. 5, unlike in classification tasks, the rotation equivariance error in the approximately rotation-equivariant model decreases gradually during training on the DOTA-v1.0 aerial object detection dataset, proving that + +![](images/93d3bae1c52c864b5a9243a985ed36ecafee41afb6e4b1d5bdb6191de0766187.jpg) +Figure 6. The impact of various rotation angles on models performance. + +aerial image object detection tasks indeed benefit more from rotation equivariance. Furthermore, the rotation equivariance error in the strictly RE-Net is naturally lower than in the approximately RE-Net, leading to improved detection performance. + +Robustness to Rotational Variations. To demonstrate the robustness of RE-Nets to rotational variations, we test both Str. and Appr. MessDet, along with the baseline RTMDet [35], by applying rotations at various angles to the DOTA-v1.0 validation set. The effect of rotational changes on model accuracy is compared. Similarly, to eliminate any unnecessary interference, MessDet uses the same head network as RTMDet. The test results are shown in Fig. 6. As can be seen, even when RTMDet is rotated by multiples of $90^{\circ}$ with no information loss, its performance decreases due to a lack of robustness to rotational variations, whereas MessDet exhibits greater robustness to such variations. + +# 6. Conclusion + +This paper proposes a novel downsampling process, implements a strictly rotation-equivariant network, and introduces a rotation-equivariant channel attention mechanism, enabling rotation-equivariant networks to adopt more advanced architectures. By combining a multi-branch head network, we present the MessDet. Experimental results show that we achieve performance comparable to state-of-the-art methods with an exceptionally low parameter count. Additionally, we quantitatively evaluate rotation equivariance error, demonstrating the necessity of rotation equivariance in aerial image object detection tasks. + +Acknowledgement. This work was supported in part by the National Natural Science Foundation of China (Nos. 62302364, 62306324, 62376279, U24A20333), the Science and Technology Innovation Program of Hunan Province (No. 2024RC3128), the Research Foundation of National University of Defense Technology (No. ZK24-30), and the Key Laboratory of Target Cognition and Application Technology (No. 2023-CXPT-LC-005). + +# References + +[1] Xinhao Cai, Qiuxia Lai, Yuwei Wang, Wenguan Wang, Zeren Sun, and Yazhou Yao. Poly kernel inception network for remote sensing detection. In CVPR, pages 27706-27716, 2024. 3, 6, 7 +[2] Kai Chen, Jiangmiao Pang, Jiaqi Wang, Yu Xiong, Xiaoxiao Li, Shuyang Sun, Wansen Feng, Ziwei Liu, Jianping Shi, Wanli Ouyang, et al. Hybrid task cascade for instance segmentation. In CVPR, pages 4974-4983, 2019. 7 +[3] Gong Cheng and Junwei Han. A survey on object detection in optical remote sensing images. 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Mask Prompt: abdomen CT scans label, with liver, liver tumor. + +![](images/7ab998307adcce676a8724ec1de69d3b58f8375d4e17ebcf0055773327dc9b94.jpg) + +Image Prompt: abdomen CT scans image, with bladder, right adrenal gland, right kidney, left kidney, left adrenal gland. Mask Prompt: abdomen CT scans label, with bladder, right adrenal gland, right + +kidney, left kidney, left adrenal gland. + +![](images/1c0ac85c4ae251cb66630b90221adfb8c2571122bdeadbfc08620aabf4d14ff9.jpg) + +Image Prompt: breast ultrasound image, with breast tumor. Mask Prompt: breast ultrasound label, with breast tumor. + +![](images/9b1f579d7c5ab00fe878978c689afb824269fcdf03d28c3b9ba40631d4dfa09c.jpg) + +Image Prompt: polyp colonoscopy image, with polyp. Mask Prompt: polyp colonoscopy label, with polyp. + +![](images/7f147ee913f0d64893dd11e01bc4bf756e695eecb2b53ed68d5468e81e49400e.jpg) + +Image Prompt: cardiovascular ventricleMRI image,with left ventricle,right ventricle,myocardium. Mask Prompt: cardiovascular ventricle mri label, with left ventricle,right ventricle,myocardium. + +![](images/7ae1add58fa481eb84b44ec5de723d599691478c2e886b607a0d6ece74aab0c0.jpg) +Figure 1. (A) MedSegFactory is a versatile medical image synthesis tool that generates paired medical images and segmentation masks solely from user-defined prompts specifying the target label and imaging modality. (B) The synthesized data generated by MedSegFactory can be then used to augment datasets, enhancing segmentation performance across various imaging modalities. + +Image Prompt: abdomen CT scans image, with kidney, kidney tumor. Mask Prompt: abdomen CT scans label, with kidney, kidney tumor. + +![](images/be51f509498caf94bcc885835c2926a10257c9b4f347e4fe6a00d8731094c133.jpg) +MedSegFactory + +![](images/73b8dbe6ba7731aecb605ca011900cdc82ff29ff71a550eee60b98c5d3f38f8f.jpg) + +![](images/f8d394342a1c2a8185c816959d534f50147a3554f5571ad080f034df1b74026a.jpg) + +![](images/66e66ae11c3574f198e352fe4bb86aa20c8eb76533471a1cdb43262372142205.jpg) + +![](images/ac8954a0bbc17e978eb5818dc3bec85228b6ec0eda8a0a1d30a04021aeb099c1.jpg) + +![](images/c3266df65856d06544f89b28de5b0c811ab018f51afdf47b7cdc73d6481e9b1f.jpg) + +![](images/e2a61f56e6cac151774910882d87a2d1e3bc3219441cff19d72e1681356cb47a.jpg) +(A) MedSegFactory Generation Stage + +![](images/eea15f8881d9eb6578ed2913dde5091db18a2c4f3225cfb144325ba851e29cdd.jpg) + +![](images/2e700f5489e465b5cb6cec5cabccb772be192bca194e9a7b081a51f23d5a3456.jpg) +Generated Dataset + +![](images/9de52bfe236239ad1de7768480bb772719555698a0ae27a76982fa11b6d4953b.jpg) +Generated Dataset + +![](images/29a43d489a6db6b650ef5920129912697a0c0f89ec2a8faab792be7d5b634851.jpg) + +![](images/d10ab247bb68d6b4f70bbdfebbbc9efb1a0e3b0ed27200f5f3c4a1e9086e138a.jpg) + +![](images/98e6ec1df476fbb3526e559f51b123ba625ff844e3128fd48d4f6ac92e242441.jpg) +Generated Dataset +(B) MedSegFactory Segmentation Stage + +![](images/5f3473176a621e9ad76c19b0d995deb499ff3211ad8e24dbd01c371c55018bae.jpg) + +![](images/89881ca8c54bc01c404a22f80182af03d838b76c5a387c5c07fc2f483bc12114.jpg) +Real Dataset + +![](images/62486fd1bbf4ba754dfa1adce94c98328d2d6f0788ea7eb85bac1ab7e85c8484.jpg) +Real Dataset +Reel Dataset + +![](images/4587934be45dda7ef97cbddfa3b0b9ef8763fbb8e587dc0f7eda174928250f54.jpg) + +![](images/971ff46b79f56fcdd47adb98614392f1cdfee4c601d88a53fd9669a2a6b21ad5.jpg) +Real Dataset + +![](images/4112e1dd5f9f5cbfb6ef685cf93ed0b0d96a963acf80cb4fc038dae5790a5caa.jpg) +Real Dataset + +![](images/3b7990cf6cf94a3e133510dedd43d5f84795b2651b602a2d6f82a98e42208309.jpg) +Liver Tumor Segmentation Model + +![](images/d7581a3bb1047bd615186462e3efe5a2e81dfea4359a88323350f973347449ce.jpg) +Abdomen Segmentation Model + +![](images/7945d8fbf1af822ba2646f9063850b20ae9b0e035ac9b09d679ad57a58da81fd.jpg) +Breast Tumor Segmentation Model + +![](images/76de34bfe5c09e0f7c4a2e8eb93a7c36ba4e34f8154a31ddf0fc05759a362f3f.jpg) +Polyp Segmentation Model + +![](images/c98b01522052118976716466091a4337fe4f6f0b5aa86082df06e2410bbcb425.jpg) +Cardiovascular Segmentation Model + +![](images/eb79091e9a0c8b5eee821f695dfddd0a796837ad91e3ea6ea91f10fd8fd3cac5.jpg) +Kidney Tumor Segmentation Model + +# Abstract + +This paper presents MedSegFactory, a versatile medical synthesis framework that generates high-quality paired medical images and segmentation masks across modalities and tasks. It aims to serve as an unlimited data repository, supplying image-mask pairs to enhance existing segmentation tools. The core of MedSegFactory is a dual-stream diffusion model, where one stream synthesizes medical images and the other generates corresponding segmentation masks. To ensure precise alignment between image-mask pairs, we introduce Joint Cross-Attention (JCA), enabling a collaborative denoising paradigm by dynamic cross-conditioning between streams. This bidirectional interaction allows both + +representations to guide each other's generation, enhancing consistency between generated pairs. MedSegFactory unlocks on-demand generation of paired medical images and segmentation masks through user-defined prompts that specify the target labels, imaging modalities, anatomical regions, and pathological conditions, facilitating scalable and high-quality data generation. This new paradigm of medical image synthesis enables seamless integration into diverse medical imaging workflows, enhancing both efficiency and accuracy. Extensive experiments show that MedSegFactory generates data of superior quality and usability, achieving competitive or state-of-the-art performance in 2D and 3D segmentation tasks while addressing data scarcity + +# 1. Introduction + +Computer-aided detection systems [27, 34, 51] have significantly enhanced medical image analysis, but their widespread adoption remains limited due to the high costs associated with accessing and annotating medical imaging data [31, 36, 38, 69-71]. Annotated datasets are costly to create and are restricted by strict privacy and regulatory policies, which hinder data sharing between institutions. Synthetic data present a promising alternative by creating large-scale annotated datasets without compromising patient confidentiality, enabling easier collaboration among researchers. + +Existing methods for medical data synthesis [9, 13, 21, 24, 32, 57] generally fall into three categories, as summarized in Fig. 2: (1) unconditional image generation [16, 20, 24, 43, 50, 57, 68], (2) unconditional paired image-mask generation [42, 53, 72], and (3) conditional image generation guided by segmentation masks [16-18, 48, 59, 65]. Each of these categories, however, has critical limitations. Unconditional methods offer limited control, complicating interpretability, debugging and resulting in images with reduced variability. Conditional methods provide greater control and interpretability, but they depend heavily on detailed mask annotations, which are expensive and difficult to obtain, limiting scalability. + +To address these fundamental limitations, we introduce a new, fourth category of data synthesis: conditional paired image-mask generation based on text prompts. Within this category, we introduce MedSegFactory, a versatile medical synthesis framework designed to generate medical images and their corresponding segmentation masks only from concise textual descriptions. Unlike previous conditional methods [18, 22, 48, 62], users no longer need to provide detailed segmentation masks; instead, they simply provide a brief text prompt describing high-level features such as target labels, imaging modalities, anatomical regions, and pathological conditions. This approach significantly simplifies the creation of customized synthetic datasets. + +To equip MedSegFactory with broad generative capability across diverse medical imaging tasks, the model is trained on multiple image modalities and tasks. At its core, MedSegFactory employs a dual-stream diffusion model, where one stream synthesizes medical images while the other generates corresponding segmentation masks. To ensure precise alignment between image-mask pairs, we introduce Joint Cross-Attention, leveraging the cross-attention interactions between the image and mask streams, dynamically conditioning each stream's output on the evolving denoising representations of the other. This mutual, interactive refinement ensures robust semantic alignment, signifi + +![](images/b98f881f41a902be6557fa2ebb79c88c235286fbce7faf8039f233015d85f30b.jpg) + +![](images/a481e7613924b080becfd285e5884d67010b7d586ec4ff67287b16aed6b5817e.jpg) +Figure 2. Different medical image generation frameworks: (1) unconditional image generation, (2) unconditional paired imaged-mask generation, and (3) conditional image generation guided by segmentation masks. (1) and (2) lack control, while (3) depends on costly and hard-to-obtain mask annotations, limiting scalability. + +![](images/4085a93f38d821addfbe009c63a03bd2a4d7855d1ffbf3adfef4fc1a82ec9a06.jpg) + +![](images/81d172df40c2fbfe43d7776b23c6f1da2c8a0b56800cf322962972070d700deb.jpg) + +cantly enhancing the quality and usability of the generated data. + +The key contribution of this paper is the MedSegFactory, a valuable tool for advancing medical imaging. MedSegFactory can accurately leverage user instructions (Fig. 6; alignment between text and generated imagedark pairs), synthesizing high-quality (Fig. 4, Tabs. 2-3; comparable or state-of-the-art medical image generation), diverse (Fig. 6; varied outputs from the same text prompt), and highly consistent medical image-segmentation pairs (Fig. 5). This capability significantly enhances the overall segmentation performance across heterogeneous datasets (Tabs. 4-5; consistently achieving comparable or state-ofthe-art performance in downstream medical segmentation tasks). + +Overall, our contributions can be summarized as follows: + +1. We introduce MedSegFactory, a dual-stream generative model designed to synthesize highly consistent imaged-mask pairs via text prompts. +2. We propose a novel Joint Cross-Attention Mechanism, which enables mutual refinement between the image and mask streams, ensuring improved semantic consistency and precise alignment in the generated pairs. +3. The synthetic data generated by MedSegFactory demonstrate comparable or superior quality and usability to previous state-of-the-art methods, as evidenced by medical image generation and downstream 2D & 3D segmentation tasks (Sec. 4.4). + +# 2. Related Work + +Diffusion Model Diffusion models learn data distributions by progressively denoising noisy inputs through a series of iterative steps. Specifically, DDPM [24] formulates diffusion models as a more stable generative framework by designing a loss function based on a Markov chain, effectively overcoming the limitations of Generative Adversar- + +ial Networks (GANs) [21]. Designs such as DDIM [56] and LCM [40] improve the sampling efficiency issue of the DDPM framework. Stable Diffusion Model (SDM) [50] explores the application of diffusion models on the latent space. Building upon the high-fidelity image generation framework of SDM, ControlNet [65] introduces various conditional controls, such as Canny edge detection, HED boundary detection, and semantic segmentation, to guide image generation in diffusion models. Due to their high-fidelity generation capabilities and precise conditional control, diffusion models have been successfully applied to various downstream tasks, including medical image generation [12, 16, 18, 20, 37, 47, 66], video synthesis [19, 30, 33, 35], and low-level vision applications [1, 60, 64]. However, generating paired medical images and segmentation labels remains a challenge for diffusion models due to privacy concerns and the high cost of annotation. + +Medical Image Generation Synthetic medical images can augment limited medical databases and help mitigate data scarcity resulting from privacy and ethical constraints. However, due to the absence of corresponding medical segmentation labels, methods [14, 15, 44, 55, 58] that generate only medical images are inadequate for supporting downstream computer-aided detection (CAD). Medical image generation schemes [18, 22, 48, 62] based on medical segmentation labels can generate clinically relevant images suitable for CAD. However, the limited diversity of available medical segmentation labels hinders advancements in CAD, as the high cost of manual annotation remains a significant challenge. Although Bhat et al. [7], Machacek et al. [42] address the aforementioned issues, their framework design remains limited in applicability to specific medical image generation tasks and corresponding CAD applications. + +Medical Segmentation As a fundamental task in CAD, medical segmentation automatically delineates lesion areas, providing precise structural information for surgical planning and detection. Conventional segmentation frameworks, such as FCN [39] and U-Net [51], demonstrated notable effectiveness in CAD by leveraging fully convolutional networks and skip connections, respectively. U-Net system [25, 27, 52, 54, 63] adaptively incorporates different network structures and sample sizes according to specific requirements to better respond to diverse scenarios and challenges. However, the limited receptive field of convolutional networks restricts their ability to effectively capture long-range dependencies and inter-region relationships within complex structures, such as lesions or organs. Thus, numerous studies [3, 4, 10, 11, 26, 45, 67] have attempted to integrate Transformers into medical segmentation frameworks to globally model lesion or organ representations. But these efforts focus only on particular medical segmentation tasks. Additionally, unified frameworks have been designed [41, 49, 61] to address discrepancies across dif + +ferent medical datasets and tasks. However, the scarcity of medical data has increasingly become a significant barrier to the continued advancement of unified segmentation. + +# 3. Method + +In this paper, we introduce MedSegFactory, a novel medical image synthesis framework that generates paired medical images and segmentation masks based on user-defined prompts. We first define this synthesis task in Sec. 3.1, then outline our training pipeline (Fig. 3) for developing a versatile model capable of synthesizing medical images across multiple modalities and tasks. Sec. 3.2 details MedSegFactory's dual-stream generation framework, where one stream synthesizes images while the other produces corresponding masks. To ensure semantic alignment, we propose a Joint Cross-Attention (JCA) mechanism (Sec. 3.3) that enables bidirectional conditioning between streams, allowing dynamic refinement and ensuring consistency between generated image-mask pairs. + +# 3.1. Task Definition + +We define a new medical image synthesis task that turns a user-defined prompt—specifying the target label and imaging modality—into the unified generation of paired medical images and segmentation labels. + +Generation. Given a real dataset $S_{r} = \{\{x_{i},p_{i},m_{i}\} \}_{i = 1}^{n}$ where $n$ is the data size in $S_{r}$ , $x_{i}\in \mathbb{R}^{3\times h\times w}$ denotes a medical image (with height $h$ and width $w$ ), $p_i$ denotes the corresponding text prompt, and $m_{i}\in \mathbb{R}^{h\times w}$ is the paired segmentation mask, our generative function $f_{g}$ can be defined as: + +$$ +\left\{\hat {x} _ {i}, \hat {m} _ {i} \right\} \leftarrow f _ {g} \left(p _ {i}\right). \tag {1} +$$ + +where $\{\hat{x}_i,\hat{m}_i\}$ are the synthesized medical image and its corresponding segmentation mask. + +Segmentation. For medical segmentation tasks, we use both real $D_r = \{\{x_i, m_i\}\}_{i=1}^n$ and generated datasets $D_g = \{\{\hat{x}_i, \hat{m}_i\}\}_{i=1}^n$ to jointly train the segmentation function $f_s$ . + +$$ +\stackrel {\circ} {m} _ {i}, \bar {m} _ {i} \leftarrow f _ {s} \left(x _ {i}\right), f _ {s} \left(\hat {x} _ {i}\right). \tag {2} +$$ + +where $\mathring{m}_i$ and $\overline{m}_i$ are the predicted segmentation labels for $x_i$ and $\hat{x}_i$ respectively. The objective of $f_s$ is to maximize the likelihood that the predicted labels $\{\mathring{m}_i, \overline{m}_i\}$ align with their corresponding ground truth labels $\{m_i, \hat{m}_i\}$ . + +# 3.2. Dual-Stream Generation + +As illustrated in Fig. 3, MedSegFactory is built upon a dual-stream generation framework, from the Stable Diffusion model [50]. The framework consists of two parallel + +![](images/36fa5fe923f7dfdc9157bec8c84bcf7e192ef209795592e9be2ed86ac6ffb203.jpg) +Figure 3. Overview of the MedSegFactory Training Pipeline. Left: A dual-stream generation framework built upon the Stable Diffusion model, where each paired image and segmentation mask $\{x_i, m_i\}$ are first encoded into latent representations and noised. These noised representations are then denoised by the Diffusion U-Net, producing the image and segmentation mask latent $\{\hat{z}_0, \hat{y}_0\}$ , which are ultimately decoded into a paired image and mask $\{\hat{x}_i, \hat{m}_i\}$ . To improve their semantic consistency, we introduce Joint Cross-Attention (JCA), which allows the denoised latent representations of both streams to act as dynamic conditions, enhancing the mutual generation of images and masks. Right: A detailed illustration of JCA, which applies two cross-attention functions to the intermediate denoising features $\{z_t, y_t\}$ , enabling the cross-conditioning of the medical image and segmentation label for improved consistency in the final outputs. + +streams: one for generating medical images and the other for generating the corresponding segmentation masks. + +During training, each paired medical image and segmentation mask $(x_{i},m_{i})$ is first encoded into latent representations $\{z_0,y_0\}$ using a pretrained variational autoencoder (VAE) encoder. At the $t$ -th denoising step, the intermediate latent representations $\{z_t,y_t\}$ are obtained by applying Gaussian noise $\{\epsilon_x,\epsilon_m\}$ to the initial encoded vectors $\{z_0,y_0\}$ , the forward diffusion process: + +$$ +\begin{array}{l} q \left(z _ {t}, y _ {t} \mid z _ {0}, y _ {0}\right) = \mathcal {N} \left(z _ {t}; \sqrt {\alpha_ {t}} z _ {0}, 1 - \alpha_ {t}\right) \tag {3} \\ \cdot \mathcal {N} \left(y _ {t}; \sqrt {\alpha_ {t}} y _ {0}, 1 - \alpha_ {t}\right), \\ \end{array} +$$ + +where $\alpha_{t}$ represents the noise scaling factor at step $t$ . + +$z_{t}$ and $y_{t}$ are then denoised through a Diffusion UNet. Specifically, as show in Fig. 3, the denoising process is performed in the Cross-Attention function $CA(Q,K,V)$ (where $Q,K,V$ are the queries, keys, and values of crossattention respectively) and self-attention $SA(Q,K,V)$ relying on the corresponding textual prompt embeddings $e_x$ and $e_m$ obtained by fixed text encoder, respectively: + +$$ +\begin{array}{l} z _ {t}, y _ {t} = C A \left(z _ {t}, e _ {x}, e _ {x}\right), C A \left(y _ {t}, e _ {m}, e _ {m}\right), \tag {4} \\ z _ {t}, y _ {t} = S A (z _ {t}, z _ {t}, z _ {t}), S A (y _ {t}, y _ {t}, y _ {t}). \\ \end{array} +$$ + +Finally, the denoised latent representations are decoded by the VAE decoder into a medical image $\hat{x}_i$ and its corresponding segmentation mask $\hat{m}_i$ . + +Unlike traditional conditional generation models [18, 22, 65], which rely on predefined segmentation masks as static conditional inputs, our approach assumes that segmentation + +masks are not readily available. MedSegFactory instead introduces a dynamic denoising process enabled by our newly proposed Joint Cross-Attention (JCA) mechanism. This mechanism, detailed below, allows both medical images and segmentation masks to be progressively refined based on each other's denoised representations, ensuring mutual enhancement throughout the generation process. + +# 3.3. Joint Cross-Attention + +Despite the success of diffusion models [24, 50, 57] in generative modeling, their application to jointly modeling the correspondence between medical images and segmentation labels remains underexplored. Unlike existing frameworks that generate medical images from predefined segmentation labels, MedSegFactory models the joint distribution of medical images and their corresponding segmentation masks, ensuring mutual refinement during the generation process. + +This can be achieved through our Joint Cross-Attention (JCA) mechanism, which enhances the UNet backbone of the diffusion model, making it more adaptable for paired data generation. Specifically, to capture the correspondence between medical images and segmentation labels, JCA applies two cross-attention functions to intermediate denoising features, enabling mutual refinement: + +$$ +z _ {t}, y _ {t} = C A \left(y _ {t}, z _ {t}, z _ {t}\right), C A \left(z _ {t}, y _ {t}, y _ {t}\right). \tag {5} +$$ + +Unlike conventional single-stream conditional generation models, which rely on static segmentation labels, MedSegFactory employs JCA to dynamically adjust both the image + +![](images/805a5202420ea0969aa93222e186caf2b1f9fcd4a31f01a709a1d865907c572f.jpg) +Figure 4. Qualitative comparison between MedSegFactory and baselines for medical image generation. Baselines exhibit issues: irregular structures (SDM, ControlNet, DiffBoost, Finetuned-SDM), artifacts (SDM, DiffBoost, Finetuned-SDM), blurred boundaries (Finetuned-SDM), unnatural saturation (ControlNet, DiffBoost), and structural missing (MAISI). MedSegFactory produces anatomically accurate, high-quality images. Zoom in for details. + +and label representations throughout the denoising process. This collaborative denoising mechanism facilitates bidirectional interaction between latent representations, enabling mutual refinement at each step, and thus ensures stronger semantic consistency between generated images and masks. + +Formally, the overall objective of MedSegFactory can be summarized as follows: + +$$ +\begin{array}{l} \mathbb {E} _ {t, \epsilon_ {x}, \epsilon_ {m}, e _ {x}, e _ {m}} [ \| \epsilon_ {x} - \epsilon_ {\theta} (z _ {t}, y _ {t}, t, e _ {x}) \| _ {1} ] \tag {6} \\ + \left\| \epsilon_ {m} - \epsilon_ {\theta} \left(y _ {t}, z _ {t}, t, e _ {m}\right) \right\| _ {1} ]. \\ \end{array} +$$ + +where $\epsilon_{\theta}$ is the neural backbone of MedSegFactory. + +# 4. Experiment + +To demonstrate the effectiveness of MedSegFactory, we show the quality of images generated by MedSegFactory in Sec. 4.3. We investigate the generated results of MedSegFactory in medical image segmentation tasks (Sec. 4.4). + +# 4.1. Dataset + +
DatasetModalitiesClasses#Train#Test
AMOS [29]CT Scan163552418537
ACDC [6]MRI419023826
BUSI [2]Ultrasound Scan2547233
CVC-ClinicDB [5] & Kvasir-SEG [28]Colonoscopy2145062
KiTS19 [23]CT Scan39705210752
LiTS17 [8]CT Scan3558152823
+ +Table 1. Dataset details for training and evaluation. + +To validate MedSegFactory generative results for paired medical images and segmentation labels, we collected seven publicly available medical segmentation datasets, includes multiple modalities from 2D and 3D databases: AMOS, ACDC, BUSI, CVC-ClinicDB, KiTS19, and LiTS17. We trained MedSegFactory and baselines using the training partitions of each dataset, including 2D slices or images from either the axial view of the whole CT scan. The test partitions were used for evaluating both the generation and downstream tasks (see Details in Tab. 1). + +# 4.2. Implementation Details and Metrics + +Implementation Details. We implemented MedSegFactory following the Stable Diffusion Model [50] (SDM) architecture configuration. The model was trained for 300 epochs using the AdamW optimizer with a learning rate of $1e-5$ and a batch size of 20. Training was conducted on 4 NVIDIA A6000 GPUs using PyTorch. To accommodate the unbalanced aspect ratios of medical slices, we follow SDXL's Multi-Aspect Training [46] while preserving a dimension close to $256^2$ pixels. We employed classifier-free guidance with a scale of 7.5 for inference, generating $256^2$ pixels medical images and corresponding segmentation labels through a 50-step denoising process. We evaluated at 256 resolution upon their original settings for baselines. + +Evaluation Metrics. For medical image generation, we use Inception Score (IS) and Fréchet Inception Distance (FID) as evaluation metrics. For segmentation, Dice coefficients (DSC) and Intersection over Union (IoU) are used to compare the performance of MedSegFactory and baselines. + +# 4.3. Medical Image Generation + +To assess the generation quality of MedSegFactory, we compare it against previous state-of-the-art methods ControlNet [65], MAISI [22], Stable Diffusion Model [50], fine-tuned SDM [50], and DiffBoost [68]. Since MAISI is designed only for 3D image generation, we use its pretrained weights from large public datasets, while the other baselines are trained on the same training set as MedSegFactory. For each method, we generate a set of images that matches the size of the corresponding test set. For fair comparison, 3D volumes from MAISI are sliced into 2D images. + +Quantitative Comparison. We evaluated the differences between the generated images and real 2D medical slices in Tabs. 2&3, respectively. As shown in Tab. 2, since Diff-Boost [68] employs the HED Boundary of medical images + +![](images/54d6f3b78305b584dd125fc5529a161e8432f4adc60f995cc09fd148b85f56b9.jpg) +Figure 5. Alignment comparison reveals misalignment or detail loss in baseline-generated medical images versus segmentation labels (highlighted in red box). MedSegFactory demonstrates superior alignment and finer details. + +
MethodAMOSKiTS19LiTS17
FID ↓IS ↑FID ↓IS ↑FID ↓IS ↑
SDM [50]98.113.5891.162.65105.582.48
Finetuned-SDM [50]91.503.19106.703.07104.112.46
MAISI [22]158.793.09161.592.29175.732.25
ControlNet [65]105.383.40117.552.14132.362.45
DiffBoost [68]73.613.2184.663.1899.322.81
MedSegFactory97.943.6295.872.4691.412.52
+ +Table 2. Performance comparison of Inception Score and Fréchet Inception Distance for the generated images from MedSegFactory and the baselines in abdominal CT generation tasks. + +
MethodACDCBUSICVC-ClinicDB
FID ↓IS ↑FID ↓IS ↑FID ↓IS ↑
SDM [50]160.983.47168.712.08235.192.24
Finetuned-SDM [50]165.193.35159.742.83246.552.39
ControlNet [65]173.772.52170.502.38250.242.31
DiffBoost [68]198.362.37184.852.33286.292.08
MedSegFactory158.113.51156.972.44227.882.43
+ +Table 3. Performance comparison of Inception Score and Fréchet Inception Distance for the generated images from MedSegFactory and the baselines on ACDC, BUSI, and CVC-ClinicDB. + +as a synthesis condition, it exhibits state-of-the-art (SoTA) IS and FID on some abdomen CT medical image generation tasks. Nonetheless, MedSegFactory still achieved SoTA or comparable generation quality to most baselines on the liver, kidney, and other abdomen CT generation tasks. Meanwhile, we provide comparison results between MedSegFactory and baselines on more generative tasks in Tab. 3. Generated medical images from MedSegFactory exhibit significantly better fidelity compared to baselines. MedSegFactory significantly improves FID and IS, although generated results still showed certain differences from the real data distribution. Note that since MAISI does not involve 2D medical image and ACDC-related generation tasks, it was not included in the comparison in Tab. 3. Collectively, these results demonstrate the potential of MedSegFactory to deliver high-fidelity medical images for a wide variety of medical tasks. + +Qualitative Comparison. Fig. 4 provides a visual comparison of MedSegFactory with baselines across datasets. As shown in the red rectangular region of Fig. 4, SDM [50], + +ControlNet [65], and DiffBoost [68] produce irregular medical image structures in some tasks, with visible artifacts appearing in the generated medical images. Moreover, ControlNet shows abnormal saturation in some generation tasks, while DiffBoost fails to preserve the color balance in colonoscopy image generation. Due to the domain gap between natural and medical images, the fine-tuned version of SDM, introducing natural image weights, results in blurred boundary details in CT image generation. Although MAISI [22] generates high-fidelity medical images, some structural inconsistencies or deficiencies remain. By comparison, MedSegFactory not only generates anatomically precise and plausible structures but also consistently preserves the quality in medical image generation. + +Alignment. The visualization in Fig. 5 reveals discrepancies or missing details between the generated medical images and the segmentation labels of the red rectangular regions for both ControlNet and DiffBoost. In contrast, the paired medical images and segmentation labels generated by MedSegFactory exhibit flexible detail alignment and consistency on various tasks. + +Diversity. Generating a diverse dataset facilitates a wide range of anatomical variations and disease manifestations, which is critical for enhancing the robustness and generalizability of CAD models across various clinical scenarios. Fig. 6 presents multiple pairs of generated results produced by MedSegFactory under the same textual prompt across different generation tasks. As shown in Fig. 6, the results generated by MedSegFactory accurately align with the provided textual prompts, while the multiple pairs of generated medical images and segmentation labels exhibit semantic consistency. Our paired generation results exhibit sufficient diversity in both medical images and segmentation. + +# 4.4. Medical Segmentation + +This section evaluates the contribution of the synthesized medical data for the downstream task of medical segmentation, using the well-established nnUNet [27]. + +![](images/b2a956ae0e19f4011bf953a9bf617c35941d908a35fe1852024dbcc26da7b22b.jpg) +Figure 6. MedSegFactory produces high-quality paired medical images and segmentation labels, precisely following given instructions while demonstrating diversity across multiple outputs under the same conditions. + +Setting. To ensure a fair comparison, the trained MedSegFactory and comparison methods provide synthetic data in the same proportion. The generated medical images and their corresponding segmentation labels are combined to train nnUNet. The testing is conducted exclusively on the held-out test set. + +Results. Tabs. 4-5 present the quantitative comparison results between MedSegFactory and other methods for downstream segmentation tasks. Compared to the nnUNet baseline trained exclusively on real datasets, the augmented + +
MethodACDCBUSICVC-ClinicDB
DSC(%)IoU(%)DSC(%)IoU(%)DSC(%)IoU(%)
nnUNet [27]86.8880.4278.7772.7389.4584.72
ControlNet [65]85.9779.2782.9478.4491.1186.36
DiffBoost [68]87.2980.6678.1172.4689.3384.63
MedSegFactory88.0281.5083.3878.7590.8586.61
+ +Table 4. Segmentation performance evaluation of nnUNet on different combined and real datasets. + +paired medical images and segmentation labels generated by MedSegFactory significantly improve performance across various medical segmentation tasks. Moreover, compared to other generative models, MedSegFactory most ef + +
MethodLiTS17KiTS19AMOS
DSC(%)IoU(%)DSC(%)IoU(%)DSC(%)IoU(%)
nnUNet [27]59.7754.7756.6552.4976.1470.01
MAISI [22]58.4753.4356.7351.6576.5670.28
ControlNet [65]60.6455.3656.8852.3477.1670.87
DiffBoost [68]59.9255.0856.9652.2076.4070.17
MedSegFactory62.3756.9058.0353.3976.7670.48
+ +Table 5. Segmentation performance evaluation of nnUNet on different combined and real CT datasets. + +
SettingaFIDaISaDSC (%)aIoU (%)
w/o JCA143.282.7561.5857.35
w/o mask-to-image branch151.712.6672.1963.50
w/o image-to-mask branch142.642.7069.8360.72
baseline138.032.8376.5771.27
+ +Table 6. Ablation study. JCA and its two internal branches enhance the quality of generated medical images and improve the overall performance across 6 datasets. + +fectively enhances the overall segmentation performance across heterogeneous datasets. These gains highlight its utility in medical segmentation, especially where annotation costs are prohibitive. + +# 4.5. Ablation Study + +We investigate the contribution of JCA and two branches within JCA: the mask-to-image branch and the image-to-mask branch of the MedSegFactory generation framework. We use MedSegFactory as the baseline to evaluate the impact of different ablation settings by reporting the average Fréchet Inception Distance (aFID), average Inception Score (aIS), average Dice coefficients (aDSC), and average Intersection over Union (aIoU) scores across all datasets. As shown in Tab. 6 and Fig. 7, JCA successfully enhances the quality of the generated image. Meanwhile, the mask-to-image and image-to-mask branches improve medical image generation and downstream task performance. When both branches are employed, boosting cross-guidance between the generated image features and segmentation features, MedSegFactory demonstrates state-of-the-art performance in both generation and segmentation tasks. + +# 4.6. Limitation + +Blurred Boundaries in Target-Free Generation. While MedSegFactory demonstrates promising capabilities in generating paired medical images and segmentation masks, certain failure cases still occur. As shown in Fig. 8, when generating medical images without segmentation targets, the absence of segmentation-guided supervision—an essential element of the JCA—can lead to blurred or imprecise anatomical boundaries. Addressing this limitation presents an opportunity for future improvement. In particular, refining prompt design and introducing more effective attention-masking strategies may help mitigate these issues and enhance generation quality in such cases. + +The 2D architecture. MedSegFactory's current frame + +![](images/2c3312f1a4fade127a7cd55b072fdd79e87e1340380453d4f1ffa1cb24c54079.jpg) +Figure 7. Visualization of the significant misalignment between the generated images and segmentation after removing JCA, along with a noticeable quality decline of the generated images. + +![](images/162ad22f7f520455219cf1efb2ba6e5b3ec0b0c35f3594b50ea3ebd80175fc7f.jpg) +Figure 8. The observed failure cases with blurred boundaries without segmentation targets. + +work is designed for 2D medical images, which may not fully capture the 3D spatial relationships critical in CT/MRI imaging. Extending the model to 3D volumetric data remains a key direction for future work. + +# 5. Conclusion + +In conclusion, this paper presents MedSegFactory, a novel framework for synthesizing high-quality, diverse, and consistent paired medical images and segmentation masks using concise text prompts. By introducing the Joint Cross-Attention mechanism, MedSegFactory ensures precise alignment and semantic consistency between images and their corresponding segmentation labels. Extensive experiments demonstrate that MedSegFactory outperforms previous state-of-the-art methods in generating medical data and improving segmentation performance across heterogeneous datasets. This work addresses data scarcity and the challenges of regulatory constraints, and provides a valuable tool for advancing computer-aided detection. + +# References + +[1] Yuang Ai, Huaibo Huang, Xiaogiang Zhou, Jiexiang Wang, and Ran He. Multimodal prompt perceiver: Empower adaptiveness generalizability and fidelity for all-in-one image restoration. 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Clinically, the collected low-resolution (LR) medical videos present unique challenges for video super-resolution (VSR) models, including camera shake, noise, and abrupt frame transitions, which result in significant optical flow errors and alignment difficulties. Additionally, tissues and organs exhibit continuous and nuanced structures, but current VSR models are prone to introducing artifacts and distorted features that can mislead doctors. To this end, we propose MedVSR, a tailored framework for medical VSR. It first employs Cross State-Space Propagation (CSSP) to address the imprecise alignment by projecting distant frames as control matrices within state-space models, enabling the selective propagation of consistent and informative features to neighboring frames for effective alignment. Moreover, we design an Inner State-Space Reconstruction (ISSR) module that enhances tissue structures and reduces artifacts with joint long-range spatial feature learning and large-kernel short-range information aggregation. Experiments across four datasets in diverse medical scenarios, including endoscopy and cataract surgeries, show that MedVSR significantly outperforms existing VSR models in reconstruction performance and efficiency. Code released at https://github.com/CUHK-AIM-Group/MedVSR. + +# 1. Introduction + +In modern medical imaging, high-resolution (HR) medical videos play a critical role in providing detailed texture and structural information, which are essential for accurate diagnosis and quantitative analysis [46]. However, obtaining HR medical videos in clinical practice is a significant challenge. The quality of medical videos is often limited by various factors, including hardware conditions, acquisition time, physiological movement, and patient comfort + +![](images/1f6f58d0421f2126424ae28a11e0865ad056b01c8dbfcf043edc3ce44837af1a.jpg) +Figure 1. (a) Example of sharp transitions and jitter in medical videos, especially for distant frames (e.g. frame $t - 2 \rightarrow t$ ), which pose significant challenges for existing alignment methods. (b) We measure the averaged error of forward and inverse backward optical flows in different datasets, lower error values denote better estimation stability. Medical videos tend to have significantly larger errors, making the alignment more challenging. + +[11, 35, 44]. As a result, medical videos frequently suffer from low-resolution (LR) and noise, which can compromise the reliability of diagnosis and treatment. + +In recent years, video super-resolution (VSR) techniques have been studied [2, 4-6, 19, 21, 33, 53, 57, 59, 60, 65] to recover the HR videos from LR sequences in the natural scenes. However, in contrast to natural domain videos, medical videos pose two unique challenges. (1) Medical videos captured during surgical or colonoscopy procedures often exhibit instabilities due to hardware device limitations or in-body environment constraints, such as camera shake, jitter, and sharp transitions between frames, which are illustrated in Fig. 1(a). These instabilities can result in optical flow estimation errors and alignment difficulties. Compared to natural domain datasets (REDS4 [42], Video90K-T [60]), medical videos display significantly larger optical flow errors, as shown in Fig. 1(b). This difficulty makes it crucial to develop a reliable propagation scheme between frames for more robust alignment. (2) Medical videos often contain tissues with continuous and nuanced structures with ho + +![](images/a058d16c5e2766b626ec61d12e48c9db6f76c2f5cec81aea48d1c189ab9cd5c5.jpg) + +![](images/c3e1e4368bfb323b734225d6065da30f3a7a2ec5184a040b42c75319931af100.jpg) + +![](images/2d5bd464bace52e702d41ab48c3e6e3e754287d1084da421498800368992f3b2.jpg) + +![](images/f76b2bec254bd8e69d9cf396c4ff80b3f0ebb0aac8d1422071775b94d8304f1c.jpg) +BasicVSR + +![](images/81f67e30b7f10e5658dc5552e5d3a009a9966787bebec702c33541ae72f5f765.jpg) +MedVSR + +![](images/f80b02adb9a66ddefcafe97845ba7065fd4c7cff177bc75a7e7d94276dc9fe60.jpg) +GT +Figure 2. Examples of texture removal and shape distortion of existing VSR method [5], which could not accurately reflect the GT and can be misleading for doctors. MedVSR reconstructs real features and produces consistent results as GT. Zoom in for details. + +mogeneous intensity profiles [29], making them highly sensitive to artifacts and reconstruction errors. Existing VSR models typically rely on stacked local CNNs with limited receptive fields [5, 6, 32], may not adequately address the reconstruction of propagated features. This limitation can lead to the introduction of artifacts, distorted object shapes, and texture removal, as shown in Fig. 2, which compromises the reliability of the algorithm severely. The propagation of these artifacts can obscure critical details that clinicians rely on for making informed decisions. + +To address the aforementioned challenges, we first propose Cross State-Space Propagation (CSSP) based on statespace models (SSM) [13, 16, 43] that could effectively leverage distant frames to enhance the feature propagation process. Instead of directly aligning these distant frames, CSSP extracts and propagates reliable features by leveraging the interaction between distant and neighboring frames. Specifically, it transforms the frame features into statespace sequences, and forwards them into a Cross State-Space Block (CSSB). The CSSB learns a control matrix from the state-space of the distant frame and a hidden state feature from the state-space of the neighboring frame. With the recurrent selective scanning paradigm in SSM, a compound state-space is formed to produce the consistent and stable features across frames for alignment, thereby mitigating the impact of imprecise alignments of distant frames caused by sharp transitions. + +Moreover, we introduce Inner State-Space Reconstruction (ISSR) that leverages the sequential processing of propagated features to enhance the inherent continuity of tissue structures in medical videos. We concatenate the features of the current frame from the forward and backward branches, and apply SSM to extract the continuous long-range spatial feature in a recurrent manner in the Inner State-Space Block (ISSB). Additionally, we incorporate large kernel separable + +blocks (LKSB) for joint short-range information aggregation during reconstruction, resulting in reduced artifacts and precise reconstructed features. This capability of preserving the continuous and detailed structures could potentially contribute to improved diagnostic accuracy and reliability in medical imaging applications. + +Based on the above insights, we propose MedVSR, a tailored medical video super-resolution framework that effectively addresses the challenges in improving the resolution of medical videos. We extensively validated MedVSR on multiple medical scenes, including endoscopy, surgical instruments, and cataract surgery. MedVSR demonstrates better performance and efficiency compared to state-of-the-art models. To summarize, our contributions are as follows: + +- We design CSSP that projects distant frames as control matrices to support the selective scanning of neighboring frames in SSM, which captures consistent features for propagation and addresses the imprecise alignment issue. +- We introduce ISSR that jointly learns long-range spatial features with SSM and aggregates short-range information with large-kernel convolutions, which enhances the details of reconstructed frames and reduces artifacts. +- We propose a MedVSR framework tailored for medical video super-resolution with CSSP and ISSR, and conduct comprehensive experiments across multiple distinct medical scenarios. MedVSR achieves state-of-the-art performance with remarkable efficiency, demonstrating its efficacy and potential for clinical application. + +# 2. Related Work + +# 2.1. Video Super-Resolution + +VSR aims to restore a sequence of HR video frames from its degraded LR counterparts [5, 6, 32, 33, 40, 52, 57, 59–62]. Its difference with image super-resolution primarily lies in the utilization of propagated temporal information for alignment, then uses the aligned feature for reconstruction. Early works [28, 49, 60] proposed to apply optical flow to estimate the motion, then propagated the warped neighboring frames for alignment. BasicVSR [5] adopted alignment at feature level, and propagated the features in a bidirectional recurrent way. BasicVSR++ [6] further improved the scheme to second-order propagation, which also aligns the distant frames. However, inaccurate flows could lead to performance degradation, especially for long-distance frames. To compensate for the deficiency of optical flow, recent works have proposed to learn the alignment via deformable convolution networks (DCN) [6] or deformable attention [32]. Meanwhile, some works [52, 59] have discovered that alignment in patchwise could enhance robustness. However, they all assume that aligning distant frames via higher-order propagation could effectively transmit the information, which does not strictly hold in the medical scene. In this paper, rather than propagating imprecisely aligned + +distant frames, we leverage them to support the learning of consistent and stable features during propagation. + +# 2.2. State-Space Models + +State-Space Models (SSMs) have gained considerable attention due to their efficacy in long-range sequence modeling, while requiring significantly less computational cost than full attention. Numerous models have been proposed based on SSMs. The most popular one is Mamba [16], which implemented a selection mechanism that makes parameters dependent on the input, all while maintaining linear complexity. Its improved version Mamba2 [13] proposed to produce the SSM parameters in parallel with the input, which is more hardware-friendly. Inspired by its efficiency, researchers have extended Mamba architectures to model 2D images and 3D videos on various vision tasks [22, 25, 30, 36, 39, 54, 58, 66]. More recently, different Mamba approaches [24, 31, 45, 64] have been proposed to handle different sequences. VL-Mamba [45] designed a Mamba module to project the features extracted from image and text modalities. Pan-Mamba [24] utilized a shared gate factor for the SSMs from different modalities. However, these methods treat SSMs primarily for intra-sequence modeling and only perform interaction on features after SSMs, thereby lacking direct inter-dependency transformations during selective scanning process. This limitation can hinder their ability to fully leverage the complementary information across different inputs. Therefore in this paper, we propose to employ the SSM in enhancing the recurrent feature propagation and reconstruction of video frames. + +# 3. Methodology + +# 3.1. Preliminaries + +State-Space Models (SSMs) [17] represent a class of sequence models inspired by control systems, which map a one-dimensional stimulation $x(t) \in \mathbb{R}$ to response $y(t) \in \mathbb{R}$ via a hidden state $h(t) \in \mathbb{R}^N$ , which are formulated as linear ordinary differential equations (ODEs): + +$$ +h ^ {\prime} (t) = \mathbf {A} h (t) + \mathbf {B} x (t), \quad y (t) = \mathbf {C} h (t), \tag {1} +$$ + +where the state transition matrix $\mathbf{A} \in \mathbb{R}^{N \times N}$ , $\mathbf{B} \in \mathbb{R}^{N \times 1}$ and $\mathbf{C} \in \mathbb{R}^{1 \times N}$ for a state size $N$ . To discretize the ODEs, S4 [17] utilized zero-order hold with a timescale parameter $\Delta$ , and transformed the parameters $\mathbf{A}$ and $\mathbf{B}$ from the continuous system into the discrete parameters $\overline{\mathbf{A}}$ and $\overline{\mathbf{B}}$ : + +$$ +\overline {{\mathbf {A}}} = \exp (\boldsymbol {\Delta} \mathbf {A}), \quad \overline {{\mathbf {B}}} = (\boldsymbol {\Delta} \mathbf {A}) ^ {- 1} (\exp (\boldsymbol {\Delta} \mathbf {A}) - \mathbf {I}) \cdot \boldsymbol {\Delta} \mathbf {B}. \tag {2} +$$ + +Therefore, the discretized model can be formulated as: + +$$ +h _ {i} = \overline {{\mathbf {A}}} h _ {i - 1} + \overline {{\mathbf {B}}} x _ {i}, \quad y _ {i} = \mathbf {C} h _ {i}. \tag {3} +$$ + +At last, from the perspective of global convolution, the output can be defined as: + +$$ +\overline {{\mathbf {K}}} = \left(\mathbf {C} \overline {{\mathbf {B}}}, \mathbf {C} \overline {{\mathbf {A B}}}, \dots , \mathbf {C} \overline {{\mathbf {A}}} ^ {L - 1} \overline {{\mathbf {B}}}\right), \quad y = \boldsymbol {x} * \overline {{\mathbf {K}}}, \tag {4} +$$ + +where $*$ represents convolution operation, $L$ is the length of sequence $x$ , and $\overline{\mathbf{K}} \in \mathbb{R}^L$ is a structured convolutional kernel. This method leverages convolution to synthesize the outputs across the sequence simultaneously, which enhances computational efficiency and scalability. + +However, the traditional SSMs like S4 used static parameterization, which restricts the capability to capture the sequence context. To address this, Mamba [16] calculated the dynamic input-dependent parameters B, C, and $\Delta$ based on the full input sequence $x$ , allowing a richer, content-aware parameterization and information selection. Then, it projected the full sequence into state-space representations, and selectively scanned over it to learn global features. Mamba2 [13] further derived a state-space duality for the dual forms between quadratic-time kernel attention and SSM. It also designed an efficient parallel projection pattern for the A, B, C, $x$ inputs by rearranging parameters in chunks. Due to its effectiveness in modeling long-range dependencies and efficiency in time and computation, it holds great potential for medical VSR, which requires accurate detail preservation and fast processing to enhance diagnostic quality. + +# 3.2. MedVSR Framework Overview + +Given a LR video sequence with frames $F_{1}, \ldots, F_{T}$ , our goal is to generate the super-resolved (SR) frames $F_{1}', \ldots, F_{T}'$ with a specific scaling factor. The overall architecture of our proposed MedVSR is shown in Fig. 3, which takes three consecutive LR frames as input and operates recurrently. It is constructed with a feature extraction part with plain convolution, multiple forward and backward Cross State-Space Propagation (CSSP) branches, and an Inner State-Space Reconstruction (ISSR) module to produce the final feature. + +# 3.3. Cross State-Space Propagation + +Instead of attempting to utilize the long-distance support frame directly through alignment for propagation, we employ it to control the mapping of the state to the output of the SSM with Cross State-Space Propagation (CSSP), as illustrated in Fig. 3(a). Specifically, let $f_{t-1}^j$ represent the feature computed at the $(t-1)$ -th timestep in the $j$ -th propagation branch. We partition this feature into local window features, denoted as $v_{t-1}^j$ . For the feature $f_{t-2}^j$ at the $(t-2)$ -th frame, we first warp it using the composite flow $o_{t-2} + o_{t-1}$ , then also partition it into window features $\overline{v}_{t-2}^j$ . The optical flows $o_{t-2}$ and $o_{t-1}$ are estimated using a pretrained SpyNet model [47] following the common practice [6, 32]. Then, we treat $\overline{v}_{t-2}^j$ as the supporting feature to support the propagation of feature $v_{t-1}^j$ : + +$$ +\tilde {f} _ {t - 1} ^ {j} = \operatorname {M L P} \left(\hat {v} _ {t - 1} ^ {j}\right) + \hat {v} _ {t - 1} ^ {j}, \tag {5} +$$ + +$$ +\hat {v} _ {t - 1} ^ {j} = \mathrm {C S S B} (\overline {{v}} _ {t - 2} ^ {j}, v _ {t - 1} ^ {j}) + v _ {t - 1} ^ {j} +$$ + +where the CSSB and MLP denote the Cross State-Space Block and multi-layer perceptron, respectively. Finally, we + +![](images/9f78d70c82a939fe81ab378070dc144c9df04aa206d21e76e4b644757198a5b7.jpg) +Figure 3. Illustration of the proposed MedVSR framework. For clarity, the main stream shows the $j$ -th propagation branch. MedVSR includes two core operations, which are CSSP that captures consistent features for enhancing propagation, and ISSR that reconstructs smooth frames with long-range spatial feature learning and short-range information aggregation. + +utilize $f_{t-1}^j$ to learn the deformable offset for the concatenated feature $[\tilde{f}_{t-1}^j, \overline{f}_{t-1}^j, f_t^j]$ in a DCN layer with residual convolutions [6, 12, 55], and obtain the final current frame feature $\hat{f}_t^j$ . The graphical illustration is presented in Fig. 4. + +Cross State-Space Block (CSSB). To facilitate the supporting distant frame to control the propagated feature, we need a long-range modeling mechanism between the distant feature $\overline{v}_{t-2}^j$ and the neighboring feature $v_{t-1}^j$ . To achieve better efficiency, we opt for the SSM that is a dual form of the quadratic-time attention [13] but with significantly less computational cost via a recurrent scanning manner. Since the original SSM in Mamba [13, 16] learns the global feature of a single state-space sequence, we extend it to process two frame sequences with separate projection layers followed by 1D convolutions to compute data-dependent parameters: $x_{t-1}^j$ , $\overline{\mathbf{B}}_{t-1}^j = \sigma(\mathrm{Conv1d}(\mathrm{LN}(v_{t-1}^j)\mathbf{W}^j))$ and $\mathbf{C}_{t-2}^j = \mathrm{LPE}(\sigma(\mathrm{Conv1d}(\mathrm{LN}(\overline{v}_{t-2}^j)\mathbf{W}_C^j))),$ where LPE represents learnable position embedding that will be discussed next. Notably, $\mathbf{C}_{t-2}^j$ is computed from the state-space sequence of the distant $(t-2)$ -th frame. By initializing the hidden state $h^j = x_{t-1}^j$ and state matrix $\overline{\mathbf{A}}_{t-1}^j$ , the output of each SSM iteration is updated by: + +$$ +h _ {i} ^ {j} = \overline {{\mathbf {A}}} _ {t - 1} ^ {j} h _ {i - 1} ^ {j} + \overline {{\mathbf {B}}} _ {t - 1} ^ {j} x _ {t - 1, i} ^ {j}, y _ {t - 1, i} ^ {j} = \mathbf {C} _ {t - 2} ^ {j} h _ {i} ^ {j}. \quad (6) +$$ + +Therefore, the propagated feature $y_{t - 1}^{j}$ is a the hidden space + +of the $(t - 1)$ -th frame controlled by the $(t - 2)$ -th frame. For the next $(j + 1)$ -th propagation branch, CSSB will also use the control matrix $\mathbf{C}_{t - 2}^{j + 1}$ derived from $\overline{v}_{t - 2}^{j + 1}$ to generate the output $y_{i + 1}^{j + 1}$ . Progressively, CSSB can compound the state-space sequences across frames and learn to propagate relevant features. After finishing the scan of entire sequences, we utilize the gate function $z_{t - 1}^j = \sigma ((\mathrm{LN}(v_{t - 1}^j)\mathbf{W}^j))$ and the scanned output $y_{t - 1}^j$ to produce the propagated output $\tilde{v}_{t - 1}^j = \mathrm{LN}(z_{t - 1}^j\times y_{t - 1}^j)\mathbf{W}_o^j$ . We also prove this characteristic through the analogy between SSM and the linear attention mechanism [20, 26] (refer to the supplementary). + +Local Windows (LW). Different from 2D convolution that aggregates local visual features, Mamba scans over all locations recurrently, which could suffer from forgetting of early pixels [18, 63]. This is particularly pronounced in VSR scenarios where the spatial resolution is much larger. Moreover, tokens within a local area are sufficient in providing critical support for effective reconstruction [9, 34, 37, 48]. To this end, we introduce a local window partitioning process prior to CSSB, as shown in Fig. 4. For an input feature with dimension $H \times W \times C$ , we define a window of size $l$ and partition the feature into $(H / l) \times (W / l)$ local windows, each with a dimension of $l \times l \times C$ . This strategy allows for a more focused analysis of local structures within the data. + +![](images/cd60ebabd474c6a904c9e18964e9c54fd15a727752d07f57a9680e197664290a.jpg) +Figure 4. Illustration of the CSSP. It propagates distant frame features to neighbor via the SSM in cross state-space block and aligns with the deformable convolution block. + +Learnable Position Embedding (LPE). In the original Mamba [16], there is no explicit position embedding [15] as the state-space model operates in a recurrent way. Consequently, the hidden state captures positional information based solely on the incoming order of tokens. However, flattening 2D frames into 1D sequences causes the loss of information regarding the beginning of new rows, hindering the model's ability to identify spatial relations in arbitrary directions. Therefore, we propose to employ a LPE layer that incorporates absolute position information and spatial context. Specifically, we reshape the 1D sequence to 2D feature and feed it into a learnable zero-padded 2D depthwise convolution [10], then reshape it back to 1D and proceed to the SSM. The LPE layer could incorporate absolute position [27] and improve the learning of spatial relations, which is essential for feature propagation and reconstruction. + +# 3.4. Inner State-Space Reconstruction + +After obtaining the features propagated from multiple forward and backward CSSP branches, we feed all features $\hat{f}_t^{1:j}$ into the proposed Inner State-Space Reconstruction (ISSR) for reconstruction, which is illustrated in Fig. 3(b). It uses ISSB with MLP that facilitates long-range spatial feature learning, followed by stacked LKSB with large-kernel convolutions for local information aggregation, leading to a detailed reconstructed feature of the $t$ -th frame $g_t$ . + +Inner State-Space Block (ISSB). Given propagated features from different branches, we first perform a channel-wise concatenation and dimension reduction with a 2D convolution, then split them into local windows: + +$$ +\hat {v} _ {t} = \mathrm {L W} \left(\operatorname {C o n v 2 d} \left([ \hat {f} _ {t} ^ {1}, \dots , \hat {f} _ {t} ^ {j - 1}, \hat {f} _ {t} ^ {j} ]\right)\right). \tag {7} +$$ + +Considering the large spatial size of the concatenated + +feature, SSM can be effective utilized for modeling the long-range spatial dependencies. We project the feature into data-dependent parameters: $x_{t}, \overline{\mathbf{B}}_{t}, \mathbf{C}_{t} = \sigma(\mathrm{Conv1d}(\mathrm{LN}(\hat{v}_{t})\mathbf{W}))$ , $z_{t} = \sigma(\mathrm{LN}(\hat{v}_{t})\mathbf{W})$ and apply SSM [13] following Eq. (3) to produce scanned result $y_{t}$ . Specially, the gating mechanism is replaced by a concatenation to produce the output: + +$$ +\hat {g} _ {t} = \operatorname {L N} ([ y _ {t}, z _ {t} ]) \mathbf {W} _ {o} + \hat {v} _ {t}. \tag {8} +$$ + +The concatenation operation enhances the learned representation with less computational complexity, which preserves more fine-grained features for reconstruction. + +Large Kernel Separable Block (LKSB). Besides learning long-range features via SSMs, we propose to reconstruct the features by gathering short-range information with large kernel convolutions: + +$$ +g _ {t} = \operatorname {L K S B} \left(\operatorname {M L P} \left(\hat {g} _ {t}\right) + \hat {g} _ {t}\right). \tag {9} +$$ + +Instead of stacking small kernel convolutions [5, 6, 57], utilizing large kernels could capture both contextual information from distant regions and details from nearby pixels [14, 38, 56], thereby improving the overall smoothness and fidelity of the reconstructed frames. + +# 4. Experiments + +# 4.1. Datasets and Implementation Details + +To evaluate our MedVSR, we conduct experiments on several medical video datasets with distinct scenes and screening devices, including HyperKvasir [3], LDPolyp [41], EndoVis18 [1], and Cataract-101 [51]. The HyperKvasir dataset is divided into training, validation, and testing sets. The Cataract-101 dataset is divided into training and testing sets. We train all models for 100,000 iterations, with a learning rate of 2e-4 and a cosine learning rate decay with a minimum value of 1e-7. The degradation process involves $4 \times$ bicubic downsampling accompanied by Gaussian noise with a covariance of 15. The number of propagation branches $j$ is 4 in our framework. During training, HR patches of size $256 \times 256$ are used. For the models trained with HyperKvasir training set, we test them on HyperKvasir testing set, LDPolyp, and EndoVis18, as they are all capturing the intra-body structures. The models trained with Cataract-101 training set are evaluated on its corresponding testing set. We follow existing VSR works [5, 59] to train the model with Charbonnier loss [7] $\mathcal{L} = \sqrt{\|F_t' - I_t\|^2 + \epsilon^2}$ , with $F_{t}^{\prime}$ as the reconstructed frame and $I_{t}$ as the ground truth frame. Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) are used as evaluation metrics. + +# 4.2. Comparison with State-of-the-Art Methods + +We compare our MedVSR with several state-of-the-art models, including EDVR [57], BasicVSR [5], BasicVSR++ + +Table 1. MedVSR performance on HyperKvasir [3], LDPolyp [41], and EndoVis18 [1] datasets with comparisons to state-of-the-art models. All models are trained from scratch with identical settings. The FLOPs and Latency are tested on Nvidia 4090 GPU using the video clip in HyperKvasir testing dataset. Best performances are highlighted in bold and second best performances are underlined. + +
ModelParams (M)FLOPs (T)Latency (s)HyperKvasir [3]LDPolyp [41]EndoVis18 [1]
PSNRSSIMPSNRSSIMPSNRSSIM
EDVR [57]20.6345.412.439827.11800.848330.08100.841721.67260.7883
BasicVSR [5]6.298.560.501831.46430.899031.68280.865030.71620.8950
BasicVSR++ [6]7.329.470.754731.72700.904231.66850.862030.79770.8958
VSRT [4]32.56112.648.119731.77890.899931.62870.859630.58710.8916
RVRT [32]10.7844.3616.021329.26210.894431.31740.857830.72220.8932
TCNet [33]9.6439.559.156531.11370.888931.38880.854730.16530.8859
IART [59]13.4144.7121.755331.29840.903031.69940.867130.46580.8924
MedVSR (Ours)7.169.461.148632.09580.906931.83330.867330.83440.8960
+ +![](images/67721b38d1317a00ee5b27f6613c5f2ef63d40566e37ed44946aa69d9461f1ad.jpg) +BasicVSR+ PSNR:33.48 + +![](images/5f485c971528dcd20948019cd1b72696cffa2d20bad389e19e4a2d48bb28185c.jpg) + +![](images/3cf603afc82ba023c9c20a1ce852d060c0c4a6195983d32c53023fafeed7a517.jpg) +Figure 5. Qualitative comparisons on HyperKvasir [3], LDPolyp [41], and EndoVis18 [1]. MedVSR reduces artifacts, provides detailed results, and reconstructs the textures accurately. For more qualitative comparisons, please refer to supplementary. Zoom in for details. + +![](images/a4da32420b3650396efc9d235900cf0040dc5cf15495fd177596db51da52b72e.jpg) + +![](images/a7419c5bf5d8933b78041b3c71b6e184c5a6ae37377b9725b1e048bb0e92c57f.jpg) + +![](images/b57268f1a1ea008c0c7fe934432e474a813a4a76187a23f413cae6979eb0f5d4.jpg) + +![](images/95b4f8a4886aa7b0e4bba42625e4f426f9efd26fa80643e8cc78df5322a093a8.jpg) + +![](images/b234bb17896affcf5579373db0284777a62b1d9b19d97b6c2158d4cd7aa73904.jpg) + +![](images/af81a6d5f08313ab82eee611d78a8a1dd37e24179133712d751f7bba0f14b5fc.jpg) + +![](images/f355020ab0d782a50f8032677223974218ff29108344b24bd9bea44e9bc7b872.jpg) + +![](images/64b8eb00614eadbde5ae461d5477cc4e9d1401c2cb71821d2b2ef97608054c13.jpg) +MedVSR PSNR:31.58 +BasicVSR++ PSNR:31.52 + +![](images/177cc93938aae7db6156c67816ac10e66c472aabbcc1e41d08948a7f9c70721a.jpg) + +![](images/41d3ef5ba3609bbab25144e2ea9251bd6fc1ed71ce73c9ec4dac079b209f1fd7.jpg) + +![](images/bff0ed482ae8ac326701d8e8993eb677517557dc40a9aa4266d0e037c74f702a.jpg) + +![](images/d821f82b784f5b2594a02d07ae0712fb21dd2c225bc8d3fe47442dd65125809f.jpg) + +![](images/1bd3ee061af3db7e6a05769275f09a4dd673fe30923986c469b3c76eda63004e.jpg) + +![](images/d01f8ab8c65437b8dc8b3e77c5ca7ec17c414ec2e16a5595316eb61ac06b92f6.jpg) + +[6], VSRT [4], RVRT [32], TCNet [33], and IART [59]. These models are trained from scratch with identical settings to ensure a fair comparison. As shown in Tab. 1, our MedVSR model outperforms compared models on all datasets. On the HyperKvasir dataset, MedVSR achieves a PSNR of 32.0958, which is 0.3169 higher than the second-best model VSRT [4], while requiring $3.5 \times$ fewer parameters and $10.9 \times$ fewer FLOPs. Similarly, on the LDPolyp dataset, MedVSR achieves a PSNR of 31.8333 and an SSIM of 0.8673, which are both higher than IART [59], while using only $3.6 \times$ fewer FLOPs and $3.7 \times$ fewer parameters. Notably, in the surgical scene dataset EndoVis18, which exhibits a larger gap and frame difference, our MedVSR remains effective, achieving a PSNR of 30.8344 and an SSIM + +of 0.8960. While the improvement over the powerful BasicVSR++ [6] may not be significant in terms of metrics, it excels in capturing nuanced details in the final super-resolved frames. This suggests that our model is also well-suited for handling complex and dynamic surgical scenes. + +In addition to its better performance, MedVSR model also demonstrates a significant advantage in inference speed, outpacing recent transformer-based models remarkably [4, 32, 59], while achieving comparable speed to CNN-based models that have been highly optimized by modern deep learning hardware [5, 6, 33]. Specifically, when measured on the HyperKvasir testing dataset with 50 frames per clip, the inference latency of MedVSR is 1.1642s, which is $6.0 \times$ faster than VSRT, $12.7 \times$ faster than RVRT, and $18.7 \times$ + +Table 2. MedVSR performance on Cataract-101 [51]. FLOPs is tested on NVIDIA 4090 GPU using the video clip in Cataract-101 test dataset. Best performances are highlighted in bold and second best performances are underlined. + +
ModelParams (M)FLOPs (T)Cataract-101 [51]
PSNRSSIM
EDVR [57]20.6342.8931.78430.9103
BVSR [5]6.298.0935.28920.9232
BVSR++ [6]7.328.9435.53580.9251
VSRT [4]32.56112.6435.24950.9230
RVRT [32]10.7844.3635.63780.9281
TCNet [33]9.6439.5534.59950.9177
IART [59]13.4144.7136.07640.9275
MedVSR7.168.9536.22750.9308
+ +faster than IART. The results demonstrate the efficacy and efficiency of using state-space transformations for propagation and reconstruction, establishing it as a robust approach for the complex and demanding medical VSR task. + +We present a qualitative comparison in Fig. 5. BasicVSR++ and IART could suffer from artifacts and blurry textures, while MedVSR successfully reconstructs the subtle vessels. Besides, MedVSR can restore the text precisely, which could be more clinically informative. The bottom right example shows that MedVSR preserves the texture of surgical tools. Notably, super-resolved tool textures offer several benefits for doctors. They can reveal microscratches and blade deformities, monitoring tool status and preventing tool failure. Also, sharper textures could enhance the accuracy of automatic tool control systems by providing more detailed visual cues. + +In Tab. 2, we list the results on the Cataract-101 dataset, which comprises different operation phases during cataract surgeries. MedVSR remains effective in different medical scenarios, which achieves 36.2275 PSNR and 0.9308 SSIM. Compared to TCNet [33] that explores long-distance consistency, our model surpasses it by 1.6280 in PSNR and 0.0131 in SSIM, meanwhile using $0.3 \times$ fewer parameters and $3.4 \times$ fewer FLOPs. In Fig. 6, qualitative results are provided. From the top case, both BasicVSR++ [6] and IART [59] produce results with inconsistent edges, which do not reflect the authentic structure. In contrast, MedVSR reconstructs the full structure precisely. In the bottom case, MedVSR preserves more detailed structure and color of the original frame. The results further demonstrate the generalization ability and robustness of our MedVSR. + +# 4.3. Ablation Study + +We conduct ablation studies on the HyperKvasir dataset [3] from the following aspects. + +Impact of the components in CSSB. We ablate CSSB + +![](images/34702ba78c9b0135e714ba7c00af6db3a45445f7a23b77b5f1502f360abee5f5.jpg) + +![](images/5bc5fee86d0ac28bcbc7ff43c087e4afe7967768dab03aa457fc414ab6e8baf7.jpg) + +![](images/939898697393828f8b1d4ebf5dc47efde98eac206307145a9cde5b6c6fe1a230.jpg) + +![](images/a198049df2f9a90b1771d1ddd67088cd671071d142c025ff04370065e5ffe804.jpg) + +![](images/d11ec1d35b53646aa36f34bf1629892590621702a9b5c0c59d4c372fc7a9cbdc.jpg) + +![](images/440b37b574fc20aad7fd17f95b6d502c02f76c0b4f0bf0fec23d6f36aa25150c.jpg) +Figure 6. Qualitative comparisons on Cataract-101 [51]. + +![](images/07841a6d700c93cffe8f5054ac1ca7655caa649298106cefc122fe8c7659b18f.jpg) + +![](images/807426610cb152a1fd6b1035126184336a61edd3f65e11cfe7bd5a0d7ab19744.jpg) + +![](images/e8d5e923954a05f3e2e784115e11097a7afe23b363dd598f3f6556dcf75e4da6.jpg) + +![](images/9bd2bd04cbe4b7282eb992805110eae828ea83e3f82d8b9c9c4f54ce920b16b5.jpg) + +by removing specific elements: the learnable position embedding (LPE), the local windows (LW), and the separate projection layers (SP). As shown in Tab. 3, the CSSB without LPE shows a 0.2856 PSNR degradation, demonstrating the efficacy of incorporating absolute position information for distant frames. Without LW, the PSNR drops by 0.2757, which indicates that scanning within local regions enhances the details more effectively. Lastly, the CSSB without SP is similar to directly concatenating the features of the two frames and process them jointly. This yields a large PSNR drop by 0.3572, which indicates the large visual gap in distant frames is difficult for the simple optical flow-based methods to propagate. The result highlights the importance of the learned consistent and stable information. + +Impact of the components in ISSB. We assess the design of ISSB, including local windows (LW) and the concatenation (CAT) in Tab. 4. Firstly, the model without LW shows a decrease in PSNR by 0.2743, suggesting that the information from early pixels during recurrent scanning are forget thus is ineffective. Secondly, replacing the original gating operation with CAT can reduce the parameters by 0.01M while improving the performance by 0.2430. + +Impact of the LKSB design. We propose LKSB to enhance the short-range information aggregation during reconstruction while alleviates artifacts, and we compare our design with other common convolution blocks in Tab. 5. Our model surpasses residual block [23] and depth-wise separable block [50] remarkably using 0.04M and 0.08M fewer parameters. Another choice is the partial block [8] that was proposed to improve efficiency, but it leads to a large decline in PSNR by 0.2152. Moreover, we ablate the kernel size. The performance continuous improves as the kernel size increases and saturates at 7. When increasing + +Table 3. Ablation study on the components in CSSB. + +
AblationParamsFLOPsPSNRSSIM
CSSB w/o LPE7.169.4631.81020.9049
CSSB w/o LW7.169.4531.82010.9050
CSSB w/o SP7.159.4431.73860.9047
CSSB7.169.4632.09580.9069
+ +Table 4. Ablation study on the components in ISSB. + +
AblationParamsFLOPsPSNRSSIM
ISSB w/o LW7.169.4531.82150.9053
ISSB w/o CAT7.179.4631.85280.9055
ISSB7.169.4632.09580.9069
+ +Table 5. Ablation study on the design of LKSB. + +
AblationParamsFLOPsPSNRSSIM
ResBlock [23]7.209.5031.80670.9053
DWBlock [50]7.249.5131.78580.9003
PBlock [8]7.129.4131.88060.9041
3×3 LKSB7.129.4031.90490.9050
5×5 LKSB7.139.4231.90770.9052
7×7 LKSB7.169.4632.09580.9069
9×9 LKSB7.209.5131.88520.9037
+ +it to 9, the PSNR drops by 0.2106, which suggests that the short-range information cannot be effectively aggregated. Therefore, we set the kernel size to 7 that achieves the optimal computational cost and performance trade-off. + +Impact of the propagation scheme. In the proposed CSSB, we utilize $(t - 2)$ -th frame to support $(t - 1)$ -th frame via SSM, which could extract stable and continuous features across frames. Here we ablate other propagation schemes in Tab. 6. When using $(t - 2)$ -th frame to support the $t$ -th frame $(t - 2 \rightarrow t)$ , the performance drops slightly as the captured consistent representations are not sufficient. When propagating the feature only from $t - 1 \rightarrow t$ , PSNR drops by 0.3224, which shows that without the long-term consistency captured at the $(t - 2)$ -th frame, the model fails to leverage the temporal information effectively. Moreover, when combining the $t - 2 \rightarrow t$ and $t - 1 \rightarrow t$ (Both), the performance is improved to 31.9116 PSNR, yet remains inferior to our design using $t - 2 \rightarrow t - 1$ with 32.0958 PSNR. The result suggests that the $t$ -th frame feature is already well extracted and may not be modified, while CSSB could produce well-aligned propagated features to enhance representations. + +# 4.4. Further Analysis + +Visualization of the effect of CSSB. In Fig. 7, we visualize the effect of utilizing our proposed CSSB. As shown in Fig. 7(b), the propagated features $\hat{f}_t^j$ without CSSB could lack the necessary details and lead to the presence of artifacts in the medical videos. Conversely, we observe a significant + +Table 6. Ablation study on the propagation scheme in CSSB. + +
Metrict-2→tt-1→tt-2→t-1Both
PSNR31.868431.773432.095831.9116
SSIM0.90530.90440.90690.9046
+ +Table 7. Performance comparison with different window sizes. + +
Metricl=4l=8l=16l=32
PSNR31.866131.901632.095831.8366
SSIM0.90510.90510.90690.9048
+ +![](images/857b69d8e01bbbda5b28a3a8e4667d3d022d0ca49dc40ac96e214e84230b24b0.jpg) + +![](images/03c157fd4dcfd9fd9bf4fa0cad7c925147f9533dfaa8dce88bcbdf24f37595d9.jpg) +(a) HR Frame + +![](images/11924ed3a1895ca9c727c0a3c87be6d0a1d448c40aa8b86a2201c3cb95cd0470.jpg) + +![](images/a658d6618f7d6aff3baae23ed9e46ec7f75fde81354ccee9b781def9904ee77c.jpg) +(b) w/o CSSB + +![](images/45af873bc2b268c49d7eeac10494b8c35a2f3a76f1d5dc348a862c06f963ee2e.jpg) + +![](images/c04887674522fd23ae20c006deec3cd0e89df4c1addfeb877c6719c1d2948361.jpg) +(c) w/ CSSB +Figure 7. Visualization of the effect of Cross State-Space Block. (a) The corresponding HR frame. (b) The propagated feature without the proposed CSSB. (c) The propagated feature with the proposed CSSB. Best viewed in color. + +enhancement in the clarity and of the visualized tissues and vessels with CSSB in Fig. 7(c). CSSB not only captures finer details but also reduces noise, which provides a more accurate representation of the underlying anatomy. + +Analysis on the window size in LW. We investigate the impact of local window size $l$ on our model's performance. As shown in Tab. 7, the best performance is achieved with a window size of 16, while a window size of 8 yields competitive results. A larger window size of 32 leads to a degradation in performance. This suggests that a moderate size 16 is optimal for capturing long-range spatial features. + +# 5. Conclusion + +In this paper, we point out that medical videos contain abrupt frame transitions and jitter, leading to optical flow errors and alignment difficulties. Besides, the inherent continuous tissue structures and nuanced vessels present difficulties for existing VSR models, which tend to reconstruct distorted features and are prone to artifacts. 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We are interested in simulating disease dynamics for clinical decision-making, leveraging recent advances in large generative models. To this end, we introduce the Medical World Model (MeWM), the first world model in medicine that visually predicts future disease states based on clinical decisions. MeWM comprises (i) vision-language models to serve as policy models, and (ii) tumor generative models as dynamics models. The policy model generates action plans, such as clinical treatments, while the dynamics model simulates tumor progression or regression under given treatment conditions. Building on this, we propose the inverse dynamics model that applies survival analysis to the simulated post-treatment tumor, enabling the evaluation of treatment efficacy and the selection of the optimal clinical action plan. As a result, the proposed MeWM simulates disease dynamics by synthesizing post-treatment tumors, with state-of-the-art specificity in Turing tests evaluated by radiologists. Simultaneously, its inverse dynamics model outperforms medical-specialized GPTs in optimizing individualized treatment protocols across all metrics. Notably, MeWM improves clinical decision-making for interventional physicians, boosting F1-score in selecting the optimal TACE protocol by $13\%$ , paving the way for future integration of medical world models as the second readers. + +# 1. Introduction + +Clinical decision-making is at the heart of patient care, driving outcomes and shaping the trajectory of healthcare interventions. Physicians constantly weigh the multimodal factors including medical images and patient history to deter + +![](images/901ac0d632aef7dfa3bfdf6dc8759eff62542bdb0034d1aacbd655d17d767445.jpg) +Figure 1. Formulation of Medical World Model. It integrates imaging observations with perception modules to form an initial state, which is then processed by a progression generative model to predict future states of disease under different treatment conditions. Recovery-conditioned policies guide treatment decisions, creating a feedback loop for optimizing clinical interventions. + +mine the best course of action for each patient. Artificial intelligence (AI) models are increasingly assuming a crucial role in this process by analyzing the complex multimodal data, revealing patterns that may be difficult to detect with human observation alone, and suggesting tailored treatment strategies based on predictive analytics. + +Foundation models [7] such as large language models (LLMs) [33, 57] present a new frontier in medical AI research and development. However, recent studies [26] show that LLMs, even those specifically tailored for medicine [13, 54, 55], diagnose significantly worse than clinicians and make less informed treatment decisions. This is due to several challenges. First, the complexity of diseases themselves, such as tumors that evolve under the influence of diverse biological and chemotherapy factors, calls for models that can adapt and account for disease progression. Second, clinical decision-making necessitates not only accurate predictions but also visually trackable insights that physicians can trust. + +Recent breakthroughs in world models (WMs) [3, 8, 39, 45, 62] provide a promising avenue for overcoming these obstacles. By generating a predictive distribution of how + +the world states evolve, WMs mirror the way human planners imagine future scenarios and then make informed decisions via inverse dynamics [3, 18]. Although they remain largely underexplored in the medical domain, world models hold significant potential for generating clinically realistic images and simulating disease progression, which in turn can facilitate more effective and visually trackable treatment planning. Figure 1 illustrates our formulation of introducing WMs into medical scenarios and how WMs integrate these capabilities to support clinical decision-making. + +In this work, we introduce Medical World Model (MeWM) to address these challenges and push the boundaries of AI-driven clinical decision support. MeWM comprises three primary components: (1) a Policy Model powered by vision-language architectures, which generates the potential action combos from a patient's current state and specific clinical scenario; (2) a Dynamics Model that forwards and simulates tumor dynamics, predicting how tumors could progress or regress under different treatment conditions by generative modeling; (3) an Inverse Dynamics Model that performs survival risk analysis on the simulated post-treatment tumor, and quantitatively evaluates treatment efficacy. Beyond forward simulation, this system heuristically explores the optimal plan with the assistance of a segmentation model. By uniting these elements, MeWM delivers a holistic framework for decision-making: it can synthesize realistic post-treatment tumors that pass Turing tests against radiologists, and it outperforms specialized GPT-like models on Transarterial Chemoembolization (TACE) Protocol Exploration (over $10\% \uparrow$ in F1-score). + +Overall, our contributions are threefold. + +- We propose the medical world models, where we develop a multimodal policy model that leverages vision-language capabilities to propose a tailored set of treatment action combos, and we design a generative dynamics model that accurately captures potential evolution of tumors, enabling forward-looking simulations for different interventions. +- We integrate an inverse dynamics model that translates these action-conditioned simulation into survival analysis metrics, thereby offering a transparent and evidence-based tool for choosing the optimal treatment protocol. +- We demonstrate a substantial leap in AI-driven decision support for interventional medicine, improving the F1-score in selecting the optimal treatment protocol by $13\%$ and offering a compelling glimpse into the future of precision healthcare. + +# 2. Related Work + +# 2.1. Generative World Modeling + +World models [23, 39] aim to simulate dynamic environments by predicting future states and rewards based on cur + +rent observations and actions. Originally developed for constrained settings like Atari games [24], their ability to model state transitions has been extended to real-world scenarios through joint learning of policies and world models, improving sample efficiency in simulated robotics [53], real-world robots [63] and autonomous driving [29, 61]. While early world models focused on simple state transitions, modern approaches integrate structured action-object relationships [59] and multi-modal conditioning [5, 21]. For instance, Du et al. [17] present long-horizon video plans by synergising vision-language models and text-to-video models. Luo et al. [46] propose to ground video models to continuous action by leveraging video-guided goal-conditioned exploration to learn a goal-conditioned policy. In embodied decision-making, Lu et al. [45] enables agents to imaginatively explore the world with high generation quality and exploration consistency using video generative models. However, there is still no work investigating the applicability of world modeling in medical image analysis and clinical decision-making. + +# 2.2. Tumor Synthesis + +Tumor synthesis has emerged as an attractive research topic across various medical imaging modalities, such as CT [11, 47, 67], MRI [4, 31, 64], and endoscopic videos [12, 41]. There are also many works on synthesizing non-cancerous lesions including chest CT synthesis [6, 47, 67, 68], and diabetic lesion synthesis in retinal images [15, 71]. Recent studies focus on improving the realism of synthetic tumors in the liver, kidney and pancreas [11, 30, 38] by leveraging the large generative models like diffusion models [28, 52, 56]. While these methods are conditioned only on shape masks, Li et al. [43] propose text-driven tumor synthesis by descriptive reports and conditional diffusion models. However, most of these works implemented tumor synthesis as a data augmentation to improve tumor detection tasks. They overlook its potential to empower clinical decision-making in treatment planning. In this work, we delve into the relatively unexplored field of tumor dynamics simulation by generating post-treatment tumors using pretreatment scans and treatment actions. + +# 2.3. Prognosis and Clinical Decision-making + +Post-treatment prognosis in medical imaging is essential for evaluating therapy effectiveness, predicting disease recurrence, and guiding further clinical decisions. CT is widely used to assess structural and functional changes in tumors following interventions such as surgery, chemotherapy, radiation therapy, transarterial chemoembolization (TACE), and immunotherapy [25, 32, 40, 44, 65, 66]. Lee et al. [40] employ a CNN-based model to predict the post-treatment survival of patients with hepatocellular carcinoma (HCC) using CT images and clinical information. In addition, + +![](images/bd2813ecb3fbf00e7203cb26c46d81c99046da3f960ba85378a0bc307199f5e6.jpg) +Figure 2. Overview of TACE Protocol Exploration by Medical World Model. (1) GPTs (Policy Model): construct the TACE action combos by the observation of pre-treatment CT, integrating clinical guidelines and policies. (2) Tumor Generative Model (Dynamics Model): simulates post-treatment tumor based on different TACE intervention protocols, predicting treatment outcomes. (3) Survival Analysis Model (Heuristic Function): assesses risk scores from both simulated post-treatment CT and pre-treatment CT to determine the most effective TACE protocol. Note that the 3D tumor masks (colored in red) can be extracted using a well-trained segmentation network (as Assistant Model). The framework enables visually trackable protocol optimization by iterating between clinical policy guidance, generative modeling, and survival analysis. + +LLMs are increasingly being explored to assist in clinical decision-making [9, 26, 36, 42]. However, little attention has been given to applying LLMs for post-treatment prognosis. They did not leverage the feedback from survival analysis to achieve prompt intervention as well. + +# 3. Medical World Models + +Overall Framework. As shown in Fig. 2, our MeWM takes a visual observation of pre-treatment CT $x_0$ , a language treatment goal $g$ to simulate the future state and explore the best treatment protocol. Policy model (§ 3.1) acquires the descriptive observation based on the visual state, and constructs a set of treatment protocols by the language goal and clinical guidelines. To perform the exploration, given the pre-treatment CT and an action combo, the dynamics model (§ 3.2) predicts the concrete resulting state, i.e., generating post-treatment CT. Finally, inverse dynamics model (§ 3.3) driven by Heuristic Function predicts the risk score from pre-treatment CT and simulated post-treatment CT with tumor masks from Assistant Model, to effectively prune branches in search and heuristically determine the optimal solution. + +# 3.1. Policy Model + +Vision-language models [10, 70] have emerged as a powerful source of prior knowledge about the clinical world, providing rich information about how to complete promising treatment from large-scale internet data and clinical guidelines. Based on TACE clinical guidelines, we set + +up the exploration configurations, including all potential chemotherapy drugs (e.g., Raltitrexed, Cisplatin) and embolism materials (e.g., Lipiodol, Gelatin Sponge). The two parts constitute the action base, which provides possible TACE protocols for Generative Dynamics Models as conditions. Then, we adopt a pre-trained large multimodal model (LMM), e.g., GPT-4o, to serve as policies. Given a high-level goal $g$ (e.g., "What TACE treatment protocols are recommended for a patient diagnosed with hepatocellular carcinoma (HCC) given the pre-treatment CT?"), the policy model $\pi_{\mathrm{VLM}}(x_0,g)$ extracts the visual observation and tumor context from the given pre-treatment CT $x_0$ to prompt the proper Transarterial Chemoembolization (TACE) actions. To constrain the excessively large tree search in the action base, we further prompt the Large Language Reasoning Model, i.e., Deepseek-R1 [22], to refine the drug set and embolism set by the clinical policies, whose final cardinalities are $D$ and $E$ , respectively. + +# 3.2. Dynamics Model + +Radiotherapy Report Extraction and Generation. While most existing studies focus on human-authored radiology reports, we aim to address radiotherapy reports to extract more comprehensive information on treatment protocols. However, raw radiotherapy reports pose significant challenges due to noise and fragmented information, which hinder controlled tumor synthesis. To mitigate these issues, we propose a two-stage text preprocessing framework consisting of data cleaning and augmentation. In the first stage, + +![](images/5494b511230b25c743d7b9697a813218f21697f258bc832563c60b056746e205.jpg) +Figure 3. Dynamics Model based on Tumor Generative Model. The training framework consists of three parts: (a) Radiotherapy Report Extraction and Generation: GPT-4o and Deepseek-R1 extract key treatment details from radiotherapy reports and generate corresponding TACE surgical actions. (b) Post-Treatment Tumor Generation: An Action-driven 3D Diffusion Model is conditioned by fused action embeddings and attenuated CT features to generate post-treatment tumors that simulate treatment outcomes. (c) Combo Contrastive Learning (CCL): The model learns from treatment variations by pushing apart dissimilar combos and pulling together similar ones, improving its ability to generate realistic and action-aware post-treatment tumor appearances. + +we perform keyword extraction by aggregating the outputs of both GPT-4o and DeepSeek-R1, focusing on key entities such as drugs, embolic agents, and their corresponding dosages. In the second stage, we leverage the same tools for text generation, constructing a structured core action description based on the extracted keywords. This approach enhances the consistency and informativeness of processed reports, facilitating downstream tasks in tumor synthesis and treatment analysis. + +Post-Treatment Tumor Generation. We adopt Latent Diffusion Models (LDMs) [52] for latent feature extraction from 3D Pre-treatment CT volumes and integrate textual action embedding for controlled tumor synthesis. Each 3D Post-treatment CT volume $x_{1} \in \mathbb{R}^{H \times W \times D}$ is encoded into a lower dimensional latent representation $z_{1} = \mathcal{E}(x_{1})$ using a 3D VQGAN autoencoder [19]. In the latent space, following the spirit of DiffTumor [11], we define a diffusion process that progressively adds noise to the latent representation $z_{1}$ over discrete time steps $t = 1, \dots, T$ . Given a pair of tumor-present pre-treatment CT volume $x_{0}$ and the mask of its tumor region $m_{0}$ , we condition the denoising model on the masked pre-treatment latent representation $z_{0}' = \mathcal{E}(m_{0}' \odot x_{0})$ where $m_{0}'$ is the attenuated mask from $m_{0}$ by our proposed Text-driven Morpho-Gaussian Attenuation. Specifically, to mimic the effects of TACE treatment, + +the process begins with occlusion assessment on radiotherapy reports. The textual descriptions (e.g., occluded, reduced, disappear) are extracted and analyzed to determine the attenuation level $l \in \{1, 2, 3, 4\}$ , where a higher value corresponds to better tumor curative effects. Then, morphological erosion and dilation with the adaptive kernel by $l$ are applied to $m_0$ , simulating occlusion-induced tumor structural dynamics. Simultaneously, adaptive Gaussian blurring is employed to exhibit the characteristics of heterogeneous intensity changes due to lipiodol deposition, necrotic transformation, and reduced perfusion. The final attenuated mask $m_0'$ is computed by the three steps, ensuring a smooth transition between tumor and organ tissues. Note that this attenuation is only used during training. + +Also, we condition the denoising model on the generated textual action. Given the action combo $a = \{a_1, \dots, a_H\}$ , each sub-action, respectively, undergoes encoding through a CLIP [51] text encoder $\phi(\cdot)$ followed by linear projection $\sigma_1(\cdot)$ , enabling dimension reduction to a latent clinical concept space. To enhance the semantics of action conditions in $D$ different drug and $E$ embolism keywords, we introduce learnable concept embeddings $c$ , which extract keyword representations from the given action combo. This explicit pharmaceutical grounding enables precise modeling of therapeutic components while maintaining robustness to + +context variations. The final action condition $\tau(a)$ is the fusion of holistic text and concept embeddings by fully connected layers $\sigma_2$ , where $[\cdot]$ denotes concatenation operation: + +$$ +\tau (a) = \sigma_ {2} ([ \left[ \right. \sigma_ {1} (\phi (a _ {1})), \dots , \sigma_ {1} (\phi (a _ {H})) ], c ]), \tag {1} +$$ + +The training objective of diffusion model is as follows: + +$$ +\mathbb {E} _ {z _ {1}, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \left\| \epsilon - \epsilon_ {\theta} \left(z _ {t}, z _ {0} ^ {\prime}, m _ {0}, \tau (a), t\right) \right\| _ {2} ^ {2} \right], \tag {2} +$$ + +where $\epsilon_{\theta}(\cdot, t)$ is a 3D U-Net with interleaved self-attention layers and convolutional layers [11, 28, 50] that predict the noise given the input variable and conditions. + +Combo Contrastive Learning. We adopt a contrastive learning strategy that aligns action combos with tumor evolution to enhance the realism and discrimination of posttreatment tumor synthesis. Given a pre-treatment anchor pair $(x_0, m_0)$ , along with an action combo $a$ , the goal is to generate a post-treatment CT $\hat{x}$ by generative model $f_{\mathrm{DM}}(\cdot)$ . + +For each anchor, positive samples, $\hat{x}^{+} = f_{\mathrm{DM}}(x_0^+,m_0^+,a^+)$ , are defined as synthetic post-treatment CT from another pair but its action combo contains the same drug/embolism keywords. Negative samples, $\hat{x}^{-} = f_{\mathrm{DM}}(x_0,m_0,a^-)$ , in contrast, are generated using the same pair but action combos with diverse keywords, leading to distinct tumor evolution patterns. This contrastive loss is incorporated into the tumor generative model: + +$$ +\mathbb {E} \left[ - \log \frac {\exp \left(\sin \left(\hat {x} , \hat {x} ^ {+}\right) / \delta\right)}{\sum \exp \left(\sin \left(\hat {x} , \hat {x} ^ {-}\right) / \delta\right) - \exp \left(\sin \left(\hat {x} , \hat {x} ^ {+}\right) / \delta\right)} \right], \tag {3} +$$ + +where $\operatorname{sim}(\cdot)$ denotes cosine similarity, $\delta$ is the temperature scaling factor. This contrastive learning strategy ensures that tumors simulated from similar treatment protocols exhibit consistent attenuation effects, while those derived from distinct protocols remain differentiable. + +# 3.3. Inverse Dynamics Model + +Inverse Dynamics Model, which empowers our full framework, aims to infer the most effective treatment strategy by analyzing relationships between pre-treatment conditions, intervention actions, and expected post-treatment outcomes. We unfold its essence in three aspects: (1) Assistant Model; (2) Heuristic Function and (3) TACE Protocol Exploration. + +Assistant Model. To better discriminate the tumor in synthesized post-treatment CT $\hat{x}$ , we introduce a tumor segmentation model as Assistant Model $H_{\mathrm{seg}}(\cdot)$ . Posttreatment tumors are characterized by heterogeneous high-intensity regions due to calcification/lipiodol deposition, irregular shapes reflecting necrotic tissue changes, and reduced or absent contrast enhancement in viable tumor areas, in contrast to traditional pre-treatment CT tumors. Thus, we adapt a pre-trained nnUNet-based [34] model to this posttreatment context by finetuning it on our ground truth pairs + +of post-treatment CT and mask. Given the well-trained Assistant Model, the simulated post-treatment CT $\hat{x}$ from Tumor Generative Model is processed for the segmentation of liver and tumor. The post-treatment CT with the predicted mask $\hat{m}$ is subsequently utilized for survival analysis. + +Heuristic Function. We use survival analysis model to implement a heuristic function $H_{\mathrm{surv}}(x_0, m_0, \hat{x}, m_0, g)$ , which quantifies the efficacy under the specific TACE action combo by the output risk score. Inspired by DeepSurv [35], we utilize a 3D convolution-based model structure, the 3D ResNet (MC3) [58], as the feature extractor of survival analysis model. Given the pre-treatment pair $(x_0, m_0)$ and simulated post-treatment pair $(\hat{x}, \hat{m})$ , we extract their concatenated CT and mask, respectively, and bidirectionally align the semantics of pre- and post-treatment by Cross-Attention Transformer [37]. After that, we adopt an attention-based aggregator to fuse pre- and post-features, followed by fc layers to determine the risk score. The action combo with a lower risk score should bring greater efficacy for the patient. Note that, for training, we leverage multi-task learning strategy, i.e., CoxPH [35] and OS regression, to improve the generalization of survival analysis. + +TACE Protocol Exploration. Given a combination of the proposed models above, we are able to predict TACE protocol from any Pre-treatment CT $x$ by a language treatment goal $g$ . To reason the optimal action combo, we propose to search for a list of actions to reach $g$ , corresponding to finding a treatment plan consisting of both drug and embolism components, which optimizes: + +$$ +\hat {x} _ {1: H} ^ {*} = \underset {\hat {x} _ {1: H} \sim \pi_ {\mathrm {V L M}}, f _ {\mathrm {D M}}} {\arg \min } H _ {\operatorname {s u r v}} \left(x _ {0}, m _ {0}, \hat {x}, H _ {\operatorname {s e g}} (\hat {x}), g\right), \tag {4} +$$ + +where $H = H_{d} + H_{e}$ + +With this objective in mind, we exhibit a tree-search exploration procedure. Our exploration algorithm initializes a set of $B$ parallel protocol beams. We sample the potential action space composed of $D$ drugs and $E$ embolisms and clinical rules using $\pi_{\mathrm{VLM}}$ . The clinical rules are introduced to prune unreasonable branches, e.g., concomitant use of multiple platinum-based agents is contraindicated due to the risk of cumulative toxicity and myelosuppression. We sequentially explore the two parts to ensure that TACE protocol contains both drugs and embolism. For each current action combo, we synthesize $T$ post-treatment tumors from $f_{\mathrm{DM}}(x_0, m_0, a)$ to obtain a more reliable simulation. We then use our heuristic function $H_{\mathrm{surv}}(x_0, m_0, \hat{x}, \hat{m}, g)$ with the assistance of $H_{\mathrm{seg}}(\hat{x})$ to select the generated tumor with the best average survival score of $T$ replicas among $D$ or $E$ actions. After every step of extending all beams, we discard the beam with the worst survival score and replace its action combo with the best beam. To prevent cumulative toxicity and organ dysfunction, we prohibit over-exploration by drug horizon $H_d$ and embolism horizon $H_e$ . Our final action combo is taken from the beam with the best survival + +Algorithm 1 TACE Protocol Exploration with MeWM +1: Input: Pre-treatment CT $x_0$ , Pre-treatment tumor mask $m_0$ , Language treatment goal $g$ +2: Functions: VLM Policy Model $\pi_{\mathrm{VLM}}$ , Dynamics Model $f_{\mathrm{DM}}$ , Heuristic Function $H_{\mathrm{surv}}$ , Assistant Model $H_{\mathrm{seg}}$ +3: Hyperparameters: Drug Actions factor $D$ , Embolism Actions factor $E$ , Tumor Generative factor $T$ , Protocol Beams $B$ , Drug horizon $H_d$ , Embolism horizon $H_e$ +4: plans $\leftarrow [[x_0] \forall i \in \{1 \dots B\}]$ # Initialize B Different TACE Protocol Beams +5: drug1:D, embo1:E, rule $\leftarrow \pi_{\mathrm{VLM}}(x_0, g)$ # Generate D Different Drug, E Embolism Actions, Clinical Rules +6: for $h = 1 \dots H_d$ do +7: for $b = 1 \dots B$ do +8: tumors $\leftarrow [f_{\mathrm{DM}}(x, drug_i)$ for j in $(1 \dots T)$ for i in $(1 \dots D)$ if rule] # Generate tumors from $x$ and plans[b] under rule +9: plans[b].append(argmin(tumors, $H_{\mathrm{surv}}, H_{\mathrm{seg}}$ ) # Add Tumor with Lowest Risk to Plan +10: end for +11: maxidx, minidx $\leftarrow$ argmax(plans, $H_{\mathrm{surv}}, H_{\mathrm{seg}}$ ), argmin(plans, $H_{\mathrm{surv}}, H_{\mathrm{seg}}$ ) +12: plans[maxidx] $\leftarrow$ plans[minidx] # Periodically Replace the Plan with High Risk +13: end for +14: for $h = 1 \dots H_e$ do +15: for $b = 1 \dots B$ do +16: tumors $\leftarrow [f_{\mathrm{DM}}(x, embo_i)$ for j in $(1 \dots T)$ for i in $(1 \dots E)$ if rule] # Generate tumors from $x$ and plans[b] under rule +17: plans[b].append(argmin(tumors, $H_{\mathrm{surv}}, H_{\mathrm{seg}}$ ) # Add Tumor with Lowest Risk to Plan +18: end for +19: maxidx, minidx $\leftarrow$ argmax(plans, $H_{\mathrm{surv}}, H_{\mathrm{seg}}$ ), argmin(plans, $H_{\mathrm{surv}}, H_{\mathrm{seg}}$ ) +20: plans[maxidx] $\leftarrow$ plans[minidx] # Periodically Replace the Plan with High Risk +21: end for +22: plan $\leftarrow$ argmin(plans, $H_{\mathrm{surv}}, H_{\mathrm{seg}}$ ) # Return Plan with Lowest Risk + +score and adopted as TACE protocol for the patient. The pseudocode of our method is also provided in Algorithm 1. + +# 4. Experiments + +HCC-TACE In-house Dataset. We collect a large repository of 338 longitudinal paired pre- and post-treatment CT scans with well-annotated liver/tumor masks and clinical records, such as TACE radiotherapy reports as gold action and Overall Survival (OS) time. We split the training set (validation set included) and testing sets in the 9:1 ratio. + +HCC-TACE-Seg Public Dataset [49]. For external validation, we use patients from HCC-TACE-Seg public dataset referring to a single-institution collection with confirmed HCC treated at The University of Texas MD Anderson Cancer Center. We conduct data curation and preprocessing to collect 78 cases containing pre-treatment CT, posttreatment CT, TACE Gold Action, and OS time. We use $80\%$ cases to fine-tune and validate MeWM and leave $20\%$ cases for the exploration evaluation. + +# 4.1. Evaluation on Generation Quality + +Visual Turing Test (Human Evaluation). We conduct an action-driven Visual Turing Test on 240 CT scans of post-treatment tumors, where 120 scans contain real posttreatment tumors, and 120 scans contain synthetic posttreatment tumors generated by different tumor synthesis models. Three radiologists (R1-R3) participated in this study, independently evaluating five groups of 48 CT scans each and classifying them as either real or synthetic. It + +is important to note that the radiologists' evaluations are based on whether the synthetic tumor closely resembles a post-treatment tumor, which typically contains a mixture of lipiodol deposition, necrotic, and viable tumor regions, distinguishing it from ordinary pre-treatment tumors. The test results are summarized in Table 1. The sensitivity scores of all radiologists remain high (above $91\%$ ), demonstrating their ability to correctly identify real post-treatment tumors. However, specificity scores vary among the methods, indicating different levels of realism in the synthetic tumors. Notably, our method MeWM achieves the lowest specificity scores (79.17% for R1, 70.83% for R2, and 75.00% for R3), suggesting that a large proportion of synthetic tumors generated by our approach are mistaken as real. This indicates superior realism compared to other methods such as SynTumor [30], Pixel2Cancer [38], DiffTumor [11], and Tex-toMorph [43]. Figure 4 illustrates examples from the test, where a real tumor is compared with synthetic tumors that radiologists correctly or incorrectly classified. This highlights synthetic tumors closely resemble real ones. + +Perceptual Evaluation. We perform perceptual evaluation using FID and LPIPS scores, where lower values indicate better simulation quality. Our method achieves the best FID (0.71) and LPIPS (0.6120), demonstrating the highest fidelity in synthetic tumor generation. These results confirm that MeWM effectively synthesizes realistic post-treatment tumors, making it more challenging for radiologists to distinguish between real and synthetic cases. + +Table 1. Action-driven Visual Turing Test involves three radiologists (R1-R3) each evaluating five groups of 48 CT scans each, with 24 real post-treatment tumors and 24 synthetic post-treatment tumors from a tumor generative model, respectively. They were tasked with categorizing each CT scan as either real or synthetic. A higher sensitivity score indicates better discriminative ability of radiologists, while a lower specificity score indicates a higher number of synthetic tumors being identified as real. We also provide perceptual evaluation using FID and LPIPS compared to corresponding real post-treatment scans. Lower FID and LPIPS indicate better simulation results. + +
MethodsR1R2R3Perceptual metrics
sensitivityspecificity ↓accuracysensitivityspecificity ↓accuracysensitivityspecificity ↓accuracyFID↓LPIPS↓
SynTumor [30]100.095.8397.9287.5095.8391.67100.095.8397.923.330.6832
Pixel2Cancer [38]95.83100.097.9291.6795.8393.75100.0100.0100.03.340.6831
DiffTumor [11]100.091.6795.8395.8387.5091.67100.087.5093.751.400.7660
TextoMorph [43]100.091.6795.8391.6783.3387.5095.8387.5091.671.030.9111
MeWM (Ours)100.079.1789.5891.6770.8381.2591.6775.0083.330.710.6120
+ +![](images/a1995562c0e085e0cf05511ca5f968a2e3fe7c02c614fd418fe72b6f1e965e00.jpg) +Figure 4. Examples of Visual Turing Test. We present one real tumor alongside examples of synthetic tumors that were correctly and incorrectly identified. A red dot indicates the radiologist classified the post-treatment tumor as synthetic, while a green dot signifies it was identified as real. + +![](images/a8d5908d0ae03f7b5985b95bf9677b49a510a340635044524707727341649391.jpg) +Figure 5. Performance of heuristic function on survival analysis. The first three heatmaps show the true risk distribution, Cox model predictions, and our heuristic function predictions. The last two depict prediction errors, with lower MSE (0.2142) for our model compared to the Cox model (0.3550), demonstrating improved accuracy in capturing localized risk patterns. + +# 4.2. Survival Analysis + +In Figure 5, we evaluate survival risk regression between the popular Cox Proportional Hazards model [20] and our heuristic function model on the HCC-TACE-Seg dataset. The true risk distribution (left) is estimated using the Nelson-Aalen estimator [14]. The Cox model fails to accurately distinguish between high- and low-risk samples from low-dimensional deep features, resulting in an overly smoothed risk distribution. In contrast, our model produces a risk map that better aligns with the true distribution, ef + +![](images/5f79db3e914699f0bc2c8b15cdab95098155c104af88b8fe02fd6903d65647dd.jpg) +Figure 6. Kaplan-Meier Survival Curves: Radiomics-based Cox Model [60] vs. our deep model. The left shows the survival curves predicted by the Cox model based on Radiomics features. The right presents the survival curves from our model based on deep features, which achieves a significantly higher c-index of 0.752 and a log-rank p-value of $6.74e - 5$ , demonstrating a stronger ability to distinguish between high- and low-risk groups. Shaded areas represent confidence intervals. + +fectively capturing variations in risk levels. Error analysis shows higher Mean Square Error (MSE), i.e., 0.3550 for Cox and lower MSE, 0.2142 for our model, indicating superior accuracy. Figure 6 further presents Kaplan-Meier survival curves comparing risk stratification performance between the Radiomics-based Cox model and our deep model. These results demonstrate that our heuristic function better estimates survival risks, reduces prediction errors, and captures complex patterns beyond the capabilities of the Cox model and radiomics features. + +# 4.3. Results on TACE Protocol Exploration + +Evaluation Strategy. For treatment planning evaluation, we utilize four metrics in Table 2: (1) $F1$ -score: harmonizes Precision and Recall, balancing redundancy and omissions; (2) Jaccard Index: measures prediction overlap with gold actions, emphasizing category-level alignment; (3) Precision: reflects recommendation purity, penalizing incorrect or redundant drugs/embolisms; (4) Recall: captures therapeutic coverage, highlighting critical omissions. + +Partial Observation Misleads GPTs. For Multimodal Large Language Models (e.g., GPT-4o, MedGPT, HuatuoGPT-Vision), they are prompted with pre-treatment CT slices and allowed to predict the action combo from the given action set. These inferior results (over -10% in F1- + +Table 2. TACE Protocol Exploration Evaluation on HCC-TACE in-house dataset and public dataset. F1-score, Jaccard index, Precision, and Recall are computed between the predicted action combo and gold action. MeWM significantly advances multimodal GPTs in exploring optimal individualized treatment protocol across all metrics, even comparable to interventional physicians. + +
MethodsIn-house datasetPublic dataset
F1-score↑Jaccard↑Precision↑Recall↑F1-score↑Jaccard↑Precision↑Recall↑
Physician w/ Pre-CT48.8138.4446.6754.6771.4363.1066.6778.57
Physician w/ MeWM61.51 (+13%)49.8960.8965.4480.00 (+9%)73.8176.1685.71
Qwen2.5-VL [2]37.0924.4934.4441.8347.1434.4053.5742.86
GPT-4o [33]41.9727.8135.9352.7844.2932.7457.1438.10
Claude-3.7-sonnet [1]40.9328.5545.8337.7844.7633.8164.2935.71
CT2Rep [27]27.7517.2130.8325.8343.6128.5753.5737.50
MedGPT [16, 48]37.5125.5732.7845.2147.1440.4850.0045.24
HuatuoGPT-Vision [69]40.1329.0840.1142.2852.6242.2654.7651.19
MeWM(Ours)52.3838.5963.0646.1764.0848.4572.6258.93
+ +Table 3. Ablation studies of TACE protocol exploration on both datasets. "AM" denotes Assistant Model, while "CCL" denotes Combo Contrastive Learning. Two components significantly contribute to better exploring the optimal treatment. + +
Metrics ↑In-house datasetPublic dataset
w/o AMw/o CCLw/o AMw/o CCL
F1-score49.13 (-3.9)50.97 (-1.4)60.03 (-4.1)62.90 (-1.2)
Jaccard35.40 (-3.2)36.76 (-1.8)45.36 (-3.1)46.97 (-1.5)
Precision56.39 (-6.7)60.57 (-2.5)75.00 (+2.4)70.10 (-2.5)
Recall45.22 (-1.0)45.36 (-0.8)52.38 (-5.6)56.72 (-2.2)
+ +score) to MeWM demonstrate that it tends to make deficient planning relying solely on vision-language models and their commonsense reasoning. This also validates the necessity of simulation from pre-treatment to post-treatment. + +MeWM as A Clinical Decision-support Tool. MeWM demonstrates significant potential in augmenting the capabilities of radiologists and physicians, underscoring its clinical relevance in optimizing TACE planning. Reliance solely on pre-treatment CT often results in partial observation and suboptimal targeting due to heterogeneous pathological conditions. By incorporating MeWM's recommended protocol, clinical decision-making is markedly enhanced, yielding performance improvements of 12.70, 11.45, 14.22, and 10.77 in F1-score, Jaccard, Precision, and Recall on our dataset. MeWM facilitates accurate tumor localization and enables predictive assessment of postembolization outcomes, thereby reducing procedural uncertainty. Moreover, its synthetic post-treatment CT projections help anticipate embolization efficacy, optimize TACE distribution, and mitigate non-target embolization risks, contributing to enhanced therapeutic precision and individualized strategies. MeWM serves as a critical decision-support tool in interventional oncology, bridging anatomical imaging with functional assessment for meaningful clinical outcomes. As shown in Figure 7, interventional physicians refine TACE protocols by MeWM intervention, aligning treatment with expert practices. + +Ablation Study. As shown in Table 3, we ablate the effectiveness of Assistant Model and Combo Contrastive + +![](images/a63cdf8224065df7f96a1362c6de3124da590ff33c4cdb24529eaa2b0dbeb508.jpg) +Figure 7. Example of MeWM intervention in clinical applications. The radiologist initially proposes a TACE protocol with Raltitrexed, Lobaplatin, Idarubicin, and embolization using Lipiodol and Gelatin Sponge. MeWM simulates a protocol with Raltitrexed, Lobaplatin, and Lipiodol. After intervention, the optimized protocol removes Idarubicin but restores Gelatin Sponge, aligning with gold action. + +Learning (CCL) in TACE Protocol Exploration. The results demonstrate that both the Assistant Model and Combo Contrastive Learning (CCL) contribute significantly to its performance. Removing the assistant model, which provides the location information of tumors for heuristic function, leads to a critical drop in F1-score $(52.38\rightarrow 49.13)$ on our dataset, as well as on public dataset. Similarly, omitting CCL reduces F1-score (e.g., $52.38\rightarrow 50.97$ ), indicating that CCL enhances the model's discrimination on action units. Overall, MeWM achieves the best results across all metrics, even outperforming radiologists in some areas. + +# 5. Conclusion + +We present Medical World Model, which marks a step toward AI-driven precision medicine by simulating disease evolution and optimizing clinical strategies. By bridging generative modeling with medical decision-making, it enables a deeper understanding of treatment outcomes and refines intervention planning. The advancements of MeWM in tumor synthesis and survival analysis set the stage for future AI systems that seamlessly integrate with clinical workflows, driving the next generation of longitudinal data-driven healthcare. + +Acknowledgement: This work was supported by the Guangdong Science and Technology Department (No. 2024ZDZX2004), the Guangzhou Municipal Science and Technology Project (No.2024312139), the Lustgarten Foundation for Pancreatic Cancer Research, the Patrick J. McGovern Foundation Award, and the National Institutes of Health (NIH) under Award Number R01EB037669. + +# References + +[1] AI Anthropic. Claude 3.5 sonnet model card addendum. 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To take the best of both camera- and LiDAR-based detectors, we propose MemDistill, a novel cross-modal knowledge distillation framework for 3D object detection. MemDistill transfers rich 3D knowledge from a LiDAR-based teacher model to a camera-based student model through a dedicated memory unit and a scene-dependent memory retrieval module. To be specific, our framework distills the teacher's 3D knowledge, optimizes the memory to store that knowledge compactly, and learns the retriever that searches the memory to produce 3D features relevant to the input scene, compensating for the missing LiDAR modality. Experiments on the nuScenes dataset demonstrate that MemDistill significantly improves performance of its camera-only baseline, achieving the state of the art in camera-based 3D object detection. + +# 1. Introduction + +3D object detection, the task of localizing and classifying objects in the 3D space at once, plays crucial roles in a wide range of applications such as autonomous driving [5, 6, 38, 39, 41], robotic navigation [1, 44] and virtual reality [11, 37]. In recent years, camera-based 3D object detectors [4, 14, 26, 29, 40, 50] have gained significant attention for their cost-effectiveness and rich semantic cues inherent in RGB images. However, their performance remains limited compared to LiDAR-based approaches [22, 31, 33, 46, 48], which achieve superior results by leveraging 3D point clouds that provide rich geometric information crucial for accurate 3D object localization. + +To take the best of both camera- and LiDAR-based detectors, knowledge distillation (KD) that transfers the rich 3D knowledge of a LiDAR-based detector to a camera-based detector has been studied. Existing techniques [7, + +![](images/3d3fee1cf52f867ea3f90fb2037243bb3138fe0356ab2deb1506d277c219c7ef.jpg) +(a) +Figure 1. Conceptual illustration of conventional KD from a LiDAR-based teacher to a camera-based student (a) and the proposed method using a memory module, dubbed MemDistill (b). The conventional one allows the student to distill useful 3D information from the teacher, but suffers from the absence of LiDAR input, which substantially limits the student's capability. MemDistill alleviates this issue with a memory module and retriever, which are trained to distill 3D LiDAR knowledge from the teacher to compensate for the missing LiDAR modality ①; the student is then further fine-tuned for better alignment with the teacher ②. + +![](images/788826945470177c7010e5cd481e9e118783d8e96a284b8856b751ad07fb915d.jpg) +(b) + +16, 20, 21, 43, 52] in this line of research adopt a teacher-student paradigm, where a camera-based detector (student) is trained to mimic the intermediate features and final predictions of a pre-trained LiDAR-based detector (teacher) so that the student inherits accurate geometric information of the teacher (Figure 1a). Despite their effectiveness, however, these methods are not optimal for cross-modal knowledge distillation in 3D object detection since the substantial modality gap between point clouds and images makes it difficult for the student to align its features originating + +![](images/d181891a0b3d667a64b68e6757ec73437d434d9a5440af0bdc396639c980a974.jpg) +Figure 2. Our cross-modal knowledge distillation framework, MemDistill, employs two detection networks: a camera-based student with a memory and its retriever, and a LiDAR-based teacher that provides geometric information to the student. The first step of our method is memory distillation, where the memory and its retriever are trained to produce features that minimize the discrepancy between the student and teacher in their intermediate features and final predictions. This is achieved by minimizing the mean squared error (MSE) loss $\mathcal{L}_{\mathrm{MSE}}$ along with the object detection loss $\mathcal{L}_{\mathrm{task}}$ , while keeping the rest of the student model frozen. After the memory distillation, the student with the memory retriever is fine-tuned to further align with the teacher, while keeping the memory frozen. In this fine-tuning stage, the same losses as in the memory distillation are used. For evaluation, we use the student model with camera input only. + +from images with those learned by the LiDAR-based detector. More importantly, the absence of LiDAR input itself for the student significantly limits its performance. + +In this paper, we propose MemDistill, a cross-modal KD method for 3D object detection that compensates for the missing LiDAR modality using a specialized memory unit; its overall framework is illustrated in Figure 2. At the core of MemDistill is a memory distillation process designed to compactly store rich 3D LiDAR features, along with a dedicated retrieval mechanism that effectively extracts and integrates complementary 3D structural information into the camera-based model. By leveraging and incorporating this distilled memory, the student enhances its feature representations and compensates for the missing LiDAR modality. However, due to the high dimensionality and diversity of 3D LiDAR features, the memory requires a specialized pipeline to ensure both compactness and expressive capability for effective retrieval of relevant 3D cues. To address this, we employ a scene-dependent memory retrieval mechanism that extracts informative 3D-aware features from the memory based on given image features; the retrieved features are then fused with the original camera features to compensate for the lack of 3D information. + +Moreover, to further facilitate the cross-modal KD, we + +carefully design both the student model's architecture and its initialization strategy. Specifically, the student retains the image backbone from a pre-trained camera-based detector while incorporating the neck and head of a pre-trained LiDAR-based detector, in addition to the memory and its retriever. This design choice ensures that the student benefits from 3D perception capability of the neck and head while leveraging the camera-based backbone for feature extraction. Note that, although the image backbone captures rich semantic features from two-dimensional images, its representations differ significantly from those of LiDAR-based models, making direct knowledge transfer challenging. By integrating the LiDAR-based detector's neck and head, the student is better aligned with the teacher in the representation space, facilitating KD. Also, this hybrid design enables the memory module to encode features that more closely resemble the actual LiDAR features, as the neck and head are shared with the teacher. + +The training process of our method consists of two stages, memory distillation followed by fine-tuning of the student, both of which are based on KD from the teacher. At first, the weights of the image backbone of the student are initialized with those of a pre-trained camera-based detector, while the weights of the neck and head are initialized + +with those of the LiDAR-based teacher. During the memory distillation stage, the memory module is trained to produce features that compensate for the absence of the LiDAR modality to minimize the discrepancy between the student and teacher in both their intermediate features and final predictions, while the rest of the student remains frozen. This allows the memory to effectively capture the spatial and structural information encoded in the teacher's LiDAR features. After the memory distillation, the student is finetuned to better align with the teacher, while freezing the memory to preserve the essential knowledge distilled earlier. This two-stage training strategy enables the memory to first learn essential 3D representations from the teacher, which then support effective fine-tuning of the student, ultimately improving 3D object detection performance. + +Following previous work [7, 20, 21, 43], we evaluated MemDistill on the nuScenes dataset [2], where it demonstrated significant performance improvement over its camera-only counterpart and achieved state-of-the-art performance. In summary, our contribution is three-fold: + +- We introduce MemDistill, a novel cross-modal knowledge distillation framework that leverages a memory module to store and retrieve rich 3D LiDAR features, enabling a camera-only model to compensate for the missing LiDAR modality and bridge the modality gap. +- We propose a scene-dependent memory retrieval mechanism that efficiently retrieves compact yet expressive LiDAR representations, ensuring effective feature alignment between the teacher and student models. +- We demonstrate that MemDistill improves camera-based 3D object detection substantially, achieving the state of the art and substantially reducing the performance gap between camera- and LiDAR-based detectors. + +# 2. Related Work + +Camera-based 3D Object Detection. Camera-based 3D object detection aims to detect objects using camera input alone. Mono3D [4] and MonoFlex [50] focus on improving depth estimation through monocular depth prediction. FCOS3D [40] extends the 2D detection paradigm to 3D by predicting attributes in the image domain. Another line of research focuses on leveraging multiple camera views. BEVDet [14] uses the Lift-splat-shoot mechanism [36] to explicitly transform images into bird's eye view (BEV) space, followed by a conventional 3D detection head. PETR [29] extends DETR [3] for 3D object detection by introducing positional encodings for 3D reference points, transforming these into image-view features. BEVFormer [26] further enhances the BEV transformation process using cross-attention to fuse multi-view features more effectively. PolarFormer [18] incorporates polar coordinates in the BEV representation, and BEVDepth [25] lever + +ages depth prediction using LiDAR points along with temporal information. Despite these advances, the lack of reliable depth cues leads to a performance gap between camera-only and LiDAR-based methods, with camera-based models often falling short in comparison. + +Knowledge Distillation in 3D Object Detection. Knowledge Distillation (KD) in 3D object detection transfers rich 3D knowledge from a LiDAR-based teacher to a camera-based student. Various KD methods focus on intra-modality distillation, where the student approximates features or predictions from a teacher using the same modality [8, 15, 49]. Recent approaches extend KD to cross-modal settings, employing a LiDAR-based teacher to train a camera-based student [7, 16, 20, 21, 43, 51, 52]. BEVDistill [7] and DistillBEV [43] use voxel and BEV transformations to align LiDAR and camera features for effective distillation, while TiG-BEV [16] improves geometry learning through inner-feature distillation in the BEV space. UniDistill [52] and SimDistill [51] propose specialized loss functions to align the sparse LiDAR features with dense camera features. $\mathrm{X}^3\mathrm{KD}$ [21] proposes cross-task KD, transferring information from instance segmentation tasks. LabelDistill [20] further enhances KD by directly leveraging ground truth labels during training. Despite their effectiveness, the existing KD methods still struggle with the substantial modality gap between point clouds and images. To address this, MemDistill introduces a specialized memory unit with a two-stage training pipeline to effectively bridge the modality gap between the teacher and the student. + +# 3. Proposed Method + +MemDistill consists of two stages: distilling LiDAR features from the teacher (i.e., LiDAR-based detector) into the memory module, followed by fine-tuning the student (i.e., camera-based detector) using the learned memory representations. In the remainder of this section, we first present the overall architecture of MemDistill (Section 3.1), and then elaborate on the two-stage training process (Section 3.2). + +# 3.1. Model Architecture + +We construct a teacher-student model pair, consisting of a LiDAR-based teacher model and a camera-based student model that incorporates a distilled memory and its retrieval module. The student takes input only from cameras, but it is augmented by the memory module, which allows it to learn complementary information from the LiDAR-based teacher, as shown in Figure 2. + +# 3.1.1. Teacher Model + +We adopt CenterPoint [48] as our LiDAR-based teacher model, which comprises a LiDAR backbone, neck, and prediction head, as illustrated in Figure 2. The teacher processes a point cloud $P$ using a LiDAR encoder $f_{\mathrm{lidar}}$ to ex + +![](images/6394ed5e4c4392a72fa1eb16d6db11997cf8808ee96fad30123a9fdcf5180351.jpg) +Memory Retriever +Figure 3. Overview of the memory retriever. First, the latent embeddings $E$ and the camera features $F_{\mathrm{cam}}$ are fed into the first transformer decoder $f_{\mathrm{dec1}}$ , where $E$ serves as the query and $F_{\mathrm{cam}}$ as the key and value. The output from the first transformer decoder is then refined through self-attention layers in the transformer encoder $f_{\mathrm{enc}}$ . Finally, the refined output and the distilled memory $M$ are fed to the second transformer decoder $f_{\mathrm{dec2}}$ , where the refined output serves as the query and $M$ as the key and value, resulting in LiDAR-informed complementing features $F_{\mathrm{cmp}}$ . + +tract bird's-eye view (BEV) features, denoted by $F_{\mathrm{bev}} = f_{\mathrm{lidar}}(P) \in \mathbb{R}^{D \times H \times W}$ , where $D$ means the channel dimension, and $H$ and $W$ denote the height and width of the BEV feature map. The BEV features are then refined by the neck module $f_{\mathrm{neck}}$ , which enhances them through multi-resolution processing to produce $F_{\mathrm{bev}}' = f_{\mathrm{neck}}(F_{\mathrm{bev}})$ . Finally, the prediction head $f_{\mathrm{pred}}$ generates classification and regression outputs, $(F_{\mathrm{cls}}, F_{\mathrm{reg}}) = f_{\mathrm{pred}}(F_{\mathrm{bev}}')$ . + +# 3.1.2. Student Model + +The student model employs an integrated architecture that combines components from both camera-based and LiDAR-based detectors, enabling it to benefit from both modalities while operating without LiDAR input at inference. Specifically, the student consists of four key components: (1) the image backbone and camera-to-BEV transformation from a camera-based detector, BEVDepth [25], (2) the neck and prediction head from the LiDAR-based teacher, CenterPoint [48], (3) a memory module and its retriever, and (4) a fusion module that combines the camera and retrieved memory features. + +At first, the student takes multi-view images $I$ as input and processes them using a 2D image encoder $f_{\mathrm{cam}}$ . The extracted features are then passed through a camera-to-BEV transformation module $f_{\mathrm{proj}}$ to produce BEV features: + +$$ +F _ {\mathrm {c a m}} = f _ {\mathrm {p r o j}} \left(f _ {\mathrm {c a m}} (I)\right) \in \mathbb {R} ^ {D \times H \times W}, \tag {1} +$$ + +where $D$ is the channel dimension, and $H$ and $W$ are the height and width of the BEV feature map. + +To compensate for the missing LiDAR modality, the student model includes a memory module $M \in \mathbb{R}^{D \times N}$ , + +where $N$ represents the memory size. The memory module stores distilled LiDAR-informed features obtained from the LiDAR-based teacher model during training. To retrieve relevant 3D features from the memory based on the scene context, we incorporate a memory retriever $f_{\mathrm{ret}}$ , inspired by Perceiver IO [17]. The retriever consists of two transformer decoders $f_{\mathrm{dec}1}$ and $f_{\mathrm{dec}2}$ , a transformer encoder $f_{\mathrm{enc}}$ , and trainable latent embeddings $E \in \mathbb{R}^{D \times Q}$ , where $Q$ is the number of the embeddings. The latent embeddings $E$ and the camera features $F_{\mathrm{cam}}$ are first fed into the first transformer decoder $f_{\mathrm{dec}1}$ , where $E$ serves as the query and $F_{\mathrm{cam}}$ acts as the key and value. This process enables the model to effectively align the latent queries with relevant spatial information from the camera features. The output from $f_{\mathrm{dec}1}$ is then further refined through self-attention layers within the transformer encoder $f_{\mathrm{enc}}$ , which allows the model to capture dependencies among the generated embeddings and enrich them by facilitating interactions across different spatial regions. Subsequently, the refined output is processed along with the distilled memory $M$ in the second transformer decoder $f_{\mathrm{dec}2}$ , where the output serves as the query and $M$ acts as the key and value, to produce LiDAR-informed complementary features $F_{\mathrm{cmp}}$ . Finally, $F_{\mathrm{cmp}}$ and the original camera features $F_{\mathrm{cam}}$ are merged by a fusion layer that takes their channel-wise concatenation as input: + +$$ +F _ {\text {f u s e d}} = f _ {\text {f u s e}} \left(F _ {\text {c a m}} \oplus F _ {\text {c m p}}\right) \in \mathbb {R} ^ {D \times H \times W}. \tag {2} +$$ + +This fusion allows the student to integrate both camera and LiDAR information to improve its 3D object detection capability. + +After the fusion process, the fused features $F_{\mathrm{fused}}$ are passed through the neck module $f_{\mathrm{neck}}$ , which processes them in a multi-resolution manner, refining the representation into $F_{\mathrm{cam}}^{\prime} = f_{\mathrm{neck}}(F_{\mathrm{fused}})$ . The prediction head $f_{\mathrm{pred}}$ then produces the final classification and regression outputs, $(\tilde{F}_{\mathrm{cls}}, \tilde{F}_{\mathrm{reg}}) = f_{\mathrm{pred}}(F_{\mathrm{cam}}^{\prime})$ . + +# 3.2. Two-stage Training + +# 3.2.1. Memory Distillation + +The first step of MemDistill is to distill LiDAR knowledge from the teacher into the student's memory. To facilitate this, the student shares the same neck and prediction head as the teacher, differing only in its image backbone and memory module: the student's architecture nearly identical to the teacher's enables to better align their intermediate features and final predictions through a straightforward distillation strategy. Let $\mathcal{L}_{\mathrm{MSE}}$ denote the mean squared error (MSE) between the student and teacher outputs, where the teacher provides supervisory signals for training the student: + +$$ +\mathcal {L} _ {\mathrm {M S E}} = \| F _ {\mathrm {b e v}} ^ {\prime} - F _ {\mathrm {c a m}} ^ {\prime} \| _ {2} + \| F _ {\mathrm {c l s}} - \tilde {F} _ {\mathrm {c l s}} \| _ {2} + \| F _ {\mathrm {r e g}} - \tilde {F} _ {\mathrm {r e g}} \| _ {2}. \tag {3} +$$ + +Also, let $\mathcal{L}_{\mathrm{task}}$ denote the task loss for object detection, which includes the bounding box regression loss and the cross-entropy loss for classification. We employ both $\mathcal{L}_{\mathrm{MSE}}$ and $\mathcal{L}_{\mathrm{task}}$ for memory distillation, where only the memory and its retriever are trained while the rest of the student model remains frozen. This allows the memory to effectively capture key LiDAR knowledge from the teacher, compensating for the absence of direct LiDAR input in the student model. + +# 3.2.2. Fine-tuning of Student + +After the memory distillation, the student is fine-tuned to further reduce discrepancies with the teacher, resulting in additional performance improvement. During the fine-tuning stage, the memory remains frozen to preserve the essential LiDAR knowledge distilled earlier. Meanwhile, the rest of the student model (i.e., the image backbone, neck, prediction head, and memory retriever) is further trained to better align with the teacher. Note that the retriever remains trainable to adapt to changes in the camera features during the fine-tuning. The losses used for the memory distillation, i.e., $\mathcal{L}_{\mathrm{MSE}}$ and $\mathcal{L}_{\mathrm{task}}$ , are adopted also for fine-tuning the student, allowing the student to learn richer feature representations from the teacher through the memory and its retriever, further boosting its 3D object detection capability. + +# 4. Experiments + +# 4.1. Experimental Setup + +Dataset and Evaluation Metrics. We train and evaluate our method on the nuScenes dataset [2], a large-scale autonomous driving benchmark. The dataset consists of 1,000 video sequences, each approximately 20 seconds long, with 3D bounding box annotations provided at $2\mathrm{Hz}$ for 10 object classes. We follow the official data split, using 700 scenes for training, 150 for validation, and 150 for testing. To assess 3D object detection performance, we use the official nuScenes metrics: mean Average Precision (mAP) and nuScenes Detection Score (NDS). Additionally, we report other metrics such as mean Average Translation Error (mATE), mean Average Scale Error (mASE), mean Average Orientation Error (mAOE), mean Average Velocity Error (mAVE), and mean Average Attribute Error (mAAE), following the common evaluation protocols [7, 20, 21, 43, 51] for more comprehensive evaluation. + +Network Architecture. We adopt CenterPoint [48] as our LiDAR-based teacher model. For the student, the image backbone and camera-to-BEV transformation module are adopted from BEVDepth [25], while the neck and head remain the same as those of the teacher. We use SECOND [46] as the LiDAR backbone for the teacher and ResNet-50/101 [12] as the image backbone for the student. The fusion layer $f_{\mathrm{fuse}}$ of the student has the structure of Conv2D-BN-ReLU-Conv2D. The memory length $N$ is + +set to 160K. The number of latent embeddings $Q$ is set to 6.4K. All the transformer encoder and decoder modules that make up the memory retriever, namely $f_{\mathrm{enc}}$ , $f_{\mathrm{dec1}}$ , and $f_{\mathrm{dec2}}$ , consist of 4 layers each. + +Implementation Details. Our method is implemented using PyTorch [35] and the MMDetection3D toolkit [9], and trained on 8 Nvidia RTX6000 ADA GPUs. The region of interest is set to $[-51.2\mathrm{m}, 51.2\mathrm{m}]$ for both the X and Y axes, and $[-5.0\mathrm{m}, 3.0\mathrm{m}]$ for the Z axis. The voxel size is set to $[0.2\mathrm{m}, 0.2\mathrm{m}, 8\mathrm{m}]$ . We use the official CenterPoint [48] checkpoint for the teacher, which remains frozen throughout the training process. Meanwhile, the student is trained for 50K iterations for memory distillation and 100K iterations for fine-tuning. For data augmentation, we apply random horizontal flipping, random scaling, and random rotation, following LabelDistill [20]. We use the AdamW optimizer [32] with a learning rate of $4\mathrm{e}-4$ and a weight decay of $1\mathrm{e}-2$ . No learning rate scheduling is applied. + +# 4.2. Main Results + +We compare MemDistill with its camera-only baseline and previous work on the nuScenes validation set. First, we assess its performance against non-KD camera-based detectors using two image backbones, ResNet-50 (R50) and ResNet-101 (R101), as shown in Table 1. MemDistill effectively distills knowledge from the teacher model, resulting in a significant performance gain of $9.2\%$ in mAP and $9.0\%$ in NDS over its baseline model, BEVDepth [25], with ResNet-50. It consistently surpasses the baseline also with ResNet-101, achieving an additional improvement of $5.3\%$ in mAP and $6.8\%$ in NDS, respectively. As a result, MemDistill clearly outperforms every non-KD camera-based detector. MemDistill is further compared with prior LiDAR-to-camera KD methods in Table 2, where it achieves the best in both mAP and NDS, with both ResNet-50 and ResNet-101. + +Figure 4 compares MemDistill and its baseline qualitatively. As highlighted by the red boxes, MemDistill improves object localization accuracy by more precisely detecting object positions, whereas the baseline tends to be less accurate in terms of both bounding box regression and its classification. It also reduces false positives, while the baseline often generates incorrect bounding boxes. + +# 4.3. Ablation Studies + +We conducted ablation studies to evaluate the impact of key components in MemDistill. Specifically, we focused on four aspects: the two-stage training process, the student model design, the scene-dependent retrieval mechanism, and the memory retriever's role in refining camera features with a distilled memory. Each experiment was performed on the nuScenes validation set using a ResNet-50 backbone with input images of size $256 \times 704$ . The results + +
MethodsModalityBackboneImage SizemAP↑NDS↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓
BEVDet4D [13]CR50256 × 7040.3230.4530.6740.2720.5030.4290.208
BEVDepth [25]CR50256 × 7040.3330.4410.6830.2760.5450.5260.226
BEVStereo [24]CR50256 × 7040.3440.4490.6590.2760.5790.5030.216
PETR v2 [30]CR50256 × 7040.3490.4560.7000.2750.5800.4370.187
FB-BEV [27]CR50256 × 7040.3500.4790.6420.2750.4590.3910.193
AeDet [10]CR50256 × 7040.3580.4730.6550.2730.4930.4270.216
P2D [19]CR50256 × 7040.3740.4860.6310.2720.5080.3840.212
BEVFormer v2 [47]CR50640 × 16000.3880.4980.6790.2760.4170.4030.189
SOLOFusion [34]CR50256 × 7040.4060.4970.6090.2840.6500.3150.204
MemDistillC*R50256 × 7040.4250.5310.5810.2710.4030.3310.225
FCOS3D [40]CR101900 × 16000.2950.3720.8060.2680.5111.1310.170
DETR3D [42]CR101900 × 16000.3490.4340.7160.2680.3790.8420.200
BEVDepth [25]CR101512 × 14080.4060.4900.6260.2780.5130.4890.226
BEVFormer [26]CR101900 × 16000.4160.5170.6730.2740.3720.3940.198
PolarFormer [18]CR101900 × 16000.4320.5280.6480.2700.3480.4090.201
P2D [19]CR101512 × 14080.4330.5280.6190.2650.4320.3640.211
Sparse4D [28]CR101900 × 16000.4360.5410.6330.2790.3630.3170.177
MemDistillC*R101512 × 14080.4590.5580.5710.2270.3850.3160.220
+ +Table 1. Quantitative comparisons with non-KD camera-based detectors on the nuScenes validation set. In the Modality column, 'C' denotes camera input and 'C*' indicates the use of LiDAR only for KD during training. + +
MethodsBaselineBackboneImage SizemAP↑NDS↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓
UniDistill [52]BEVDetR50256 × 7040.2600.373-----
BEVDistill [7]BEVDepthR50256 × 7040.3300.452-----
TiG-BEV [16]BEVDepthR50256 × 7040.3660.461-----
SimDistill [51]BEVFusion-CR50256 × 7040.3730.438-----
DistillBEV [43]BEVDepthR50640 × 16000.3890.4980.6300.2670.5040.3600.202
X3KD [21]BEVDepthR50256 × 7040.3900.5050.6150.2690.4710.3450.203
LabelDistill [20]BEVDepthR50256 × 7040.4190.5280.5820.2580.4130.3460.220
MemDistillBEVDepthR50256 × 7040.4250.5310.5810.2710.4030.3310.225
UVTR [23]FCOS3DR101900 × 16000.3920.4880.7200.2680.3540.5340.206
BEVDistill [7]BEVFformerR101900 × 16000.4170.524-----
TiG-BEV [16]BEVDepthR101512 × 14080.4300.514-----
DistillBEV [43]BEVDepthR101512 × 14080.4500.547-----
LabelDistill [20]BEVDepthR101512 × 14080.4510.5530.5790.2520.3310.3570.207
MemDistillBEVDepthR101512 × 14080.4590.5580.5710.2270.3850.3160.220
+ +Table 2. Quantitative comparisons with LiDAR-to-camera KD methods on the nuScenes validation set. Baseline denotes the baseline of the student model. + +highlight the effectiveness of MemDistill's design in enhancing knowledge transfer and feature alignment between the student and teacher models. + +# 4.3.1. Two-stage Training Process + +MemDistill employs a two-stage training process that consists of memory distillation (MD) and fine-tuning (FT) of the student. To evaluate the effectiveness of each component, we design three experimental setups in Table 3: (a) training the memory and its retriever through distillation without fine-tuning the student, (b) directly fine-tuning the student without utilizing memory, and (c) the full MemDistill approach, where the student undergoes both distillation and fine-tuning. The results in Table 3 indicate that + +(a) effectively distills essential LiDAR features into memory, while (b) enables the student to learn meaningful feature representations from the teacher but remains suboptimal due to the absence of LiDAR input. Ultimately, (c) achieves the best performance by leveraging both distillation and fine-tuning. Additionally, we compare this two-stage process with an end-to-end training approach, where the student including memory is simultaneously optimized to minimize discrepancies with the teacher in both intermediate features and final predictions. The comparison, as shown in Table 4, reveals that the two-stage training approach outperforms the end-to-end method, as isolating the memory distillation stage enhances the capture of LiDAR features, leading to more effective fine-tuning of the stu + +![](images/736992cc9d6a22f53fa99032dc495d4508fddc8bf21272d3907b5ac465b47ff4.jpg) + +![](images/06f3459cc829368b03bee05576d7167587f89f623152cd9897c424a56a09dc1f.jpg) + +![](images/0687450b27c5088246a3cf372d97cd0f4bdf8bd87b126cd1d756b9a8a0ba9a77.jpg) + +![](images/3fc33e09cac07a9e64da3ab7d9096db5772224c67b5d566fd5432bb64d66c013.jpg) +(a) Ground-Truth + +![](images/c65c3f4391cc073e0d3011d8da4b2b0839f2e04f9b2c734885cf1dfa9cebea44.jpg) +(b) BEVDepth + +![](images/201aeee86840a070722183585b695c697d68427345e5a0718f3bfdaec606ba5a.jpg) +(c) MemDistill (Ours) +Figure 4. Qualitative results of the Ground-Truth, BEVDepth, and MemDistill (Ours) on the nuScenes validation set. + +dent. These result highlight the importance of two-stage training, where sequentially training memory and student learning contributes to superior performance. + +# 4.3.2. Design Choice for the Student + +In our approach, the student model retains the image backbone from a pre-trained camera-based detector while integrating the neck and head from the LiDAR-based teacher to facilitate effective knowledge distillation. To assess the impact of this design choice, we conduct a series of experiments, with the results presented in Table 5. Specifically, we evaluate four different configurations: (a) a student model utilizing both the neck and head from the camera-based detector, (b) a student model incorporating the neck and head from the LiDAR-based teacher, (c) a student model employing the LiDAR-based neck and head along with memory distillation, and (d) our proposed method. To quantify the effect of these variations, we measure L2 distance between two key feature representations, $F_{\mathrm{bev}}'$ and $F_{\mathrm{cam}}'$ , on the nuScenes validation set, reporting the average distance across all validation samples. The results indicate that adopting the neck and head from the LiDAR-based teacher significantly reduces the feature discrepancy between the teacher and student models. Moreover, the in + +tegration of memory distillation further enhances this alignment, effectively bridging the gap between the two models and improving overall performance. + +# 4.3.3. Scene-Dependent Retrieval Mechanism + +The scene-dependent retrieval mechanism enables the student to effectively utilize complementary LiDAR features based on camera inputs, ensuring context-aware and adaptive fusion process. To assess its effectiveness, we conduct experiments comparing its performance against a baseline approach. Specifically, we evaluate two experimental setups: (a) a scene-agnostic approach and (b) a scene-dependent approach. In the scene-agnostic setting, the memory retriever is removed, and instead, a 4-layer transformer encoder is incorporated into the memory module. The output features generated by this transformer encoder are then processed by the student's fusion module, serving as LiDAR-informed features. In contrast, the scene-dependent setting corresponds to our MemDistill framework, which includes both the memory module and its retriever. The results in Table 6 indicate that the scene-agnostic approach leads to inferior performance compared to the scene-dependent approach, emphasizing the retrieval mechanism in effectively utilizing relevant LiDAR features. + +
ModalitymAP↑NDS↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓
CenterPoint [48]L0.5610.6460.2950.2530.3080.2930.194
BEVDepth [25]C0.3330.4410.6830.2760.5450.5260.226
(a) MDC*0.3480.4750.5910.2830.4340.4300.254
(b) FTC*0.3820.4980.5840.2790.4220.3950.250
(c) MD+FT (Ours)C*0.4250.5310.5810.2710.4030.3310.225
+ +Table 3. Ablation study on memory distillation (MD) and fine-tuning (FT). We compare three setups: (a) training the memory and retriever via distillation without student fine-tuning, (b) directly fine-tuning the student without memory, and (c) our approach. + +
ModalitymAP↑NDS↑mATE↓mASE↓mAOE↓mAVE↓mAAE↓
CenterPoint [48]L0.5610.6460.2950.2530.3080.2930.194
BEVDepth [45]C*0.3330.4410.6830.2760.5450.5260.226
(a) End-to-EndC*0.3690.4750.6110.2770.4920.4860.228
(b) Two-Stage (Ours)C*0.4250.5310.5810.2710.4030.3310.225
+ +Table 4. Comparison between end-to-end training and the two-stage training process. (a) represents end-to-end training where the student and memory are jointly optimized, while (b) follows the two-stage approach, where memory is first distilled before fine-tuning the student. + +
Neck & HeadMDFTL2 distance
(a)Camera501.1
(b)LiDAR395.7
(c)LiDAR✓344.3
(d) OursLiDAR✓✓333.9
+ +Table 5. Ablation study on different student model designs. We compare four configurations: (a) a student model with a camera-based neck and head, (b) a student model using the LiDAR-based neck and head, (c) the same setup as (b) but incorporating memory distillation, and (d) our proposed approach. L2 distance measures the discrepancy between the camera features and BEV (LiDAR) features, $F_{\mathrm{cam}}^{\prime}$ and $F_{\mathrm{bev}}^{\prime}$ , on the nuScenes validation set. + +
Memory Retriever fretmAP↑NDS↑
(a) Scene-agnostic0.3920.499
(b) Scene-dependent (Ours)0.4250.531
+ +# 4.3.4. Enhancing Camera Features with Memory + +The memory retriever enhances the student's camera features by integrating distilled memory through a simple fusion layer. To evaluate the impact of this fusion process with memory retrieval, we conduct a series of experiments, with the results summarized in Table 7. Specifically, we compare two configurations: (a) the L1, L2, and $\mathrm{L}_{\infty}$ distances between the raw camera features and BEV (LiDAR) features, and (b) the L1, L2, and $\mathrm{L}_{\infty}$ distances between the fused features (obtained via memory retrieval) and BEV + +Table 6. Ablation study on scene-dependent retrieval mechanism. We compare two approaches: (a) a scene-agnostic method where the memory retriever is replaced with a 4-layer transformer encoder, and (b) a scene-dependent method, which corresponds to our MemDistill framework. + +
L1 distanceL2 distanceL∞ distance
(a) Fbev and Fcam14443.8975.2252.6
(b) Fbev and Ffused7219.5604.5106.7
+ +Table 7. Ablation study on memory retrieval for enhancing camera features. We compare two configurations: (a) computing the L1, L2, and $\mathrm{L}_{\infty}$ distances between the raw camera features and BEV (LiDAR) features, and (b) computing the same distance metrics after applying memory retrieval and fusion. These distance metrics comprehensively measure the discrepancy between the (enhanced) camera features and BEV (LiDAR) features. + +features, using the nuScenes validation set. We report the average distance across all validation samples. The results indicate that the memory retriever consistently reduces the discrepancy between camera and BEV features across all three distance metrics, effectively bridging the gap between the student and teacher models. + +# 5. Conclusion + +We present MemDistill, a novel cross-modal knowledge distillation framework for 3D object detection. 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To analyze and study these vulnerabilities, various MIA methods have been proposed. Despite the significance and popularity of MIAs, existing works on MIAs are limited in providing guarantees on the false discovery rate (FDR), which refers to the expected proportion of false discoveries among the identified positive discoveries. However, it is very challenging to ensure the false discovery rate guarantees, because the underlying distribution is usually unknown, and the estimated non-member probabilities often exhibit interdependence. To tackle the above challenges, in this paper, we design a novel membership inference attack method, which can provide the guarantees on the false discovery rate. Additionally, we show that our method can also provide the marginal probability guarantee on labeling true non-member data as member data. Notably, our method can work as a wrapper that can be seamlessly integrated with existing MIA methods in a post-hoc manner, while also providing the FDR control. We perform the theoretical analysis for our method. Extensive experiments in various settings (e.g., the black-box setting and the lifelong learning setting) are also conducted to verify the desirable performance of our method. + +# 1. Introduction + +Deep neural networks (DNNs) have been successfully adopted in various computer vision tasks [18, 22, 25, 32, 40, 42, 68, 84, 85]. Due to the high sample complexity of such models, they require large amounts of training data. However, recent research highlights privacy risks and vulnerabilities of DNNs to membership inference attacks (MIAs) [37]. MIAs on DNNs aim to infer whether a specific data record was used to train a target model or not, thus posing severe privacy risks to individuals. For instance, if attackers infer that a clinical record has been used to train a model as- + +sociated with a certain disease, they can infer that the owner of the record has that disease with high probability. A recent report [64] published by the National Institute of Standards and Technology (NIST) specifically highlights that an MIA revealing that an individual was included in the dataset used to train the target model is a confidentiality violation. + +On the other hand, beyond traditional privacy attacks, MIAs have diverse applications and play a crucial role in fields such as machine unlearning [17, 65] and lifelong learning [71]. For example, in the context of machine unlearning, MIA methods are used to evaluate the effectiveness of unlearning methods and help verify that specific samples have been successfully unlearned, thus respecting individuals' rights to have their data removed. Note that machine unlearning refers to the process of selectively removing the influence of specific samples from trained models [11, 15, 29, 53, 72, 83]. Additionally, in lifelong learning, where a model aims to learn continuously from new data over time while retaining previously acquired knowledge, MIAs can be used to gauge the degree of memorization for certain data. This allows us to assess how well the model retains specific information and preserves prior knowledge. + +Currently, various MIA methods have been proposed. Based on the differentiation principles, existing MIA methods can be generally divided into: classifier-based, metric-based, likelihood ratio-based, and quantile regression-based. Specifically, classifier-based MIAs [16, 34, 61] usually train a binary membership classifier indicator to distinguish the behavior of training members from that of nontraining members. Metric-based MIAs [20, 23, 41] involve defining a specific metric on model outputs to distinguish training members from non-members. Likelihood ratio-based MIAs [12, 78] utilize parametric techniques to model the loss distributions of models that have been trained or not trained on the target test example. Quantile regression-based MIAs [10] utilize quantile regression on non-member distributions without training surrogate models. + +Despite the significance and popularity of MIAs, existing MIA methods cannot provide guarantees on the false discovery rate (FDR), which is defined as the expected + +proportion of instances classified as training data (members) but are, in reality, not part of the training data (non-members) among total instances classified as training data. Traditional MIA works usually focus on empirical comparisons, and fail to provide the theoretical guarantees for member and non-member decisions. Although [10, 75] consider the ratio of non-members incorrectly identified as members, they cannot provide the guarantees on the false discovery rate. In practice, the false discovery rate provides a more precise indication of the error rate [5, 8, 9, 39], and is crucial in settings involving simultaneous evaluations. By managing the FDR, we can mitigate the risks associated with evaluating the reliability of positive discoveries and make more informed decisions under conditions of uncertainty [7, 27, 47, 49, 50]. Additionally, existing MIAs also fail to provide the marginal probability guarantee on labeling true non-member data as member data. + +Our goal in this paper is to provide the guarantees on the false discovery rate for MIAs, which refers to the proportion of false discoveries among total positive discoveries in the overall testing procedure. Note that existing works on MIAs are typically framed as a hypothesis testing problem, with the alternative hypothesis asserting that the test data is from the training dataset and the null hypothesis positing it is not. However, managing the false discovery rate in the context of MIAs presents unique challenges. First, the distribution of scores for non-training data remains unknown and challenging to model accurately, which complicates the derivation of the membership indicators. Additionally, the estimated non-member probabilities usually exhibit interdependence. However, traditional multiple hypothesis testing techniques usually assume that inputs must either be independent or adhere to certain conditions of dependency. This assumption is hard to be satisfied in practice, which complicates the process of accurately controlling the FDR and makes it difficult to ensure that the proportion of false discoveries remains within acceptable limits. + +To address the above challenges, in this paper, we propose MIAFdR, a novel membership inference attack that can provide the false discovery rate guarantees. Specifically, in our method, given that the underlying true distribution of the member data and that of the non-member data are hard to know, we first design a novel conformity score function, which can reflect the conformity degree of test data to the non-member data. Next, based on estimated pointwise conformity scores, we present a non-member relative probability estimation strategy, which essentially reflects the likelihood of not making discoveries. We also show that based on these estimated non-member probabilities, we can provide the marginal probability guarantee on labeling true non-member data as member data. However, these generated point-wise non-member relative probabilities exhibit interdependence, making it challenging to provide the false + +discovery rate control. To address this, we then present an adjustment method that corrects these calculated non-member probabilities by accounting for their interdependencies and employing a weighted correction scheme. We also show that these adjusted non-member probabilities allow for controlling the false discovery rate at a predetermined significance level for prediction results. Notably, our method can be seamlessly integrated with existing MIAs to provide FDR control while preserving their attack performance. We conduct the theoretical analysis for our method. Our extensive experiments verify the effectiveness of our method. We also empirically show that our method can help data memorization-based machine learning (ML) tasks, including machine unlearning and lifelong learning. + +# 2. Related Work + +Membership inference attacks (MIAs) are designed to determine whether a given data sample has been used to train a particular model. The concept of MIAs is first proposed by [36], which aims to detect sensitive and private information leakage. Specifically, this work trains multiple shadow models to mimic the behavior of the victim model to distinguish between training samples from the training dataset and test samples. Since their inception, MIAs have gained significant attention in the research community, leading to the development of numerous MIA methods [10, 12, 20, 23, 34, 41, 48, 55, 81]. Notably, numerous studies have sought to elucidate mechanisms behind MIAs, primarily attributing their operations to model memorization [2, 13, 26, 31, 55, 59], a phenomenon linked to overfitting. Due to memorization in DNNs, prediction confidence tends to be higher for data used for training. This difference in prediction confidence helps MIA methods to determine which image data were used for training. In [76], the authors theoretically analyze the relationship between overfitting and MIAs. Therefore, beyond detecting sensitive information leakage, MIAs can also offer valuable insights into the extent of memorization in the victim model. + +Currently, MIAs have been successfully achieved in many domains and problems, including semantic image segmentation [35, 79], healthcare [30, 74], image classification [37, 55], and recommendation systems [19, 80]. For example, [35] shows that such membership inference attacks can be successfully carried out on state-of-the-art models for semantic segmentation. However, existing MIAs cannot guarantee the false discovery rate, which refers to the proportion of false discoveries among total discoveries during the attack procedure. This oversight is particularly problematic when the proportion of actual members within the test data is high. In this work, we build upon conformal inference [6, 7, 14, 28, 44, 46, 51, 54, 66, 67, 69, 77], which aims to quantify the uncertainty in predictions with a specified coverage probability. However, traditional conformal infer + +![](images/531b03eca50ba4deee9f5b50fd95e4f83b4a417e7132195dcc709656b95e983b.jpg) +Figure 1. Overview of our proposed membership inference attacks with the false discovery rate guarantee. + +ence works cannot be directly applied to provide the false discovery rate guarantees for MIAs. As aforementioned, this limitation arises because calculated non-member probabilities for test data are conditional on the shared calibration dataset and exhibit interdependence, making it challenging to provide the false discovery rate control. In contrast, our method can provide the false discovery rate guarantee, even under existing defenses against MIAs [1, 52, 60]. + +# 3. Threat Model + +We consider a threat model that includes a model holder and an adversary. The model holder owns a well-trained DNN classifier $f(\theta^{*})$ , which is trained over its training data $D_{tr} = \{(x_i, y_i)\}_{i=1}^N$ using the loss function $\mathcal{L}$ (e.g., cross-entropy loss), where $x_i \in \mathbb{R}^d$ is a $d$ -dimensional feature vector and $y_i \in [Y]$ denotes its associated label. For a given input $x$ , we can generate its softmax probability vector as + +$$ +f (x; \theta^ {*}) = \left[ f _ {1} (x; \theta^ {*}), f _ {2} (x; \theta^ {*}), \dots , f _ {Y} (x; \theta^ {*}) \right]. \tag {1} +$$ + +For the given input data $x$ , we can determine its class label as $y(x) = \arg \max_{y\in [Y]}f_y(x;\theta^*)$ , where a label $y\in [Y]$ with the largest probability is assigned to this given data $x$ . + +The adversary aims to distinguish the training (members) and test data (non-members) of the victim model. Let $D_{ts} = \{x^t\}_{t=1}^T$ denote the test dataset available to the adversary. As shown in Definition 1, for each $x^t \in D_{ts}$ , the adversary's goal of determining whether $x^t \in D_{tr}$ or $x^t \notin D_{tr}$ can be formulated as a Hypothesis Testing, where the null hypothesis (i.e., $H_0$ ) represents non-membership, while the alternative hypothesis $H_1$ represents membership. + +Definition 1 (Hypothesis Testing for MIA). Let $x^t$ denote the test data. Let $\theta^*$ denote the pre-trained model trained on its private training dataset $D_{tr}$ . Then we can establish a hypothesis test where the null hypothesis posits that $x^t$ was not part of the private training dataset $D_{tr}$ for the target victim model $\theta^*$ , as outlined below + +$$ +H _ {0}: x ^ {t} \notin D _ {t r}, H _ {1}: x ^ {t} \in D _ {t r}, \tag {2} +$$ + +where $D_{tr}$ is the private training dataset for $f(\theta^{*})$ . + +For the adversary's knowledge, we consider two realistic attack settings: grey-box and black-box. + +- In the grey-box setting, we assume that the adversary does not have access to the exact private training dataset $D_{tr}$ , and has no knowledge of the victim model parameters. We consider that the adversary is aware of the knowledge of the owner's learning algorithm and architecture. +- In the black-box setting, we assume that the adversary does not have any prior knowledge about the private training dataset, the learning algorithm, or the target pretrained model, including its architecture and parameters. This setting produces a realistic threat model in real-world applications, where adversaries typically operate with minimal information. + +In the above two settings, we consider a realistic adversary who has limited knowledge and does not have access to the private training dataset $D_{tr}$ . However, we allow the adversary to have access to an auxiliary dataset $D_{au}$ , distinct from the private dataset, sampled from the same distribution. This assumption is reasonable given the widespread availability of public data, and has been a common assumption for black-box attacks in existing literature [38]. Notably, our proposed MIAFdR builds upon existing MIA methods, serving as a wrapper to ensure FDR control. Since existing MIAs [10, 12, 34, 61, 82] typically leverage on auxiliary data for training surrogate models or regression models, we similarly integrate auxiliary data into MIAFdR, aligning with the established practices. By exploring these two settings, we aim to gain comprehensive insights into the different levels of threats posed by attackers with varying degrees of knowledge about the target model. + +# 4. Methodology + +In this section, we utilize the classifier-based setting to present our method. Note that our method serves as a wrapper for existing MIAs with FDR control. Discussions on other settings are deferred to the full version of the paper. + +Overview. Figure 1 shows the overall framework of our proposed method, which can ensure control over the false + +discovery rate. Specifically, our method involves three essential components: non-member conformity score calculation, where we design a novel conformity score function to assess the degree to which each test sample conforms to the non-member data distribution; non-member relative probability estimation, where we utilize the previously calculated non-member conformity score to estimate the non-member relative probability for each test data, which can reflect the likelihood of this given test data being non-training data; and adjustment-based membership decision, where we adjust the previously estimated related probabilities for these test data samples and then compare them against a predefined significance level to make membership decisions. Below, we will detail each of the three essential components. + +Non-member Conformity Score Calculation. Note that based on Definition 1, to determine whether $x^{t}$ comes from $D_{tr}$ , we can establish the following hypothesis test: the null hypothesis (i.e., $H_0$ ) posits that $x^{t}$ is not from the private training dataset $D_{tr}$ (non-members) for the victim model $f(\theta^{*})$ , and the alternative hypothesis (i.e., $H_1$ ) posits that it is from the private dataset. By leveraging the information of the target victim model $f(\theta^{*})$ , we can reduce this hypothesis testing to the problem of determining whether the output (i.e., $f(x^{t};\theta^{*})$ ) of the test data $x^{t}$ belongs to the final softmax output distribution of the victim model $\theta^{*}$ . However, in practice, it is very difficult to obtain its underlying true final output distribution. To address this, we will estimate the empirical output distribution by considering the private training samples' final output predictions (i.e., $\{f(x_i;\theta^*) : x_i \in D_{tr}\}_{i=1}^N$ ). Then we can estimate the empirical probability distribution $\hat{f}_N(\nu)$ via the average of delta functions, where $\nu$ is any real number. Thus, we can construct the below null hypothesis testing + +$$ +\tilde {H} _ {0}: f \left(x ^ {t}; \theta^ {*}\right) \not \sim \hat {f} _ {N} (\nu) = \frac {1}{N} \sum_ {i = 1} ^ {N} \delta \left(\nu - f \left(x _ {i}; \theta^ {*}\right)\right), \tag {3} +$$ + +where $\delta$ is the Dirac delta function, which returns $\infty$ if the condition $f(x_{i};\theta^{*}) = \nu$ is true, and 0 otherwise. + +However, in practice, the attacker usually does not have access to the private training dataset $D_{tr}$ for the victim model $f(\theta^{*})$ , which makes it difficult to characterize the population of non-members. Therefore, it is intractable to directly adopt the hypothesis testing constructed in Eqn. (3). To address this, we first train $K$ surrogate models (denoted as $\{f(\tilde{\theta}^k)\}_{k = 1}^K$ ) and collect their predictions to estimate the empirical score distribution of non-members. Specifically, as shown in Figure 1, to obtain $K$ surrogate models, we first divide the auxiliary dataset $D_{au}$ into two disjoint subsets, i.e., $D_{au}^{1}$ and $D_{au}^{2}$ , where $D_{au}^{1} \cap D_{au}^{2} = \emptyset$ and $D_{au}^{1} \cup D_{au}^{2} = D_{au}$ . From $D_{au}^{1}$ , we will create $K$ subsets (i.e., $\{D_{au}^{1,k}\}_{k = 1}^{K}$ ) by sampling a fraction $\eta$ of the data without replacement. Then, we can optimize the $k$ -th surrogate model as $\tilde{\theta}^k \gets \arg \min_\theta \sum_{(x_i,y_i) \in D_{au}^{1,k}} \mathcal{L}((x_i,y_i); \theta)$ , + +where $\mathcal{L}$ is the victim model's loss assumed in the grey-box setting. Thus, we can train $K$ surrogate models (i.e., $\{f(\tilde{\theta}^k)\}_{k=1}^K$ , which can approximate the behavior of the victim model $f(\theta^*)$ . + +Based on these $K$ surrogate models (i.e., $\{f(\tilde{\theta}^k)\}_{k=1}^K$ , for all samples within $D_{au}^{1,k}$ , we can obtain their predictions $\mathcal{Y}_{au}^{1,k} = \{f(x_i; \tilde{\theta}^k)\}_{i=1}^{|D_{au}^{1,k}|}$ , where $\tilde{\theta}^k$ is the $k$ -th surrogate model trained on $D_{au}^{1,k}$ . We then split the $D_{au}^{2}$ into two disjoint sets $D_{au}^{2,tr}$ and $D_{au}^{2,ca}$ , where $D_{au}^{2,tr} \cap D_{au}^{2,ca} = \emptyset$ , and $D_{au}^{2,tr} \cup D_{au}^{2,ca} = D_{au}^{2}$ . Similarly, for each sample $x_i \in D_{au}^{2,tr}$ and $x_j \in D_{au}^{2,ca}$ , we can obtain $\mathcal{Y}_{au}^{2,i} = \{f(x_i; \tilde{\theta}^k)\}_{k=1}^K$ and $\mathcal{Y}_{au}^{2,j} = \{f(x_j; \tilde{\theta}^k)\}_{k=1}^K$ . Thus, we have + +$$ +\mathcal {Y} _ {a u} ^ {1} = \cup_ {k = 1} ^ {K} \mathcal {Y} _ {a u} ^ {1, k}, \quad \mathcal {Y} _ {a u} ^ {2, t r} = \cup_ {i = 1} ^ {\left| D _ {a u} ^ {2, t r} \right|} \mathcal {Y} _ {a u} ^ {2, i}, \tag {4} +$$ + +$$ +\text {a n d} \mathcal {Y} _ {a u} ^ {2, c a} = \cup_ {j = 1} ^ {\left| D _ {a u} ^ {2, t r} \right|} \mathcal {Y} _ {a u} ^ {2, j}, +$$ + +where $D_{au}^{2,tr} \cup D_{au}^{2,ca} = D_{au}^2 \subset D_{au}$ . Based on this, we will construct the below membership dataset + +$$ +D _ {m e} = \{(y _ {i}, 0): y _ {i} \in \mathcal {Y} _ {a u} ^ {1} \} \cup \{(y _ {i}, + 1): y _ {i} \in \mathcal {Y} _ {a u} ^ {2, t r} \}. +$$ + +The above constructed membership dataset $D_{me}$ can effectively capture the member distribution using the member samples labeled as 0 and the non-member prediction using the non-member samples labeled as $+1$ . + +Based on the constructed membership dataset $D_{me} = \{z_i = (y_i, l_i)\}_{i=1}^{|\mathcal{Y}_{au}^1| + |\mathcal{Y}_{au}^{2,tr}|}$ , where $l_i \in \{0, +1\}$ , we will train the following binary classifier $f_{bc}(\theta_{bc})$ to distinguish between members and non-members + +$$ +\theta_ {b c} = \arg \max _ {\theta} \sum_ {z _ {i} \in D _ {m e}} \mathcal {L} _ {b c} \left(z _ {i} = \left(y _ {i}, l _ {i}\right); \theta\right), \tag {5} +$$ + +where $\mathcal{L}_{bc}$ is the loss for training this classifier. Note that for $z_{i} = (y_{i},l_{i})\in D_{me}$ , it is either labeled $l_{i} = 0$ (members) or $l_{i} = +1$ (non-members). Then, for the given test data $x^{t}$ , to reflect how typical it is with respect to the calibration data, we define the below non-member conformity score function + +$$ +S \left(y ^ {t}; \theta_ {b c}\right) = \lambda \log \left(\frac {f _ {b c} \left(y ^ {t} ; \theta_ {b c}\right)}{1 - f _ {b c} \left(y ^ {t} ; \theta_ {b c}\right)}\right) + (1 - \lambda) f _ {b c} \left(y ^ {t}; \theta_ {b c}\right), \tag {6} +$$ + +where $y^{t} = f(x^{t};\theta^{*})$ , $f_{bc}(\theta_{bc})$ denotes the trained binary classifier based on Eqn. (5) and $\lambda$ is a hyper-parameter to control the weight between the logit-transformed probability and raw probability. Note that for the test data $x^{t}$ , a larger non-member conformity score $S(y^{t};\theta_{bc}) \in \mathbb{R}$ means that it is coming from the non-member prediction; otherwise, it is more likely to be from the member distribution. + +Non-member Relative Probability Estimation. Based on the above conformity score function $S(\cdot; \theta_{bc})$ , for all the samples within the set $\mathcal{Y}_{au}^{2,ca}$ , we can calculate their conformity scores as $\mathcal{C}_{au}^{2,ca} = \{S(y_i; \theta_{bc}) : y_i \in \mathcal{Y}_{au}^{2,ca}\}_{i=1}^{\left|\mathcal{Y}_{au}^{2,ca}\right|}$ . Then, we define $P_{nm}^*$ as the true distribution of these conformity scores $\mathcal{C}_{au}^{2,ca} = \{S(y_i; \theta_{bc})\}_{i=1}^{\left|\mathcal{Y}_{au}^{2,ca}\right|}$ . To determine + +whether the given test data $x^{t}$ is from the private dataset $D_{tr}$ , we reformulate the hypothesis test in Eqn. (3) into + +$$ +\hat {H} _ {0}: S (y ^ {t}; \theta_ {b c}) \sim P _ {n m} ^ {*}, \hat {H} _ {1}: S (y ^ {t}; \theta_ {b c}) \not \sim P _ {n m} ^ {*}, \tag {7} +$$ + +where $P_{nm}^{*}$ is the underlying true distribution of these conformity scores $\mathcal{C}_{au}^{2,ca} = \{S(y_i;\theta_{bc}):y_i\in \mathcal{Y}_{au}^{2,ca}\}_{i = 1}^{\lvert\mathcal{Y}_{au}^{2,ca}\rvert}$ . + +However, the underlying true distribution $P_{nm}^{*}$ is usually unknown, which presents significant challenges for performing the hypothesis testing procedure in Eqn. (7). On the other hand, directly adopting existing empirical distribution estimation methods cannot provide theoretical guarantees for the false discovery rate control, and they also usually require the assumption of underlying distributions. To address this, as demonstrated in Figure 1, instead of estimating underlying distributions, we propose to calculate the below non-member relative probability for the test data $x^{t}$ + +$$ +p \left(x ^ {t}\right) = \frac {\left| \mathbb {S} ^ {k} \in \mathcal {C} _ {a u} ^ {2 , c a} \cup \left\{S \left(y ^ {t} ; \theta_ {b c}\right) \right\} : \mathbb {S} ^ {k} \leq S \left(y ^ {t} ; \theta_ {b c}\right) \right|}{1 + \left| \mathcal {C} _ {a u} ^ {2 , c a} \right|}, \tag {8} +$$ + +where $\mathcal{C}_{au}^{2,ca} = \{S(y_i;\theta_{bc})\}_{i = 1}^{\left|\mathcal{V}_{au}^{2,ca}\right|},y^t = f(x^t;\theta^*)$ and $S(y^{t};\theta_{bc})$ is the conformity score for the test data $x^t$ . The calculated non-member relative probability $p(x^t)$ is essentially the proportion of the calibration samples with conformity scores smaller than or equal to that of $x^t$ . This can reflect the conformity degree of $x^t$ to the non-member calibration scores. Thus, we can use the calculated nonmember probability $p(x^{t})$ to assess the likelihood that $x^t$ was not used to train the target victim model $f(\theta^{*})$ + +Theorem 1. Let $\mathcal{G}$ denote the sequence containing all the samples from dataset $D_{au}^{2,ca}$ and the given test data $x^t$ , i.e., $\mathcal{G} = (x^1, x^2, \ldots, x^{|D_{au}^{2,ca}|}, x^{|D_{au}^{2,ca}| + 1})$ , where $|D_{au}^{2,ca}|$ is the number of samples in $D_{au}^{2,ca}$ , and $x^{|D_{au}^{2,ca}| + 1}$ is the extra term represented by $x^t$ . Note that $D_{au}^{2,ca}$ is a subset of the auxiliary dataset $D_{au}$ . Assume that this sequence is exchangeable. Then, for significance level $\alpha \in (0,1)$ , we have + +$$ +\mathcal {P} \left(p \left(x ^ {t}\right) \leq \alpha \mid x ^ {t} \notin D _ {t r}\right) \leq \alpha , \tag {9} +$$ + +where $p(x^t)$ is the calculated non-member probability for test data $x^t$ , and $D_{tr}$ represents the private training dataset. + +In Theorem 1, we show that for a true non-member test data $x^{t}$ , the probability that its non-member relative probability $p(x^{t})$ is not larger than $\alpha$ is at most $\alpha$ . For this true non-member data $x^{t}$ , it does not come from the private dataset $D_{tr}$ (i.e., $x^{t} \notin D_{tr}$ ). This ensures that the error rate for labeling true non-member data as member data does not exceed the predefined threshold $\alpha$ , providing a guarantee on the reliability of the membership labeling process. Note that the exchangeability assumption in Theorem 1 is much less restrictive than the traditional independent and identically distributed (i.i.d.) assumption [4, 7, 21]. The proof for Theorem 1, and more discussions of our method on other MIA settings are deferred to the full version of the paper. + +Adjustment-based Membership Decision. Next, we discuss how to provide the false discovery rate control for the test dataset $D_{ts} = \{x^t\}_{t=1}^T$ , based on the above estimated non-member relative probabilities. From Definition 2, we can see that the false discovery rate is the expected proportion of false discoveries among all discoveries. However, these calculated p-values (i.e., non-member probabilities $\{p(x^t)\}_{t=1}^T$ ) for the test data $D_{ts}$ are conditional on the calibration dataset $D_{au}^{2,ca}$ ; specifically, it applies uniformly across all test data, as each calculation involves the identical calibration dataset. Consequently, the p-values obtained for the membership inference attack exhibit interdependence, which makes it challenging to provide the false discovery rate control. To control the number of false discoveries among total discoveries in the overall testing procedure, we will adjust the calculation of the original p-value in Eqn. (8). Specifically, we first arrange these calculated $\{p(x^t)\}_{t=1}^T$ in ascending order, and obtain the ranked set $\{p^{(t)}\}_{t=1}^T$ , where $p^{(t)}$ is the non-member probability ranked at position $t$ . Subsequently, for $p^{(t)}$ , as illustrated in Figure 1, we calculate its adjusted non-member probability as + +$$ +p _ {\mathrm {a d j}} ^ {(t)} = \min \{1, \min _ {m \in \{t, t + 1, \dots , n \}} \left\{\frac {n}{m} \cdot p ^ {(m)} \right\} \}, \tag {10} +$$ + +where $p^{(m)}\in \{p^{(t)}\}_{t = 1}^{T}$ ranks at position $m$ + +Definition 2 (False Discovery Rate (FDR)). Let $A$ denote the MIA attack algorithm, where $A(x^t) \in \{0,1\}$ , with 0 indicating that $x^t$ is a member of the private training dataset $D_{tr}$ of the target victim model and 1 indicating it is not. Let $D_{ts}$ denote the test dataset. Then we can define the false discovery rate as $\xi = |v_{fp}| / (|v_{fp}| + |v_{tp}|)$ , where $v_{fp} = \{x^t \in D_{ts} \mid A(x^t) = 0, \text{and } x^t \notin D_{tr}\}$ and $v_{tp} = \{x^t \in D_{ts} \mid A(x^t) = 0, \text{and } x^t \in D_{tr}\}$ . + +Based on these adjusted probabilities, for each test data $x^{(t)} \in D_{ts}$ , we can obtain its null hypothesis $H_{0,(t)}$ , i.e., $H_{0,(t)}: x^{(t)} \notin D_{tr}$ . Then, for $x^{(t)}$ , we can determine + +$$ +\left\{ \begin{array}{l l} \text {i f} p _ {\mathrm {a d j}} ^ {(t)} \leq \alpha , & H _ {0, (t)} \text {d o e s n o t h o l d}, \\ \text {i f} p _ {\mathrm {a d j}} ^ {(t)} > \alpha , & H _ {0, (t)} \text {h o l d s}, \end{array} \right. \tag {11} +$$ + +where $p_{\mathrm{adj}}^{(t)}$ is the adjusted non-member probability calculated by Eqn. (10) and $\alpha$ is a pre-defined value for determining the significance level for the multiple hypothesis testing. In the above equation, if $p_{\mathrm{adj}}^{(t)} \leq \alpha$ , we should reject the null hypothesis, suggesting that the test data $x^{(t)}$ does not belong to the non-members and comes from the training data $D_{tr}$ of the victim model $\theta^{*}$ ; otherwise, we should accept the null hypothesis, indicating that $x^{(t)} \notin D_{tr}$ . Based on the above, for test dataset $D_{ts}$ , we can obtain following decisions + +$$ +\mathcal {R} \left(D _ {t s}\right) = \{t: t \in [ T ], \text {a n d} p _ {\mathrm {a d j}} ^ {(t)} \leq \alpha \}, \tag {12} +$$ + +where $p_{\mathrm{adj}}^{(t)}$ is the adjusted non-member probability for the sample ranked at position $(t)$ and $\alpha$ is the significance level. + +Note that $\mathcal{R}(D_{ts})$ is the set of indices of test data within the test dataset $D_{ts}$ for which the null hypothesis is rejected. This indicates that these test samples are likely members of the private training dataset $D_{tr}$ . + +Theorem 2. Let $\mathcal{H}_0^*(D_{ts}) = \{t : t \in [T],$ and $H_{0,(t)}^*$ is true} denote the subset of true non-members in the test data $D_{ts}$ , where $H_{0,(t)}^*$ is the ground truth. Let $\pi_0$ denote the proportion of true non-members, i.e., $\pi_0 = \mathcal{H}_0^*(D_{ts}) / T$ . Then we can control the false discovery rate (FDR) at level $\alpha \cdot \mathcal{H}_0^*(D_{ts}) / T$ as follows + +$$ +\mathbb {E} \left[ \frac {\left| \mathcal {R} \left(D _ {t s}\right) \cap \mathcal {H} _ {0} ^ {*} \left(D _ {t s}\right) \right|}{\max \{1 , \left| \mathcal {R} \left(D _ {t s}\right) \right| \}} \right] \leq \alpha \cdot \frac {\mathcal {H} _ {0} ^ {*} \left(D _ {t s}\right)}{T} \leq \alpha , \tag {13} +$$ + +where $\mathcal{R}(D_{ts})$ is the obtained positive discovery results, and $\alpha$ is the significance level in Eqn. (12). + +Theorem 2 states that our method allows for controlling the false discovery rate at a predetermined level for the generated positive discovery results (i.e., $\mathcal{R}(D_{ts})$ for test dataset $D_{ts}$ ), thereby limiting the proportion of false discoveries among the total discoveries [7]. The proof for Theorem 2, and more discussions of our method on other MIA settings are deferred to the full version of the paper. + +Discussion. Note that in the above, we focus on the grey-box setting. For the threat of MIAs, we also consider the black-box setting, where attackers have no prior knowledge of the target model, including its private training data and model architecture. In this black-box setting, attackers can utilize varying architectures to train on the auxiliary dataset to approximate the target model's behavior and obtain score distributions. This strategy leverages the transferability property that arises from shared decision boundaries across different models [45, 58, 70]. In this way, attackers can effectively conduct MIAs in the black-box scenario. + +![](images/6b8ba0a6489fa1e42c76df2954499575b47a330a741df3e998d3d9dda3dd4766.jpg) +(a) Statistical validity for p-value + +![](images/6013d7621b79414025100e5bc3e84d93793573b1d358939017a0a8273a8fd434.jpg) +(b) Running time +Figure 2. Statistical validity and running time. + +# 5. Experiments + +In this section, we conduct extensive experiments to evaluate the effectiveness of our proposed MIAFdR. More experimental details and results (e.g., Quantile Regression-based MIAs and differential privacy-based MIA defenses) are deferred to the full version of the paper. + +Datasets and Models. In the experiments, we adopt the following popular benchmark image datasets: TinyImageNet [24], CIFAR-100 [43], and CIFAR-10 [43]. Additionally, our experimental evaluations are also conducted + +on various deep learning models, including ResNet-50, ResNet-18 [33], VGG-16 [62], MobileNetV2 [57], and a multi-layer perception (MLP) network. + +Baselines. In experiments, we compare our method with the following popular MIAs: classifier-based method such as shadow training [61]; metric-based methods, including Softmax [56], Modified Entropy (Entropy) [63], Loss [76], and Difficulty Calibration (Calibration) [73]; likelihood ratio-based method represented by Likelihood Ratio Attack (LiRA) [12]; and quantile regression-based method like Quantile Regression Attack [10]. + +Attack Setup. In experiments, we split the available dataset into: a private set used for training a target model, accessible only to the model holder, and a public set employed for training a surrogate model and querying conformity scores for attackers. In likelihood ratio-based and quantile regression-based methods, the public set serves as an auxiliary set for computing conformity scores. In classified-based and metric-based methods, we allocate $40\%$ of data for calibration and $60\%$ for training the discriminative model using MLP. The evaluation is repeated 10 times, with the mean and standard deviation reported. + +# 5.1. Attack Performance + +First, we perform experiments to validate the Theorem 1, which establishes the validity of p-values generated by Eqn. (8). We employ our proposed method with the shadow training technique [61] from classifier-based MIAs, utilizing the ResNet-18 model on the CIFAR-10 dataset. Initially, we partition $30\%$ of the auxiliary dataset $D_{au}$ to form $D_{au}^{1}$ , allocating the remaining $70\%$ to $D_{au}^{2}$ . From $D_{au}^{2}$ , we then sample a fraction $\eta = 3/7$ to obtain $\{D_{au}^{1,k}\}$ . For each test data, we classify it as a member if its non-member probability is less than or equal to a predefined threshold $\alpha$ . As shown in Figure 2a, our approach ensures that the expected error rate for false discoveries among non-training data does not exceed $\alpha$ , thereby guaranteeing the reliability of the membership labeling process. + +In addition, we aim to demonstrate the computation efficiency of our proposed method and the effectiveness of the adjusted non-member probabilities in managing the final membership decisions with respect to FDR. We follow the same experimental setup in Figure 2a. Notably, our MIAfDr serves as a wrapper for existing MIAs and maintains the same training time. In Figure 2b, we present an analysis of the inference runtime for the baseline method and our approach. The experimental results in Figure 2b show that our approach requires only a minimal additional running time compared to the baseline. For instance, with 7,000 test samples, the traditional classifier-based MIA takes 137.84 seconds, while our method adds only 0.01 seconds to the overall running time. In Figure 3, we present the results of the FDR against varying significance level $\alpha$ for $\pi_0 = 0.25$ and $\pi_0 = 0.5$ in both classifier-based and metric-based (Soft- + +![](images/9fe1eb8b3510eb3d4a0f3b42a251bd8639ea396f28efd300a90b576d36565146.jpg) +(a) Classifier-based with $\pi_0 = 0.25$ + +![](images/31b941fa626838d75e19fc5e4a3ee915b3b90568610c46a9ba72460601d2647c.jpg) +(b) Classifier-based with $\pi_0 = 0.5$ +Figure 3. FDR control of classifier-based and metric-based MIAFdR. + +![](images/f0b94f783b390ffae58ec7b091705a3d0582b7777ed9f6084279cbd43cc2e9de.jpg) +(c) Metric-based with $\pi_0 = 0.5$ + +max) settings, where $\pi_0$ is the proportion of non-members in the test dataset. From this figure, we can see that the FDR is mostly bounded by $\alpha$ , indicating that our method can effectively produce membership decisions with FDR control. + +Next, we examine the effectiveness of our method in the presence of existing MIA defenses. We first evaluate the MIAFdR performance against the knowledge distillation-based (KD) defense. Specifically, we first train a teacher model and use its soft outputs with temperature $T = 20$ alongside the hard labels to train the student via a combined cross-entropy and KL divergence objective. The results are presented in Figure 4. From Figure 4a, we can see that our method successfully maintains control over FDR even under MIA defenses. This underscores the validity of our estimated non-member relative probability and the adjustment-based membership decision, confirming their robustness even under defenses. Additionally, Figure 4b illustrates that our method can preserve MIA prediction accuracy and AUROC under MIA defenses. More experimental results on MIAFdR against existing differential privacy-based defenses can be found in the full version of the paper. + +![](images/5812607f3ab022c86d79ce1b870bc1fa6a394a10e648d85ae10f819ef50389d2.jpg) +(a) FDR under KD defense +Figure 4. MIAFdR against KD defense. + +![](images/f9250d70b6c2ff8e082f7529a59552743a26b335dd13d45e5b6078a7ab3ecc68.jpg) +(b) Metrics under KD defense + +Moreover, we investigate the attack effectiveness of MIAFdR with classifier-based MIAs, extending our analysis beyond the FDR control. Our assessment contrasts the baseline classifier-based MIA [61] with an enhanced version that incorporates our proposed MIAFdR across multiple datasets. The experimental results, presented in Table 1, further demonstrate that our MIAFdR achieves comparable or even superior attack performance than the baseline classifier-based MIA in terms of attack accuracy and the AUROC score. For instance, on the CIFAR-100 dataset, our MIAFdR method attains an attack accuracy of approximately $78.2\%$ , outperforming the baseline accuracy + +of $76.8\%$ . These outcomes underscore the effectiveness of our classifier-based MIAFdR in accurately identifying data membership across member and non-member distributions. + +
DatasetMethodAccuracy (%)AUROC (%)
CIFAR-100Classifier76.81 ± 1.0184.35 ± 0.98
Classifier (MIAFdr)78.19 ± 0.7984.46 ± 0.93
Tiny-ImageNetClassifier69.67 ± 0.8576.99 ± 1.63
Classifier (MIAFdr)71.18 ± 1.5377.06 ± 1.52
+ +Table 1. Attack performance of classifier-based MIAFdR. + +Further, we examine the performance of our proposed MIAFdR with likelihood ratio-based MIAs. Specifically, we evaluate the performance of the original LiRA [12] framework, which incorporates 64 shadow models, in comparison to its modified iteration, which integrates our MIAFdR approach. Figure 5a depicts the ROC curves of our proposed attacks and LiRA on CIFAR-10 using log scales. As we can see, our MIAFdR with LiRA approach yields superior log-scale ROC curves, exhibiting a higher True Positive Rate (TPR) at a lower False Positive Rate (FPR). Additionally, our MIAFdR with LiRA approach effectively manages FDR, as evidenced in Figure 5b. For instance, with $\pi_0 = 0.5$ and $\alpha = 0.15$ , we achieve an empirical FDR of 0.145, which closely aligns with the analytical guarantee. Hence, our proposed attacks can be effectively integrated with likelihood ratio-based membership inference attacks to achieve both controlled FDR and good attack precision. + +![](images/b5e4e5ecbe6984cd3e30a5e636b7bb5061d4e92e882394ab201a45784bc99f64.jpg) +(a) ROC curves on CIFAR-10 +Figure 5. Attack performance of LiRA-based MIAFdR. + +![](images/c0c9496e39c2fb566c136146f48abb0ad236fafa08f0bfd84842cec8d884b058.jpg) +(b) FDR with $\pi_0 = 0.5$ + +At last, we conduct experiments in the black-box setting, where the attacker lacks any prior knowledge about the private training dataset or the target pre-trained model, including its architecture and parameters. Here, we train the surrogate model in MIAFdR using an architecture that differs from the target model's. Figure 6a shows the attack + +![](images/e301847118d64596c61919fc22283c42a6678e61580deca4f14e7677a1ec754e.jpg) +(a) Black-box transferability + +![](images/e17809e838199fc3893d1b797f0e9ea6edec89e0e85ea3d3d429df5aa37bdf54.jpg) +(b) Impact of calibration set size +Figure 6. Black-box setting and ablation study of MIAFdR on CIFAR-10. + +![](images/e3964b9a7f714bc9ab7e52c513d37bc85d92451abb6ece754ad230d6570af926.jpg) +(c) Impact of evaluate set + +accuracy for various model architectures on Entropy-based MIAFdR. The reported experimental results in this figure demonstrate that our MIAFdR maintains robust attack performance across various model architectures, underscoring the effectiveness of our method in the black-box setting. + +# 5.2. Ablation Study + +We first perform an ablation study to explore the effectiveness of MIAFdR over calibration set size and the ratio of member to non-member data. We first investigate the impact of calibration set size on metric-based MIAFdR. As shown in Figure 6b, with a larger calibration set size, the attack accuracy tends to increase. This is because the inclusion of additional calibration data enhances the reliability of the non-member relative probability estimation, leading to more stable predictions in our MIAFdR. Next, we examine the impact of the evaluation set on MIAFdR. Figure 6c presents the AUROC score of MIAFdR across various ratios of member to non-member data. Remarkably, our method consistently exhibits a robust AUROC score irrespective of the ratio of member to non-member data in the evaluation set, thereby underscoring its consistent effectiveness. + +![](images/7fe1832a208e664bee4d77af27f5644247455fe806a4831a6829819d524e57df.jpg) +(a) FDR control +Figure 7. Machine unlearning with MIAFdR. + +![](images/cec45d14ba52199759e033d27a1f0711e7f05264faa6cb32dd9930f547afb18f.jpg) +(b) Accuracy + +Additionally, we conduct ablation experiments to show the impact of our MIAFdR in enhancing traditional data memorization-based ML tasks. First, in Figure 7a, we report the obtained expected proportion results of instances erroneously identified as not unlearned in the context of machine unlearning. The results demonstrate that this proportion is effectively controlled across different significance levels. Here, we utilize a widely adopted popular unlearning method, i.e., SISA [11]. Figure 7b highlights that our method significantly outperforms the baselines in accuracy. + +At last, we also evaluate our method in the lifelong learning task and adopt the fine tuning-based lifelong learning method [3]. For this lifelong learning setting, we report the + +derived experimental results in Figure 8a and Figure 8b. Specifically, Figure 8a indicates the effectiveness of our method in controlling the expected proportion of samples incorrectly reported to be memorized when they have actually been forgotten. Figure 8b presents the evaluation results regarding the effectiveness of lifelong learning in terms of memorizing data from previous tasks, as compared to evaluation based on accuracy. All of these experimental results verify the desired performance in traditional data memorization-based ML tasks with our proposed MIAFdR. + +![](images/7904df32eb1e3349ae895da4c5729c1d39c0232f169ca3b1cf0209f6fe07e8cb.jpg) + +![](images/46499586d10f9581c9ca626dc087b252517748ee90888c6039fec8a9fda6d258.jpg) +Figure 8. Lifelong learning with MIAFdR. + +# 6. Conclusion + +In this paper, we design a novel membership inference attack method, which can provide the false discovery rate guarantees. Notably, our proposed MIAFdR can work as a wrapper that can be seamlessly integrated with existing MIA methods in a post-hoc manner. Specifically, in our method, given the typically unknown true distributions of member and non-member data, we first design a novel conformity score function, which can reflect the conformity degree of test data to the non-member data. Then, based on the obtained point-wise conformity scores, we develop a non-member relative probability estimation strategy to assess the likelihood of not making discoveries. Following this, we introduce a novel adjustment method that modifies the initially estimated non-member relative probabilities to ensure the false discovery rate control, effectively addressing the challenges posed by interdependent non-member relative probabilities. We conduct the theoretical analysis for our method. Extensive experiments are conducted to verify the desired performance of our method. In particular, we also empirically show that our method can help data memorization-based ML tasks, including the unlearning verification task and the lifelong learning task. + +# Acknowledgements + +This work is supported in part by the US National Science Foundation under grant CNS-2350332 and IIS-2442750. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. + +# References + +[1] Martin Abadi, Andy Chu, Ian Goodfellow, H Brendan McMahan, Ilya Mironov, Kunal Talwar, and Li Zhang. Deep learning with differential privacy. In Proceedings of the 2016 ACM SIGSAC conference on computer and communications security, pages 308-318, 2016. 3 +[2] Chirag Agarwal, Daniel D'souza, and Sara Hooker. Estimating example difficulty using variance of gradients. 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However, they incur substantial memory overhead due to the storage demands of non-diagonal preconditioning matrices. To address this, we introduce 4-bit quantization for Shampoo's preconditioners. We introduce two key methods: First, we apply Cholesky decomposition followed by quantization of the Cholesky factors, reducing memory usage by leveraging their lower triangular structure while better preserving spectral properties to minimize information loss. To our knowledge, this is the first quantization approach applied to Cholesky factors of preconditioners. Second, we incorporate error feedback in the quantization process, efficiently storing Cholesky factor and error state in the lower and upper triangular parts of the same matrix. Through extensive experiments, we demonstrate that combining Cholesky quantization with error feedback enhances memory efficiency and algorithm performance in large-scale deep-learning tasks. Theoretically, we also provide convergence proofs for quantized Shampoo under both smooth and nonsmooth stochastic optimization settings. + +# 1. Introduction + +Deep learning has achieved significant advancements across numerous fields in recent years, including language modeling [7, 48], computer vision [16], and multi-modality [38]. These advancements are primarily driven by the scaling of model size, dataset volume, and computational power, as outlined in scaling laws that demonstrate the impact of increased resources on model performance [24, 25]. This trend of scaling has further extended into specialized domains such as finance [54], material science [56], and healthcare [30]. + +Along with the size growth of large-scale models, stochastic gradient descent (SGD) has become a widely adopted method for training thanks to its efficiency and simplicity [23, 41, 45]. However, adaptive gradient methods, e.g., Adagrad [17], Adam [26], and AdamW [35], ap + +![](images/b27109851b9fc40ea7a2b228c5b3ece718337253de00589ee7cd0ad4807b7e92.jpg) +Figure 1. Comparison of test accuracy and peak memory usage for training ResNet-34 on CIFAR-100 dataset. + +ply a diagonal preconditioning to the gradient, which enables faster convergence than SGD [17, 63]. These adaptive methods have demonstrated empirical advantages in various applications [16, 58] and are now the standard optimizers for training large-scale neural networks. + +Building on adaptive gradient methods, full-matrix preconditioned gradient methods offer theoretically superior convergence by capturing richer correlations among parameters [17]. Despite these theoretical advantages, however, the memory overhead associated with non-diagonal matrices poses a significant challenge for large-scale neural networks, which can contain millions of parameters [16, 23, 34]. To address this, a range of efficient preconditioned gradient methods, such as K-FAC [36], Shampoo [22], K-BFGS [20], and AdaBK [60], aim to make full-matrix preconditioning computationally feasible by approximating the full-matrix preconditioner, e.g., block-diagonal precondition matrix. These algorithms have shown faster convergence rates in practice when compared to both SGD and adaptive gradient methods [3, 43, 60]. + +Nevertheless, these efficient preconditioned methods still impose substantial memory costs that restrict their scalability in practical and large-scale model applications. As shown in Fig. 1, the peak memory usage of methods like Shampoo remains significantly higher than SGD. While quantizing precondition matrices in these preconditioned methods from high-precision to low-precision, e.g., 32-bit to 4-bit, effectively reduces memory usage, it also inevitably introduces information loss, which, in turn, severely degrades the performance of these preconditioned + +methods. This is validated by Fig. 1: compared with 32-bit Shampoo, 4-bit Shampoo enjoys much less memory cost but suffers from much worse performance. Therefore, for these efficient preconditioned methods, carefully designed strategies are essential to effectively compress precondition matrices without compromising optimization quality. + +Contribution. We focus on Shampoo due to its simplicity, effectiveness, and popularity, aiming to enable efficient 4-bit quantization of preconditioners while maintaining the stability and efficiency of preconditioned gradient methods. Our main contributions are as follows: + +- We introduce Cholesky quantization to improve memory efficiency and stability. Instead of directly quantizing preconditioners, we apply Cholesky decomposition and quantize the Cholesky factors. This reduces storage by half while better preserving spectral properties, mitigating quantization-induced information loss. To the best of our knowledge, this is the first quantization approach applied to Cholesky factors of preconditioners. +- We propose an error feedback strategy for Cholesky quantization to further reduce quantization error. Inspired by low-precision communication in distributed training [42, 46, 57], we maintain a 4-bit error state that exponentially-moving averages past quantization errors for stable error estimation. This state compensates the Cholesky factor at each iteration, reducing information loss. Moreover, the triangular structure of the Cholesky factor allows efficient joint storage with its error state. +- We establish convergence guarantees for quantized Shampoo in both smooth and nonsmooth stochastic nonconvex optimization. In the smooth case, our 4-bit Shampoo achieves the optimal $\mathcal{O}\left(\frac{1}{\sqrt{T}}\right)$ convergence rate. In the nonsmooth case (e.g., ReLU-based networks [23]), we provide the first proof of global convergence for preconditioned gradient descent, showing convergence to stationary points under mild conditions. +- We develop 4-bit Shampoo using these techniques and evaluate it on image classification with convolutional neural networks (CNNs) and vision transformers (ViTs). It outperforms vanilla 4-bit Shampoo, and significantly reduces memory usage compared to 32-bit Shampoo while maintaining comparable test performance, enabling larger models to be trained within existing resource constraints. + +Discussion: Recent work [51] also studies preconditioner compression. Our approach improves it in two key aspects. First, we introduce error feedback (EF) to relieve the information loss from quantization, which [51] overlooks. EF helps retain critical curvature information during training. Second, our Cholesky Quantization (CQ) stores only lower-triangular factors, making it more memory-efficient than [51], which stores full orthogonal matrices. Moreover, Cholesky decomposition has lower computational cost $(\mathcal{O}(n_p^3 / 3))$ than the QR decomposition used in [51] + +$(\mathcal{O}(2n_p^3 /3))$ . These improvements lead to better efficiency and performance across models (see Tab. 7). + +# 2. Related Work + +Preconditioned Stochastic Optimization. Adaptive gradient methods are the most widely used preconditioned gradient methods in training neural networks, with Adagrad [17], RMSProp [47], and Adam [26] being notable examples. They use diagonal preconditioners to rescale the gradients, been shown to improve convergence in stochastic settings. Preconditioned gradient methods with non-diagonal preconditioners offer faster convergence in theory [17], and are widely explored recently due to faster convergence than adaptive gradient methods in practice [20, 22, 36, 60]. Among them, Shampoo [22] receives extensive concern for its simplicity and effectiveness [37, 50, 51], and it has been developed for large-scale distributed training [3, 43]. + +Quantization for Optimizers. Quantization has been widely used for gradient compression to enable efficient communication in large-scale optimization, particularly for distributed training [2, 49, 52]. Recent works have extended quantization to optimizer states—such as the momentum or second-moment estimates used by adaptive optimizers like Adam—to decrease peak memory usage during neural network training [15, 32]. Despite its computational efficiency, quantization incurs information loss, which can degrade algorithmic performance. To address this, ongoing research explores techniques such as error feedback compensation to mitigate these effects and improve robustness [40, 42]. + +# 3. Preliminaries + +Here we introduce practical Shampoo from [3], and linear-square (linear-2) quantization [15] to compress the preconditioning matrices in our algorithm. + +Notations. Let $\| A\| _F = \sqrt{\sum_{ij}A_{ij}^2}$ denote the Frobenius norm of a matrix $A$ , and $\langle A,B\rangle = \sum_{ij}A_{ij}B_{ij}$ its inner product. The Kronecker product of $A$ and $B$ is denoted by $A\otimes B$ . For a symmetric matrix $H$ $\lambda_{\mathrm{max}}(H)$ and $\lambda_{\mathrm{min}}(H)$ represent its maximum and minimum eigenvalues, respectively. For square symmetric matrices $A$ and $B$ we write $A\succeq B$ if $B - A$ is positive semidefinite (PSD). Quantization and dequantization operations denoted by $\mathcal{Q}$ and $\mathcal{D}$ + +# 3.1. Practical Shampoo + +When minimizing a nonconvex stochastic objective: + +$$ +F (W) := \mathbb {E} _ {\xi \sim \Xi} [ F (W, \xi) ], \tag {1} +$$ + +where $W \in \mathbb{R}^{m \times n}$ is the parameter of the learning model, and data $\xi$ is drawn from an unknown distribution $\Xi$ . At each iteration, we sample a mini-batch of data points to compute the stochastic gradient $G \in \mathbb{R}^{m \times n}$ , and use this stochastic gradient to update the model parameter $W$ . + +To accelerate convergence, Shampoo preconditions the stochastic gradient used in first-order optimizers. Specifically, at iteration $k$ , it updates the preconditioning states $L_{k}$ + +and $R_{k}$ with stochastic gradient $G_{k}$ for preconditioning: + +$$ +\left\{ \begin{array}{l} L _ {k} = \beta L _ {k - 1} + (1 - \beta) G _ {k} G _ {k} ^ {T}, \\ R _ {k} = \beta R _ {k - 1} + (1 - \beta) G _ {k} ^ {T} G _ {k}, \\ \hat {G} _ {k} = L _ {k} ^ {- 1 / 4} G _ {k} R _ {k} ^ {- 1 / 4}, \end{array} \right. \tag {2} +$$ + +where $\beta \in (0,1)$ , and the $1/4$ -th root inverse is computed efficiently using the Schur-Newton algorithm [21]. + +Next, first-order base optimizer $\mathcal{F}$ like SGD can use the preconditioned gradient $\hat{G}_k$ in Eq. (2) to replace vanilla $G_{k}$ for model update. For efficiency, Shampoo stores $(L_{k},R_{k},L_{k}^{-1 / 4},R_{k}^{-1 / 4})$ , and updates $(L_{k},R_{k})$ for every $T_{1}$ iterations and $(L_k^{-1 / 4},R_k^{-1 / 4})$ every $T_{2}$ iterations. See practical Shampoo algorithm in Algorithm 2 of Appendix A. + +# 3.2. Linear Square Quantization for Compression + +Quantization compresses tensors from high precision floating-point to low precision, reducing memory usage. Following [15, 32], we use block-wise quantization to mitigate outlier effects. Below, we introduce the quantization and dequantization processes, focusing on the two-dimensional tensor (matrix) case of Shampoo. + +Quantization. For a floating-point matrix $X \in \mathbb{R}^{m \times n}$ , we partition it into blocks of size $B \times B$ , resulting in $P = \lceil m / B \rceil \times \lceil n / B \rceil$ blocks $\{X_p\}_{p=1}^P$ . In each block $X_p$ , a normalization factor $N_p = \max \{|X_p|\}$ scales elements to $[-1,1]$ via $\bar{X}_p = X_p / N_p$ . Each element $\bar{x}_p$ in $\bar{X}_p$ is then quantized to a $b$ -bit integer using a quantization mapping $\mathcal{M} : [0,2^b - 1] \cap \mathbb{Z} \to [-1,1]$ , calculated by: + +$$ +q _ {p} = \underset {j \in [ 0, 2 ^ {b} - 1 ] \cap \mathbb {Z}} {\arg \min } | \bar {x} _ {p} - \mathcal {M} (j) |. \tag {3} +$$ + +Common quantization mappings include linear, dynamic, and quantile mappings [15, 32, 51]. Here we use a linear-2 mapping for simplicity and efficiency when $b = 4$ : + +$$ +\mathcal {M} (j) = \left\{ \begin{array}{l l} - (- 1 + \frac {2 j}{2 ^ {b} - 1}) ^ {2}, & j < 2 ^ {b - 1} - 1, \\ 0, & j = 2 ^ {b - 1} - 1, \\ (- 1 + \frac {2 j}{2 ^ {b} - 1}) ^ {2}, & j > 2 ^ {b - 1} - 1, \end{array} \right. \tag {4} +$$ + +where $j \in \{0, 1, \dots, 2^b - 1\}$ . This block-wise quantization can be efficiently executed in parallel on GPUs [19, 59]. + +Dequantization. Dequantization $\mathcal{D}$ reverses the quantization process. For each quantized block $Q_{p}$ , we map each element $q_{p}$ back to $[-1,1]$ via $\bar{x}_p' = \mathcal{M}(q_p)$ to obtain $\bar{X}_p'$ . We then restore the original scale using $N_{p}$ , giving $X_{p}^{\prime} = \mathcal{D}(Q_{p}) = N_{p}\bar{X}_{p}^{\prime}$ . Like quantization, dequantization is parallelizable on GPUs. + +For block size $B \times B$ , it balances accuracy and memory cost: smaller blocks improve accuracy but increase the number of normalization factors, raising memory overhead. + +# 4. Memory-Efficient Shampoo Via Compensated Cholesky Quantization + +We first present a direct quantization method to reduce the memory overhead of Shampoo's preconditioning matrices in Sec. 4.1. Then, in Sec. 4.2, we introduce a more memory- + +efficient Cholesky quantization approach that better preserves spectral properties to enhance vanilla quantization. Finally, in Sec. 4.3, we propose a compensation strategy to mitigate information loss from Cholesky quantization. + +# 4.1. Quantization for Shampoo Compression + +From Sec. 3.1, one knows that Shampoo requires storage of four preconditioning matrices $(L_{k},R_{k},L_{k}^{-1 / 4},R_{k}^{-1 / 4})$ , each sized $d\times d$ , where $d$ denotes the model parameter dimension. This brings much additional GPU memory cost, and becomes even more pronounced when training modern neural networks, which are often extremely high-dimensional. So reducing Shampoo's memory overhead is essential for efficient and scalable network training. + +A straightforward approach is to use a quantizer $\mathcal{Q}$ , e.g., the linear-2 quantization in Sec. 3.2, to compress the preconditioners in Shampoo for saving memory, and then adopt a dequantizer $\mathcal{D}$ to recover them for subsequent usage. Formally, at iteration $k$ , we can compute two low-precision preconditioning states $(\bar{L}_k,\bar{R}_k)$ as + +$$ +L _ {k} = \beta \mathcal {D} (\bar {L} _ {k - 1}) + (1 - \beta) G _ {k} G _ {k} ^ {T}, \bar {L} _ {k} = \mathcal {Q} (L _ {k}), \tag {5} +$$ + +$$ +R _ {k} = \beta \mathcal {D} (\bar {R} _ {k - 1}) + (1 - \beta) G _ {k} ^ {T} G _ {k}, \bar {R} _ {k} = \mathcal {Q} (R _ {k}). +$$ + +In this work, we use 4-bit precision for efficient storage. For $\bar{L}_k^{-1/4}$ , $\bar{R}_k^{-1/4}$ , we update them as + +$$ +L _ {k} = \mathcal {D} (\bar {L} _ {k}), \bar {L} _ {k} ^ {- 1 / 4} = \mathcal {Q} ((L _ {k} + \lambda_ {\max } ^ {L} \epsilon I _ {m}) ^ {- 1 / 4}), \tag {6} +$$ + +$$ +R _ {k} = \mathcal {D} (\bar {R} _ {k}), \bar {R} _ {k} ^ {- 1 / 4} = \mathcal {Q} ((R _ {k} + \lambda_ {\max } ^ {R} \epsilon I _ {n}) ^ {- 1 / 4}), +$$ + +where, same as vanilla Shampoo, $\lambda_{\mathrm{max}}^{L}\epsilon I_{m}$ and $\lambda_{\mathrm{max}}^{R}\epsilon I_{n}$ provide numerical stability during the Schur-Newton iterations used to calculate the inverse $1 / 4$ -th roots, in which $\lambda_{\mathrm{max}}^{L},\lambda_{\mathrm{max}}^{R}$ are the maximal singular values of $L_{k},R_{k}$ ,and $\epsilon$ is a small constant [60]. + +Accordingly, one can store 4-bit $(\bar{L}_k,\bar{R}_k,\bar{L}_k^{-1 / 4},$ $\bar{R}_k^{-1 / 4})$ instead of their original 32-bit versions, and dequantize them for usage, e.g., dequantizing $(\bar{L}_k^{-1 / 4},\bar{R}_k^{-1 / 4})$ to compute preconditioned gradient in Eq. (2). + +Despite its simplicity, direct quantization of preconditioners as in Eq. (5) and Eq. (6) can lead to performance degradation due to information loss, e.g., quantizing them from 32-bit to 4-bit precision. For instance, when training ViT-Small [16] on CIFAR-100 [27] with Shampoo using AdamW as the base optimizer, the 32-bit version Shampoo achieves $77.95\%$ test accuracy, substantially outperforming the 4-bit quantized Shampoo, which reaches only $74.56\%$ . Further experimental comparisons can be found in Sec. 6. + +# 4.2. Efficient and Stable Cholesky Quantization + +Here we introduce Cholesky quantization (CQ) to further improve memory efficiency and also stability of quantization in Sec. 4.1. Instead of quantizing $L_{k}$ and $R_{k}$ , we apply Cholesky decomposition on $L_{k}$ and $R_{k}$ , and quantize their corresponding Cholesky factors as $\bar{C}_k^L$ and $\bar{C}_k^R$ which + +are lower triangular matrices and require much less storage. Formally, at iteration $k$ , this process can be written as + +$$ +L _ {k - 1} = \mathcal {D} (\bar {C} _ {k - 1} ^ {L}) \mathcal {D} (\bar {C} _ {k - 1} ^ {L}) ^ {T}, R _ {k - 1} = \mathcal {D} (\bar {C} _ {k - 1} ^ {R}) \mathcal {D} (\bar {C} _ {k - 1} ^ {R}) ^ {T}, +$$ + +$$ +L _ {k} = \beta L _ {k - 1} + (1 - \beta) G _ {k} G _ {k} ^ {T}, R _ {k} = \beta R _ {k - 1} + (1 - \beta) G _ {k} ^ {T} G _ {k}, +$$ + +$$ +C _ {k} ^ {L} = \text {C h o l e s k y} \left(L _ {k} + \epsilon I\right), C _ {k} ^ {R} = \text {C h o l e s k y} \left(R _ {k} + \epsilon I\right), \tag {7} +$$ + +where $\mathrm{Cholesky}(L_k + \epsilon I)$ computes a lower triangular matrix $C_k^L$ such that $C_k^L C_k^{LT} = L_k + \epsilon I$ . The small term $\epsilon I$ is added for numerical stability, with $\epsilon$ as small constant. Once $C_k^L$ and $C_k^R$ are computed, they are quantized as: + +$$ +\bar {C} _ {k} ^ {L} = \mathcal {Q} \left(C _ {k} ^ {L}\right), \quad \bar {C} _ {k} ^ {R} = \mathcal {Q} \left(C _ {k} ^ {R}\right). \tag {8} +$$ + +Accordingly, we can only store two quantized lower triangular matrices $\bar{C}_k^L$ and $\bar{C}_k^R$ . Here we quantize the off-diagonal part of $\bar{C}_k^L$ and $\bar{C}_k^R$ into 4-bit precision while retaining the diagonal elements for 32-bit. This approach is used because off-diagonal elements have less impact on numerical stability, allowing reduced precision with minimal accuracy loss. In contrast, diagonal elements are crucial for overall stability and accuracy, so keeping them in 32-bit helps prevent error accumulation in the factorization. + +Now we discuss two advantages of CQ. Firstly, Cholesky factors are lower triangular matrices, requiring nearly half memory compared to storing full preconditioners in Sec. 4.1 or full orthogonal matrices in [51], reducing peak GPU memory. Secondly, the preconditioner $L_{k}$ recovered from $L_{k} = \mathcal{D}(\bar{C}_{k}^{L})\mathcal{D}(\bar{C}_{k}^{L})^{T}$ remains symmetric and positive definite (PD), better preserving spectral properties. Consequently, its inverse 1/4-th root more closely approximates the original 32-bit preconditioner. To quantify this preservation, we consider the Frobenius norm relative error (NRE) and angle error (AE) between matrices [51], given by + +$$ +\mathrm {N R E} = \left\| A ^ {- 1 / 4} - g (A) ^ {- 1 / 4} \right\| _ {F} / \left\| A ^ {- 1 / 4} \right\| _ {F}, +$$ + +$$ +\mathrm {A E} = \arccos \left(\frac {\langle A ^ {- 1 / 4} , g (A) ^ {- 1 / 4} \rangle}{\| A ^ {- 1 / 4} \| _ {F} \| g (A) ^ {- 1 / 4} \| _ {F}}\right), \tag {9} +$$ + +where $g$ represents the combined effect of quantization and dequantization. We evaluate these metrics using both synthetic PD matrices and preconditioners from 32-bit Shampoo training of VGG-19 on CIFAR-100. As shown in Tab. 1, CQ significantly reduces both NRE and AE, demonstrating its effectiveness in preserving spectral properties. See Appendix C.2 for further details. + +Table 1. NRE and AE on synthetic and real preconditioners for vanilla quantization (VQ) and Cholesky quantization (CQ). + +
PreconditionerVQCQ
NREAENREAE
Synthetic46.14127.1879.1889.204
Epoch 5029.04119.3535.3675.366
Epoch 10025.71218.5054.8524.853
Epoch 15025.35119.3174.7884.788
Epoch 20034.90820.7956.1526.154
+ +![](images/60565a9418a954d47830a783eb1ffad9abbb3809bad68c2a5465fe5dc2418458.jpg) +Figure 2. Efficient storage for Cholesky factor and error state. + +Finally, we analyze the computational cost of CQ. In practice, parameter per layer is divided into $1200 \times 1200$ blocks before preconditioning (Appendix C.3), keeping the per-block CQ cost at $\mathcal{O}(n_p^3)$ with $n_p \leq 1200$ . As shown in Tabs. 5 and 6, CQ introduces minimal overhead. + +# 4.3. Compensated Cholesky Quantization + +To mitigate the information loss from quantization, we introduce error feedback (EF) for Cholesky factors. Error feedback was original proposed to alleviate the information loss caused by gradient compression for communication in distributed training setting [40, 42]. The key idea is to compensate for compression errors by adding them back into the gradients before compression in the next step. Practical adaptations of EF has also been explored in [46, 57] to combine EF with adaptive gradient methods. + +Different from previous work, our focus in this work is the compression of preconditioners of preconditioned gradient methods, and therefore our error feedback is conducted on the preconditioners. At each iteration, an additional low-precision (4-bit) error state, denoted as $\bar{E}_k^L$ , is maintained to capture quantization error for the Cholesky factor $\bar{C}_k^L$ . This error state is then used in the next iteration to enhance precision by compensating for potential quantization errors. + +Specifically, at iteration $k$ , we first compute the Cholesky factors $C_k^L$ and $C_k^R$ following the standard steps in Eq. (7). Before quantizing, we apply error compensation as follows: + +$$ +E _ {k - 1} ^ {L} = \mathcal {D} (\bar {E} _ {k - 1} ^ {L}), \quad \bar {C} _ {k} ^ {L} = \mathcal {Q} \left(C _ {k} ^ {L} + E _ {k - 1} ^ {L}\right), \tag {10} +$$ + +$$ +E _ {k - 1} ^ {R} = \mathcal {D} (\bar {E} _ {k - 1} ^ {R}), \qquad \bar {C} _ {k} ^ {R} = \mathcal {Q} (C _ {k} ^ {R} + E _ {k - 1} ^ {R}). +$$ + +Next, we update the error states $\bar{E}_k^L$ and $\bar{E}_k^R$ using an exponential moving average to improve stability: + +$$ +E _ {k} ^ {L} = \beta_ {e} E _ {k - 1} ^ {L} + (1 - \beta_ {e}) \left(C _ {k} ^ {L} + E _ {k - 1} ^ {L} - \mathcal {D} \left(\bar {C} _ {k} ^ {L}\right)\right), \tag {11} +$$ + +$$ +E _ {k} ^ {R} = \beta_ {e} E _ {k - 1} ^ {R} + (1 - \beta_ {e}) \left(C _ {k} ^ {R} + E _ {k - 1} ^ {R} - \mathcal {D} \left(\bar {C} _ {k} ^ {R}\right)\right), +$$ + +where $\beta_{e}$ is the momentum parameter. Since the Cholesky factors $C_k^L$ and $C_k^R$ are lower triangular and quantization excludes diagonal elements, the error states $E_k^L$ and $E_k^R$ are also triangular with zero diagonals. This enables efficient storage, as each error state can be stored as the upper triangular part as illustrated in Fig. 2, incurring no additional memory overhead compared to vanilla 4-bit Shampoo. + +Finally, we can compute the inverse $1/4$ -th root of the + +# Algorithm 1 4-bit Shampoo via Compensated Cholesky Quantization + +Input: initial weight $W_0 \in \mathbb{R}^{m \times n}$ , initial Cholesky factors $\bar{C}_0^L = \sqrt{\epsilon} I_m$ , $\bar{C}_0^R = \sqrt{\epsilon} I_n$ , quantization error states $\bar{E}_0^L = 0$ , $\bar{E}_0^R = 0$ , initial preconditioners $\hat{L}_0 = I_m$ , $\hat{R}_0 = I_n$ . Total training iterations $T$ , interval of updating preconditioners $T_1$ and $T_2$ , momentum parameter $\beta, \beta_e \in (0,1)$ . First-order optimizer $\mathcal{F}$ with initial optimizer state $s_0$ . + +# Output: final weight $W_{T}$ . + +1: for $k = 1,2,\ldots ,T$ do +2: Compute gradient $G_{k} = \nabla \mathcal{L}_{k}(W_{k})$ +3: if $k\% T_{1} \equiv 0$ then +4: Update Cholesky factors according to Eq. (7) +5: Conduct error compensation following Eq. (10) +6: Update quantization error states as Eq. (11) +7: else +8: $\bar{C}_k^L = \bar{C}_{k - 1}^L$ $\bar{C}_k^R = \bar{C}_{k - 1}^R$ +9: end if +10: if $k\% T_2 \equiv 0$ then +11: Compute inverse 1/4-th root of the preconditioners following Eq. (12) +12: else +13: $\hat{L}_k = \hat{L}_{k - 1},\hat{R}_k = \hat{R}_{k - 1}$ +14: end if +15: $\hat{G}_k = \mathcal{D}(\hat{L}_k)G_k\mathcal{D}(\hat{R}_k)$ +16: $W_{k},s_{k} = \mathcal{F}\bigl (W_{k - 1},s_{k - 1},\hat{G}_{k}\bigr)$ +17: end for + +preconditioners with stored Cholesky factors via + +$$ +\hat {L} _ {k} = \mathcal {Q} \left(\left(\mathcal {D} \left(\bar {C} _ {k} ^ {L}\right) \mathcal {D} \left(\bar {C} _ {k} ^ {L}\right) ^ {T} + \lambda_ {\max } ^ {L} \epsilon I _ {m}\right) ^ {- 1 / 4}\right), \tag {12} +$$ + +$$ +\hat {R} _ {k} = \mathcal {Q} \left(\left(\mathcal {D} \left(\bar {C} _ {k} ^ {R}\right) \mathcal {D} \left(\bar {C} _ {k} ^ {R}\right) ^ {T} + \lambda_ {\max } ^ {R} \epsilon I _ {n}\right) ^ {- 1 / 4}\right). +$$ + +Next, with SGD as the base optimizer, the model parameters are updated with the preconditioned gradient: + +$$ +W _ {k + 1} = W _ {k} - \eta_ {k} \mathcal {D} (\hat {L} _ {k}) G _ {k} \mathcal {D} (\hat {R} _ {k}), \tag {13} +$$ + +where $\eta_{k}$ is the learning rate for iteration $k$ that is often scaled by $\| G_k\| _F / \| \hat{G}_k\| _F$ according to the grafting trick [1]. The preconditioned stochastic gradient $\mathcal{D}(\hat{L}_k)G_k\mathcal{D}(\hat{R}_k)$ can also be fed into another first-order optimizer $\mathcal{F}$ , such as Adam, for model updates. Accordingly, we have arrived at our compensated Cholesky quantization based Shampoo summarized in Algorithm 1. + +# 5. Theoretical Analysis + +Here we provide theoretical analysis of Algorithm 1 with SGD base optimizer as an example. We first define + +$$ +x _ {k} := \operatorname {V e c} \left(W _ {k}\right), g _ {k} := \operatorname {V e c} \left(G _ {k}\right), \tag {14} +$$ + +$$ +H _ {k} := \mathcal {D} (\hat {R} _ {k}) \otimes \mathcal {D} (\tilde {L} _ {k}), +$$ + +where Vec reshapes the matrix into a vector by concatenating the columns of the matrix. Then, we rewrite Shampoo with SGD as base optimizer in Eq. (13) into an equivalent + +vectorization formulation: + +$$ +x _ {k + 1} = x _ {k} - \eta_ {k} H _ {k} g _ {k}. \tag {15} +$$ + +See this equivalent derivation in Appendix B. In the following, we analyze Shampoo with SGD as base optimizer in Eq. (15) under different situations. + +# 5.1. Smooth Nonconvex Training Loss + +Here we analyze the smooth nonconvex $f$ , which is defined according to loss function Eq. (1) as + +$$ +f (x) := F (W), \tag {16} +$$ + +where $x = \operatorname{Vec}(W)$ is the vectorized model parameter. To this end, we introduce the necessary assumptions. + +Assumption 5.1. a) Assume the training loss $f$ is $L$ -Lipschitz smooth, i.e., $\| \nabla f(x) - \nabla f(y)\| _2\leq L\| x - y\| _2$ b) Suppose the stochastic gradient $g_{k}$ is unbiased and its variance can be bounded: $\mathbb{E}[g_k] = \nabla f(x_k)$ and $\mathbb{E}[\| g_k - \nabla f(x_k)\| _2^2 ]\leq \sigma^2 (1 + \| \nabla f(x_k)\| _2^2)$ + +c) Assume the preconditioner $H_{k}$ has bounded eigenvalues, i.e., $\sup_k\lambda_{\max}(H_k)\leq \lambda_{H,\max} < \infty$ and $\inf_k\lambda_{\min}(H_k)\geq \lambda_{H,\min} > 0$ . + +For Assumptions 5.1a) and b), these conditions are standard for stochastic first-order methods (in fact, Assumption 5.1b) is even milder than the commonly assumed condition $\mathbb{E}[\| g_k - \nabla f(x_k)\| _2^2 ]\leq \sigma^2$ . Assumption 5.1c) requires the preconditioner $H_{k}$ to be upper bounded and positive definite, which is guaranteed by the implementation of the Schur-Newton method, the regularization step in Eq. (7), and Proposition 5.1. Specifically, (i) the upper bound follows from Eq. (7) where an $\epsilon I$ regularization is added to ensure a lower bound on $C_k^L$ ; then, applying the $-\frac{1}{4}$ exponent yields an upper bound while the operator $\mathcal{DQ}$ keeps the quantization error bounded. (ii) The strict positive definiteness (i.e., the lower bound) is ensured by the Gershgorin Circle Theorem and the Schur-Newton method. In particular, if $S_{k}$ denotes the inner matrix in Eq. (12) such that $\mathcal{D}(\hat{L}_k) = \mathcal{DQ}\big(S_k^{-1 / 4}\big)$ , then the Schur-Newton method (applied for a limited number of steps) yields a diagonally dominant matrix $Z_{k}$ approximating $S_{k}^{-1 / 4}$ ; writing $\mathcal{D}(\hat{L}_k) = Z_k + E_k^Z$ with $E_{k}^{Z}$ denoting the quantization error, the Gershgorin Circle Theorem guarantees that if $Z_{k}$ is strictly diagonally dominant and $\| E_k^Z\|$ is sufficiently small, then $Z_{k} + E_{k}^{Z}$ remains strictly positive definite, as further supported by Proposition 5.1. Empirical evidence in Fig. 3 also demonstrates that the eigenvalues of the dequantized preconditioners $\mathcal{D}(\hat{L}_k)$ and $\mathcal{D}(\hat{R}_k)$ remain positive throughout training, further validating Assumption 5.1c). + +Proposition 5.1. For the 4-bit Shampoo in Algorithm 1, let $M_{k} \coloneqq (\mathcal{D}(\bar{C}_{k}^{L})\mathcal{D}(\bar{C}_{k}^{L})^{T} + \lambda_{\max}^{L}\epsilon I_{m})^{-1 / 4}$ , if $\| M_k\|_{\mathrm{off,max}}\leq C_B$ , then its preconditioners hold that + +$$ +\mathcal {D} (\hat {L} _ {k}) \preceq M _ {k} + C _ {B} n _ {k} 2 ^ {- b} I, +$$ + +![](images/6c6446e8bc4e990c93b7e3bb696e3f592a409d720f6cb04038c9276ff77ace3c.jpg) +Figure 3. Eigenvalue frequency of the dequantized preconditioners $\mathcal{D}(\hat{L})$ and $\mathcal{D}(\hat{R})$ of VGG-19 on CIFAR-100 at 50, 100, 150, and 200 training epochs, all eigenvalues are greater than 0. + +![](images/01d86dea3eec44bc6ec9f154a4f402f4ab4aeb9b6c780d71de17cd7b833d86c6.jpg) + +![](images/d2e01a5739f058fab79d68f9ab3dda7136383f975585adbf8415bcaea6e42007.jpg) + +![](images/086ec0206a5d2358250df7ab5398b3439a760ae3ac90ab5949655d966f72e3ec.jpg) + +where $\| \cdot \|_{\mathrm{off,max}}$ is the maximal absolute value of all off-diagonal entries and $n_k$ is the number of rows in $W_{k}$ . Furthermore, if for every row index $i$ it holds that $|[M_k]_{ii}| > \left(1 + \frac{2}{2^b - 1}\right)\sum_{j\neq i}|[M_k]_{ij}|$ , then $\mathcal{D}(\hat{L}_k) \succ 0$ . + +This proposition shows that the sequence $\{\mathcal{D}(\hat{L}_k)\}$ can be bounded above and below. Now we are ready to derive the convergence, and state the main results below. + +Theorem 5.1. Suppose Assumption 5.1 holds. Let $\eta_{k} = \frac{c}{\sqrt{T} + 1}$ with $c \in \left(0, \frac{\lambda_{H,\min}}{2L(1 + \sigma^2)\lambda_{H,\max}^2}\right)$ , then we have + +$$ +\mathbb {E} \left[ \| \nabla f (\bar {x} _ {T}) \| _ {2} ^ {2} \right] \leq \frac {2 (f (x _ {0}) - \bar {f} + c ^ {2} L \sigma^ {2} \lambda_ {H , \max} ^ {2})}{c \lambda_ {H , \min} \sqrt {T + 1}}, +$$ + +where $\bar{x}_T$ is randomly selected from $\{x_0, x_1, \dots, x_T\}$ and $\bar{f} := \min_{x \in \mathbb{R}^d} f(x)$ . + +See its proof in Appendix B. Theorem 5.1 shows that for smooth nonconvex training loss, our 4-bit Shampoo with SGD as the base optimizer can converge at the rate of $\mathcal{O}\left(\frac{1}{\sqrt{T}}\right)$ . This convergence rate is optimal as shown in [8], indicating that our 4-bit Shampoo maintains the optimal convergence rate despite the potential information loss introduced by quantization. + +# 5.2. Nonsmooth Nonconvex Training Loss + +In this subsection, we analyze the nonsmooth nonconvex training loss function, particularly in cases where the activation function is nonsmooth, such as the ReLU in ResNet [23]. The iterative scheme can be written as: + +$$ +x _ {k + 1} = x _ {k} - \eta_ {k} H _ {k} \left(d _ {k} + \xi_ {k}\right), +$$ + +where $d_k \in \partial f(x_k)$ , $\partial f$ denotes the subgradient of $f$ , and $\{\xi_k\}$ is the sequence of the random noise in the subgradient. Relevant concepts are provided in Appendix B.2. Given a process $\{\xi_i\}_{i=0}^{\infty}$ , let $\mathcal{F}_k$ denote the history up to iteration $k$ . To this end, we introduce the necessary assumptions. + +Assumption 5.2. a) The function $f$ is $\ell$ -Lipschitz continuous. Additionally, $f$ is a Whitney stratifiable function. + +b) The noise in the subgradient is unbiased and has bounded variance + +$$ +\mathbb {E} \big [ \xi_ {k} | \mathcal {F} _ {k - 1} \big ] = 0, \quad \mathbb {E} \big [ \| \xi_ {k} \| _ {2} ^ {2} | \mathcal {F} _ {k - 1} \big ] \leq \sigma^ {2}, +$$ + +c) For any convergent subsequence $x_{k_j}\to \bar{x}$ , we have $\lim_{N\to \infty}\frac{1}{N}\sum_{j = 1}^{N}H_{k_j} = \bar{H}$ for some positive definite matrix $\bar{H}$ . Additionally, $\sup_{k\geq 0}\lambda_{\max}(H_k)\leq M$ . + +The class of Lipschitz continuous functions is broad and includes pathological cases where subgradient flows fail to converge to stationary points [12]. To address this, we focus on Whitney stratifiable functions, which generalize most practical cases, including loss functions in neural networks with nonsmooth activations like ReLU [5, 13]. Assumption 5.2c) requires only Cesàro summability of $\{H_k\}$ , a mild condition crucial for handling non-time-homogeneity. + +Theorem 5.2. Suppose that Assumption 5.2 holds and the sequence $\{x_{k}\}$ remains within a compact set. If the learning rate satisfies $\sum_{k=1}^{\infty} \eta_{k} = \infty$ and $\sum_{k=1}^{\infty} \eta_{k}^{2} < \infty$ , then + +$$ +\lim _ {k \to \infty} \operatorname {d i s t} (x _ {k}, \Omega) = 0, +$$ + +where $\Omega \coloneqq \{x:0\in \partial f(x)\}$ is the set of stationary points. + +For a stratifiable function, the result of convergence to the stationary point set is tight. There are no complexity results due to the challenges posed by its complex nonconvexity and nonsmoothness [5, 13]. This result ensures the convergence of our proposed algorithm on nonsmooth training losses, including those arising in deep neural networks such as ReLU-based architectures. + +# 6. Experiments + +In this section, we evaluate our 4-bit Shampoo Algorithm 1 on classical image classification and large language model (LLM) pre-training. We compare its performance against vanilla 4-bit and 32-bit Shampoo when using SGD with momentum (SGDM) [45] or AdamW [35] as base optimizer, and the base optimizer itself. For all experiments, we report test accuracy and peak memory usage to assess both algorithmic performance and GPU memory overhead. + +Training Setting. Following standard benchmarks for image classification [23, 31, 53], we train VGG-19 [44], ResNet-34 [23], Swin Transformer Tiny (Swin-Tiny) [34], and Vision Transformer Small (ViT-Small) [16] on CIFAR100 [27] and Tiny-ImageNet [29], as well as ResNet-50 and ViT-Base on ImageNet [14]. For LLM pre-training, we follow [33, 64] to train LLaMA [48] on the C4 dataset [39] with varying model sizes. Training hyperparameters for Shampoo match those of the base optimizer, except that the base optimizer is trained for additional epochs in image classification to achieve comparable performance. All experiments are conducted on a single NVIDIA A100 GPU (80GB). Further details are provided in Appendix C.3. + +![](images/19968dc825d340203f2434d6f4c745a297643b792e8be300af2b0538c7c32c5f.jpg) +Figure 4. Comparison of training loss and test accuracy $(\%)$ for training ResNet-34 on CIFAR-100 and ViT-Small on Tiny-ImageNet. The left figure shows ResNet-34 results, and the right figure shows ViT-Small results. + +Table 2. Test accuracy (\%) and peak memory (MB) of vanilla 4-bit Shampoo with off-diagonal and original block-wise quantization for VGG-19 on CIFAR-100 and Swin-Tiny on Tiny/ImageNet. + +
MethodVGG-19Swin-Tiny
AccuracyMemoryAccuracyMemory
Original74.20661.760.831126.2
Off-Diagonal74.36662.261.281126.9
+ +Table 3. Test accuracy $(\%)$ and peak memory (MB) on CIFAR100. Here VQ denotes vanilla quantization, CQ denotes Cholesky quantization, and EF denotes error feedback. + +
ModelOptimizerAccuracyMemory
VGG-19SGDM74.43597.3
SGDM + 32-bit Shampoo75.021065.2
SGDM + 4-bit Shampoo (VQ)74.36662.2
SGDM + 4-bit Shampoo (CQ)74.99646.0
SGDM + 4-bit Shampoo (CQ+EF)75.21662.2
ResNet-34SGDM79.121254.7
SGDM + 32-bit Shampoo80.691882.6
SGDM + 4-bit Shampoo (VQ)79.451341.0
SGDM + 4-bit Shampoo (CQ)80.271319.5
SGDM + 4-bit Shampoo (CQ+EF)80.521341.0
Swin-TinyAdamW78.281095.3
AdamW + 32-bit Shampoo79.841248.6
AdamW + 4-bit Shampoo (VQ)78.331116.8
AdamW + 4-bit Shampoo (CQ)79.291111.5
AdamW + 4-bit Shampoo (CQ+EF)79.451116.8
ViT-SmallAdamW73.002930.0
AdamW + 32-bit Shampoo77.953448.9
AdamW + 4-bit Shampoo (VQ)74.563001.7
AdamW + 4-bit Shampoo (CQ)77.342983.7
AdamW + 4-bit Shampoo (CQ+EF)77.743001.7
+ +# 6.1. Test Performance + +To ensure a fair comparison between vanilla 4-bit Shampoo and our method, we apply off-diagonal 4-bit blockwise quantization to Shampoo's preconditioners while retaining diagonal elements in 32-bit, defining this as vanilla 4-bit Shampoo. As shown in Tab. 2, off-diagonal quantization only slightly increases peak memory but improves test performance. Thus, we adopt off-diagonal quantization for vanilla 4-bit Shampoo in all experiments. + +As shown in Tab. 3, 4-bit Shampoo with Cholesky quantization consistently outperforms vanilla 4-bit Shampoo. For instance, with SGDM as the base optimizer for ResNet-34 on CIFAR-100, it achieves $80.27\%$ test accuracy versus $79.45\%$ for vanilla 4-bit Shampoo. Similarly, with AdamW for ViT-Small on CIFAR-100, it reaches $77.34\%$ compared + +Table 4. Test accuracy (\%) and peak memory (MB) on TinyImageNet. Here VQ denotes vanilla quantization, CQ denotes Cholesky quantization, and EF denotes error feedback. + +
ModelOptimizerAccuracyMemory
VGG-19SGDM62.191632.8
SGDM + 32-bit Shampoo63.362102.5
SGDM + 4-bit Shampoo (VQ)62.341697.8
SGDM + 4-bit Shampoo (CQ+EF)63.511697.8
ResNet-34SGDM68.274221.3
SGDM + 32-bit Shampoo69.114846.0
SGDM + 4-bit Shampoo (VQ)68.434307.7
SGDM + 4-bit Shampoo (CQ+EF)68.884307.7
Swin-TinyAdamW60.741105.5
AdamW + 32-bit Shampoo62.731256.8
AdamW + 4-bit Shampoo (VQ)61.281126.9
AdamW + 4-bit Shampoo (CQ+EF)62.811126.9
ViT-SmallAdamW55.212944.2
AdamW + 32-bit Shampoo58.113468.1
AdamW + 4-bit Shampoo (VQ)56.473016.0
AdamW + 4-bit Shampoo (CQ+EF)57.513016.0
+ +to $74.56\%$ . This improvement stems from Cholesky quantization's ability to recover preconditioners from Cholesky factors, better preserving the spectral properties of 32-bit Shampoo preconditioners (Sec. 4.2). + +Moreover, experimental results in Tab. 3 validate the effectiveness of the error compensation strategy for Cholesky factors introduced in Sec. 4.3. With SGDM as the base optimizer for ResNet-34 on CIFAR-100, 4-bit Shampoo with compensated Cholesky decomposition improves test accuracy by $0.25\%$ over 4-bit Cholesky quantization. Similarly, with AdamW for ViT-Small on Tiny/ImageNet, it achieves a $0.4\%$ improvement. This consistent gain stems from EF, which retains and integrates quantization errors from previous steps into the updated Cholesky factors before each quantization, iteratively minimizing quantization errors. + +Experimental results on larger image classification datasets (Tabs. 4 and 5) further validate the superiority of our 4-bit Shampoo with compensated Cholesky quantization. On Tiny-ImageNet, it consistently improves test accuracy by over $0.45\%$ compared to vanilla 4-bit Shampoo, whether using SGDM or AdamW as the base optimizer. For ResNet-50 and ViT-Base on ImageNet, it increases test accuracy by $0.27\%$ and $0.73\%$ , respectively, achieving performance close to the original 32-bit Shampoo. + +For LLM pre-training experiments (Tab. 6), our 4-bit + +Table 5. Comparison of test accuracy $(\%)$ , wall-clock time (min), and peak memory (MB) on the ImageNet dataset. + +
ModelOptimizerAccuracyTimeMemory
ResNet-50Base77.562106.411356.2
32-bit78.061841.111986.4
4-bit (VQ)77.731882.811445.2
4-bit (ours)78.001899.411445.2
ViT-BaseBase72.591741.611839.7
32-bit75.471392.413319.1
4-bit (VQ)72.281406.212052.3
4-bit (ours)75.011409.612052.3
+ +Table 6. Comparison of test perplexity (PPL, lower is better), update time (min), and peak memory (GB) on the C4 dataset. + +
ModelOptimizerPPLTimeMemory
LLaMA-130MBase27.32162.945.9
32-bit26.93169.148.2
4-bit (VQ)28.08170.546.2
4-bit (ours)26.98178.946.2
LLaMA-350MBase24.29431.752.9
32-bit24.07443.858.8
4-bit (VQ)25.14445.353.7
4-bit (ours)23.99456.253.7
LLaMA-1BBase48.39403.759.0
32-bitOut of GPU Memory
4-bit (VQ)48.53411.461.9
4-bit (ours)46.31425.061.9
+ +Shampoo with compensated Cholesky quantization consistently achieves lower test perplexity than vanilla 4-bit Shampoo and the base optimizer. Its performance closely matches 32-bit Shampoo, provided the 32-bit version fits within GPU memory. These results demonstrate the effectiveness of our quantization strategy in preserving test performance for large-scale neural network training. + +# 6.2. Memory and Computational Efficiency + +For GPU memory usage, Tabs. 3 to 6 show that 4-bit quantization significantly reduces the peak memory consumption of 32-bit Shampoo. For instance, with SGDM as the base optimizer for ResNet-34 on CIFAR-100, 4-bit Shampoo lowers peak memory by over 540MB, reducing usage by more than $28\%$ . Similarly, with AdamW for LLaMA-350M on C4, it reduces peak memory by 5.1GB. Moreover, when training LLaMA-1B, 32-bit Shampoo exceeds GPU memory limits on an A100 (80GB), whereas our 4-bit Shampoo runs efficiently with strong test performance. + +Additionally, as shown in Tab. 3, 4-bit Cholesky quantization further reduces peak GPU memory usage compared to vanilla quantization. For example, when training ResNet-34 on CIFAR-100 with SGDM, it reduces peak memory by 21.5MB, accounting for $25\%$ of the 86.3MB overhead introduced by vanilla 4-bit Shampoo's preconditioners. This efficiency arises from storing only the lower triangular Cholesky factors $\bar{C}_k^L$ , $\bar{C}_k^R$ , which require half the memory of full matrices $L_k$ , $R_k$ (Sec. 4.2). Thus, 4-bit Shampoo with Cholesky quantization achieves additional memory savings over vanilla 4-bit Shampoo. See Ap + +pendix C.4 for further details. + +For computational efficiency, Tabs. 5 and 6 show that the overhead introduced by compensated Cholesky quantization over vanilla 4-bit quantization is minimal. When training ResNet-50 and ViT-Base on ImageNet, the additional computation time is under 20 minutes, accounting for less than $1\%$ of the total training time. For LLaMA training on the C4 dataset, it adds less than 15 minutes, contributing to under $5\%$ of the total training time. + +# 6.3. Ablation Study + +Comparison with [51]. We compare our 4-bit Shampoo with [51] across a variety of tasks. As shown in Tab. 7, our method consistently outperforms [51]. + +Table 7. Test accuracy (%) and PPL of [51] and our algorithm. + +
Model MetricVGG-19 Acc. (↑)Swin-Tiny Acc. (↑)LLaMA-350M PPL (↓)LLaMA-1B PPL (↓)
4-bit ([51])74.7179.0424.3948.32
4-bit (ours)75.2179.4523.9946.31
+ +Effects of $\beta$ and $\beta_{e}$ . Following modern Shampoo algorithms [3, 43], we maintain an exponential moving average of Cholesky factors and error states. Tab. 8 shows the robustness of our method to momentum coefficients $\beta, \beta_{e}$ . + +Table 8. Test accuracy $(\%)$ for ResNet-34 on CIFAR-100. + +
β,βe0.60.70.80.90.950.98
Accuracy80.4080.3680.4480.4780.5280.30
+ +More Optimizers. We further evaluate RMSprop as the base optimizer. As shown in Tab. 9, our 4-bit Shampoo consistently outperforms vanilla 4-bit Shampoo while reducing memory usage compared to the 32-bit version. + +Table 9. Test accuracy $(\%)$ and peak memory (MB) for Swin-Tiny on CIFAR-100 with RMSprop as the base optimizer. + +
OptimizerAccuracyMemory
RMSprop74.351066.1
RMSprop+32-bit Shampoo75.671219.5
RMSprop+4-bit Shampoo (VQ)74.821087.5
RMSprop+4-bit Shampoo (ours)75.311087.5
+ +# 7. Conclusion + +We propose 4-bit Shampoo, a memory-efficient preconditioned gradient method that significantly reduces GPU usage while maintaining performance close to 32-bit Shampoo. By quantizing only the lower-triangular Cholesky factors to 4 bits, our approach halves memory cost while preserving spectral properties. An error feedback mechanism further corrects quantization errors at each step. We prove convergence in nonconvex settings and demonstrate strong results on image classification and LLM pre-training. + +Limitations. (a) Our CQ and EF are currently tested only with Shampoo, though they are applicable to other preconditioned methods, which we leave for future work. 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However, as these models grow larger, deploying and fine-tuning them becomes increasingly challenging. While conventional quantization techniques help reduce model size, they struggle to achieve high compression rates without significant performance loss. As a result, memory footprint remains a critical challenge for generative models. In this work, we explore the extreme compression of generative models through codebook quantization, drastically reducing model size while maintaining performance. We extend product quantization for model compression, significantly increasing codebook capacity, which is crucial for preserving the generative quality of diffusion models. We also introduce a codebook compression method for memory efficiency. To further minimize performance degradation, we develop EM calibration with re-initialization that optimizes both assignments and centroids. By compressing the model to as low as 1 bit (achieving a $13 \times$ reduction in model size), we obtain a highly compact generative model with remarkable image quality. Extensive experiments on ImageNet demonstrate the superiority of our method over existing techniques. Furthermore, we validate its effectiveness across various generation, language and 3D tasks, highlighting its broad applicability and robust performance. + +# 1. Introduction + +Deep learning has achieved remarkable success across a wide range of tasks [3, 18, 46]. In particular, recent advancements in diffusion models have enabled the generation of high-quality images [22, 55], videos [2, 68], and other contents [6, 45]. However, despite their impressive performance, the extensive model size and computational overhead make them highly resource-intensive, limiting their practicality for real-world applications. To address the chal + +![](images/305f1a94ead55a9b7f52524e1e13faffd54680f7f50c49b642463cf2416e5736.jpg) +Figure 1. Compression results at low bit-widths. PTQ methods (top right) exhibit significant performance degradation at low bit-widths, whereas our method demonstrates superior performance at 1-2 bits. * indicates our implemented version and baseline model is DiT-XL/2 (step=250, CFG=1.5) + +lenges of diffusion models in resource-constrained environments, compression techniques, particularly quantization [5, 32, 51], play a vital role in reducing model size and accelerating inference. By converting weights and activations from floating-point to lower precision formats, 4-8 bits post-training quantization (PTQ) achieves a balance between compression effectiveness and performance. + +However, most PTQ methods suffer from severe degradation at extremely low bit-widths (e.g., 1-2 bits shown in Fig. 1), restricting the compression ratio to at most $4 \times$ (assuming an FP16 baseline). This limitation makes them far from sufficient for model compression given the rapid growth in model size. A realistic challenge is that many users struggle to access the SOTA generative models due to memory limitations. Even after quantization, which may facilitate inference, training or fine-tuning these models remains difficult. On mobile devices, frequent loading from ROM to RAM also remains a bottleneck due to the large model size. Thus, further reducing the memory footprint of generative models is crucial for real-world applications — a challenge that existing quantization and compression methods have yet to fully address. + +![](images/9b4fa7159c734f979d1a2632cccd80e6a275cd6a685d234b993546f94a0f448a.jpg) +Figure 2. Comparison with existing model compression methods. While methods (A)-(B) reduce model redundancy through pruning or decomposition, and method (C) employs low-precision formats, our efficient product quantization (D) achieves a significantly higher compression ratio, ensures broad device compatibility, and enhances both training and inference efficiency. + +Unlike conventional quantization, vector quantization (VQ) jointly compresses multiple values by storing the indices of the nearest neighbors in the codebook, which is highly effective for compressing weights to extremely low bit-widths. Its validity has been demonstrated in CNN [37, 56], LLM[9, 59], and 3DGS [40, 62]. However, it has been rarely applied to generative models. In our experiments, we found that although VQ outperforms other methods, reducing the bit-width still results in a significant performance drop (as shown in Fig. 1). We attribute this to a key limitation of VQ — low capacity, as accurately representing high-dimensional vectors becomes increasingly challenging with a fixed-length, shared codebook. Moreover, the iterative nature of diffusion amplifies cumulative errors, exacerbating the impact of reduced capacity. + +To tackle this limitation, we extend product quantization (PQ) [14, 26] for compressing diffusion models. By decomposing the vector space into a Cartesian product of multiple low-dimensional subspaces, each quantized into a set of codewords, the effective codebook capacity increases exponentially. We also introduce a novel approach to compress the codebook itself based on the usage frequency and similarity of centroids. To further minimize performance loss, we introduce an EM-based calibration with codebook reinitialization, enhancing output reconstruction, generative fidelity, and codebook utilization. Our key contributions can be summarized as follows: + +- We are the first to extend PQ to diffusion models, introducing an extremely low-bit compression method that significantly reduces memory footprint. +- By integrating codebook compression, EM-based calibration, and code re-initialization, our method achieves a high compression ratio while minimizing performance degradation for generative models. +- Our approach achieves superior performance in compressing diffusion models and delivering up to $13 \times$ + +and $8 \times$ compression for C2I and T2I models, respectively. Additionally, results on LLM and 3DGS further demonstrate its robustness and broad applicability. + +# 2. Related Work + +Diffusion models. Diffusion [22, 25, 52, 54] has surpassed generative adversarial networks (GANs) [17] and demonstrated exceptional success in producing high-quality images [41, 47, 48]. Recent research has increasingly shifted towards transformer-based architectures [7] and led to the development of Diffusion Transformers (DiTs) [43], which set new benchmarks in image generation. The scalability of DiTs makes them highly promising for a wide range of generative tasks [38, 43, 68], but their model size and parameters also grow rapidly. For instance, DiT-XL contains 675M parameters, while text-to-image models are even larger. SDXL [44] has 2.6B parameters, SD3 [10] expands to 8B, and FLUX.1 [29] reaches 12B. As models continue to scale, the community faces increasing challenges in utilizing and researching these advanced models due to memory constraints. Thus, an effective method to significantly reduce memory footprint is urgently needed. + +Model compression. Model compression has been extensively studied, with techniques such as pruning, low-rank compression, and quantization (as shown in Fig. 2 (A)-(C)) proposed to address this challenge. Structural pruning [36, 63, 67] identifies and removes redundant components within neural networks, while low-rank compression [27, 66] leverages the assumption that network weights exhibit low-rank properties, allowing them to be decomposed and compressed using SVD. + +Post-training quantization [12, 13, 34, 64] is another widely used technique to reduce model size and accelerate inference by converting weights and activations to lower-precision representations. For generative models, quantiza + +![](images/6347aca8ed529038900bdc79c02647031c7f8677460a572aa25dd10ec0c34f7a.jpg) +Figure 3. Comparison between VQ and PQ. The VQ-compressed model shows degradation and distortions, which become more severe as the bit rate decreases. In contrast, our method largely preserves the model's capacity (left). VQ causes quantization errors in each block's output to accumulate over diffusion steps, whereas our method effectively limits quantization error within a controlled range (right). + +![](images/db984d4a47dd30e57d51aaac10efdd3559b498b803ffcbf80acdea49730a08ff.jpg) +Comparison of MSE Error Across Models + +![](images/424eca911f0aa76b46f613a7fc5d3e663a747b9ad5fafa421909f0cdd7d7d43e.jpg) + +![](images/4f0f6e9bd3102cff590b8803aafba9af6cab6a945fed8c9c670be760dcdfec90.jpg) + +![](images/5ed180dc1d41237a101aa8e0827e11e236b2ec6cdf5e1fe59179fe646e526a79.jpg) + +tion has also been extensively explored. SVDQuant [32] combines SVD decomposition with SmoothQuant [64] to achieve 4-bit quantization for diffusion models, while Q-DiT [5] addresses weight and activation variance, outperforming other U-Net-based methods [21, 33, 51]. We do not cover quantization-aware training (QAT) [11, 20, 39] or models requiring full training [35, 61] or full finetuning [19], as they demand significantly more memory than PTQ, making them computationally impractical. Additionally, we exclude 1.58-bit FLUX [65] due to the lack of publicly available implementation details. + +A key limitation of existing compression methods is that they fall short in reducing model size sufficiently. In many resource-constrained scenarios, the primary challenge is not acceleration but the ability to run models within limited memory. Another limitation of quantization is that it prevents further training, restricting model adaptability for research and applications. Model size reduction has been largely overlooked and remains an unsolved challenge. Therefore, our focus is solely on compressing model size. + +Vector quantization for compression. Vector quantization [15] provides an efficient approach for compressing model weights and has been applied to CNN [37, 56], LLM [9, 30, 49, 59, 60], and 3DGS [40, 62]. VQ4DiT [8] extends VQ to DiT models, introducing a zero-data, blockwise calibration process to refine codebooks layer by layer. However, its results are underwhelming, showing significant degradation. Applying VQ to diffusion models remains challenging and has yet to yield satisfactory results. + +Product quantization was originally designed for nearest-neighbor search [14, 26, 42] as an multi-codebook approach to high-dimensional vector quantization. It reduces complexity by partitioning vectors into smaller subvectors, each quantized independently. To our knowledge, we are the first to successfully adapt and scale PQ for dif + +fusion models, addressing its limitations through codebook compression, EM calibration, and re-initialization. + +# 3. Preliminary + +Vector quantization. Let $\mathbf{W} \in \mathbb{R}^{m \times n}$ represents the input to the quantizer. Vector quantization discretize a floating-point vector to an integer index to a centroid within a codebook. The codebook is typically trained using K-Means, and the assignment is calculated by finding the nearest centroids. To be specific, the quantizer set the sub-vector dimension and partitions $\mathbf{W}$ into $\mathbf{w}_{i,j} \in \mathbb{R}^{1 \times d}$ . These sub-vectors are quantized using a codebook $\mathbf{C} \subseteq \mathbb{R}^{k \times d}$ . The original weight $\mathbf{W}$ can then be expressed by an assignment $\hat{\mathbf{W}}$ , whose elements are calculated as: + +$$ +\hat {w} _ {i, j} \triangleq \underset {p} {\arg \min } \| \mathbf {w} _ {i, j} - \mathbf {c} _ {p} \| ^ {2}, \tag {1} +$$ + +which represents the index of each codeword that best fits each sub-vector $\mathbf{w}_{i,j}$ . The assignments require $m \times n / d \times \lceil \log_2 k \rceil$ bits for storage, and bits per value after quantization become $\frac{\lceil \log_2 k \rceil}{d}$ . We neglect the codebook's storage because it is small. Since compression targets both numerical precision and weight size, it achieves higher efficiency in model size reduction than direct quantization. + +Diffusion model. At every training step, the diffusion model samples a mini-batch of images $x_0$ and adds noise to obtain $x_t$ : $q(x_t \mid x_0) = \mathcal{N}(\sqrt{\bar{\alpha}_t} x_0, (1 - \bar{\alpha}_t)I)$ . After training a diffusion model $\theta$ to get $p_{\theta}(x_{t-1} \mid x_t)$ , we reverse the above process step by step to recover the original image $x_0$ from pure noise $x_T \sim \mathcal{N}(0, I)$ . The training objective is to reduce the gap between the added noise in the forward process and the estimated noise in the reverse process: + +$$ +L _ {\mathrm {D D P M}} = \mathbb {E} _ {t \sim [ 1, T ]} \| \epsilon_ {t} - \epsilon_ {\theta} (\sqrt {\bar {\alpha} _ {t}} x _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \epsilon_ {t}, t) \| ^ {2}, (2) +$$ + +where $\epsilon_t\sim \mathcal{N}(0,I)$ is the noise added to original images and $\epsilon_{\theta}$ is the noise estimated by the trainable model. + +![](images/5f2036d2c45ef748466cc08c09e8b1b8978a14bda1eee83db6c78c43ce8417cb.jpg) +Figure 4. Overview of our method. We compress parameters to extremely low-bits. Stage 1 quantizes weight groups by mapping them to centroids in individual codebooks, which are further compressed for effective size reduction. Stage 2 calibrates the compressed parameters by refining assignments via output reconstruction loss (E-step) and fine-tuning codebooks through DDPM loss (M-step). + +
MethodBit-widthFID↓Model Size (MB)C Size (MB)W Size (MB)
FP165.411349.4--
GPTQ2280.11173.2--
Q-DiT2313.63168.5--
VQ4DiT211.87162.1--
VQ (1 ep)212.33171.70.5159.6
VQ (10 ep)212.12171.70.5159.6
Ours26.84211.339.8159.6
+ +Table 1. Comparison of compression methods with their FID and compressed size. + +# 4. Method + +We first evaluate whether existing quantization methods can compress models under 2-bits precision. We apply compression to DiT-XL/2 with 250 steps and a CFG of 1.5. FID is calculated using 10,000 samples. As shown in Tab. 1, traditional methods fail at extremely low bit-widths, prompting us to explore VQ as an alternative solution. + +# 4.1. VQ Compression for Diffusion + +We first apply the VQ method to the DiT model by quantizing the weights of all linear layers in each DiT block, excluding the bias terms. Specifically, we partition the weights into groups with each sub-vector dimension $d = 4$ and use INT8 quantization, meaning each sub-vector $\mathbf{w}_{i,j}$ in each group is quantized to an INT8 integer. Consequently, the weights $\mathbf{W}$ are quantized to $\hat{\mathbf{W}} \in \mathbb{N}_0^{m \times \frac{n}{4}}$ together with a codebook $\mathbf{C} \in 256 \times 4$ , computed using K-means with 1000 iterations. This results in a $8 \times$ compression of the model, or equivalently, 2-bit compression from FP16. + +Directly applying VQ to the DiT model leads to a significant performance drop, as shown in Fig. 3. To mitigate + +this, we calibrate the compressed model using Eq. (2). After training for one epoch, generative performance improves substantially, as reported in Tab. 1. We also compare our approach with VQ4DiT [8]—despite some differences in implementation, our results remain comparable. + +Compared to VQ-compressed LLMs [9, 59, 60] and 3DGS [40, 62], which maintain nearly lossless performance, DiT experiences significant degradation. Moreover, 1-bit compression severely impacts performance, making current solutions fall short in both effectiveness and compression ratio. This highlights fundamental flaws in applying VQ to diffusion models and underscores the need to identify key bottlenecks in their compression. + +One possible explanation is underfitting, but extending calibration to 10 epochs yields minimal improvement. A more likely issue is that VQ introduces reconstruction errors, which are especially problematic for diffusion models. To investigate, we visualize the L2 distance between the output features of the VQ-compressed and original models at intermediate layers. As shown in Fig. 3 (right), VQ-induced errors arise from the start and rapidly accumulate during sampling, causing significant output deviation and performance degradation. Unlike LLMs and 3DGS, diffusion models rely on multiple iterative steps, making VQ-induced errors far more impactful. The high reconstruction error suggests that VQ lacks the capacity to effectively represent high-dimensional vectors for diffusion model compression. Therefore, a higher-capacity method is needed for more precise representation. + +# 4.2. Efficient Product Quantization + +Since diffusion models require higher reconstruction precision, product quantization offers a more suitable solution. Unlike VQ, PQ efficiently handles cases requiring an expo + +nentially large number of codewords. It achieves this by decomposing the vector space into $N = n / d$ low-dimensional subspaces, each quantized into $k$ distinct codewords. This gives an effective $k^N$ codewords in the original space while keeping the storage cost at $O(kN)$ . As illustrated in Fig. 2 (D), PQ employs a codebook $\mathbf{C} \in \mathbb{R}^{N \times k \times d}$ , where each sub-vector in the weight matrix is assigned an INT8 value, computed as follows: + +$$ +\hat {w} _ {i, j} = \underset {p} {\arg \min } \| \mathbf {w} _ {i, j} - \mathbf {c} _ {j, p} \| ^ {2}. \tag {3} +$$ + +Codebook compression. In PQ, the storage cost of the codebook is significantly higher than in VQ, increasing from $k \times d$ to $k \times n$ , making it no longer negligible. To improve memory efficiency, we compress the codebook to keep its size within $\frac{1}{4}$ of the assignment storage. To achieve this, we introduce a codebook pool of size $N' \times d$ . Given the memory requirements of the assignment $\hat{\mathbf{W}} \left( m \times \frac{n}{d} \times 8 \text{ bits} \right)$ and the new codebook $\mathbf{C}' \left( N' \times d \times 16 \text{ bits} \right)$ , we derive the target size as $N' = \frac{mn}{8d^2}$ . Accounting for additional storage needed for projection, we refine this to $N' = \frac{mn}{16d^2}$ , ensuring the codebook remains within the desired size (details of calculation is listed in appendix). + +To compress the codebook, we leverage the observation that many vectors in codebook $\mathbf{C}$ are similar. We define a threshold $\tau_{c}$ and consider two sub-vectors similar if their L2 distance is below $\tau_{c}$ , making them candidates for merging. We first assess the importance of each centroid by counting how many codes are assigned to it and sort them by importance. For each centroids, we check its proximity to those already in the pool. If the pool is not full and the vector is not close to any existing entries, it is added. The overall compression process follows this structured approach: + +$$ +\mathbf {C} ^ {\prime} = \left\{\mathbf {c} _ {j} \mid \min _ {I (\mathbf {c} _ {i}) > I (\mathbf {c} _ {j})} \| \mathbf {c} _ {i} - \mathbf {c} _ {j} \| _ {2} > \tau_ {c} \right\}, \tag {4} +$$ + +$$ +\hat {c} _ {i, j} = \underset {\mathbf {c} _ {p} ^ {\prime} \in \mathbf {C} ^ {\prime}} {\arg \min } \left\{\left(I (\mathbf {c} _ {i, j}) - I (\mathbf {c} _ {p} ^ {\prime})\right) \mid \| \mathbf {c} _ {i, j} - \mathbf {c} _ {p} ^ {\prime} \| _ {2} < \tau_ {c} \right\}, \tag {5} +$$ + +where $I(\cdot)$ represents the importance score. After compression, we store a reduced codebook $\mathbf{C}' \in \mathbb{R}^{N' \times d}$ along with a projection matrix $\hat{\mathbf{C}} \in \mathbb{N}_0^{n/d \times k}$ , where each entry is stored in INT16 format. This compression significantly enhances memory efficiency in PQ while effectively increasing its capacity compared to VQ. As shown in Tab. 1, our method achieves a high compression ratio with minimal performance loss after calibration. + +# 4.3. EM Calibration with Re-initialization + +After product quantization, the diffusion model is significantly compressed in both memory and parameters, making calibration feasible and affordable. We propose a more effective method with improved targets compared to existing + +Algorithm 1: Codebook Re-initialization +$\mathbf{R}\gets \mathrm{concat}(\mathbf{R}[:m],\mathbf{w}_{i,j}[\mathrm{rand\_sample}(m)]);$ $\mathbf{U}_p = \bigvee_{i,j}(\hat{w}_{i,j} == p)$ +code_age $= 1$ , code_age[U] $= 0$ +if∑11(code_ age $\geq \tau_{dead}) / \| \mathbf{C}\| >0.03$ then $\begin{array}{rl} & {\mathbf{C}_{\mathrm{live}} = \mathbf{C}[\mathrm{code\_age} < \tau_{\mathrm{dead}}];}\\ & {\mathbf{C}_{\mathrm{all}} = \mathrm{concat}(\mathbf{R},\mathbf{C}_{\mathrm{live}});}\\ & {\mathbf{C}_{\mathrm{new}} = \mathrm{kmeans} + + (\mathbf{C}_{\mathrm{all}});}\\ & {\mathbf{C}\leftarrow \mathbf{C}_{\mathrm{new}};}\\ & {\mathrm{code\_age} = 0;} \end{array}$ +// ▷ Continue calibration + +approaches. While block-wise distillation, as used in [8], is an alternative, it suffers from suboptimal optimization targets and cannot prevent loss accumulation. Our calibration process, akin to an approximate EM algorithm, alternates between an E-step for assignment updates and an M-step for centroid optimization. + +E-Step. In PQ, the assignment optimizes the quantization error by minimizing $\| \mathbf{w}_{i,j} - \mathbf{c}_{j,p}\|^2$ . However, this formulation does not account for the output feature. Instead, we redefine the assignment objective to minimize the discrepancy between the original and quantized features: $\min \| \mathbf{Wx} - \mathbf{W}'\mathbf{x}\|^2$ , where $\mathbf{W}'$ denotes the reconstructed weight matrix. In this step, given the current centroids $\mathbf{C}$ we reassign each quantized weight $\hat{w}_{i,j}$ by solving: + +$$ +\hat {w} _ {i, j} = \underset {p} {\arg \min } \| \mathbf {w} _ {i, j} \mathbf {x} _ {j} - \mathbf {c} _ {j, p} \mathbf {x} _ {j} \| ^ {2} \tag {6} +$$ + +where $\mathbf{x}_j$ represents the activations corresponding to the $j$ -th sub-vector. This step can be viewed as the E-step, where we infer the most likely assignments $\hat{\mathbf{W}}$ that minimize the expected reconstruction error. + +M-Step. Unlike other methods using closed-form solutions, we optimize centroids via gradient-based methods by backpropagating the DDPM loss: + +$$ +\mathbf {C} \leftarrow \mathbf {C} - u \left(\frac {\partial \mathcal {L} _ {\mathrm {D D P M}}}{\partial \mathbf {C}}, \Theta\right), \tag {7} +$$ + +This corresponds to the M-step, where we refine the codebook $\mathbf{C}$ using the reassigned weights from the previous E-step. Our calibration strategy follows an EM algorithm: the E-step updates the assignments $\hat{\mathbf{W}}$ , while the M-step optimizes the centroids $\mathbf{C}$ via gradient descent, enhancing both reconstruction and generative performance. In contrast, other calibration methods either update only the centroids, prioritize weight reconstruction alone, or fail to accommodate diffusion models. + +Codebook re-initialization. To prevent codebook collapse and ensure efficient centroid utilization [31], we maintain a randomly updated reservoir of past vectors. When + +
ModelBit-widthMethodSize (MB)FID ↓sFID ↓IS ↑Precision ↑
DiT-XL/2 (250 steps)16FP1349.45.3317.85275.130.8216
2GPTQ172.8280.11142.363.970.0326
Q-DiT168.3313.63211.171.280.0001
Ours211.36.8418.75190.990.7685
DiT-XL/2 (100 steps)16FP1349.45.3117.61245.850.8077
2GPTQ172.8270.68132.214.170.0001
Q-DiT168.3310.06213.411.190.0003
Ours211.38.1820.40179.690.7460
DiT-XL/2 (50 steps)16FP1349.46.2718.45204.470.8343
2GPTQ172.8311.09154.834.330.0006
Q-DiT168.3312.16210.281.280.0005
Ours211.311.0423.92157.610.7194
LDM-4 (20 steps)16FP801.811.697.92361.180.9219
2Q-Diffusion100.243.9617.1549.080.4318
PTQD100.239.3715.1453.360.4589
Ours127.67.988.67197.210.8011
+ +a significant portion of the codebook remains unused for an extended period (i.e., becomes "dead"), we trigger reinitialization by selecting recently used code vectors, merging them with the reservoir, and applying k-means to generate new centroids, which then replace the old codebook. This process keeps all centroids actively engaged. The pseudo-code is provided in Algorithm 1. + +The overall method is illustrated in Fig. 4 and consists of two main stages. The first stage is data-free, where we apply our method to compress the weights. The second stage leverages training data for calibration. By integrating these compression and calibration strategies, our approach enhances product quantization, enabling more effective model compression for diffusion. + +# 5. Experiments + +# 5.1. Experiments on Class-conditional Generation + +Settings. For class-to-image(C2I) models, we conduct our experiments primarily on DiT [43]. We use DiT-XL/2 with CFG of 1.5 as our floating-point baseline. Most experiments are conducted at an image resolution of $256 \times 256$ , with results for $512 \times 512$ resolutions provided in the appendix. To further examine the effectiveness, we also perform experiments on LDM-4 [48], a classical U-Net diffusion models. LDM is sampled by DDIM [53] for 20 steps by default. We set $d = 2, 3, 4, 8$ for 4-, 3-, 2-, and 1-bit compression, respectively. The thresholds are set as $\tau_{c} = 0.05$ and $\tau_{dead} = 256$ . The codebook and codewords are initialized using K-means with 20 iterations. For calibration, we use the AdamW optimizer with a constant learning rate of $1 \times 10^{-4}$ . By default, the DiT model is calibrated for one epoch. Models are evaluated on the ImageNet validation set using 10,000 sampled images. The primary metrics + +Table 2. Class-conditional generation results on ImageNet at a resolution of ${256} \times {256}$ . The best result is highlighted in bold. + +
Bit-widthMethodSize (MB)FID ↓IS ↑Precision ↑Recall ↑
16FP1349.45.41269.840.81970.5712
4VQ339.96.26217.710.75470.6943
Ours354.16.25215.120.75760.6842
3VQ234.77.20175.230.75330.6823
Ours257.47.01188.520.74030.6868
2VQ171.712.34105.670.67500.5910
Ours211.36.84190.990.76850.6588
1VQ89.191.7113.510.24810.4110
Ours103.914.03110.230.68630.6652
+ +Table 3. Performance of our implementation of VQ and our proposed method on ImageNet at $256 \times 256$ resolution. + +include Fréchet Inception Distance (FID) [17], spatial FID (sFID) [50], and Inception Score (IS) [1, 23]. + +Ours vs. VQ. Section 5.1 presents a performance comparison between our implementation of VQ and the proposed method, evaluated on the DiT-XL/2 with 250 sampling steps. Across various bit-widths, our method consistently outperforms VQ, especially as bit-width decreases. The most significant improvement is observed at 1-bit precision: while VQ suffers from a notable collapse in performance, with an FID dropping to 91.71, we achieve a much improved FID of 14.03, along with significantly higher IS (110.23 vs. 13.51) and Precision (0.6863 vs. 0.2481). This demonstrates that our method effectively handles high-dimensional sub-vector compression and is suitable for extremely low-bit settings. Under a more typical 2-bit compression setting, our model also significantly surpasses VQ, improving the FID by 5.50 and increasing the IS by 85.32. As the bit-width increases, the performance gap narrows but remains still. While our method has a slightly larger + +![](images/8e9cd5eb694a91adb4308a77a0fddda92bc1381c95701ffa514fdc3ee61d6aed.jpg) +1 bit + +![](images/9c1704da3fb0c6338fa7b4f014732cb1e46f8e8c51b73f807aa918c510020a06.jpg) + +![](images/f97da7fc0fad91cee10d8ec30b54044a6112c07983bbe976ebae69e3f563ac30.jpg) + +![](images/02c26831721a40733a25dc4c91955917f721f74146acde8446f32e752c18084c.jpg) + +![](images/56fc0d4b8d30653eec7758ce7560351f3f6de9afd2765113d26f2b052bf9b21f.jpg) + +![](images/1989b6fb83ec6e9eae5da332900ece59513e3a16f283fe0541250cac74f3d14b.jpg) + +![](images/26f88b84545eabc80e14a8352392c77b78175bfb1ee899551d13878e1be9d65c.jpg) + +![](images/f548a6eab11219496e2cc8566cb7dd586ce3f5143cf6261d337a4f9df63c6177.jpg) + +![](images/60662658d64118f9b0de9421705f1e65c1bbbf2536d65f1aada9b5abcb663477.jpg) + +![](images/b4da2eff74736cd5985f973013eac67e3f800ac07b51817fa2be70c67a0102f6.jpg) +2 bit + +![](images/0d44e7dc9c006da25e3827fc2c8681a9a2d4f5a0d9371f63263c84a1a0b1cfc6.jpg) + +![](images/5f88b37f7810984c53456317cffc0c83e255f3aa293d1e9faed171ba32503412.jpg) + +![](images/32a7db57e4fa833ca663f72a1375ba075e896b631be2c91db47c099800de57e3.jpg) + +![](images/feefabc865ad26859042327cdce9208ef1753fad077c56fa46be355132f61b77.jpg) + +![](images/06216035f83d8744df238b4f712f2180abf74c9f1ee4e632272f74a48d3fa066.jpg) + +![](images/5f6dd346c293a9685100f37e37d49364140b2f15b3d7ef34d337f1de05a59711.jpg) + +![](images/c02d5ae902f0c4de5bad68a20ce7097c2613db4ef4e0651e370fe9ae6ee2b33f.jpg) + +![](images/ef361b4e56613bfb5769d73ef759085915ebf5cffff605e206a1e975c6699f76.jpg) + +![](images/db85c49c954512858df8cdee1f24bffb59530921e327ff1e9a4e6feca01dd796.jpg) +4 bit + +![](images/4262fc3d3f9af72195ed2eb447f003ba3364a452282dc29a503a1c8c165f3cab.jpg) +Figure 5. The generation results of our compressed DiT-XL/2 model, evaluated with 250 steps and a CFG of 1.5, demonstrate promising performance across various bit-widths consistently. + +![](images/527d39fecdca20d1ad14a90418f6f2660232f880f04a28ab9a934870734ff111.jpg) + +![](images/a728c0d319562ef03b4224ca87b0a1b8b177105b4d1dc1fede2570edbb3084c9.jpg) + +![](images/95674ae3f28956d8182839c8667d889b540ef0869a810cd571d2b8937ddeb5fb.jpg) + +![](images/11065128b0ade120fa58ecc224a884d73256b6af66ab2dfdf7d5d590f9712939.jpg) + +![](images/04cd340c08d3578c3acecbf523e915b2ca0fa2240971ead998fc137fd8f442fb.jpg) + +![](images/57126663c5595bfc71f8c89857275f3504fa9d65ddb710fa747a5e2fbd337e67.jpg) + +![](images/05a277a73649e71d26dd585443f3ef2a757b0d2722ff20ba247439c675a4b7db.jpg) + +
ModelBit-widthMethodGenEvalT2I-Compbench
Single Obj.Two Obj.CountingColorsPositionColor Attr.OverallColorShapeTexture
PixArt-α16FP0.980.500.440.800.080.070.480.690.560.70
2SVDQuant0.410.180.170.220.010.020.170.240.160.32
Ours0.960.460.440.770.060.070.460.680.540.69
FLUX.1-dev16FP0.980.810.740.790.220.450.660.750.510.63
2SVDQuant0.480.320.460.390.080.210.320.330.270.39
Ours0.950.770.430.720.140.390.570.710.460.61
+ +Table 4. Text-to-image generation results evaluated on GenEval and T2I-Compbench at a resolution of ${1024} \times {1024}$ . + +model size due to the additional codebook size, this modest cost yields substantial performance gains, making it a worthwhile trade-off. Our method achieves an impressive compression rate of up to $13 \times$ for the DiT model. Images generated by our compression method across different bit-widths are shown in Fig. 5. + +Comparison with PTQ methods. We compare our method with GPTQ [12] and Q-DiT [5] for DiT, as well as Q-Diffusion [33] and PTQD [21] for LDM. The results of VQ4DiT [8] are not included, as it can be considered a less effective variant of our implemented VQ method, which is listed in Sec. 5.1. Additionally, methods that require training or fine-tuning [11, 19] with significant memory overhead are also omitted. Section 4.3 shows a comparison on the ImageNet $256 \times 256$ dataset. Across different timesteps (250, 100, and 50), our method consistently achieves lower FID and sFID values compared to other methods, indicating improved generative quality and image fidelity. Notably, across all quantization settings, all methods except ours exhibit significant performance degradation, producing nearly meaningless and distorted images. The existing PTQ methods fail to achieve effective compression at extremely low-bit settings. In contrast, our approach stands out as the only one that successfully achieves a high compression + +ratio while maintaining promising generation quality. Beyond the DiT architecture, we further apply our method to the U-Net structure based on LDM-4. As shown in Section 4.3, our method effectively compresses the CNN-based diffusion architecture, demonstrating its broad applicability across different diffusion models. + +# 5.2. Experiments on Text-to-image Generation + +Settings. For text-to-image (T2I) models, we primarily conduct our experiments on two open-source models. PixArt- $\alpha$ [4] is a DiT-based model comprising 28 transformer blocks with a total of 600M parameters, designed for efficient training. We evaluate it under the default 20-steps setting. FLUX.1 [29], the leading open-source DiT-based diffusion model, features 12B parameters. Our evaluation is based on its 50-step guidance-distilled variant (FLUX.1dev). We set $d = 4$ , corresponding to a 2-bit compression, and perform calibration on the JourneyDB dataset [57]. To assess our method's effectiveness, we evaluate it on GenEval [16] and T2I-CompBench [24]. GenEval measures generation quality from five key aspects: single-object, two-object, counting, colors, position, and attribute binding. Meanwhile, T2I-CompBench focuses on evaluating T2I models' capabilities in color, shape, and texture rep + +![](images/5845767cb1ba2be2fa0e214be435b212c2d471230c2868eadc82f7f1b43f5df9.jpg) +Figure 6. Generation results of 2-bits FLUX.1-dev compressed by our method. The prompt is provided by GenEval. + +
ModelPSNR↑SSIM↑LPIPS↓
Baseline23.140.8410.183
Compact3D23.390.8360.200
Ours23.570.8380.192
+ +Table 5. Quantization results of 3DGS + +
ModelWino.↑PiQA↑Hella.↑
Baseline67.2578.4556.69
Quip#62.4371.3842.94
Ours64.8773.9648.12
+ +Table 6. Quantization results of LLM + +
PQDDPM lossBlockwise DistillationAssignment AdjustmentFID↓
✓✓7.21
✓✓8.52
✓✓✓6.84
+ +Table 7. Ablation study of each module + +resentation. Most experiments are conducted at an image resolution of $1024 \times 1024$ . + +Results. Sec. 5.1 shows that our method demonstrates strong performance across various benchmarks for both models. Compared to SVDQuant [32], a PTQ method designed for diffusion models, our approach achieves significant improvements at 2-bit quantization, with overall GenEval score gains of 0.29 and 0.25 for PixArt- $\alpha$ and FLUX.1-dev, respectively. On certain benchmarks, the compression is nearly lossless, highlighting the effectiveness of our method for large-scale T2I models. Our approach enables up to $7.7\times$ compression with minimal performance degradation. Additionally, the compressed model remains suitable for both inference and further training, potentially advancing the application and research of diffusion models. The generated results from our compressed model are presented in Fig. 6. + +# 5.3. Experiments on LLM and 3DGS + +Our method can be adapted to any VQ-based approaches, enhancing their capacity and delivering general benefits. To demonstrate its versatility, we extend our method to 3DGS [28] and apply it to Compact3D [40], evaluating its performance on the Tanks and Temples. The results, presented in Sec. 5.1, highlight its effectiveness. Similarly, our approach can be integrated into LLM by refining the VQ mechanism. Building upon Quip# [59], which is based on LLAMA-2 7B [58], we present the results in Sec. 5.1. Both experiments demonstrate consistent improvements, underscoring the broad applicability of our method. + +# 5.4. Ablation Study + +We evaluate the contributions of each module in our method. Since PQ alone cannot compress the model while maintaining the generation of appealing images, we enable PQ by default. Our experiments in Sec. 5.1 indicate that the DDPM loss is more effective for calibrating the codebook and achieving better performance. Additionally, adjusting the assignments during the forward pass also enhances the performance of the compressed model. + +# 6. Conclusion and Limitations + +In this work, we introduced a novel method for compressing generative models to extremely low bit-widths. Our analysis identifies the primary challenges when applying quantization to diffusion models: the difficulty in representing high-dimensional vectors accurately at low bit-widths and the tendency for quantization errors to accumulate over multiple diffusion steps. To address these issues, we revamped the product quantization (PQ) to allow for precise quantization with minimal codebook size. We propose a method to compress the PQ codebooks based on the usage frequency of centroids, and an EM-based calibration method that adjusts assignments according to activations and optimizes codebooks based on the diffusion loss. Experiments demonstrate that our method effectively compresses weights to as low as 1-bit precision while preserving high-quality image generation capabilities. The main limitation of our method is that, while it significantly reduces model size and alleviates memory constraints, it does not directly accelerate inference compared to PTQ. In future work, we aim to achieve both compactness and speed. + +# Acknowledgments + +This work was partly supported by the National Natural Science Foundation of China under Grant 62276123. + +# References + +[1] Shane Barratt and Rishi Sharma. A note on the inception score. arXiv preprint arXiv:1801.01973, 2018. 6 +[2] Andreas Blattmann, Tim Dockhorn, Sumith Kulal, Daniel Mendelevitch, Maciej Kilian, Dominik Lorenz, Yam Levi, Zion English, Vikram Voleti, Adam Letts, et al. Stable video diffusion: Scaling latent video diffusion models to large datasets. arXiv preprint arXiv:2311.15127, 2023. 1 +[3] Tom B Brown. 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However, previous works often require priors such as class labels of a speaker or additional 3D facial meshes at inference, which makes them fail to reflect the speaking style and limits their practical use. To address these issues, we propose MemoryTalker which enables realistic and accurate 3D facial motion synthesis by reflecting speaking style only with audio input to maximize usability in applications. Our framework consists of two training stages: $<1$ -stage> is storing and retrieving general motion (i.e., Memorizing), and $<2$ -stage> is to perform the personalized facial motion synthesis (i.e., Animating) with the motion memory stylized by the audio-driven speaking style feature. In this second stage, our model learns about which facial motion types should be emphasized for a particular piece of audio. As a result, our MemoryTalker can generate a reliable personalized facial animation without additional prior information. With quantitative and qualitative evaluations, as well as user study, we show the effectiveness of our model and its performance enhancement for personalized facial animation over state-of-the-art methods. Project page: https://cau-irislab.github.io/ICCV25-MemoryTalker/ + +# 1. Introduction + +Speech-driven 3D facial animation is a challenging task that aims to synthesize realistic 3D facial motion synchronized with the given speech [2, 5, 10, 11, 16, 20, 27, 31, 39, 46, 51, 53]. This technique can be widely utilized in various immersive applications, including VR telepresence, character animation for film production and gaming. Recently, the advent of large-scale 3D facial animation datasets [6, 13, 26, 34, 36] and advancements in deep learning have significantly increased interest in this field. + +![](images/21c866365d3e56730d09d577fb4d206c415c8b215dc2d7f3b2ebdc94a6e39189.jpg) +Figure 1. The intuition of MemoryTalker for personalized speech-driven 3D facial animation, Memorizing and Animating. Memorizing: Storing and retrieving facial motion. Animating: Synthesizing the personalized 3D facial motion with the stylized motion memory. Our MemoryTalker can accurately produce the personalized 3D facial motion for different speakers using only audio input. + +The core challenge lies in developing algorithms that not only achieve precise speech-motion synchronization but also capture individual speaking styles - the subtle yet distinctive patterns in how different speakers articulate the same words. + +This work addresses personalization issues in speech-driven 3D facial animation by considering the speaking style of a speaker, including the amplitude of mouth opening and closing, the extent of pouting, etc. (see Fig. 1). To deal with that, most previous works [6, 12, 41, 45] have employed one-hot encoding of the identity classes for different speakers in the training set. However, these models necessarily require human identity classes even at inference time (Fig. 2 (a)). + +![](images/521311f6027d0bebbddfec3cc405cad15326cc3371da19151ba7f94ec64fd08a.jpg) +Figure 2. Explored approaches for personalized speech-driven 3D facial animation. (a) In the one-hot encoding approaches, while the identities of training speakers can be encoded with a one-hot vector, it is impossible to match the unseen speaker's speaking style during inference. (b) In the approaches of utilizing 3D facial mesh sequence, by providing an additional sequence of 3D facial mesh deformation during inference, they can produce the personalized 3D facial motion. However, it is not practical. (c) In our model, both during training and inference, personalized 3D facial animation is generated solely from the given audio input. + +![](images/6836a4e247968300ba1119230a872c2155ee9d8cd73419f5fed8d537db05444b.jpg) + +![](images/120738a77872edbbf70c01e4559402198313ca75d6d38eadaef53f2ad29be1b4.jpg) + +![](images/60cba9346d30bdba4cddec34c6c29da7f5af7f36a696029e1c8995d43d93efaf.jpg) + +Furthermore, the inherent limitation of one-hot encoding makes it impossible for them to deal with unseen speakers at all. The most recent studies [19, 44, 47] have explored using a sequence of 3D facial mesh deformation to control the different speaking styles of each speaker. Unlike one-hot encoding approaches, these methods can capture speaking styles of speakers by encoding the speaking style feature from their arbitrary facial motion sequences without class labels. Feeding 3D facial motion would ideally reflect the speaking style, but requiring such additional data at inference is not practical for real-world applications (Fig. 2 (b)). + +To overcome these limitations, we propose a novel speech-driven 3D facial animation model named MemoryTalker which can capture and predict speaking styles solely from audio input (see Fig. 2 (c)). It involves key-value multimodal memories that can effectively bridge different modalities. Our method consists of two training stages: $<1$ -stage> is for storing general motion into a motion memory (i.e., Memorizing), and $<2$ -stage> is for stylizing the motion memory to synthesize personalized animations (i.e., Animating). + +In the first stage, we leverage a pre-trained ASR model to extract general motion feature representations with respect to the text aspect, ensuring consistent movements for a single phoneme. For example, when people say the word "who", the lips generally first come together and move forward to form the 'W' sound, then round to produce the 'OO' vowel sound. To explicitly store the facial motion features, we design a motion memory and access the stored motion features using the text representations with a key-value structure. This key-value memory allows the model to map one modality to another effectively through accessing the stored + +motion features with different modal features in completely separate feature spaces. It alleviates the domain gap from inconsistent distributions of different modalities. However, it is difficult to synthesize accurate facial motion only with text representations because there exist different speaking styles even for the same word "who" such as variations in the extent of pouting. + +To address this issue, in the second stage, our model is guided to generate personalized facial motions via audioguided stylization. To this end, we personalize the trained motion memory based on audio signals. By distinguishing audio style features according to speaker types, we can achieve distinct style representations and refine the memory to synthesize the desired personalized motion effectively. Importantly, the proposed method does not require any prior knowledge (e.g., ID class, additional facial meshes) at inference time, which makes our model more practical for real-world applications. + +Our contributions are summarized as follows: + +- We propose MemoryTalker, a novel framework for speech-driven 3D facial animation that can reflect speaking styles from audio input alone. To the best of our knowledge, this is the first work to address the personalization issue in this task without requiring additional prior information at inference time, which makes our approach practical. +- We introduce a new two-stage training strategy: (i) memorizing general facial motions aligned with neutral text representations, and (ii) animating personalized facial motions based on the stylized motion memory. This allows generating realistic animations that are accurate in terms of text content, while reflecting speaking styles effectively. + +![](images/ae0409c4718aa7a8d62ea92edc8798486b96f09e8fbc82dc215986cc0d48d585.jpg) +Figure 3. Illustration of the proposed MemoryTalker model for personalized 3D facial animation. (a) Learning to store facial motion feature in the facial motion memory and align motion features with text features. (b) Learning to disentangle unique speaking style of each speaker from audio and stylizing facial motion memory. + +![](images/bac0ebf5813646920d7ebb076080750e545eaad48b3852cfdb73caad9c67963e.jpg) + +# 2. Related Work + +# 2.1. Speech-Driven 3D Facial Animation + +Earlier methods [1, 7, 9] for 3D facial animation usually employ a predefined facial template consisting of 3DMM parameters. Recently, various studies have been conducted to consider not only the mapping of speech to 3D facial mesh movements but also to reflect identity-specific speaking styles. Existing works [6, 12, 36, 45] have proposed a one-hot encoding of the identities of the training set. However, these models have a limitation in that they fail to predict new speaking styles during inference due to the use of the one-hot label slots for the subjects used in training. + +To reflect subtle speaking styles better, Imitator [41] introduces a two-stage style adaptation to synthesize speaker-independent movement in the first stage and capture speaker-dependent style in the second stage using reference 2D video. To achieve careful control over speech-independent factors (e.g., speaking style), several methods have been proposed using reference 3D motion. Wu et al. [44] proposed an adaptive modulating module to consider both speech-independent composite and facial-dependent regional movements. Mimic + +[19] learned two disentangled latent spaces (content and style) for style-content disentanglement and 3D facial animation generation with identity-specific speaking styles. Finally, when generating 3D animation, they generate motion aligned to the audio in content space and apply a randomly provided speaking style in style space. Yang et al. [47] proposed a method to apply fine-detailed styles incrementally using reference 3D movements. Initially, coarse facial motion is learned from audio. Then, 3D facial motion with style is gradually learned from the provided reference 3D movement. However, these methods require a reference 2D video or a sequence of 3D facial meshes as well as audio signals as inputs during inference, which are resource-consuming and impractical for real-world applications. In contrast, we propose a novel approach that leverages speech-driven personalized memory networks to capture identity-specific speaking styles from speech signals alone. + +# 2.2. Memory Network + +Memory networks can enhance inference capability by being read from and written with external long-term memory components [28, 43]. The key-value memory network + +architecture, enabling models to use keys to access relevant memories and retrieve corresponding values, has been widely adopted in various computer vision tasks including object tracking [14, 48], few-shot learning [4, 52], and anomaly detection [15, 23, 29, 30]. In recent years, the memory networks have been used in multi-modal modeling [21, 22, 24, 35, 50]. In [32, 40, 49], memory networks have been proposed to solve the alignment of associations between audio and visual information for 2D talking face generation. Compared to the previous works, we introduce a novel two-stage training strategy that enables storing and retrieving general motion and then generating personalized facial animation with the motion memory stylized by the audio-driven speaking style feature. + +# 3. Proposed Method + +Fig. 3 shows an overview of our personalized speech-driven 3D facial animation. To synthesize realistic 3D facial animation, we propose a two-stage training strategy: 1) storing and recalling general facial motion and 2) generating personalized facial motion with the stylized motion memory. In the first stage, our goal is to store facial motion features $f_{m}^{t}$ in the motion memory $\mathbf{M}_{m} = \left\{s_{m}^{i}\right\}_{i=1}^{n}$ and recall general facial motion information from input audio $a^{t}$ at time $t$ . To achieve this, we encode the text representation $f_{txt}^{t}$ from $a^{t}$ and align it with $f_{m}^{t}$ . This allows us to map the facial motion of various speakers for a single phoneme to the consistent text representation $f_{txt}^{t}$ , thereby obtaining the general facial motion from the audio query $a^{t}$ . In the second stage, we synthesize the personalized facial motion reflecting the speakers' speaking styles from audio $a^{1:T}$ . To this end, we refine the pre-trained motion memory $\mathbf{M}_{m}$ into the stylized motion memory $\tilde{\mathbf{M}}_{m}$ while refining the text representation utilizing speaking style features $f_{s}$ . The speaking style feature learns distinct characteristics from speaker-specific audio by adopting a triplet loss. Finally, the recalled personal motion features from the stylized motion memory $\tilde{\mathbf{M}}_{m}$ are combined with the refined text representation and fed to the motion decoder to synthesize personalized 3D facial animation. + +# 3.1. Facial Motion Memory + +First, we design a motion memory $\mathbf{M}_m\in \mathbb{R}^{n\times c}$ with $n$ slots and $c$ channels to store motion feature $f_{m}^{t}\in \mathbb{R}^{c}$ . The facial motion $v^{t}\in \mathbb{R}^{3}$ denotes the 3D movement of vertices over a neutral-face mesh template for the $t$ -th frame [45]. To this end, $v^{t}$ is transformed into facial motion feature $f_{m}^{t}$ using a motion encoder $E_{m}$ . The encoded facial motion feature is used as a query to access our motion memory $\mathbf{M}_m$ . When the facial motion feature $f_{m}^{t}$ is given as a query in the motion memory $\mathbf{M}_m$ , the attention weight $w_{m}^{i}$ can be obtained by calculating the similarity between the $f_{m}^{t}$ and each slot $s_m^i$ + +in $\mathbf{M}_m$ . This addressing procedure can be formulated as + +$$ +w _ {m} ^ {i} = \frac {\exp (\kappa \cdot d \left(s _ {m} ^ {i} , f _ {m} ^ {t}\right))}{\sum_ {j = 1} ^ {n} \exp (\kappa \cdot d \left(s _ {m} ^ {j} , f _ {m} ^ {t}\right)}, \tag {1} +$$ + +where $d(\cdot, \cdot)$ indicates the cosine similarity function. $\kappa$ is a scaling factor. We omit the superscript $t$ here for simplicity. Let $\mathbf{V}_m^t = \{w_m^1, w_m^2, \dots, w_m^n\}$ denote the value address vector, which is a set of attention weights for the corresponding motion memory slots at time $t$ . The recalled motion feature $\hat{f}_{m,\text{val}}^t$ can be retrieved using $\mathbf{V}_m^t$ and $\mathbf{M}_m$ by a weighted sum for each memory slot as follows: + +$$ +\hat {f} _ {m, v a l} ^ {t} = \sum_ {i = 1} ^ {n} w _ {m} ^ {i} \cdot s _ {m} ^ {i}. \tag {2} +$$ + +To explicitly embed motion features into the motion memory, we adopt the memory reconstruction loss between the recalled and reference motion features. Motion information is stored in $\mathbf{M}_m$ by minimizing $\mathcal{L}_{mem}$ . + +$$ +\mathcal {L} _ {m e m} = \sum_ {t = 1} ^ {T} \left\| f _ {m} ^ {t} - \hat {f} _ {m, v a l} ^ {t} \right\| _ {2} ^ {2}. \tag {3} +$$ + +We search for motion features that are synchronized with the input audio after storing memory. At this time, to reduce the influence of individual speaking style variations in the audio (i.e., mapping various speaking styles to a single phoneme when the same pronouncing), we use the encoded text representation $f_{txt}^{t}$ from the encoder of automatic speech recognition (ASR) $E_{aud}$ as a query to access memory. This leads us to query common facial motion (i.e., common lip shapes for the same word regardless of the speaker). The encoded text representation $f_{txt}^{t}$ can be written as + +$$ +f _ {t x t} ^ {1: T} = \psi_ {\rightarrow n} (\operatorname {I n t e r p} (E _ {a u d} (a))) \in \mathbb {R} ^ {T \times n}, \tag {4} +$$ + +where $\psi_{\rightarrow n}(\cdot)$ is a single linear layer that projects to fit the number of slots. $a$ represents the input audio signal. The pretrained ASR encoder in HuBERT [18] is used as $E_{aud}$ to map the source audio segment $a^t$ to the text representation $f_{txt}^{t}$ . $\mathrm{Interp}(\cdot)$ is a linear interpolation function to synchronize the motion features and the text representations as video fps. + +Let $\mathbf{K}_{txt}^{t} = \left\{w_{txt}^{1}, w_{txt}^{2}, \dots, w_{txt}^{n}\right\}$ denote the key address vector, which is a set of attention weights for the corresponding motion memory slots. The key address vector $\mathbf{K}_{txt}^{t}$ is obtained by applying a softmax function to the projected text representation $f_{txt}^{t}$ . It can be written as + +$$ +\mathbf {K} _ {t x t} ^ {t} = \operatorname {s o f t m a x} \left(f _ {t x t} ^ {t}\right) \in \mathbb {R} ^ {n}. \tag {5} +$$ + +The key address vector $\mathbf{K}_{txt}^{t}$ derived from $f_{txt}^{t}$ is used to recall the general facial motion information across various speakers. Finally, the motion feature $\hat{f}_{m,key}^{t} \in \mathbb{R}^{c}$ is + +retrieved from motion memory using the text address aligned to the motion address for general facial motion synthesis. + +$$ +\hat {f} _ {m, \text {k e y}} ^ {t} = \sum_ {i = 1} ^ {n} w _ {\text {t x t}} ^ {i} \cdot s _ {m} ^ {i}. \tag {6} +$$ + +To recall the corresponding motion features from $\mathbf{M}_m$ using key address vector $\mathbf{K}_{txt}^t$ , it is required to align the key address vector $\mathbf{K}_{txt}^t$ with the value address vector $\mathbf{V}_m^t$ . For this purpose, we employ KL divergence between them as an alignment loss $\mathcal{L}_{align}$ , which can be defined as + +$$ +\mathcal {L} _ {\text {a l i g n}} = \sum_ {t = 1} ^ {T} \mathbf {K} _ {t x t} ^ {t} \log \frac {\mathbf {K} _ {t x t} ^ {t}}{\mathbf {V} _ {m} ^ {t}}. \tag {7} +$$ + +To synthesize facial motion $v^t$ , we employ a motion decoder $D_m(\cdot)$ based on a Transformer decoder structure as in [12]. The facial motion can be generated as follows: + +$$ +\hat {v} ^ {t} = D _ {m} ([ f _ {t x t} ^ {t}; \hat {f} _ {m, k e y} ^ {t} ], f _ {t x t} ^ {t}). \tag {8} +$$ + +The motion decoder is trained to minimize the reconstruction loss between the synthesized 3D facial motion $\hat{v}^t$ and ground truth 3D facial motion $v^t$ . It can be written as + +$$ +\mathcal {L} _ {m s e} = \sum_ {t = 1} ^ {T} \left\| v ^ {t} - \hat {v} ^ {t} \right\| ^ {2}. \tag {9} +$$ + +In addition, we introduce a velocity loss $\mathcal{L}_{vel}$ to address the issue of jittery output frames when using only reconstruction loss [33]. $\mathcal{L}_{vel}$ is defined as + +$$ +\mathcal {L} _ {v e l} = \sum_ {t = 0} ^ {T - 1} \left\| \left(v ^ {t + 1} - v ^ {t}\right) - \left(\hat {v} ^ {t + 1} - \hat {v} ^ {t}\right) \right\| ^ {2}. \tag {10} +$$ + +The total loss at the first training stage is defined as + +$$ +\mathcal {L} _ {1 \text {- s t a g e}} = \mathcal {L} _ {m s e} + \mathcal {L} _ {v e l} + \lambda_ {1} \left(\mathcal {L} _ {\text {m e m}} + \mathcal {L} _ {\text {a l i g n}}\right), \tag {11} +$$ + +where we set $\lambda_{1}$ to 0.01. + +# 3.2. Stylized Motion Memory + +To synthesize the personalized 3D facial motion, the speaking style feature $f_{s}$ is encoded from the audio $a$ . Without loss of generality, we assume that the audio signals include inherently speaking styles such as volume, pitch, and speaking speed. These speaking styles lead to differences in mouth opening size or the extent of pouting in 3D facial animation even when speakers say the same word or sentence. + +To encode the speaking style feature $f_{s}$ from audio $a$ , we use the mel-spectrogram, which provides a representation aligned with human auditory perception. The speaking style feature $f_{s} \in \mathbb{R}^{c}$ can be defined as + +$$ +f _ {s} = E _ {s} \left(\phi^ {a 2 m} (a)\right), \tag {12} +$$ + +where $E_{s}$ is a speaking style encoder and $\phi^{a2m}$ is a function that converts audio into a mel-spectrogram. + +In particular, to encode more discriminating style features, we introduce a speaking style loss $\mathcal{L}_{\text{style}}$ using a triplet loss. The speaking style loss is designed to learn a feature space where similar speaking styles are closer (i.e., minimize intraclass variation) to each other and different speaking styles are further apart (i.e., maximize inter-class variation). + +$$ +\mathcal {L} _ {\text {s t y l e}} = \max \left(\left\| f _ {s} - f _ {s} ^ {p} \right\| _ {2} ^ {2} - \left\| f _ {s} - f _ {s} ^ {n} \right\| _ {2} ^ {2} + l, 0\right), \tag {13} +$$ + +where $f_{s}^{p}$ and $f_{s}^{n}$ are the speaking styles of positive samples (i.e., same speaker) and negative samples (i.e., different speakers), respectively. They are obtained through the same process as $f_{s}$ . $l$ indicates a margin. + +With the speaking style feature $f_{s}$ , the pre-trained motion memory $\mathbf{M}_m$ can be updated to the stylized motion memory $\tilde{\mathbf{M}}_m = \{\tilde{s}_m^i\}_{i=1}^n \in \mathbb{R}^{n \times c}$ , which can be written as + +$$ +\tilde {\mathbf {M}} _ {m} = \left\{\tilde {w} _ {s} ^ {i} \cdot s _ {m} ^ {i} \right\} _ {i = 1} ^ {n}, \tag {14} +$$ + +where $\tilde{\mathbf{M}}_m$ is obtained by multiplying the style weight $\tilde{w}_s^i$ with the $i$ -th memory slot in $\mathbf{M}_m$ . + +To update each memory slot, we design the style weight $\tilde{w}_s = \{\tilde{w}_s^i\}_{i=1}^n \in \mathbb{R}^n$ as follows: + +$$ +\tilde {w} _ {s} = \operatorname {s i g m o i d} \left(\psi_ {\rightarrow n} ^ {\prime} \left(f _ {s}\right)\right) \cdot \psi_ {\rightarrow 1} \left(f _ {s}\right) \tag {15} +$$ + +where $\psi_{\rightarrow n}^{\prime}$ and $\psi_{\rightarrow 1}$ are single linear layers that project to fit a $n$ -dimensional vector and a scalar value, respectively. The values obtained from $\psi_{\rightarrow n}^{\prime}(f_s)$ are processed with the sigmoid function to score each slot, and then scaled by the result of $\psi_{\rightarrow 1}(f_s)$ . By applying the $\tilde{w}_s$ to the motion memory $\mathbf{M}_m$ , the stylized motion memory $\tilde{\mathbf{M}}_m$ can reflect different speaking styles for each speaker via audio only. + +Finally, the personalized motion $\tilde{v}^t\in \mathbb{R}^3$ can be reconstructed by incorporating the personalized motion feature $\tilde{f}_{m,key}$ recalled in $\tilde{\mathbf{M}}_m$ . + +$$ +\tilde {v} ^ {t} = D _ {m} ([ f _ {t x t} ^ {t}; \tilde {f} _ {m, k e y} ^ {t} ], f _ {t x t} ^ {t}), \tag {16} +$$ + +where $\tilde{f}_{m,key}^{t} = \sum_{i=1}^{n} w_{txt}^{i} \cdot \tilde{s}_{m}^{i}$ , which is computed in the same way as the weighted sum used to calculate $f_{m,key}^{t}$ . + +As a result, by explicitly embedding the speaking style features into the motion memory and recalling it, we can produce more realistic and personalized 3D facial animation. + +In the second stage, to train our model, we additionally employ a lip vertex loss $\mathcal{L}_{lip}$ , which is a mean square error for the lip region (i.e., lower-face vertices) to focus on carefully synthesizing lip movements according to various speaking styles. The total loss for the second stage is defined as + +$$ +\mathcal {L} _ {2 \text {- s t a g e}} = \mathcal {L} _ {m s e} + \mathcal {L} _ {v e l} + \lambda_ {2} \left(\mathcal {L} _ {l i p} + \mathcal {L} _ {\text {s t y l e}}\right), \tag {17} +$$ + +where we set $\lambda_{2}$ to 0.01. + +
MethodVOCASET [6]BIWI [13]
FVE ↓ (×10-6)LVE ↓ (×10-5)FID ↓ (×10-1)LDTW ↓ (×10-5)Lip-max ↓ (×10-4)FVE ↓ (×10-4)LVE ↓ (×10-4)FID ↓ (×10-1)LDTW ↓ (×10-4)Lip-max ↓ (×10-3)
FaceFormer [12]0.6390.4133.5830.5070.4520.9810.2078.2040.1140.477
CodeTalker [45]0.7210.4983.7130.5540.4840.9790.2119.4190.1200.478
SelfTalk [33]0.5930.3823.2790.4750.4161.0300.2227.3200.1180.496
Imitator [41]0.6860.4563.9180.5540.472-----
ScanTalk [31]0.6090.3753.6230.4570.420-----
UniTalker [11]0.5700.3823.2560.5070.4070.9190.1967.2340.1090.461
MemoryTalker0.5060.2933.0450.4180.3310.9010.1877.2020.1070.398
+ +Table 1. Quantitative evaluation for speech-driven 3D facial animation on VOCASET[6] and BIWI[13]. + +![](images/fa1d9f247fdc3c482cc54326b186d63dea9353d9ff0d34c1bc161e54f095544f.jpg) +Figure 4. Visual comparisons with state-of-the-art methods on (a) VOCASET and (b) BIWI. Note that the second and fourth rows represent the visualization of per-vertex errors. Note that we displayed the best one-hot encoding results [12, 41, 45] for the ID with the lowest error. + +# 4. Experiments + +# 4.1. Datasets + +We train and evaluate our model on VOCASET [6] and BIWI [13], which are widely used datasets for 3D facial animation. Both datasets contain audio-3D facial scan pairs that demonstrate English speech pronunciation. VOCASET [6] consists of 255 unique sentences, some shared across speakers, and contains 480 facial motion sequences from 12 subjects, captured at 60 fps for approximately 4 seconds per sequence. Each 3D face mesh is registered to the FLAME [25] topology with 5,023 vertices. BIWI [13] includes 40 unique sentences shared across all speakers. It consists of two parts: one with emotions and one without. There are 40 sentences uttered by 14 subjects. Each recording is repeated twice in neutral or emotional situations, capturing a dynamic + +3D facial scan at 25 fps. The registered topology exhibits 23,370 vertices, with the average sequence length of 4.67s. + +# 4.2. Implementation Details + +Our experiments were conducted on an NVIDIA A6000 GPU. A single linear layer is used as motion encoder $E_{m}$ as in [12, 45]. The structure in [8] is employed as our style encoder $E_{s}$ . To encode the text representation from the audio, we utilize the pre-trained ASR model [18]. The projection layer $\psi_{\rightarrow n}$ in ASR consists of a single linear layer to project audio features onto the text logit and is fine-tuned during 1-stage training. In the first stage, we train our model (except for $E_{s}$ ) for 100 epochs with a learning rate of 0.0001. In the second stage, we freeze all layers of the first stage and train only the speaking style encoder $E_{s}$ with a learning rate of 0.00005 for 100 epochs. Quantitative evaluations + +
MethodFVE ↓ (×10-6)LVE ↓ (×10-5)FID ↓ (×10-1)
FaceFormer [12]0.639±0.0360.413±0.0583.583±0.358
CodeTalker [45]0.721±0.0560.498±0.0373.713±0.373
Imitator [41]0.686±0.0690.456±0.0673.918±0.536
MemoryTalker0.5060.2933.045
+ +Table 2. Error variability according to the used one-hot identity about a given audio on VOCASET [6]. + +
MethodInference TimeParameter #
FaceFormer [12]38.1 ms92 M
CodeTalker [45]297.6 ms315 M
SelfTalk [33]10.1 ms450 M
UniTalker [11]9.7 ms313 M
MemoryTalker7.8 ms94 M
+ +Table 3. Efficiency comparison of models based on inference time and number of parameters on VOCASET[6]. + +were performed on VOCA-Test and BIWI-Test-B datasets by averaging the identities of all speakers. + +# 4.3. Evaluation Metrics + +We adopt five quantitative evaluation metrics to evaluate the results: Face Vertex Error (FVE) and Lip Vertex Error (LVE) are the differences between the reference vertices and the generated vertices for the entire face and lip region, respectively. Lip Dynamic Time Warping (LDTW) is used to compute the temporal similarity of the lip region using DTW [37] as in [41]. Fréchet Inception Distance (FID) score [17] is used to evaluate the quality of the images rendered from the vertices [3]. In addition, we use Lip-max that averages the highest error among lip regions [36, 41]. + +# 4.4.Quantitative Results + +Tab. 1 illustrates that our MemoryTalker outperforms state-of-the-arts on both datasets. Our model achieves the lowest prediction errors. The lowest LDTW of our MemoryTalker means the highest temporal similarity for the lip region. Tab. 2 illustrates the problem of one-hot encoding approaches. They employ various identities in the training set for single audio during inference. Thus, they cannot reflect the speaking style of an unseen speaker during inference. As a result, the rendering quality for the same speaker can vary depending on the identity selected from the training set. On the other hand, our MemoryTalker can reflect the audio-driven speaking style feature, matching the speaker. + +To evaluate the computational efficiency, as seen in Tab. 3, we measure the number of learnable parameters and inference time with a 1-second audio sample on VOCASET [6]. Compared to FaceFormer [12], CodeTalker [45], Self + +![](images/4cfa3ae71d695862a2740defe9ffbecf390ba129fdfafc68945d1b08a7e1fb99.jpg) +Figure 5. Qualitative results from "w/o 2-stage" and "w/ 2-stage". The last column represents the mean of 3D optical flow while pronouncing "Stab". The darker the red, the higher the motion. + +![](images/70b53ca759ca6c2b9de0cb43512313d8dd4e290ae4ef32ae01e341e429396784.jpg) +Figure 6. The t-SNE visualization of the recalled motion features across different speakers at each stage. + +Talk [33], and UniTalker [11], our MemoryTalker achieves efficient 3D facial animations with about 120 fps. + +# 4.5. Qualitative Results + +# 4.5.1. Visual Comparisons + +Fig. 4 shows the visual results of our MemoryTalker, compared to existing methods. When pronouncing "How" and "And" with a mouth open, our results provide more accurate mouth shapes. For pronunciations with mouth protrusion like "Most", "What", our results show similar mouth shapes to the reference (i.e., ground-truth). Although recent models generate some extent of mouth opening and closing according to the pronunciation, they lead to larger prediction errors around lip regions (lower-face vertices), compared to our MemoryTalker. + +
Proposed 1-stage trainingProposed 2-stage trainingFVE ↓ (×10-6)LVE ↓ (×10-5)
XX0.6380.460
✓X0.5310.313
✓✓0.5060.293
+ +# 4.5.2. Adaptation of Speaking Style + +To verify the effectiveness of our stylized motion memory at the 2-stage, we evaluate the dynamics of facial vertices sequence using 3D optical flows. Fig. 5 shows an example of visual results and the mean of optical flows from 1-stage and 2-stage when pronouncing "Stab". As shown in Fig. 5, the model trained at both stages delivers more accurate lip movements than the one trained at 1-stage only (without training the model at 2-stage). + +To explore the effectiveness of the stylized motion memory in the latent space, we visualize the recalled features before decoding each subject's facial motion at each stage using t-SNE [42]. In Fig. 6, each point represents facial motion features for each sentence, and different colors indicate different speakers. Fig. 6 (a) shows that the distribution of each speaker is not separated because general facial motion is retrieved at 1-stage. In Fig. 6 (b), the distribution for each speaker is well-clustered, indicating that the speaking style of each speaker is captured at 2-stage. + +# 4.6. Ablation Study + +# 4.6.1. Memory and Style Encoder + +To demonstrate the effectiveness of two-stage training, we evaluate the performance at each stage. In Tab. 4, the baseline (w/o 1-stage and 2-stage) is a model without our motion memory structure and is trained by adopting common reconstruction loss $\mathcal{L}_{mse}$ and velocity loss $\mathcal{L}_{vel}$ . As seen in Tab. 4, by explicitly storing and recalling the facial motion in 1-stage, FVE and LVE are reduced. It means that the facial motion recalled from the facial motion memory can support the facial synthesis results from text representation. In addition, by incorporating the personalized facial motion through the stylized motion memory in 2-stage, our model achieves the best performance. + +# 4.6.2. Constraints + +We investigate the impact of removing different constraints which are $\mathcal{L}_{lip}$ and $\mathcal{L}_{style}$ (see Tab. 5). When removing the $\mathcal{L}_{lip}$ , performance is slightly worse than those with $\mathcal{L}_{lip}$ . This is because the lip vertex loss is only relevant to the lowerface vertices. When removing the triplet loss for $\mathcal{L}_{style}$ , we can observe that training becomes unstable and performance drops significantly. It highlights the importance of effectively learning personal speaking styles. + +Table 4. Ablation study for various modules on VOCASET [6]. + +
LossFVE ↓ (×10-6)LVE ↓ (×10-5)FID ↓ (×10-1)LDTW ↓ (×10-5)
w/o Lclip0.5140.2973.0570.435
w/o Lstyle0.5130.2953.0580.431
Full0.5060.2933.0450.418
+ +Table 5. Ablation study for our components on VOCASET [6]. + +
CompetitorsLip Sync(%)Realism(%)Speaking Style(%)
vs. FaceFormer [12]83.985.580.6
vs. CodeTalker [45]85.583.971.8
vs. Imitator [41]87.187.178.2
vs. ScanTalk [31]94.491.192.8
vs. UniTalker [11]79.880.686.3
+ +Table 6. User study: our method vs. competitors on VOCASET [6]. + +# 4.7. User Study + +We conduct A/B tests on VOCASET to evaluate perceptual lip-sync, realism, and speaking style of synthesized 3D facial animations. A total of 33 subjects participated in the user study. To evaluate speaking style, lip-sync, and realism, we compare our MemoryTalker with 5 other methods (FaceFormer, CodeTalker, Imitator, ScanTalk, UniTalker) on 50 samples. To measure lip-sync and realism, we present each pair of identical sentences to the subject and the subject chooses the better one. To evaluate speaking style, we present participants with samples from our model, a comparison model, and the ground truth (reference). Participants are then asked to choose which of the two model-generated samples appears to have a speaking style most similar to the ground truth, considering factors such as the amplitude of mouth opening and closing, the degree of pouting, and other relevant aspects. As shown in Table 6, our results are generally favorable over other state-of-the-art methods across a variety of perceptual factors. + +# 5. Conclusion + +In this study, we demonstrate the ability of motion memory networks to bridge different modalities, which are 3D facial motion and speech, without additional information for personalized speech-driven facial animations. To effectively train our model, we introduce a two-stage training strategy: 1) storing and retrieving general motion and 2) performing the personalized 3D facial motion synthesis with the stylized motion memory. Extensive experiments highlight the superior performance of our MemoryTalker compared to the recent speech-driven 3D facial animation models. In particular, our MemoryTalker achieves more favorable results not only in quantitative evaluations but also in the user study from a perceptual perspective. We hope this work can pave the way in real-world VR and metaverse applications. + +# 6. Acknowledgments + +This research was 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 2023 (Project Name: Acquisition of 3D precise information of microstructure and development of authoring technology for ultra-high prediction cultural restoration, Project Number: RS-2023-00227749) and the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (RS-2025-00563942). + +# References + +[1] A. Verma, N. Rajput, and L.V. Subramaniam. Using viseme based acoustic models for speech driven lip synthesis. In 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03), pages V-720, 2003. 3 +[2] Shivangi Aneja, Justus Thies, Angela Dai, and Matthias Nießner. Facetalk: Audio-driven motion diffusion for neural parametric head models. 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However, the full potential of the existing diverse datasets remains underutilized, as they are typically employed in isolation. Models trained on a single dataset often suffer considerable performance degradation when deployed to real-world scenarios or datasets involving disparate LiDARs. To address this limitation, we introduce MergeOcc, a generalized pipeline designed to handle different LiDARs by leveraging multiple datasets concurrently. The gaps among LiDAR datasets primarily manifest in geometric disparities and semantic inconsistencies, which correspond to the fundamental components of datasets: data and labels. In response, MergeOcc incorporates a novel model architecture that features a geometric realignment and a semantic label mapping to facilitate multiple datasets training (MDT). The effectiveness of MergeOcc is validated through extensive experiments on two prominent datasets for autonomous vehicles: OpenOccupancy-nuScenes and SemanticKITTI. The results demonstrate its enhanced robustness and performance improvements across both types of LiDARs, outperforming several SOTA methods. Additionally, despite using an identical model architecture and hyper-parameter set, MergeOcc can significantly surpass the baselines thanks to its ability to learn from diverse datasets. To the best of our knowledge, this work presents the first cross-dataset 3D occupancy prediction pipeline that effectively bridges the domain gap for seamless deployment across heterogeneous platforms. + +# 1. Introduction + +With the capability to acquire precise geometric information of entire scenes, LiDAR has become an indispensable sensor for many autonomous vehicles. Current LiDAR-based occupancy prediction models primarily adhere to the paradigm of training and testing within a single dataset, thus + +![](images/2cf1a9265df003e3771b829c6bbbfd17e0a3e25970b42895d28f0229b4e5f948.jpg) +Figure 1. Challenges of cross-LiDAR issue: 1) Only OO-nu and Only SK refer to the baseline model L-CoNet trained on each dataset. 2) Direct Merging represents training the same model on the simply merged dataset. 3) MergeOcc-V denotes the proposed method using the same model trained on these two datasets. + +constraining the source data to a limited domain. However, deploying these dataset-specific models directly onto platforms or datasets equipped with different LiDARs often incurs notable performance degradation, as shown in Fig. 1, rendering that this paradigm fails to yield a robust and generalized perception model. This cross-LiDAR issue arises from substantial domain shifts between LiDARs. In terms of 3D data, the gaps manifest in two principal dimensions: 1) significant divergence in point cloud density stemming from variations in LiDAR beams and angular resolutions, as detailed in Tab. 1, and 2), diversified scenarios and inconsistent semantic label spaces caused by disparate taxonomies. + +Traditionally, addressing these challenges involves annotating data from the target domain followed by fine-tuning the model. However, annotating a frame of LiDAR point cloud consumes approximately $20 \times$ more time than annotating an image[24]. Fully leveraging all available 3D LiDAR data could save time and resources. Moreover, fine-tuning the model with a new domain often results in "catastrophic forgetting"[13], wherein the model loses previously acquired knowledge. A question naturally arises: can these limitations be alleviated by bridging the gap between different LiDARs to obtain a more robust and generalized model? + +
DatasetsBeamHARVFOVPoint RangeGT RangeGT shapeCollection Location
SemanticKITTI640.08°[-23.6°, 3.2°]L=[-72.0, 72.0]mW=[-72.0, 72.0]mH=[-3.4, 3.0]mL=[0, 51.2]mW=[-25.6, 25.6]mH=[-3.4, 3.0]m[256, 256, 32]Germany
OpenOccupancy-nuScenes320.08° - 0.33°[-30.0°, 10.0°]L=[-51.2, 51.2]mW=[-51.2, 51.2]mH=[-5.0, 3.0]mL=[-51.2, 51.2]mW=[-51.2, 51.2]mH=[-5.0, 3.0]m[512, 512, 40]USA/Singapore
+ +Table 1. Differences of typical 3D LiDAR datasets for autonomous driving. HAR denotes horizontal angular resolution, VFOV denotes vertical field of view, and L, W, and H represent the length, width, and height of LiDAR range, respectively. + +Motivated by these challenges, this paper introduces MergeOcc, a pioneering 3D occupancy prediction framework designed to simultaneously handle different types of LiDARs. Unlike prevailing LiDAR-based occupancy prediction algorithms[17, 21, 30] that primarily focus on developing a novel framework performs well on a singular dataset, we endeavor to furnish a methodology that enables existing 3D occupancy prediction models to leverage broader and more diverse LiDAR data, thereby enhancing model performance when directly deployed to real-world scenarios and reducing time and cost during migration across LiDARs. + +The contributions of this paper are as follows: + +- To the best of our knowledge, MergeOcc stands as the first complete approach enabling one single model to simultaneously handle different LiDARs for 3D occupancy prediction tasks. MergeOcc features a geometric realignment module to capture unique statistical characteristics of each LiDAR within the model, alongside a semantic label mapping module to harmonize the label space across disparate datasets. These components effectively bridge the gaps between disparate LiDARs, allowing the model to learn from broader data, thereby enhancing its adaptability and performance across heterogeneous data domains. +- To assess the efficacy of the proposed method in addressing domain gaps, we conduct extensive experiments on two prominent occupancy prediction datasets, nuScenes and SemanticKITTI. MergeOcc exhibits exceptional robustness and performance with both types of LiDARs, achieving improvements of up to $+33.4\%$ in IoU and $+17.2\%$ in mIoU compared to the D.M. method. Moreover, MergeOcc surpasses SOTA LiDAR and multimodality methods using weaker baselines. +- Despite using an identical hyper-parameter set and architecture, MergeOcc can significantly outperform two typical baselines due to the superiority of the MDT, warning of the insufficient capacity of current LiDAR datasets. + +# 2. Related Works + +# 2.1.3D Occupancy Prediction + +3D semantic occupancy prediction involves transforming the sensor data into fine-grained dense semantic occupancy grids, providing a comprehensive representation of the en + +vironment. This task is crucial for autonomous vehicles yet still requires further in-depth exploration. + +Recently, Vision-centric methods have gained prominence. Wang et al.[21] introduced the pioneering benchmark OpenOccupancy-nuScenes for surrounding semantic occupancy perception in driving scenarios. SurroundOcc[22] proposed a multi-camera-based 3D occupancy prediction pipeline, with training supervised by LiDAR-generated occupancy ground truths. TPVFormer[11] developed a novel tri-perspective view representation (TPV), which deviates from traditional voxel-based approaches, utilizing three orthogonal 2D planes to effectively model the 3D scene. + +In contrast, LiDAR point clouds contain inherently richer and more precise geometric information than images, and LiDAR-based methods deserve more exploration. Several early studies[8, 18, 23, 25] conducted on SemanticKITTI made preliminary exploration of LiDAR-based semantic scene completion (SSC) task and demonstrated commendable performance. PointOcc[30] transforms point clouds into TPV space and leverages a 2D-backbone to model detailed 3D structures, achieving comparable performance to voxel-based methods on the nuScenes. Occupancy-MAE[17] proposed a self-supervised masked auto-encoding framework, reducing the reliance on labeled 3D data. + +Nevertheless, all the aforementioned works adhere to the single-dataset training and testing paradigm. Consequently, they are susceptible to significant performance degradation in deployment across disparate LiDARs. + +# 2.2. Multiple Datasets Training (MDT) + +Training across multiple datasets is a proven strategy to enhance model robustness. Given the similar grid structure of images, the primary challenge in vision fields lies in unifying label space to ensure the consistency of semantic outputs. Early work attempted manually crafting the taxonomy[14, 28]. With the advent of large language models (LLM), differing from previous works, BigDetection [4] harnessed the power of BERT[9] to construct an initial unified label space across datasets, followed by manual verification to finalize the taxonomy. However, these methods still require extensive human annotation, making them non-scalable to larger scopes. To address this limitation, Zhou et al.[29] introduced an automatic approach based + +![](images/1a88866a7a5fddc8f5a89311502e35689d9c3582544779da742db11a4b739105.jpg) +Figure 2. The framework of MergeOcc including: 1) point range alignment, 2) cylindrical voxelization, 3) shared 3D backbone with dataset-specific normalization, 4) dataset-specific occupancy heads, 5) semantic label mapping, and 6) coarse to fine stage. + +on combinatorial optimization to unify the output space of a multi-dataset detector. This approach leverages images' similarity and intrinsic properties to derive the final taxonomy, offering a more scalable solution. + +Unlike the consistency observed in the vision domain, 3D LiDAR data exhibits substantial disparities at both the geometric and semantic levels. Research on training with multiple LiDAR datasets remains limited. Uni3D [27] stood out as the pioneering effort focused on 3D multi-dataset object detection but focused exclusively on three key categories within autonomous driving scenarios, which is a prevalent setting[19, 26] in related works. In contrast, this paper addresses the dense-predict task on 3D occupancy grids, employing distinct strategies and incorporating all available labels to construct a more comprehensive semantic space. + +# 3. Method + +# 3.1. Preliminary + +In the context of semantic occupancy prediction from a single dataset, the task involves processing an input frame of LiDAR points $\hat{X}_i\in \mathbb{R}^{N\times 3}$ to predict the corresponding occupancy labels $\mathcal{F}(\hat{X}_i)\in \mathbb{R}^{H\times W\times Z}$ , where $H$ , $W$ , and $Z$ represent the volumetric dimensions of the entire scene. Training an occupancy prediction model on a single dataset usually follows a simple recipe: minimize a total loss $\ell$ , which often includes elements such as cross-entropy loss, semantic mIoU, and geometric IoU, across a set of sampled point clouds $\hat{X}$ and its corresponding annotated occupancy ground truth $\hat{L}$ from the dataset $\mathcal{D}_i$ : + +$$ +\min _ {\Theta} \mathbb {E} _ {(\hat {X}, \hat {L}) \in D _ {i}} \left[ \ell (\mathcal {F} (\hat {X}; \Theta), \hat {L}) \right] \tag {1} +$$ + +Consider a dataset characterized by a joint probability + +distribution $P_{XL}$ over the input point cloud and label space $\mathcal{X} \times \mathcal{L}$ . In the MDT paradigm, we denote the number of datasets $\mathcal{D}_i = (\mathbf{x}^{(i)},\mathbf{l}^{(i)})_{i=1}^N$ by $N$ , where each $\mathcal{D}_i$ is associated with a unique data distribution $P_{XL}^i$ . The objective of MDT is to leverage multiple datasets $\mathcal{D}$ to develop a more generalized model $F: \mathcal{X} \to \mathcal{L}$ . For MDT, a straightforward strategy is to merge all data into a significantly larger dataset $\mathcal{D}_{\mathrm{total}} = \mathcal{D}_1 \cup \mathcal{D}_2 \cup \dots$ and amalgamate their label spaces $\mathcal{L}_{\mathrm{total}} = \mathcal{L}_1 \cup \mathcal{L}_2 \cup \dots$ . This approach optimizes the same loss function over a merged dataset: + +$$ +\underset {\Theta} {\min } \mathbb {E} _ {(\hat {X}, \hat {L}) \in \mathcal {D} _ {\text {t o t a l}}} \left[ \ell \left(\mathcal {F} (\hat {X}; \Theta), \hat {L} _ {\text {t o t a l}}\right) \right] \tag {2} +$$ + +In the Secs. 3.2 to 3.4, we present the design of MergeOcc, dive into technical details, and show how to train a 3D occupancy model that performs well on different LiDARs. + +# 3.2. Overview of MergeOcc + +The ambition of MergeOcc is to construct a comprehensive model capable of learning across $K$ distinct datasets $\mathcal{D}_1, \dots, \mathcal{D}_K$ with respective label spaces $\mathcal{L}_1, \dots, \mathcal{L}_K$ . Given the uniform task objective and similar data structure of the input, the network can share the backbone parameters and just use dataset-specific heads. This can be considered training $K$ partitioned dataset-specific models $\mathcal{F}_1, \dots, \mathcal{F}_K$ in parallel, where each dataset uses its own classification layer and loss $\ell_k$ at the end. The objective of the training process is to minimize the cumulative loss across all datasets, as formalized in the following equation: + +$$ +\min _ {\Theta} \mathbb {E} _ {D _ {k}} \left[ \mathbb {E} _ {(\hat {X}, \hat {L}) \in D _ {k}} \left[ \ell_ {k} \left(\mathcal {F} _ {k} (\hat {X}; \Theta), \hat {L} _ {\text {t o t a l}})\right) \right] \right] \tag {3} +$$ + +The MergeOcc framework is thoroughly illustrated in Fig. 2, which details the sequential processing stages from + +
MethodsOpenOccupancy-nuScenes RangeSemantickittiKITTI RangeGeometric IoU
tested on OO-nutested on SK
Not Align.L=[-51.2, 51.2]mL=[0, 51.2]m
W=[-51.2, 51.2]mW=[-25.6, 25.6]m25.436.7
H=[-5.0, 3.0]mH=[-3.4, 3.0]m
Align MaxL=[-51.2, 51.2]mL=[-51.2, 51.2]m
W=[-51.2, 51.2]mW=[-51.2, 51.2]m16.5 (-8.9)53.1 (+16.4)
H=[-5.0, 3.0]mH=[-5.0, 3.0]m
Align Min(MergeOcc)L=[0, 51.2]mL=[0, 51.2]m
W=[-25.6, 25.6]mW=[-25.6, 25.6]m38.2 (+12.8)70.0 (+33.3)
H=[-3.4, 3.0]mH=[-3.4, 3.0]m
+ +Table 2. Inconsistent LiDAR point cloud and annotation ranges will cause a significant model performance drop. For the intuitiveness of presentation, we only show the geometric IoU. The model employs L-CONet[21] trained on both datasets. + +the acquisition of raw LiDAR data to the generation of fine-grained occupancy prediction outputs. The core components of MergeOcc consist of a geometric realignment module and a semantic label mapping module. The former involves point range alignment and dataset-specific normalization layers to ensure adaptability across different LiDARs. The latter is applied to the heads' outputs to transcode the original categories into a unified label space. + +Inspired by OpenOccupancy[21], MergeOcc incorporates an upsampling process for coarse-grained occupancy grids through geometric coarse-to-fine queries. While the primary objective of upsampling is to balance model performance with GPU memory usage, we posit that it serves to achieve self-regression outputs through a non-autoregressive mode, thereby enhancing the model's efficiency. The implementation details are provided in the Appendix A.5. + +# 3.3. Geometric Realignment + +# 3.3.1. Geometric Disparities + +Unlike 2D images, which are organized in a fixed grid structure of pixels, 3D point clouds are acquired through a set of lasers that varies across LiDARs, making them inherently unordered. This variability introduces a geometric distributional discrepancy across LiDARs. The principal differences between the two datasets under study are detailed in Tab. 1. + +# 3.3.2. Point Cloud Range Alignment + +Drawing inspiration from Uni3D[27], we investigate the impact of point range on dense-predict generative tasks. The results delineated in Tab. 2, prompt us to adopt distinctly different restriction strategies based on the task at hand. + +For the object detection task, Uni3D advocates for utilizing the maximum point cloud range as the correction metric. This approach is justified by the observation that objects are generally located within areas covered by the LiDAR point cloud returns. As a result, selecting an extended range enhances the model's capability to detect objects at greater distances. However, our analysis, as summarized in Tab. 2, indicates that employing the maximum point cloud range for realignment in dense-predict generative tasks negatively + +affects performance. The discrepancy in occupancy grid shapes and annotation ranges will disrupt the learning process, leading to confusion in areas with inconsistent annotations for unified models. Consequently, choosing the minimum point cloud range for the occupancy prediction task yields more favorable outcomes than the maximum range. + +# 3.3.3. Geometric Statistic Data Alignment + +As a proven and effective approach in transfer learning[6, 27], a dataset-specific normalization operation is introduced to bridge the domain gap between different LiDARs. Our intuition is to encapsulate the unique statistical characteristics of each LiDAR within our model framework. The geometric statistic data realignment strategy is delineated as Eq. (4): + +$$ +\hat {y} _ {k} ^ {j} = \gamma^ {j} \hat {x} _ {k} ^ {j} + \beta^ {j} = \gamma^ {j} \frac {x _ {k} ^ {j} - \mu_ {k} ^ {j}}{\sqrt {\sigma_ {k} ^ {j} + \xi}} + \beta^ {j} \tag {4} +$$ + +where the $\mu_k^j$ and $\sigma_k^j$ represent the dataset-specific mean and variance corresponding to the input samples, the $\xi$ is introduced for numerical stability, and the parameters $\gamma$ and $\beta$ are utilized to restore the model's representational capacity. + +Traditional BatchNorm[12] estimates the statistical properties of the data within the current batch by standardizing the inputs for each layer across a network to attain a mean $\mu^j$ of 0 and a standard deviation $\sigma^j$ of 1. However, this conventional normalization, which relies on shared statistics, becomes less meaningful and may negatively impact model performance in the MDT paradigm, where data within a single batch may originate from different datasets. Therefore, we employ dataset-specific mean and variance to capture the diverse statistical properties of the data. Notably, $\gamma$ and $\beta$ are shared across datasets. We also investigate the optimal range for this module, which is detailed in Appendix A.4. + +The geometric realignment module can be easily integrated with previous perception models. To verify its generality, we applied this method to a voxel-based 3D backbone (ResNet3D[10]) and a projection-based 2D backbone (Swin Transformer[16]). The results demonstrate that this approach can enhance their adaptability and performance across disparate data sources. + +![](images/ba8938dac99411ac9fa0115b1bbc98bab4f9ddd94057d66a22edd8d7fb969744.jpg) +(a) ST3D et al. use the intersection + +![](images/6597ab49ea314ab3bf473f2c601642f7c873fde278d9500462c9a5f980ac4fda.jpg) +(b) MergeOcc uses the union of label space +Figure 3. Comparison of previous label space intersection approach and our unified label space. A simple example of $\mathcal{T}_k$ is also provided to facilitate a clearer understanding of the subsequent analysis. + +# 3.4. Semantic Label Mapping (SLM) + +# 3.4.1. Motivation of SLM + +As delineated in Appendix A.6, semantic discrepancies across different datasets, stemming from varying class definitions and annotation granularity, present significant challenges in the MDT paradigm. Specifically, multi-head models often yield duplicate outputs for identical objects that appear in multiple datasets, leading to uncertainty and redundancy that adversely impact downstream tasks. Therefore, SLM is necessary for aligning initial outputs to a unified label space in the MDT paradigm. + +Traditional approaches include manually crafted mappings $\mathcal{T}$ [14, 20] and LLM-based merging strategies [4]. However, these methods often suffer from label ambiguity and require substantial human effort for label correction, which limits their scalability to a larger scale. Moreover, both Wang et al. [20] and MSeg [14] have observed noticeable performance degradation in unified models compared to dataset-specific models, primarily due to the challenges of integrating multiple domain sources. + +To address these issues, we introduce SLM to obtain unique semantic outputs in an automated and scalable manner, while maintaining the generalized model's performance. + +# 3.4.2. Learn a Unified Label Space + +In the realm of MDT, each dataset with its own label space $\mathcal{L}_1,\mathcal{L}_2,\dots$ , collectively ascertain a unified label space $\mathcal{L}$ This involves establishing a mapping function $\mathcal{T}_k:\mathcal{L}\to \mathcal{L}_k$ for each dataset, enabling the conversion from dataset-specific labels to the unified label space. Furthermore, the transformation $\mathcal{T}_j\mathcal{T}_i^\top$ facilitates the translation of output from label space $\mathcal{L}_i$ to another $\mathcal{L}_j$ + +Previous related 3D object detection studies[19, 26, 27] predominantly employed a straightforward approach for label space merging, focusing solely on the critical intersection of label spaces, as illustrated in Fig. 3(a). This approach confines their attention to a limited subset of categories—namely, vehicles, pedestrians, and cyclists—owing to their importance in autonomous driving contexts. While + +this is a prevalent practice, it may impede the models' generalization to real-world scenarios. To address this limitation, inspired by Zhou et al.[29], we introduce a data-driven optimization method for automatically constructing a unified label space encompassing a broader spectrum of categories, as depicted in Fig. 3(b). This union strategy enhances the model's generalization ability by integrating a more comprehensive and representative set of categories, aligning more closely with the complex and varied nature of the real world. + +Mathematically, $\mathcal{T}_k\in \{0,1\}^{\lfloor \mathcal{L}_k\rfloor \times \lfloor \mathcal{L}\rfloor}$ represents a boolean linear transformation. Each label, $l_{k}\in \mathcal{L}_{k}$ , specific to a dataset, is mapped to exactly one unified label $l_{\mathrm{uni}}\in \mathcal{L}$ such that: $\mathcal{T}_k\mathbf{1} = \mathbf{1}$ . Additionally, each unified label corresponds to at most one dataset-specific label, as indicated by: $\mathcal{T}_k^\top \mathbf{1}\leq \mathbf{1}$ , which implies that no dataset contains duplicate classes. The objective of SLM is to determine a set of mappings $\mathcal{T} = [\mathcal{T}_1,\dots ,\mathcal{T}_N]$ and implicitly define the unified label-space $\mathcal{L}$ , while maintaining the performance of the unified model unaffected. + +Further analysis of $\mathcal{T}_k$ facilitates subsequent more efficient optimization. The cardinality of unified label set $\mathcal{L}$ corresponds to the number of columns of $\mathcal{T}$ . Additionally, since at most one label is merged per dataset, we have $\mathcal{T}_k^\top \mathbf{1} \leq \mathbf{1}$ . Thus, for each dataset $\mathcal{D}_k$ , a column $\mathcal{T}_k(c) \in \mathbb{T}_k$ can only take one of $|\hat{\mathcal{L}}_k| + 1$ values: $\mathbb{T}_k = \{\mathbf{0}, \mathbf{1}_1, \mathbf{1}_2, \dots\}$ , where $\mathbf{1}_i \in \{0, 1\}^{\lfloor \mathcal{L}_k \rfloor}$ serves as an indicator vector of the $i$ -th element. An illustrative example of $\mathcal{T}_k$ is provided in Fig. 3. + +Thus, each column $\mathcal{T}(c) \in \mathbb{T}$ is selected from a finite set of potential values $\mathbb{T} = \mathbb{T}_1 \times \mathbb{T}_2 \times \dots$ , where $\times$ representing the Cartesian product. Instead of optimizing directly over the label set $\mathcal{L}$ and transformation $\mathcal{T}$ , we adopt combinatorial optimization over the potential column values $t \in \mathbb{T}$ . Let $x_t \in \{0, 1\}$ denote whether a combination $t \in \mathbb{T}$ is selected. In this formulation, the constraint $\mathcal{T}_k \mathbf{1} = \mathbf{1}, \forall k \in N$ is translated to: $\sum_{t \in \mathbb{T} | t(c) = 1} x_t = 1$ for all dataset-specific labels $c$ . This scalable and automatic approach significantly reduces the need for additional human intervention in label rectification. + +Back to the occupancy task, for a set of dataset-specific models' occupancy predictions $o_i^1 \in \mathbb{R}^{|\mathcal{L}_1|}, o_i^2 \in \mathbb{R}^{|\mathcal{L}_2|}, \dots$ , we construct a joint prediction score $d_i$ by averaging the + +outputs across classes: + +$$ +d _ {i} = \frac {\sum_ {k} \mathcal {T} _ {k} ^ {\top} \boldsymbol {o} ^ {k}}{\sum_ {k} \mathcal {T} _ {k} ^ {\top} \mathbf {1}} \tag {5} +$$ + +where the division is performed elementwise. + +The dataset-specific outputs can then be reconstructed as $\tilde{o}_i^k = \mathcal{T}_k d_i$ . To optimize the label mapping function, we maximize the similarity between the results obtained through two reciprocal mappings, $\mathcal{T}_k \mathcal{T}_k^\top o_i^k$ , which transform predictions from a specific dataset into the learned unified label space and then back to the original label space. This approach exploits correlations within the outputs of dataset-specific occupancy prediction models across LiDAR datasets, which act as proxies for perceptual consistency, thus addressing the challenge of label ambiguity. + +Building upon the above analysis of the nature of $\mathcal{T}_k$ , our objective is to minimize this loss across all outputs while respecting the boolean constraints imposed on our mapping: + +$$ +\mathcal {J} = \sum_ {\boldsymbol {t} \in \mathbb {T}} x _ {\boldsymbol {t}} \underbrace {E _ {\mathcal {D} _ {k}} \left[ \sum_ {c \in \mathcal {L} _ {k} | \boldsymbol {t} (c) = 1} \ell_ {c} \left(O ^ {k} , \tilde {O} ^ {k}\right) \right]} _ {c _ {\boldsymbol {t}}} + \lambda \sum_ {\boldsymbol {t} \in \mathbb {T}} x _ {\boldsymbol {t}} \tag {6} +$$ + +Here, the $O^k = [o_1^k,o_2^k,\dots ]$ represents the outputs of the dataset-specific occupancy head for dataset $\mathcal{D}_k$ , and $\ell_c$ denotes a loss function that assesses the fidelity of the transcoded results $O_{\mathrm{uni}}^k$ with unified label $l_{\mathrm{uni}}\in \mathcal{L}$ and their re-projections $\tilde{O}^{k} = \mathcal{T}_{k}\frac{\sum_{k}\mathcal{T}_{k}^{\top}O^{k}}{\sum_{k}\mathcal{T}_{k}^{\top}\mathbf{1}}$ with original label $l_i^k\in \mathcal{L}_k$ in the occupancy grids. The penalty term $\lambda \sum_{t\in \mathbb{T}}x_t$ encourages a small and concise label space. + +The merge cost $c_t$ can be precomputed for any subset of labels $t$ , leading to a computationally efficient formulation. + +This yields a concise integer linear programming formulation of the objective Eq. (6): + +$$ +\operatorname {m i n i m i z e} _ {x} \quad \mathcal {J} = \sum_ {\boldsymbol {t} \in \mathbb {T}} x _ {\boldsymbol {t}} (c _ {\boldsymbol {t}} + \lambda) +$$ + +$$ +\text {s u b j e c t} \quad \sum_ {\boldsymbol {t} \in \mathbb {T} | \boldsymbol {t} _ {c} = 1} x _ {\boldsymbol {t}} = 1 \quad \forall c \in \mathcal {L} _ {k} \tag {7} +$$ + +When more than two datasets are involved, this objective extends to NP-hard weighted graph matching. The size of this optimization problem grows exponentially with the number of datasets: $|\mathbb{T}| = O(|\hat{L}_1||\hat{L}_2||\hat{L}_3|\ldots)$ . Further analysis and an algorithm with a time complexity of $\mathbf{O}(|\mathcal{T}'|\max_{\mathbf{i}}|\hat{\mathbf{L}}^{\mathbf{i}}|)$ are provided in the Appendix A.6, which may enhance the scalability of SLM module. + +# 4. Experiments + +# 4.1. Experiment Settings + +In this section, we primarily present the essential datasets and baseline selection. More detailed settings and supplementary results are provided in the Appendices A.2 to A.4. + +Given the relative scarcity of large-scale outdoor occupancy datasets, those available predominantly consist of data collected using 32-beam and 64-beam LiDARs. In this context, we select representative and widely used datasets. Specifically, we choose the nuScenes, which utilizes a 32-beam LiDAR, and the SemanticKITTI, which uses a 64-beam LiDAR, to represent the primary configurations in current autonomous vehicles. + +To verify the effectiveness of the proposed method, we select two baseline models: 1) a 3D voxel-based method, L-CoNet [21], whose backbone is ResNet3D[10], augmented by an FPN [15] to integrate features across multiple scales, and 2) a 2D projection-based method, PointOcc [30], whose backbone is the Swin Transformer[16]. + +
MethodInputIoUmIoUbarrierbicyclebuscarconst. veh.motorcyclepedestriantraffic conetrailertruckdrive. suf.other flatsidewalkterrainmannadevegetation
MonoScene[5]C18.46.97.13.99.37.25.63.05.94.44.94.214.96.37.97.410.07.6
TPVFormer[11]C15.37.89.34.111.310.15.24.35.95.36.86.513.69.08.38.09.28.2
3DSketch[7]C&D25.610.712.05.110.712.46.54.05.06.38.07.221.814.813.011.812.021.2
LMSCNet[18]L27.311.512.44.212.812.16.24.76.26.38.87.224.212.316.614.113.922.2
JS3C-Net[25]L30.212.514.23.413.612.07.24.37.36.89.29.127.915.314.916.214.024.9
C-CONet[21]C20.112.813.28.115.417.26.311.210.08.34.712.131.418.818.716.34.88.2
M-CONet[21]C&L29.520.123.313.321.224.315.315.918.013.315.320.733.221.022.521.519.623.2
L-CONet(V-baseline)[21]L30.915.817.55.213.318.17.85.49.65.613.213.634.921.522.421.719.223.5
MergeOcc-V (D.M.)L25.45.72.00.11.45.40.30.30.40.32.82.528.110.310.910.36.59.9
MergeOcc-V (Tr both)(ours)L40.222.923.48.822.927.513.415.821.912.715.319.439.825.026.427.530.835.0
PointOcc† (P-baseline) [30]L33.318.721.55.218.723.211.720.410.83.413.818.036.322.321.320.524.228.0
MergeOcc-P (Tr both)(ours)L42.726.127.715.728.933.118.627.820.711.915.722.443.625.725.925.333.739.5
+ +Table 3. 3D Semantic occupancy prediction results on OpenOccupancy-nuScenes. Notably, MergeOcc uses the R.A. module while other methods are evaluated under the full annotation range on this dataset. The C, L, and D denote camera, LiDAR, and depth, respectively. † denotes results that the authors reproduce. ‘-V’ and ‘-P’ denote the voxel-based method and the projection-based method. + +
MethodInputIoUmIoUroad (15.30%)sidewalk (11.13%)parking (1.12%)other-grnd (0.56%)building (14.1%)car (3.92%)truck (0.16%)bicycle (0.03%)motorcycle (0.03%)other-veh. (0.20%)vegetation (39.3%)trunk (0.51%)terrain (9.17%)person (0.07%)bicyclist (0.07%)motorcyl. (0.05%)fence (3.90%)pole (0.29%)traf.-sign (0.08%)
■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■■\( L - \text{CONet}^{\dagger } \) (V-baseline) [21]
LMSCNet [18]L31.47.146.719.513.53.110.314.30.30.00.00.00.00.00.00.00.00.00.010.80.010.40.00.00.05.40.00.00.00.05.40.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.10.10.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.20.28.71.90.30.32.1
3DSketch [7]C&D26.96.237.719.80.00.012.117.10.00.012.117.10.00.00.00.00.00.00.012.10.016.10.00.00.03.40.00.00.00.03.40.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.00.01.90.3
JS3C-Net [25]L34.09.047.321.719.92.812.720.10.80.00.00.00.00.00.04.114.23.112.40.00.28.71.90.3
MonoScene [5]C34.211.154.727.124.85.714.418.83.30.50.74.414.92.419.51.01.40.419.51.01.40.411.13.32.1
+ +Table 4. 3D Semantic occupancy prediction results on SemanticKITTI. We select similar settings as OpenOccupancy-nuScenes. + +# 4.2. 3D Semantic Occupancy Prediction Results + +The class-wise 3D occupancy prediction results are presented in Tab. 3 and Tab. 4, along with the visual performance comparison of primary methods shown in Fig. 4. Visualization of the primary models' occupancy prediction results is provided in Appendix A.8. These results underscore the superior performance and robust cross-LiDAR scalability of the proposed method. In this section, we focus on presenting key experimental findings and discussing the underlying reasons for these outcomes. + +Compared with D.M. Method At the outset of this research, we use L-CoNet as the baseline to explore whether current perception models can directly utilize different LiDAR data. Experimental results indicate that the D.M. method is not satisfactory, and the proposed MergeOcc effectively bridges the domain gap between disparate LiDARs, enabling the model to leverage broader and more diverse data. Specifically, without bells and whistles, MergeOcc-V enhances occupancy prediction in the OpenOccupancy-nuScenes dataset by $14.8\%$ in geometric IoU and $17.2\%$ in semantic mIoU. In the SemanticKITTI dataset, MergeOcc-V improves the occupancy prediction accuracy by $33.4\%$ and $12.5\%$ respectively, marking a significant performance advancement compared to the D.M. method. + +Compared with Baseline Trained on Single Domain A crucial and intriguing observation is that, despite using an identical architecture and hyper-parameter set, MergeOcc exhibits a significant performance improvement due to its ability to learn from broader data, which is unprecedented in 3D perception field. Specifically, the in-domain performance gains of MergeOcc-V are as follows: + +$$ +G _ {\mathrm {nu}}: + 9.3 \%, S _ {\mathrm {nu}}: + 7.1 \%; G _ {\mathrm {sk}}: + 14.5 \%, S _ {\mathrm {sk}}: + 9.8 \%. +$$ + +Similarly, the improvements of MergeOcc-P are as follows: + +$$ +G _ {\mathrm {nu}}: + 9.4 \%, S _ {\mathrm {nu}}: + 7.4 \%; G _ {\mathrm {sk}}: + 4.8 \%, S _ {\mathrm {sk}}: + 11.9 \% +$$ + +This substantial performance gain indicates that the current capacity of 3D Occ datasets is insufficient and highlights the crucial potential for the MDT paradigm. + +Notably, MergeOcc simultaneously exhibits excellent performance on both types of LiDARs. When evaluated under the cross-LiDAR setting, MergeOcc's performance significantly surpasses the dataset-specific baseline. + +Compared with SOTA MergeOcc-P demonstrates superior performance compared to the SOTA multi-modality model M-CONet by $13.2\%$ and $6.0\%$ in IoU and mIoU on the nuScenes. Additionally, MergeOcc-P outperforms the SOTA camera-based model SurroundOcc by $38.0\%$ and $8.2\%$ in IoU and mIoU on the SemanticKITTI, underscoring its efficacy in extracting insights from diverse data sources. Furthermore, using the weaker baseline L-CoNet, MergeOcc-V outperforms the LiDAR-based SOTA method PointOcc [30] by $6.1\%$ in IoU. + +![](images/21262fd470f95ba36da03f10ffad3dd40c59f211619adc131e6d05a3d5391a54.jpg) +Figure 4. Performance comparison and analysis of MergeoCC. The vertical axis represents the geometric IoU, with a maximum value of $80\%$ , and the horizontal axis represents the semantic mIoU, with a maximum value of $40\%$ . + +# 4.3. Ablation Experiments + +For all the ablation experiments, we use the more general voxel-based method L-CoNet as the baseline. + +# 4.3.1. Ablation Design and Comparison of Methods + +a) w/o P.T. (Single-dataset): We utilize the off-the-shelf occupancy prediction network L-CONet[21] as baseline, which is trained from scratch and evaluated within a single dataset. + +b) P.T. (Pre-training): We adopt the standard fine-tune paradigm, where the baseline model is initially pre-trained on the source domain and subsequently finetuned on the target domain. The training and fine-tuning processes on the two datasets are conducted independently. + +
Trained onMethodTested on OpenOccupancy-nuScenesTested on SemanticKITTI
Geometric IoUSemantic mIoUGeometric IoUSemantic mIoU
only SKMergeOcc-V (w/o P.T.)4.10.155.64.7
MergeOcc-V (w/ P.T. on OO-nu)4.3 (+0.2)0.153.3 (-2.3)4.0 (-0.7)
only OO-nuMergeOcc-V (w/o P.T.)30.115.83.80.3
MergeOcc-V (w/ P.T. on SK)26.3 (-3.8)7.1 (-8.7)5.7 (+1.9)0.1 (-0.2)
SK+OO-nuMergeOcc (w/D.M.)25.45.736.72.0
MergeOcc-V (w/G.A.)14.7 (-10.7)1.6 (-4.1)51.2 (+14.5)3.0 (+1.0)
MergeOcc-V (w/R.A.)38.2 (+12.8)21.3 (+15.6)70.0 (+33.3)13.4 (+11.4)
MergeOcc-V (w/G.R. (R.A. +G.A.))38.4 (+13.0)21.4 (+15.7)69.9 (+33.2)14.5 (+12.5)
MergeOcc-V (w/G.R. + SLM)40.2 (+14.8)22.9 (+17.2)70.1 (+33.4)14.5 (+12.5)
+ +Table 5. Ablation results of core components of MergeOcc on OpenOccupancy-nuScenes and SemanticKITTI datasets. We use the more general voxel-based method L-CoNet as the baseline. + +c) D.M. (Direct Merging): By simply combing multiple 3D datasets into a single merged dataset, dataset-specific models can be trained on it with a combined loss, which serves as a simple method to assess whether the existing 3D models can be improved by broader data. +d) G.R. $(\mathbb{R},\mathbb{A}, + \mathbb{G},\mathbb{A})$ : As introduced above, we perform point cloud range alignment (R.A.) and geometric statistical data alignment (G.A.) to bridge the geometric gap between different LiDARs and encapsulate the unique statistical characteristics of each LiDAR into our model framework. +e) G.R. +SLM: This represents the complete MergeOcc. + +Notably, for all settings, we use the identical hyperparameter set and training strategy to ensure fairness. + +# 4.3.2. Further Analysis + +a) Large disparity across 3D LiDAR datasets: As illustrated in Tab. 5, the efficacy of dataset-specific models significantly deteriorates when applied to unseen domains. This cross-LiDAR issue primarily arises from the over-fitting to the source domains and unreasonable shortcuts within dataset-specific models, thereby overlooking the inherent domain-invariant features. +b) Limited efficacy of the pre-training strategy: Upon comparing the baselines P.T and w/o P.T., as depicted in Tab. 5, it is evident that despite pre-training, models will forget knowledge acquired from the preceding pre-trained dataset. Although there is a marginal enhancement within the source domain, the pre-existing knowledge hinders the models' performance in the target domain. +c) Assessment of MergeOcc's effectiveness and robustness: By comparing w/ P.T. and D.M baselines from Tab. 5, it reveals that 3D SDT paradigm fails to yield a robust and generalized perception model. As shown in Tabs. 3 to 5, MergeOcc consistently outperforms all baseline methods across all classes on both datasets, thus confirming its superior ability to bridge domain gaps across varied LiDAR systems and to fully exploit the available data. + +An intriguing finding is that the improvements are more pronounced for frequent and large classes (e.g., road, car) compared to infrequent and small ones (e.g., bicycle, motorcycle). Since model architecture and training parameters + +keep identical across all experiments, the consistent improvements may come from broader and diverse data, and the varying degrees are likely influenced by the long-tail distribution. + +Additionally, ablation experiments indicate that the R.A. module is important in performance improvement. To elucidate the underlying causes, we conducted additional experiments focusing on R.A., with results detailed in Appendix A.3, demonstrating that R.A. is beneficial exclusively within the MDT paradigm. Conversely, under the single dataset training and testing paradigm, R.A. is detrimental due to inherent data limitations. + +In all, the R.A., G.A., and SLM. modules all enhance the accuracy of occupancy prediction. It is critical to note that these performance improvements are attributed to the learning afforded by larger and more diverse datasets (i.e., MDT). These modules serve merely as the bridge to address the existing gap between different domains. This outcome highlights the superiority and critical importance of the MDT paradigm. + +# 5. CONCLUSIONS + +This paper explores training strategies for constructing a generalized 3D occupancy prediction model capable of handling different LiDAR sensors, leading to more robust and effective perception. The proposed MergeOcc framework, which integrates a geometric realignment module and a semantic label mapping module, successfully addresses challenges arising from domain divergence. Extensive experiments conducted on two prominent autonomous driving benchmarks validate its effectiveness. We applied MergeOcc to two representative occupancy prediction models: voxel-based L-CoNet and projection-based PointOcc. Both baselines exhibit consistent and significant improvements, demonstrating the potential of our approach in handling the cross-LiDAR issue. These findings also highlight the inadequacy of current 3D occupancy datasets, underscoring the need for further research in the MDT paradigm. The current approach does not yet extend to handling unseen LiDARs; we will endeavor to resolve this limitation in the future. + +# ACKNOWLEDGEMENT + +# References + +[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyrill Stachniss, and Jurgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. 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Recently, a line of research has focused on autoregressively generating meshes. This approach processes meshes into a sequence composed of vertices and then generates them vertex by vertex, similar to how a language model generates text. These methods have achieved some success but still struggle to generate complex meshes. One primary reason for this limitation is their inefficient tokenization methods. To address this issue, we introduce MeshAnything V2, an advanced mesh generation model designed to create Artist-Created Meshes that align precisely with specified shapes. A key innovation behind MeshAnything V2 is our novel Adjacent Mesh Tokenization (AMT) method. Unlike traditional approaches that represent each face using three vertices, AMT optimizes this by employing a single vertex wherever feasible, effectively reducing the token sequence length by about half on average. This not only streamlines the tokenization process but also results in more compact and well-structured sequences, enhancing the efficiency of mesh generation. With these improvements, MeshAnything V2 effectively doubles the face limit compared to previous models, delivering superior performance without increasing computational costs. + +# 1. Introduction + +Due to the controllable and compact advantages of meshes, they serve as the predominant 3D representation in various industries, including games, movies, and virtual reality. For decades, the 3D industry has relied on human artists to manually create meshes, a process that is both time-consuming and labor-intensive. + +To address this issue, very recently, a line of work [2, + +4, 5, 15, 19, 28] has focused on automatically generating Artist-Created Meshes (AMs) to replace manual labor. Inspired by the success of large language models (LLMs), these approaches treat AMs as sequences of faces and learn to generate them with autoregressive transformers [24] in a manner similar to LLMs. Unlike methods that produce dense meshes in a reconstruction manner, these methods learn from the distribution of meshes created by human artists, thereby generating AMs that are efficient, beautiful, and can seamlessly replace manually created meshes. + +Although these methods have achieved some success, they still face significant challenges. One major limitation is that current methods [2, 4, 5, 15, 19, 28] cannot generate meshes with a large number of faces. A primary reason for this constraint is the inadequacy of existing mesh tokenization methods. These methods treat a mesh as a sequence of faces, where each face consists of three vertices, and each vertex typically requires three tokens to represent. Consequently, each mesh is tokenized into a sequence nine times the number of its faces, resulting in substantial computational and memory demands. Besides, the resulting token sequence is highly redundant, which harms sequence learning and reduces performance. + +Observing the above issues, we focus on the tokenization method of mesh generation in this work, aiming to improve the efficiency and quality of mesh generation. Extensive research in language models has demonstrated the importance of tokenization in sequence learning [10, 17, 30]. Moreover, unlike text, which inherently has a sequential structure, meshes are graph-based structures with 3D characteristics. For any given mesh, there are countless ways to represent it as a 1D token sequence, making the influence of tokenization methods even more pronounced for meshes. Therefore, we emphasize that research on mesh tokenization methods is of great importance. + +The impact of mesh tokenization on autoregressive mesh generation can be considered in two main aspects. The first is efficiency: representing a mesh with shorter, more + +![](images/1ffb3514088f9ce4add9f88a8aeea4b5c449966ae3c65a8c3903d716764439db.jpg) +Figure 1. Equipped with the newly proposed Adjacent Mesh Tokenization (AMT), MeshAnything V2 significantly surpasses MeshAnything [5] in both performance and efficiency. MeshAnything V2 generates Artist-Created Meshes (AM) up to 1600 faces aligned with given shapes. Combined with various 3D asset production pipelines, it efficiently achieves high-quality, highly controllable AM generation. + +compact token sequences leads to reduced context length, thereby decreasing memory and computational complexity. The second aspect is the regularity of the token sequence. A shorter token sequence is not always better for mesh generation; the regularity and pattern consistency of the sequence are crucial for effective sequence learning. Effective mesh tokenization must balance both efficiency and regularity to + +achieve high-quality, efficient mesh generation. + +Considering the above, we introduce MeshAnything V2, an advanced model for generating Artist-Created Meshes. This model incorporates several key improvements to boost both performance and efficiency. At the core of MeshAnything V2 is our novel Adjacent Mesh Tokenization (AMT) method. AMT optimizes the tokenization process by repre + +senting each face with a single vertex rather than the traditional three. As illustrated in Fig. 1 and Algo. 1, AMT encodes adjacent faces using just one additional vertex, largely reducing the sequence length. When an adjacent face cannot be identified, a special token $\&$ is introduced to indicate this interruption, allowing the model to resume from an un-encoded face. + +In previous mesh generation works, users were unable to control the number of faces generated by the model, often resulting in meshes that did not meet application requirements. To address this, we introduce a face count condition, allowing users to specify an approximate number of faces, ensuring that generated meshes align with desired specifications. Additionally, to enhance the robustness of AMT during inference, we incorporate Masking Invalid Predictions [15] to prevent the model from producing invalid tokens, such as generating another '&&' token immediately after an '&&' token. + +Extensive experiments on the Objaverse [6] dataset demonstrate that AMT can halve the sequence length on average. This reduction translates to nearly a fourfold decrease in computational load and memory usage within the attention block. Furthermore, AMT remains effective across various mesh generation settings, including unconditional and conditional approaches [19], even when using VQ-VAE [23]. Finally, with the integration of AMT, MeshAnything V2 doubles the maximum number of faces generated compared to previous models, significantly boosting both performance and efficiency. + +In summary, our contributions are: + +1. We introduce MeshAnything V2, a novel Artist-Created Mesh Generation model. V2 doubles the maximum number of faces that can be generated while achieving significantly better accuracy and efficiency. +2. The core of V2 is our newly proposed mesh tokenization method, Adjacent Mesh Tokenization (AMT). Compared to previous tokenization methods, AMT requires approximately half the token sequence length to represent the same mesh, thereby fundamentally reducing the computational burden of Artist-Created Mesh generation. +3. We conduct extensive experiments on various mesh tokenization methods to explore the essential properties required for effective mesh tokenization. Our experiments demonstrate that AMT significantly improves the efficiency and performance of mesh generation, and that the token sequence produced by mesh tokenization methods must balance compactness and regularity. + +# 2. Related Works + +# 2.1. Artist-Created Mesh Generation + +Diverging from previous works that produce dense meshes, recent works have focused on generating meshes created by + +Algorithm 1: Adjacent Mesh Tokenization (AMT) +Input: $\mathcal{M}$ : a triangle mesh Output: A token sequence Seq that represents M 1 Sort the vertices of $\mathcal{M}$ in ascending order by their coordinates; 2 Sort the faces of $\mathcal{M}$ in ascending order by their vertex indices; 3 Initialize an empty token sequence Seq; 4 Initialize a face list UnvisitedFaces as the faces of $\mathcal{M}$ . Remove the first face from UnvisitedFaces; 6 Append the three vertices of the removed face to Seq; Define a SpecialToken & to indicate break signal. 8 while UnvisitedFaces is not empty do 9 if the last token in Seq is & then 10 Remove the first face from UnvisitedFaces; 11 Append the three vertices of the removed face to Seq; 12 else 13 AdjacentVertices $\leftarrow$ vertices adjacent to both the last two vertices in Seq; 14 Filter out vertices from AdjacentVertices that form faces with the last two vertices in Seq that are not in UnvisitedFaces; 15 if AdjacentVertices is not empty then 16 Sort AdjacentVertices in ascending order by their coordinates; 17 Append the first vertex in AdjacentVertices to Seq; 18 else 19 Append & to Seq; +20 return Seq; + +human artists, i.e., Artist-Created Meshes (AMs) [2, 4, 5, 15, 19, 20, 28]. These methods process meshes into ordered face sequences and learn to generate this sequence. [15] first proposed using autoregressive transformers to sequentially generate vertices and faces. [19] use VQ-VAE to learn a mesh vocabulary and then learn this vocabulary with a decoder-only transformer. [2] differ from other methods by using a discrete diffusion model to generate AMs instead of an autoregressive transformer. [4] propose directly using the discretized coordinates of the vertex as the token index, bypassing the need for VQ-VAE as in [19]. [28] use pivot vertices as a coarse mesh representation and then generate the complete mesh tokens. [5] generate AMs aligned with given shapes, which can be integrated with various 3D asset production methods to convert their results into AMs. + +![](images/7fb0b302729e25511a11a7a22aa0b3becb5c10f994c9a7ac7c17b35317c38a00.jpg) +Previous Mesh Tokenization Methods + +![](images/17bbabb055d16782de6a5c2117abaafff22ea120cff008f298316c5d45599d1c.jpg) +Adjacent Mesh Tokenization (AMT) +Figure 2. Illustration of Adjacent Mesh Tokenization (AMT). Unlike previous methods that use three vertices to represent a face, AMT uses a single vertex whenever possible. When this is impossible, AMT adds a special token & and restarts. Our experiments demonstrate that AMT reduces the token sequence length by half on average. Its compact, and well-structured sequence representation enhances sequence learning, thereby significantly improving both the efficiency and performance of mesh generation. + +As shown in Fig. 2, all of these methods process meshes into face sequences and use three vertices to represent a single face, resulting in highly redundant representations. Different from these methods, our newly proposed Adjacent Mesh Tokenization (AMT) uses a single vertex to represent a single face, providing a more compact and well-structured mesh representation, thereby significantly improving the efficiency and performance of mesh generation. + +# 2.2.3D Generation + +In recent years, 3D generation has gradually become one of the mainstream research directions in the field of 3D research. This area focuses on generating diverse, high-quality 3D assets for the 3D industry. Generative Adversarial Networks (GANs) [1, 7, 29] produce synthetic 3D data by training a generator and a discriminator network to distinguish between generated and real data. Very recently, a new line of works [9, 11, 12, 18, 21, 22, 26, 27, 31] directly generate 3D assets in a feed-forward manner. [9] pioneer these methods and use a transformer to directly regress the parameters of 3D models given conditions. Besides, applying + +diffusion models [8] to directly generate 3D assets has also been widely researched [2, 13, 14, 16, 32, 35]. [32] lead the SOTA of current 3D generation methods by first generating high-quality 3D shapes with DiT and then producing detailed textures with material diffusion models. + +As mesh is a crucial component in 3D generation, Artist-Created Mesh Generation [2, 4, 5, 15, 19, 28] is closely related to 3D generation. However, it differs significantly from previous 3D generation methods as it mainly focuses on sequence learning, which is rarely seen in other 3D generation methods, to produce high-quality mesh topology. + +# 3. Method + +In this work, we introduce a novel mesh tokenization method, named Adjacent Mesh Tokenization (AMT). Compared to previous tokenization methods, AMT reduces the token sequence length by approximately half to represent the same mesh, thereby significantly lowering the computational overhead of mesh generation. AMT is detailed in Section 3.1. + +Next, in Section 3.2, we integrate AMT into MeshAny- + +thing [5] and introduce MeshAnything V2. + +# 3.1. Adjacent Mesh Tokenization + +In this section, we detail Adjacent Mesh Tokenization (AMT), a novel tokenization method for Artist-Created Mesh (AM) generation. Compared to previous methods, AMT processes the mesh into a more compact and well-structured token sequence by representing each face with a single vertex whenever possible. For simplicity, we describe AMT on triangle mesh. But it is worth noting that AMT can be easily generalized to the generation of meshes with variable polygons. + +Tokenization is a crucial part of sequence learning, as it processes various data formats, such as text, images, and audio, into token sequences. The processed tokens are then used as ground truth inputs for training the sequence model. During inference, the sequence model generates a token sequence that is subsequently detokenized into the target data format. Therefore, tokenization plays a vital role in sequence learning, determining the quality of the data sequence that the sequence model learns from. + +We first illustrate the tokenization methods used in previous methods [2, 4, 5, 15, 19, 28]. Although there are slight differences in detail, the previous tokenization methods can be unified as follows: Given a mesh $\mathcal{M}$ , vertices are first sorted in ascending order based on their z-y-x coordinates, where z represents the vertical axis. Next, faces are ordered by their lowest vertex index, then by the next lowest, and so on. The mesh is then viewed as an ordered sequence of faces: + +$$ +\mathcal {M} := \left(f _ {1}, f _ {2}, f _ {3}, \dots , f _ {N}\right), \tag {1} +$$ + +where $f_{i}$ represents the $i$ -th face in the mesh, and $N$ is the number of faces in $\mathcal{M}$ . + +Then, each $f_{i}$ is represented as an ordered sequence of three vertices $v$ : + +$$ +f _ {i} := \left(v _ {i 1}, v _ {i 2}, v _ {i 3}\right), \tag {2} +$$ + +where $v_{i1}, v_{i2}$ , and $v_{i3}$ are the vertices that form the $i$ -th face $f_i$ in the mesh. It is worth noting that $v_{i1}, v_{i2}$ , and $v_{i3}$ have already been sorted and have a fixed order. + +Substituting Equation (2) into Equation (1) gives: + +$$ +\mathcal {M} := \left(\left(v _ {1 1}, v _ {1 2}, v _ {1 3}\right), \dots , \left(v _ {N 1}, v _ {N 2}, v _ {N 3}\right)\right) = \operatorname {S e q} _ {V} \tag {3} +$$ + +Due to the sorting, the resulting $\mathrm{Seq}_V$ is unique and its length is three times the number of faces in the mesh. It is evident that $\mathrm{Seq}_V$ contains a significant amount of redundant information, as each vertex appears as many times as the number of faces it belongs to. + +To resolve this issue, we propose Adjacent Mesh Tokenization (AMT) to obtain a more compact and well-structured $\mathrm{Seq}_V$ than previous method. Our key observation + +is that the main redundancy of $\mathrm{Seq}_V$ comes from representing each face with three vertices as in (2). This results in vertices that have already been visited appearing redundantly in $\mathrm{Seq}_V$ . Therefore, AMT aims to represent each face using only a single vertex whenever possible. As shown in Fig. 2 and Algo. 1, AMT efficiently encodes adjacent faces during tokenization, using only one additional vertex. When no adjacent face is available, as illustrated in the last step of Fig. 2, AMT inserts a special token & into the sequence to denote this event and restarts the process from a face that has not yet been encoded. To detokenize, simply reverse the tokenization algorithm as described in Algo. 1. + +In the ideal case, where the special token "&" is rarely used, AMT can reduce the length of $\mathrm{Seq}_V$ obtained by previous methods to nearly one-third. Of course, in extreme cases, such as when each face in the mesh is completely disconnected from others, AMT performs worse than previous methods. However, since the datasets [3, 6] used for AM generation are created by human artists, the meshes generally have well-structured topologies. Thus, the overall performance of AMT is significantly better than previous methods. As shown in Sec. 4.3, on the Objaverse test set, AMT can reduce the length of $\mathrm{Seq}_V$ by half on average. + +Vertices Swap. Considering two faces $f_{1}$ and $f_{2}$ : + +$$ +f _ {1} = \left(v _ {1}, v _ {2}, v _ {3}\right), f _ {2} = \left(v _ {1}, v _ {3}, v _ {4}\right). +$$ + +These two faces are connected by edge (v1, v3). Assuming we first represent f1 as (v1, v2, v3), AMT will be interrupted because f2 does not contain v2, even though f1 and f2 are actually adjacent. To solve this issue, we introduce a special token $ to swap vertices. When the $ token appears in front of a vertex, it indicates that the next face will be formed by the first and the last vertex of the previous face, instead of the last two. For example, the token sequence (v1, v2, v3, $, v4) implies the mesh consists of two faces: (v1, v2, v3) and (v1, v3, v4), i.e. f1 and f2. + +When swap is enabled, AMT can explore more adjacent faces when searching for the next face. Specifically, in line 13 of Algo. 1, AdjacentVertices can be modified to additionally include vertices adjacent to the last and third-to-last vertices in Seq. + +Although the swap operation introduces an additional special token, it reduces the number of interruptions and effectively shortens the token sequence. While adding a special token may potentially increase the difficulty of sequence learning, our experiments in Sec. 4.3 show that it has no noticeable impact. + +Discussion on Sorting in Mesh Tokenization. Both previous methods and AMT initially sort the vertices and faces of the mesh. The primary goal is to process the mesh data into a sequence with a fixed pattern, making it easier for the learning of the sequence model. In AMT, to maintain this design, we consistently choose the face with the earlier index in + +the sorted list whenever there are multiple choices. Besides, thanks to this design, the token sequence processed by AMT is unique for each mesh. Additionally, AMT prioritizes visiting adjacent faces whenever possible. In contrast, previous methods naively follow the sorted order, often resulting in token sequences where spatially distant vertices are adjacent in the sequence, potentially increasing sequence complexity. As shown in Sec. 4.3, compared to previous methods, AMT demonstrates significant advantages in both speed and memory usage, as well as improved accuracy, proving that the sequences generated by AMT are more compact and well-structured. + +Discussion on AMT and the use of VQ-VAE. After obtaining $\mathrm{Seq}_V$ , mesh generation methods then need to process it into a token sequence for sequence learning. [19] propose to train a VQ-VAE [23] to achieve this. They take $\mathrm{Seq}_V$ as input and learn a vocabulary of geometric embeddings with the VQ-VAE. After training the VQ-VAE, they then use the VQ-VAE's quantized features as the input for the transformer [24]. Very recently, [4] proposed another method to process $\mathrm{Seq}_V$ into a token sequence. They discard VQ-VAE and directly use the discretized coordinates of the vertex as the token index. It is important to emphasize that whether or not VQ-VAE is used does not affect AMT's effectiveness. This is because AMT operates before the aforementioned methods. For example, in the case of using VQ-VAE, AMT first shortens the $\mathrm{Seq}_V$ that represents $\mathcal{M}$ , and the shortened $\mathrm{Seq}_V$ is then quantized into an embedding sequence with the VQ-VAE. + +# 3.2. MeshAnything V2 + +In this section, we introduce MeshAnything V2. It is equipped with AMT and scales up its maximum generated face count from 800 to 1600. Without increasing the number of parameters, MeshAnything V2 achieves shape conditioned Artist-Created Mesh (AM) generation with significantly better performance and efficiency. We also use it as an example to demonstrate how AMT can be applied to mesh generation. + +Following [5], MeshAnything V2 also targets generating AMs aligned to a given shape, allowing integration with various 3D asset production pipelines to achieve highly controllable AM generation. That is, we aim to learn the distribution: $p(\mathcal{M}|\mathcal{S})$ , where $\mathcal{M}$ represents the AM and $S$ represents the 3D shape condition. + +As in [5], V2 uses point clouds as the shape condition input $S$ . We also use the same point cloud-Artist-Created Mesh data pairs $(\mathcal{M},\mathcal{S})$ collected in [5]. The target distribution $p(\mathcal{M}|\mathcal{S})$ is learned with a decoder-only transformer with the same size and architecture as in [5]. To inject $S$ into the transformer, we first encode it with a pretrained point cloud encoder [34] into a fixed-length token sequence $\mathcal{T}_S$ and then set it as the prefix of the transformer's token + +sequence. We then process paired $\mathcal{M}$ into mesh token sequence $\mathcal{T}_M$ . It is concatenated to the point cloud token sequence as the transformer's ground truth sequence. After training the transformer with cross-entropy loss, we input $\mathcal{T}_S$ and let the transformer autoregressively generate the corresponding $\mathcal{T}_M$ , which is then detokenized into $\mathcal{M}$ . + +The key difference between [5] and our method is the way we obtain $\mathcal{T}_M$ . Instead of the naive mesh tokenization method used in [5], we process $\mathcal{M}$ with the newly proposed Adjacent Mesh Tokenization (AMT) and obtain a more compact and efficient sequence $\mathrm{Seq}_V$ . Following [4], we discard the VQ-VAE and directly use the discretized coordinates from $\mathrm{Seq}_V$ as token indices. We then add a newly initialized codebook entry to represent the & in the AMT sequence. Finally, we sequentially combine the coordinate token sequence and the special token for & to obtain the mesh token sequence $\mathcal{T}_M$ for transformer input. As mentioned in Sec. 3.1, it is worth noting that whether or not VQ-VAE is used does not affect the application and effectiveness of AMT. + +To facilitate the transformer's learning of the sequence patterns of AMT, in addition to the absolute positional encoding used in [5], we add the following embeddings for Adjacent Mesh Tokenization (AMT): when representing a face with three vertices, we add a specific embedding for the three new vertices; when representing a face with one vertex, we add a different embedding for the single new vertex. Additionally, we provide a distinct embedding for the & token. + +Face Count Condition. Considering that some applications require control over the approximate face count, we explored the addition of a face count condition in mesh generation. We initialized an embedding book with a size equal to the maximum allowed number of faces. Based on the current face count in the mesh, we retrieve the corresponding embedding from this book and place it after the point cloud prefix to represent the face count. During training, we add a random variable to the face count to introduce some variation and prevent overfitting to an exact condition. During training, we add a random variable to the face count to introduce some variation and prevent overfitting to an exact condition. Additionally, we drop this condition with a $10\%$ probability to further improve condition robustness. + +Masking Invalid Predictions. PolyGen [15] introduces Masking Invalid Predictions during inference. In PolyGen, vertices are generated first, followed by faces, and both vertices and faces are sorted. Without applying constraints during inference, generative models may produce results that do not follow the sequence structure, such as generating faces before completing all vertices or generating vertices that violate the sorted coordinates order. PolyGen [15] addresses this issue by masking invalid logits during the inference phase, ensuring that only valid results are generated. + +Table 1. Ablation Study on AMT. We compare MeshAnything V2 with its variant without AMT. Please refer to Section 4.3 for detailed explanation. + +
MethodCD↓(×10-2)ECD↓(×10-2)NC↑#V↓#F↓V_Ratio↓F_Ratio↓S_Ratio↓
V2 W/O AMT0.8954.8320.924302.4556.71.1051.0621.000
V20.8744.7210.933308.6571.81.1271.0970.497
+ +We followed this design in our PolyGen experiments. Due to the widespread use of coordinate sorting in meshes, this design can also be adopted in other tokenization methods. In the AMT experiments, we incorporated this design as well. For example, we enforced a rule in AMT where, when starting a new strip, at least three vertices must be generated before allowing any interruptions. + +# 4. Experiments + +# 4.1. Implementation Details + +The main experimental setting of MeshAnything V2 remains consistent with [5], except we equipped it with the newly proposed Adjacent Mesh Tokenization (AMT). We still use OPT-350M [33] as our autoregressive transformer [24] and the pretrained point encoder from [34]. + +For dataset preparation, we adopt a similar dataset preparation technique as used in [5], with several modifications. Firstly, we noticed that Objaverse contains some duplicate mesh data, where the meshes are identical in shape but differ in texture. We detected these duplicates by calculating the differences in vertex coordinates and retained only one instance of each mesh. Additionally, in [5], the ground truth meshes were first processed into SDF using mesh2pdf [25]. While mesh2pdf occasionally produces some failure cases, we filtered out these failures using Chamfer Distance. Different from the dataset used in [5], we used meshes with fewer than 1600 faces as the experimental dataset, compared to 800 in the previous work, and also included a small portion of data from ObjaverseXL. This resulted in a dataset containing 230K point clouds and mesh pairs. We randomly sampled 4K data samples as the evaluation dataset. + +To accommodate meshes with more faces, we sampled 8192 points instead of 4096 for each point cloud. Besides, unlike [5], we update the point encoder from [34] during training because we find its accuracy insufficient for handling complex meshes with up to 1600 faces. + +MeshAnything V2 is trained with 32 A800 GPUs for four days. The batch size per GPU is 8. + +# 4.2. Qualitative Experiments + +We present the qualitative results of MeshAnything V2. As shown in Fig. 1, MeshAnything V2 effectively generates high quality Artist-Created Mesh aligned to given shapes. When integrated with various 3D assets production pipelines, + +V2 successfully achieves highly controllable AM generation. + +# 4.3.Quantitative Experiments + +Evaluation Metrics. We follow the evaluation metric settings of [5] to quantitatively assess mesh quality. We uniformly sample point clouds from both the ground truth meshes and the generated meshes and compute the following metrics on our 2K evaluation dataset: + +- Chamfer Distance (CD): Evaluates the overall quality of a reconstructed mesh by computing chamfer distance between point clouds. + +- Edge Chamfer Distance (ECD): Assesses the preservation of sharp edges by sampling points near sharp edges and corners. + +- Normal Consistency (NC): Evaluates the quality of the surface normals. + +- Number of Mesh Vertices (#V): Counts the vertices in the mesh. + +- Number of Mesh Faces (#F): Counts the faces in the mesh. + +- Vertex Ratio (V_Ratio): The ratio of the estimated number of vertices to the ground truth number of vertices. + +- Face Ratio (F_Ratio): The ratio of the estimated number of faces to the ground truth number of faces. + +- Perplexity: We report training perplexity to measure how well the mesh generation model predicts a sample. A lower perplexity indicates more accurate predictions. + +- Sequence Ratio (S_Ratio): The sequence length compression ratio of the used mesh tokenization methods. + +Ablation Study. We ablate the effectiveness of AMT by comparing the results of MeshAnything V2 with its variant without AMT. The variant follows exactly the same settings as V2, except that AMT is replaced with naive mesh tokenization as in previous methods [4, 5, 19]. This also serves as a fairer comparison with [5], as the original model of [5] was trained on data with fewer than 800 faces rather than 1600. Moreover, [5] is trained on a small total batch size of 64 while we observed a noticeable performance improvement when the batch size was increased to V2's 256. We sample 100K points on each mesh to calculate the aforementioned metrics. + +As shown in Table 1, our results indicate that V2 significantly outperforms its variant, demonstrating the effectiveness of AMT. It shows that AMT not only improves training + +Table 2. Comparison of Tokenization Methods. We compare various mesh tokenization methods and their impact on the generated mesh results in mesh generation. Note that the metrics are calculated by sampling 10K points cloud on each mesh. + +
MethodCD↓ (×10-2)ECD↓ (×10-2)NC↑#V↓#F↓V_Ratio↓F_Ratio↓S_Ratio↓Perplexity↓
Baseline2.47818.210.89395.4178.90.9740.9401.0001.150
Unsort8.15131.860.794117.4213.11.1891.2191.0001.234
PolyGen(AMT)3.22622.970.87293.2172.20.9280.9360.3721.589
AMT2.34819.330.904102.7187.11.0130.9830.4921.363
AMT(Swap)2.51719.860.913110.8198.91.0981.1020.4551.416
+ +speed and reduces memory pressure but also enhances generation quality. Notably, although V2 and its variant were trained for the same number of iterations, the variant consumed nearly two times the GPU hours of V2. Additionally, the table shows that AMT takes slightly more vertices and faces. A likely reason for this is that the variant's performance is still too weak, and it tends to ignore details and use a simpler topology when representing complex meshes with high face counts. We also observe that both AMT and the variant have vertex and face ratios greater than 1.0, meaning they use more faces on average relative to the ground truth, unlike the results in [5], which were less than 1 (around 0.88). We suspect this is because the dataset for V2 contains more complex meshes with over 800 faces, which causes the model to occasionally produce more complex topology for simple shapes. + +Comparison of Tokenization Methods. Below, we list the methods to be compared in the following sections, along with their specific implementation details. In the tokenization methods comparison experiments, we use the smaller OPT-125M [33] and select meshes with up to 400 faces from the aforementioned datasets as the experimental dataset. We sample 10K points on each mesh. + +- Baseline. This refers to the naive mesh tokenization method used in previous works, where each face is strictly represented by three vertices. +- PolyGen(AMT). This is a combination of the tokenization method from PolyGen [15] with AMT. Polygen first generates vertex coordinates and then expresses the faces by generating vertex indices. We discuss this setting in detail in the Supplementary Materials. +- AMT. This refers to the Adjacent Mesh Tokenization proposed in Sec. 3.1, as shown in Figure Aug1. +- AMT(Swap). As described in Sec. 3.1, this method combines the AMT algorithm with vertices swap. An additional special token is used to represent the swap operation. +- Unsort. This is based on the naive mesh tokenization method from previous works [15, 19], but without sorting the mesh. Instead, the mesh is used in the order in which it is stored. It is important to note that the meshes in Objaverse [6] are created by human, and their storage may already include some level of inherent order. The purpose + +of this method is to compare with the Baseline and verify the importance of sorting. + +The results are shown in Tab. 2. Unsort vs Baseline comparison validates the importance of tokenization method regularity for mesh generation. + +PolyGen(AMT) [15] achieves the best S_Ratio (sequence length compression ratio), indicating its high efficiency. However, there is a noticeable performance gap compared to Baseline and AMT, indicating the produced mesh quality is not high enough. The primary reason for this might be that the autoregressive model struggles to interact accurately with previously generated vertices when producing faces, which increases the difficulty of sequence learning. + +The results from AMT demonstrate that it shortens the token length without compromising mesh quality, as confirmed by its comparison with the Baseline. Additionally, in AMT(Swap), the introduction of the Swap special token further increases the compression ratio without affecting mesh quality. + +From the above experiments, we can conclude that both the regularity of the token sequence and the compression ratio are crucial. Although PolyGen [15] achieves a better compression ratio, its token sequence organization is not well-suited for sequence learning, making it a sub-optimal mesh tokenization method compared to AMT. In contrast, both AMT and AMT(Swap) reduce the compression ratio without increasing the difficulty of sequence learning, making them more suitable for mesh generation. + +# 5. Conclusion + +In this work, we present MeshAnything V2, a shape-conditioned Artist-Created Mesh (AM) generation model that generates AM aligned to given shapes. V2 significantly outperforms MeshAnything [5] in both performance and efficiency with our newly proposed Adjacent Mesh Tokenization (AMT). Different from previous methods that use three vertices to represent a face, AMT uses a single vertex whenever possible. Our experiments demonstrate that AMT averagely reduces the token sequence length by half. 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We propose MeshLLM, a method for effectively injecting text-serialized meshes into large language models, enabling the understanding and generation of 3D mesh through more natural conversational interactions. + +![](images/c34cb8704437dabb435d69abdeb4cdd6a72b971260381e2c97143a7fa1d8e7d6.jpg) + +![](images/340f1854b63ec94fa450dbf5c85a43ea3cdd53cf8207e3490ef117d3875b7cde.jpg) + +# Abstract + +We present MeshLLM, a novel framework that leverages large language models (LLMs) to understand and generate text-serialized 3D meshes. Our approach addresses key limitations in existing methods, including the limited dataset scale when catering to LLMs' token length and the loss of 3D structural information during mesh serialization. We introduce a Primitive-Mesh decomposition strategy, which divides 3D meshes into structurally meaningful subunits. This enables the creation of a large-scale dataset with $1500k+$ samples, almost $50 \times$ larger than previous methods, which aligns better with the LLM scaling law principles. Furthermore, we propose inferring face connectivity from vertices and local mesh assembly training strategies, significantly enhancing the LLMs' ability to capture mesh topology and spatial structures. Experiments show that MeshLLM outperforms the state-of-the-art LLaMA-Mesh in both mesh generation quality and shape understanding, highlighting its great potential in processing text-serialized 3D meshes. + +# 1. Introduction + +In recent years, large language models (LLMs), exemplified by the GPT [1, 6, 50, 54] series, have achieved groundbreaking advancements. Their powerful text generation and comprehension capabilities, along with their broad applicability, have continuously propelled them toward the goal of artificial general intelligence [3, 4, 13, 32, 59-62, 67]. Concurrently, the rise of multimodal learning has made the integration of language models with other modalities a prominent research focus, such as vision and speech [22, 43-45, 57, 73]. However, the modeling and comprehension of 3D data by LLMs remain underexplored. With the rapid development of virtual reality and robotic interaction, equipping LLMs with 3D perception and spatial reasoning capabilities has become a pressing challenge. + +Against this backdrop, existing research has attempted to integrate LLMs with 3D data [11, 21, 26, 33, 69, 71]. These methods typically rely on pretrained 3D encoders to map 3D structures into discrete token sequences before inputting them into LLMs for reasoning and question-answering tasks. While these methods have demonstrated + +![](images/cf6923d53ba331212db4e0cd6a6768ec22a0eb0917d57f5f30d778edfaa9766a.jpg) +Figure 2. Differences between LLaMA-Mesh and MeshLLM. LLaMA-Mesh applies a single text-mesh alignment optimization strategy on only $31\mathrm{k}$ available meshes. In contrast, our proposed MeshLLM leverages local mesh patches and thus expands the trainable data to $1500\mathrm{k}$ , enhancing model performance through vertex-to-face prediction and local mesh assembly strategies. + +the feasibility of LLMs in 3D tasks, they face several challenges, including dependency on specific encoders, the need to expand the LLMs' vocabulary, and potential information loss during encoding. Recently, LLaMA-Mesh [64] has proposed representing 3D meshes directly in text-serialized format, enabling LLMs to parse and generate 3D meshes in their native text-processing manner. This approach is based on two key observations. First, text-based mesh serialization requires no additional encoders, making it naturally compatible with LLMs' text modeling capabilities. Second, LLMs show compatibility with other rule-based text formats such as programming code [1, 48, 60] and SVG [53, 68, 74], suggesting the potential of LLMs on the simpler mesh. + +Despite pioneering the exploration of understanding and generating text-serialized mesh, LLaMA-Mesh poses new challenges to the research community: 1) Data scale limitations: As suggested by the Scaling Law [36], large-scale data is key to enhancing LLMs performance. However, due to the limitation of LLMs' token length, LLaMA-Mesh discards a large number of long mesh sequences, and only 31k samples are used for training, significantly constraining its potential. 2) Insufficient 3D structural awareness: Directly learning text-serialized mesh representations causes LLMs to overlook the inherent spatial structure (e.g., connectivity and semantic segmentation) of 3D mesh. Introducing dedicated mechanisms within LLMs to capture and maintain structural information remains a technical bottleneck. + +To address these challenges, this paper proposes MeshLLM, which differs from LLaMA-Mesh as shown in Fig. 2, and includes the following key designs: 1) Primitive-Mesh construction: As shown in Fig. 3, we first utilize K-Nearest Neighbors (KNN) to pre-decompose complex meshes into multiple localized subunits—termed Primitive-Mesh. This simple approach enables us to quickly construct a largescale dataset comprising $1500\mathrm{k}+$ training samples. However, these samples may not capture the underlying semantic coherence. To this end, we further leverage a high + +quality 3D mesh segmentation tool [70] to curate a subset of over 100K semantic-level Primitive-Mesh samples. These samples provide accurate structural and semantic details, much like LLMs process local windows in natural language, further enhancing the model's comprehension of 3D mesh. 2) Task-Specific training strategies: Based on the constructed dataset, we design two additional training tasks of vertex-face prediction and local mesh assembly. The former enhances LLMs' topological reasoning abilities by inferring face connectivity from vertices, while the latter improves global modeling capabilities by reconstructing complete meshes from local structures. This strategy enables the LLMs to robustly capture both local and global 3D structural information from the text-serialized mesh. Complementing these tasks, we implement a progressive training process that transitions from large-scale pretraining on the extensive Primitive-Mesh dataset to targeted fine-tuning on specific tasks. + +The main contributions of our work are as follows: + +- We introduce a mesh decomposition strategy to create $1500\mathrm{k}+$ Primitive-Meshes, expanding the scale of the trainable dataset by nearly 50 times, which deeply enhances the LLMs performance in text-serialized mesh generation and understanding. +- We propose the MeshLLM framework, incorporating vertex-face prediction and local mesh assembly training tasks to enhance LLMs' structural awareness of 3D mesh. +- Experimental results show that MeshLLM significantly outperforms LLaMA-Mesh, offering new insights into integrating LLMs with text-serialized mesh representations. + +# 2. Related Work + +Large Language Models and Multimodal Expansion. In recent years, LLMs have achieved remarkable advancements in natural language processing. Models such as GPT [1, 6, 50, 54], LLaMA [24, 61, 62], and the DeepSeek [5, 25, 41, 42] series have demonstrated exceptional capabilities in text generation and comprehension, driven by massive datasets and large-scale parameterization. LLMs are progressively expanding into the multimodal domain [20, 23, 28, 38, 39, 43, 44, 72, 73]. Approaches like LLaVA [43, 44], Video-LLaMA [73] and SpeechGPT [72] extend LLMs to image, video and speech processing, showcasing their potential in temporal and visual understanding. Due to challenges such as the difficulty of directly textualizing image and speech data or the excessive length of textualized data, these methods often require customized tokenizers to embed multimodal data into a unified space, thereby bridging the gap with language. + +Mesh Generation. Meshes are a fundamental 3D representation widely used in computer vision and graphics. Various methods have been proposed for mesh generation. + +![](images/fa5a349ac8cb80c6545fa33e8f616051915385122455ff8fa2d74fea0f2ad65c.jpg) +Figure 3. Illustration of Primitive-Mesh. We utilize both KNN clustering and semantic segmentation to partition meshes into Primitive-Meshes that retain local structural information. This strategy greatly expands the scale of the trainable dataset. + +![](images/e652fedfaf8e4be5c4c4c1c69fb12de807bf4b9756cf55e035463736b6f8bedd.jpg) + +Some approaches extract meshes from other 3D representations [12, 14, 19, 27, 34, 35, 47], such as SDF [52], NeRF [46], and Gaussian Spalting [37], prioritizing shape and color accuracy. However, the resulting meshes are often overly dense [9, 10]. In contrast, this work focuses on direct mesh generation. Existing methods in this way typically convert meshes into sequential representations [2, 8-10, 31, 49, 58, 65, 66] using predefined sorting strategies and learning their distribution on large-scale datasets for generation. For example, PolyGen [49] employs an autoregressive Transformer to generate mesh vertices and faces sequentially. MeshGPT [58] adopts a similar framework but encodes mesh using a pretrained VQ-VAE. MeshXL [8] combines implicit neural embeddings with explicit coordinates for generation. MeshAnything [9] converts 3D representations into point clouds before generating meshes, with MeshAnythingV2 [10] introducing a more compact sequence representation for improved efficiency. + +Mesh Understanding. Research on mesh understanding remains relatively limited. Y2Seq2Seq [29] aggregates multi-view semantic information to enhance mesh comprehension, while ShapeCaptioner [30] introduces part detection for finer-grained descriptions, and ShapeGPT [71] maps 3D shapes to word embeddings using an encoder to capture semantic information. Despite these advancements, existing methods treat mesh generation and understanding as separate tasks. Recently, LLaMA-Mesh [64] has explored integrating textualized meshes with LLMs, achieving unified generation and understanding, highlighting the potential of LLMs in directly modeling text-serialized meshes. However, LLaMA-Mesh suffers from inefficient utilization of existing datasets and loss of structural information during text serialization. This paper proposes improvements to address these issues, aiming to achieve more accurate mesh generation and understanding using LLMs. + +# 3. Method + +We first describe the process of converting 3D mesh data into a textual sequence compatible with LLMs. Next, we in + +troduce the concept of Primitive-Mesh. Finally, we outline the supervised fine-tuning tasks designed for LLMs, along with corresponding data formats and training workflows. + +# 3.1. Preliminaries: Text-serialized Mesh + +To enable 3D mesh data to be directly modeled by LLMs, we need to convert it into purely textual sequences. Similar to LLaMA-Mesh [64], we adopt the OBJ-format as the fundamental representation for a mesh. Given a mesh $\mathcal{M} = (\mathcal{V},\mathcal{F})$ , where $\mathcal{V} = \{v_{i}\}_{i = 1}^{N_{v}}$ represents $N_{v}$ vertices, each vertex $v_{i}\in \mathbb{R}^{3}$ corresponds to a spatial coordinate, i.e., $v_{i} = (x_{i},y_{i},z_{i})$ . The set of faces $\mathcal{F} = \{f_j\}_{j = 1}^{N_f}$ consists of $N_{f}$ triangular face elements defined by three vertex indices. + +The mesh is textualized through the following steps: 1) Quantization: The coordinate values of the mesh vertices are mapped to the integer values in [0, 64], thereby confining infinite numerical values to a finite range. Since characters 'v', 'f', and digits 0 through 64 are common symbols, there is no need to modify the LLMs' tokenizer or vocabulary. 2) Sorting: Employing a sorting strategy akin to PolyGen [49], we assign a unique sequence to each mesh. Specifically, vertices are sorted in ascending order based on their $z - y - x$ coordinates. Faces are then sorted according to the smallest vertex index within each face. 3) Textual sequence unfolding: The sorted mesh is flattened into a text format, with special characters (e.g., newline symbols) replaced to yield a final textual sequence representation: + +$$ +\mathcal {M} = [ \text {V e r t e x L i s t} ] \| [ \text {F a c e L i s t} ], \tag {1} +$$ + +where $\parallel$ denotes sequence concatenation. + +# 3.2. Primitive-Mesh + +Training LLMs directly on the above text-serialized mesh poses several challenges: 1) The limited token length of LLMs constrains the number of trainable samples; 2) The text sequences fail to convey the intrinsic 3D structure; 3) Learning from long sequences is inherently difficult for LLMs. To address these issues, we propose decomposing a mesh into multiple localized components, termed PrimitiveMesh, which can be formulated as follows: + +$$ +\mathcal {M} = \left\{\mathcal {M} _ {1}, \mathcal {M} _ {2}, \dots , \mathcal {M} _ {N} \right\}, \tag {2} +$$ + +where $N$ denotes the number of Primitive-Mesh units. This design is motivated by the observation that LLMs benefit from truncated local text in natural language tasks. Similarly, localized mesh components retain spatial information, aiding LLMs in perceiving 3D spatial structures. Furthermore, Primitive-Mesh sequences are shorter and significantly more numerous, allowing for deeper exploitation of LLMs' potential on large-scale datasets. + +As shown in Fig. 3, we construct Primitive-Mesh using two strategies: 1) KNN-Based: Given a mesh $\mathcal{M}$ , we begin by densely sampling point clouds from the mesh and + +![](images/ebb6ef3690069117132d8991f44e362fdf01425ef433ca8d6e98837e85e6510a.jpg) +Figure 4. Illustration of the MeshLLM framework. We adopt a progressive training process: Stage 1: Training on Primitive-Meshes obtained through KNN clustering, where two tasks are performed: predicting faces from vertices and assembling complete meshes from Primitive-Meshes. Stage 2: Training on more refined Primitive-Meshes generated by semantic segmentation, performing the same tasks as in Stage 1. Stage 3: Training on tasks specific to mesh generation and understanding. +Figure 5. Example of the constructed SFT data for training LLM. + +Human: A 3D mesh described as "a muscular humanoid"; its part mesh vertices are "v 32 12 11 v 32 21 13..." Based on this, please provide the possible part faces. LLM:f1 32f4 35... + +Human: Here are several part 3D files of a muscular humanoid: "v 32 12 11 v 32 21 13...", "v 26 1 12 v 32 1 12"... Based on these files, provide the possible full 3D model. +LLM: v 1 1 2 v 2 3 4 ... f 281 284 290 f 287 289 290 + +(1) pretrain on cluster primitive-mesh + +Human: A 3D mesh described as "a muscular humanoid"; its head part mesh vertices are "v 28 51 23 v 33 51 23..." Based on this, please provide the possible part faces. LLM:f132f435... + +Human: Several 3D part meshes of a muscular humanoid are: head: "v012v234...", leg: "v023v456... Based on these files, provide the possible full 3D model. LLM:v112v234...f281284290f287 289290 + +(2) pretrain on semantic primitive-mesh + +Human: Create a 3D obj mesh using the following description: a muscular humanoid character with armored and horn-like structures. +LLM: v012v234 ...f132f435 ... + +Human: A 3D obj file is as below: v 0 1 2 v 2 3 4 v 0 3 ... f 1 3 2 f 4 3 5 ... What is this? +LLM: This is a muscular humanoid character with armored and horn-like structures. + +(3) finetune on specific task + +then apply farthest point sampling (FPS) and KNN to identify central points and point clusters, thereby partitioning the mesh into multiple local regions. This approach is computationally efficient and applicable to any existing mesh dataset. Using this strategy, we generate over $1500\mathrm{k}+$ training samples. However, the mesh parts obtained through KNN may lack semantic coherence. Therefore, we construct an additional dataset to complement and refine the existing data. 2) Semantic-based: To obtain Primitive-Meshes with well-defined semantic boundaries, we leverage 3DSAMPart [70] to perform mesh segmentation on a curated subset after aesthetically filtering [56]. This yields over $100\mathrm{k}+$ high-quality Primitive-Mesh samples. As depicted in Fig. 3, this method accurately segments a humanoid mesh into regions such as the head, hands, and legs. These semantically meaningful datasets further enhance the LLMs' comprehension of high-level semantic information. + +# 3.3. Training Task Design + +Building on the constructed dataset, we design four supervised fine-tuning tasks to enhance the LLMs' ability to un- + +derstand and generate 3D meshes, as shown in Fig. 4. + +Vertex-Face Prediction. Given a set of vertex coordinates $\mathcal{V}$ and its corresponding faces $\mathcal{F}$ , the LLM is optimized according to the following objective: + +$$ +\max _ {\theta} P (\mathcal {F} \mid \mathcal {V}, \theta), \tag {3} +$$ + +where $P$ is modeled by the LLM, and $\theta$ is its parameters. This task enables the LLM to predict face connectivity given vertices, thereby learning the topological relationships between vertices. + +Mesh Assembly. Given a complete mesh $\mathcal{M}$ and its corresponding set of Primitive-Mesh components $\{M_{ij}\}_{i=1}^{k}$ , the LLM learns to reconstruct the full mesh by optimizing: + +$$ +\max _ {\theta} P \left(\mathcal {M} \mid \left\{\mathcal {M} _ {i} \right\} _ {i = 1} ^ {k}, \theta\right). \tag {4} +$$ + +This task captures the geometric relationships between local Primitive-Mesh units, mitigating the loss of 3D spatial information inherent in textual serialization, thereby improving the model's ability to infer mesh structures. + +![](images/9d8478f7d0b591b2a32371f9d3b47b260941281e9b8e222d2fa85313d4eb656f.jpg) +Figure 6. Gallery results. MeshLLM demonstrates an ability to generate diverse and high-quality meshes. + +Mesh Understanding. Given a mesh $\mathcal{M}$ and its textual description $\mathcal{T}$ , the following learning objective is constructed: + +$$ +\max _ {\theta} P (\mathcal {T} \mid \mathcal {M}, \theta). \tag {5} +$$ + +This enables the LLM to generate accurate and fluent descriptions based on mesh data, thereby acquiring an understanding of high-level semantic information. + +Mesh Generation. Given a textual description $\mathcal{T}$ and a Mesh $\mathcal{M}$ , the LLM is trained to optimize: + +$$ +\max _ {\theta} P (\mathcal {M} \mid \mathcal {T}, \theta). \tag {6} +$$ + +This encourages LLM to learn to generate plausible mesh structures from textual descriptions. + +It is important to note that these tasks are not independent but are implemented in a progressive training process as shown in Fig. 4. Initially, vertex-face prediction and mesh assembly tasks familiarize the model with fundamental mesh structures and local semantics. Subsequently, mesh understanding and mesh generation tasks refine the model's grasp of complex 3D structures and high-level semantics. + +# 3.4. SFT Data Curation + +In LLMs' downstream task alignment training, Supervised Fine-Tuning (SFT) is one of the most widely used strategies. As illustrated in Fig. 5, we construct various forms of SFT data encompassing the aforementioned four training tasks. It employs high-quality input-output data pairs with standard language modeling objectives to fine-tune LLMs, thereby better adapting LLM to 3D tasks. + +# 4. Experimental Results + +# 4.1. Implementation Details + +Dataset. MeshLLM is trained primarily on two datasets: Objaverse-XL [15] (including the sketch and GitHub subsets) and ShapeNet [7]. For the construction of KNN-based Primitive-Mesh data, we perform clustering with 2 to 10 categories based on the number of faces in the original mesh, resulting in over $1500\mathrm{k}+$ Primitive-Meshes. For the creation of semantic-based Primitive-Meshes, we first conduct an aesthetic evaluation [56] of the original datasets, marking approximately $25\mathrm{k}+$ high-quality mesh subsets. We then generate semantic-level Primitive-Meshes on this subset using the SamPart3D method [70], yielding over $100\mathrm{k}+$ semantic-level Primitive-Meshes. This process utilized 128 A800 GPUs and took approximately 3 days. For the mesh assembly, understanding and generation tasks involving full-mesh data, we follow a procedure similar to PolyGen [49]. Specifically, we apply planar simplification to meshes with fewer than 3k faces and restrict the number of faces in the final full-mesh representation to 800, ensuring compatibility with the LLM's maximum token length. We follow dataset split configurations from previous works [8, 49], extracting $10\%$ of the 4 subsets (chair, table, bench, lamp) from ShapeNet and 1K samples from Objaverse-XL as the test set to evaluate the quality of mesh generation and understanding, respectively. + +Training Details. We use LLaMA-8B-Instruct [24] as the base LLM model and finetune its full 8 billion parameters based on our constructed data. We employ the AdamW optimizer with a learning rate of 2e-5 and set the maximum context length to 8192. We train for 2 epochs on the KNN-based Primitive-Mesh dataset, 3 epochs on the se + +![](images/63e408b07b6d38df9ebb71a86524f5ee4120fc1c582ad92a727306610b92679e.jpg) +Figure 7. Dialogue results. MeshLLM extends the capabilities of LLMs to the domain of 3D mesh while retaining their advanced dialogue abilities, such as question-answering and mathematical reasoning. This expansion enables MeshLLM to understand and generate 3D meshes through natural and intuitive language interactions, further solidifying LLMs as versatile and powerful tools. + +matic Primitive-Mesh dataset, and 3 epochs on the mesh-generation and understanding datasets. Additionally, to mitigate catastrophic forgetting and retain the LLM's conversational capabilities, we randomly sample the data from the previous phase and ultra-chat dataset [17] with a $30\%$ probability during each training phase. We employ data augmentation when training meshes, including random scaling and random translation. The training process is conducted using 128 A800 GPUs and took approximately 6 days. + +Metrics. To evaluate the quality of mesh generation, we adopt the same metrics as previous studies [8, 18, 49, 58]. These metrics include Minimum Matching Distance (MMD, lower is better), Coverage (COV, higher is better), and 1-Nearest Neighbor Accuracy (1-NNA, the optimal value is $50\%$ ). Please refer to the supplementary materials for a detailed explanation. We also calculate the Frechet Inception Distance (FID) and Kernel Inception Distance (KID) on 8 rendered images for feature-level evaluation. We generate 1000 meshes for each evaluated category and report their average metrics. For the mesh understanding task, we use the BLEU-1 [51], CIDEr [63], ME-TEOR [16], and ROUGE [40] metrics to evaluate the accuracy of the generated captions. In addition, we render 8 different images of the meshes and compute the CLIP similarity [55] between these images and the text to assess the alignment between the mesh and the text. + +Baselines. Our method primarily focuses on enabling LLMs to perceive and generate text-serialized mesh. The most directly related baseline to our approach is LLaMA + +Mesh [64]. Additionally, we also compare the mesh quality with MeshXL (under text-conditional settings) [8] and PolyGen (class-conditional) [49]. All comparative experiments used the same text prompt, except for PolyGen, which only supports inputting the category of mesh. + +# 4.2. Dialogue Ability + +We design a variety of interactive dialogue scenarios that simulate user interactions with mesh through natural language instructions. Experimental results in Fig. 1 and Fig. 7 indicate that MeshLLM not only generates 3D mesh structures that faithfully match the textual descriptions provided by the user but also provides explanatory feedback on mesh details and topological structures during the dialogue while retaining its inherent natural language generation ability, facilitating smooth and coherent multi-turn conversations. These findings demonstrate that our approach successfully integrates text-serialized 3D information into LLMs. In particular, the constructed data sets and training pipeline are fully compatible with any existing LLM without necessitating additional complex encoder-decoder designs. + +# 4.3. Performance Evaluation + +We compare MeshLLM with existing methods across two primary dimensions: mesh generation quality and mesh understanding capability. + +Mesh Generation. Fig. 6 demonstrates the ability of our method to generate diverse meshes. We further compare it with state-of-the-art methods in Fig. 8. It can be seen that MeshLLM generates finely detailed geometric struc + +![](images/0ab69ff6f95c44226273fb88f12b0f9320ebca51fe9f26a73d402e3ec2cab509.jpg) +Figure 8. Comparisons on the mesh generation. MeshLLM generates 3D meshes with clean geometric details, outperforming the LLM-based LLaMA-Mesh and achieving performance comparable to Polygen and MeshXL, which are specifically designed for mesh generation. + +![](images/c3c32d563285fb1adeeeefdf3b9d15964aae8540715213271f74f023ec05c3c1.jpg) +Figure 9. Comparisons on the mesh understanding. The green text is generated by LLaMA-Mesh, while the purple text is produced by our MeshLLM. MeshLLM better captures the semantic information of the mesh, generating more accurate textual descriptions. + +tures, achieving significantly superior results compared to LLaMA-Mesh. Moreover, when compared with methods specifically designed for mesh generation like PolyGen and MeshXL, the overall performance of MeshLLM is comparable. Quantitative evaluations, as presented in Tab. 1, reveal that our method surpasses LLaMA-Mesh on multiple metrics and achieves a performance comparable to that of MeshXL, thereby validating the effectiveness of our Primitive-Mesh construction strategy and training task design. It is worth noting that while MeshXL and PolyGen excel in mesh generation tasks, neither possesses mesh understanding or interactive dialogue capabilities, which are + +unique advantages of our LLM-based approach. + +Mesh Understanding. As shown in Fig. 9 and Tab. 2, we qualitatively and quantitatively evaluate the mesh textual descriptions generated by the LLM. MeshLLM excels at capturing high-level semantic information of meshes. The generated descriptions are fluent and accurate and effectively reflect the structural characteristics of the meshes, which significantly surpass the LLaMA-Mesh baseline. The improvement primarily stems from the finer-grained semantic information embedded in Primitive-Meshes, as well as the mesh assembly task, which reinforces the connection between local and global semantics. + +Table 1. Quantitative comparisons of mesh quality. Bold and underline denote the 1st and 2nd best-performing models, respectively. MeshLLM surpasses the same-type method LLaMA-Mesh and is comparable to encoder-based MeshXL. However, unlike our MeshLLM, MeshXL lacks the ability to understand mesh and dialogue with users. + +
CapacitiesChairTableBenchLamp
Methodgeneration understanding dialogueCOV↑MMD↓1-NNAFID↓KID↓COV↑MMD↓1-NNAFID↓KID↓COV↑MMD↓1-NNAFID↓KID↓COV↑MMD↓1-NNAFID↓KID↓
PolyGen [49]✓××8.2315.7288.4460.2041.9242.923.9470.3856.1715.7232.504.4688.7569.9312.3536.227.4875.0463.8910.47
MeshXL [8]✓××46.163.4558.7640.332.4147.743.1856.7442.641.4251.422.0541.4241.81.2651.044.7246.1333.551.06
LLaMA-Mesh [64]✓✓✓19.538.6477.7849.8323.3738.984.7275.6060.4910.7136.574.2270.5356.748.9531.069.9882.7665.2912.01
MeshLLM✓✓✓47.335.7260.8242.392.2549.263.1558.7739.594.2649.383.3460.7936.631.0949.853.3059.4835.701.44
+ +Table 2. Quantitative comparisons of mesh understanding. MeshLLM significantly surpasses the LLaMA-Mesh method. + +
MethodBLEU-1↑CIDEr↑Meteor↑ROUGE↑CLIP↑
LLaMA-Mesh0.4830.3970.1940.3560.124
MeshLLM0.7631.7530.4450.7020.391
+ +Table 3. Ablation studies of MeshLLM. "PM" denotes PrimitiveMesh. We report the impact of key components on mesh generation (chair class) and understanding. + +
Mesh Generation
COV↑MMD↓1-NNAFID↓KID↓
w/o KNN PM42.365.7472.4049.336.44
w/o semantic PM41.366.0668.8752.768.29
w/o v to f44.805.8161.7748.684.90
w/o mesh assembly40.176.4370.2554.267.32
Full47.335.7260.8242.392.25
Mesh Understanding
BLEU-1↑CIDEr↑Meteor↑ROUGE↑CLIP↑
w/o KNN PM0.6920.9210.3570.6100.324
w/o semantic PM0.6460.7820.3010.5430.282
w/o v to f0.7371.2290.4330.6270.376
w/o mesh assembly0.7050.8940.3590.5960.344
Full0.7631.7530.4450.7020.391
+ +# 4.4. Ablation Studies + +We conduct a series of ablation experiments, the results of which are summarized in Tab. 3. The primary ablation settings include: 1) KNN-based Primitive-Mesh: This design is critical for constructing a large-scale usable dataset. Removing it leads to a significant decline in all evaluation metrics, underscoring its essential role in the MeshLLM framework. 2) Semantic-based Primitive-Mesh: This component is derived from high-quality, filtered meshes, providing more accurate and rich semantic information. Excluding it results in a slight reduction in mesh generation quality and a marked degradation in mesh understanding performance. 3) Vertex-Face prediction strategy: This module facilitates the learning of topological relationships between vertices and faces. Its removal causes deviations in reconstructing the mesh topology, resulting in a significant drop in overall generation quality. 4) Mesh assembly strategy: Designed to capture global spatial relationships among text-serialized 3D data, this module is crucial for enhancing global structural reconstruction. Ablating this component also leads to + +a pronounced performance decrease. + +# 5. Limitation and Future Work + +While MeshLLM shows the potential of LLMs for 3D mesh understanding and generation, certain limitations remain, highlighting future research areas: 1) The scale of available mesh data is still vastly smaller than the corpora used in NLP. It is critical to construct larger and higher-quality datasets to fully leverage LLMs' abilities. 2) The limited dataset size results in imprecise alignment between text and geometric structures, constraining the ability to perform fine-grained generation and refinement of meshes. Incorporating additional modalities, like images, to encode structural information could enhance LLMs' performance, especially when data is scarce. 3) Handling more complex meshes can benefit from compact serialization methods (e.g., MeshAnything-V2 [10]) and LLMs with larger token capacities. These optimizations are orthogonal to our current work. 4) Another promising direction is designing external intelligent agents to analyze interaction results and leverage reinforcement learning to refine geometric accuracy and achieve specific aesthetic objectives. + +# 6. Conclusions + +In this paper, we propose MeshLLM, a novel approach that rethinks the paradigm of generating text-serialized meshes using Large Language Models, which addresses two key limitations of existing approaches: 1) insufficient utilization of available datasets and 2) disruption of underlying 3D structures caused by 2D serialization. Our solution introduces a Primitive-Mesh strategy to divide meshes, expanding the trainable dataset to over $1500\mathrm{k}$ samples. Additionally, we construct a meticulously curated dataset containing more than $100\mathrm{k}$ high-quality, semantically segmented meshes to enhance the LLM's ability to understand and reason mesh structures. Building on the constructed dataset, we propose a structured training paradigm that models meshes hierarchically from vertices to faces and mesh assembly, enabling LLMs to effectively perceive the 3D world. We hope that our findings will foster deeper integration between LLMs and the 3D mesh domain, offering the research community a new perspective for developing powerful multimodal intelligent agents. + +# Acknowledgments + +This work was supported by the National Natural Science Foundation of China (U24B6013), China Scholarship Council (202406020139), and JSPS Grant-in-Aid, Japan (JP23K16921). M.-H. 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Denoising diffusion models based on MeshMamba are able to generate dense 3D articulated meshes with around 10,000 vertices, capturing clothing deformations and hand grasp poses. MeshMamba can generate a mesh with 10475 vertices in a few seconds using 100 DDIM sampling steps, which is $6 - 9\times$ faster than diffusion transformer. + +![](images/bf4d0b404fc3ff1da8160bf3df75e14fab8515fb8f46c816c96cbee21f8a8989.jpg) + +![](images/63959203082d42e8501c2204bfdce80b11d6229299ceb63093e904b88c0a0183.jpg) + +# Abstract + +In this paper, we introduce MeshMamba, a neural network model for learning 3D articulated mesh models by employing the recently proposed Mamba State Space Models (Mamba-SSMs). MeshMamba is efficient and scalable in handling a large number of input tokens, enabling the generation and reconstruction of body mesh models with more than 10,000 vertices, capturing clothing and hand geometries. The key to effectively learning MeshMamba is the serialization technique of mesh vertices into orderings that are easily processed by Mamba. This is achieved by sorting the vertices based on body part annotations or the 3D vertex locations of a template mesh, such that the ordering respects the structure of articulated shapes. Based on MeshMamba, we design 1) MambaDiff3D, a denoising diffusion model for generating 3D articulated meshes and 2) Mamba-HMR, a 3D human mesh recovery model that reconstructs a human body shape and pose from a single image. Experimental results showed that MambaDiff3D can generate dense 3D human meshes in clothes, with grasping hands, etc., and outperforms previous approaches in the 3D human shape generation task. Additionally, Mamba-HMR extends the capabilities of previous non-parametric human mesh recovery approaches, which were limited to handling body-only poses using around 500 vertex tokens, to the whole-body setting with face and hands, while achiev + +ing competitive performance in (near) real-time. + +# 1. Introduction + +Generating and reconstructing 3D articulated mesh models in diverse body shapes and poses is a crucial problem in computer vision and computer graphics, with broad applications in VR, AR, gaming and VFX. The main approaches for solving these tasks can be categorized into parametric and non-parametric vertex-based paradigms [73]. Parametric approaches [30, 90, 91] rely on human body models, such as SMPL [44] and SMPL-X [55], to represent a human body using shape and pose parameters. In contrast, vertex-based approaches [14, 39] directly manipulate the mesh vertices of a surface and reconstruct them using neural networks. The first paradigm dominates the current field due to its compact representation of body kinematics, while the latter employs a neural network friendly representation of a 3D surface [48, 63, 94] and holds the potential to capture complex deformations including those of clothing in a general and unified manner. In both paradigms, transformers have become the dominant architecture which offers large improvements in reconstruction performance especially when a large-scale training data is available. + +However, the main challenge with transformers is their quadratic complexity with respect to the input sequence length [72]. In particular, vertex-based transformer + +approaches are typically limited to processing coarse-resolution meshes with around 500 vertices [38, 39] due to memory consumption and inference speed constraints. These approaches thus require an additional upsampling process to obtain a full-resolution mesh with several thousand vertices but it would lose local geometric shapes, which is why the current approaches are limited to body-only pose reconstruction without hand pose and facial expression. + +State Space Models (SSMs) are a family of sequence model that extend RNNs and have recently attracted attention as a potential next-generation sequence model following transformers [22]. By representing transitions between time frames using a linear system, a sequence can be processed using convolution. Unlike RNNs, SSMs can therefore be trained on all the frames simultaneously, akin to transformer, while still maintaining efficient inference speed. Notably, Mamba [21] introduced hardware-friendly selective mechanisms for modeling transitions from data, enhancing the expressivity of SSMs. Mamba has quickly spread to various computer vision tasks, including processing images, videos and 3D point clouds [36]. The key to gaining Mamba's potential in these domains lies in how to serialize the input data into a sequence, as opposed to transformer that is agnostic to sequence ordering. + +In this paper, we present a method for generating and reconstructing dense 3D articulated mesh models based on Mamba-SSMs, dubbed MeshMamba. To serialize mesh vertices into a sequence that is easier for SSMs to process, we propose a vertex serialization technique that exploits body part UV maps [58] and the 3D coordinates of a template body model. Additionally, we explore ways to preserve local geometry of a dense mesh surface by incorporating surface normals through gradient domain mesh representation and a training loss. + +Experimental results show that MeshMamba outperforms previous generative models in unconditional 3D human mesh generation tasks. More importantly, MeshMamba can generate dense human body meshes with more than 10,000 vertices, capturing clothing deformation and hand grasp poses (Fig. 1). Furthermore, we present a novel Mamba-based whole-body 3D human mesh recovery approach, which runs in real-time. + +The contributions of this paper include: + +- MeshMamba: a network model for learning dense 3D articulated meshes based on Mamba-SSMs. We design a serialization technique of mesh vertices based on body part UV maps and the 3D coordinates of a template body mesh for effective training of MeshMamba. +- MambaDiff3D: a denoising diffusion model for generating 3D articulated meshes based on MeshMamba. MambaDiff3D is able to generate whole-body human body models, capturing deformations of clothing and hands. It + +is faster than the transformer-based approach by a factor of $\times 6 - 9$ and outperforms previous generative models in the unconditional 3D human generation task. + +- Mamba-HMR: a method for 3D human mesh reconstruction from a single image. Mamba-HMR performs competitively with previous approaches in whole-body human mesh reconstruction. It increases the number of input vertex tokens to more than 10,000 vertices, while running at a (near) real-time rate. + +# 2. Related Work + +State space models (SSMs) Drawing inspiration from the continuous formulation of state space models in control theory, SSMs have been proposed as a solution to efficiently learn long-range dependencies in input sequences [24, 54, 76]. Notably, Mamba [21] introduced a selective scan mechanism to enhance the expressiveness of SSMs by modeling transitions between time frames as a function of the input data. Although Mamba was originally proposed for learning long-range sequences in time-series data such as signals and language, it has quickly been adopted across various domains. In the vision domain, ViM [97] was proposed to enhance vision transformers by employing a bidirectional scan mechanism to handle high-resolution images. DiS [95] extended the ViM model to the image generation task. Mamba has been adapted to the 3D domain, so far, for point cloud processing and analysis [36, 93]. + +Generative models for 3D shape and pose For 3D shape and pose reconstruction, various generative models have been used to build 3D pose and shape priors for various downstream tasks: e.g. variational autoencoders (VAEs) [2, 16, 18, 28, 47, 55, 57, 71, 78, 87, 96], generative adversarial networks (GANs) [11, 12, 17, 30], normalizing flows [5, 34, 80, 88] and diffusion models [20, 45, 64, 92]. Some works [1, 26] combine generative models and gradient-domain deformable models to achieve detail-preserving shape deformation with neural network models. Extending the ideas from 2D [25, 59] and 3D domain [46, 89], recent works utilize diffusion models in 3D human recognition [13, 20, 35, 41, 43, 64]. ScoreHMR effectively solves inverse problems for various applications [66] without retraining the task-agnostic diffusion model by guiding its denoising process with a task specific score. ROHM [92] and DPoser [45] design human pose and motion priors based on diffusion models. + +3D human mesh recovery from image Human mesh recovery approaches [73] estimate a 3D human body mesh from a single image or video frames, which can be broadly divided into 1) parametric approaches that regress the body shape and pose parameters of human body models [7, 13, 30, 90] and 2) non-parametric approaches that learns a regression model from an image to 3D vertex coordinates [15, 33, 39, 41, 49, 84]. Transformer has been em + +![](images/b4e361fee1573b7402552bc58c86284504e72a4064f67f510e14550beecd852e.jpg) +Figure 2. Network block and architectures of MeshMamba. (a) Mamba block with feature permutation based on serialized tokens. (b) Vertex serialization using DensePose IUV annotations or $xyz$ vertex coordinates of a template mesh. (c) Our diffusion model takes in the noisy 3D coordinates of surface vertices $\mathbf{x}_t \in \mathbb{R}^{N \times 3}$ and predicts noise. (d) Our 3D human mesh recovery model extracts image features from CNN and inputs joint queries and mesh vertex queries to Mamba blocks, along with position embedding. + +![](images/6610a83c8d393b8fef71545fb2a4158e4867706a5bc91c87742da26edece1e8c.jpg) + +![](images/11c71caefe15d80092066e2679cfecbae93ef184994df38038673f2b47a78485.jpg) + +ployed in both parametric and vertex-based human mesh recovery, demonstrating strong performance [14, 19, 37-39, 86]. Building on these transformer network architectures, recent studies have developed foundational models for 3D human body pose and shape reconstruction by learning from various datasets, including both synthetic and real data [10]. For whole-body human mesh recovery that reconstructs not only body pose but also hands and face, the dominant approaches in the field are parametric-based [4, 10, 37, 56, 60, 69]. Neural localization field (NLF) [63] is a recent whole-body human mesh reconstruction technique that relies on a continuous shape representation and is able to learn from different dataset formats e.g. body joints, SMPL or SMPL-X meshes. Yet its reconstruction quality around face and hands still has room for improvements. + +# 3. Background + +State space models (SSMs) A state-space model represents the dynamics of a system using a set of first-order differential equations which describe linear time-invariant (LTI) systems [21, 22]. A multi-input, multi-output LTI system, where the current inputs and states determine changes in the state space of the system, can be described by the following continuous state-space equation: + +$$ +h ^ {\prime} (t) = \mathbf {A} h (t) + \mathbf {B} x (t), \quad y (t) = \mathbf {C} h (t) \tag {1} +$$ + +where $x(t)$ , $y(t)$ and $h(t)$ are the inputs, outputs and hidden states of the current system, respectively. $\mathbf{A} \in \mathbb{R}^{N \times N}$ , $\mathbf{B} \in \mathbb{R}^{N \times 1}$ and $\mathbf{C} \in \mathbb{R}^{1 \times N}$ are continuous parameter of the system. Based on the zero-order hold (ZOH) rule with a time scale parameter $\Delta$ , the continuous state space equation in Eq. (1) can be discretized as follows: + +$$ +h ^ {\prime} (t) = \bar {\mathbf {A}} h (t) + \bar {\mathbf {B}} x (t), \quad y (t) = \bar {\mathbf {C}} h (t) \tag {2} +$$ + +where $\bar{\mathbf{A}} = \exp (\Delta \mathbf{A})$ , $\bar{\mathbf{B}} = (\Delta \mathbf{A})^{-1}(\exp (\Delta \mathbf{A}) - I)\cdot \Delta \mathbf{B}$ and $\bar{\mathbf{C}} = \mathbf{C}$ are the discrete parameters. Eq. (2) can be rewritten using global convolution for parallelization: + +$$ +\bar {\mathbf {K}} = \left(\bar {\mathbf {C B}}, \bar {\mathbf {C A B}}, \dots , \bar {\mathbf {C A}} ^ {k} \bar {\mathbf {B}} \dots\right), y = x * \bar {\mathbf {K}} \tag {3} +$$ + +Mamba proposes a linear time-variant (LTV) system formulation with a selective scan mechanism by introducing time-varying system parameters. + +$$ +h ^ {\prime} (t) = \mathbf {A} (\bar {\mathbf {x}} (\mathbf {t})) h (t) + \mathbf {B} (\bar {\mathbf {x}} (\mathbf {t})) x (t), y (t) = \mathbf {C} (\mathbf {x} (\mathbf {t})) h (t) +$$ + +This allows Mamba to overcome the limitations of previous SSMs, i.e., the lack of context awareness, in other words their ability to selectively remember or forget relevant information. However, this also makes the convolution computation in Eq. (3) impractical. To address this, Mamba introduces a hardware-aware parallel algorithm for selective scanning, which achieves near-linear complexity. + +# 4. MeshMamba + +We propose MeshMamba, Mamba-based neural network architectures for 3D mesh generation and reconstruction. To do so, we employ a standard Mamba block [21], which consists of a selective SSM layer, linear layers, a convolution layer and nonlinear activation layers (Fig. 2 (a)). The main challenge in adapting Mamba for 3D data lies in the design of strategy for converting the data into a 1D sequence [36, 42, 93]. We therefore design a serialization technique for mesh vertices (Sec. 4.1) based on body parts or a template mesh shape structure (Fig. 2 (b)). With our MeshMamba layer, equipped with this serialization technique, we develop a generative diffusion model for 3D human body mesh generation, named MambaDiff3D (Sec. 4.2), and a + +regression model for recovering a 3D human mesh recovery from an image, named Mamba-HMR (Sec. 4.3). The network architectures are illustrated in Fig. 2 (c) and (d). + +Notation and assumption We represent an articulated body using a mesh comprising $N$ vertices and $F$ triangle faces. The 3D positions of vertices are denoted as $\mathbf{x} \in \mathbb{R}^{N \times 3}$ . To train our MeshMamba models, we prepare a template mesh $\mathcal{M}_0$ in a canonical pose, along with training meshes $\mathcal{M}_1 \ldots \mathcal{M}_M$ in various body poses and shapes. We assume that the connectivity of the template and all training meshes is the same; in other words, the training meshes are constructed by fitting the template mesh and the point-to-point correspondences between the meshes are known. + +# 4.1. Vertex serialization + +Unlike transformers, Mamba requires ordered input sequences [76]. Therefore, it is crucial to design a method for serializing 3D mesh vertices into a 1D sequence so that Mamba can process them more effectively. Recent Mamba approaches for 3D point cloud analysis use space-filling curves predefined in the volumetric space like z-order and Hilbert curves to sort points [36, 42, 93]. However, these methods are unsuitable for mesh generation and reconstruction tasks, which start from random noise or images and deal with deforming articulated bodies. + +Our proposed serialization strategy is as follows. Given training meshes with known correspondences, we can serialize all training meshes consistently using sorting indices derived from a template mesh. We explore two serialization approaches that leverage body part UV maps from Dense-Pose annotations [58] and 3D coordinates of a template body mesh, which derive sorting indices directly from mesh vertices without transforming them into other representations like 3D voxels (Fig. 2 (b)). To serialize mesh vertices based on their corresponding 3D coordinates in a template mesh, which is in a T-pose for the human case, we sort the vertices primarily along one of the three axes (e.g., x, y, or z). If the values are identical along the primary axis, we then consider the second axis, followed by the third. Similarly, with the DensePose body part IUV maps, we sort the mesh vertices primarily based on the I segmentation map, followed by the U and V maps. + +Combining multiple serialization strategies at each Mamba layer helps MeshMamba learn mesh features effectively as reported in previous works e.g. [93]. For T-posede nce coordinates, we generate six serialization methods by varying the order and sign of the x, y, and z axes: "xyz", "-xyz", "yzx", "-yzx", "zxy", and "-zxy". For DensePose annotations, the 24 body parts are sorted based on their centroid coordinates using the same six variations as with the above template mesh based serialization. Then, the vertices within each part are sorted by U and V maps. However, changing serialization approaches for all layers requires in + +dexing through tokens or "gather" operations, which can be time-consuming for a deep model with multiple Mamba layers. To balance computational efficiency and shape reconstruction performance, we found that using a combination of two different serialization strategies is effective. Specifically, one serialization strategy is applied across all Mamba layers except for one layer, where the other strategy is used. + +# 4.2. MambaDiff3D + +Network model Our diffusion model for 3D generation is inspired by U-ViT [3] and its variants [85, 95], which we name MambaDiff3D. It takes in the noisy 3D coordinates of surface vertices $\mathbf{x}_t \in \mathbb{R}^{N \times 3}$ and predicts noise $\epsilon_{\theta}^x \in \mathbb{R}^{N \times 3}$ (Fig. 2 (c)). Our MambaDiff3D consists of $L + 1$ layers of Mamba blocks and input/output MLP layers. The Mamba blocks are categorized into the first half shallow group with $L / 2$ blocks, a mid block and a second half deep group with $L / 2$ blocks. Skip connections are used to connect the blocks in the first group to those in the second group. Each Mamba block contains hidden layers with $d$ channels. The input MLP layer converts $\mathbf{x}_t$ into $d$ -dimensional embedding features and the output MLP layer converts the Mamba-processed features into $\epsilon_{\theta}^x$ . The time embedding corresponding to timestep $t_x$ is incorporated to every Mamba block by summation. + +Train loss and sampling We adopt the v-prediction parameterization [62] for the training objective of MambaDiff3D, along with a cosine variance scheduler. This corresponds to the training loss with the weighting $w_{t} = e^{-\lambda_{t} / 2}$ [32]: + +$$ +L = \mathbb {E} _ {t, \mathbf {x} _ {0}, \epsilon} w _ {t} \| \epsilon - \epsilon_ {\theta} (\mathbf {x} _ {t}, t) \| _ {2} ^ {2} \tag {4} +$$ + +For sampling, we employ the DDIM [65] sampler. We set the diffusion time step to $T = 1000$ and tested sampling steps with [50, 100, 250]. + +Combining surface normals and vertex positions The recent papers [51, 83] reported that vertex-based generation is prone to local noise, whereas integrating learned Jacobian-fields [1, 67] produces globally distorted meshes likely due to error accumulations in tangential components. As our method generates vertices of a dense mesh, we experience this issue especially when training is not long enough or the number of sampling steps is small. + +Instead of generating 3D positions at vertices or Jacobians at triangles, we perform generation of position and normal at each vertex. Then, inspired by the techniques that transfer details in the gradient domain [9, 52, 77], we combine surface normals and positions by solving a Poisson system. This allows for smoother reconstruction by removing noise in vertices, while maintaining surface details and global shape structure (Fig. 7). + +Specifically, in a similar manner as in [52], the gradient at each triangle $m$ is obtained by combining smoothed ver + +tex positions and surface normals in the gradient domain: $\mathbf{G}_m = \mathbf{R}_m\mathbf{T}_m$ , where $\mathbf{T}_m \in \mathbb{R}^{3 \times 3}$ is the Jacobian of the generated vertices after smoothing and $\mathbf{R}_m \in \mathbb{R}^{3 \times 3}$ is the relative rotation between the generated normals and those obtained from smoothed vertices. These gradients are then plugged into the Poisson system [1, 67] to stitch together into a whole mesh. Note that the right-hand side of the Poisson system does not change for the mesh with the same connectivity. Thus, we can reuse the factorization of the system, thereby maintaining the overall generation time without a large overhead [1, 67]. Differently from previous approaches [1], our approach is not end-to-end, i.e., the generation and the surface reconstruction by solving the Poisson system are done independently, where no gradient is flowing from the Poisson system to the MambaDiff3D model during training. + +# 4.3. Mamba-HMR + +We present a simple yet effective vertex-based baseline for human mesh recovery based on our MeshMamba, dubbed Mamba-HMR. As Mamba-HMR deals with the full-resolution SMPL and SMPL-X meshes without down sampling them, Mamba-HMR is applicable to both body-only and whole-body settings. + +Network model The network architecture of Mamba-HMR follows Mesh transformer [39] where we essentially replace their transformer blocks with MeshMamba blocks with our vertex serialization strategies. Our Mamba-HMR feeds CNNs image features to Mamba as body joint queries and vertex queries, along with position embedding (Fig. 2 (d)). The key difference from previous vertex-based approaches [14, 31, 33, 41] is that Mamba-HMR does not necessarily need upsamplers and its Mamba-blocks directly output a full-resolution mesh, which leads to a large reduction in model parameters. Like our MambaDiff3D, Mamba-HMR consists of the shallow, mid and deep Mamba block groups and uses skip connections, except that we do not input time embeddings. + +Training loss Our training loss follows [38, 39] but is augmented with local geometric losses such as the surface edge, Laplacian and normal losses, $L_{\mathrm{edge}}$ , $L_{\mathrm{lap}}$ and $L_{\mathrm{normal}}$ for regularization. The total loss is defined as: + +$$ +\begin{array}{l} L = \lambda_ {\mathrm {3 D}} ^ {\mathrm {V}} L ^ {\mathrm {V}} + \lambda_ {\mathrm {3 D}} ^ {\mathrm {J}} (L _ {\mathrm {3 D}} ^ {\mathrm {J}} + L _ {\mathrm {r e g 3 D}} ^ {\mathrm {J}}) + \lambda_ {\mathrm {2 D}} ^ {J} (L _ {\mathrm {2 D}} ^ {\mathrm {J}} + L _ {\mathrm {r e g 2 D}} ^ {\mathrm {J}}) \\ + \lambda_ {\text {e d g e}} L _ {\text {e d g e}} + \lambda_ {\text {l a p}} L _ {\text {l a p}} + \lambda_ {\text {n o r m a l}} L _ {\text {n o r m a l}} \tag {5} \\ \end{array} +$$ + +where $L^{\mathrm{V}}, L_{\mathrm{3D}}^{\mathrm{J}}, L_{\mathrm{reg3D}}^{\mathrm{J}}, L_{\mathrm{2D}}^{\mathrm{J}}$ and $L_{\mathrm{reg2D}}^{\mathrm{J}}$ are the vertex, 3D joint, 3D regressed joint, 2D joint and 2D regressed joint loss, respectively. $\lambda_{\mathrm{3D}}^{\mathrm{V}}, \lambda_{\mathrm{3D}}^{\mathrm{J}}, \lambda_{\mathrm{2D}}^{\mathrm{J}}, \lambda_{\mathrm{edge}}, \lambda_{\mathrm{lap}}$ and $\lambda_{\mathrm{normal}}$ are the weights for controlling the relative strengths of respective terms. + +The local geometric losses $L_{\mathrm{edge}}$ , $L_{\mathrm{lap}}$ and $L_{\mathrm{normal}}$ are vital for local shape preservation in our dense mesh reconstruction (Fig. 3), which are defined as follows: + +Laplacian loss The Laplacian loss $L_{\mathrm{lap}}$ is written as: + +$$ +L _ {\mathrm {l a p}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left\| \mathbf {d} _ {i} - \bar {\mathbf {d}} _ {i} \right\| _ {1} \tag {6} +$$ + +where $\mathbf{d}_i$ and $\bar{\mathbf{d}}_i$ are the predicted and ground truth of mean curvature normal vector at vertex $i$ derived from the cotangent Laplacian matrix, respectively. + +Edge loss The edge loss $L_{\mathrm{edge}}$ is defined as: + +$$ +L _ {\text {e d g e}} = \frac {1}{E} \sum_ {e = 1} ^ {E} \left| \left| \mathbf {e} _ {e} - \bar {\mathbf {e}} _ {e} \right| \right| _ {1} \tag {7} +$$ + +where $\mathbf{e}_e$ and $\bar{\mathbf{e}}_e$ are the predicted and ground truth of edge length at edge $e$ , respectively. + +Normal loss The normal loss $L_{\mathrm{normal}}$ is defined as: + +$$ +L _ {\text {n o r m a l}} = \frac {1}{F} \sum_ {m = 1} ^ {F} \left\| \mathbf {n} _ {m} - \bar {\mathbf {n}} _ {m} \right\| _ {1} \tag {8} +$$ + +where $\mathbf{n}_m$ and $\bar{\mathbf{n}}_m$ are the predicted and ground truth of face normal at triangle face $m$ , respectively. + +![](images/cff978025e9fbe13b53a4c333cc4c10bb684efee1291d6c15d81a446d9eb6157.jpg) + +![](images/43b1f0569207b7259280a06028bbaa0162bb259cb607110d8388d83f5aa30df9.jpg) +w/o regularize + +w/o regularize + +![](images/3f9551fc742f614610f0ad4452d201ded30e5db716b76d57fb6a67f5b73e50d9.jpg) ++Ledge +Figure 3. Importance of local geometric regularization in dense human mesh reconstruction. + +![](images/2599d46bba451dd0210ac0b6ae71315ce87c55acf94629626b0c641ac7a7e6e3.jpg) ++Ledge+Lap + +![](images/dc2bb83e63d1116382ade0681c18dd018494c4c5fcc6809a5e6d5a7dd894921a.jpg) ++Ledge +L1ap +Lnormal + +# 5. Experimental results + +# 5.1. Training and evaluation settings + +# 5.1.1. 3D articulated mesh generation: MambaDiff3D + +We trained our models on the SURREAL [75], DFAUST [8], CAPE [47], GRAB [70], AMASS [50], BARC [61] and Animal3D [81] datasets. The training meshes were preprocessed to align their global positions and orientations at the root. Our models were trained using either a single cluster node with 8 NVIDIA A100 GPUs or 6 nodes with 4 NVIDIA V100 GPUs. We used the Adam optimizer for training. The learning rate was reduced by a factor of 10 after $1/2$ of the total training epochs beginning from $1 \times 10^{-4}$ . + +MambaDiff3D is compared against the following pose-based baselines: VPoser [55], Pose-NDF [74], NRDF [23], and denoising diffusion on SMPL parameters (Param. Diff.). For these pose approaches, identity parameters are drawn from the standard deviations of the AMASS dataset. We also compared MambaDiff3D with the vertex-based + +![](images/0f51725409441192631ed302e5be8bccdbf8e2b90be46ebbe77bc0fa322b6236.jpg) +Figure 4. Unconditional generation results of dense 3D meshes. MambaDiff3D can generate human body meshes with 6890 and 10475 vertices, corresponding to the full resolutions of SMPL and SMPL-X, respectively. Notably, MambaDiff3D can capture grasp hands in GRAB and cloth deformations in CAPE. + +![](images/302237f4d306b6f032a21d75a829a04d8e04ccd7a16bed627bd3cb29c9a47648.jpg) +Figure 5. Example results of whole-body 3D human mesh recovery from a single image using 10475 vertex tokens on UBody. + +bases [2], LIMP [16], and DiffSurf [85]. Evaluation of 3D human generation was conducted on the SURREAL test set (200 meshes). We used the 1-NNA metric [82], the standard metric in 3D shape generation for quantifying the distributional similarity between generated shapes and the validation set. We also employed the FID and APD metrics used in pose generation [23], which calculates scores from joint locations. + +# 5.1.2. Human mesh recovery: Mamba-HMR + +We evaluated our method on UBody comparing against the state-of-the-art approaches: OSX [37], SMPLer-X [10], + +![](images/2d9cd47fa1266404f2e9f411d67c7b9d468438fe3154dbfe5289432965ad886f.jpg) + +![](images/a25886641854bb6ea2c3679a29de8b065850069d2f04fb8dc6ea7fa10abd244b.jpg) + +![](images/f9200c2cc9781561c17eb6543662535aebf2e19be8fae0dbdc73340b554566f9.jpg) + +![](images/b627011e9fb10855b8a707269defff97be3637cbbeedf0b7c8c475c9696af673.jpg) + +![](images/997fd03dc917c45f766460eb7aac426a46bb0c08c79ab3680e691585ee398936.jpg) +Our: +METRO + +![](images/9fc04eb92dd0e4f205a04daa2e8b89314ac6656397566e55cbd103e37f6b4339.jpg) + +![](images/d8f4f3ef6804e0c6e1717bebfaf7d4f73022b52c290b8c52c888d0a6e32a37a8.jpg) + +![](images/3f85b27630f45831fa8d7f8ae91f5465497390806a0faa1c01f8954d2937650e.jpg) + +![](images/b053d34d6ead86e08241d7977f6e08a299e5601bd4d3256315d17f03ced04e6c.jpg) +Ours(Parametric) + +![](images/1b168baa38188df98ac5f8a563e5917fd1a1dcfe173c1b442922b1a8317d1dda.jpg) +NLF (Non-parametric) + +![](images/b50b9ad598103b7a1039645fe887d2079bb5af86647cb49b2f091c838296b367.jpg) +Figure 6. Qualitative comparisons. Top: Human mesh generation VS. DiffSurf, PoseNDF and NRDF. Middle: Body-only 3D human mesh recovery on 3DPW comparing against METRO, where no fine-tuning on 3DPW is performed. Bottom: comparison with NLF on whole-body mesh reconstruction. + +![](images/b3d1703109dfe74a7dc1f033890af549ea4b421ca31645f224be88bb829a96cf.jpg) +NLF (parametric) + +Table 1. Comparisons with other generative models for unconditional human generation. The 1-NNA metric $[\%]$ assesses the diversity and quality of generated results. A lower value on this metric signifies superior performance. + +
MethodTrain Set1NNA [%] ↓FID ↓APD ↑
Pose-NDF [74]AMASS92.03.9237.81
NRDF [23]AMASS81.60.6423.12
VPoser [55]AMASS60.70.0514.68
Param diffAMASS59.6——
GDVAE [2]SURREAL93.8——
LIMP [16]FAUST81.3——
DiffSurf [85]SURREAL54.4——
Ours (MambaDiff3D)SURREAL53.10.3223.01
Ours (MambaDiff3D)AMASS55.10.2223.8
+ +AiOS [69], Multi-HMR [4] and NLF [63], which run faster than interactive rate 10 FPS and are trained on various dataset or fine-tuned on the UBody dataset [37]. Following previous approaches such as [4, 10, 37], Mamba-HMR is trained on Human3.6M [27], COCO [40], AGORA [53], BEDLAM [6] and UBody [37]. We employ HRNet-w48 [68] as our CNN backbone, initialized with the weights pretrained on the 2D human pose detection tasks. It uses a + +Table 2. Comparisons with whole-body 3D mesh recovery approaches on UBody. $\dagger$ indicates fine-tuned on UBody. + +
MethodPA-MVE ↓ (mm)MVE ↓ (mm)
AllHandsFaceAllHandsFaceFPS
OSX-L [37]42.410.82.492.447.724.914
OSX-L [37] †42.28.62.081.941.521.214
SMPLer-X-L [10]33.210.62.861.543.323.124
SMPLer-X-L [10] †31.910.32.857.440.221.624
AiOS [69]32.57.32.858.639.019.6—
Multi-HMR-B [4]31.49.86.165.133.122.623
NLF-L [63]66.819.46.6———41
Ours26.310.72.454.438.817.722
Ours †25.99.72.151.733.915.922
+ +Table 3. Ablation studies on network layer blocks and serialization methods. The 1-NNA metric $[\% ]\downarrow$ is used. + +
Animation1NNA ↓
Block1NNA ↓SMPL connectivity × 160.0
part-IUV × 154.4
MLP73.7part-IUV × 253.7
GNN74.2part-IUV × 453.7
Transformer53.6part-IUV × 753.0
Mamba53.1SMPL × 1 + IUV × 153.5
SMPL × 1 + XYZ × 153.1
SMPL × 1 + XYZ × 653.5
+ +$384 \times 288$ image as input and extracts an $12 \times 9$ feature map, which is pre-trained on the COCO-whole body dataset [29]. The weights in the Mamba blocks are randomly initialized. Whole-body HMR results on EHF and AGORA-val, as well as body-only results on Human3.6M and 3DPW, are provided in the Appendices. + +Evaluation metrics We used the following metrics for evaluation. Mean-per-Vertex-Error (MVE) measures the Euclidean distances between the (pseudo) ground truth and the predicted vertices. The PA-MVE metric, where PA stands for Procrustes Analysis, measures the reconstruction error after removing the effects of scale and rotation. All reported errors are in units of millimeters. + +# 5.2. Inference and training efficiency + +Figure 1 shows a comparison between Mamba and transformer in terms of inference speeds when used as a layer block in denoising diffusion models. The gap between the two widens as the number of token increases. On an NVIDIA A100 GPU, it takes approx. 4.5 sec for Mamba to generate a mesh with 10475 vertices using 250 DDIM sampling steps, whereas it takes 28.1 sec for the transformer with Pytorch Flash attention enabled. In this case, Mamba is $6 \times$ faster than transformer. Notably, with 50 DDIM steps, MambaDiff3D can generate reasonable quality meshes of the same resolution in about 1 sec. On a V100 GPU where hardware optimization is not available, Mamba is about $9 \times$ faster than transformer (6.6 sec VS. 58.3 sec). These results highlight the scalability of Mamba w.r.t the number of input tokens. Furthermore, the training time of MeshMamba for + +6890 vertex tokens is approx. 18 min per epoch using $6 \times 4$ Nvidia V100 GPUs with batch size of 8, compared to 100 minutes for the transformer under the same settings. + +# 5.3. Qualitative results + +Figures 1 and 4 show some example results of unconditional and class conditional 3D human generation. As visualized, MambaDiff3D can generate 3D human meshes in diverse body shapes and poses, including grasping hands and cloth deformations. Given clothing types as conditions, MambaDiff3D can generate human meshes in different clothing styles such as blazer and polo from the CAPE dataset. + +Figure 5 shows the results of whole-body 3D human mesh recovery using Mamba-HMR on UBody. Mamba-HMR can reconstruct a realistic, dense 3D human mesh from a single image. In Figure 6, we qualitative comparisons of the 3D human shape generation and human mesh recovery results. As visualized in Figure 6 (top), our approach generates more realistic poses than PoseNDF [74] and NRDF [23]. Figure 6 (middle and bottom) shows that Mamba-HMR produces reconstruction results with less distortion compared to METRO [39], which requires an additional upsampling process, and NLF [63], which requires a parametric model to obtain a dense mesh. Note that Mamba-HMR is able to project the resulting surfaces to a parametric pose representation by employing a method such as VPoser [55], but the quality of the reconstructions does not change significantly, with no large visual difference. + +# 5.4. Quantitative comparisons + +3D Human Generation In Table 1, we list the metric scores of MambaDiff3D and the baseline methods. MambaDiff3D outperforms both the parametric pose-based and non-parametric surface-based approaches. In fact, MambaDiff3D achieves state-of-the-art (SOTA) performance on the 1-NNA metric. The pose metric scores FID and APD further indicate that MambaDiff3D generates diverse yet more realistic results than NRDF [23], as depicted in Fig. 6. + +Whole-body human mesh recovery Table 2 presents the comparison of whole-body mesh recovery methods on UBody. Mamba-HMR outperforms the SOTA parametric and non-parametric approaches [4, 10, 63, 69], including those pre-trained on a large-scale dataset. + +# 5.5. Ablation studies + +Network block Table 3 (left) presents the results of ablation studies on network blocks, where we replaced the Mamba block in each layer with MLP, GNN and transformer self-attention. As shown, transformer and Mamba blocks perform significantly better than MLPs and GNNs, which led to unsuccessful training and produced locally very noisy surface results (see Appendix). + +Serialization In Table 3 (right), we present the ablation + +![](images/7411837e9a228c431de8dfe6a061e7482d8506b4b5f8051b3d1509c3ff5ff3bb.jpg) +Figure 7. Comparisons of mesh representation in 3D generation. Left: Generation of vertices exhibits noise locally while Jacobians are prone to distortions globally. In contrast, our approach utilizing surface normals can preserve shape structure and achieves smooth reconstruction. Right: Performing generation on a down-sampled mesh cannot recover hand shapes and loses fingers. + +study on mesh vertex serialization approaches. When vertices were sorted with a random ordering, MeshMamba was unable to learn properly. Using the default ordering derived from the SMPL mesh connectivity solely ("SMPL connectivity" in Table 3 (right)), it leads to a worse 1-NNA score and visually noticeable large distortions. With a single serialization strategy derived from the body part IUV maps, the 1-NNA score improved. Combining two or more serialization strategies leads to better 1-NNA scores but increasing the number of strategies needs a longer inference time due to memory access via "gather" operations. Based on these results, we empirically found that a combination of two strategies balances efficiency and quality. + +Mesh representation In Fig. 7 we compared our mesh representation that combines vertices and surface normals for mesh generation against generation vertices and Jacobians [1, 67, 83]. As reported in the recent works [51, 83], the vertex and Jacobian generation approaches are prone to noise and distortions. In contrast, our approach utilizing surface normals can preserve shape structure and achieves smooth reconstruction. Furthermore, performing generation on a downsampled mesh as in [41, 85] cannot recover hand shapes and loses fingers. + +# 5.6. Shape interpolation + +Using MambaDiff3D, it is possible to perform shape interpolation by blending Gaussian noise with SLERP and sampling from the blended noise with the DDIM sampler. Compared to ARAPReg [26] which enforces locally as-rigid-as possible constraints when constructing mesh latent vectors and performs interpolation based on them, MambaDiff3D can faithfully preserves arm shapes even when elbows are deeply bent during interpolation (Fig. 8). Additionally, MambaDiff3D is generalizable to other mammal models. + +# 5.7. Limitations + +MeshMamba still has limitations that could be addressed in future research. First, it is limited to tight clothing with a + +![](images/3a3f3c20a54bb2ebccd2460ecb0542bb665b50aaa697a75e5890db4efb7f4899.jpg) +Figure 8. Shape interpolation. Compared to ARAPReg which enforces locally as-rigid-as possible constraints on mesh latent vectors, MambaDiff3D can faithfully preserves arm shapes while elbow bending. Also, MambaDiff3D is capable of generating other mammals (3889 vertex tokens) by training on Animal3D datasets. + +fixed topology. We aim to tackle more challenging in-the-wild clothed human mesh recovery [79] by further increasing image and mesh resolution. Second, its generalization capability to new datasets not used in training is still limited, compared to approaches trained on diverse datasets [10]. + +# 6. Conclusion + +We presented MeshMamba, a neural network model for learning dense 3D articulated mesh models based on Mamba-SSMs. The key to effectively training MeshMamba lies in the serialization technique of mesh vertices, which leverages prior knowledge about the mesh structure encoded in a template mesh through its 3D coordinates or DensePose body part annotations. Building upon MeshMamba, we presented MambaDiff3D and Mamba-HMR for dense 3D human mesh generation and reconstruction. MambaDiff3D achieves state-of-the-art performance in the benchmark and, more importantly, it can generate 3D human meshes with clothing deformations and hand grasping poses. Mamba-HMR is the first Mamba-based approach to 3D human mesh recovery tasks, achieving competitive performance at a near real-time rate. + +# Acknowledgments + +This work was supported by JSPS KAKENHI Grant Number 23K28116 and 22H00545 in Japan. 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MeshPad enables interactive mesh creation and editing with sketches. We decompose this complex task into two sketch-conditioned operations: addition and deletion. Top: our method allows for a user to create and modify artist-reminiscent triangle meshes by simply drawing and editing 2D sketches, achieving intuitive and interactive 3D modeling. Bottom (left): our method generates a variety of complex yet compact meshes. Bottom (right): our interactive user interface allows users to iteratively edit the mesh, with each edit step taking a few seconds. + +# Abstract + +We introduce MeshPad, a generative approach that creates 3D meshes from sketch inputs. Building on recent advances in artist-reminiscent triangle mesh generation, our approach addresses the need for interactive mesh creation. To this end, we focus on enabling consistent edits by decomposing editing into 'deletion' of regions of a mesh, followed by 'addition' of new mesh geometry. Both operations are invoked by simple user edits of a sketch image, facilitating an iterative content creation process and enabling the construction of complex 3D meshes. Our approach is based on a triangle sequence-based mesh representation, exploiting a large Transformer model for mesh triangle addition and deletion. In order to perform edits interactively, we introduce a vertex-aligned speculative prediction strat + +egy on top of our additive mesh generator. This speculator predicts multiple output tokens corresponding to a vertex, thus significantly reducing the computational cost of inference and accelerating the editing process, making it possible to execute each editing step in only a few seconds. Comprehensive experiments demonstrate that MeshPad outperforms state-of-the-art sketch-conditioned mesh generation methods, achieving more than $22\%$ mesh quality improvement in Chamfer distance, and being preferred by $90\%$ of participants in perceptual evaluations. + +# 1. Introduction + +Triangle meshes are one of the most predominant 3D representations used in 3D production applications, from video games to virtual reality and movies. Mesh creation and editing is thus a central element of computer graphics. In + +![](images/1bb0d3847cdc3550484aeef4a6936604e7352037754f9c3362ad7d920afdddea.jpg) +Figure 2. Method Overview. We show the decomposition of mesh creation and editing into addition and deletion operations (left and right, respectively). ADD: in mesh addition, a transformer generates new mesh regions corresponding to newly added strokes (in red) in the input sketch. The generated mesh triangles are then merged with the existing mesh. DEL: in mesh deletion, we show a deletion operation applied to the mesh addition output. We erase sketch strokes to remove corresponding mesh regions, and overlay the erased strokes in red alongside untouched regions to provide more context to the deletion network. We then predict which mesh vertices correspond to regions to be deleted, and prune the mesh accordingly. After each addition or deletion operation, we automatically generate an updated sketch corresponding to the current output mesh, to enable further sketch-based editing. + +contrast to 3D representations such as voxels [17, 18, 47], points [54, 57, 62], or neural implicit representations [26, 29, 40], triangle meshes represent surfaces in a compact, structured fashion, as well as enabling efficient fine-scale detail and naturally integrating into modern rendering and editing pipelines, achieving high fidelity with relatively few primitives. + +Recent advances in generative 3D models have shown significant potential in generating 3D meshes directly [14, 15, 25, 49, 53]; however, these output meshes are not editable, which is a crucial component for artistic design in content creation. More specifically, artistic content creation is an iterative process that encompasses not only the initial generation, but also requires multiple cycles of manipulation and editing in order to refine an output to achieve a precise artistic vision. In order for such editing to fit with content creation pipelines, various edits must be performed interactively, affecting only the intended region of the mesh. + +We thus propose MeshPad, an interactive sketch-based approach for 3D mesh generation and editing. From an input sketch of a shape drawn by a user, we produce a corresponding 3D mesh. The resulting mesh can then be edited simply by editing the sketch. To achieve efficient and precise mesh editing, we decompose this into simpler subtasks: deletion and addition of mesh geometry by removing or adding strokes in the sketch. Crucially, this modeling paradigm also leads to easy supervised training of both deletion and addition of elements in the mesh (by simply removing and adding back parts of ground-truth meshes), without requiring collection of real mesh editing sequences for supervision. Our editing-based approach allows for the generation of more complex triangle meshes by iteratively applying a series of edits to construct the final shape. + +Algorithmically, MeshPad leverages a hybrid approach + +combining an autoregressive network for addition and a token-classification network for deletion. Unlike existing artist-reminiscent mesh generation methods, our addition network generates partial shapes only corresponding to new sketch strokes, rather than repeatedly synthesizing the entire mesh. This naturally solves the problem of preserving unedited mesh regions during editing. Additionally, based on the triangle sequence representation [15], we introduce a vertex-aligned speculative decoder to accelerate autoregressive generation and reduce computational time. Instead of predicting one vertex coordinate at a time, the speculator allows us to predict 3 coordinates, i.e., one vertex, at a time. We find that jointly training the speculative head and aligning it with the vertex tokens reduces generation time while maintaining generation quality. We further demonstrate our method through a user interface (Fig. 1) that allows users to interactively edit 3D meshes by drawing on 2D sketches. Extensive experiments show that our method outperforms state-of-the-art methods in sketch-conditioned mesh generation, producing cleaner meshes that more accurately align with the sketch input and excelling in partial mesh editing tasks. Finally, our speculative prediction acceleration enables interactive mesh generation and editing within seconds while maintaining overall shape quality. + +In summary, our contributions are: + +- We introduce a novel method for interactive mesh creation and editing by decomposing the process into addition and deletion. This enables easy training without requiring collection of edited ground-truth meshes, and enables finer-grained control over an iterative 3D mesh creation process. +- Our vertex-aligned speculative classification head for addition notably accelerates the triangle mesh generation by $2.2 \times$ without quality loss. + +# 2. Related Work + +3D Mesh Generation. Direct mesh generation offers the compelling advantage of producing outputs that closely resemble artist-crafted 3D shapes. Early approaches proposed various parameterizations of an irregular mesh structure, including altases [24] and graphs [16]. Recently, Polygen [41] and MeshGPT [49] have demonstrated the remarkable potential of transformers in autoregressively generating artist-crafted meshes. Follow-ups such as MeshAnything [14], MeshAnything V2 [15], EdgeRunner [53], and Meshtron [25] each proposed improvements in tokenization, attention mechanisms, or shape coverage, pushing the limit of direct mesh generation. PolyDiff [2] instead uses a diffusion backbone for polygonal mesh synthesis. Despite solid progress, these methods focus on full-shape generation and cannot easily handle local editing tasks. + +Conditional 3D Generation. The history of sketch-driven methods starts with techniques that inflate 2D contours [27, 42] or retrieve 3D models from sketch-based queries [19, 21]. Modern sketch-based modeling methods explored representations like SDF [48, 61], NeRF [39], and CAD commands [33]. With the advancement in large text-to-image models, DreamFusion [43] proposes score distillation sampling with 2D diffusion for text-to-3D generation, followed by Magic3D [35], Fantasy3D [11], and Meta 3D AssetGen [50]. Text conditions lack precision for fine-grained control [56] and additional image condition is often required [3, 44]. In contrast, our method uses iterative sketch conditioning for fine-grained shape control. + +3D Shape Editing. With the same concept of SDS, many 3D shape editing methods rely on neural representations [30, 37] and use region-specific masks [5, 9, 13]. SPAGHETTI [26], SALAD [31], and PartGen [10] advance part-level neural shape editing with disentangled control, diffusion-based manipulation, and multi-view diffusion for generating and editing meaningful 3D parts, respectively. + +Recently, sketch-based 3D editing has emerged as an intuitive alternative to text- and image-based methods. SKED [39] and SketchDream [36] leverage sketch-conditioned 2D diffusion models for 3D modeling. Other approaches, including SENS [6], Doodle your 3D [4], and Masked LRM [23], focus on abstraction-aware part manipulation, robust part isolation, and masked reconstruction for fast local edits, respectively. + +However, such works struggle to produce an artist-reminiscent mesh. Techniques based on polygonal meshes or other explicit representations can rely on an expensive optimization [1, 22], deformation priors [52], specialized parametric families [20] or procedural generators [60]. Such approaches do not generalize easily to arbitrary geometry and have difficulties making local edits without conflicting with the global constraints. In contrast, our ap + +proach addresses these issues using a sequence-based mesh representation to perform partial editing by removing and adding triangles. + +Speculative Decoding. Speculative decoding accelerates autoregressive generation by predicting multiple tokens in parallel [8, 32, 38, 55]. We extend this approach to mesh sequences with a vertex-aligned curator, enabling faster partial additions for iterative mesh editing. + +# 3. Method + +MeshPad enables interactive mesh creation and editing by iteratively performing addition and deletion operations guided by input sketches. An input sketch image $\mathcal{I}$ guides the generation of a 3D mesh $\mathcal{M}$ as a sequence of mesh triangles. $\mathcal{M}$ can be further edited by removing strokes from $\mathcal{I}$ to delete mesh regions, or adding new strokes for new geometry. To achieve interactive rates for editing, we introduce a vertex-aligned speculator into our mesh addition transformer to accelerate its autoregressive generation. An overview of our approach is shown in Fig. 2. + +# 3.1. Mesh Creation and Editing + +We decouple sketch-based mesh creation and editing into two subtasks: addition and deletion. Both operations are conditioned on a sketch image $\mathcal{I}$ , a bitmap where colored line strokes indicate regions to be added or deleted. We define a mesh $\mathcal{M}$ as a set of triangles $\mathcal{M} = \{\mathcal{F}\}$ , where triangles $\mathcal{F} = \{\pmb{v}_1, \pmb{v}_2, \pmb{v}_3\}$ and $\pmb{v} \in \mathbb{R}^3$ represents vertices. + +Line strokes in the input sketch image $\mathcal{I}$ are divided into two mutually exclusive sets, $\mathcal{I}_k$ and $\mathcal{I}_r$ , colored black and red in our visualizations, respectively. When performing an addition or deletion, $\mathcal{I}_r$ corresponds to the user edit, i.e., the part to be added or deleted, respectively, while $\mathcal{I}_k$ represents the untouched sketch regions. We denote the mesh parts corresponding to $\mathcal{I}_r$ and $\mathcal{I}_k$ as mutually exclusive sets $\mathcal{M}_r$ and $\mathcal{M}_k$ , respectively, and thus $\mathcal{M}_r \cup \mathcal{M}_k = \mathcal{M}$ . The operation—addition or deletion—is determined by whether the $\mathcal{I}_r$ is added as new strokes (addition), or erased from existing strokes (deletion). This also enables simple supervision of both deletion and addition networks by removing or adding back random regions of mesh geometry of 3D shapes, without requiring ground-truth sequences of mesh edits (see Sec. 3.4 for more detail). + +Sketch-Conditioned Mesh Deletion. Given a current mesh state $\mathcal{M}$ and a sketch image $\mathcal{I}$ containing a non-empty set of deletion strokes $\mathcal{I}_r$ , the goal is to obtain a mesh $\mathcal{M}_k \subsetneq \mathcal{M}$ that excludes parts corresponding to $\mathcal{I}_r$ . This is formulated as a binary classification task over the sequence of triangles composing $\mathcal{M}$ ; those predicted as corresponding to $\mathcal{I}_r$ are then removed. + +We employ a transformer-based architecture (Sec. 3.2) to predict a binary label for each vertex in the mesh sequence, + +forming a set of vertices $\mathcal{V}_r^\prime$ corresponding to $\mathcal{I}_r$ . Then we predict the target mesh $\mathcal{M}_k^\prime$ by deleting triangles with any vertex predicted as deleted: + +$$ +\mathcal {M} _ {r} ^ {\prime} = \left\{\mathcal {F} \in \mathcal {M} \mid \exists \boldsymbol {v} \in \mathcal {F}: \boldsymbol {v} \in \mathcal {V} _ {r} ^ {\prime} \right\}; \quad \mathcal {M} _ {k} ^ {\prime} = \mathcal {M} \backslash \mathcal {M} _ {r} ^ {\prime}, \tag {1} +$$ + +where $\backslash$ is the set subtraction operator. + +We train this by automatically generating 2D sketches and removal regions from 3D shapes in a self-supervised fashion (Sec. 3.4) to obtain the ground truth $\mathcal{V}_r = \bigcup_{\mathcal{F} \in \mathcal{M}_r} \mathcal{F}$ and set the binary label of each vertex as: + +$$ +l _ {\boldsymbol {v}} = \left\{ \begin{array}{l l} 0 & \text {i f} \boldsymbol {v} \in \mathcal {V} _ {r}, \\ 1 & \text {o t h e r w i s e .} \end{array} \right. \tag {2} +$$ + +The network is trained with a binary cross-entropy loss between the predicted binary probability per vertex and the vertex label. Once deletion is performed, we assign $\mathcal{M} \gets \mathcal{M}_k'$ and $\mathcal{M}_k \gets \mathcal{M}_k'$ , and automatically generate the updated $\mathcal{I}_k$ corresponding to the new output mesh $\mathcal{M}$ (Sec. 3.4), which can be further edited. + +Sketch-Conditioned Mesh Addition. The addition task is the inverse process of deletion. The input is a mesh $\mathcal{M}_k$ and a sketch $\mathcal{I}$ containing non-empty $\mathcal{I}_r$ , and the goal is to generate the mesh $\mathcal{M}$ . We use a similar architecture as with deletion to autoregressively generate tokens of $\mathcal{M}_r^\prime$ and merge it with $\mathcal{M}_k$ to obtain the predicted mesh $\mathcal{M}'$ . This is supervised by a cross-entropy loss between the ground-truth mesh tokens of $\mathcal{M}_r$ and the predicted token probabilities. After merging, we assign $\mathcal{M} \gets \mathcal{M}'$ and $\mathcal{M}_k \gets \mathcal{M}'$ . + +We automatically generate an updated sketch $\mathcal{I}_k$ reflecting the latest mesh geometry. This enables iterative mesh generation and editing. A user first draws a sketch to produce an initial mesh or loads in a mesh from which we automatically generate a corresponding sketch. Editing can then be performed on this initial mesh and sketch; a user can erase a sketch part with an eraser tool, labeling part of $\mathcal{I}_k$ as $\mathcal{I}_r$ and triggering deletion of the corresponding mesh part. The user can also draw new strokes alongside the current $\mathcal{I}_k$ to introduce new mesh geometry. This iterative editing process avoids re-synthesis of the whole shape, preserving mesh structures in unedited regions. Note that mesh generation from scratch is treated as addition to an empty mesh. + +# 3.2. Network Architecture + +The detailed model structure is shown in Fig. 3. We use a pre-trained image encoder RADIO 2.5-h [46] to encode the sketch input as tokens. We follow MeshAnythingV2 [15] to use the same Open Pre-trained Transformer (OPT) [59] network as our backbone. We also adopt the tokenizer $\mathcal{T}$ from MeshAnythingV2 to transform a mesh into a sequence $S = \mathcal{T}(\mathcal{M})$ . The sequence $S$ is defined as an ordered list consisting of control tokens (, , ) and vertex coordinate tokens $V$ . The and tokens + +![](images/9e5fcc4b10577a42b0af8a2c5ee96b3f32c40a088b76a8b8fbd164acf19c9f2a.jpg) +Figure 3. Model Architecture. We use the Open Pre-trained Transformer (OPT) in both the addition and deletion networks as the backbone to process the embedded triangle sequence and the sketch embeddings from a pre-trained image foundation model, RADIO (frozen during training). Top (right): the deletion network is a classification network that labels each input mesh vertex for removal. The deletion head takes the $xyz$ coordinate embeddings of a vertex as input and produces a masking label for the vertex. Bottom (right): the addition network is an autoregressive generation model that predicts new mesh tokens with a curator. The CTransformer backbone uses causal attention instead of full attention. During the speculative prediction, we align the curator to the vertex axis so that it always takes the $x$ coordinate as input and predicts the vertex's $y$ and $z$ coordinates. E, M, V, and represent Transformer hidden states, vertex masks, vertex coordinate tokens, and the token, respectively. + +indicate the sequence bounds. The token splits the sequence into subsequences containing only vertex tokens, which define a series of adjacent triangles [15]. Please refer to the supplemental for more sequence structure details. + +To perform mesh addition, we use the OPT model to autoregressively predict the probability distribution $P$ of the next sequence token $S_r^{\prime (i + 1)}$ given the sketch $\mathcal{I}$ , input mesh sequence $S_{k} = \mathcal{T}(\mathcal{M}_{k})$ , and the previously generated tokens $S_r^{\prime (1\dots i)}$ : + +$$ +P \left(S _ {r} ^ {\prime (i + 1)} \mid S _ {k}, \mathcal {I}, S _ {r} ^ {\prime (1 \dots i)}\right) = \operatorname {O P T} \left(S _ {k}, \mathcal {I}, S _ {r} ^ {\prime (1 \dots i)}\right). \tag {3} +$$ + +The token $S_r^{\prime(i+1)}$ is obtained by sampling with the distribution $P$ , and then conditions the generation of $S_r^{\prime(i+2)}$ . We detokenize the generated sequence $S_r^\prime$ to mesh triangles and then merge them with the input partial mesh: + +$$ +\mathcal {M} ^ {\prime} = \mathcal {M} _ {k} \cup \mathcal {T} ^ {- 1} \left(S _ {r} ^ {\prime}\right). \tag {4} +$$ + +Instead of generating one token at a time, we introduce a vertex-aligned speculator to predict multiple tokens in a single run (Sec. 3.3). + +The deletion network predicts a mask label for each vertex with a deletion head, which processes the encoded states of every three coordinate tokens corresponding to a vertex. While using the same OPT architecture, the deletion network does not share weights with the addition network. The attention layers in the deletion network are switched to per + +form bi-directional attention for each position to capture the global context. After the inference, we aggregate $\mathcal{V}_r^\prime$ according to Eq. 2, and then obtain the deleted mesh with Eq. 1. + +# 3.3. Vertex-Aligned Speculator + +As we perform mesh addition autoregressively, generating an $n$ -token sequence requires $n$ forward passes, significantly limiting mesh generation speed for interactive applications. One effective way of accelerating generation is to use a curator to generate multiple tokens in a single run. In contrast to natural language, a tokenized mesh sequence contains strong low-level structure—each vertex $v$ is defined by exactly 3 tokens $V_{\{x,y,z\}}$ representing its $x$ , $y$ , and $z$ coordinates. Aligning the curator with vertex tokens by letting it predict only $V_{\{y,z\}}$ , as shown in Fig. 3, ensures a consistent context of input and output for the curator. + +We adopt the MLP discriminator described in [55]. In natural language processing tasks, a discriminator can be trained with a frozen pre-trained large language model to accelerate generation. However, in our experiments, we found that this results in performance degradation. We thus train our discriminator jointly with the mesh addition task, so that the addition transformer learns to inform the discriminator with contextual information in hidden states. + +As shown in Fig. 3, the curator predicts the $y,z$ coordinates of a vertex $\pmb{v}^{\prime}$ by: + +$$ +P \left(V _ {\{y, z \}} ^ {\prime}\right) = \operatorname {S p e c u l a t o r} \left(E _ {x}, V _ {x} ^ {\prime}\right), \tag {5} +$$ + +where $E_{x}$ represents Transformer hidden states corresponding to $V_{x}$ . The curator is trained with a cross-entropy loss between ground truth $V_{\{y,z\}}$ and the prediction. When jointly trained with OPT, the OPT loss function supervises $V_{x}$ and control tokens only. + +# 3.4. Training Data Generation for Mesh Editing + +By decomposing sketch-conditioned mesh editing into separate deletion and addition subtasks, we can generate training data for each subtask from 3D shape datasets without requiring real mesh editing sequences. Fig. 4 shows our data generation process. + +Given a complete 3D mesh sample $\mathcal{M}_c$ , we select its triangles to form two mutually exclusive subsets $\mathcal{M}_r$ and $\mathcal{M}_k$ , representing the edited and unedited parts, respectively. Note that $\mathcal{M}_r \cup \mathcal{M}_k = \mathcal{M}_c$ is not required, as intermediate meshes in interactive editing can be incomplete before deletion or after addition. To achieve this, we sample two volumes $\mathcal{L}$ and $\mathcal{L}_k \subsetneq \mathcal{L}$ within the bounding volume of $\mathcal{M}_c$ . An example is shown in Fig. 4. For each volume, we crop a partial mesh by selecting all triangles containing at least one vertex within the given volume: + +$$ +\mathcal {M} = \left\{\mathcal {F} \in \mathcal {M} _ {c} \mid \exists \boldsymbol {p} \in \mathcal {F}: \boldsymbol {p} \in \mathcal {L} \right\}, \tag {6} +$$ + +![](images/4f96f72fb0a92e0ae88d4f571b993dc19e36f1ae8f49bb6157c7bbd1c598aaf6.jpg) +Figure 4. An example of training data generation: the volume $\mathcal{L}$ is sampled to cover a large portion from the top, while $\mathcal{L}_k$ covers the chair backrest. The meshes $\mathcal{M}$ and $\mathcal{M}_k$ contain triangles with any vertex in $\mathcal{L}$ and $\mathcal{L}_k$ , respectively—that is, triangles fully or partially inside the volumes. $\mathcal{M}_r$ is the difference between $\mathcal{M}$ and $\mathcal{M}_k$ . The red and black line strokes in sketch $\mathcal{I}$ corresponds to $\mathcal{M}_k$ , and $\mathcal{M}_r$ , respectively. + +and the same for $\mathcal{M}_k, \mathcal{L}_k$ . We compute $\mathcal{M}_r = \mathcal{M} \setminus \mathcal{M}_k$ , which is mutually exclusive from $\mathcal{M}_k$ . The volume sampling and mesh cropping details can be found in the supplemental. We use the resulting meshes to supervise both the addition and the deletion networks defined in Sec. 3.1. + +Sketch Generation. During training, we generate synthetic sketches corresponding to the processed mesh data by performing Canny edge detection on mesh normal and depth renderings. We randomly sample rendering viewpoints and apply image augmentations to synthesize different line drawing styles. The trained model can thus handle human freehand sketches from various viewpoints. We provide the sketch generation details in the supplemental. + +# 4. Experiments + +# 4.1. Implementation Details + +Data. Following MeshGPT [49] and MeshAnythingV2 [15], we preprocess and filter the ShapeNet dataset [7] to obtain approximately 28k meshes from 55 categories, which each have a face count $< 768$ for training. We sample around 500 meshes for validation and 1000 meshes for testing. Other meshes are used for training. + +Training. Both the mesh addition and deletion networks are initialized using the OPT weights from the MeshAnythingV2 checkpoint. The RADIO model is frozen during training. We employ a learning rate schedule from $1 \times 10^{-4}$ to $1 \times 10^{-6}$ . For the addition model, training begins with a batch size of 56 for 128 epochs, followed by 20 epochs with a batch size of 224. The deletion model is trained with a batch size of 32 for 128 epochs. Using 4 NVIDIA A100 GPUs, the training process takes approximately 5 days for the addition network and 2 days for the deletion network. + +# 4.2. Metrics and Baselines + +We evaluate the generated mesh quality as well as its consistency with the input sketch. For mesh quality, we report the Chamfer Distance (CD) to the target mesh. A smaller CD indicates better geometric consistency with the target. + +![](images/f7014d337848eabaee96e66215a03966a087d71fb3c6edc092856aa7bbce6427.jpg) +Figure 5. Visual comparison of generation and editing results. We show generation and editing results of LAS [61], SENS [6], and their results post-processed by MeshAnythingV2 (MA) [15]. Our method produces 3D meshes that not only match the sketch inputs and edits, but also offer high fidelity. + +For perceptual mesh quality evaluation, we employ shading image-based Fréchet Inception distance (FID) following MeshGPT [49] and SENS [6]. We also evaluate sketch-based CLIP [45] similarity, following LAS [61], to measure the similarity between the generated mesh and the sketch. We additionally introduce sketch-based LPIPS [58] to evaluate sketch-to-mesh correspondence: while CLIP shows the similarity of the global context, LPIPS focuses more on local features. For our method, we analyze runtime with the token generation speed in tokens/second (T/s). For this, we measure the time of generating the first 300 tokens of the addition task, which eliminates the speed difference caused by the varying lengths of generated sequences. + +We further conduct both unary and binary perceptual studies. In the unary study, participants evaluate mesh quality (GQ) and sketch matching (GM) for mesh generation. For mesh editing, they rate edited mesh quality (EQ), edited sketch matching (EM), and edited mesh consistency (EC) of the unedited part. Each is rated on a scale of 1 to 5 (=best). In the binary study, we ask participants to compare our method with baselines and select their preferred method. We report the percentages of preferences for our method compared to the baselines. + +We compare with two state-of-the-art sketch-conditioned 3D generation methods, LAS [61] and SENS [6]. These methods produce signed distance fields or occupancy grids, and we use marching cubes to convert their outputs to triangle meshes. Since LAS and SENS were trained on fewer categories than our method, we report the metrics considering only the results of their respective trained categories (LAS: chair, car, airplane, table, and rifle; SENS: airplane, chair, and lamp). For our method, the metrics are computed on all data in the test set. We alternatively use Me + +shAnythingV2 [15] to post-process LAS and SENS results (LAS-MA and SENS-MA, respectively), producing more artistically-styled meshes for these baselines. + +# 4.3. Experimental Setup + +We use the test set described in Sec. 4.1 and automatically generate sketches from one of five views: top-left, top-front-left, top-front, top-front-right, or top-right, for the generation task. To further show the robustness of our method, we use the IKEA dataset [34, 51], which contains 188 furniture models. We use automatically generated sketches (following Sec. 3.4) for generation tasks because they aid the analysis of sketch-to-mesh correspondence by the CLIP and LPIPS scores. In our qualitative experiments, we show that our method generalizes to hand-drawn sketches. Additionally, we randomly select 50 shapes of airplanes, chairs, and lamps (on which SENS is trained) from the two datasets, automatically generate their sketches for generation, and then manually edit the sketches for one-step editing evaluation. + +For the generation task, our method predicts an entire mesh from scratch conditioned on the sketch input. We provide additional camera view conditions in all LAS runs as suggested in [61]. We also apply dilation and resizing to sketches to match the input to the training data of LAS. As SENS is category-specific, we use its checkpoint corresponding to the category of the target mesh for each evaluation run. + +For the editing task, we let LAS generate from scratch conditioned on the edited sketch, since it does not support localized editing. SENS was designed for editing, and we ran its editing using its original design. For our method, while providing only the original sketch and the edited + +![](images/b58ab01e26afcc8952c8d2ba3b7accab2ed99567a6f003fe625c0e4d346638c3.jpg) +Figure 6. Sequence visualization of mesh creation with MeshPad. We show the input sketch on the top left of each of our method outputs. Green and purple arrows represent addition and deletion, respectively. The “+++” inside a green arrow indicates multiple addition steps. + +
DatasetMethodCD↓LPIPS↓CLIP↑FID↓
ShapeNetLAS15.020.274294.6146.90
LAS-MA22.060.296393.6318.52
SENS8.950.275393.3681.88
SENS-MA29.430.334891.8842.93
Ours6.200.179095.859.38
IKEALAS16.270.297094.8369.54
LAS-MA20.360.315193.7946.56
SENS8.760.272294.38115.33
SENS-MA19.180.303794.3799.08
Ours6.780.183796.6729.67
+ +Table 1. Evaluation on sketch-conditioned mesh generation. We compare with LAS [61], SENS [6], and further use MeshAnythingV2 (MA) [15] to post-process LAS and SENS outputs. The unit of CD is 0.001. Our results are generated by one addition operation from scratch. MeshPad outperforms baselines in both mesh quality and consistency with input sketches. + +sketch, we first automatically generate input for deletion by identifying the difference between the two sketches, then perform the deletion-addition operation. + +# 4.4. Comparison to State of the Art + +Mesh Generation. Tab. 1 evaluates MeshPad in comparison with state of the art on mesh generation. Quantitatively, our method outperforms baselines in all evaluation metrics, indicating superior mesh quality and sketch-to-mesh correspondence. We also conduct a perceptual study with 35 participants, and show results in Tabs. 2 and 3, further demonstrating user preference for our generated meshes. Fig. 5 provides qualitative comparison across the methods. While MeshAnythingV2 can convert marching cube meshes to meshes with more artist-reminiscent design, it is not robust enough to handle various artifacts in outputs of LAS and SENS (e.g., floaters or incomplete parts), resulting in an overall worse quality than our method, which bridges directly sketch to mesh. + +Mesh Editing. Based on the results of the perceptual study, together with the sketch metrics reported in Tabs. 2 and + +
MethodSketch MatchingGen. RatingEdit Rating
LPIPS↓CLIP↑GQ↑GM↑EQ↑EM↑EC↑
LAS0.316492.733.23.02.72.22.5
LAS-MA0.335791.522.82.62.42.02.0
SENS0.317991.493.43.52.91.83.7
SENS-MA0.365190.202.72.82.11.62.5
Ours0.221895.714.34.34.34.24.3
+ +Table 2. Sketch-based metrics and unary perceptual study ratings (ranged 1-5) on generation and editing results of our hand-drawn sketch evaluation set. We benchmark against LAS [61] and SENS [6], with outputs further refined using MeshAnythingV2 (MA) [15]. For mesh generation, participants evaluate mesh quality (GQ) and sketch matching (GM). For mesh editing, participants rate edited mesh quality (EQ), edited sketch matching (EM), and edited mesh consistency (EC) of the unedited part. + +
OperationLASLAS-MASENSSENS-MA
Generation93.3%94.2%83.7%91.0%
Editing94.4%96.5%91.9%94.4%
+ +Table 3. Binary perceptual study. Participants choose their preferred output between our method and each baseline (LAS [61], SENS [6], and their results post-processed by MeshAnythingV2 (MA) [15]). Our method is preferred by a large margin for both generation and editing. + +3, our method achieves the best LPIPS and CLIP scores among baselines and reaches the highest rating and preference among users. From the visual comparisons provided in Fig. 5, we notice that baseline methods suffer not only from poor editing results but also from inconsistency in unedited regions. This is because these methods regenerate the whole shape after the edit, can change regions not intended to be edited. Our method solves this problem by decoupling the editing procedure into deletion and addition, ensuring that only edited regions are changed. We present editing sequences with real human inputs in Fig. 6, demonstrating our method's generalizability. Moreover, our method can edit meshes that are not generated by our networks, which is difficult for baselines, and the results are provided in the supplemental. + +Novelty Analysis. Fig. 7 shows a qualitative novelty analysis, retrieving for our interactively created meshes the 3 + +![](images/137f0938e4b126cce97bc8c1bcc6b423833327063b39962961dc9b34dc710d6f.jpg) +Figure 7. Novelty of interactively created shapes. We retrieve the nearest neighbors of the meshes by first aligning them to each train mesh with Iterative Closest Point (ICP) and then computing the Chamfer distance. MeshPad can generate new shapes different from those in the train set and can generate shapes beyond the categories of the training data (third row). + +nearest neighbors from the training set, based on Chamfer distance. Our generated shapes differ from their nearest neighbors in both overall shape and triangulation, which demonstrates that our method can generate new shapes. + +# 4.5. Ablations + +Tab. 4 ablates our vertex-aligned speculator design choices. We conduct ablation studies on three variants of the addition network: without speculator, without vertex-aligned decoding (with the same decoding length of 2), and without joint training with the OPT. + +Joint training provides context-rich hidden states as a precursor input. We find that the vanilla speculator training scheme with frozen transformer [55] does not work in our mesh generation setting, as the hidden states from our pre-trained transformer do not contain enough contextual information. As shown in Tab. 4, by instead training the speculator jointly with the OPT, our model achieves strong mesh quality performance. In contrast, training the speculator with the OPT frozen results in poor performance. This indicates the OPT learns to encode contexts into the hidden states when jointly trained. + +Vertex-alignment preserves mesh quality while achieving comparable speedup as vanilla MLP speculators. + +Comparing no speculator (w/o speculator) and speculator without vertex alignment (w/o vert-alignment), we can see that the speculator, without aligning to vertex tokens, results in a notable speedup, but at large penalty cost in mesh quality and sketch-to-mesh correspondence. By aligning the speculator to vertex tokens, our method reaches the same level of sketch-to-mesh correspondence as the no speculator version while maintaining the naive speculator's advantage in generation speed. Additionally, applying the vertex + +
MethodQuality MetricsSpeed T/s↑
CD↓LPIPS↓CLIP↑FID↓
w/o speculator7.660.176595.5932.5960.7
w/o vert-alignment9.000.199294.4335.65138.9
w/o joint training57.130.513484.52211.46130.8
Ours6.780.183796.6729.67131.1
+ +Table 4. Ablation study. We ablate our curator, vertex alignment of our curator (using a common MLP curator [55] with the same length of 2), and its joint training with our mesh transformer. The unit of CD is 0.001. T/s represents tokens per second and is measured on NVIDIA A100. Our vertex-aligned curator accelerates generation by $2.16 \times$ without loss in mesh quality. Compared to an MLP curator without vertex-alignment, which suffers from quality loss, our method runs at a comparable speed. + +aligned curator results in slightly higher metrics in mesh quality. This is likely due to the vertex-aligned curator reducing the complexity of the linear prediction head. Rather than predicting control tokens and all $x, y$ , and $z$ coordinate tokens, it is trained to predict only control tokens and $x$ coordinate tokens, which reduces the overall prediction error. Thus, equipped with the vertex-aligned curator, our method achieves strong performance and fast generation speeds (approximately 26.7 faces per second considering the average face density of the mesh sequences). As a result, mesh additions, which typically generate about $1/5$ of a complete shape, run in about 1 to 5 seconds (depending on the number of faces added), enabling interactive runtimes for editing. + +Limitations. Similar to recent mesh generation methods [12, 49], our transformer model is limited by context length. Although there are recent attempts [25] to extend the context length, their outputs (thousands of triangles) still fall below the requirement of modern computer graphics applications (millions of triangles). Leveraging techniques, like token compression [28], is a promising avenue to explore. Nevertheless, our approach achieves interactive mesh generation and editing with easy-to-use sketches, enabling iterative creation of novel and complex 3D shapes. + +# 5. Conclusion + +MeshPad introduces interactive editing into autoregressive mesh generation, by decomposing editing into addition and deletion operations on sequentialized mesh tokens. In contrast to existing works which focus on full shape generation, MeshPad enables fine-grained and localized control over the artistic generation process. To enable interactive feedback, our vertex-aligned speculator notably speeds up mesh face generation, running in just a few seconds in response to user sketch updates. Our sketch-conditioned approach also enables ease of use in creation of complex 3D meshes from novice users. We believe that MeshPad represents a significant step toward democratizing content creation, enabling everyone to create artist-reminiscent 3D meshes. + +# Acknowledgements + +This work was funded by AUDI AG. Lei Li and Angela Dai were supported by the ERC Starting Grant SpatialSem (101076253) and Matthias Nießner by the ERC Consolidator Grant Gen3D (101171131). 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Recently, great advances have been made by the end-to-end methods, thanks to deep learning techniques, but they face limitations of representation inconsistency in multivariable integration and struggle to effectively capture the dependency between variables, which is required in complex weather systems. Treating different variables as distinct modalities and applying a two-stage training approach from multimodal models can partially alleviate this issue, but due to the inconvenience in training tasks between the two stages, the results are often suboptimal. To address these challenges, we propose an implicit two-stage training method, configuring separate encoders and decoders for each variable. In detailed, in the first stage, the Translator is frozen while the Encoders and Decoders learn a shared latent space, in the second stage, the Encoders and Decoders are frozen, and the Translator captures inter-variable interactions for prediction. Besides, by introducing a self-attention mechanism for multivariable fusion in the latent space, the performance achieves further improvements. Empirically, extensive experiments show the state-of-the-art performance of our method. Specifically, it reduces the MSE for near-surface air temperature and relative humidity predictions by $28.82\%$ and $23.39\%$ , respectively. The source code is available at https://github.com/ShremG/Met2Net. + +# 1. Introduction + +Global climate change and the increasing frequency of extreme weather events make accurate weather prediction crucial [10]. While traditional statistical and physical models are effective in some areas, they often struggle with complex nonlinear relationships and high-dimensional + +![](images/3b8003af1c75d5d9e6f9e4a926d50959c7fb4102d4ca25bb44994f8e937396e9.jpg) +(a) Data distributions. + +![](images/d5e3d6180475bc2014bd20b29d0a11c7df84d4560a73040f887a0bea332275bd.jpg) +(b) First-order difference. + +![](images/83a37a5ad6cc3b4225c356babacab648db7a55c39bb1f318eadd57e6b86e6afa.jpg) +(c) T2M variable. + +![](images/4b30ae812dadd77e08c970386c22908f4ed5c7e43a3eeb84d2aa6296de9a3dc9.jpg) +(d) TCC variable. +Figure 1. (a) Spatiotemporal distributions of the meteorological variables TCC and T2M highlight their heterogeneity. (b) First-order differences illustrate variations in trends and rates. (c) and (d) show that incorporating multiple variables did not enhance and even degraded TAU's performance, while the two-stage training scheme also produced suboptimal results. + +data. Recently, advancements in artificial intelligence have driven the rapid development of spatiotemporal prediction models, significantly improving weather forecasting accuracy [16, 17, 31, 32, 50, 51]. The success of these methods is attributed not only to their focusing on temporal nonstationarity but also to their incorporation of spatial dependency to capture more complex weather patterns. + +However, variables such as temperature, humidity, wind speed, and precipitation interact with each other, forming a complex climate system [1, 5, 7, 8, 12]. The prevailing methods aim to analyze a single variable, fail to capture these dynamic relationships, thus leading to prediction errors. Therefore, integrating multiple meteorological variables enables the model to better understand weather patterns, identify potential extreme weather events, and provide more reliable warnings and decision support in re + +![](images/eb7685c934a14580c8a146ba7505e5b5d60775721acd84ac37f3acea8b2026b2.jpg) +Figure 2. (a) End-to-End (E2E) training strategy. (b) Generative model training strategy, where task inconsistency exists between the two stages. (c) $\mathrm{Met}^2\mathrm{Net}$ training strategy, which ensures task consistency across both stages. The Translator module is responsible for learning spatiotemporal features. The Translator module is responsible for learning spatiotemporal features. + +sponse to climate change [8, 12]. + +During implementation, we found that simply incorporating multiple meteorological variables into the existing spatiotemporal prediction framework did not significantly improve accuracy; in some cases, it even decreased. As shown in Figure 1c and 1d, the experimental results confirm this performance decline. Different from image data with RGB channel, which could be regarded as multi-variables, the meteorological variables demonstrate a high degree of divergence [21, 52]. As an illustration, we present the distribution of each variable's values across spatial and temporal dimensions, as shown in Figure 1a, 1b. (Detailed experimental setting is given in Appendix.) These distribution divergences make it challenging for simple end-to-end training to effectively integrate these variables [9, 37, 41], leading to (i) representation inconsistency. The reason is that when a single model processes highly divergent data, it can easily lead to a loss of the original characteristics of the data as features across different dimensions are forcibly integrated into the same space, resulting in an inconsistency between the representation and the input variables. + +To address representation inconsistency, two-stage training approaches, inspired by multi-modal generation models [11, 47, 59], treat different meteorological variables as distinct modalities. This strategy, widely used in modern generative models like Latent Diffusion [47] and autoregressive for image [30, 62] and video [24, 61], maps diverse modalities into a shared latent space, transforming heterogeneity into homogeneity [43] and enhancing model performance. However, its application to spatiotemporal prediction remains rare. + +When we adapted this two-stage strategy, results were unsatisfactory (Figure 1c, 1d), which we attribute to (ii) task inconformity. In generative tasks, the first stage typically employs Auto-encoders or Variational Auto-encoders [6, 27] to reconstruct data, mapping it into a latent space. The second stage then uses models like diffusion to gener + +ate representations from noise [36, 38, 63], continuing the reconstruction process. However, in spatiotemporal prediction, while the first stage aligns with generative training, the second stage shifts to a prediction task rather than denoising reconstruction. This mismatch hinders the effectiveness of learned representations, leading to suboptimal accuracy, as shown in Figure 1c and 1d. + +To address this issue, we propose $\mathrm{Met}^2\mathrm{Net}$ , a decoupled two-stage spatio-temporal forecasting model for complex meteorological systems, as shown in Figure 2c. Specifically, to eliminate representation inconsistency and task inconformity, we freeze the gradients of the Translator in the first stage and those of the Encoder and Decoder in the second stage, ensuring alignment between training objectives. Momentum updates [18] adjust the frozen components in both stages, maintaining stability and enabling smooth parameter adaptation. Additionally, a prediction loss in the latent space ensures a unified learning objective, keeping both stages focused on forecasting rather than shifting from reconstruction to prediction. This design allows $\mathrm{Met}^2\mathrm{Net}$ to function within a single continuous training cycle, eliminating explicit stage separation. To further improve performance, dedicated encoders and decoders preserve variable-specific features, while a self-attention mechanism in the Translator enables effective multivariable integration. By addressing both representation inconsistency and task inconformity, $\mathrm{Met}^2\mathrm{Net}$ achieves more accurate and stable multivariate spatiotemporal prediction. To summarize, our contribution in this work is as follows: + +- We propose an implicit two-stage training paradigm that freezes module gradients at specific stages and employs momentum updates. By introducing prediction loss in the latent space, the approach effectively aligns training objectives, enhancing spatiotemporal prediction. +- We treat each meteorological variable as an independent modality, using separate encoders and decoders, and introduce a self-attention mechanism in the Translator to capture inter-variable relationships. +- We construct a general multivariate spatiotemporal prediction dataset to evaluate the robustness and generalization of our method. Empirical results show that $\mathrm{Met}^2\mathrm{Net}$ achieves SOTA performance, reducing the MSE of T2M and R by $28.82\%$ and $23.39\%$ , respectively. Additionally, it improves hurricane trajectory prediction accuracy, demonstrating its effectiveness in weather forecasting. + +# 2. Related works + +Spatiotemporal predictive learning. The advancements in recurrent-based models have greatly enhanced our understanding of spatiotemporal predictive learning. The ConvLSTM model [48] combines convolutional networks with LSTM to capture spatiotemporal patterns. Following this, PredRNN [53] and PredRNN++ [54] used spatiotemporal + +LSTM (ST-LSTM) and gradient highway units to better capture temporal dependencies and reduce gradient vanishing. MIM [56] uses the difference between hidden states to improve handling of nonstationarity. E3D-LSTM [55] adds 3D convolutions to LSTM to improve feature extraction across time and space. PhyDNet [16] separates partial differential equation (PDE) dynamics from unknown factors using a recurrent physical unit. MAU [4] introduces a motion-aware unit to capture motion-related information. Lastly, PredRNNv2 [58] uses a curriculum learning strategy and memory decoupling loss to improve performance. Unlike recurrent-based methods, which have high computational costs in spatiotemporal prediction, SimVP [14] introduces a non-recurrent spatiotemporal prediction framework that reduces computational costs while achieving competitive performance. Subsequently, non-recurrent models such as TAT [39], TAU [50], DMVFN [20], and Wast [40] made further progress by incorporating triplet attention, temporal attention, dynamic multiscale voxel flow, and a 3D wavelet framework. However, these methods are based on single-variable spatiotemporal training, and although they have achieved top-tier performance in weather prediction, they fail to fully exploit the potential of multivariable data in weather forecasting. To address this, we propose a solution that independently encodes and decodes each variable and introduce an implicit two-stage training strategy. + +Weather forecasting. Weather forecasting, as a specific application of spatiotemporal prediction, has also benefited from these advancements, leading to significant improvements in prediction accuracy and computational efficiency. Han et al. [17] applied the SimVP model for radar extrapolation and achieved competitive performance in precipitation prediction scenarios. Chen et al. [8] introduced the TAU model, integrating satellite data to alleviate the issue of severe abrupt changes in precipitation scenarios. Eusebi et al. [12] utilized PINN to fuse barometric pressure for hurricane reconstruction. Jiang et al. [22] employed GNN to integrate multiple variables, further enhancing the accuracy of wind speed predictions. Models such as Pangu [1], FuXi [7], and Fengwu [5] incorporate a wide range of meteorological variables, achieving near-perfect predictions of typhoon paths and highlighting their capability for medium-range forecasting. This underscores the necessity and effectiveness of integrating multiple variables and multimodal data in weather forecasting. + +Two stage training methods. Two-stage training is widely used in generative tasks, where models like Stable Diffusion [47], MAGVIT [62], and VideoPoet [24] map diverse modalities into a shared latent space for improved representation learning. Typically, the first stage employs Auto-encoders (AE) or Variational Auto-encoders + +(VAE) [6, 27] for data reconstruction, while the second stage utilizes diffusion models [36, 38, 63] to generate latent representations from noise. Recent research on two-stage training focuses on enhancing the generality of representations learned in the first stage through large-scale pretraining [3, 15, 18, 42]. While this improves transferability across tasks, it requires extensive data, limiting its feasibility in scenarios with constrained datasets. However, in spatiotemporal prediction, the challenge lies not only in obtaining general representations but also in addressing task inconformity, where the second stage shifts from reconstruction to forecasting. This misalignment reduces the effectiveness of learned representations for prediction, leading to suboptimal accuracy. Our work tackles this issue by designing a training strategy that better aligns the objectives of both stages, improving prediction performance without requiring large-scale pretraining. + +# 3. Method + +# 3.1. Preliminaries + +We formally define the multivariable spatiotemporal predictive learning problem as follows. Given a multivariable time sequence $X_{t - T + 1}^{t} = \{x_{i}^{t}\}_{t - T + 1}^{t}$ at time $t$ with the past $T$ frames, we aim to predict the subsequent $T'$ frames $Y_{t + 1}^{t + T'} = \{y_i^{t + 1}\}_{t + 1}^{t + T'}$ from time $t + 1$ , represents a collection of $N$ variables, each with channels $C$ , height $H$ , and width $W$ . In practice, we represent the time sequences as tensors, i.e., $X_{t - T + 1}^{t} \in \mathbb{R}^{T \times N \times C \times H \times W}$ and $Y_{t + 1}^{t + T'} \in \mathbb{R}^{T' \times N \times C \times H \times W}$ . For example, the wind variable has two channels, U and V, and its dimensions can be represented as $\mathbb{R}^{T \times 1 \times 2 \times H \times W}$ . + +In this paper, we denote the Encoder by $\mathcal{E}$ , the Decoder by $\mathcal{D}$ , and the Translator by $\mathcal{T}$ . We denote the true input data by $X$ and the label by $Y$ . The reconstructed or predicted corresponding data are represented by $X'$ and $Y'$ , respectively. $Z_x$ represents the encoded state of $X$ processed by $\mathcal{E}$ , and $Z_y$ represents the encoded state of $Y$ processed by $\mathcal{E}$ . $Z_y'$ denotes the predicted state of $Z_x$ processed by $\mathcal{T}$ . + +# 3.2. Overview + +As shown in Figure 3, training is divided into two stages. In the first stage, the Translator is frozen while the Encoder and Decoder are trained to focus on spatial feature compression and reconstruction. In the second stage, the Encoder and Decoder are frozen, and a latent space prediction loss is introduced to train the Translator for inter-variable relationship modeling and prediction. During inference, only the fully trained modules are used, excluding those with frozen gradients. Thus, while this approach adds parameters and computation during training, the parameter count and computational load during inference remain the same as a standard end-to-end model. To better handle multi-variable sce + +![](images/f89c049f61378bc9a93d582b613d5b7c6162c1ed3321f737dd92844f20b363f5.jpg) +Figure 3. Training pipeline and Inference pipeline. The training pipeline consists of two stages: In Stage I, the Translator (blue snowflake icon) is frozen while the Encoder and Decoder (orange flame icon) are trained. In Stage II, the Encoder and Decoder are frozen, and the Translator is trained. Momentum updates, represented by dashed arrows, are applied to the frozen parameters at the end of each stage. Multiple encoders and decoders are used for different meteorological variables, enabling independent feature extraction and reconstruction. The inference pipeline uses the trained Encoder, Translator, and Decoder to generate the final output. + +narios, each variable has its own Encoder-Decoder pair. + +# 3.3. Implicit two-stage training strategy + +Inspired by the two-stage training approach used in multimodal models in the generative domain [24, 47, 62], we propose an implicit two-stage training strategy. This strategy involves freezing the gradients of different components at various stages within a single training process and using momentum updates to adjust parameters. While ensuring consistency of objectives between the two stages, this method retains the advantages of traditional two-stage training strategies, such as effective module transferability and efficient modality fusion. + +In implementation, we should stop gradients of Translator $(\mathcal{T})$ during the first stage and gradients of Encoder $(\mathcal{E})$ & Decoder $(\mathcal{D})$ during the second stage. However, the Translator and Encoder & Decoder cannot be optimized alternatively with naive stop-gradient operation. To address this issue, we introduce the momentum update method to update the corresponding parameters. Formally, denoting the parameters of $f_{m}$ and $f$ as $\theta_{m}$ and $\theta$ , we update $\theta_{m}$ by: + +$$ +\theta_ {m} \leftarrow \alpha \theta_ {m} + (1 - \alpha) \theta \tag {1} +$$ + +Here $\alpha \in [0,1]$ is a momentum coefficient. $f$ represents the components $\mathcal{E},\mathcal{D}$ , and $\mathcal{T}$ whose parameters are updated through backpropagation, while $f_{m}$ represents the corresponding components with frozen gradients. + +During the training process, the objective function for the first stage is consistent with the end-to-end model, aiming to minimize the gap between $Y'$ and $Y$ . The objective for the second stage is to minimize the gap between $Z_y'$ and $Z_y$ . Ultimately, our loss function can be expressed as: + +$$ +\mathcal {L} = \mathcal {L} _ {1} \left(Y ^ {\prime}, Y\right) + \mathcal {L} _ {2} \left(Z _ {y} ^ {\prime}, Z _ {y}\right) \tag {2} +$$ + +where $\mathcal{L}_1$ and $\mathcal{L}_2$ represent the loss functions for the first and second stages, respectively, and both are defined as Mean Squared Error (MSE) in this study. $Y$ represents the target data, $Y'$ is the model's output data, $Z_y'$ is the output of the second stage $\mathcal{T}$ , and $Z_y$ is the output of $Y$ after being processed by $\mathcal{E}$ . + +# 3.4. Multiple meteorological variables fusion + +In meteorological forecasting, integrating multiple variables is essential in that meteorological factors, as different physical quantities, are mutually coupled and influence each other within an actual geophysics dynamic system [22, 26, 33, 35, 57]. Merging different variables can be regarded as multimodal fusion, and we thus, enlighten by the latest techniques in multimodal fusion [2, 19, 24, 44], design independent $\mathcal{E}$ and $\mathcal{D}$ for each meteorological variable and then used a $\mathcal{T}$ in the latent space to achieve the fusion and prediction. + +Each meteorological variable is assigned a pair of $\mathcal{E}$ and $\mathcal{D}$ with the same configuration. For $\mathcal{E}$ and $\mathcal{D}$ , we use a two-dimensional architecture. $\mathcal{E}$ independently compresses each variable into the latent space along the spatial dimensions, while $\mathcal{D}$ restores the embeddings from the latent space back to the original space. Formally, denoting the two input meteorological variables as $X_{1}, X_{2}$ , the fusion steps read + +$$ +Z _ {1} = \mathcal {E} _ {1} \left(X _ {1}\right), Z _ {2} = \mathcal {E} _ {2} \left(X _ {2}\right) \tag {3} +$$ + +$$ +Z = \operatorname {S t a c k} \left(Z _ {1}, Z _ {2}\right) \tag {4} +$$ + +$$ +\hat {Z} ^ {\prime} = \mathcal {T} (Z) \tag {5} +$$ + +$$ +\hat {X} _ {1} ^ {\prime} = \mathcal {D} _ {1} (\operatorname {S l i c e} \left(\hat {Z} ^ {\prime}\right)), \hat {X} _ {2} ^ {\prime} = \mathcal {D} _ {2} (\operatorname {S l i c e} \left(\hat {Z} ^ {\prime}\right)) \tag {6} +$$ + +Here, $\mathrm{Stack}(\cdot)$ and $\mathrm{Slice}(\cdot)$ represent stacking and slicing + +Table 1. Quantitative comparison of predictions across multiple meteorological variables, including UV10, T2M, TCC, and R, measured using MSE, MAE, and RMSE metrics. # Params denote the parameters of the model during the inference stage. N represents the number of models required to predict the four variables. ↓ indicates lower is better. + +
MethodDate#Params. N (M)UV10T2MTCCR
MSE↓MAE↓RMSE↓MSE↓MAE↓RMSE↓MSE↓MAE↓RMSE↓MSE↓MAE↓RMSE↓
ConvLSTM[48]NeurIPS'201514.9841.89760.92151.37751.52100.79491.23300.04940.15420.222335.14604.01205.9280
PredRNN[53]NeurIPS'201723.5741.88100.90681.37151.33100.72461.15400.05500.15880.234637.61104.09606.1330
PredRNN++[54]ICML'201838.4041.87270.90191.36851.45800.76761.20700.05480.15440.234145.99304.73106.7820
MAU[4]NeurIPS'20215.4641.90010.91941.37841.25100.70361.11900.04960.15160.222634.52904.00405.8760
SimVP[14]CVPR'202214.6741.99930.95101.41401.23800.70371.11300.04770.15030.218334.35503.99405.8610
ConvNeXt[34]CVPR'202210.0941.69140.86981.30061.27700.72201.13000.04740.14870.217833.17903.92805.7600
HorNet[45]NeurIPS'202212.4241.55390.82541.24661.20100.69061.09600.04690.14750.216632.08103.82605.6640
TAU[50]CVPR'202312.2241.59250.84261.26191.16200.67071.07800.04720.14600.217331.83103.81805.6420
Wast[40]AAAI'202414.464---1.09800.63381.0440-0.14520.2150-3.69405.5690
\( Met^2 \)NetOurs8.6511.50550.81961.22700.82710.57700.90940.04220.13700.205424.38543.32094.9382
+ +Table 2. The statistics of datasets. The training or testing set has $N_{\text{train}}$ or $N_{\text{test}}$ samples, composed by $T$ or $T'$ images with the shape $(C, H, W)$ . The weather refers to the multivariate prediction dataset. The subscript $L$ denotes low spatial resolution, $HA$ represents high-altitude variables, $H$ and indicates high spatial resolution. The MvMmfnist is a dataset we constructed for the general multivariate spatiotemporal prediction scenario. + +
NtrainNtestCHWTT'
WeatherL5255917495532641212
WeatherHA54019288312326444
WeatherH52559174955641281212
ERA543801873741281281212
UV105255917495132641212
T2M5255917495132641212
TaxiBJ1962713342323244
MvMmfnist1000010000364641010
+ +operations, respectively. $\hat{X}_1^{\prime},\hat{X}_2^{\prime}$ represent the model's prediction results for the two meteorological variables. + +# 3.5. Translator + +To model the complex dynamic dependencies of multiple meteorological variables, we utilize an attention mechanism to effectively capture the correlations between variables [13] and achieve effective decoupling between multiple variables. + +Before processing with the $\mathcal{T}$ , the embeddings of each variable for all time steps need to be arranged sequentially along the channel dimension. For a spatiotemporal signal with $N$ variables, the length of $T$ , and the spatial resolution of $(H,W)$ , which is denoted by $Z \in \mathbb{R}^{N \times T \times H \times W}$ , the attention matrix over variable axis reads as: + +$$ +\mathbf {A} = \operatorname {s o f t m a x} \left(\frac {Q K ^ {\intercal}}{\sqrt {d}}\right), \tag {7} +$$ + +where $Q, K \in \mathbb{R}^{N \times D \times H \times W}$ are query and key, which are extracted by two different 2D-CNNs, and $\sqrt{d}$ is a scaling term. After the softmax $(\cdot)$ function, $\mathbf{A} \in \mathbb{R}^{N \times N}$ demonstrates the correlations between different variables. Subsequently, the fusion is performed by $Z_{a} = \mathbf{A}V$ , where + +$V \in \mathbb{R}^{N \times T \times H \times W}$ is the value term, extracted by another 2D-CNN, $Z_{a} \in \mathbb{R}^{N \times T \times H \times W}$ is the fused embeddings. We denote the above operations using $\mathrm{VA}(\cdot)$ (Variable Attention). Next, we use a spatiotemporal feature extractor written as $\mathrm{ST}(\cdot)$ to extract spatiotemporal features and map them into predictions, as + +$$ +\mathcal {T} (Z) = \operatorname {S T} (\operatorname {V A} (Z)) \tag {8} +$$ + +In this paper, we utilize TAU Block[50] as the practical implementation of $\mathrm{ST}(\cdot)$ . We discuss the impact of using different blocks on the results in the appendix. + +# 4. Experiment + +In this section, we present experiments demonstrating the effectiveness of our method across two tasks: multivariate weather prediction and general spatiotemporal prediction. For multivariate weather prediction, we tested low- and high-resolution spatial data as well as high-altitude data, and we conducted a hurricane trajectory prediction experiment using real ERA5 data. For general spatiotemporal prediction, both single-variable and multivariate experiments were conducted to assess the method's generalization and versatility. The datasets used are listed in Table 2. + +The datasets $\mathrm{Weather}_L$ and $\mathrm{Weather}_H$ use UV10 (10-meter u and v components of wind), T2M (2-meter temperature), TCC (total cloud cover), and R (relative humidity), for a total of four variables, with the two components of wind considered as a single variable. The $\mathrm{Weather}_{HA}$ dataset uses U (u component of wind), V (v component of wind), T (temperature), and R (relative humidity), for a total of four variables. Additionally, the ERA5 dataset includes MSL (mean sea level pressure), U10, V10, and T2M, also consisting of four variables. For the ERA5 dataset, we performed spatial cropping within the range of $110^{\circ}\mathrm{E} - 142^{\circ}\mathrm{E}$ and $12.25^{\circ}\mathrm{N} - 44^{\circ}\mathrm{N}$ . The dataset was split into three subsets: 2017-2021 for training, 2022 for validation, and 2023 for testing. + +![](images/d822dbf5a84370654a72fff7286a7a84e6d38ed9c78b841bba246933722cbf99.jpg) +(a) $t = 1$ + +![](images/dd4c4b4b6df22920df2856f04725e5ea2745e97ec7b756a837ec18ad77c685a0.jpg) +(b) $t = 12$ +Figure 4. Visualization of prediction results for different lead times. (a) Results at a forecast time of 1 hour. The background in white represents the absolute error $(|Y' - Y|)$ for each model. (b) Results at a forecast time of 12 hours. Across both 1-hour and 12-hour forecasts, the error of the TAU model is consistently higher than that of our Met $^2$ Net model. + +Table 3. Quantitative comparison of predictions across multiple high-altitude variable meteorological variables, including R, T, U, and V, measured using MSE, MAE, and RMSE metrics. $\downarrow$ indicates lower is better. + +
MethodDateRTUV
MSE↓MAE↓RMSE↓MSE↓MAE↓RMSE↓MSE↓MAE↓RMSE↓MSE↓MAE↓RMSE↓
ConvLSTM[48]NeurIPS'2015368.1513.4919.196.30301.76952.510730.0023.89235.477430.7893.82385.5488
PredRNN[53]NeurIPS'2017354.5713.1718.8305.59661.64112.365727.4843.67765.242528.9733.66175.3827
PredRNN++[54]ICML'2018363.1513.2519.0565.64711.64332.376328.3963.73225.328829.8723.70675.4655
MAU[4]NeurIPS'2021363.3613.5019.0625.62871.68102.372527.5823.74095.251927.9293.67005.2848
SimVP[14]CVPR'2022370.0313.5819.2366.10681.75542.471228.7823.84355.364929.0943.76145.3939
ConvNeXt[34]CVPR'2022367.3913.5219.1686.17491.74482.484929.7643.86885.455631.3263.84355.5969
HorNet[45]NeurIPS'2022353.0213.0218.7895.58561.61982.363428.1923.71425.309630.0283.71485.4798
TAU[50]CVPR'2023342.6312.8018.5104.90421.53412.214524.7193.50604.971925.4563.47235.0454
Met2NetOurs337.9812.7418.384.13761.36882.034122.8323.34494.778323.9003.35974.8888
+ +![](images/3e8c883ba4e285213ddd828897b43b96a2f15b2141bfaa1f5e2e3e2029137cea.jpg) +Figure 5. $\mathrm{Met}^2\mathrm{Net}$ effectively resolves representation inconsistency by maintaining higher CKA values across layers compared to TAU. The TAU model exhibits a gradual increase in CKA values through the Translator section but maintains relatively lower CKA values overall. In contrast, $\mathrm{Met}^2\mathrm{Net}$ sustains higher CKA values across all layers, particularly in the Encoder and Translator sections, indicating improved representation consistency. + +# 4.1. Setup + +The baseline experiments were conducted using the OpenSTL [51] library, with all meteorological variable data sourced from the WeatherBench [46] dataset. The settings followed the OpenSTL configuration, where each variable inputs 12 frames and predicts the subsequent 12 frames. + +The optimizer used was Adam [23], with a training batch size of 16, running for 50 epochs, and a momentum parameter $\alpha$ set to 0.999. We evaluated the test set using three metrics: MSE, MAE, and RMSE. + +# 4.2. Multiple Meteorological Variables Prediction + +Low-Resolution. Table 1 presents a quantitative comparison between our method and existing models for low-resolution multivariable meteorological prediction. Our method achieves SOTA performance across all major metrics, including MSE, MAE, and RMSE. Compared to TAU, our approach reduces MSE by $5.46\%$ , $28.82\%$ , $10.59\%$ , and $23.39\%$ for the four variables, respectively. To illustrate these differences more intuitively, Figure 4 presents a visual comparison between models, where $\mathrm{Met}^2\mathrm{Net}$ demonstrates smaller spatial prediction errors across the four variables, highlighting its advantage in accuracy. + +High-Altitude Variable. To further validate the robustness of our approach under varying atmospheric conditions, we conducted an experiment on high-altitude meteorological prediction. Table 3 compares the performance of different models in this task, showing that our method maintains SOTA performance. This experiment evaluates model performance at three altitude levels—150, 500, and 850 hPa—using 6-hour intervals. Specifically, the previous 4 + +Table 4. Quantitative comparison of predictions across multiple high-resolution meteorological variables, including UV10, T2M, TCC, and R, measured using MSE, MAE, and RMSE metrics. $\downarrow$ indicates lower is better. + +
MethodDateUV10T2MTCCR
MSE↓MAE↓RMSE↓MSE↓MAE↓RMSE↓MSE↓MAE↓RMSE↓MSE↓MAE↓RMSE↓
ConvLSTM[48]NeurIPS'20151.56910.86531.25181.13850.67741.06540.04500.14310.212128.95803.65945.3769
PredRNN[53]NeurIPS'20171.40830.80371.18591.18620.66951.08730.04820.14440.219530.15903.73345.4875
MAU[4]NeurIPS'20211.57810.85781.25541.24930.70971.11610.04460.14510.211130.78813.79895.5442
SimVP[14]CVPR'20221.76540.93321.32791.27500.73331.12780.04480.14510.211532.78494.01325.7217
ConvNeXt[34]CVPR'20221.48040.83991.21601.21550.70481.10100.04570.14550.213631.99443.88415.6518
TAU[50]CVPR'20231.30380.78871.14111.05990.65921.02820.04340.14030.208228.22913.63075.3090
\( Met^2Net \)Ours1.27450.78351.12830.89360.61940.94460.03780.12700.194421.54153.16064.6382
+ +Table 5. Quantitative comparison of predictions performance on the ERA5 dataset, including MSL, U10, V10, and T2M, measured using MSE, MAE, and $\mathbf{R}^2$ metrics. $\downarrow$ indicates lower is better, while $\uparrow$ indicates higher is better. + +
MethodDateMSELU10V10T2M
MSE↓MAE↓R²↑MSE↓MAE↓R²↑MSE↓MAE↓R²↑MSE↓MAE↓R²↑
ConvLSTM[48]NeurIPS'201516577.4290.83900.96771.72360.92380.93971.87280.98130.90602.05040.92360.9873
ConvNeXt[34]CVPR'202215618.9892.78480.96961.53580.84950.94621.68110.90200.91561.28600.73470.9920
HorNet[45]NeurIPS'202214585.9488.77720.97161.49640.84430.94761.61840.88960.91881.19620.70870.9926
MogaNet[29]ICLR'202418617.73100.86130.96381.55820.87560.94541.65470.90840.91701.40310.76180.9913
TAU[50]CVPR'202316541.8593.70000.96781.49790.84040.94761.61210.88240.91911.28080.72050.9920
Met²NetOurs9645.2870.39760.98121.20700.75180.95771.31240.79540.93410.81760.58660.9949
+ +![](images/0b3213399677a4e6cdd4469e7b636894d7a6894319459e60c5bdcfed18435789.jpg) +Figure 6. Comparison of predicted and ground truth tracks of Typhoon Mawar (3-hour lead time). The figure shows the observed trajectory alongside predictions from TAU and $\mathrm{Met}^2\mathrm{Net}$ . $\mathrm{Met}^2\mathrm{Net}$ more closely follows the ground truth, demonstrating improved accuracy in typhoon trajectory forecasting. + +frames (representing one day's data) are used to predict the next 4 frames, simulating a forecast of the following day's weather based on current data. + +High-Resolution. To assess the model's ability to capture fine-scale meteorological patterns, we conducted an experiment on high-resolution meteorological prediction. Table 4 + +presents a quantitative comparison across multiple high-resolution variables—UV10, T2M, TCC, and R—using MSE, MAE, and RMSE as evaluation metrics. $\mathrm{Met}^2\mathrm{Net}$ demonstrates competitive performance across all metrics, achieving the lowest error values, which underscores its robustness and accuracy in high-resolution prediction tasks. + +Tracking Tropical Cyclones. Our method was evaluated on Typhoon Mawar's trajectory prediction using the ERA5 dataset, which includes MSL, U10, V10, and T2M variables. As shown in Figure 6, our model closely follows the ground truth while outperforming the TAU model, particularly in the early and mid-stages. Notably, it achieves higher accuracy with a 3-hour lead time while using fewer parameters. The quantitative results in Table 5 further confirm its superiority, with the lowest MSE and MAE and the highest $\mathbb{R}^2$ across all variables, demonstrating its efficiency and effectiveness in tropical cyclone forecasting. + +Further analysis. To demonstrate the effectiveness of our method in addressing representation inconsistency, we analyzed the Centered Kernel Alignment (CKA) [25] values across layers for two meteorological variables: T2M and TCC. As shown in Figure 5, this analysis compares CKA values for both variables in the TAU and Ours models, focusing on the Encoder, Translator, and Decoder sections. CKA values, which measure similarity between layer representations, reflect each model's alignment with the internal structure of T2M and TCC, where higher values indicate stronger representation consistency. The TAU model shows a gradual increase in CKA values through the Translator section, whereas the Ours model maintains consistently higher values, particularly in the Encoder and Trans + +lator sections. This suggests that the Ours model better preserves representation consistency across variables. + +Table 6. Quantitative comparison on the MvMmfnist. The learning rate was optimized by selecting the best value from $\{1e^{-4}, 1e^{-3}, 5e^{-3}\}$ . + +
MethodMSE↓MAE↓SSIM↑PSNR↑
SimVP155.52397.100.881219.2825
ConvNeXt174.97434.630.868218.7304
TAU147.69385.130.883319.5075
Met2Net132.89328.670.908619.9069
+ +# 4.3. General Spatiotemporal Prediction + +To evaluate the generalization capability of our model, we conducted experiments on single-variable and multivariable spatiotemporal prediction datasets. TaxiBJ was chosen for single-variable prediction, representing urban traffic flow, while a three-channel MvMmfnist dataset was created for multivariable prediction. These experiments aim to assess the model's ability to handle diverse data types and spatiotemporal patterns, validating its applicability across different domains. + +MvMmfnist. The dataset simulates the complexity of multivariate spatiotemporal prediction scenarios. It contains three channels, each functioning as an independent moving dataset. To better represent real-world scenarios, such as multivariate weather prediction, the channels are interrelated yet retain some independence. Specifically, all channels share the same movement trajectory: the second channel's moving object is from the Fashion MNIST [60] dataset instead of MNIST [49], while the third channel is generated by flipping the foreground and background of the first channel. This design introduces both unique features and interrelationships among the channels. Experiments on this dataset, with results shown in Table 6, indicate that the $\mathrm{Met}^2\mathrm{Net}$ achieved state-of-the-art performance, demonstrating its effectiveness in multivariate spatiotemporal prediction scenarios. All models were trained using the Adam optimizer for 200 epochs, with the best-performing epoch selected for evaluation, ensuring a fair comparison. + +TaxiBJ. Table 7 shows experimental results on the TaxiBJ dataset, where the only difference between our method, $\mathrm{Met}^2\mathrm{Net}$ , and the TAU model is the training strategy, with all other configurations kept identical. Results indicate that $\mathrm{Met}^2\mathrm{Net}$ achieves comparable performance to TAU across all metrics, including MSE, MAE, SSIM, and PSNR. This similarity suggests that our training approach provides advantages in multivariable prediction tasks without compromising performance in single-variable scenarios. + +Table 7. Quantitative comparison on the Taxibj. The subscript $S$ in Baseline ${}_{S}$ indicates the single-variable model. + +
MethodMSE↓MAE↓SSIM↑PSNR↑
ConvLSTM[48]0.335815.320.983639.45
PredRNN[53]0.319415.310.983839.51
PredRNN++[54]0.334815.370.983439.47
MAU[4]0.326815.260.983439.52
SimVP[14]0.328215.450.983539.45
MogaNet[28]0.311415.060.984739.70
HorNet[45]0.318615.010.984339.66
TAU[50]0.310814.930.984839.74
Met2NetS0.316414.820.985139.81
+ +Table 8. Ablation study of the proposed method on MSE. MED (Multiple Encoder and Decoder). ITS (Implicit two-stage). The subscript $S$ in $\mathbf{Baseline}_S$ indicates the single-variable model. + +
MethodUV10T2MTCCR
\( Baseline_S \)1.59251.16200.047231.8310
Baseline1.83472.22470.043929.0749
+MED1.83271.67080.044528.8003
+VA(·)1.62871.54320.042826.6849
+ITS1.50550.82470.042224.3854
+ +# 4.4. Ablation Study + +Table 8 presents ablation study results for the proposed method in multivariable prediction. Using the TAU model as a baseline for multivariate meteorological forecasting, results indicate that model performance declines when handling multiple variables compared to single-variable predictions. This suggests that complex variable interactions challenge model precision, highlighting the need for optimized multivariable fusion strategies. + +Starting from the baseline model, we progressively introduced Multi-Encoder-Decoder (MED), Variable Attention (VA), and Implicit Two-Stage Training (ITS). Results show a consistent MSE decrease across all variables, with substantial improvements after incorporating MED and VA, indicating that these enhancements decouple variable relationships and significantly improve accuracy. Further gains with ITS confirm the effectiveness of our training strategy. + +# 5. Conclusion + +In this paper, we proposed a novel implicit two-stage training paradigm to improve spatiotemporal prediction tasks involving multiple meteorological variables. By treating each variable as an independent modality and incorporating separate encoders, decoders, and a self-attention mechanism, our framework, $\mathsf{Met}^2\mathsf{Net}$ , effectively captures complex interactions between variables and enhances prediction accuracy. We also constructed a general multivariate spatiotemporal prediction dataset, demonstrating the robustness and generalization of our method across different tasks. + +# Acknowledgement + +This research was partly supported by the Sichuan Science and Technology Achievement Transfer and Transformation Demonstration Project (2024ZHCG0026), the Sichuan Science and Technology Program (2024NSFJQ0035), and the Talents Program supported by the Organization Department of the Sichuan Provincial Party Committee. + +# References + +[1] Kaifeng Bi, Lingxi Xie, Hengheng Zhang, Xin Chen, Xiaotao Gu, and Qi Tian. Accurate medium-range global weather forecasting with 3d neural networks. Nature, 619(7970): 533-538, 2023. 1, 3 +[2] Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. Align your latents: High-resolution video synthesis with latent diffusion models. 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However, this clean set often becomes dominated by easy examples, limiting the model's meaningful exposure to more challenging cases and reducing its expressive power. To overcome this limitation, we introduce a novel metric called Dynamic Center Distance (DCD), which can quantify sample difficulty and provide information that critically complements loss values. Unlike approaches that rely on predictions, DCD is computed in feature space as the distance between sample features and a dynamically updated center, established through a proposed meta-learning framework. Building on preliminary semi-supervised training that captures fundamental data patterns, we incorporate DCD to further refine the classification loss, down-weighting well-classified examples and strategically focusing training on a sparse set of hard instances. This strategy prevents easy examples from dominating the classifier, leading to more robust learning. Extensive experiments across multiple benchmark datasets, including synthetic and real-world noise settings, as well as natural and medical images, consistently demonstrate the effectiveness of our method. + +# 1. Introduction + +In supervised learning, labeled data is a crucial resource for training effective models. However, acquiring high-quality labeled data is often challenging, leading to the introduction of noisy labels in many datasets [35, 44, 54]. This label noise poses significant challenges, especially as deep learning models are highly expressive and prone to overfitting—even when exposed to noisy labels [5, 7, 40, 43]. This tendency to overfit noise can severely degrade model performance, making the mitigation of label noise a key area + +![](images/0bf8a1d4574b251d199810472881bf83b88797a9a9f0473983eb9533561b429b.jpg) +Figure 1. (a) Existing methods tend to prioritize simple, low-loss samples, potentially overlooking harder, more informative samples that could enhance model performance. (b) Our approach emphasizes the importance of selecting both easy and hard samples, resulting in a more robust model that learns from a broader range of data, mitigating overfitting and improving generalization. + +of active research [2, 3, 29, 48, 52, 55, 56, 58]. + +Existing methods for handling label noise generally fall into two main categories: statistically consistent and statistically inconsistent approaches [30, 34, 57]. Statistically consistent methods model the label noise by estimating a noise transition matrix [12, 37]. While these methods are theoretically robust, their practical effectiveness diminishes under high noise levels or when dealing with datasets with large class counts, as accurately estimating the noise matrix becomes difficult in such conditions [16]. In contrast, statistically inconsistent approaches adopt various heuristic like memorization effect [14], co-teaching [59], label correction [63], and small-loss [13] sample selection to combat noisy labels. Most of these methods are implemented by constructing a subset of samples, often deemed less noisy. However, these methods tend to misidentify hard-to-learn samples as noisy, based on shared features such as high loss or low prediction confidence. As a result, they favor simpler, easier-to-learn samples, which can limit model learning by excluding informative ones. + +Current methods for distinguishing between easy and hard samples also face limitations in high-noise scenarios [29, 49, 54]. For example, sample separation methods, such as those based on small-loss strategy [11, 17, 19], often fail to differentiate between genuinely noisy samples and those that are simply hard to learn. This misclassification leads to the exclusion of critical samples, adversely impacting model learning and generalization. Consequently, there is a growing need for advanced methods that can more accurately differentiate between noisy and informative samples, ensuring a more balanced learning process and the preservation of valuable information. + +To address the aforementioned challenges, we propose DCD, an innovative method that incorporates with a meta-learning framework to dynamically differentiate easy and hard samples. DCD is computed as the Euclidean distance between each sample's feature representation and an evolving class center, which continuously adapts throughout training to capture each class's shifting feature distribution. By constructing category-specific center vectors from all samples, DCD achieves a detailed representation of each class, assigning weights based on sample distance from the center to prioritize harder, more distant examples. Additionally, to better estimate the true class centers, we introduce a weighted sample averaging technique with weights derived from a novel meta-learning approach. This weighted averaging substantially enhances the precision of class center estimates, allowing DCD to more accurately and reliably identify challenging and complex samples. In summary, these mechanisms enable the model to further focus on hard samples on the basis of the original semi-supervised training focusing on simple samples, thus improving the model's generalization in noisy label settings. + +We evaluate DCD across six synthetic and real-world noisy benchmarks, including natural image classification datasets—CIFAR-10 [21], CIFAR-100 [21], Tiny-ImageNet [22], Clothing1M [54], and WebVision [26]—and a medical image segmentation dataset, PROMISE12 [28]. For synthetic noise, DCD achieves $65.3\%$ classification accuracy on CIFAR-100 with $90\%$ symmetric noise and $68.4\%$ on Tiny-ImageNet with $50\%$ symmetric noise, outperforming L2B [64] by $4.6\%$ and $4.1\%$ . In real-world noise settings, DCD achieves $78.34\%$ on Clothing1M, surpassing the best baselines by $0.84\%$ , respectively. Additionally, DCD improves performance in medical image segmentation, achieving a $1.98\%$ gain on the PROMISE12 dataset. + +The main contributions can be summarized as follows: + +- We introduce DCD, a novel metric that measures sample difficulty by computing the Euclidean distance between sample features and a dynamically updated class center. This allows the model to focus on more challenging samples, improving robustness in noisy label settings. + +- We propose a meta-learning framework that integrates DCD to dynamically adjust sample loss weights, allowing the model to prioritize hard examples and refine the feature centers during training. This enhances the model's ability to handle noisy labels more effectively. +- Achieves SOTA results on both synthetic/real-world noisy labels across natural and medical image datasets. + +# 2. Related Work + +Learning with Noisy Labels. Learning with noisy labels is widely studied, with methods divided into model-based and model-free approaches. Model-based methods estimate a noise transition matrix to recover an optimal classifier, but they struggle with heavy noise or many classes [13, 16, 47]. Model-free methods, such as noisy sample detection [38, 61] and pseudo-label refinement [24], aim to reduce noise impact. Despite progress, both face challenges in high-noise or data-scarce scenarios. Recent efforts in unsupervised contrastive learning [19, 25, 62] focus on learning robust features without label correction. Robust, scalable representation learning remains challenging due to noisy labels' complex ties to model generalization. + +Hard Example Mining. Hard example mining is commonly used in machine learning to identify difficult samples for improved model training. Two primary approaches are employed: one for SVMs, where the working set of examples is dynamically updated to focus on hard examples violating the model's margin [10], and another for non-SVMs, where false positives are added to the training set after model convergence [6]. However, when applied to noisy label problems, these methods face challenges. Existing techniques, such as noise transition matrices or pseudolabeling, often assume known noise transitions, which is unrealistic in practice [12, 37, 53]. To address this challenge, we introduce DCD, a metric that focuses training on harder examples by measuring distance to a dynamic class center, enhancing model performance in noisy label settings. + +Meta Learning. Meta-learning has proven effective in enhancing model generalization. By leveraging a small clean set or auxiliary tasks, it optimizes model parameters and hyper-parameters efficiently, often through techniques like bi-level optimization and instance re-weighting [23, 41, 51]. These techniques enable better sample selection and weight assignment. Some methods treat label correction as a metaprocess, where the model iteratively corrects noisy labels [51, 61, 63], while others prevent overfitting by learning robust loss functions [23]. Recent techniques, such as CMWNet [42], adapt to data biases by generating adaptive sample weights, and DMLP [46] combines self-supervised learning with meta-learning for label correction. Unlike these approaches, our method integrates true and pseudo-label reweighting into meta-learning, optimizing per-sample loss weights and implicitly relabeling data. + +![](images/57755503671eaebf568295eefba815b5c4acce6e1dc4407681ae84b4f0e10e47.jpg) +Figure 2. Overview of our model: First, sample selection splits the dataset into clean and noisy subsets. Sample importance is then computed using DCD based on distance to class centroids, which guides loss weighting. Meta-learning generates adaptive weights to refine labels. Finally, weighted features are fed into the classifier and projection head to compute loss and update the model. + +# 3. Methodology + +# 3.1. Preliminaries + +Let the training set be $D_{\mathrm{train}} = \{(x_i,\hat{y}_i)\}_{i = 1}^N$ , where $x_{i}$ is the $i$ -th input image, $\hat{\pmb{y}}_i$ is the corresponding observed noisy label. We aim to learn a robust model with this noisy training set, which can generalize well to unseen test examples. Specifically, we can employ a deep neural network (DNN) model $f(x;\theta)$ with parameters $\theta$ as a feature extractor and use a cross-entropy loss to obtain a noisy robust classification model: + +$$ +\mathcal {L} = - \frac {1}{N _ {c l e}} \sum_ {\left(x _ {i}, \hat {y} _ {i}\right) \in D _ {c l e}} \boldsymbol {t} _ {i} \log \boldsymbol {p} _ {i}, \tag {1} +$$ + +where $t_i$ is the target, which can be either the observed noisy label or a combination of noisy labels and pseudolabels. The term $p_i = \text{softmax}(f(x_i; \theta))$ represents the predicted probability for the $i$ -th sample. To handle noisy labels, existing methods try to construct a clean subset $D_{cle} \subseteq D_{train}$ , where samples are assumed to be correctly labeled, and $N_{cle}$ represents the size of this clean set. By training the model with this clean set, the impact of noisy labels can be significantly reduced. + +To obtain the clean set, existing methods typically employ two strategies: (1) sample selection, which identifies examples with low loss values as likely correctly labeled; and (2) label correction, which adjusts the labels of examples exhibiting high predictive probabilities. Although these strategies differ in approach, both are grounded in shared indicators, such as low loss or high prediction confidence. Consequently, they primarily concentrate on "easy" examples, often neglecting more challenging cases [19]. Therefore, this selective focus can hinder the model's ability to + +capture complex patterns, ultimately constraining its representational capacity. + +To address the above challenge, we propose DCD, a novel and innovative approach to tackle sample selection bias by focusing on key and representative samples despite label noise. DCD differentiates between hard-to-learn and noisy samples, prioritizing informative and crucial instances. In the next section, we introduce Meta Dynamic Center Adjustment, which refines sample selection and weight assignment to improve DCD's robustness and generalization. + +# 3.2. Meta Dynamic Center Adjustment + +In the presence of noisy labels, a major challenge is distinguishing noisy samples from genuinely informative hard samples. Traditional methods [19, 27, 39] often fail by treating all samples equally, neglecting the potential value of hard samples. To address this, our approach dynamically adjusts sample importance through Dynamic Center Distance (DCD) and meta-learning. DCD helps assess sample difficulty based on the distance to class centers, guiding the selection and weighting of samples. Meta-learning further refines this process by learning adaptive sample weights, ensuring better initialization. We elaborate on each of these components in the following. + +DCD Calculation. First, we calculate the DCD to evaluate the difficulty of each sample. For a given sample $x_{i}$ , its feature representation is denoted as $h(x_{i})$ . The DCD is defined as the Euclidean distance between this feature and the dynamic class center: + +$$ +\mathrm {D C D} \left(x _ {i}\right) = \left\| h \left(x _ {i}\right) - c _ {k} \right\|, \tag {2} +$$ + +where $c_k$ represents the dynamic feature center of class $k$ . + +We can simply get $c_k$ by averaging the features in the $k$ -th class. However, since some examples may be wrongly labeled, directly averaging them is not an optimal solution. + +To ensure that the class centers remain consistent with the true feature distribution, we propose a meta-learning framework to adaptively learn weights for each example and calculate a weighted mean as the class center. Moreover, since the sample weights are updated periodically with the changing of models, we denote the obtained centers as dynamic class centers. Assuming that the obtained weight for $x_{i}$ is $\lambda_{i}$ , then the dynamic class center for class $k$ can be obtain with: + +$$ +c _ {k} = \frac {\sum_ {i \in C _ {k}} \lambda_ {i} \cdot f (x _ {i} ; \theta)}{| C _ {k} |}, \tag {3} +$$ + +where $C_k$ denotes the set of samples in class $k$ and $|C_k|$ is the set size. The weight $\lambda_i$ ensures critical samples have a greater impact on the center update and is updated with the following meta-learning framework. + +Meta-Learning Driven Sample Weighting. Inspired by [38], we define the target $\pmb{t}_i$ in Eq. (1) as a weighted combination of the noisy label and pseudo-label: + +$$ +\boldsymbol {t} _ {i} = \alpha_ {i} \hat {\boldsymbol {y}} _ {i} + \beta_ {i} \tilde {\boldsymbol {y}} _ {i}, \tag {4} +$$ + +where $\tilde{\pmb{y}}_i$ represents the pseudo-label derived from the model's current prediction, and $\alpha_{i}$ and $\beta_{i}$ are the respective weights. In [38], the constraint $\alpha_{i} + \beta_{i} = 1$ is imposed, ensuring equal treatment for each sample. However, to account for the variability introduced by noisy labels, we relax this constraint, allowing for individual weight assignments. + +To achieve precise sample selection and weight calculation, our method assigns adaptively initialized, metalearned weights to each training sample. In each training iteration, given the dataset, these optimal weights are refined through meta-learning, representing the contributions of the observed noisy label $\hat{\pmb{y}}$ and pseudo-label $\tilde{\pmb{y}}$ . By employing this meta-learning approach, the model dynamically adjusts $\alpha_{i}$ and $\beta_{i}$ for each sample. Thus, the primary learning objective is defined by substituting Eq. (4) into Eq. (1): + +$$ +\theta^ {*} (\boldsymbol {\alpha}, \boldsymbol {\beta}) = \arg \min _ {\theta} \sum_ {i = 1} ^ {N} \alpha_ {i} H \left(\boldsymbol {p} _ {i}, \hat {\boldsymbol {y}} _ {i}\right) + \beta_ {i} H \left(\boldsymbol {p} _ {i}, \tilde {\boldsymbol {y}} _ {i}\right), \tag {5} +$$ + +where $H(\cdot)$ is the cross-entropy loss, $\alpha$ and $\beta$ are the weight vectors with $\alpha_{i}$ and $\beta_{i}$ be the $i$ -th element. Specifically, The weights $\alpha_{i}, \beta_{i} \geq 0$ are meta-learned based on performance on a validation set, allowing the model to dynamically adjust the relative contributions of the real label loss and pseudo-label loss. Unlike traditional guided loss methods, the sum of $\alpha_{i}$ and $\beta_{i}$ does not have to equal 1, providing greater flexibility to maximize the model's performance. + +The optimal weights are obtained by minimizing the validation loss on a clean validation set $\mathcal{D}_{\mathrm{val}} = \{(x_i^{\mathrm{val}},y_i^{\mathrm{val}})\}_{i = 1}^{M}$ + +$$ +\alpha^ {*}, \beta^ {*} = \arg \min _ {\alpha , \beta \geq 0} \frac {1}{M} \sum_ {i = 1} ^ {M} H \left(\operatorname {s o f t m a x} \left(f \left(x _ {i} ^ {\mathrm {v}}; \theta^ {*} (\alpha , \beta)\right), y _ {i} ^ {\mathrm {v}}\right). \right. \tag {6} +$$ + +Through the above dual optimization in Eq. (5) and (6), we can dynamically learn the model parameter $\theta$ and the weights for noisy labels $\alpha$ and pseudo-labels $\beta$ . Details on the bi-level optimization are in Supplementary Materials. + +Since $\alpha_{i}$ and $\beta_{i}$ are weights for the noisy label and pseudo-label for $x_{i}$ , the sum $(\alpha_{i} + \beta_{i})$ can reflect the reliability of the sample $x_{i}$ . Therefore, we set the weight $\lambda_{i}$ in Eq. (3) for the sample $x_{i}$ as: + +$$ +\lambda_ {i} = \alpha_ {i} + \beta_ {i}. \tag {7} +$$ + +Based on the obtained weight, we recalculate the distance between the sample and the class center to obtain the Dynamic Center Distance: + +$$ +\mathrm {D C D} _ {\text {m e t a}} \left(x _ {i}\right) = \left\| h \left(x _ {i}\right) - c _ {k} \right\|. \tag {8} +$$ + +Finally, we classify examples with a large DCD as hard examples, as they lie farther from the representation center. The importance weight for each example is then determined by normalizing the exponential of the DCD: + +$$ +\Gamma_ {i} = \frac {\exp \left(\mathrm {D C D} _ {\text {m e t a}} \left(x _ {i}\right)\right)}{\sum_ {j = 1} ^ {N} \exp \left(\mathrm {D C D} _ {\text {m e t a}} \left(x _ {j}\right)\right)}. \tag {9} +$$ + +In Eq. (9), both the contributions of the meta-learned weights and the distance between each sample and its class center are taken into account. The DCD term modulates the relative influence of the real label loss and pseudolabel loss, while normalization based on DCD further refines these weights according to each sample's proximity to its class center. Meanwhile, we explain why $\lambda_{i}$ is not used directly as the weight for $x_{i}$ in Sec. 4.7. + +# 3.3. Loss Function + +After completing the weight calculation, we first select a clean subset with normal sample selection and label correction techniques [19]. Then, we employ a weighted cross-entropy to focus more on the hard-clean examples: + +$$ +\mathcal {L} _ {\mathcal {H F}} = - \sum_ {i = 1} ^ {N} \Gamma_ {i} \cdot H \left(y _ {i}, h \left(f \left(x _ {i}; \theta_ {f}\right); \theta_ {h}\right)\right). \tag {10} +$$ + +To integrate both clean and noisy samples in a semi-supervised learning (SSL) framework [4], we combine the supervised loss with additional loss terms to handle label + +noise and improve robustness. The overall training objective is then defined as: + +$$ +\mathcal {L} _ {\mathrm {D C D}} = \mathcal {L} _ {\mathcal {H F}} + \lambda_ {u} \mathcal {L} _ {u} + \lambda_ {r} \mathcal {L} _ {r} + \lambda_ {\mathcal {C}} \mathcal {L} _ {\mathcal {C}}, \tag {11} +$$ + +where $\mathcal{C}$ is the contrastive loss. $\mathcal{L}_u$ and $\mathcal{L}_r$ handle unlabeled data and regularization, respectively. The hyperparameters $\lambda_u, \lambda_r$ , and $\lambda_{\mathcal{C}}$ are set according to the experimental configuration in [19]. Details about the above SSL are provided in the Supplementary Materials. + +# 4. Experiments + +# 4.1. Datasets + +CIFAR-10/100 [21]: CIFAR-10/100 (50K train, 10K test) use synthetic noise for robustness evaluation: symmetric noise (random class reassignment) and asymmetric noise (realistic mistakes, e.g., Truck $\rightarrow$ Auto; CIFAR-100 flips within superclasses), due to natural data's inherent noise. + +Tiny-ImageNet [22]: This dataset is a smaller version of the original ImageNet in terms of the number of classes and the image resolution. There are in total 200 classes containing 500 images per class. The image size is $64 \times 64$ . + +Clothing1M [54]: Clothing1M is a large-scale real-world dataset with noisy labels. It contains 1M images from 14 different cloth-related classes. Since the labels are produced by the seller provided surrounding texts of the images, a large portion of confusing classes (e.g., Knitwear and Sweater) are mislabeled. + +Webvision [26]: This dataset contains 2.4 million images (obtained from Flickr and Google) that are categorized into the same 1,000 classes as in the ImageNet ILSVRC12. Following the previous studies [24], we use the first 50 classes of the Google image subset as the training data. + +PROMISE12 [28]: The dataset consists of 50 training cases of transversal T2-weighted MR images of the prostate from multiple clinical centers and vendors, with varying acquisition protocols, slice thickness, and endorectal coil usage. It includes both benign prostate conditions and prostate cancer cases. + +# 4.2. Training Details + +We utilize the PreAct ResNet18 architecture for CIFAR-10 and CIFAR-100 datasets. For these tasks, we implement the SGD optimizer with the following configuration: an initial learning rate (LR) of 0.02, a weight decay of $5e^{-4}$ , a momentum of 0.9, and a batch size of 64. Each network is trained for approximately 350 epochs, with a linear learning rate decay of 0.1 every 120 epochs. A warmup period of 30 epochs is applied prior to the main training phase. We set $\lambda_u$ , $\lambda_r$ , and $\lambda_C$ as 30, 1, and 0.025 for all datasets. + +In the case of Tiny-ImageNet, we employ the ResNet50 architecture, starting with an initial LR of 0.01, a weight decay of $1e^{-3}$ , and a batch size of 32. The network is trained + +for 350 epochs, with a learning rate decay of 0.1 every 100 epochs and a warmup period of 15 epochs. For the Clothing1M dataset, we adopt a similar approach, using an initial LR of 0.002 and a weight decay of $1e^{-3}$ , training the model for 100 epochs with a lr-decay of 0.1 every 40 epochs. The same settings are applied for the WebVision dataset to ensure consistency in performance. + +Data augmentation is performed following the Autoaugment policy, as specified in previous works. For CIFAR-10 and CIFAR-100, we use the CIFAR-10-Policy, while the ImageNet-Policy is applied to Tiny-ImageNet. Due to the transferable nature of these policies, the ImageNet-Policy is also utilized for both Clothing1M and WebVision datasets, optimizing the model's generalization capabilities across different datasets. + +# 4.3. Clean Meta Data Construction + +The clean meta-dataset $D_{\mathrm{cle}}$ constitutes $2\%$ of the entire dataset in all experiments [64]. This ratio was determined through preliminary experiments on CIFAR-10 under $90\%$ symmetric label noise, where $2\%$ demonstrated optimal cost efficiency in balancing test accuracy gains against computational overhead. We define the Cost Efficiency (CE) metric as $\mathrm{CE} = \Delta \mathrm{Accuracy} / (\Delta \mathrm{Time} \times \Delta \mathrm{Memory} \times \Delta \mathrm{Meta})$ , where $\Delta$ denotes relative change versus the $1\%$ baseline. As shown in Table 2, increasing beyond $2\%$ yields diminishing returns in test accuracy while substantially increasing resource demands. + +For datasets such as CIFAR-10/100 and Tiny/ImageNet, clean data were randomly sampled from the training set and removed, while for Clothing1M and Webvision, clean data were selected from the test set and removed accordingly. The overall data split follows an 8:1:1 ratio for training, testing, and validation. + +# 4.4. Performance Comparisons + +![](images/7de8685124166b79eab97c2f10bf51affe44e0421d9cd6fbd68f69366b11c8b7.jpg) +(a) Test Accuracy $(\%)$ +Figure 3. Test accuracy (\%) and ROC-AUC performance on CIFAR-10 across varying noise levels. As the model becomes more precise, the test-time performance improves accordingly. The shaded region in the figure represents the error margin from four experiments, while the solid line denotes the mean value. + +![](images/eec82b8c3f6dfbaa60a06b1b414b40a28d4f88bac03255cde36846818e99553d.jpg) +(b) ROC AUC Score + +
Noise ModeSymmetric noiseAsymmetric noise
DatasetCIFAR-10CIFAR-100CIFAR-10CIFAR-100
Method20%50%80%90%20%50%80%90%10%30%40%10%30%40%
Standard CE86.879.462.942.762.046.719.910.188.881.776.168.153.344.5
DMix [24]96.194.692.976.077.374.660.231.593.892.591.771.669.555.1
ELR [29]95.894.893.378.777.673.660.833.495.494.793.077.374.673.2
UNION [19]96.095.693.990.878.977.663.944.895.394.894.178.275.674.8
SFT [9]92.688.542.110.571.965.527.07.9------
Sel-CL+ [8]95.593.989.281.976.572.459.648.895.694.593.478.776.474.2
TCL [17]94.993.892.389.277.873.164.747.995.394.992.578.375.575.3
OT-Filter [11]96.095.394.090.576.773.861.842.8------
L2B [64]96.795.694.894.480.178.169.660.795.194.794.078.575.475.1
DCD96.896.295.395.183.180.773.365.396.195.895.680.178.678.4
Δ±0.17±0.21±0.24±0.29±0.22±0.28±0.35±0.38±0.12±0.17±0.22±0.11±0.18±0.25
↑0.1↑0.6↑0.5↑0.7↑3.0↑2.6↑3.7↑4.6↑0.5↑0.9↑1.5↑1.4↑2.2↑3.1
+ +Table 1. Test accuracies $(\%)$ achieved by various techniques under both symmetric and asymmetric noise conditions. The highest accuracy values are highlighted in green, while the second-highest results are shaded in gray. This color scheme is consistently applied across all tables in the following sections. Different baselines use varying datasets. We compare each dataset with the baseline that utilized it. + +
Meta Data SizeAccuracyTime/EPOCHMemoryCE
1%94.3%0.7 min5.3 GB-
2%95.1%0.9 min6.9 GB2.50
4%95.5%1.3 min9.4 GB0.20
6%95.7%2.1 min11.2 GB0.07
+ +Table 2. Performance comparison with different meta-data size + +
Noise (%)02050
Alg.BestAvg.BestAvg.BestAvg.
Standard CE57.456.735.835.619.819.6
F-correction [36]--44.544.433.132.8
MentorNet [18]--45.745.535.835.5
Co-teaching+ [59]52.452.148.247.741.841.2
M-correction [1]57.757.257.256.651.651.3
NCT [39]62.461.558.057.247.847.4
UNION [19]63.162.759.258.452.752.4
DISC [27]68.568.267.967.564.363.9
DCD70.369.970.269.668.467.7
Δ↑1.8↑1.7↑2.3↑2.1↑4.1↑3.8
+ +CIFAR-10 and CIFAR-100 Datasets: The experimental results on CIFAR-10 and CIFAR-100 datasets, demonstrating that DCD consistently achieves the highest test accuracies across different noise levels under both symmetric and asymmetric label noise, as shown in Table 1. For CIFAR-10, DCD outperforms other methods under symmetric noise, reaching $95.1\%$ accuracy at $90\%$ noise level, surpassing L2B [64] by $0.7\%$ . In CIFAR-100, DCD achieves $65.3\%$ accuracy at $90\%$ noise, significantly exceeding L2B [64]. Under asymmetric noise, DCD also excels, achieving $95.6\%$ accuracy at $40\%$ noise in CIFAR-10 and showing improvements of $1.5\%$ to $3.1\%$ in CIFAR-100 + +Table 3. Test accuracies (\%) on Tiny-ImageNet dataset under symmetric noise settings. + +
MethodBackboneTest Accuracy
Standard CEResNet-5069.21
OT-Filter [11]ResNet-5074.51
DMix [24]ResNet-5074.76
ELR [29]ResNet-5074.81
TCL [17]ResNet-5074.85
UNION [19]ResNet-5074.98
SFT [9]ResNet-5075.08
SNSCL [50]ResNet-5075.31
L2B [64]ResNet-5077.50
DCDResNet-5078.34 ±0.17
Δ-↑ 0.84
+ +Table 4. Experimental results on Clothing1M dataset. Results for previous techniques were copied from their respective papers. + +
DatasetWebVisionILSVRC12
MethodTop-1Top-5Top-1Top-5
D2L [31]62.6884.0057.8081.36
DivideMix [24]77.3291.6475.2090.84
ELR [29]77.7891.6870.2989.76
UNION [19]77.6093.4475.2993.72
TCL [17]79.1292.3175.4192.43
Sel-CL+ [8]79.9692.6476.8493.04
DISC [27]80.2892.2877.4492.28
LSL [20]81.4093.0077.0091.84
DCD83.29±0.2894.51±0.1778.54±0.3194.17±0.27
Δ↑1.89↑1.07↑1.10↑0.45
+ +Table 5. Experimental results on Webvision and ILSVRC12. All methods are trained on the Webvision while evaluated on both Webvision and ILSVRC12 validation set. + +across various noise rates. These results highlight DCD's robustness in handling class-dependent noise. We also visualized DCD's test accuracy $(\%)$ and ROC-AUC performance under different noise levels on CIFAR-10, as shown in Figure 3a and 3b, demonstrating DCD's robustness and + +![](images/3769d45d324d0daaf6a28bcc1cdd62267fa1574f259f3a6bbe988e4fda0c94de.jpg) + +![](images/59ed47fef43e65f20a472a9a21910535c1d929a822199d4034e8e7a2974405e9.jpg) +$C_{r1} = 20\%$ + +![](images/032e681836c12f322da5426e973284a63a4f27ed03a6c0b98b704bf181574b9b.jpg) + +![](images/efb6fa969257ed6e17be30c171e8bcf828bbe9eefe832d916556f033b60463ad.jpg) +$C_{r2} = 40\%$ + +![](images/c55f6aaad6e51c4db8ee3c44cac52eba0f7a1b573b21a65c2954a5ca22c7f9f6.jpg) +Figure 5. Visualizing independence of DCD and hard examples. + +![](images/efdd5bcc31214256a162095dd7ed665c405caa3f43f4ba95ee5384fb6cfa69fc.jpg) +$C_{r3} = 60\%$ +Figure 4. Experimental results under different corrupted ratios $C_r$ of $20\%$ , $40\%$ , and $60\%$ with precise (red outline), noise (yellow outline), and correction (blue outline). + +
MethodDice (%)\( ↑ \)HD (voxel)\( ↓ \)ASD (voxel)\( ↓ \)
UNet++ [65]73.7411.633.70
NL re-weighting [32]76.648.332.75
CRF [33]78.007.452.57
L2B [64]80.836.682.10
DCD82.816.521.78
\( \Delta \)↑ 1.98↓ 0.16↓ 0.32
+ +superior performance. This strong performance arises from its dynamic adaptation to noise, focusing on clean samples for learning and enhancing feature representation, ultimately improving model accuracy and robustness. + +Tiny ImageNet Dataset: Table 3 compares the performance of DCD with other state-of-the-art methods. TinyImageNet is challenging, and its difficulty increases with label noise. Among baselines, UNION [19] uses a consistent selection mechanism with contrastive learning, while DISC [27] applies dynamic instance selection for noise robustness. However, both methods underperform compared to DCD. As shown in Table 3, DCD achieves $1.8\%$ to $4.1\%$ higher accuracy than DISC, depending on label noise levels. + +Clothing1M Dataset: Table 4 provides a comparison of performance on this real-world dataset with noisy labels. Our method outperforms L2B [64] by $0.84\%$ . For Clothing1M, performance gains may fluctuate based on the warm-up period's length, as prolonged cross-entropy (CE)-based training can lead to memorization effects. In our approach, we apply a warm-up period of 2,000 steps. + +WebVision Dataset: Table 5 demonstrates DCD's superior performance, establishing new state-of-the-art Top1/Top-5 accuracy on Webvision and ILSVRC12. On Webvision, DCD outperforms LSL [20] with $1.89\%$ and $1.51\%$ gains in Top-1/Top-5 accuracy; on ILSVRC12, it + +![](images/7122561658fbcc7355c918eba313c521c0b7015730dc70d3896d381196273b98.jpg) +(a) DCD vs Loss. + +![](images/5273bd768842a944a9f8e6e11bdeb9926223bf4e1e2f3504d7260550ac5707a9.jpg) +(b) Visualize hard examples + +Table 6. Segmentation performance comparison under noisysupervision on PROMISE12. + +
MethodDice (%)↑
baseline - Cr182.01
DCD - Cr184.72
baseline - Cr280.83
DCD - Cr282.81
baseline - Cr377.70
DCD - Cr379.68
+ +Table 7. L2B for segmentation under different noise levels. + +achieves $1.10\%$ and $0.45\%$ improvements over prior baselines. These results confirm DCD's enhanced robustness against label noise compared to existing methods. + +# 4.5. Generalization to Image Segmentation + +We evaluated the performance of our method under noisy supervision using the PROMISE12 dataset and compared it with several state-of-the-art approaches, including UNet++ [65], NL re-weighting [32], Mix-up [60], and L2B [64]. As summarized in Table 6, our approach outperforms all others in key evaluation metrics such as Dice score, Hausdorff Distance (HD) [45], and Average Surface Distance (ASD) [15]. Specifically, our model achieved a Dice score of $82.81\%$ , with improvements in HD and ASD as well, demonstrating its robustness under noisy conditions. + +Furthermore, we evaluate the robustness of our method under different noise levels by varying the corrupted ratios of the training set to $C_{r1}$ , $C_{r2}$ , and $C_{r3}$ , which represent corruption rates of 20%, 40%, and 60%, respectively. As shown in Table 7, we compared the baseline model [64], which is trained directly on the noisy datasets, with our DCD approach across these varying noise levels. The Dice scores achieved by DCD were 84.72% for $C_{r1}$ , 82.81% for $C_{r2}$ , and 79.68% for $C_{r3}$ . In contrast, the baseline scores dropped significantly from 82.01% to 77.70%. This indicates that DCD maintains high performance and is robust even as the noise levels increase, demonstrating significant improvements, particularly under severe noise conditions. + +# 4.6. Analyzing Independence of DCD + +We validated DCD as an independent measure of sample hardness through scatter plot analysis (Figure 5a), which showed no direct correlation with classification loss be + +
DatasetCIFAR10CIFAR100
Noise Rate50%80%90%50%80%90%
MethodBestLastBestLastBestLastBestLastBestLastBestLast
DCD w/o meta-pipeline95.7295.6894.7394.3193.8293.7179.3279.1572.1671.9863.9163.75
DCD w/o D95.8195.7594.6594.3793.0392.8378.4878.2768.7468.5163.3063.14
DCD w/o CL95.5195.4994.9394.8294.2394.1179.8279.5372.2872.1764.7364.57
DCD96.2896.1795.3195.2595.1495.0780.7480.6973.3573.2465.3265.19
+ +Table 8. Ablation study with different training settings. Both the meta-pipeline and DCD components significantly affect the performance, particularly under high noise rates. Removing contrastive loss (CL) also leads to noticeable performance degradation, especially as noise levels increase. Test results at last epoch are also shown here. + +
Method20%50%80%
baseline (OT-Filter)76.773.861.8
α = 072.971.960.9
β = 078.375.864.8
α + β = 181.678.672.2
α,β ≥ 083.180.773.3
+ +tween epochs 210-220. Our method uses DCD to prioritize high-DCD samples for better generalization and downweight low-DCD samples for increased robustness. Figure 5b illustrates this mechanism: simple samples (gray circles) are confidently classified far from decision boundaries, while hard samples (colored circles) cluster near boundaries with ambiguous class membership and lower confidence. This confirms DCD's role in identifying boundary-proximate hard samples, aligning with adversarial training to enhance model robustness. + +# 4.7. Compare with direct weight $\lambda_{i}$ + +We conducted additional experiments exploring the direct use of the meta-learning weights $\lambda_{i}$ for sample selection. Experimental results show that while the direct application of these weights for sample selection yields improvements, the enhancements are relatively marginal compared to the original method. This is reflected in the reduced variance of the results, as shown in Table 10, which demonstrates that the original method provides more stable and consistent outcomes under various noise levels. + +# 4.8. Ablation Study + +Effect of Meta Learning: Removing meta-learning from DCD degrades performance across all noise levels (Table 8). At $90\%$ noise, CIFAR-10 accuracy drops by $1.32\%$ (best) and $1.36\%$ (last), while CIFAR-100 shows $1.41\%$ and $1.44\%$ reductions respectively. + +Effect of DCD: The effect of removing the Dynamic Center Distance (DCD) component is also prominent in Table 8. Without DCD, the model experiences a performance de + +Table 9. Ablation of $\alpha, \beta$ under diverse symmetric noise in CIFAR-100. $\alpha, \beta \geq 0$ achieves best performance. + +
Symmetric noise20%40%60%
Direct weight (λi)94.82±0.2193.23±0.2791.94±0.33
DCD (Γi)96.78±0.1796.38±0.1895.61±0.23
+ +Table 10. Compare ${\Gamma }_{i}$ with direct weight ${\lambda }_{i}$ in CIFAR-10. + +cline at each noise level. In CIFAR-10, while the reduction in accuracy is subtle, especially at moderate noise rates (50% and 80%), it becomes more pronounced at 90% noise, with a decrease of about 2.11% in the best accuracy compared to the full DCD configuration. For CIFAR-100, excluding DCD leads to a 2.02% decrease in the best accuracy at 90% noise. These results suggest that DCD plays a critical role in maintaining model accuracy, particularly under higher noise conditions, by enhancing feature learning and robustness against noisy labels. + +Significance of $\alpha$ and $\beta$ : Table 9 shows that $\alpha = 0$ causes minor degradation, while $\beta = 0$ improves over baseline but underperforms joint optimization. Constraining $\alpha + \beta = 1$ yields moderate improvements but restricts flexibility. Independent $\alpha / \beta$ optimization achieves optimal performance through maximized balance and adaptability. + +# 5. Conclusion + +We propose DCD, an innovative method that incorporates a meta-learning framework to address noisy labels and sample difficulty. By dynamically prioritizing challenging samples based on distance from evolving class centers, DCD improves training robustness. Extensive experiments across multiple benchmark datasets, including synthetic and real-world noise settings, and natural and medical images, demonstrate the effectiveness of our method, promising solution for robust learning in noisy environments. + +# 6. Acknowledgments + +Our work was supported in part by the National Natural Science Foundation of China (62132016 and 62202365), Natural Science Basic Research Program of Shaanxi (2020JC-23), Fundamental Research Funds for the Central Universities (QTZX23073), and Young Elite Scientists Sponsorship Program by CAST (2023QNRC001). + +# References + +[1] Eric Arazo, Diego Ortego, Paul Albert, Noel O'Connor, and Kevin McGuinness. Unsupervised label noise modeling and loss correction. In ICML, pages 312-321, 2019. 6 +[2] Yingbin Bai, Erkun Yang, Bo Han, Yanhua Yang, Jiatong Li, Yinian Mao, Gang Niu, and Tongliang Liu. Understanding and improving early stopping for learning with noisy labels. NeurIPS, 34:24392-24403, 2021. 1 +[3] Yingbin Bai, Erkun Yang, Zhaoqing Wang, Yuxuan Du, Bo Han, Cheng Deng, Dadong Wang, and Tongliang Liu. Rsa: reducing semantic shift from aggressive augmentations for self-supervised learning. 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However, it is observed that even when DMs are properly unlearned before release, malicious finetuning can compromise this process, causing DMs to relearn the unlearned concepts. This occurs partly because certain benign concepts (e.g., "skin") retained in DMs are related to the unlearned ones (e.g., "nudity"), facilitating their relearning via finetuning. To address this, we propose meta-unlearning on DMs. Intuitively, a meta-unlearned DM should behave like an unlearned DM when used as is; moreover, if the meta-unlearned DM undergoes malicious finetuning on unlearned concepts, the related benign concepts retained within it will be triggered to self-destruct, hindering the relearning of unlearned concepts. Our meta-unlearning framework is compatible with most existing unlearning methods, requiring only the addition of an easy-to-implement meta objective. We validate our approach through empirical experiments on meta-unlearning concepts from Stable Diffusion models (SD-v1-4 and SDXL), supported by extensive ablation studies. + +# 1. Introduction + +Diffusion models (DMs) have achieved remarkable success in generative tasks [11, 35], leading to the emergence of large-scale models like Stable Diffusion (SD) for text-to-image generation [31]. However, training these models often requires vast datasets that may inadvertently contain private or copyrighted content, as well as harmful concepts that are not safe for work (NSFW) [32]. These challenges have sparked interest in machine unlearning algorithms for DMs [3, 4, 15, 16], which modify pretrained models to forget specific inappropriate data (forget set) while retaining performance on the remaining benign data (retain set). + +While unlearning methods designed for DMs are promising, recent studies reveal that unlearned models may be maliciously finetuned to relearn the unlearned concepts, even when the finetuning is performed on unrelated benign data [24, 29, 33, 36]. Although these studies focus primarily on language models, we observe similar phenomena on DMs as shown in Fig. 4. This partly occurs because certain benign concepts (e.g., "skin" in the retain set) related to unlearned ones (e.g., "nudity" in the forget set) are still retained in DMs, easing their relearning during finetuning. + +To tackle this challenge, we draw inspiration from meta-learning [2] and propose the meta-unlearning framework. This framework comprises two key components: (1) a standard unlearning objective to ensure the model effectively forgets specified data before public release, while preserving performance on benign data; and (2) a meta objective designed to slow down the relearning process if the model is maliciously finetuned on the forget set. Additionally, it induces the benign knowledge related to the forget set to self-destruct, as illustrated in Fig. 1. + +Our meta-unlearning framework is compatible with most existing unlearning methods for DMs, requiring only the addition of a simple-to-implement meta objective, as outlined in Algorithm 1. This meta objective can be efficiently optimized by automatic differentiation [23]. We conduct extensive experiments on SD models (SD-v1-4 and SDXL) to validate the effectiveness of various instantiations of our meta-unlearning approach. + +# 2. Related work + +Recent studies have shown that DMs can be misused to generate unsafe content, such as images depicting sexual acts, harassment, or illegal activities [5, 30, 32]. To mitigate this issue, early-stage DMs are equipped with NSFW filters designed to block the generation of inappropriate images [30]. However, this approach does not prevent the model from generating harmful imagery at its core, and these filters can be bypassed, exposing security vulnerabilities [1, 31]. + +Machine unlearning on DMs. Several methods have been proposed to unlearn or erase harmful, private, or copy- + +Figure 1. Mechanisms of finetuning unlearned models (left) and meta-unlearned models (right) on a forget subset $\mathcal{D}_{\mathrm{FT}} \subset \mathcal{D}_{\mathrm{forget}}$ . According to the first-order approximation described in Eq. (4), our meta-unlearning can slow down relearning unlearned concepts inside $\mathcal{D}_{\mathrm{FT}}$ , while self-destructing related benign concepts from $\mathcal{D}_{\mathrm{retain}}$ , i.e., $\mathcal{L}_{\mathrm{DM}}(\theta; \mathcal{D}_{\mathrm{retain}})$ increases when $\mathcal{L}_{\mathrm{DM}}(\theta; \mathcal{D}_{\mathrm{FT}})$ decreases. +![](images/8eb3f8d920d97d15ed73b252e5cabacf0b54383fdaa8d334ef26197409bfcc0d.jpg) +Finetuning track $\longrightarrow \nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})$ + +# Meta-Unlearned Models + +![](images/e1041b6c19e732e12f25d1f6016860c683b5e6d62cefdc28a635caa42fe8057d.jpg) +Minimizing $\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})^{\top}\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{retain}})$ +(self-destructing related benign concepts) +Minimizing $\| \nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})\| _2^2$ (slowing down relearning unlearned concepts) + +righted concepts from DMs [12, 20, 22, 27, 38, 41, 43]. For instances, ESD [3] leverages negative guidance to finetune the U-Net, removing the specified style or concept. Concept ablation [16] works by making the distribution of the target concept similar to that of an anchor concept. However, these methods are vulnerable to adversarial attacks. To this end, several adversarial-resistant unlearning methods have been proposed [13, 14, 18, 39]. AdvUnlearn [43] enhances the robustness of concept erasure by incorporating adversarial training principles, while RECE [6] derives new target embeddings for inappropriate content and iteratively aligns them with harmless concepts in cross-attention layers. Nevertheless, models unlearned by these methods can still be maliciously finetuned to relearn unlearned concepts, as observed in our experiments. + +Unlearned models can be attacked. Recent studies have shown that unlearned models are vulnerable to generating previously unlearned concepts through adversarial attacks [7, 21, 25, 26, 37, 40, 42] and malicious finetuning [29, 33, 36, 44]. UnlearnDiffAtk [42] introduces an evaluation framework that uses adversarial attacks to generate adversarial prompts by exploiting the inherent classification capabilities of DMs. In the domain of language models, several works have revealed that finetuning can recover unlearned concepts. For example, [29] demonstrates that safety alignment and/or unlearning in language models can be undermined through finetuning with a small set of adversially crafted training examples. Additionally, [36] show that refusal mechanisms and unlearning safeguards can be bypassed with minimal iterations of finetuning, while [44] recover most supposedly unlearned capabilities. + +# 3. Preliminaries + +This section provides a brief review of diffusion models (DMs) [11, 35] and commonly used machine unlearning methods in the DM literature. + +# 3.1. Diffusion Models + +We focus on discrete-time DMs that serve as the cornerstone of Stable Diffusion [31]. We consider random vari + +ables $\pmb{x} \in \mathcal{X}$ and $\pmb{c} \in \mathcal{C}$ , where $\pmb{x}$ denotes the latent feature and $\pmb{c}$ the conditional context, e.g., text prompts. Let $q(\pmb{x}, \pmb{c})$ denote the data distribution. Consider a forward diffusion process over time interval $[0, T]$ with $T \in \mathbb{N}^{+}$ . The Markov transition probability from $\pmb{x}_{t-1}$ to $\pmb{x}_t$ is $q(\pmb{x}_t | \pmb{x}_{t-1}) \triangleq \mathcal{N}(\pmb{x}_t | \sqrt{1 - \beta_t} \pmb{x}_{t-1}, \beta_t \mathbf{I})$ , where $\pmb{x}_0 = \pmb{x}$ and $\beta_1, \dots, \beta_T$ correspond to a variance schedule. Note that we can sample $\pmb{x}_t$ at an arbitrary timestep $t$ directly from $\pmb{x}$ , since there is $q(\pmb{x}_t | \pmb{x}) = \mathcal{N}(\pmb{x}_t | \sqrt{\alpha_t} \pmb{x}, (1 - \overline{\alpha}_t) \mathbf{I})$ , where $\alpha_t \triangleq 1 - \beta_t$ and $\overline{\alpha}_t \triangleq \prod_{i=1}^t \alpha_i$ . + +Sohl-Dickstein et al. [34] show that when $\beta_{t}$ are small, the reverse diffusion process can also be modeled by Gaussian conditionals. Specifically, the reverse transition probability from $\pmb{x}_t$ to $\pmb{x}_{t - 1}$ is written as $p_{\theta}(\pmb{x}_{t - 1}|\pmb{x}_t,\pmb{c}) = \mathcal{N}(\pmb{x}_{t - 1}|\pmb{\mu}_{\theta}(\pmb{x}_t,\pmb{c}),\sigma_t^2\mathbf{I})$ , where $\theta \in \mathbb{R}^d$ is the model parameters and $\sigma_{t}$ are time dependent constants. Instead of directly modeling the data prediction $\pmb{\mu}_{\theta}$ , we choose to model the noise prediction $\epsilon_{\theta}$ based on the parameterization $\pmb{\mu}_{\theta}(\pmb{x}_t,\pmb{c}) = \frac{1}{\sqrt{\alpha_t}}\left(\pmb{x}_t - \frac{\beta_t}{\sqrt{1 - \overline{\alpha}_t}}\pmb{\epsilon}_{\theta}(\pmb{x}_t,\pmb{c})\right)$ . The training objective of $\epsilon_{\theta}(\pmb{x}_t,\pmb{c})$ can be derived from optimizing the (weighted) variational bound of negative log-likelihood, formulated as follows: + +$$ +\min _ {\theta} \mathcal {L} _ {\mathrm {D M}} (\boldsymbol {\theta}; \mathcal {D} _ {\mathrm {t r a i n}}) = \mathbb {E} _ {(\boldsymbol {x}, \boldsymbol {c}) \sim \mathcal {D} _ {\mathrm {t r a i n}}, \boldsymbol {\epsilon}, t} \left[ \| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\boldsymbol {\theta}} (\boldsymbol {x} _ {t}, \boldsymbol {c}) \| _ {2} ^ {2} \right], +$$ + +where $\pmb{x}_t = \sqrt{\overline{\alpha}_t}\pmb{x} + \sqrt{1 - \overline{\alpha}_t}\pmb{\epsilon}$ , the pairs $(\pmb{x},\pmb{c})$ are sampled from the training set $\mathcal{D}_{\mathrm{train}}$ , $\epsilon \sim \mathcal{N}(\epsilon |0,\mathbf{I})$ is a standard Gaussian noise, and $t\sim \mathcal{U}([1,T])$ is a uniform distribution. + +# 3.2. Machine Unlearning for DMs + +DMs, despite their high capability, may generate unsafe content or disclose sensitive information that is not safe for work (NSFW) [32]. Several recent studies have investigated concept erasing or machine unlearning for DMs to address safety, privacy, and copyright concerns [8, 16, 43]. Let $\epsilon_{\theta^{*}}$ denotes the DM pretrained on the dataset $\mathcal{D}_{\mathrm{train}}$ where $\theta^{*} = \arg \min_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{train}})$ . The goal of machine unlearning is to unlearn a forget set $\mathcal{D}_{\mathrm{forget}}\subset \mathcal{D}_{\mathrm{train}}$ from $\epsilon_{\theta^{*}}$ , while preserving performance on the retain set + +$\mathcal{D}_{\mathrm{train}} = \mathcal{D}_{\mathrm{train}}\backslash \mathcal{D}_{\mathrm{forget}}$ Below we describe four unlearning methods for DMs that we use as baselines. + +Erased Stable Diffusion (ESD) [3] intervenes pretrained DMs by steering generation away from the concept intended to be forgotten. Ideally, the unlearned DM is expected to predict $\widetilde{\epsilon}_{\theta^{*}}(\boldsymbol{x}_t,\boldsymbol{c}) = \epsilon_{\theta^{*}}(\boldsymbol{x}_t,\emptyset) - \eta [\epsilon_{\theta^{*}}(\boldsymbol{x}_t,\boldsymbol{c}) - \epsilon_{\theta^{*}}(\boldsymbol{x}_t,\emptyset)]$ when fed in $(\boldsymbol{x},\boldsymbol{c}) \sim \mathcal{D}_{\mathrm{forget}}$ where $\eta > 0$ is a hyperparameter and $\emptyset$ indicates unconditional context. The unlearning objective of ESD is + +$$ +\begin{array}{l} \min _ {\theta} \mathcal {L} _ {\mathrm {E S D}} (\theta ; \mathcal {D} _ {\text {f o r g e t}}) \\ = \mathbb {E} _ {\left(\boldsymbol {x}, \boldsymbol {c}\right) \sim \mathcal {D} _ {\text {f o r g e t}}, \epsilon , t} \left[ \| \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, \boldsymbol {c}\right) - \widetilde {\epsilon} _ {\theta^ {*}} \left(\boldsymbol {x} _ {t}, \boldsymbol {c}\right) \| _ {2} ^ {2} \right], \\ \end{array} +$$ + +where $\theta$ is initialized from the frozen $\theta^{*}$ . Gandikota et al. [3] use ESD-x- $\eta$ to indicate only cross-attention parameters are finetuned with hyperparameter $\eta$ ; likewise, ESD-u- $\eta$ indicates only non-cross-attention parameters are finetuned, and ESD-f- $\eta$ indicates full finetuning. + +Safe self-distillation diffusion (SDD) [15] is a self-distillation paradigm to erase concepts from DMs. The unlearning objective of SDD is to optimize + +$$ +\begin{array}{l} \min _ {\theta} \mathcal {L} _ {\mathrm {S D D}} (\theta ; \mathcal {D} _ {\text {f o r g e t}}) \\ = \mathbb {E} _ {\left(\boldsymbol {x}, \boldsymbol {c}\right) \sim \mathcal {D} _ {\text {f o r g e t}}, \boldsymbol {\epsilon}, t} \left[ \left\| \boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t}, \boldsymbol {c}\right) - \operatorname {s g} \left(\boldsymbol {\epsilon} _ {\theta} \left(\boldsymbol {x} _ {t}, \emptyset\right)\right) \right\| _ {2} ^ {2} \right], \\ \end{array} +$$ + +where $\mathfrak{sg}$ is the stop-gradient operation and $\theta$ is initialized from the frozen $\theta^{*}$ . To mitigate catastrophic forgetting, SDD employs an EMA teacher. Note that in the original implementations of both ESD and SDD, there are only text prompts $c$ in the forget set, while the noisy latents $\pmb{x}_t$ are generated by the frozen DM $\epsilon_{\theta^*}$ . + +Unified concept editing (UCE) [4] edits the pretrained DMs via a closed-form solution without finetuning. Let $W^{*}$ be the attention matrices of $\theta^{*}$ (Key/Value matrices), $\mathcal{T}$ be the text embedding mapping in $\epsilon_{\theta^{*}}$ , then the unlearning objective of UCE is to optimize + +$$ +\begin{array}{l} \min _ {W} \mathbb {E} _ {\boldsymbol {c} _ {f}, \boldsymbol {c} _ {r}} \left[ \| W \mathcal {T} (\boldsymbol {c} _ {f}) - W ^ {*} \mathcal {T} (\emptyset) \| _ {2} ^ {2} + \right. \\ \left. \lambda_ {1} \| W \mathcal {T} (\boldsymbol {c} _ {r}) - W ^ {*} \mathcal {T} (\boldsymbol {c} _ {r}) \| _ {2} ^ {2} + \lambda_ {2} \| W - W ^ {*} \| _ {2} ^ {2} \right], \\ \end{array} +$$ + +where $c_{f} \sim \mathcal{D}_{\mathrm{forget}}$ , $c_{r} \sim \mathcal{D}_{\mathrm{retain}}$ , and $\lambda_{1}, \lambda_{2}$ are hyperparameters. Gandikota et al. [4] prove that the above minimization problem has closed-form solution $W_{\mathrm{UCE}}$ . + +Reliable and efficient concept erasure (RECE) [6] first performs UCE, after which iteratively creates new erasing embeddings and obtains updated attention matrices. Specifically, let $\widetilde{W} \gets W_{\mathrm{UCE}}$ and use subscripts $i$ to denote the $i$ -th attention matrix in the model; then RECE iteratively constructs $c'$ by optimizing + +$$ +\min _ {\boldsymbol {c} ^ {\prime}} \sum_ {i} \left\| \widetilde {W} _ {i} \mathcal {T} (\boldsymbol {c} ^ {\prime}) - W _ {i} ^ {*} \mathcal {T} (\boldsymbol {c} _ {f}) \right\| _ {2} ^ {2} + \lambda \| \mathcal {T} (\boldsymbol {c} ^ {\prime}) \| _ {2} ^ {2}, +$$ + +Algorithm 1 The general framework of meta-unlearning +Require: Pretrained $\theta^{*}$ , forget set $\mathcal{D}_{\mathrm{forget}}$ , retain set $\mathcal{D}_{\mathrm{retain}}$ +Require: Unlearning objective $\mathcal{L}_{\mathrm{unlearn}}$ , finetuning objec +tive $\mathcal{L}_{\mathrm{FT}}$ , meta objective $\mathcal{L}_{\mathrm{meta}}$ +Require: Outer (steps $N$ , learning rate $\omega$ ), inner (steps $M$ +learning rate $\tau$ ), scale factors $\gamma_{1},\gamma_{2}$ # If $\mathcal{L}_{\mathrm{unlearn}}$ is ESD/SDD that needs optimization. +1: $\theta_0\gets \theta^*$ # If $\mathcal{L}_{\mathrm{unlearn}}$ is UCE/RECE that has closed-form solution +2: $\theta_0\gets \theta^{\mathrm{UN}} = \arg \min_{\theta}\mathcal{L}_{\mathrm{unlearn}}$ +3: for $n = 1$ to $N$ do +4: Sample a finetuning set $\mathcal{D}_{\mathrm{FT}}\subset \mathcal{D}_{\mathrm{forget}}$ +5: Initialize $\pmb {g} = \pmb{0}$ and $\theta^{\mathrm{FT}} = \theta_{n - 1}$ # If $\mathcal{L}_{\mathrm{unlearn}}$ is ESD/SDD +6: $\pmb {g}\gets \pmb {g} + \gamma_{1}\cdot \nabla_{\theta_{n - 1}}\mathcal{L}_{\mathrm{unlearn}}(\theta_{n - 1};\mathcal{D}_{\mathrm{forget}},\mathcal{D}_{\mathrm{retain}})$ +7: for $m = 1$ to $M$ do +8: $\theta^{\mathrm{FT}}\gets \theta^{\mathrm{FT}} - \tau \cdot \nabla_{\theta^{\mathrm{FT}}}\mathcal{L}_{\mathrm{FT}}(\theta ;\mathcal{D}_{\mathrm{FT}})$ +9: end for # Meta objective +10: $g\gets g + \gamma_{2}\cdot \nabla_{\theta_{n - 1}}\mathcal{L}_{\mathrm{meta}}(\theta^{\mathrm{FT}};\mathcal{D}_{\mathrm{FT}},\mathcal{D}_{\mathrm{retain}})$ +11: $\theta_{n}\gets \theta_{n - 1} - \omega \cdot g$ +12: end for +13: return $\theta_N$ + +where $\lambda$ is a hyperparameter. The constructed $c'$ is used to derive $\widetilde{W'}$ by UCE, then update as $\widetilde{W} \gets \widetilde{W'}$ and finally obtain $W_{\mathrm{RECE}} = \widetilde{W}$ . + +# 4. Meta-unlearning for DMs + +In Section 3.2, we briefly introduce the commonly used unlearning methods for DMs. In general, the unlearning objective can be summarized as forgetting knowledge from $\mathcal{D}_{\mathrm{forget}}$ and preserving performance on $\mathcal{D}_{\mathrm{retain}}$ , i.e., solving + +$$ +\begin{array}{l} \min _ {\theta} \mathcal {L} _ {\text {u n l e a r n}} (\theta ; \mathcal {D} _ {\text {f o r g e t}}, \mathcal {D} _ {\text {r e t a i n}}) \tag {1} \\ \triangleq \mathcal {L} _ {\text {f o r g e t}} (\theta ; \mathcal {D} _ {\text {f o r g e t}}) + \lambda \cdot \mathcal {L} _ {\text {r e t a i n}} (\theta ; \mathcal {D} _ {\text {r e t a i n}}), \\ \end{array} +$$ + +where $\mathcal{L}_{\mathrm{forget}}$ is to unlearn the forget set, $\mathcal{L}_{\mathrm{retain}}$ is to keep performance on the retain set, and $\lambda$ is a trade-off hyperparameter. Various unlearning methods correspond to different instantiations of $\mathcal{L}_{\mathrm{forget}}$ and $\mathcal{L}_{\mathrm{retain}}$ . In particular, ESD and SDD require optimizers to solve Eq. (1), whereas UCE and RECE have closed-form solutions. In optimization, the initialized parameters are usually set to the pretrained $\theta^{*}$ and the unlearned parameters are denoted as $\theta^{\mathrm{UN}}$ . + +# 4.1. Meta-unlearning framework + +A publicly released DM can potentially be finetuned to adapt to various downstream tasks. However, as observed in previous studies, finetuning or modifying weights of a model could comprise its alignment and/or unlearning [29, 36]. This underscores the need for mechanisms to simulate the finetuning process in advance, ensuring DMs are + +![](images/25f66af54421a208b37217f69ddcea8c08e46fb65154a353de2092342dc57a61.jpg) +T +Figure 2. Images generated by copyright prompts. The top panel displays images generated using the original SDXL model for copyright prompts. In the following panels, we show images generated using ESD-u-1 unlearned and meta-unlearned SDXL models before and after finetuning (FT) on the dataset of unlearned copyright concept for 100 steps, respectively. The forget copyright concept for the left three columns is "SpongeBob", while the right is "Snoopy". + +resilient against relearning the unlearned concepts. Inspired by meta-learning [2], we propose the meta-unlearning framework, as illustrated in Algorithm 1. Our framework consists of two components: (1) the standard unlearning objective $\mathcal{L}_{\mathrm{unlearn}}$ , as described above, and (2) the meta objective $\mathcal{L}_{\mathrm{meta}}$ , which resists the relearning of unlearned concepts, even after finetuning on the forget set. + +Formally, we define $\mathcal{L}_{\mathrm{FT}}$ as the finetuning objective, and let $\mathcal{D}_{\mathrm{FT}} \subset \mathcal{D}_{\mathrm{forget}}$ represent the malicious finetuning dataset, which is designed to intentionally make the model relearn concepts from the forget set. The finetuned model parameters $\theta^{\mathrm{FT}}$ are updated by one or more gradient descents. For example, when using one gradient update from $\theta$ , there is $\theta^{\mathrm{FT}} \gets \theta - \tau \cdot \nabla_{\theta} \mathcal{L}_{\mathrm{FT}}(\theta; \mathcal{D}_{\mathrm{FT}})$ , where $\tau$ is the step size. The parameters $\theta$ is trained by the meta objective $\mathcal{L}_{\mathrm{meta}}$ as: + +$$ +\begin{array}{l} \min _ {\theta} \mathcal {L} _ {\text {m e t a}} \left(\theta^ {\mathrm {F T}}; \mathcal {D} _ {\mathrm {F T}}, \mathcal {D} _ {\text {r e t a i n}}\right) \tag {2} \\ = \mathcal {L} _ {\text {m e t a}} (\theta - \tau \cdot \nabla_ {\theta} \mathcal {L} _ {\mathrm {F T}} (\theta ; \mathcal {D} _ {\mathrm {F T}}); \mathcal {D} _ {\mathrm {F T}}, \mathcal {D} _ {\text {r e t a i n}}). \\ \end{array} +$$ + +To optimize the RHS of Eq. (2), the gradients are backpropagated through both $\theta$ and $\nabla_{\theta}\mathcal{L}_{\mathrm{FT}}(\theta ;\mathcal{D}_{\mathrm{FT}})$ that can be efficiently computed by automatic differentiation [23]. + +# 4.2. Meta objective $\mathcal{L}_{\mathrm{meta}}$ + +Our design goal for meta-unlearning is to ensure that after the model is maliciously finetuned on $\mathcal{D}_{\mathrm{FT}} \subset \mathcal{D}_{\mathrm{forget}}$ , it cannot relearn the unlearned concepts. Additionally, we further encourage the model to self-destruct knowledge from the retain set. Given this, a natural instantiation of $\mathcal{L}_{\mathrm{meta}}$ is + +$$ +\begin{array}{l} \min _ {\theta} \mathcal {L} _ {\mathrm {m e t a}} (\theta^ {\mathrm {F T}}; \mathcal {D} _ {\mathrm {F T}}, \mathcal {D} _ {\mathrm {r e t a i n}}) \triangleq - \mathcal {L} _ {\mathrm {D M}} (\theta^ {\mathrm {F T}}; \mathcal {D} _ {\mathrm {F T}}) \\ - \zeta \cdot \left[ \mathcal {L} _ {\mathrm {D M}} \left(\theta^ {\mathrm {F T}}; \mathcal {D} _ {\text {r e t a i n}}\right) - \mathcal {L} _ {\mathrm {D M}} \left(\theta ; \mathcal {D} _ {\text {r e t a i n}}\right) \right], \\ \end{array} +$$ + +where $\mathcal{L}_{\mathrm{DM}}$ is the diffusion loss described in Section 3.1 and $\zeta$ is a hyperparameter. Now we take a close look at how the meta objective in Eq. (3) works. In practice, the finetuning objective $\mathcal{L}_{\mathrm{FT}}$ is typically set to $\mathcal{L}_{\mathrm{DM}}$ ; and following Eq. (2), the first-order approximation of $\mathcal{L}_{\mathrm{meta}}(\theta^{\mathrm{FT}}; \mathcal{D}_{\mathrm{FT}}, \mathcal{D}_{\mathrm{retain}})$ can be written as (up to a $\mathcal{O}(\tau^{2})$ error) + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {m e t a}} \approx - \mathcal {L} _ {\mathrm {D M}} (\theta ; \mathcal {D} _ {\mathrm {F T}}) + \tau \cdot \| \nabla_ {\theta} \mathcal {L} _ {\mathrm {D M}} (\theta ; \mathcal {D} _ {\mathrm {F T}}) \| _ {2} ^ {2} \\ + \tau \zeta \cdot \nabla_ {\theta} \mathcal {L} _ {\mathrm {D M}} (\theta ; \mathcal {D} _ {\mathrm {F T}}) ^ {\top} \nabla_ {\theta} \mathcal {L} _ {\mathrm {D M}} (\theta ; \mathcal {D} _ {\text {r e t a i n}}), \tag {4} \\ \end{array} +$$ + +where we colorize the terms that play key roles in our meta-learning framework. Note that this approximation corre + +![](images/4384180343ab5edd0ac02bd2537b4cc5a0b4992acf318ec78bdf63c3ee486492.jpg) +Figure 3. Images generated by style prompts. The top panel displays images generated using the original SDXL model for style prompts. In the following panels, we show images generated using ESD-u-1 unlearned and meta-unlearned SDXL models before and after finetuning (FT) on the dataset of unlearned copyright concept for 100 steps, respectively. The forget style of left three columns is "Thomas Kinkade" and the right is "Kelly McKernan". + +sponds to $M = 1$ in Algorithm 1; for $M > 1$ (i.e., multi-step gradient descent), the approximation formula remains unchanged but with equivalent step size $M\tau$ . + +Remark. As in Fig. 1, minimizing $\| \nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})\| _2^2$ decreases gradient norm and thus delays relearning of forget set. Minimizing $\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})^{\top}\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{retain}})$ induces a $>90^{\circ}$ angle between the gradients $\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})$ and $\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{retain}})$ , such that when the model is finetuned along $\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})$ (the loss $\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})$ decreases), the knowledge inside the retain set will self-destruct (namely, the loss $\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{retain}})$ increases). + +# 5. Experiments + +Below we first describe the basic setups of our experiments: + +Base models. We choose SD-v1-4 [31] and SDXL [28] as the base models for their widespread use. + +Datasets. We use SD-v1-4 and SDXL to generate both $\mathcal{D}_{\mathrm{forget}}$ and $\mathcal{D}_{\mathrm{retain}}$ for meta-unlearning. Subsequently, we employ FLUX.1 [17] to create three safety-related fin-tuning datasets HRM-s, HRM-m, CLEAN for evaluation, by applying a single harmful prompt, multiple harmful + +prompts and benign prompts, respectively. We also utilize FLUX.1 to create two finetuning datasets related to copyright and two others related to image style. Detailed information can be found in Appendix E.1. Additionally, the 10K subset of COCO-30K [19] is used to evaluate the generation quality of unlearned DMs while the nudity subset in the Inappropriate Image Prompts (I2P) dataset [32] is used to test the unlearning performance. + +Baselines. We use four established unlearning methods as baselines, including ESD [3] and SDD [15], which remove the target concept through gradual optimization; UCE [4] and RECE [6] that achieve target concept erasure through closed-form solutions. Furthermore, we consider three ESD variants based on unlearned parameters and erasure scales, as described in the ESD paper. We use the ESD-u-1, which erases U-Net models excluding cross-attention parameters under weak erase scale $\eta = 1$ , ESD-u-3, which erases the same parameters as ESD-u-1 but under strong erase scale $\eta = 3$ , and ESD-f-3, which erases the full parameters of the U-Net with erase scale $\eta = 3$ . + +Evaluation metrics. We use FID [10] and CLIP scores + +![](images/2223b4f6f7a0f498508188c644d6122e3d52d3b4da6f9ff7a0dca343002486f7.jpg) +Figure 4. Images generated by harmful prompts. The top panel displays images generated using the original SDXL model for harmful prompts. Following panels show the images generated using unlearned and meta-unlearned SDXL models before finetuning (FT), after FT on the HRM-m dataset for 100 steps, and after FT on the CLEAN dataset for 100 steps, respectively. The left three columns display images generated by ESD-u-1 and its meta variant, while the right three columns display images generated by UCE and its meta variant. + +![](images/4f164aaf2e56ee8b43dfc35cef3c4f3901404b332492083eba23216ae7c2c49e.jpg) +Figure 5. Images generated by benign prompts after finetuning on CLEAN. Unlearned and meta-unlearned SDXL models are finetuned on the CLEAN dataset for 100 steps. As seen, our methods will not affect performance when the meta-unlearned models are finetuned on benign data. + +[9] to evaluate the model's generation quality. To evaluate + +the effect of unlearning harmful content and resistance to malicious finetuning, we calculate nudity score [32] based on the percentage of nude images in all generated images. + +Evaluation details. We first use an unlearned model to generate images based on COCO 10K subset, and compute the FID and CLIP scores using the generated images and COCO subset data. Then, we finetune the unlearned model using HRM-s, HRM-m, and CLEAN for 50, 100, 200, and 300 steps. Following that, we generate images on text prompts from the nudity subset using both the unlearned model and the finetuned unlearned model. Finally, we use the nudity detector [32, 42] to determine the nudity score for the generated images. + +Table 1. Nudity evaluation. The nudity score of unlearned and meta-unlearned SD-v1-4 models, based on six unlearning methods similar to Table 2. The results are reported for models before or after finetuning (FT) on three datasets for 50, 100, 200, and 300 steps. + +
MethodTypeBefore FTFT on HRM-mFT on HRM-sFT on CLEAN
0501002003005010020030050100200300
SD-1.4-97.18-------------
ESD-u-1Unlearn6.3419.0121.8330.2834.5123.2424.6545.0753.5211.2713.3812.6814.79
Meta-Unlearn0.008.4513.3823.9426.064.2312.6830.2838.032.822.114.234.23
ESD-u-3Unlearn3.5226.7638.7336.6233.8023.2428.1731.6935.925.634.937.756.34
Meta-Unlearn0.003.5219.0126.7626.768.4518.3120.4226.062.112.824.232.82
ESD-f-3Unlearn6.3432.3956.3460.5655.6347.8951.4140.1459.8612.6816.9018.3114.79
Meta-Unlearn0.002.1126.0638.0333.105.6318.3124.6535.923.524.935.635.63
SDDUnlearn1.4133.1057.0452.1154.2342.9650.7053.5253.5214.0816.2017.6118.31
Meta-Unlearn0.0020.4245.0742.2548.5915.4928.1731.6935.212.115.636.347.75
UCEUnlearn16.9036.6244.3747.8936.6228.1734.5140.1457.7523.9425.3523.2426.76
Meta-Unlearn1.4124.6528.1730.2825.3518.3119.0121.1342.964.935.634.934.23
RECEUnlearn4.9316.2019.7222.5422.5411.2714.7917.6122.546.349.867.047.75
Meta-Unlearn4.237.0410.5615.4913.385.638.4513.3815.494.235.634.935.63
+ +# 5.1. Harmful content removal + +Tables 1 and 2 show the evaluation results of the unlearned and meta-unlearned SD-v1-4. Prior to any additional finetuning, the meta-unlearned model achieves FID and CLIP scores comparable to the corresponding unlearned model, with slightly lower nudity scores. After malicious finetuning on the HRM-s and HRM-m datasets, the unlearned model shows a rapid increase in nudity scores. In contrast, meta-unlearned SD yields significantly lower nudity scores than the unlearned model. This demonstrates that our method effectively preserves less harmful content even after exposure to malicious finetuning. Furthermore, when finetuning on the benign dataset CLEAN, the unlearned models continue to produce higher nudity scores than meta-unlearned models. Fig. 10 (in Appendix) shows images generated by unlearned and meta-unlearned models on benign prompts before finetuning, indicating that meta-unlearned models can produce comparable images with corresponding unlearned models. Then we show the images generated by harmful prompts in Fig. 11 (in Appendix). The unlearned and meta-unlearned models are finetuned on the HRM-m dataset for 50, 100, 200, and 300 steps. As finetuning steps increase, unlearned models rapidly relearn the ability to generate harmful images. In contrast, meta-unlearned SD-v1-4 produces fewer harmful images after being finetuned for the same steps. + +Fig. 8 (in Appendix) presents images generated on benign prompts by unlearned and meta-unlearned SDXL. As seen, for benign prompts, the meta-unlearned SDXL also achieves a high generation quality comparable to that of the corresponding unlearned method. Fig. 4 displays the harmful images generated by the unlearned and meta-unlearned models before and after being finetuned on the HRM-m and + +![](images/594fcc7765442d00eaf56008147fe070dbc038362918ef2ef7c624c7c16ae439.jpg) +Figure 6. The value of $\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})^{\top}\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{retain}})$ for each step of meta-unlearning. Because the value is noisy, we use the regression line to represent a smoothed trend. + +CLEAN datasets. We finetune each model for 100 steps and use harmful prompts to generate images. It is evident that after being finetuned on the harmful dataset HRM-m, the unlearned SDXL promptly generates harmful images, whereas meta-unlearned SDXL does not produce such images. Besides, after being finetuned on the benign dataset CLEAN, the unlearned models still have a probability of generating harmful images, while meta-unlearned models consistently ensure the generation of harmless images. + +# 5.2. Copyright and style removal + +We use ESD-u-1-based unlearning and meta-unlearning to remove copyright/style concepts from images. + +Copyright removal. Fig. 2 shows removal of two copyrighted cartoon characters, SpongeBob and Snoopy. After unlearning, neither unlearned nor meta-unlearned models are able to produce the removed copyright concepts. However, after maliciously finetuned on unlearned concepts, the unlearned model becomes to relearn the unlearned concepts, while the meta-unlearned model is resistant to relearning and avoids copyright infringement. + +Table 2. Quality evaluation. The FID and CLIP scores of unlearned and meta-unlearned SD-v1-4 models, based on six unlearning methods: ESD-u-1, ESD-u-3, ESD-f-3, SDD, UCE, and RECE. + +
MethodMetricOriginalESD-u-1ESD-u-3ESD-f-3SDDUCERECE
UnlearnFID16.7116.0120.5221.3821.1217.5917.47
CLIP score31.0930.3229.6530.0029.2731.0130.70
Meta-UnlearnFID-16.9819.9818.5421.7819.2018.19
CLIP score-30.2029.8629.9330.6131.2530.23
+ +![](images/0a965305bd9df6402507e872322738f8dfc2d60d79725eed76943595f6e1467e.jpg) +Figure 7. Images generated for the word "woman" during finetuning 1-12 steps on dataset HRM-s. + +Style removal. Fig. 3 shows the removal of two painting styles Thomas Kinkade and Kelly McKernan. After unlearning, neither the unlearned nor the meta-unlearned models can produce these styles. Nevertheless, the unlearned model regains the capacity to replicate the removed styles after malicious finetuning, while the meta-unlearned model will not relearn these removed styles. + +Performance on unrelated concepts. Fig. 9 (in Appendix) displays images generated on prompts unrelated to removed concepts before the unlearned or meta-unlearned model is maliciously finetuned. This shows that both unlearned and meta-unlearned models can maintain the capability to generate images on unrelated/benign concepts. + +# 5.3. More analyses + +In this section, we first discuss the relationship between the unlearn concept and its related concept during meta-unlearning and malicious finetuning. Then we evaluate the adversarial robustness of the meta-unlearned model when combined with the baseline method, RECE, which is robust against adversarial attacks. Refer to Appendix B for the performance of our method under more metrics and Appendix F for hyperparameter analysis. + +Concept relationship during meta-unlearning. To show how our meta-unlearning changes the relationship between the target unlearn concept ("nudity") and its related concept in DMs, we calculate the value of the orthogonal term $\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{FT}})^{\top}\nabla_{\theta}\mathcal{L}_{\mathrm{DM}}(\theta ;\mathcal{D}_{\mathrm{retain}})$ for each step during meta-unlearning. We utilize UCE-based meta-unlearning to train 100 steps as an example. To clearly demonstrate the relationship changes between the target unlearn concept and its related concept, we only optimize the first cross-attention layer and normalize the gradients before calculating the orthogonal term. Fig. 6 illustrates the changes in the orthogonal term value during the meta-unlearning process. Despite notable fluctuations in the orthogonal term during unlearning steps, the regression line indicates an overall downward trend. + +Concept relationship during malicious finetuning. Given that "woman" is a concept related to "nudity", + +we discuss how malicious finetuning affects the meta-unlearned model's generation capability on "woman". We finetune the UCE-based meta-unlearned model for 1 to 12 steps. Fig. 7 shows how the capability changes in generating "woman" during malicious finetuning. In step 1, the generated image has no human features. As the finetuning progresses, the ability to produce female images improves; however, the overall quality remains relatively low. + +Performance of models finetuned on benign dataset. Since our objective is to ensure that the unlearned model only self-destruct when finetuned on harmful datasets, the model should retain normal generative capabilities when trained on benign concepts. Fig. 5 illustrates the generative performance of the meta-unlearned model compared to the corresponding unlearned after 100 training steps on the CLEAN dataset. As observed, the meta-unlearned model's generative ability remains unaffected by finetuning on benign data, and self-destruction does not occur. + +Robustness to adversarial attacks. Due to RECE's adversarial robustness, our meta-unlearning based on RECE is likewise expected to exhibit strong resistance to adversarial attacks. We utilize UnlearnDiffAtk [42] as the evaluation framework for adversarial robustness. Compared with the attack successful rate (ASR) for the RECE unlearned model, $64.79\%$ , the ASR on our meta-unlearned model achieves $62.68\%$ . Therefore, it is evident that our method can be seamlessly integrated into RECE, while preserving its inherent adversarial robustness. + +# 6. Conclusion + +Our meta-unlearning framework combines a meta objective with existing unlearning methods, ensuring that if an already unlearned model is maliciously finetuned on unlearned data, related benign concepts will self-destruct, impeding the relearning process. Extensive experiments on SD-v1-4 and SDXL reveal that our method maintains benign generation quality while largely reducing generation of unlearned concepts. Meta-unlearning is compatible with a variety of unlearning techniques and offers a simple yet effective solution for preventing DMs from potential misuse. + +# Acknowledgements + +This work is supported in part by NSF of China (Nos. 92470118, 62306176), Natural Science Foundation of Shanghai (No. 23ZR1428700), CCF-ALIMAMA TECH Kangaroo Fund (NO. CCF-ALIMAMA OF 2025010), and CCF-Zhipu Large Model Innovation Fund (No. CCF-Zhipu202412). + +# References + +[1] Abeba Birhane, Vinay Uday Prabhu, and Emmanuel Kahembwe. Multimodal datasets: misogyny, pornography, and malignant stereotypes. arXiv preprint arXiv:2110.01963, 2021. 1 +[2] Chelsea Finn, Pieter Abbeel, and Sergey Levine. Model-agnostic meta-learning for fast adaptation of deep networks. In International Conference on Machine Learning (ICML), 2017. 1, 4 +[3] Rohit Gandikota, Joanna Materzynska, Jaden Fiotto-Kaufman, and David Bau. Erasing concepts from diffusion models. 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VPiT teaches an LLM to predict discrete text tokens and continuous visual tokens from any input sequence of image and text data curated in an instruction-following format. Our empirical investigation reveals several intriguing properties of VPiT: (1) visual generation ability emerges as a natural byproduct of improved visual understanding, and can be unlocked efficiently with a small amount of generation data; (2) while we find understanding and generation to be mutually beneficial, understanding data contributes to both capabilities more effectively than generation data. Building upon these findings, we train our MetaMorph model and achieve competitive performance on both visual understanding and generation. In visual generation, MetaMorph can leverage the world knowledge and reasoning abilities gained from LLM pretraining, and overcome common failure modes exhibited by other generation models. Our results suggest that LLMs may have strong "prior" vision capabilities that can be efficiently adapted to both visual understanding and generation with a relatively simple instruction tuning process. + +# 1. Introduction + +Multimodal Large Language Models (MLLMs) have advanced considerably in visual understanding, progressing from basic image captioning to complex visual inferences [4, 14, 36]. These models process multimodal inputs—primarily images and language—and generate text tokens. Multimodal LLMs often leverage a pretrained vision encoder [16, 52], a pretrained language model [3, 66], and align these modalities through connectors such as MLP [36, 37] or cross-attention modules [4, 14]. Among MLLM training methods, visual instruction tuning [36] has become widely used [2, 67]. It treats output embeddings of pretrained vision encoders as continuous-valued "visual tokens" and directly feeds them as inputs to pretrained LLMs. + +One benefit of visual instruction tuning is that it is data and compute efficient. A pretrained LLM can be repurposed as a Multimodal LLM by instruction tuning with modest compute and data on the order of millions of image-text question-answer pairs [32, 63]. The effectiveness of visual instruction tuning indicates that LLMs already possess a considerable amount of inherent visual knowledge which allows them to learn and develop visual understanding during the instruction tuning process [85]. Inspired by this, we investigate whether LLMs can also be finetuned to generate visual information with comparable efficiency and effectiveness. + +Current attempts toward "unified" models—models capable of both multimodal understanding and generation—often treat visual generation as an orthogonal capability to visual understanding. They tend to require substantial changes to the original MLLM architecture and significant multimodal pretraining and/or finetuning. Designing such methods is challenging, and past research takes different approaches including tokenizing visual inputs into discrete tokens [39, 62, 73], incorporating diffusion objectives [75, 86], and decoupling vision into separate understanding and generation modes [71]. For example, approaches like LWM [39], Show-o [75], and Chameleon [62] require billions of imag-text pairs [17, 56] for extensive pretraining and finetuning. + +In this work, we propose Visual-Predictive Instruction Tuning (VPiT)—a simple extension to visual instruction tuning which builds upon the existing paradigm of passing continuous visual tokens as input to the LLM. VPiT trains an LLM to output both continuous visual tokens and discrete text tokens in the finetuning stage. The model takes pretrained vision encoder embeddings as well as text tokens as input, and outputs a combination of text tokens and continuous visual tokens. To visualize the generated visual tokens, we finetune a diffusion model to map the embeddings back into pixel space (see Fig. 1 for an example). This framework allows us to study the synergy between visual understanding, visual generation, and pretrained LLMs, which leads to several intriguing findings outlined below. + +First, we show that the ability to predict visual tokens emerges from understanding visual inputs and requires minimal additional training. Similar to visual instruction tuning, + +![](images/7eec868618959ebbd77f203728f42cbf33ffea27535957d91c70fb1b8d62ef8b.jpg) +Figure 1. VPit Training, Inference, and Examples of MetaMorph. Left: In Visual-Predictive Instruction Tuning (VPiT), we finetune a pretrained LLM to generate both text and visual tokens using separate text and vision heads. Middle: During inference, the model accepts an arbitrary input sequence of image(s) and text and outputs discrete text tokens and continuous visual tokens. These visual tokens can be visualized via a separately finetuned diffusion model, which is trained to condition on the vision encoder's output. Right: An example conversation from MetaMorph trained with VPiT. Here, the model implicitly solves a visual puzzle to generate a butterfly. The conversation continues with new user questions as the model continues to process autoregressively, independent of the diffusion-based visualization. + +VPiT efficiently and effectively morphs an LLM into an "unified" model that understands and generates multimodal tokens. When trained jointly with sufficient visual understanding data, this process requires as little as $200k$ additional visual generation data. + +We further establish that the abilities to understand and generate visual tokens are intrinsically linked and asymmetrical. Specifically, increasing understanding data improves visual understanding (measured by higher VQA scores) and generation (measured by lower FID scores). Conversely, increasing generation data enhances generation quality and also contributes to stronger visual understanding—but to a lesser degree. Importantly, our findings highlight an asymmetry in how training each ability impacts the model's overall vision performance: understanding-centric training substantially outperforms generation-centric training in improving both visual understanding and generation. + +Building upon these findings, we train a unified model called MetaMorph to predict multimodal tokens with VPiT. We leverage diverse data sources ranging from common visual question answering datasets to pure image and video data without text annotations. MetaMorph achieves competitive performance on both visual understanding and visual generation benchmarks. Furthermore, we show this unified modeling approach allows models to leverage the power of LLMs. For instance, MetaMorph can extract knowledge from the pretrained LLM when generating visual tokens. More surprisingly, we observe that MetaMorph can implicitly perform reasoning steps before generating visual tokens—e.g. when prompted with "the animal resulting from a monarch caterpillar's metamorphosis", MetaMorph successfully generates an image of a butterfly (Fig. 1). + +Our results suggest that 1) training a unified model with instruction tuning is feasible, and 2) LLMs have strong preexisting visual capabilities which can be activated using significantly fewer samples compared to extensive pretraining. These insights shed light on the development of mixed-modality models. As the community continues to improve visual understanding in Multimodal LLMs [32, 63, 67] by + +advancing base LLMs, instruction tuning techniques, and data, we highlight that these efforts may also implicitly lead to models that are better at visual generation. + +# 2. Visual-Predictive Instruction Tuning + +Visual instruction tuning as introduced by LLaVA [36] demonstrates that LLMs can be taught to understand visual inputs. This is achieved by finetuning on million-scale data. The success of late-fusion instruction tuning suggests that LLMs may already possess innate visual understanding ability. This ability simply needs to be unlocked through lightweight finetuning. Analogously, we hypothesize that LLMs already possess a degree of innate visual generation ability which just needs to be unlocked with finetuning. + +Motivated by this, we present Visual-Predictive Instruction Tuning (VPiT, Fig. 1)—a simple design which extends existing instruction tuning methods to additionally generate visual tokens rather than text alone. We use the same architecture and next-token prediction paradigm to unlock visual generation capabilities without bells and whistles. We take a pretrained LLM and finetune it to predict both discrete text tokens and continuous visual tokens. The visual tokens can be visualized with an adapted diffusion model. + +# 2.1. From Unimodal to Multimodal Next-Token Prediction + +The standard instruction tuning setup consists of an input sequence of conversation rounds [61, 69]: $(P_i,R_i)_{i = 1}^N$ , where $P_{i}$ and $R_{i}$ represent prompts and responses for the $i$ -th round of conversation, respectively. The model is trained to generate responses based on the prompt. VPiT adds the following mechanisms to a standard instruction tuning setup to unlock visual understanding and generation. + +Tokenizing multimodal data. We extend $P_{i}$ and $R_{i}$ to include both text and images. To integrate visual data into a pretrained LLM, we process data closely following visual instruction tuning [36]: + +- Text Data: Text is tokenized into discrete tokens with a standard tokenizer used by the LLM. +- Visual Data: Images are encoded with a pretrained vision encoder such as SigLIP [81]. The output is continuous visual tokens which are then interpolated to $m = 64$ tokens. To pass the visual tokens as input to the LLM, we apply a trainable projection layer to align the dimensions. + +Model architecture. We take a pretrained LLM and finetune it to process arbitrary sequences of text and visual tokens (detailed next in Sec. 2.2). We keep the original LLM head for text prediction, and attach a separate vision head to the LLM for predicting visual tokens, i.e., the output tokens generated by the vision encoder when processing images. The vision head is a projection layer that projects from the LLM's dimension to the vision encoder's dimension. All response tokens can then be trained and predicted autoregressively, with prompt tokens as context. + +Unlike conventional visual instruction tuning, in VPiT, visual tokens are also outputs of the LLM—not just inputs. To make the LLM aware of the presence of visual tokens, we introduce special tokens $\langle \mathrm{image\_start}\rangle$ and $\langle \mathrm{image\_end}\rangle$ to indicate the boundaries of visual token sequences and when to use the vision head. + +Loss functions. The language head outputs a probability distribution over the vocabulary and is trained with cross-entropy loss for next-token prediction. Visual prediction uses cosine similarity loss between the LLM's predicted visual tokens and those from the vision encoder. Consistent with instruction tuning practices, the model only makes predictions and incurs loss on response tokens. + +# 2.2. Using Broad Types of Data + +Because VPiT enables the model to predict both text and visual tokens in its responses, it allows the use of a broader range of training data. Traditional visual instruction tuning, on the other hand, primarily relies on question-and-answer pairs. The majority of our dataset is publicly available, and we categorize it into three major categories below. This categorization enables us to systematically study the model, as detailed in Sec. 3 and Sec. 4. All data types are formatted as instruction tuning style prompt & response pairs. See further details in Appendix C.2. + +1. Visual Understanding Data: This category includes data that takes image(s) or video as input and outputs text responses. See Fig. 1 for an example. We use: + +- ImageQA: Cambrian-7M [63]. The model answers questions based on input image(s). + +$$ +\begin{array}{l} P _ {i} \in \{\langle \text {v i s u a l t o k e n s} \rangle , \langle \text {t e x t p r o m p t} \rangle \} \\ R _ {i} \in \{\langle \text {t e x t r e s p o n s e} \rangle \} \end{array} +$$ + +- VideoQA: VideoStar [87] and ShareVideo [83]. The model answers questions based on the input video. For videos in VideoQA, we process frames at 1 FPS. + +$$ +\begin{array}{l} P _ {i} \in \{\langle \text {v i s u a l t o k e n s} \rangle , \dots , \langle \text {v i s u a l t o k e n s} \rangle , \\ \langle \text {t e x t p r o m p t} \rangle \} \end{array} +$$ + +$$ +R _ {i} \in \{\langle \text {t e x t r e s p o n s e} \rangle \} +$$ + +2. Visual Generation Data: MetaCLIP [76]. The model predicts visual tokens based on an image description. We using at most 5 million pairs. We curate the data into question-answering formats. + +$$ +\begin{array}{l} P _ {i} \in \{\langle \text {t e x t p r o m p t} \rangle \} \\ R _ {i} \in \{\langle \text {t e x t r e s p o n s e} \rangle , \langle \text {v i s u a l t o k e n s} \rangle \} \\ \end{array} +$$ + +We prompt the model to generate visual tokens with instructions like "Generate an image of...". The text responses are "Here is an image based on your request...". See Fig. 1 for an example. + +3. Other Visual Data: This category includes data that requires the model to predict visual tokens given interleaved input visual tokens and text tokens. We use: + +- Video Data: SomethingSomethingV2 [21] and HowTo100M [47]. The model predicts frames in a sequential order. We design different question-answer pairs to probe into the video, such as asking about future frames, past frames, and reordering frames. + +$$ +\begin{array}{l} P _ {i} \in \{\langle \text {v i s u a l t o k e n s} \rangle , \dots , \langle \text {v i s u a l t o k e n s} \rangle , \\ \langle \text {t e x t p r o m p t} \rangle \} \end{array} +$$ + +$$ +R _ {i} \in \{\langle \text {v i s u a l t o k e n s} \rangle , \dots , \langle \text {v i s u a l t o k e n s} \rangle \} +$$ + +- Visual Thinking Data: Visualization-of-Thought [57] and VStar [72]. The model predicts multimodal tokens in its response before addressing problems. For instance, it predicts a zoomed-in view of an image before generating textual responses. + +$$ +P _ {i} \in \{\langle \text {v i s u a l t o k e n s} \rangle , \langle \text {t e x t p r o m p t} \rangle \} +$$ + +$$ +\begin{array}{l} R _ {i} \in \{\langle \text {t e x t r e s p o n s e} \rangle , \langle \text {v i s u a l t o k e n s} \rangle , \\ \langle \text {t e x t r e s p o n s e} \rangle \} \end{array} +$$ + +- Image-to-Image Data: InstructPix2Pix [10] and Aurora [28]. The model generates a transformed image conditioned on a text description and an input image. + +$$ +P _ {i} \in \{\langle \text {v i s u a l t o k e n s} \rangle , \langle \text {t e x t p r o m p t} \rangle \} +$$ + +$$ +R _ {i} \in \{\langle v i s u a l t o k e n s \rangle \} +$$ + +# 2.3. Mapping Tokens to Images through Diffusion + +Because models trained with VPiT learn to predict continuous visual tokens, we need to map the predicted tokens back into pixel space. We leverage the concept of a "Diffusion Autoencoder" [9, 27, 34, 50, 51] in which the diffusion model can be adapted to condition on image embeddings. Specifically, we finetune an existing diffusion model to condition on outputs from the vision encoder using held-out data. + +At inference time, if $\langle \mathrm{image\_start} \rangle$ is generated, the model begins outputting visual tokens until $\langle \mathrm{image\_end} \rangle$ . We then plug the generated visual tokens into the diffusion model to visualize the prediction in pixel space. We use latent diffusion model training procedures. Details on the hyperparameters and training are provided in Appendix A.2. + +![](images/77b1152729dbf77304def221f1146e7901be583f692a66b022043ce0833f7313.jpg) +Figure 2. Generation-only training vs. Joint training with other data. Training solely on generation data results in inferior performance. Joint training with additional data enables visual generation with only 5k generation data and yields high-quality outputs with 200k generation data. + +# 3. Findings on Unlocking Visual Generation + +We study the following questions about the effects and synergy of visual understanding and generation, under VPiT: +§3.1 Can visual generation be unlocked through lightweight tuning, or does it require extensive data? +$\S 3.2$ Are visual understanding and generation mutually beneficial or orthogonal? +§3.3 How much does more visual understanding or generation data contribute to understanding and generation quality? +$\S 3.4$ Which visual understanding tasks correlate the most with generation performance? + +Evaluation settings. We use 9 ImageQA benchmarks (MM-Bench, Seed, VStar, MMVP, MMMU, ChartQA, TextVQA, ScienceQA, RealWorldQA) to evaluate different aspects of the model. For image generation, we use the finetuned diffusion model to visualize generated visual tokens and measure FID score (lower is better) and CLIP score (higher is better) on the COCO-30K dataset. Unless otherwise specified, we use LLaMA-3 8B [3] / SigLIP ViT-SO400M-14@384 [81] as the pretrained LLM / vision encoder. We also study the effect of different LLMs in Sec. 3.2. We use instruction tuned versions of the LLMs. We pretrain the adapter between the vision encoder and the LLM following visual instruction tuning. For experiments in this section, we provide training details in Appendix A and full results in Appendix B. + +# 3.1. Visual Generation Can Be Unlocked Efficiently by Joint Training with Visual Understanding + +We start by investigating the number of image-text samples required to teach a language model to generate high-quality visual tokens. To this end, we randomly sample $\{1\mathrm{k}, 5\mathrm{k}, 10\mathrm{k}, 50\mathrm{k}, 200\mathrm{k}, 1\mathrm{M}, 3\mathrm{M}, 5\mathrm{M}\}$ image-text pairs from our generation data (MetaCLIP dataset [76]). We explore two settings: (1) finetuning the LLM using only visual generation data, and (2) joint training visual generation with visual understanding and the rest of data types described in Sec. 2.2. + +In Fig. 2, we see that training solely on visual genera + +![](images/6f276c419b3ed3302ab093a756ce06a836ccddcee4e5a4bf762865f6f050ae6d.jpg) +Figure 3. Impact of different data types on visual generation. The baseline of training on only visual generation data is red; Joint training with other data is yellow; Joint training with visual understanding data is green; and all data is blue. Joint training with additional data improves the baseline, with visual understanding tasks contributing the most to enhancing visual generation. + +tion performs significantly worse than joint training with all other data. With over 3 million image-text pairs, the model struggles to generate high-quality visual images ( $\sim$ 40 FID score), and performance remains inferior to joint training with 5 million pairs. This suggests that training solely on visual generation data is significantly less sample efficient. This finding aligns with a prior study [84] which also suggests that LLMs cannot be easily tuned to generate visual tokens when trained with only generation data. In contrast, joint training with other datasets substantially improves generation performance. The model generates effective visual tokens with just $5k$ generation data, and performance stabilizes around $200k$ samples. This indicates that visual generation is not an orthogonal capability but rather an ability that emerges more effectively with joint training. + +To better understand how each type of data contributes to visual generation, we conduct a controlled experiment using 200k visual generation data, joint training individually with each data type defined in Sec. 2.2. We also compare them with training all the data together and show results in Fig. 3. While all data types enhance the model's visual generation, the degree of improvement varies. Visual understanding data, such as ImageQA and VideoQA, significantly boost the model's visual generation capabilities. This indicates a strong link between the ability to understand visual content and generate visual tokens. Additionally, combining all data types in training further improves performance, suggesting that the benefits from different data types can be additive. + +Finding 1: Visual generation can be unlocked with significantly less generation data when the model is jointly trained with visual understanding data, in contrast to training only on generation data. + +# 3.2. Visual Understanding and Generation are Mutually Beneficial + +More understanding data leads to better understanding and generation. Building upon findings from the previous subsection, we perform a controlled experiment to investigate how visual understanding correlates with visual genera + +![](images/39f9bb0f1dd3405c140e7fdf03951b9f35d3eb4eb8748a91b2f2af8e4817bad2.jpg) + +![](images/fb464eda3a8ea9786e8007666242e41aee89ca08e03ce1e9542ea89a6dac2901.jpg) + +![](images/fccc7d1473008747f1d44aaebd43e6c0cd01a3ef3dccbb2f8668145316802a23.jpg) +Figure 4. VQA Performance vs. Generation Performance with generation data controlled at 200k. Increasing understanding data improves VQA and generation performance. + +![](images/61397c89df972bf30163e19c5214d1a422c411d1b86a463833ab04401279ee1a.jpg) + +![](images/31f09ed75fae94bdec1ecdd51f61ae62a9612966d7d22363c3d887c44baf2b8b.jpg) + +![](images/50ec316a46925f1906be58aef5cbf1352531f3aa0f25a8e42ea6b950dae2a6d9.jpg) +Figure 5. Generation Performance vs. VQA Performance with VQA data controlled at 1M. Increasing generation data improves generation and VQA performance. + +tion ability. We ablate our model using a fixed set of 200k generation data while varying VQA data from 1M to 7M samples from Cambrian-7M to develop different levels of visual understanding. The results presented in Fig. 4 indicate that stronger VQA ability correlates with better generation. + +More generation data leads to better understanding and generation. Here, we investigate the reverse direction: does enhancing the model's visual generation capability also relate to higher VQA performance? To explore this, we conduct a controlled experiment using 1M fixed VQA samples as the baseline for understanding. We then vary the amount of generation data ( $\{200\mathrm{k}, 500\mathrm{k}, 1\mathrm{M}, 2\mathrm{M}, 3\mathrm{M}, 4\mathrm{M}\}$ ) to adjust generation capacity while joint training with the fixed 1M VQA data. We present results in Fig. 5. Within the 1M VQA setting, stronger generation ability is correlated with improved VQA performance. This implies that increasing the amount of generation data not only enhances generation but also positively impacts VQA performance. + +This synergy scales across different LLMs. We examine whether the findings transfer across LLM backbones. Using a data composition of 7M VQA and 1M generation data, we train VPiT on LLaMA-3 8B, LLaMA-3.1 8B, and LLaMA-3 70B. Fig. 6 shows scaling behaviors across different LLMs. + +![](images/e11986adf2b842f0fd7d0a885f4ad476be847a55bbd4bf6eebe356210ed77721.jpg) + +![](images/605495bbac40ec4f3c8af07770b79e1e244fc68e5930e5748aae12e46bfbac59.jpg) + +![](images/2bf291eb774e117981c167f0a7f0df0c0ea9e5eb2201481d1130e1dbfca72889.jpg) +Figure 7. Heatmap visualization of Average VQA Score, FID Score, and CLIP Score across varying amounts of VQA data and generation data. Darker colors indicate better performance. Increasing VQA data is more effective for improving both understanding and generation capabilities. + +![](images/7041cba4999db8b846c26b1139e2e45fb39df4171b214c8fef6990709ed78c64.jpg) +Figure 6. Comparison between different language backbones. We jointly train 7M VQA and 1M Generation data on different language backbones (LLaMA-3 8B, LLaMA-3.1 8B, LLaMA-3 70B). We observe that the synergy between understanding and generation transfer across LLMs. + +![](images/f3def55af64221589685d5e34cae42e9508628e33dce4a6d076fd124714c78bb.jpg) + +Finding 2: Visual understanding and generation are synergistic. Increasing data for either capability enhances both simultaneously. + +# 3.3. Understanding Data Contributes More + +We investigate whether understanding and generation data contribute equally. Here, we jointly train different scales of VQA data $\{1\mathrm{M}, 4\mathrm{M}, 7\mathrm{M}\}$ and generation data $\{200\mathrm{k}, 500\mathrm{k}, 1\mathrm{M}, 2\mathrm{M}, 3\mathrm{M}, 4\mathrm{M}\}$ . Fig. 7 summarizes these findings, with the x-axis representing VQA data, and the y-axis representing generation data. Results are visualized on heatmaps using darker colors for better performance. + +The results indicate that increasing VQA data yields the most significant improvements in all three metrics. When VQA data is relatively low (1M), increases in generation data lead to noticeable improvements, as reflected by the gradual darkening in the plot. However, as the VQA data scales up (from 1M to 4M to 7M), the impact of VQA data becomes more pronounced, demonstrated by a sharp color transition in the heatmap. Ultimately, with 7M VQA data, increases in generation data contribute minimally. These results demonstrate the critical role of understanding data in enhancing both understanding and generation performance. + +Finding 3: While increasing data improves performance overall, the impact of visual understanding data is more significant than visual generation data. + +![](images/713df7ebeedfe6f957f29fb59b977fe626a038a45d051bcf68c20be6624390d4.jpg) +Figure 8. Correlation analysis between generation and various understanding benchmarks. Results are collected by joint training different amounts of VQA data combined with varying quantities of generation data. Each subplot shows the correlation $(\rho)$ with a fitted regression line. Stars represent data points. We analyze General VQA, Vision-Centric VQA, Text&Chart VQA, High-Resolution VQA, and Knowledge VQA. For most tasks, generation performance and VQA performance are strongly correlated: higher VQA performance indicates better generation and vice versa. Knowledge-intensive and high-resolution VQA tasks exhibit weaker correlations with generation. + +# 3.4. Certain Understanding Tasks Correlate More with Generation Performance + +Given the diverse nature of understanding tasks such as OCR, Vision-Centric tasks, and Knowledge-based tasks, we investigate which tasks most strongly correlate with generation ability. Inspired by Cambrian-1, we categorize VQA tasks into five groups: General, Text&Chart, High-Resolution, Knowledge, and Vision-Centric VQA. Using the results from our earlier experiments, which jointly train various VQA data scales with different amounts of generation data, we plot each benchmark's VQA performance against generation performance in Fig. 8. We also calculate the Pearson correlation $(\rho)$ between VQA scores and FID/CLIP Scores. + +Fig. 8 shows that General, Vision-Centric, and Text&Chart VQA tasks strongly correlate with generation performance, each with a $\rho$ above 0.85. High-Resolution VQA exhibits moderate correlation, with $\rho$ around 0.7. In contrast, Knowledge VQA tasks show weak correlation with generation performance. These findings suggest that generation ability aligns more closely with the model's vision capabilities rather than knowledge-specific tasks. + +Finding 4: General, vision-centric, and text VQA tasks exhibit strong correlations with visual generation, whereas knowledge VQA tasks do not. + +# 4. MetaMorph Model + +Based on the insights in Sec. 3, we train our unified model, MetaMorph, based on LLaMA-3.1 8B [3], using VPiT with the data in Sec. 2.2. We present our results in three parts: quantitative performance (Sec. 4.1), evidence of MetaMorph leveraging LLM knowledge in visual generation (Sec. 4.2), and multimodal implicit reasoning skills. (Sec. 4.3). + +# 4.1. Competitive Performance + +We compare MetaMorph with other unified models and summarize results in Tab. 1. Since these models are trained on different datasets and base LLMs (or pretrained from scratch), an apples-to-apples comparison is difficult. Never + +theless, MetaMorph demonstrates competitive performance and outperforms other unified models on most benchmarks—even when prior models may have been trained on more data. Compared to models trained from scratch, such as EMU-3 [68] and Chameleon [62], MetaMorph leverages latest LLMs and achieves competitive understanding and generation performance. MetaMorph highlights that unified models can be developed effectively from pretrained LLMs. + +# 4.2. MetaMorph can Leverage LLM Knowledge + +MetaMorph effectively leverages the world knowledge embedded in pre-trained LLMs. We show examples on the left side of Fig. 9. We prompt the model to generate concepts requiring non-trivial and specialized knowledge. Examples include "Chhogori" (the world's second-highest mountain), "Oncilla" (a small wildcat from South America), and "Chizarira" (an isolated wilderness area in Zimbabwe). + +MetaMorph successfully translates domain-specific knowledge into accurate visual tokens, thereby displaying the ability to leverage world knowledge from LLMs. In contrast, the latest Text-to-Image (T2I) model, Stable Diffusion-3.5 8B, struggles to generate the correct concept despite producing high-quality images. This issue may stem from the text embedding models it uses—CLIP [52] and T5 [54]—which fail to properly encode these specialized terms [80]. + +On the right side of Fig. 9, we demonstrate how MetaMorph handles common semantic challenges more effectively than text embedding models such as CLIP and T5. These challenges include negation and subjectivity [64]. MetaMorph differentiates semantic nuances such as "slightly" versus "very" and "few" versus "many", which are common failures in existing text-to-image systems. + +# 4.3. Reasoning in Multimodal Generation + +In Fig. 10, we present examples where the model generates images in response to puzzle prompts such as "The national flag of the country where Yellowstone National Park is located". For each puzzle, we directly use the prompt "Generate an image of {puzzle}", without calling Chain-of-Thought + +
MethodBase LLMImage QAVideo QAGeneration
MMBenchENSEEDRealworldQAMMVPSQAMMMUVStarChartQATextVQAMV-BenchCOCO (FID)
Visual Understanding Only
GPT-4V*75.869.161.450.075.756.855.078.578.043.5-
Visual Generation Only
Stable Diffusion 1.5*----------9.6
Dalle 2*----------10.4
Imagen*----------7.3
Unified Models
EMU-3*58.568.257.4\(36.6^{\dagger}\)89.231.6\(51.8^{\dagger}\)68.664.7-12.8
Janus*DeepSeek 1.3B69.463.7---30.5----8.5
\(\text{VILA - U}_{256}{}^{ \dagger}\)LLaMA-2 7B66.657.146.622.067.132.238.711.448.3*40.819.6
Transfusion*----------6.7
Chameleon-7B†35.727.219.60.050.328.437.10.00.0-26.7*
MetaMorph (ours)LLaMA-3.1 8B75.271.858.348.383.241.844.037.160.548.811.8
+ +Table 1. Comparison of MetaMorph with other unified models. MetaMorph offers competitive performance compared to other leading unified models. Models in gray are understanding-only or generation-only. Unified models without a base LLM are trained from scratch. *We use numbers reported in original papers. †We obtain results using official open-sourced model weights. + +![](images/1a64bc4bbbbadcde67f16580fe616190f32b52d75763b3e8a855fed74821715b.jpg) +Figure 9. Examples of MetaMorph leveraging LLMs to generate visual tokens. Left: MetaMorph can leverage knowledge from the LLM to generate visual tokens for professional terms that need domain-specific understanding. Right: MetaMorph also avoids common mistakes seen in T2I models that condition on text embeddings (e.g., Stable Diffusion-3.5 8B). + +(CoT) [70] in the prompts. MetaMorph generates correct images from prompts that require multi-step reasoning. + +For example, when answering the question "A musical instrument, this instrument is often played by the scientist who formulated the theory of special relativity", the model needs to implicitly complete three reasoning steps: it identifies Albert Einstein as the scientist formulated the theory of special relativity, recognizes that his preferred instrument is the violin, and then directly generates correct visual tokens—a violin—without explicitly separating these steps during the generation process. This result implies that MetaMorph im + +plicity solves the puzzle and generates correct visual tokens immediately following the prompt. These results align with the findings in Physics of LMs [5, 77], that LLMs precompute reasoning graphs before autoregressively generating subsequent tokens. Here, we demonstrate that this capability transfers to the unified multimodal model setting. + +# 5. Related Work + +Instruction tuning and visual instruction tuning. Instruction tuning [61, 69] finetunes a pretrained LLM to learn the + +![](images/a3f1f9e4deaac10e52ae31e1258505f07e805a262a030e349459eb711b3caa58.jpg) +Figure 10. Examples of MetaMorph solving reasoning problems in visual generation. We design puzzles that require multi-step reasoning. We include reference logic chains needed to solve the puzzles, and reference solution examples. When prompting each model, we directly feed in the puzzle without any CoT hints or logic chains. MetaMorph has the ability to implicitly solve these puzzles and generate the correct image without explicitly creating or processing a logic chain. + +format and unleash the capabilities acquired during pretraining [85]. LLaVA [36] extends instruction tuning into the multimodal domain. Different lines of work focus on improving data [11, 29, 30], visual representation [13, 26, 63], and training strategies [18, 38]. Using only a few million data, open-source MLLMs [32, 38, 63] reach performance levels comparable to proprietary models [6, 48] on a number of benchmarks [40, 78, 79] and applications [49, 82]. + +From Multimodal LLMs to unified models. Recent efforts to construct unified models have primarily relied on either extensive pretraining or heavy fine-tuning on billion-scale datasets. Some studies also use continuous embeddings for predicting visual tokens, integrating regression losses [59, 60], or leveraging diffusion methods [15]. Other approaches [1, 39, 42, 43, 62, 68, 73] tokenize all data into discrete tokens. Recent research also explored combining autoregressive and diffusion objectives [75, 86]. Different from previous study, we demonstrate that unified models can be effectively trained in low-data regimes during instruction tuning, while also providing insights into the reciprocal relationship between visual understanding and visual generation. + +# 6. Discussion + +In this work, we propose VPiT—a simple yet effective extension to visual instruction tuning—that enables LLMs to predict multimodal tokens. VPiT unlocks the use of a more + +diverse range of instruction tuning data than just visual question answering, such as text-to-image data. Through controlled experiments, we find that visual generation ability emerges as a natural byproduct of improved visual understanding and requires modest additional generation data. In addition, we find that while visual understanding and generation are mutually beneficial, adding more visual understanding data disproportionately improves overall performance compared to adding more generation data. + +Leveraging these insights, we train MetaMorph by fine-tuning LLaMA-3.1 8B with VPiT. With a simple training process, MetaMorph achieves competitive performance in both visual understanding and generation. Qualitative evaluation of our model shows that MetaMorph can leverage world knowledge and reasoning abilities of the base LLM during visual generation. For example, it can perform multimodal tasks that typically require multiple-step reasoning, such as generating images of specialized proper nouns ("Chhogori") or solving visual puzzles ("generate an image of the animal resulting from a monarch caterpillar's metamorphosis"). This indicates that LLMs already possess a degree of "prior" visual knowledge which can be activated with only minimal instruction tuning with VPiT. Overall, LLMs may have a similar representation space as unified and multi-functional models [25]. We hope these insights inspire more exploration toward developing models for general intelligence. + +# 7. Acknowledgements + +ST is supported by the Meta AI Mentorship (AIM) Program. SX also acknowledges support from the OpenPath AI Foundation, IITP grant funded by the Korean Government (MSIT) (No. RS-2024-00457882, National AI Research Lab Project) and NSF Award IIS-2443404. + +# References + +[1] Armen Aghajanyan, Bernie Huang, Candace Ross, Vladimir Karpukhin, Hu Xu, Naman Goyal, Dmytro Okhonko, Mandar Joshi, Gargi Ghosh, Mike Lewis, et al. Cm3: A causal masked multimodal model of the internet. arXiv preprint arXiv:2201.07520, 2022. 8 +[2] Pravesh Agrawal, Szymon Antoniak, Emma Bou Hanna, Devendra Chaplot, Jessica Chudnovsky, Saurabh Garg, Theophile Gervet, Soham Ghosh, Amélie Héliou, Paul Jacob, et al. Pixtral 12b. arXiv preprint arXiv:2410.07073, 2024. 1 +[3] AI@Meta. Llama 3 model card. 2024. 1, 4, 6 +[4] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. 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Prevailing research remains limited to conventional cameras employing convex lenses, where the physical constraints with millimetre-scale thickness impose serious impediments on the micro-level clinical. Recently, with the emergence of meta-optics, ultramicro imaging based on metalenses (micron-scale) has garnered great attention, serving as a promising solution. However, due to the physical difference of metalens, there is a large gap in data acquisition and algorithm research. In light of this, we aim to bridge this unexplored gap, advancing the novel metalens endoscopy. First, we establish datasets for metalens endoscopy and conduct preliminary optical simulation, identifying two derived optical issues that physically adhere to strong optical priors. Second, we propose MetaScope, a novel optics-driven neural network tailored for metalens endoscopy driven by physical optics. MetaScope comprises two novel designs: Optics-informed Intensity Adjustment (OIA), rectifying intensity decay by learning optical embeddings, and Optics-informed Chromatic Correction (OCC), mitigating chromatic aberration by learning spatial deformations informed by learned Point Spread Function (PSF) distributions. To enhance joint learning, we further deploy a gradient-guided distillation to transfer knowledge from the foundational model adaptively. Extensive experiments demonstrate that MetaScope not only outperforms state-of-the-art methods in both metalens segmentation and restoration but also achieves impressive generalized ability in real biomedical scenes. + +# 1. Introduction + +Miniaturized endoscopy provides reliable internal visual perception within the human body (Fig. 1a). Recent advancements in computer vision have significantly enhanced real-time clinical support, such as segmenting the gastroin + +![](images/38c06f37c3f72e0d060241cce937c4b96c37acd048e0645b75935fcf97c315d7.jpg) + +![](images/92d1d3b74f8f178629ec3df709cbcbf143f56ea464a773966c16cb6ffa4f7df5.jpg) +Figure 1. (a) Miniaturized endoscopy; (b) Comparing convex-lens and our meta-lens about physical nature and imaging quality. + +![](images/7225605a496d7481f47084b82a7fb54defd08a45689a6a8959aa28da54a74218.jpg) + +testinal tract. This is vital for the early detection of serious diseases, aiding medical professionals in surgical decisions. + +To facilitate endoscopic diagnosis and surgery [57, 67, 72, 73], lots of efforts have been made to develop more robust, accurate, and efficient solutions for disease recognition and segmentation. Some works [1, 9, 32, 41, 50, 56] focus on data engineering by enhancing diversity, quality, and scale. Some other works [2, 23, 39, 55, 92, 95] develop more advanced deep-learning models by addressing numerous algorithmic challenges, including domain generalization [2, 46, 47], privacy preservation [17, 35, 58], and label-efficient learning [48, 60, 88], among others. + +Despite significant algorithmic advancements, existing studies are limited to conventional cameras that utilize convex lenses [44, 52], whose physical constraints pose substantial barriers to micro-level clinical applications. The inherent curvature limitations of convex lenses (Fig. 1b left) hinder the development of ultra-lightweight profiles, restricting them to millimetre-scale thickness. This impairs navigation through narrow or curved anatomical structures and negatively impacts device size, power consumption, and operational efficiency, hindering progress toward micro-miniaturized clinical applications. + +Recently, with the emergence of meta-optics [13, 36, 69, 70, 82], ultra-micro imaging based on metalenses has garnered significant attention in micro-robotics, showing a + +promising solution [19, 66]. As shown in Fig. 1b, these ultra-thin lenses utilize nanostructured arrays to manipulate light at subwavelength scales. In contrast to conventional in-vivo lenses, which typically weigh around 2.5 grams with 5-millimetre thickness, meta-lenses weigh less than 0.05 milligrams and measure under 850-nanometer in thickness. These superior physical properties significantly reduce the device size [59, 61, 63]. This enables access to narrow anatomical structures and facilitates minimally invasive technologies within the human body. + +While promising, these advancements pose challenges in maintaining imaging quality, as severe chromatic aberration [14, 52, 86] fundamentally limits their diagnostic reliability by distorting spectral signatures critical for tissue characterisation. The key challenge lies in achieving achromatic design, where the main difficulty stems from the wavelength-dependent phase modulation of nanostructures. Their resonant properties and material dispersion make it physically challenging to achieve consistent wavefront control across broad spectra, causing different wavelengths of light to focus at different points. Current physical solutions typically stack multiple layers [43] or frequency-dependent phase engineering combining geometric-phase and propagation-phase elements [15], but these face limitations in fabrication complexity, limited bandwidth, and trade-offs between efficiency and device size. Hence, we propose the computer vision solution for computationally achromatic meta-lens endoscopy (refer to Sec. 3.1), underscoring its substantial industrial and academic value [82]. + +To address this challenge, we delve into the nature of chromatic aberration with optical simulation, encapsulating it into two sub-issues (Sec. 3.2). (1) Color and Position-Dependent Intensity Loss: Different colors are attenuated unevenly with inherent optical prior. (2) Color-Dependent Blur and Misalignment: Different color has a varied "blur kernel" (Point Spread Function, PSF). Mismatched color offsets create color fringing around objects, especially at high-contrast edges. Based on these observations, we further propose MetaScope, a novel optics-driven network to eliminate chromatic aberration and deliver precise segmentation for clinical applications. MetaScope employs a metalens encoder to correct distorted representations via Optics-informed Intensity Adjustment (OIA) and Optics-informed Chromatic Correction (OCC). Additionally, it incorporates a dual-branch decoder designed for accurate segmentation, enhanced by an auxiliary restoration branch (see Fig. 3). Specifically, with optical simulations, OIA encodes optical priors into optical embeddings and then adjusts the attention map. OCC estimates PSF distributions by learning implicit distributions adaptively, eliminating chromatic aberrations through spatial aggregation. Furthermore, to enhance the robustness against chromatic aberration, we introduce gradient-informed distillation, which transfers foun + +ditional knowledge to enhance restored representation. By addressing both hardware and algorithmic barriers, we make clinical micro-miniaturization possible with enhanced physical efficiency. The contributions are fivefold: + +- We are the first to break through the endoscopy barrier via metalenses from both data and algorithmic aspects, illuminating ultra-micro applications of healthcare robotics. +- We propose five datasets for metalens-based diagnostics and surgery, starting and advancing the clinical research. +- Delving into two imaging challenges with optical simulations, we propose a novel MetaScope to achieve joint restoration and segmentation guided by optical priors. +- The proposed MetaScope consists of an Optics-informed Intensity Adjustment to correct intensity attenuation with encoded optical embedding and an Optics-informed Chromatic Correction to rectify chromatic aberration. Besides, a gradient-informed distillation is proposed to enhance joint restoration-aware learning. +- Extensive experiments verify that MetaScope achieves SoTA segmentation and restoration, which also works impressively in real biomedical scenarios (Supp. C). + +# 2. Related Works + +Metalens Imaging uses optical metasurfaces to enhance the imaging capabilities of cameras [36, 69, 70, 82], which consist of arrays of nano-scale structures for precise focusing control, as shown in Fig. 2a. Their lightweight design and wide fields of view, make them highly suitable for applications in augmented reality, micro-robotics, and in-vivo healthcare [19, 66]. However, manufacturing imperfections and inherent limitations lead to image distortion with severe chromatic aberration [83]. To break through this, artificial intelligence has been increasingly integrated into meta-lens imaging to facilitate meta-lens design [5, 33, 78, 87, 96] and enhance image quality through deep models [22, 29, 80, 81]. Unlike existing studies focusing on restoration, we are the first to explore microminiaturized endoscopic applications, proposing a unified perception model driven by optical priors. + +Medical Image Segmentation [6, 40, 62] autonomously delineates intricate anatomical structures, streamlining clinical procedures. With the U-Net architecture [79], numerous variants [10, 20, 27, 30, 45, 54, 76, 77, 85, 91] have been developed to enhance multi-scale fusion, skip connections, and bottleneck features [30]. Recently, U-shaped models such as UNeXt [84], DC-UNet [65], Rolling-Unet [64], U-Mamba [68], and U-KAN [42] have improved model efficiency and interoperability. Additionally, generic segmentation methods have shown remarkable efficacy in medical applications, such as Mask2Former [18], EDAformer [93], and SegNext [25]. Unlike traditional methods that rely on high-fidelity images, our approach targets the more challenging metalens images via optical observations. + +![](images/3335e09a20870a49d5ca92b8793d85cd8576536e2bfe37f48a7833d20b60fd21.jpg) +(a) Meta-lens +Figure 2. (a) Our metalens nanostructure via scanning electron microscope; (b) Optical setup for meta-lens data collection; (c) Intensity loss in metalens imaging with color and spatial dependence; (d) Color-dependent blur and misalignment due to inconsistent PSF patterns. + +![](images/7e91561b3950015cc955a060e98422d44cd8cc4e3ee7c1f9762c51598d27417f.jpg) +(b) Meta-lens dataset establishment + +![](images/51bd521bad262a79a53f96fded9c7b4546bb44483c36efa6febe66239da3ccab.jpg) +(c) Color and position-dependent intensity loss + +![](images/9aeb52b80702fde426d00cf5f3e6d89dddde4063da454511a44de4522022cf5c.jpg) +(d) Color-dependent kernel - PSF + +Image Restoration [11, 21, 37, 51, 53] seeks to reconstruct high-quality images from degraded inputs, such as rainy, foggy, etc [16, 93]. Chen et al. [11] proposes a comprehensive study of restoration-oriented CNN design and introduces NAFNet, a lightweight model for efficient image restoration. With the scalability of the Transformers architecture, SwinIR [51] employs shifted-window attention to enhance global context while preserving local details. Additionally, some methods, such as Restormer [94], SFHformer [34], and MambaIR [24] have gained attention due to their novel network architectures. Instead of focusing on the natural restoration with convex lenses, we investigate advanced meta-lens imaging driven by distinct optical simulation and explore its potential to assist perception tasks. + +# 3. Preliminaries + +Metalens Imaging. Conventional lenses achieve light focusing by varying thickness in a convex geometry and using multiple lens elements, which poses challenges for micronminiaturized practice due to the bulky optical systems. In contrast, metalenses employ nanoscale structures, meta-atoms patterned on a flat surface (Fig. 2a) to manipulate the light wavefront in a much more compact way. Each meta-atom provides specific amplitude and phase modulation. The focusing phase profile can be expressed as: + +$$ +\phi (r, \lambda) = - \left[ \frac {2 \pi}{\lambda} \left(\sqrt {r ^ {2} + f ^ {2}} - f\right) \right], \tag {1} +$$ + +where $\phi (r,\lambda)$ is the required phase for the meta-atom at position $r$ for wavelength $\lambda$ , and $f$ is the desired focal length. Without achromatic design, metalenses exhibit wavelength-dependent focal lengths, expressed as $f(\lambda)$ . This variation prevents different wavelengths from converging on a single imaging plane. We designed and fabricated polarization-independent gallium nitride (GaN) metalens with a diameter of $2.6\mathrm{mm}$ and a focal length of $10\mathrm{mm}$ . + +# 3.1. Metalens Dataset Establishment + +Due to the limited imaging quality of metalens cameras, a significant barrier exists to clinical practice, resulting in insufficient endoscopic data collection. This scarcity of data impedes the design of algorithms aimed at correcting chromatic aberration. To overcome this, we employ a + +proxy photographic solution to establish datasets, as shown in Fig. 2b. As the chromatic aberration patterns adhere to consistent physical principles, we can create paired metalens mapping data with and without distortion to train the model that approximates the restoration function. Based on this insight, we construct the necessary pairs by projecting images from publicly available endoscopic datasets onto a screen and capturing images with a metalens camera. Thus, we can generate the metalens dataset with a triple data format, including the metalens image, associated high-quality ground truth, and the corresponding semantic labels, such as segmentation. Note that we empirically find that the model trained on our datasets exhibits generalization capacity to real scenes with varied depth and different metalenses, demonstrating significant value to the community. More details can be found in the Supp C. + +# 3.2. Identifying Metalens Imaging Challenges + +The challenge of metalens images arises from the wavelength dependence of the focal length, which fails to focus all light onto a single focal plane. To explore this unique characteristic, we conduct optical simulations and identify two derived issues, motivating our method designs. + +(1) Color and Position-Dependent Intensity Loss. We illuminate the metalens with the directional white light of uniform intensity while the CMOS sensor applies gains of 1.67, 1, and 2.34 to RGB channels (built-in white balance function). We analyze the resulting intensity variations in the captured images, as shown in Fig. 2c, summarizing two observations: (a) Imbalanced RGB Channel Intensities: Even under the automatic white balance, color channels exhibit inconsistent brightness due to wavelength-dependent responses of meta-atoms. Specifically, non-optimized wavelengths (e.g., red/blue) suffer from simultaneous amplitude and phase mismatch in meta-atoms, significantly reducing modulation efficiency and causing light intensity loss. (b) Vignetting and Structured Noise: The surrounding regions experience significantly greater attenuation compared to the central area, which is analogous to the dark channel observed in de-hazing [26]. This is because of the superposition of off-axis efficiency drop of nanostructures $\eta_{\mathrm{meta}}(\theta)$ and traditional geometric vignetting $(\cos^4\theta$ law), which could be approximated as $I_{\mathrm{total}}(\theta) =$ + +![](images/c1fcaff445bc92914a97b943dd9f717cb863b9c05a7762c309319fa09cb10cb9.jpg) +Figure 3. Illustration of the proposed MetaScope, which consists of two optics-informed modules, named (a) OIA and (b) OCC injected in the encoder to correct the meta-distortion, and a (c) gradient-guided distillation strategy to facilitate the restoration-aware representation. + +$\eta_{\mathrm{meta}}(\theta) \cdot \cos^4 \theta \cdot I_0$ . Inhomogeneous amplitude responses of different meta-atoms and nanofabrication defects induce local random fluctuations in transmitted light intensity, manifesting as spatially correlated brightness noise. Motivation: To fully leverage observed optical priors, we propose to encode the efficiency and radial priors to adjust the feature learning with restoration awareness (Sec. 4.1). + +(2) Color-Dependent Blur and Misalignment. PSF is the imaging response of an optical system to an ideal point light source, directly governing spatial resolution and color fidelity, which could be approximated as $I_{\mathrm{output}} = \sum_{\lambda} \left[ T(\lambda) \cdot \left( \eta_{\mathrm{meta}}(\theta) \cdot \cos^4 \theta \cdot I_0(\lambda) * \mathrm{PSF}(\lambda, x, y) \right) \right] + \epsilon$ , where $\epsilon$ is noise. Fig. 2d shows the simulated PSFs of a coherent plane wave (ideal light source) under the wavelength of $532 \mathrm{~nm}$ (green). In metalenses, chromatic aberrations cause wavelength-dependent PSF variations. Each wavelength (color) has a different focal length for a sensor fixed at the design wavelength (e.g., green), shorter (red) and longer (blue) wavelengths defocus, broadening their PSFs. Blue/red edges appear more blurred than green ones, akin to applying color-specific Gaussian kernels. Imperfect phase gradient compensation of the metalens results in PSF centroid displacement across wavelengths. Hence, high-contrast edges exhibit color fringing, as misaligned RGB PSFs create artificial chromatic gradients. Our observations indicate that such blur and fringing cause the signal to spread from the source pixel into adjacent pixels. Motivation: To tackle this issue, we propose a novel solution by estimating the full-color PSF distribution via learning inherent Gaussian mixtures adaptively, thereby spatially guiding correction of chromatic aberrations (Sec. 4.2). + +Problem Formulation. We have triplet data $\{I_m, I_c, Y\}$ for training, including degraded images captured by metalens $I_m$ , the associated high-quality ones captured from the + +convex lens $I_{c}$ , and the segmentation mask $Y$ . Our goal is to train a unified model $\mathcal{F}$ that can achieve reliable perception $\tilde{Y}$ and restoration $I_{c}$ using metalens images $I_{m}$ . In the test stage, the model can predict restored images and masks directly from metalens images: $\{\tilde{Y},\tilde{I}_c\} = \mathcal{F}(I_m)$ . + +# 4. Methodology + +As shown in Fig. 3, given metalens images $I_{m}$ , we employ a metalens encoder $\mathcal{F}_{\mathrm{enc}}$ , which consists of two key modules, (a) OIA and (b) OCC, to generate the restoration-aware latent $\hat{X}$ , addressing the two issues in chromatic aberration (Sec. 3.2) with optical priors. Then, $\tilde{X}$ is sent to a dual-branch decoder $\mathcal{F}_{\mathrm{dec}}$ to generate both the restored image $\tilde{I}_m$ and the segmentation mask $\hat{Y}$ . In this process, the intermediate feature of meta-restoration (low-level) guides the segmentation branch with a simple residual connection. During the training, we implement (c) gradient-guided distillation that encodes the convex-lens image $I_{c}$ with the foundation model to facilitate the learning of restoration. + +# 4.1. Optics-informed Intensity Adjustment + +Metalens images experience severe attenuation in adhering to specific priors. However, the limited data scale makes it challenging to learn these priors solely through data fitting. To overcome this, we aim to adjust the feature using the optical priors derived from simulations, as shown in Fig. 3a. Optical Prior Encoding. We begin by sending the metalens image $I_{m}$ through a metalens encoding block to obtain the feature $\tilde{X}$ . Due to inconsistent wavelengths, the captured images $I_{m}$ exhibit varying intensity attenuation with optical evidence. To tackle this, we use the optical simulation to generate two types of optical priors (see Sec. 3.2): the color-dependent vector $\mathbf{T} \in \mathbb{R}^{L}$ encoding the efficiency of $L$ visible light in sequential wavelengths, and spatial at + +tenuation prior $\mathbf{Y} \in \mathbb{R}^{H \times W}$ . Note that those priors can be generalized to different metalens due to the similar attenuation patterns. Then, we encode them into the optical embedding at the channel $\mathbf{E}_{\mathrm{ch}} \in \mathbb{R}^{\hat{C}}$ and spatial $\mathbf{E}_{\mathrm{sp}} \in \mathbb{R}^{\hat{H} \times \hat{W}}$ levels to calibrate the input feature $X \in \mathbb{R}^{\hat{C} \times \hat{H} \times \hat{W}}$ : + +$$ +\mathbf {E} _ {\mathrm {c h}} = \mathcal {F} _ {\mathrm {F c}} ^ {\text {E n c}} (\mathbf {T}); \mathbf {E} _ {\mathrm {s p}} = \mathcal {F} _ {\text {C o n v}} ^ {\text {E n c}} \left(\mathbf {Y} \oplus \mathbf {C} _ {x} \oplus \mathbf {C} _ {y}\right), \tag {2} +$$ + +where $\mathbf{C}_{x / y} \in \mathbb{R}^{H \times W}$ indicate the normalized coordinates, $\oplus$ is the concatenation, and $\mathcal{F}_{\mathrm{Fc}}^{\mathrm{Enc}} / \mathcal{F}_{\mathrm{Conv}}^{\mathrm{Enc}}$ are simple fully connected and convolutional based layers, abbreviated as Conv/Fc in following sections. These optical embeddings provide significant optical guidance to correct the intensity attenuation at the spatial and channel levels. + +Feature Adjustment with Optical Prior. To integrate optical prior, a natural idea is to inject embedding into the network like diffusion models [28]. However, instead of sharing across all features, metalens images introduce attenuation patterns exhibiting variability across wavelengths and positions. Hence, we consider the distinct physical properties of efficiency (color-based) and spatial priors (position-based) and propose a simple yet effective method that uses optical embedding to rectify channel and spatial attention. Specifically, the adjusted attention is integrated as follows: + +$$ +\operatorname {A t t n} _ {\mathrm {c h}} (X) = \text {S i g m o i d} \left(\mathcal {F} _ {\mathrm {F c}} ^ {\text {P r o j}} \left(\operatorname {M e a n} _ {\mathrm {s p}} (X) + \mathbf {E} _ {\mathrm {c h}}\right)\right), \tag {3} +$$ + +$$ +\operatorname {A t t n} _ {\mathrm {s p}} (X) = \operatorname {S i g m o i d} \left(\mathcal {F} _ {\text {C o n v}} ^ {\text {P r o j}} \left(\operatorname {M e a n} _ {\mathrm {c h}} (X) + \mathbf {E} _ {\mathrm {s p}}\right)\right), +$$ + +where $\mathrm{Mean}_{\mathrm{sp / ch}}$ indicates the averaging over the spatial and channel dimension, and $\mathcal{F}_{\mathrm{Fc / Conv}}^{\mathrm{Proj}}$ is a projection layer. Then, given the feature $X$ , the adjusted one can be represented as: $X_{\mathrm{OIA}} = \mathrm{Conv}(\mathrm{Attn}_{\mathrm{sp}}(X) \odot (\mathrm{Conv}(\mathrm{Attn}_{\mathrm{ch}}(X) \odot X))) + X$ , where $\odot$ is Hadamard product. Thus, by embedding the optical prior, the model can dynamically adjust representations based on the color-specific and spatially varying optical prior, improving the restoration-aware encoding. + +# 4.2. Optics-informed Chromatic Correction + +Metalens images suffer from chromatic artifacts due to wavelength-specific PSFs. Considering the difficulty in estimating explicit PSFs, we model the implicit PFS distribution via Gaussian Mixture Models (GMM) in an adaptive manner for chromatic correction (Fig. 3b). + +Formulating Implicit PSF Distribution. Given an input light with wavelength $\lambda$ , metalens projects it to the 2-D image at a specific position $\mathbf{p} = [x, y]$ coupled with dispersed components to the neighbouring pixels, which can be formulated as the spatial dispersion $\Delta \mathbf{p} = [\Delta x, \Delta y]$ , adhering the implicit PSF distribution $P(\Delta \mathbf{p})$ . As shown in Fig. 2 (d), such dispersion can be naturally modeled as a mixture of Gaussians with a main lobe accompanied by symmetric side lobes. Based on this observation, we formulate the im + +plicit PSF distribution with GMM as follows, + +$$ +P (\Delta \mathbf {p}) = \sum_ {k = 1} ^ {K} \pi_ {k} \mathcal {N} \left(\Delta \mathbf {p} \mid \mu_ {\mathbf {p}, k}, \sigma_ {\mathbf {p}, k} ^ {2}\right), \tag {4} +$$ + +where $P(\Delta \mathbf{p})$ represents the dispersion probability, $\mathbf{p} = [x; y]$ is the 2-D position, $\pi_k$ is the coefficient for the $k$ -th Gaussian parameterized with mean $\mu_{\mathbf{p},k}$ and variance $\sigma_{\mathbf{p},k}^2$ . Learning PSF Distribution via Multi-Expert Gaussian. Based on the GMM formulation, we aim to learn a spatial deformation $\Delta \mathbf{p}$ for each position $\mathbf{p}$ to model PSFs, adhering $P(\Delta \mathbf{p})$ . This can thereby facilitate the adaptive aggregation of dispersed information. However, directly estimating the GMM in Eq. 4 with conventional methods like the EM algorithm is time-consuming and challenging since each wavelength $\lambda$ is associated with a specific GMM with diverse patterns. To break through this barrier, inspired by the Mixture of Experts (MoE) [71], we propose a Multi-expert Gaussian (MeG) paradigm with $K$ Gaussian experts, where each expert $\mathrm{MeG}_k$ serves for a specific Gaussian pattern. Notably, instead of directly estimating the Gaussian parameters, the expert is designed to estimate the linear transformation from a normal Gaussian, i.e., residual part, based on the scaling invariance of the Gaussian. + +Specifically, given the input feature $X$ , we first assume a normally distributed latent $P(z|X)$ with variational autoencoding for the PSF distributed offset space. To this end, we deploy two linear layers for the mean $\mu(X)$ and log-variance $\log \sigma^2(X)$ as Gaussian parameters and implement Kullback-Leibler divergence to ensure that offset space to be Gaussian: KL $(q_{\phi}(z|X) || \mathcal{N}(0, \mathbf{I}))$ as [38], where $q_{\phi}$ is simply formulated with the former Conv block [49]. Then, we establish $K$ experts by leveraging the linear invariance property of Gaussian distributions, where each of the experts parameterized with $\{\mathbf{a}_k, \mathbf{b}_k\}$ aims to learn a linear projection based on a sampled $z \sim P(z|X)$ using the reparameterization trick [38]. Thus, this can generate a transformed Gaussian for each expert: $\mathrm{MoG}_k(X) \sim \mathcal{N}(\mathbf{a}_k \boldsymbol{\mu}(X) + \mathbf{b}_k, \mathbf{a}_k^2 \boldsymbol{\sigma}^2(X))$ . Concretely, each MeG is deployed with a convolution layer outputting $2 \times M \times M$ channels where $M = 3$ , which generates $M^2$ offset candidates $[\Delta x; \Delta y]$ modeling the implicit PSFs1. Finally, a small router layer $\mathrm{Router}(X)$ is deployed with Conv-Pooling to learn the aggregation weight with $K$ -channel output. Thus, the whole process can be formally represented as, + +$$ +\Delta \mathbf {p} = \sum_ {k = 1} ^ {K} \pi_ {k} \cdot \operatorname {M e G} _ {k} (X), \text {w h e r e} \pi = \operatorname {R o u t e r} (X), \tag {5} +$$ + +and $\Delta \mathbf{p}$ is the estimated spatial offsets in modeling dispersion patterns. These offsets are utilized to aggregate dispersed points with the well-estimated guidance of PSFs. + +Metalens Segmentation + +
In-Vivo DiagnosisIn-Vivo Surgery
Meta-CVC-ClinicMeta-CVC-ColonMeta-Kvasir-SegMeta-EndoVis-17Meta-EndoVis-18Average
MethodmIoUmDICEmIoUmDICEmIoUmDICEmIoUmDICEmIoUmDICEmIoUmDICE
UNet [79]0.66230.77100.62380.73060.48140.61710.71740.82740.59310.71810.61560.7328
Atten-UNet [74]0.67050.77520.63360.73060.48840.62550.70400.81630.58950.72000.61720.7335
UNet++ [97]0.67650.77700.64170.73910.47460.60840.71950.82870.60030.72960.62250.7366
UNext [84]0.70060.79480.68550.77070.55040.66510.72900.83770.52350.64960.63780.7436
Rolling-UNet [64]0.74990.82590.65970.74600.53760.64820.79780.88470.60920.73590.67080.7681
U-KAN [42]0.74540.82600.71910.79240.59290.69370.77530.86920.64820.77660.69620.7916
DeepLabV3+ [12]0.65740.75060.61210.69430.46290.58820.78870.87840.67490.79560.63920.7414
UperNet [89]0.63120.72010.71590.80410.58390.69100.80380.88100.67740.79990.68240.7792
Segformer [90]0.76120.83780.68630.77290.47390.59700.80250.88780.67450.79650.67970.7784
EDAformer [93]0.81690.88590.75070.83120.57050.68130.81610.89650.73100.83800.73700.8266
SegNext [25]0.76390.83990.65280.73520.57900.68030.82070.89940.62660.75550.68860.7821
Mask2former [18]0.79120.86120.73530.81570.66640.75580.83670.90100.73000.83710.75190.8342
MetaScope (Ours)0.85550.91370.78680.86040.69720.78450.88020.93550.80570.88960.80510.8767
+ +Metalens Restoration + +
MethodPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
SwinIR [51]25.31000.844224.12850.833823.76430.832826.19580.914325.27480.878624.93470.8607
Restomer [94]33.56400.958133.95410.971931.37380.977830.99820.956130.61640.935632.10130.9599
NAFNet [11]33.89700.966834.68340.985631.59390.979330.96600.955330.90870.939732.40980.9653
DRMI [80]33.55170.978434.77550.967231.66200.970531.67090.960131.47670.945132.62740.9643
MambaIR [24]25.55170.868926.94770.912824.78440.916524.16410.885224.32460.857225.15450.8881
NeRD-Rain [16]30.33510.937031.14230.955828.37910.956425.78740.907225.49420.871228.22760.9255
MetaScope (Ours)34.84830.985435.66030.985632.44540.981832.03650.961931.86640.947433.37140.9724
+ +Table 1. Comparison with state-of-the-art methods on five benchmarks in terms of metalens segmentation (top) and restoration (bottom). The best and second-best results are highlighted in red and blue, respectively. + +Chromatic Correction. With the learned offsets, we further aggregate the spatially dispersed points with a simple deformable convolution layer, facilitating local aggregation of dispersed information. This can ensure that the pixel colors are accurately reconstructed by aligning with the underlying physical distribution modeled by the GMM, denoted as $X(\mathbf{p})_{\mathrm{OCC}} = \sum_{i=1}^{M+N} w_i \cdot X(\mathbf{p} + \Delta \mathbf{p}_i)$ , where $\Delta \mathbf{p}_i$ represents the learned offset for the $i$ -th element ( $i \in [1, M \times M]$ ) at location $\mathbf{p}$ , and $w_i$ is the learnable weight. By learning the positions of the sampled points, we can effectively mitigate color dispersion caused by PSFs, leading to more accurate and visually consistent color correction. + +# 4.3. Optimization + +Gradient-guided Distillation. To better optimize the proposed optics-informed modules in chromatic aberration learning, we propose a distillation method that leverages the pre-trained DINO v2 [75] to refine under-optimized regions of $\tilde{X}$ , as illustrated in Fig. 3c. Given the feature $\tilde{X}$ we back-propagate the restoration Loss $L_{\mathrm{Rest}}$ and collect the gradient amplitude map $\mathbf{M} = |\frac{\partial L_{\mathrm{Rest}}}{\partial\tilde{X}}|$ to guide the feature distillation, which can be denoted as follows, + +$$ +L _ {\text {D i s t i l l}} = \frac {1}{\operatorname {s u m} (\tilde {\mathbf {M}})} \sum \tilde {\mathbf {M}} \odot \left| \mathcal {F} _ {\text {D I N O}} \left(I _ {c}\right) - \mathcal {F} _ {\text {C o n v}} ^ {\text {P r o j}} (\tilde {X}) \right| _ {1}, \tag {6} +$$ + +where $\tilde{\mathbf{M}} = \frac{\mathbf{M} - \min(\mathbf{M})}{\max(\mathbf{M}) - \min(\mathbf{M})}$ is the normalized gradient map, $\mathcal{F}_{\mathrm{Conv}}^{\mathrm{Proj}}$ is a projection layer structured as Conv - ReLU-LayerNorm-Conv to match the dimension. Consequently, the mask with higher values corresponds to areas with greater distortion and under-optimization, enabling the distillation to focus preferentially on critical regions. + +Overall Objective. During the training stage of MetaScope, the overall optimization objective is denoted as: + +$$ +\mathcal {L} _ {\text {M e t a S c o p e}} = L _ {\text {S e g}} + \lambda L _ {\text {R e s t}} + \omega_ {d} L _ {\text {D i s t i l l}} + \omega_ {k} L _ {\mathrm {K L}}, \tag {7} +$$ + +where $L_{\mathrm{Rest}}$ is for the auxiliary metalens restoration task, deployed with PSNR loss, $L_{\mathrm{Seg}}$ is the segmentation loss, implemented with CE loss, $L_{\mathrm{KL}}$ is the variational loss to ensure the Gaussian [38] in OCC estimating PSF distributions. $\omega_d$ and $\omega_k$ balance the two representation learning modules. $\lambda$ is used to balance the segmentation and restoration. + +# 5. Experiments + +# 5.1. Benchmark Setup + +Dataset Setup. We build up five benchmarks focusing on two critical clinical procedures: diagnosis and surgery. After establishing the metalens optical system, as described in Sec. 3.1, we are able to capture the metalens image $I_{m}$ + +![](images/15234fcf62a44c95576d5f1146108c2a4668a8867720bfe0de06fdebd1f91f55.jpg) +Figure 4. Comparison between conventional systems using high-quality ground-truth images without Meta, and our metalens system using the degraded images in Meta version dataset. + +by photographing the publicly available database $\{I_c,Y\}$ projected on the screen, thereby generating the triplet data: $\{I_m,I_c,Y\}$ in $1024\times 1024$ resolution. Based on our dataset, we carry out two streams of research to advance the metalens vision, including metalens segmentation with $\{I_m,Y\}$ (perception), metalens restoration $\{I_m,I_c\}$ (low-level vision). Hence, we name our datasets by adding the Meta prefix on the following five database: (1) CVCClinic [8], (2) CVC-Colon [7] (3) Kvasir-Seg [31], (4) EndoVis-17 [3], and (5) EndoVis-18 [4], such as MetaEndoVis-18. More details can be found in Supp. D. + +Evaluation Metrics. Evaluation is conducted in alignment with two clinical needs. (1) Clinical assistance: Metalens segmentation adopts mIoU and mDICE [42] (IoU/DICE for single-class datasets). (2) Clinical visualization: Metalens restoration uses PSNR and SSIM [94]. + +Implementation Details. The proposed model is based on the NAFNet [11] and is trained using the AdamW optimizer with a learning rate of $1 \times 10^{-3}$ , a batch size of 2, and a weight decay of $1 \times 10^{-4}$ . The training schedules of all benchmarked methods are consistent. Training was conducted on two 24G GPUs for 50,000 iterations. The number of MeG is set to $K = 3$ . The $\omega_{d}$ and the $\omega_{k}$ are both set to 1, and the $\lambda$ is set to 0.01/0.1 for diagnostics/surgery datasets. The simulation details and results of the optical priors in Eq. 2 are in Supp. B. + +# 5.2. Comparison with State-of-the-art Methods + +Metalens Segmentation. In Tab. 1 (top), we compare with state-of-the-art methods in both the medical field like U-KAN [42] and Rolling-UNet [64] and the natural imaging, including Mask2former [18]. Our MetaScope achieves superior performance, attaining an $80.51\%$ mIoU and $87.67\%$ mDICE across all five benchmarks, significantly outperforming the latest counterpart, EDAformer [93], by $6.81\%$ in mIoU and $5.01\%$ in mDICE. Most importantly, MetaScope exhibits the best performance across all five settings, encompassing varied clinical devices, in-vivo scenes, and diverse classes, demonstrating substantial robustness. + +Metalens Restoration. Given promising achromatic met- + +
SettingSegmentationRestoration
-w/omIoUmDICEPSNRSSIM
Seg-Base-0.73760.8272--
Meta-Base-0.77490.857331.17480.9538
+ Grad-DistillGrad0.79750.875032.48700.9632
-0.83120.892732.81530.9610
+ Grad-Distill;MeG0.83820.901232.80780.9482
+ OCC-0.85120.908834.00110.9603
+ Grad-Distill;Prior0.85230.910934.13410.9806
+ OCC; + OIA-0.85550.913734.84830.9854
+ +Table 2. Detailed ablation study of the proposed modules on the Meta-CVC-Clinic benchmark, where 'w/o' indicates removing the sub-components, and 'Grad' indicates the gradient guidance. + +
ModuleSettingmIoUmDICEPSNRSSIM
Optical PriorLearned0.87000.929331.68960.9600
Only ch.0.87150.930331.87510.9615
Only sp.0.87460.932032.01410.9612
Full0.88020.935532.03650.9619
Num. MeG K in Eq. 510.86820.927931.87800.9616
30.88020.935532.03650.9619
50.87930.934932.06370.9625
Loss Weight λ in Eq. 70.010.86760.928029.86460.9452
0.10.88020.935532.03650.9619
1.00.84970.916832.04910.9622
+ +Table 3. Sensitivity analysis of the simulated optical prior and hyper-parameters on the Meta-EndoVis-17 benchmark, where 'Learned' indicates directly learning optical embedding. + +alenses [52], we benchmark metalens restoration and compare our method with state-of-the-arts, as shown in Tab. 1 (bottom). MetaScope achieves the best performance with a PSNR of $33.3714\mathrm{~dB}$ and an SSIM of 0.9724, surpassing the latest metalens restoration method DRMI [80] and the natural imaging method MambaIR [24], revealing that our method can thoroughly correct distorted patterns. We also observe that methods tailored for specific restoration, such as NeRD-Rain for de-raining, perform unsatisfactorily, highlighting the unique characteristics of metalens (Sec. 3). + +Comparing Metalens and Conventional Systems. Fig. 4 presents a more challenging comparison between metalens and conventional systems, where the latter utilizes high-quality ground-truth images and state-of-the-art segmentation algorithms. Surprisingly, despite metalens introducing chromatic aberration, our system (red bar) achieves the best performance across all benchmarks. This demonstrates that our method is robust to chromatic aberration and capable of unleashing the potential of metalens. Notably, our system transcends the physical weight limitations and algorithmic precision constraints of conventional lens systems. + +![](images/a813d37bc2ad6419acd2156ef42b63a8e305782694f791d76b8725aff6497e54.jpg) +Figure 5. Qualitative comparison in terms of state-of-the-art segmentation methods and image restoration methods. + +![](images/cd181328ff20bfa7cf6b04e55b2d19f57b9bda63eb47bf4fd83fc65ddbeed068.jpg) +Figure 6. Heatmaps of the feature before and after each module. + +# 5.3. Ablation Study + +Effect of Each Module. We conduct a comprehensive ablation study presented in Tab. 2 and summarize several valuable observations. (1) Compared with the pure baseline (Seg-Base), introducing the restoration branch (Meta-Base) to guide segmentation yields a noticeable $3.01\%$ mDICE gain. (2) The gradient-guided distillation contributes an additional $3.54\%$ mDICE enhancement, highlighting the critical role of the restoration gradient (Grad). (3) Introducing OCC enhances the mDICE by $1.61\%$ and achieves a 1.18 dB gain in PSNR, with the restoration gains primarily arising from the MeG design, emphasizing the importance of modeling dispersion patterns. (4) Incorporating OIA further refines the restoration representation, achieving the best performance in both segmentation $(91.37\%$ mDICE) and restoration (34.8483 PSNR), demonstrating the effectiveness of the optical prior in meta-restoration. + +Sensitivity Analysis. We further conduct in-depth exploration in Tab. 3. (1) Removing the spatial and channel priors results in a noticeable decrease in PSNR, highlighting the essential role of correcting intensity attenuation. (2) Regarding the number of MeG, the performance remains robust when $K \geq 3$ but experiences a noticeable decrease when $K = 1$ , revealing the effectiveness of modeling PSFs by the Gaussian mixture. (3) There is a trade-off in joint learning: Increasing the restoration loss weight yields further gains in PSNR while sacrificing some mDICE. + +# 5.4. Qualitative Analysis + +Qualitative Comparison. Fig. 5 shows a comparison between segmentation (top) and restoration methods (bottom). Compared to the latest method, EDAFormer [93], MetaScope shows visually significant improvements in the spatial completeness of challenging local regions. This is particularly evident in the prograsp forceps (green) and monopolar curved scissors (cyan) in row 1. Regarding the metalens restoration, Metascope achieves significant gains in both color accuracy and structural fidelity of local regions. + +Analyze each Module with Heatmaps. In Fig. 6, we progressively visualize features before and after each module, highlighting insightful interoperability and well-aligned optical motivation. (1) By modulating features with spatial priors, OIA enhances the near-border regions and relieves the position-dependent intensity loss, showing a similar pattern to Fig. 2c. (2) OCC encourages each pixel to cluster with its surrounding pixels, addressing PSF-caused dispersion with a spatial grouping (consistent with Fig. 2d). It also focuses on more distorted regions (bottom part) instead of segmenting targets, perfectly aligning with chromatic correction designs. (3) Without distillation, only low-level details are focused, yet lacking semantic guidance. + +# 6. Conclusion + +For the first attempt, we study endoscopic intelligence on the microscale with advanced metalenses. We establish benchmarks with five datasets across diagnostic and surgical applications. To address the chromatic aberration, we propose a novel MetaScope with two key components: Optical-informed Intensity Adjustment corrects intensity attenuation by learning optical embeddings; Optical-informed Chromatic Correction models and eliminates PSF distortion with multi-expert Gaussian. A gradient-guided distillation is integrated to enhance the meta-representation. Extensive experiments demonstrate that MetaScope significantly surpasses state-of-the-art methods. + +# Acknowledgement + +This research was partly supported by Hong Kong PhD Fellowship from Research Grants Council of Hong Kong. This work was supported by Innovation and Technology Fund ITS/229/22, PRP/082/24FX and Hong Kong Research Grants Council (RGC) General Research Fund 14204321. We acknowledge the support from the University Grants Committee / Research Grants Council of the Hong Kong Special Administrative Region, China [Project No. AoE/P-502/20, CRF Project C5031-22G, GRF Project: CityU11305223; CityU11300224, CityU11310522, CityU11300123], National Natural Science Foundation of China [Grant No. 62375232], Guangdong Basic and Applied Basic Research Foundation [2025A1515011846], City University of Hong Kong [Project No. 9380131, 9610628] and the Shenzhen Research Institute, City University of Hong Kong [RIND27901]. + +# References + +[1] Sharib Ali, Felix Zhou, Christian Daul, Barbara Braden, Adam Bailey, Stefano Realdon, James East, Georges Wagnieres, Victor Loschenov, Enrico Grisan, et al. Endoscopy artifact detection (ead 2019) challenge dataset. arXiv preprint arXiv:1905.03209, 2019. 1 +[2] Sharib Ali, Noha Ghatwary, Debesh Jha, Ece Isik-Polat, Gorkem Polat, Chen Yang, Wuyang Li, Adrian Galdran, Miguel-Ángel González Ballester, Vajira Thambawita, et al. 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Bruckstein1 + +3Munich Center for Machine Learning + +# Abstract + +Standard convolutions are prevalent in image processing and deep learning, but their fixed kernels limits adaptability. Several deformation strategies of the reference kernel grid have been proposed. Yet, they lack a unified theoretical framework. By returning to a metric perspective for images, now seen as two-dimensional manifolds equipped with notions of local and geodesic distances, either symmetric (Riemannian) or not (Finsler), we provide a unifying principle: the kernel positions are samples of unit balls of implicit metrics. With this new perspective, we also propose metric convolutions, a novel approach that samples unit balls from explicit signal-dependent metrics, providing interpretable operators with geometric regularisation. This framework, compatible with gradient-based optimisation, can directly replace existing convolutions applied to either input images or deep features of neural networks. Metric convolutions typically require fewer parameters and provide better generalisation. Our approach shows competitive performance in standard denoising and classification tasks. + +# 1. Introduction + +In the realm of computer vision and deep learning, traditional convolutions have established themselves as indispensable image processing tools [30, 31], forming the backbone of various neural network architectures, and in particular of the effective convolutional neural networks (CNNs) [32, 39, 49, 64, 68]. Traditional convolutions involve applying fixed-size isotropic $k \times k$ filters to images, a strategy known for its weight-sharing property and parameter efficiency. However, their inherent rigidity becomes evident when dealing with deformable objects, complex spatial transformations, or multi-scale phenomena, limiting their adaptability and, consequently, their effectiveness. + +To address this limitation, a diverse research community has explored alternative convolutions. We focus on methods modifying $k \times k$ kernel samples, distinct from those increasing kernel width [28], concatenating [17, 68] or linearly combining [16, 41, 43, 75] responses from different kernels. Dilated convolutions [14, 15, 78, 79] extend the scale + +![](images/e7eb2128ba85d9094f1b98b987878f283e311fd2dde844a5c564589bb4f60196.jpg) +Figure 1. Unlike rigid standard convolutions, adaptive kernels avoid sampling undesired locations, e.g. background near object boundaries. Our metric convolutions sample unit balls, tangent (UTB) or geodesic (UGB), of explicit metrics, providing geometric interpretability and inductive bias, while other methods only rely on metrics implicitly. + +![](images/09d55fa5ef5374762b133e316b2fc0e3e0920afcb94c7b9c82b09360ab5cde74.jpg) + +![](images/a20a51248b603ad3783c181e27c5f5e416022a248210ee53c38af4a217f373f6.jpg) + +of the convolution grid, improving the effective receptive field [51], but rely on a predetermined uniform scale, lacking adaptability to data variations. Spatial transformer networks (STN) [34, 44] employ data-dependent parametrized transformations, such as affine transforms, for feature sampling. Yet, STNs are constrained to predefined transformation families and apply transformations uniformly across the entire feature map. Active convolutions [36] introduce learnable offsets for anisotropic sampling grids but share these offsets across all pixel locations and without data adaptability at inference. Deformable convolutions [25, 80] address these issues by learning signal-dependent offsets at each pixel location. In [77], undesirable offset interactions are recognized, leading to entire deformable convolutions which introduce a single input and location-dependent offset for the entire sampling grid. Another approach, combining dilation and deformable convolution [42], scales the grid to be deformed non-uniformly and signal-dependently. This involves applying multiple deformable convolutions at fixed scales followed by pooling to select the optimal dilation. Unlike other methods discussed here, this approach requires aggregating across multiple deformed convolutions, offering adaptability only within a fixed set of candidate scales. While all these methods have demonstrated improved performance in handling deformations and spatial variations, the theoretical framework underpinning these deformations remains elusive, hindering a comprehensive understanding of their capabilities and limitations. + +In response, this paper takes a novel perspective by introducing a unifying framework rooted in metric theory. Metric theory treats images as manifolds endowed with a met + +ric, allowing for the computation of distances and neighbourhoods that can deviate from those induced by the typically used Euclidean norm in the image plane. This perspective enables us to reinterpret existing modern convolutions as weighted filtering of samples from the unit ball of a latent metric, effectively linking convolution approaches to implicit metrics. Such an idea echoes yet differs from existing methods working directly on graphs and surfaces [6]. Metric convolutions extend this concept by explicitly incorporating signal and location-dependent parameterised metrics, offering an interpretable, versatile, and adaptable approach to deformable convolutions (see Fig. 1). + +The main contributions of this work are threefold: + +- A unifying metric theory that provides geometric interpretability to both existing convolutions and the CNNs employing them. +- Introducing metric convolutions, a novel convolution that can be anisotropic and asymmetric, based on Finsler geometry, that deforms convolution kernels based on explicit, adaptable, and interpretable metrics on the image manifold, promising robustness and versatility. +- The explicit interpretable geometric bias of metric convolutions enables their direct application to full-resolution images outside of neural networks, rather than solely deep inside a CNN. They are also compatible with neural network architectures. + +In the following sections, we provide preliminaries on metric geometry (Sec. 2), present our unifying metric theory to convolutions (Sec. 3), and explore metric convolutions (Sec. 4), their theoretical foundations, practical implementation, and empirical evaluations (Sec. 5). + +# 2. Preliminaries on Metric Geometry + +# 2.1. The concept of distance + +In this work, we reinterpret images as parametrised surfaces on the unit plane $\Omega$ and explore them from a metric perspective, as was popular prior to the rise of deep learning [10, 13, 18, 48, 57, 60, 66, 67]. Metric geometry focuses on curved spaces, or manifolds, denoted as $X$ , each with well-defined tangent planes $T_{x}X$ at every point $x \in X$ . Manifolds are equipped with metrics, positive functions on the tangent bundle $X \times T_{x}X \to \mathbb{R}_{+}$ for local distance calculations (see Fig. 2). This enables computing curve lengths, geodesic curves, and geodesic distances between points. Different metrics lead to varying geodesic curves and distances. Henceforth, images are two-dimensional manifolds, i.e. surfaces, such as greyscale intensity height maps. + +Riemann. The common metric choice is the Riemannian metric $R$ , defined by a $2 \times 2$ positive definite matrix $M(x)$ at each point $x$ , inducing a scalar product on the tangent plane. Formally, the Riemannian metric is $R_x(u) = \sqrt{u^\top M(x) u}$ . + +![](images/c4d312859b757eab31c382cc8022cf4b7e1651b72a647ee2750bb005bea678a6.jpg) +Figure 2. Metrics provide distance measurements in the tangent space (top), and can be fully described via the shape of their convex unit tangent balls. Riemannian metrics can be isotropic or anisotropic, but they remain symmetric as the unit tangent balls are centred. Finsler metrics generalise them by allowing asymmetry, leading to asymmetric geodesics (bottom - courtesy of [24, 72]). + +at point $x$ and tangent vector $u \in T_xX$ . It yields symmetric distances, making traversal direction irrelevant. The metric is isotropic if $M$ is everywhere a scaled identity matrix, and it is non-uniform yet isotropic if the scale differs between points, but it is at times mistakenly called anisotropic [57]. + +Finsler. While Riemannian metrics create symmetric tangent space neighbourhoods, Finsler metrics provide a generalisation allowing for asymmetric ones. For example, near object boundaries, asymmetric neighbourhoods can prevent neighbours from extending outside the object (see Fig. 1). Finsler metrics $F$ define Minkowski norms on tangent spaces, where $F_{x}(-u)$ and $F_{x}(u)$ may differ for $u \in T_{x}X$ at point $x$ . Consequently, local and global distances no longer adhere to symmetry. Formally, a Finsler metric $F$ satisfies $F_{x}(u) = 0$ if and only if $u = 0$ , it obeys the triangular inequality, and is positive-homogeneous, i.e., $F_{x}(\lambda u) = \lambda F_{x}(u)$ for any $\lambda > 0$ (see Appendix A.1). + +Randers. General Finsler metrics are not parametrisable, leading us to consider a common [24, 72] subset: Randers metrics. They combine a Riemannian metric, parameterised by $M$ , with a linear drift component, parameterised by $\omega \in T_xX$ . Formally, a Randers metric with parameters $(M,\omega)$ is defined as $F_{x}(u) = \sqrt{u^{\top}M(x)u} +\omega (x)^{\top}u$ . For metric positivity, we require $\| \omega (x)\|_{M^{-1}(x)} < 1$ (details in Proposition 1). Notably, Riemannian metrics result from $\omega \equiv 0$ . Other choices for parametric Finsler metrics are possible, like the $(\alpha ,\beta)$ ones, inducing Kropina or Matsumoto metrics [35]. + +Henceforth, the metric, most generally Finsler, is written $F$ . + +# 2.2. Unit Balls + +In metric geometry, a key concept is the unit ball at point $x$ , a collection of objects within unit distance of $x$ according to the metric $F$ . Depending on the context, the unit ball may refer to different objects. + +Unit Tangent Ball. Sometimes, unit balls focus on the tangent plane. The unit tangent ball $B_1^t(x)$ at point $x$ is the set $B_1^t(x) = \{u \in T_xX; F_x(u) \leq 1\}$ . For any metric satisfying the triangular inequality, the unit tangent ball (UTB) and its projection onto the image plane are convex sets. In particular, the UTB of a Randers metric is an ellipse, off-centred if $\omega(x) \neq 0$ , with equation $u^\top M_xu = (1 - \omega(x)^\top u)^2$ . A higher norm of $\omega(x)$ results in less symmetry. In image manifolds, we often project tangent planes onto the image plane and associate the UTB on the tangent space with its projection. If $x$ represents a pixel coordinate, we informally say that $B_1^t(x)$ is the set of pixel coordinates $B_1^t(x) = \{y \in \Omega; F_{X(x)}(y - x) \leq 1\}$ . + +Unit Geodesic Ball. The unit geodesic ball $B_1^g(x)$ contains all points within a unit geodesic distance from $x$ : $B_1^g(x) = \{y \in X; \mathrm{dist}_F(x, y) \leq 1\}$ , where $\mathrm{dist}_F(x, y)$ is the geodesic distance determined by the metric $F$ . It is the minimum length of a smooth curve from $x$ to $y$ (see Appendix A.3). Computing unit geodesic balls (UGB) is challenging as they lack closed-form expressions, unlike UTBs, requiring instead to integrate the metric along geodesics. They can take diverse shapes and may not be convex, especially after projection onto the image plane. As for the UTB, we associate the UGB with its projection on the image plane: $B_1^g(x) = \{y \in \Omega; \mathrm{dist}_F(X(x), X(y)) \leq 1\}$ . + +# 3. A Unifying Metric Theory to Convolutions + +For simplicity, we assume images are continuous and single-channel, with our theory extendable to multi-channel data. Our domain is $\Omega = [0,1]^2$ , and images are two-dimensional signals $f:\Omega \to \mathbb{R}$ . Discrete images are viewed as samples of the continuous domain, with interpolation (e.g. bilinear) for querying non pixel centre position. Note that presenting image convolutions and their anisotropic variants in the continuum is unusual in the neural network community. + +While we focus on images, our theory generalises to higher manifold or feature dimensions (see Appendix B.1). + +# 3.1. Pre-existing Convolutions + +# 3.1.1. Traditional Fixed Support Convolutions + +The convolution $f*g$ of a signal $f:\Omega \to \mathbb{R}$ with a kernel $g:\Omega \to \mathbb{R}$ is traditionally defined as + +$$ +(f * g) (x) = \int_ {\Omega} f (x + y) g (y) d y. \tag {1} +$$ + +Padding allows querying outside $\Omega$ . Often, the kernel function $g$ is assumed to be localised on a small compact support + +$\Delta$ , usually containing 0. The convolution then becomes + +$$ +(f * g) (x) = \int_ {\Delta} f (x + y) g (y) d y. \tag {2} +$$ + +Henceforth, we focus on local convolutions. Traditional convolutions assume a fixed kernel support $\Delta$ . The weights, i.e., the values of $g$ , are either predefined or learnt. In the discrete world, $\Delta$ is usually localised around and includes the entry 0. It is universally discretised into a small $k \times k$ odd square grid, often $3 \times 3$ , a prevalent choice in CNNs. We use the word support and $\Delta$ -based notations for both continuous and sampled discrete convolution supports. + +# 3.1.2. From a Fixed to a Changeable Support + +We present three major variations of traditional convolutions based on the shape of the support $\Delta$ . While other approaches like [42] may offer different implementation and optimisation strategies, their kernel support formulation typically fits into one of these categories. They originate from prior work in the discrete world. Starting from a $k \times k$ grid forming a reference support $\Delta^{ref}$ , each grid cell is shifted to create a new set of $k^2$ points, forming the modified support $\Delta$ . While not traditional convolutions, they maintain the weight sharing principle, with kernel weights $g(y)$ independent of the convolution position $x$ , even if the positions of the support samples $y$ may vary. + +Dilated Convolutions. Dilated convolutions, introduced by [14, 15] for neural networks, uniformly scale cell positions in the reference support $\Delta^{ref}$ by a dilation factor $s^2$ , e.g. with $k = 3$ and $s = 4$ , the dilated support includes pixels at indices $\{(i,j); i,j \in \{-4,4,0\}\}$ . Non-standard non-uniform yet isotropic dilated convolution can use different scales $s_x$ per pixel for scale-sensitive filters [42]. + +Shifted Convolutions. Also called entire deformable convolutions [77], they shift the entire reference kernel support $\Delta^{ref}$ by a single offset vector $\delta_x$ per pixel $x$ . + +Deformable Convolutions. Devised by [25], these convolutions use different offsets $\delta_x^y$ for each cell in the reference support $\Delta^{ref}$ , inducing complex deformations. + +Signal-dependent deformations, as in [25], make deformable convolutions, both entire and regular, and nonstandard dilated convolution with adaptive scale [42] nonlinear operations. However, computing deformations by traditional convolutions, as in shifted and deformable convolutions, leaves them shift-equivariant. All convolutions presented so far can be seen as specific deformable convolutions with special offset choices. Beyond support deforma + +![](images/e72c075ad273ec3b285cdd7ab9b18879f865295cba60a1fbec49467567788b17.jpg) +Figure 3. Traditional convolutions, standard or with kernel support deformations, act as weighted averages over unit ball samples of implicit metrics. This theory unifies the various existing convolutions and leads to metric convolutions, a novel convolution paradigm, that samples unit balls of explicit metrics, either learnt or provided by geometric heuristics. The unit balls refer to those in the tangent space or to the geodesic ones on the image manifold, both projected onto the image plane. + +![](images/06124fb15a94b4f870495ac3765964cfa10c9812450e1444ac25a83f478203fb.jpg) + +tion, other modifications to the traditional convolution have emerged, such as the modulation idea. + +Modulation. Breaking the weight sharing assumption, kernel weights $g(y)$ can be modulated by $m_x(y) \in [0,1]$ depending on $x$ [59, 77, 80], see Appendix C.2. + +Generally, non-standard convolution strategies are largely empirical. This diverse field can seem like a multitude of performance-driven tricks lacking a unified theoretical framework. We propose to present and generalise these methods in a systematic way from a metric perspective. + +# 3.2. Unifying Convolutions Through a Metric Lens + +All previous convolutions can be expressed as follows. + +Theorem 1. If convolution refers to standard, dilated, shifted, or deformable convolutions, then the convolution of a signal $f$ with a kernel $g$ can be expressed as + +$$ +(f * g) (x) = \int_ {\Delta_ {x}} f (x + y) g (y) d m _ {x} (y), +$$ + +where $dm_x(y) = m_x(y)dy$ is a distribution with density $m_x(y) \in [0,1]$ , and $\Delta_x$ is a local support depending on $x$ (and sometimes also on $f$ ), and it is given by a transformation of a reference local support $\Delta^{ref}$ . In the absence of modulation, then $dm_x(y) = dy$ . + +See Appendix C.1 for a proof. Convolutions discussed so far perform weighted averaging over local neighbourhoods $\Delta_x$ , eventually learnt. Modulation breaks uniformity in $x$ , and it can be seen from a discrete perspective as a nonuniform sampling probability distribution of $\Delta_x$ . + +Viewing images as metric manifolds, local neighbourhoods $\Delta_x$ can be reinterpreted as the points within a small distance of $x$ for some metric $F$ , taken to be 1 without loss of generality by scaling the metric. Thus, we see $\Delta_x$ as a unit ball. This suffices to reveal the existence of implicit metrics harnessed by convolutions, according to the following well-known theorem [35]. + +Theorem 2. A metric is uniquely determined by its unit tangent balls. + +A proof is provided in Appendix C.3 for completeness, and we push to Appendix C.4 a discussion on how to reconstruct the metric from unit geodesic balls. We thus understand the multitude of existing anisotropic convolutions as weighted signal averages in unit balls of implicit, possibly non parametric, metrics $F$ . In this context, modulation acts as a non-uniform distribution for sampling the unit balls. + +In practice, we reinterpret discrete convolution kernels $\Delta_x$ as finite samples of unit balls. With finite samples, metric uniqueness is lost (see Appendix C.5), yet convolutions described so far (see Fig. 3) can be approximately explained using Randers metrics. Other interpretations are possible with different metrics, potentially more suitable as Randers UTBs are confined to ellipses. Standard and dilated convolutions imply an underlying scaled isotropic Riemannian metric. The kernel shift in shifted convolutions can be modelled with the drift component $\omega$ of a Randers metric. All three of these can be understood from the perspective of UTBs. Due to constraints on the offset magnitudes, deformable convolution supports usually resemble sampled convex set, which likens to sampling the UTB of a Randers metric. However, UGB sampling is a better interpretation for more involved theoretical deformations resembling the sampling of non-convex sets (see Appendix C.6). + +# 4. Metric Convolutions + +With our new metric perspective, existing convolutions are weighted averages over unit balls of an underlying metric, potentially with non-uniform sampling. This understanding allows us to change the convolution paradigm by explicitly constructing a metric $F$ and deriving its unit balls for the filtering operation (see Figs. 4 and 12). Unit balls should result from a transformation of a reference set, e.g. $\Delta^{ref}$ , where weights (output values of $g$ ) are well-defined. Termed metric convolutions, they generalise existing convolutions relying on implicit metrics by using explicit ones, + +offering interpretability, strong geometric priors as implicit regularisation, and a fixed small number of parameters for metric encoding, regardless of the number of samples. + +We provide simple, differentiable metric convolution implementations compatible with gradient-based optimisation. We sample unit balls uniformly for simplicity, but our constructions generalise to modulation with a parameterised density $m_x(y)$ , e.g. Gaussian [59]. Our main focus is on UTB-based metric convolutions, with an option for UGB-based ones. The general idea for our proposed methods is the following. Consider a class of parametric metrics $F^{\gamma}$ which smoothly depend on location-dependent parameters $\gamma$ . For instance, we take for Riemannian metrics $\gamma = M$ and for Randers metrics $\gamma = (M,\omega)$ . Given $\gamma$ , explicitly compute unit balls to define (sampled) neighbourhoods $\Delta_x$ for calculating weighted averages. We can choose metric parameters $\gamma$ based on geometric or image-related properties and can opt for interpretable filtering methods like fixed uniform kernels $g$ . Both kernel weights $g$ and metric parameters $\gamma$ can be learnt through gradient-based optimisation. + +Like our theory, metric convolutions are generalisable to higher manifold or feature dimensions (see Appendix B.2). + +![](images/4df67e9b221ce284e423f5d4a074f77c7dc905860d5baa89a2d3d6e1dc987427.jpg) +Figure 4. Our metric convolutions compute metrics explicitly for unit ball sampling, while traditional convolutions compute offsets directly. In non-heuristic methods, our intermediate convolution encodes general metrics with only 5 to 7 numbers, compared to $2k^2$ for the offsets in a $k \times k$ deformable convolution. Our heuristic methods are compatible with adaptive signal-dependent sampling. + +![](images/0d48c6e3137cd8b853d4f7330433bbe5fe5abfee3e19e5ed51b6d39b4e2bfd40.jpg) + +# 4.1. Unit Tangent Ball Metric Convolution + +The unit ball $B_1^t(x)$ is obtained by deforming the unit Euclidean disk. Recall that unit tangent balls (UTB) are convex, e.g. ellipses for Randers metrics. Thus, we can use angles $\theta$ as a monotonic parameterisation of the unit circle. Let $y_x(\theta, \gamma) \in B_1^t(x)$ be the point on the unit circle at angle $\theta$ for the Finsler metric of parameters $\gamma$ . That is, $y_x(\theta, \gamma) = \| y_x(\theta, \gamma) \|_2 u_\theta$ , where $u_\theta = (\cos \theta, \sin \theta)^\top$ . The $F_x^\gamma$ -unit vector, $y_x(\theta, \gamma)$ , satisfies $F_x^\gamma(y_x(\theta, \gamma)) = 1$ . The positive homogeneity of the metric implies that $\| y_x(\theta, \gamma) \|_2 = \frac{1}{F_x^\gamma(u_\theta)}$ . The unit circle is thus given by the points + +$$ +y _ {x} (\theta , \gamma) = \frac {1}{F _ {x} ^ {\gamma} (u _ {\theta})} u _ {\theta}. \tag {3} +$$ + +With polar coordinates for integrals, convolution becomes + +$$ +(f * g) (x) = \int_ {s, \theta} f (x + s y _ {x} (\theta , \gamma)) g (s y _ {x} (\theta , \gamma)) d s d \theta . \tag {4} +$$ + +For a signal-dependent metric, we can compute $\gamma$ directly from the image, e.g. with a standard convolution (as in deformable convolution) we name the intermediate convolution. Since $M$ is symmetric definite positive, it is parameterisable by 3 numbers using its Cholesky decomposition $LL^{\top} = M$ where $L$ is a lower triangular matrix with positive diagonal. However, we also used a more stable spectral implementation using extra numbers when necessary, where two numbers encode the first eigenvector of $M$ and the two others are its eigenvalues, eventually adding one more number encoding the scale of the eigenvalues. As $\omega$ requires two numbers, our intermediate convolution only needs 5 to 7 output channels to compute $\gamma$ , depending on which implementation we choose, unlike deformable convolution which requires $2k^{2}$ channels for the offsets of $k\times k$ samples. In Appendices D.1 and D.2, we explain how to recover $\gamma = (M,\omega)$ from these numbers while enforcing $\| \omega \|_{M^{-1}(x)} < 1 - \varepsilon_{\omega} < 1$ , where $\varepsilon_{\omega}\in (0,1]$ is a hyperparameter controlling the maximum tolerated asymmetry. + +By analogy with existing convolutions, we can simply discretise the UTB by sampling $k^2$ points using polar coordinates $s \in [0,1]$ and $\theta \in [0,2\pi]$ (see Appendix D.3), yielding support locations $P_x^\gamma(s,\theta) = sy_x(\theta,\gamma)$ for $\Delta_x$ . While straightforward, this implementation is compatible with common neural networks and can be differentiated as explained in Appendix D.4. + +Notably, metric convolutions satisfy the following property. + +# Theorem 3. Metric convolutions are shift-equivariant. + +We provide a detailed proof in Appendix D.5. The reason is that we use shift-equivariant offsets for sampling the image, thanks to shift-equivariant heuristics or standard convolutions as intermediate operations to extract metric parameters, and that we satisfy the weight sharing assumption, as the values taken by $g$ are the same for each pixel $x$ . Invariance though is achieved by combining metric convolutions with pooling, as in standard convolutions. + +# 4.2. Unit Geodesic Ball Metric Convolution + +Efficient geodesic metric convolution implementations are challenging due to costly geodesic extraction (see Appendix D.6). We propose a faster approximation inspired by [19]. It computes geodesic flow fields using normalised gradients of initial Finsler heat flows at pixel $x$ from a simplified local solution with the Finsler-Gauss kernel [55, 76]. Then, a set of candidate sample locations initially near $x$ flows along the geodesics for a fixed duration, providing samples of the unit geodesic ball. See Appendix D.7 for full details. Although faster than accurate geodesic extractors + +[3, 4, 19, 70] and fully differentiable, it is not fast enough for real scenarios such as neural network modules. + +# 5. Experiments + +# 5.1. Denoising Whole Images with a Single Local Convolution + +Here, we focus on image denoising, a fundamental task for convolutions as they filter out noise. Surprisingly, modern non-standard convolutions are untested on it, as they are only used in later stages of neural networks for feature learning. We add Gaussian noise of standard deviation $\sigma_{n}$ to greyscale images and we set the following constraints. + +- All methods use $k \times k$ kernel samples with same $k$ . +- All methods apply a single filtering convolution with interpolation allowed for non-pixel centre sampling. +- Convolutions are local. Non-local ones are excluded, e.g. [11, 20, 69]. + +We explore three filter variations and learning is done either on a single image or on a dataset. + +Geometric heuristic design. To geometrically design filters, we recall that to preserve edges, neighbourhoods should not cross them. Thus, the eigenvectors of $M$ are taken as the image gradient $\nabla f(x)$ and its orthogonal $\nabla f(x)^{\perp}$ . Anisotropy is induced by different eigenvalues: a smaller one stretches the unit ball further in its eigendirection due to the inverse in Eq. (3). For denoising, a natural choice for the Randers drift component is $\omega \equiv 0$ , yet we also test with different asymmetry levels by aligning $\omega$ with $\nabla f(x)^{\perp}$ at various scales controlled by a hyperparameter $\varepsilon_{\omega}$ . If $\varepsilon_{\omega} = 1$ , then $\omega \equiv 0$ . We visualize some unit balls in Fig. 5. Notice how UTBs remain convex, while UGBs deform more. Our method gets better filtering (higher PSNR), compared to other manually designed approaches. Further results and implementation details can be found in Appendix E.1. + +![](images/c4eab9bd5d2e7c59ad394a6ceb20d08b255041f957b66ad121ef928de74793f5.jpg) +Figure 5. Heuristic unit balls, tangent (left) and geodesic (right). Convolution kernel locations are sampled in them. The different balls correspond to various values of $\varepsilon_{\omega}$ controlling the scale of $\omega$ . + +Learning sample locations only. As an intermediate experiment, between manual design and learning from a training set, we considered learning the metric parameters of UTBs and the offsets of deformable convolutions when applied to a single image. Our method is systematically on par or outperforms deformable convolution (Tab. 1). As our UTB samples are always derived from a metric, yielding a valuable geometric regularisation, our approach remarkably + +does not overfit, with low and consistent generalisation errors, in contrast to deformable convolution's severe overfitting due to the absence of prior knowledge on the structure of the kernel support. For more details and more quantitative and visual results see Appendix E.2. + +Learning filtering on a small dataset. In these experiments, we train a single-layer convolution network on standard datasets of $256 \times 256$ greyscale images from BSDS300 [52] and PascalVOC Segmentation [29]. Gaussian noise with standard deviation $\sigma_{n} \in \{0.1, 0.3, 0.5\}$ is added to the images consistently within each experiment. We follow the methodology of [25], making positional parameters, i.e. deformation offsets or metric parameters $\gamma$ , data-dependent and shift-equivariant by computing them from an intermediate standard $k \times k$ convolution layer (see Fig. 4), with the same $k$ as in the final convolution with deformed support. This intermediate convolution has as many output channels as the required number of parameters per pixel. Deformable convolution needs $2k^2$ intermediate channels, while our UTB approach uses only 5 for any $k$ as we use the Cholesky-based implementation. The final convolutions can have fixed uniform kernel weights (FKW) or learnable kernel weights (LKW). We test our method with $\varepsilon_{\omega} \in \{0.1, 0.9\}$ , controlling the metric asymmetry. We provide full training details in Appendix E.3. + +Results in Tab. 2 for learning filtering on datasets show MSE scores and generalisation gaps $\delta_{MSE}$ . Our results are on par with deformable convolution, despite our metric UTB convolutions, constrained to ellipses, being theoretically less general. Increasing asymmetry using $\varepsilon_{\omega}$ improves performance. Surprisingly, fixing or training kernel weights provides similar results for both methods. Thus, perhaps learning the shape of the kernel is as vital as learning the weights. However, it could also be due to differences in gradient magnitudes for sampling location parameters, as indicated by suggested learning rates (see Appendix E.4). + +# 5.2. From Single to Stacked Convolutions: An Example of CNN Classification + +We show how our metric convolutions can be used with neural networks, specifically CNNs. We work on the MNIST [40], Fashion-MNIST [74], CIFAR-10 and CIFAR-100 [38] classification benchmarks. We follow the methodology of [25, 77, 80] to convert standard convolution modules of a CNN to deformed versions. We test shifted, deformable, and metric UTB convolutions against a standard convolution baseline. Specifically, we replace the $3 \times 3$ standard convolutions in the later stages, from layer2 to layer4, of a ResNet18 [32] by our metric convolution using the same number of sample locations. As is common for this resolution, we set conv1 stride to 1 and avoid pooling to retain information. In our experiments, we either fix the ker + +
kDeformableUnit tangent ball (ours) [εω = 0.9]Unit tangent ball (ours) [εω = 0.1]
511315112151131511215113151121
MSE7.26E-38.97E-31.99E-22.83E-26.18E-28.13E-37.43E-37.58E-38.64E-38.28E-38.10E-37.32E-37.45E-37.52E-37.82E-3
δMSE2657428186.61.10.91.10.81.21.31.11.31.41.5
+ +Table 1. Single image denoising results (with noise level $\sigma_{n} = 0.3$ ). We also provide the normalised generalisation gap $\delta_{MSE} = \frac{MSE_{test} - MSE_{train}}{MSE_{train}}$ . The parameter $\varepsilon_{\omega}$ controls the metric asymmetry. + +
Deformable\( \varepsilon_{\omega}=0.1 \)Unit tangent ball (ours)
FKWLKWFKWLKWFKWLKW
511315113151131511315113151131
MSEBSDS3000.11.12E-41.83E-41.72E-31.72E-41.70E-41.29E-31.19E-41.19E-47.20E-41.64E-41.32E-47.72E-41.20E-41.24E-47.24E-41.35E-41.32E-47.74E-4
0.32.92E-42.67E-41.89E-33.47E-43.33E-42.10E-33.62E-43.45E-42.04E-33.66E-43.60E-42.09E-33.64E-43.40E-42.05E-34.01E-43.59E-42.11E-3
0.54.91E-44.13E-43.13E-36.44E-46.01E-43.67E-36.67E-46.05E-43.74E-37.15E-46.33E-43.77E-36.66E-46.08E-43.76E-37.03E-46.33E-43.79E-3
PASCALVOC0.18.59E-51.56E-41.35E-31.02E-49.81E-57.62E-41.01E-41.00E-47.95E-31.06E-41.12E-47.71E-41.02E-41.02E-47.76E-41.17E-41.12E-47.77E-4
0.32.40E-42.37E-41.84E-33.03E-42.87E-42.14E-33.18E-42.95E-42.27E-33.33E-42.96E-42.05E-33.19E-42.96E-42.28E-33.10E-42.96E-42.06E-3
0.54.28E-43.66E-43.20E-35.77E-45.47E-44.01E-36.05E-45.71E-44.30E-36.23E-45.41E-43.72E-36.37E-45.59E-44.33E-36.20E-45.71E-43.74E-3
\( \delta_{MSE} \)BSDS3000.10.280.140.070.240.200.050.180.210.020.170.210.030.170.210.020.170.210.03
0.30.230.190.0010.210.200.050.180.220.040.170.210.040.180.240.040.180.210.04
0.50.220.160.010.200.200.050.190.210.050.190.220.040.180.210.040.190.220.04
PASCALVOC0.10.030.010.110.030.030.020.030.030.020.030.030.020.030.030.020.030.030.02
0.30.030.020.010.030.030.010.020.030.010.020.030.020.020.030.010.030.030.03
0.50.010.020.080.020.020.0010.020.020.010.020.020.020.010.020.010.020.020.02
+ +nel weights (FKW) of non-standard convolutions to uniform values or learn simultaneously sample locations and the weights (LKW). The weights, up to module conversion, are either learned from scratch (SC) or transfer learned (TL) from Imagenet [26] classification with vanilla modules. Due to resource constraints, we only trained a single run on the MNIST and Fashion-MNIST datasets, but train 8 runs on the CIFAR-10 and CIFAR-100 datasets. Full implementation and training details of our and other methods are provided in Appendix E.6. We also ablate in Appendix E.7 on different replacement strategies and using Riemannian instead of Finsler metric convolutions. + +Table 2. Denoising results on the greyscale versions of BSDS300 and PascalVOC datasets with noise level ${\sigma }_{n}$ . Positional parameters of the $k \times k$ convolutions are learnt with a single regular convolution. The weights of the learnt kernel are either fixed (FKW) or learnt as well (LKW). Top are test MSE losses, bottom are the generalisation gaps ${\delta }_{MSE}$ . Lower is better. + +
DATASETMETHODFKWLKW
SCTLSCTL
MNISTSTANDARD--99.61%99.66%
DEFORMABLE83.79%99.16%99.51%99.64%
SHIFTED99.11%99.15%99.39%99.64%
METRIC UTB (OURS)99.14%99.17%99.64%99.68%
Fashion-MNISTSTANDARD--92.37%93.30%
DEFORMABLE75.50%90.66%92.54%92.74%
SHIFTED82.43%89.40%92.75%93.45%
METRIC UTB (OURS)89.85%90.87%92.76%93.49%
+ +Table 3. Test accuracies of ResNet18 trained using standard or non-standard convolutions. Higher is better. The main results are those of the LKW-TL columns. + +We provide test accuracies in Tabs. 3 and 4 and list the following observations. 1) Our metric CNN consistently outperforms deformable and shifted CNNs, with only rare cases where it is only on par with deformable ones. 2) Our geometric construction is a powerful prior leading to a strong implicit bias since 2)a) like standard CNNs, our metric CNN is barely affected by training from scratch (SC), occasionally improving results, and 2)b) our metric CNNs + +remain effective with fixed convolution weights (FKW). In comparison, deformable and shifted CNNs see a significant performance drop when trained from scratch, especially on CIFAR-10 and CIFAR-100, and act close to random predictors when the convolution kernels are fixed. While it could be argued that shifted convolutions has a stronger prior, since its kernel position has only 2 degrees of freedom compared to the 5 to 7 ones for our metric kernel, these results prove that a geometric approach backed by a metric theory has better regularisation than an efficient yet solely empirical approach. 3) The results of our metric CNNs have a significantly lower standard deviation, even when they only match deformable convolution. Thus, our CNNs are more stable, hence more reliable if limited to single training runs. 4) Our method is not much more expensive than deformable convolution (see Appendix E.6 and Tabs. 9 and 10). It even outperforms at lower costs an advanced method with larger kernel sizes and modulation [59]. + +We also plot GradCAM [61] visualisations on randomly chosen images and classes from the CIFAR-100 test set (for LKW-TL trained networks) in Fig. 6. These heatmaps are the ReLU of a weighted sum of the feature representations after the last convolution layer, where the weights are given by the gradient with respect to the groundtruth label. They are then resized and superimposed on the original image. GradCAMs highlight image regions positively contributing to the prediction of the correct class. We see that our metric CNN better focuses than CNNs using other types of convolutions on the relevant objects and their meaningful parts, e.g. the face or fins of a dolphin, rather than on the background. It is also able to handle multiple instances unlike the other CNNs, rather than focusing on one of them. These visual results point towards the superiority of CNNs + +
CIFAR-10CIFAR-100
FKWLKWFKWLKW
SCTLSCTLSCTLSCTL
TOP1STANDARD--92.26% (±0.20%)92.64% (±0.18%)--70.48% (±0.29%)70.52% (±0.38%)
DEFORMABLE33.21% (±2.05%)34.10% (±6.48%)72.30% (±7.86%)93.10% (±0.17%)10.47% (±0.79%)6.82 (±1.44%)54.51% (±8.04%)70.05% (±0.43%)
SHIFTED37.89% (±2.06%)29.52% (±17.19%)86.63% (±4.49%)92.58% (±0.28%)14.47% (±2.40%)2.67 (±0.66%)47.14% (±9.05%)68.58% (±0.48%)
METRIC UTB (OURS)69.83% (±2.43%)72.15% (±0.98%)91.83% (±0.18%)93.07% (±0.13%)40.63% (±0.79%)38.04% (±0.77%)70.03% (±0.45%)70.38% (±0.38%)
TOP5STANDARD------90.30% (±0.10%)90.03% (±0.22%)
DEFORMABLE----30.75% (±1.55%)23.36% (±3.37%)78.85% (±5.64%)89.71% (±0.32%)
SHIFTED----37.73% (±3.72%)10.67% (±2.21%)74.34% (±6.56%)88.77% (±0.29%)
METRIC UTB (OURS)----71.70% (±0.78%)69.22% (±0.63%)90.42% (±0.19%)90.23% (±0.17%)
+ +Table 4. Median test accuracies of ResNet18 trained using standard or non-standard convolutions, with 8 independent runs per configuration. Higher is better. In parenthesis is the standard deviation (lower is better). The main results are those of the LKW-TL columns. + +![](images/a3a27f21ff4f095334e3ec2c1f7a48da31097b88722ee62906dc086101031d31.jpg) +Figure 6. GradCAM heatmaps on random samples of the dolphin, lamp, and tank classes of CIFAR-100. Our metric CNN better focuses on relevant objects and meaningful parts and can handle multiple instances unlike the other CNNs. Red means high values, blue means 0. + +![](images/f18314f673f9477c6d07fffd5da6379dad7b1a35af5c32f165b96aa8eb80cd64.jpg) + +![](images/d0d0065fd7e09a5c0bb881d7ce578805700af89af294ab281aa977912f781adb.jpg) + +with metric convolutions rather than other existing types of convolutions. Not only are metric convolutions more interpretable due to the use of metric theory, but the results seem more interpretable as well. Our experiments demonstrate how to combine metric convolutions with complex neural architectures for high level tasks and that networks benefit from our metric approach to convolutions. + +# 6. Conclusion + +By viewing images as metric manifolds, we provided a unified theory explaining the various existing deformed convolution operators as methods sampling unit balls of various implicit metrics. With this new perspective, we designed a novel framework for adaptive image convolutions, called metric convolutions, that sample unit balls of explicit metrics of various complexity to compute kernel locations. This approach allows for adaptive, feature-dependent neighbourhoods that capture anisotropic and asymmetric patterns, providing a geometric inductive bias improving stability and interpretability. Our experiments demonstrated competitive results on standard benchmarks while improving interpretability and incorporating strong geometric regularisation, albeit at a higher computational cost from the rigid standard convolution, which is unavoidable for adaptive convolution methods. Metric convolutions offer a valu- + +able tool for tasks where explicit metrics or pixel similarities are needed, such as extracting feature-sensitive edges or tubular structures via geodesics [76]. We hope that this work will help popularise the image manifold paradigm and the use of Finsler metrics to the modern computer vision and deep learning community. + +Limitations and future works. First, our choice of Randers metrics constrains unit tangent balls to ellipses. Other convex shapes would be of interest, yielding different types of Finsler unit balls. Second, our current implementation of unit geodesic ball metric convolutions is too slow for practical use. Improving it and using them in neural networks is a future research direction. Third, our metric convolutions inherit the drawback shared by all non-standard convolutions, which is the need to store in memory sampling offset locations per pixel. This high memory footprint can make learning on high resolution images challenging especially when working on high batch sizes. Consequently, we focused on smaller resolution benchmarks, and leave tests on higher resolution data and more efficient implementation to future works. We also focused on a couple of tasks, yet we are intrigued by how beneficial our metric-based learned representations would be for downstream tasks. Viewing individual images as a metric manifold is largely uncharted in modern machine learning and requires further study. + +# Acknowledgments + +This work was supported by the Israel Science Foundation (ISF) (grant No. 3864/21), by ADRI – Advanced Defense Research Institute – Technion and by the Rosenblum Fund. + +# References + +[1] P Morales Álvarez, Miguel Sánchez Caja, and Miguel Angel Javaloyes Victoria. An introduction to Lorentz-Finsler Geometry. PhD thesis, Master Thesis, U. Granada. Master FisyMat, supervisors MA. Javaloyes & M..., 2015. 4 +[2] Alan F Beardon. The geometry of discrete groups. Springer Science & Business Media, 2012. 4 +[3] Fethallah Benmansour, Guillaume Carlier, Gabriel Peyre, and Filippo Santambrogio. Derivatives with respect to metrics and applications: subgradient marching algorithm. Numerische Mathematik, 116:357-381, 2010. 6, 13 +[4] Théo Bertrand, Nicolas Makaroff, and Laurent D Cohen. Fast marching energy CNN. 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a bedroom with a queen-sized bed, two night stands, a large wooden wardrobe...
moonlight streams through glass windows, ... an ancient gothic cathedral.
a chocolate factory filled with various sweet making stations including...
+ +# Abstract + +We present MiDSummer, a two-stage framework for generating immersive Gaussian Splating scenes that leverages multiple diffusion guidance signals to enable structured layout control, enhanced physical realism, and improved visual quality. While 3D scene generation has seen significant recent advances, current approaches could benefit from: (1) achieving precise, reliable layout control while preserving open-world generalization and physical plausibility, (2) balancing high-level semantic reasoning with low-level, directly controllable geometric constraints, and (3) effectively utilizing layout knowledge for visual refinement. Our work addresses these challenges through a structured two-stage planning-assembly framework. For planning, we introduce a dual layout diffusion guidance approach to bridge semantic reasoning and geometric controllability. Our approach uniquely integrates LLMs' open-vocabulary reasoning with Graph Diffusion Models' (GDM) geometric precision by incorporating multi-level self-consistency scores over scene graph structures and layout bounding box parameters. This + +fusion enables fine-grained control over scene composition while ensuring physical plausibility and faithful prompt interpretation. For assembly, we propose a layout-guided optimization technique for scene refinement. We effectively incorporate layout priors obtained during the planning stage into a Stable Diffusion (SD)-based refinement process that jointly optimizes camera trajectories and scene splats. This layout-aware joint optimization, constrained by multi-view consistency, produces visually compelling immersive scenes that are structurally coherent and controllable. + +# 1. Introduction + +Scene design and prototyping are used in many artistic and engineering applications, including film set design, game environment drafting, and interior visualization. Designers often need to enforce strict placement constraints on key story-relevant objects, while maintaining flexibility in other elements to promote visual diversity and realism. This makes the ability to control spatial relationships and gauge their uncertainty fundamental to practical scene synthesis. + +Recent advances in LLMs [1, 2] and Graph Diffusion Models (GDMs) [3, 4] have shown promise in compositional scene synthesis, yet they exhibit distinct limitations: foundation models like LLMs excel in open-world semantic reasoning and are aware of object functionalities but struggle with precise spatial control, often failing to adhere to relationship constraints or introducing hallucinated elements. Conversely, specialist layout models like GDMs trained on domain-specific scenes can faithfully enforce geometric relationships but are constrained by their dataset priors, limiting their generalization to out-of-domain scenarios. + +While significant advances in LLM-driven 3D scene generation have been made [5], we notice two potential opportunities for improvement. Firstly, relying only on LLM proposals can lead to high output variance (Figure 6) and diminished control over fine-grained object relationships (Table 4), which could benefit from the more consistent geometric constraints that GDMs provide. Secondly, explicit layout and room geometry information provide significant value for spatial arrangement and downstream scene geometry and appearance refinement. However, current methods typically restrict their focus to spatial arrangement only, leaving their refinement potential either underutilized [5] or only implicitly integrated [3]. This prevents these methods from fully embracing the benefits of layout-aware scene optimization. Therefore, we explore two research questions (RQs) in controllable compositional scene generation: + +RQ1: How can we reap the benefits of open-world semantic reasoning and geometric constraints in layout planning? +RQ2: How can explicit scene layout and geometry priors contribute beyond mere object placement to enable global optimization of scene coherence? + +In response to the above RQs, we propose MiDSummer, a two-stage multi-guidance diffusion pipeline for immersive scene generation, consisting of a planning stage for layout optimization and an assembly stage for composition and visual refinement. Our key contributions include: + +1. Joint Layout Diffusion Guidance. We present a hybrid framework that combines the broad reasoning capabilities of LLMs with the precise controllability of GDMs to generate scene layouts that are semantically coherent with open-world knowledge while respecting geometric relationship constraints from user prompts. +2. Self-Consistency-Driven Guidance Weighting. We explicitly model cross-prompt consistency at multiple levels of hierarchical scene graph representations to dynamically weight guidance signals. This consistency-based approach balances creative flexibility with geometric constraints during layout diffusion. +3. Layout-Aware Multi-View Refinement. We leverage explicit scene layout from the planning stage to generate adaptive camera trajectories for a multi-view-consistent, geometry prior-guided Stable Diffusion refinement pro + +cess, mitigating occlusion and undersampling artifacts while enhancing visual coherence. + +# 2. Related Works + +# 2.1. Gaussian Splitting and Generative Extensions + +Gaussian Splatting (GS) [6] provides a versatile and efficient point-based representation for modeling spatial structures. Recent works in 3D diffusion-based generative models [7-10] have extended their capabilities to GS generation. Approaches such as GSGEN [11], GaussianDiffusion [12], GaussianDreamer [13], and LucidDreamer [10] integrate diffusion-based generative priors into text-to-GS pipelines [14, 15], using various techniques to ensure multiview consistency. While these methods excel at generating individual objects, compositional scene generation presents additional challenges in layout validity, spatial coherence, and physically plausible object arrangements. + +# 2.2. Compositional Scene Generation + +Recent advances in compositional scene generation [16-20] have experimented with scene construction using diverse representations, including Neural Radiance Fields (NeRFs) [21] and Signed Distance Functions (SDFs) [22, 23]. However, many of these approaches require manual layouts as inputs, limiting their scalability for data-driven scene synthesis. Recently, LLM-driven approaches [5, 24, 25] enable open-vocabulary procedural generation but remain object-centric and lack immersive $360^{\circ}$ capabilities. Our method bridges this gap through joint layout-aware refinement with room-object integration and multi-view consistency constraints. Scene graph based methods [3, 26-29] capture spatial relationships but focus primarily on local object relationships. We extend these scene graphs by introducing multi-level self-consistency quantification that enhances both placement accuracy and spatial cohesion. + +# 2.3. Layout Learning + +Foundation Vision-Language Models (VLMs) encode extensive world knowledge and can infer object relationships from textual prompts, make them potentially suitable layout designers or interpreters in 3D scene structuring [30]. LI3D [31] and SceneWiz3D [32] connect LLMs to NeRF-based scene generation pipelines. Closely related to our research, GALA3D [5] employs global-local layout refinement but does not fully utilize layout information during scene refinement. Our approach differs by introducing joint LLM-GDM guidance with self-consistency quantification, integrating layout knowledge throughout both planning and assembly stages. Specialized layout models [3, 33-35] capture domain-specific spatial relationships but struggle with out-of-distribution generalization, while our approach combines the broad knowledge of LLMs with the precise spatial + +understanding of specialized models to ensure semantically valid yet creative scene arrangements. + +# 2.4. From Objects to Immersive Navigable Scenes + +Immersive and explorable $360^{\circ}$ scene synthesis remains a challenging task despite recent efforts [20, 36-44]. Progress in this domain is driven by advancements in several related areas. Notably, the field of 3D world generation has evolved through procedural, LLM-based, and learning-based methods [42-56]. Concurrently, panoramic generation leverages diffusion models for $360^{\circ}$ synthesis [57-65], and video-based approaches utilize video diffusion models with 3D constraints for creating dynamic scenes [66-80]. Our approach extends immersive generation pipelines [41, 81, 82] with improved object disentanglement and layout control, incorporating layout-aware camera trajectories [83] that reduce artifacts [82, 84] and enhance visual appeal. + +# 3. Methods + +We present a two-stage framework, consisting of planning and assembly (depicted in Figure 1), capable of highly controllable and modularized compositional scene generation. During planning, we generate layout plans through self-consistency-weighted dual guidance signals from a LLM and a specialist GDM while also initializing 3D asset. They are then assembled according to the layout plan then refined using layout-aware adaptive camera trajectories with multiview consistency enforcement. + +# 3.1. Planning + +In the planning stage, we leverage the complementary strengths of Large Language Models (LLMs) and specialist layout Graph Diffusion Models (GDMs) to generate high-quality layout plans that balance physical plausibility and structured controllability through textual prompts. This stage begins with repeated chain-of-thought (CoT) prompting to generate variations of high level scene plans in the form of scene graphs which are then used to condition a layout diffusion process via a GDM. This stage concludes with a layout plan generated through this diffusion process coguided by both scene graph conditioning and LLM's layout proposals, weighted by self-consistency across these LLM proposals. In parallel, we also initialize individual assets in preparation for scene assembly. + +# 3.1.1. Scene Graph and Layout Proposals from LLM + +To fully capture information from textual prompts, we employ a multi-step CoT prompting technique that translates text into scene graphs and their corresponding layout plans in a structured, top-down manner. + +Text to Scene Graph. We begin by querying an LLM to propose a scene graph draft that satisfies the requirements specified in the text prompts. A scene graph [85] serves + +as a structured representation of a visual scene, describing spatial and semantic relationships, denoted as $\mathcal{G} = \{\mathcal{V},\mathcal{E}\}$ . In this representation, nodes $\mathcal{V} = \{v_{i}\}_{i = 1}^{N}$ refers to the set of objects, while directed edges $\mathcal{E} = \{e_{i\rightarrow j}\mid i,j\in [1,N],i\neq j\}$ connecting a pair of nodes $v_{i}\to v_{j}$ encode positional or semantic relationships between objects. + +Scene Graph to Layout Proposal with LLM. Since text prompts typically provide only partial or implicit spatial relationships between object pairs, the initial scene graph is not complete enough for scene assembly. We therefore enable the LLM to design a layout proposal based on the scene graph draft to augment more explicit relationships between objects in the scene. The layout proposal of a scene with $N$ objects can be described by the set of bounding boxes of constituent objects $\mathbf{B} = \{\mathbf{b}^i\}_{i=0}^N$ . We parameterize each box as $\mathbf{b}_0^i = \{l, h, w, x, y, z, \theta\}$ where $l, h, w$ represent the box dimensions, $x, y, z$ denote the center positions and $\theta$ is the azimuthal orientation. + +Given a textual description $\mathcal{T}$ of a scene, we obtain densified scene graphs and layout proposals $(\mathcal{G},\mathbf{B})$ with a four-step prompting procedure: + +1. Node Extraction: We first extract a list of objects as graph nodes $\mathcal{V} = \{v_{i}\}_{i = 1}^{N}$ along with an overall scene description for a special room node $v_{0}$ that will be used for room initialisation (Sec. 3.2). +2. Edge (Relationship) Initialisation: Given $\mathcal{V}$ as context, following [3], we query an LLM to generate multigraph edges $\mathcal{E}$ by identifying the presence of spatial (left, right, front, back, etc.) and semantic (material, style, supercategory, etc.) relationships between each object pair, prioritizing those that are explicitly specified in user prompts. +3. Leaf-Level Layout: Given $\mathcal{V}$ and $\mathcal{E}$ as context, we then generate bounding boxes $\mathbf{B} = \{\mathbf{b}^i\}_{i=0}^N$ with prompts that guide the LLM to incorporate both explicit spatial constraints from user prompts and implicit factors such as common sense, gravity, and object functionality. +4. Cliques or Hierarchical Grouping: Finally, given $(\mathcal{V},\mathcal{E},\mathbf{B})$ as context, we prompt the LLM to identify cliques and meaningful node groupings based on the presence of fully connected subgraphs (with respect to all edge types) as well as several relational factors including vertical stacking (e.g. range hood above stove, books on a desk) and functional grouping (e.g. dining table and chairs, a bed and nightstands). + +The resultant layout proposal is augmented with relationships between every pair of objects based on real world knowledge of the LLM for a frozen and complete design. + +Once the spatial relationships are captured in the layout, we use it to backward densify the initial scene graph with augmented spatial relationships information between object pairs (e.g. when a prompt does not specify that $v_{3}$ should be larger than $v_{2}$ but in the layout it turns out to be larger, an edge would be amended). For objects arranged in hier- + +![](images/ccbf8efdc31d341c1ea57aca3f3d39ed67927398cb6923ecdd6e152161a4e759.jpg) +Figure 1. An overview of our multi-guidance two-stage planning-assembly workflow. The planning stage generates layout using LLM and GDM guidance while initializing 3D assets, followed by assembly that constructs and refines scenes using layout-aware camera trajectories. + +archical groups, we perform this densification at the group level rather than single objects. This results in high-quality densified scene graphs that are ensured to be in agreement with its corresponding bounding box proposals. + +**Proposal Sampling.** To account for the inherent randomness of LLM models, we repeat the aforementioned process $M$ times to generate layout proposal variations. In the end, we obtain $M$ densified scene graphs corresponding to $M$ layout proposals designed by the LLMs. Both sets of proposals serve as guidance signals during the final layout generation diffusion process. + +# 3.1.2. Dually-guided Layout Denoising with GDMs + +To refine the initial layout proposals, we introduce a graph denoising procedure guided by two complementary sources of information. The first is a denoising prediction from a specialist GDM, conditioned on $M$ densified scene graphs to rigorously enforce their specified spatial relationships. The second is a corresponding set of $M$ layout proposals from a LLM, which supplies not only spatial information but also better semantic properties for bounding boxes (e.g., dimensions) derived from its real-world knowledge. We found that naively averaging these two signals yields suboptimal performance (Table 4). Therefore, drawing inspiration from prior work on prompt ensembling [86-88] and cross-prompt consistency [89-92], we attempt to systematically quantify cross-proposal consistency in both classes of models to gain insights into effectively leveraging these two complementary guidance signals, as detailed below. + +Self-Consistency Characterization. We first examine GDM's aleatoric variability by running multiple forward passes with the same scene graph $\mathcal{G}$ but different random seeds. GDMs exhibit high self-consistency, with low variance in bounding box parameters (details in Appendix C). However, when summarizing the $M$ LLM proposals from LLM Proposal Sampling (Figure 6), we observed high consistency in object dimensions but low consistency in positions. To properly handle the consistency issues in LLM proposals and balance the LLM's real-world knowledge with scene graph constraints, we introduce a consistency-aware weighting mechanism inspired by prior work in graph-based scene representation [26]. To quantify consistency across multiple levels in the hierarchical layout proposals for deciding the weighting, in this work, we propose an intuitive solution with three key cross-sample consistency measures (where node indices $i,j\in [1,N]$ ): + +Bounding Box Parameter Consistency $\mathbf{C}_B\in \mathbb{R}^{N\times 8}$ quantifies the consistency of eight bounding box parameters across layout proposals through a transformed version of parameter variance where $\tau$ controls sigmoid steepness and $\nu$ sets the variance threshold. + +$$ +\sigma_ {\mathbf {b} ^ {i}} ^ {2} = \frac {1}{M} \sum_ {m = 1} ^ {M} \left(\mathbf {b} _ {m} ^ {i} - \bar {\mathbf {b}} ^ {i}\right) ^ {2}; \mathbf {C} _ {B} ^ {(i)} = \operatorname {s i g m} \left(\tau \left(\sigma_ {\mathbf {b} ^ {i}} ^ {2} - \nu\right)\right) \tag {1} +$$ + +Edge Consistency $\mathbf{C}_E\in \mathbb{R}^N$ captures the consistency of pairwise relationships across proposals. It is computed by first tallying the occurrence of each edge across proposals, + +then normalizing the row-wise sum: + +$$ +\mathbf {E} _ {i j} = \sum_ {m = 1} ^ {M} \mathbb {I} \left(e _ {i j} \in \mathcal {E} _ {m}\right); \quad \mathbf {C} _ {E} ^ {(i)} = \frac {1}{N - 1} \sum_ {j = 1} ^ {N} \mathbf {E} _ {i j} \tag {2} +$$ + +Clique Consistency $\mathbf{C}_G\in \mathbb{R}^N$ similarly to $\mathbf{C}_E$ we first compute a clique (complete subgraph or spatio-functional grouping) co-occurrence $\mathbf{G}\in \mathbb{R}^{N\times N}$ for each pair of nodes across proposals, then convert it to a consistency score for each node via row-wise summation and normalization: + +$$ +\mathbf {G} _ {i j} = \frac {1}{M} \sum_ {m = 1} ^ {M} \mathbb {I} \left(\left(v _ {i}, v _ {j}\right) \in \mathcal {G} _ {m}\right); \quad \mathbf {C} _ {G} ^ {(i)} = \frac {1}{N - 1} \sum_ {j = 1} ^ {N} \mathbf {C} _ {i j} \tag {3} +$$ + +Each of these measures provides complementary structural insights, enabling consistency-guided weighting in the layout diffusion process. When the LLM proposals are highly self-consistent, we can rely more on the LLM's guidance; otherwise, the model gravitates towards the conservative geometric constraints of the GDM. To understand how each consistency measure impacts the overall performance, please refer to ablation results in Table 5, Section 4. + +Graph Diffusion Model (GDM). With the cross-sample consistency from both guidance signals quantified, we introduce the GDM that leverages this consistency during the diffusion process. We adopt the layout branch of EchoScene [3], dubbed EchoLayout, a SoTA method of this class, as a base specialist layout diffusion model. + +In EchoLayout, each node is denoised while interacting with other nodes at every time step. To perform diffusion denoising on a graph, we first encode the contextual graph structure to obtain latent relational embeddings via a triplet-based encoder [4, 27, 93, 94] that processes triplets of the form $(v_{i},e_{i\rightarrow j},v_{j})$ , where the embeddings of the source node, edge, and target node are concatenated. The initial embeddings for before diffusion are set as $v_{i} = [p_{i},o_{i}]$ and $e_{ij} = [p_{i\rightarrow j},\tau_{i\rightarrow j}]\in \mathbb{R}^{512}\times \mathbb{R}^{128}$ , where $p_i$ and $p_{i\rightarrow j}$ are CLIP text embeddings, and $o_i$ and $\tau_{i\rightarrow j}$ are categorical object and relationship embeddings, respectively. An encoder $E_{r}$ refines the embeddings over multiple layers, capturing the spatial and functional interactions between objects. The set of diffused bounding boxes at time step $t$ is denoted by $\mathbf{B}_t = \{\mathbf{b}_t^i |i\in [1,N]\}$ , where each $\mathbf{b}_t^i$ represents the noisy bounding box parameters for object $i$ at time $t$ . The DDPM denoising process operates on $\mathbf{b}_t^i$ , maintaining structural coherence while iteratively refining object sizes and placements. + +The specialist layout model, trained on the 3D-FRONT dataset [33], has limited open-vocabulary capabilities due to its reliance on categorical embeddings $o_i$ . To test its zero-shot generalizability on out-of-distribution (OOD) objects, we conducted preliminary experiments where we re + +placed $o_i$ with random noise, forcing the model to reason using only the general-purpose CLIP embedding $p_i$ (see Appendix C). While this OOD setting increased object size estimation errors, the model still, to a large extent, successfully preserved the relative spatial relationships defined in the scene graph. This result highlights the complementary strengths that motivate our dual-guidance strategy: the GDM excels at enforcing relational structure, while the LLM provides the semantic understanding needed for physical plausibility and realism. + +Layout Diffusion with Dual Guidance. In this section, we demonstrate how we combine the dual guidance signals, i.e. graph-guided layout diffusion of the GDM and layout proposals from the LLM, based on the aforementioned self-consistency characterization. + +At each timestep $t$ of the reverse diffusion process $\prod_{n}^{N}\prod_{t}^{T}p_{\theta}(\hat{\mathbf{b}}_{t - 1}^{(n)}|\hat{\mathbf{b}}_{t}^{(n)})$ , the noise $\epsilon_{\theta}(\mathbf{b}_{t}^{(i)},t)$ predicted by the layout diffusion model provides an estimate of the final layout configuration $\hat{\mathbf{b}}_0^{(i)}$ for object $i$ by: + +$$ +\hat {\mu} _ {G D M} \left(\mathbf {b} _ {t} ^ {(i)}, t\right) = \frac {1}{\bar {\alpha} _ {t}} \left(\mathbf {b} _ {t} ^ {(i)} - \bar {\beta} _ {t} \epsilon_ {\theta} \left(\mathbf {b} _ {t} ^ {(i)}, t\right)\right), \tag {4} +$$ + +where $\mathbf{b}_t^{(i)}$ is the noisy bounding box parameters at timestep $t$ of object $i$ and $\bar{\alpha}_t, \bar{\beta}_t$ are scheduling parameters. + +To integrate guidance from both the LLM and the GDM, we adjust the original estimate $\hat{\mu}_{GDM}(\mathbf{b}_t^{(i)}, t)$ by defining a consistency-weighted mean prediction that blends the two supervision signals. Rather than naively averaging (which is suboptimal due to the discrete nature of the graph domain, as shown in the 0.5-0.5 row of Table 4), we compute a weight $\mathbf{w}_{\mathrm{LLM}} \in [0,1]^{N \times 8}$ based on our multi-level cross-sample consistency measures $\mathbf{C}_B \in \mathbb{R}^{N \times 8}$ , $\mathbf{C}_E$ , and $\mathbf{C}_G \in \mathbb{R}^N$ (see Eq. 1-3). Specifically, we take a geometric mean between $K$ types of consistency measures, for example, in the case of $K = 3$ : + +$$ +\mathbf {w} _ {\text {L L M}} ^ {(i)} = \left(\mathbf {C} _ {B} ^ {(i)} \odot \mathbf {C} _ {E} ^ {(i)} \odot \mathbf {C} _ {G} ^ {(i)}\right) ^ {\frac {1}{3}} \tag {5} +$$ + +The adjusted target direction is then given by: + +$$ +\tilde {\mu} _ {t} ^ {(i)} = \mathbf {w} _ {\text {L L M}} ^ {(i)} \odot \mathbf {b} _ {\text {L L M}} ^ {(i)} + \left(\mathbf {1} - \mathbf {w} _ {\text {L L M}} ^ {(i)}\right) \odot \hat {\mu} _ {G D M} \left(\mathbf {b} _ {t} ^ {(i)}, t\right), \tag {6} +$$ + +Then following the standard DDPM [95] schedule, the final denoising update for object $i$ at a given timestep $t$ is: + +$$ +\mathbf {b} _ {t - 1} ^ {(i)} = s _ {t} \mathbf {b} _ {t} ^ {(i)} + d _ {t} \tilde {\mu} _ {t} ^ {(i)} + \sigma_ {t} \epsilon , \quad \epsilon \sim \mathcal {N} (0, I). \tag {7} +$$ + +This formulation encourages higher reliance on LLM outputs when the particular object and parameter is highly consistent across the LLM proposals, leveraging its open-world knowledge and reasoning capabilities. Otherwise, we fall back to GDM, gravitating towards more conservative adherence to learned prior geometric and spatial constraints. + +# 3.1.3. Asset Initialisation + +With layout proposal generated from the aforementioned diffusion process, we initialize scene assets (empty room backdrop and individual object) using various foundation models for image generation and depth estimation. + +Gaussian Splatting (GS). Each GS asset $\mathcal{P}^i = (\mathbf{p},\mathbf{c},\alpha ,\boldsymbol {\Sigma})$ is defined by a set of points with center position $\mathbf{p} = (p_x,p_y,p_z)\in \mathbb{R}^3$ , color $\mathbf{c}$ , opacity $\alpha$ , covariance $\boldsymbol{\Sigma} = \mathbf{RSS}^\top \mathbf{R}^\top$ , where $\mathbf{S}$ is the scale matrix and $\mathbf{R}$ is the rotation matrix. A compositional scene with $N$ object nodes is a collection of assets $\mathcal{P} = \{\mathcal{P}^i |i\in [0,N]\}$ where $i = 0$ indicates room backdrop splats. + +Individual asset initialisation. We initialize individual 3D assets from object node texts using existing diffusion-based GS models [11, 15]. Our experiments are performed with DiffSplat [96] and GaussianDreamer [13] as asset source model. To ensure compliance to layout plans, based on the aspect ratios of assets, we perform a volume-preserving adjustment for layout bounding boxes. + +Coarse room generation and registration. We use SD 2.1 [97] to generate an initial frame [81] of the room using paired positive and negative room prompts obtained from the four-step prompting procedure outlined in Sec. 3.1.1. This initial frame, combined with an estimated depth map [98, 99] and camera parameters, are then used to initialize a room asset $\mathcal{P}^0$ , following [81]. Subsequently, the room is registered to world coordinates by aligning its ground normal with $-y$ of the world space. + +# 3.2. Layout-Guided Assembly and Refinement. + +In this stage, we introduce a layout-aware camera trajectory planning and update technique that works with multi view-consistent sampling from VistaDream [81] to enhance scene appearance and geometry. While building upon VistaDream's framework, our key contributions include: (a) Initializing a two-pass trajectory with $V$ camera views for image-based refinement, balancing inward and outward views for object and room coverage; (b) Rendering $V$ images from adaptively optimized camera angles and refining them with SD, balancing scene detail and multi-view consistency through joint SD-scene geometry sampling guidance; (c) Fine-tuning object and room splats as well as camera trajectory for enhanced visual appeal. + +We denote refinement optimisation steps as $s \in [0, S]$ and DDIM [100] denoising steps of stable diffusion as $t \in [0, T]$ . + +Camera Trajectory Initialization. A camera trajectory at the $s$ -th iteration of the refinement loop consists of a sequence of camera intrinsic $\mathbf{K}$ and extrinsic $\mathbf{E}$ matrices $\mathbf{T}_s = \{\mathbf{K}, \mathbf{E}_s^v | v \in [1, V]\}$ assuming we use $V$ camera views. The intrinsics remain fixed. The extrinsics can be computed from parameters that can be more directly con + +ditioned on scene layout: $\mathbf{E}_s^v (\mathbf{p}_s^v,\boldsymbol{\tau}_s^v,u)$ which refers to a camera position $(\mathbf{p}_s^v)$ , a look-at target $(\boldsymbol{\tau}_s^v)$ and an updirection $(u)$ which is fixed to $[0, - 1,0]$ . The initial trajectory $\mathbf{T}_0$ results from layout and scene boundaries. First, we sample $V$ azimuthal angles. For each angle, the camera's $x$ and $z$ coordinates are determined by mapping the angle onto a curve defined by interpolating between two reference sequences: (1) the inner bound $C_{inner}(v)$ , obtained from the convex hull of object splats projected onto the $XZ$ plane i.e., $\mathbf{c}_{inner}(v) = \mathrm{ConvexHull}(\{\mathrm{proj}_{XZ}(\mathcal{P}_i)\mid i\in [1,V]\})$ , and (2) the outer bound $C_{outer}(v)$ derived from scene boundaries. For each sampled azimuthal angle $v$ , the camera's $x$ and $z$ coordinates are set as $\mathbf{c}_s^v = (1 - \alpha_t)\mathbf{c}_{inner}(v) + \alpha_t\mathbf{c}_{outer}(v)$ , with $\alpha_{t}\in [0,1]$ controlling the interpolation (where 0 corresponds to the convex hull and 1 to the scene boundary). The camera's $y$ -coordinate is fixed at half of the scene's height. The look-at target $\boldsymbol{\tau}_s^v$ is always set to the object splats convex hull centroid $\mathbf{c}_{center}$ for inward views $\boldsymbol{\tau}_s^{0:\frac{V}{2}} = \mathbf{c}_{center} - \mathbf{c}_s^v$ and reversed for outward views. + +View-Adaptive Refinement. Following VistaDream [81], given renderings $\mathbf{x}_s^{(1:V)}$ at refinement iteration $s$ captured by layout-aware cameras, we employ a multi-view consistent refinement process. Each rendered frame (RGB-D) is projected into the SD latent space at a prior denoising timestep through noise injection. Multi-view consistency is then enforced through a guided denoising process where the denoising direction is steered toward a known geometric prior, similar to (6): $\tilde{\mu}_t^{(n)} = w_t\gamma_t^{(n)}\bar{\mu}_t^{(n)} + (1 - w_t)\hat{\mu}_t^{(n)}$ where $\hat{\mu}_t^{(n)}$ represents SD's prediction of the clean image for view $n$ , $\bar{\mu}_t^{(n)}$ is the rendering from a temporary scene for geometric consistency, and $\tilde{\mu}_t^{(n)}$ is the resulting blended target direction. This refinement process balances SD-generated details with multi-view consistency based on layout confidence. Higher $w_t$ enforces stronger consistency but may lead to over-smoothing, while lower $w_t$ emphasizes retention of finer details over cross-view coherence. We demonstrate this trade-off in Fig. 8 in Appendix D. The scene is updated through gradient backpropagation as in Eq. (8), where learning rates $\eta_{\mathcal{P}}$ differs for object and room background splats. + +$$ +\mathcal {P} _ {s + 1} = \mathcal {P} _ {s} - \eta_ {\mathcal {P}} \nabla_ {\mathcal {P}} \| \tilde {\mu} _ {s, T} ^ {(1: V)} - \mathbf {x} _ {s, T} ^ {(1: V)} (\mathcal {P} _ {s}, \mathbf {T} _ {s}) \| _ {2} ^ {2} \tag {8} +$$ + +Additionally, we introduce regularization terms targeting regions with specific artifacts, including depth inconsistencies, discontinuous normals, or insufficient splat density. A quality-aware trajectory update mechanism identifies these problematic regions and dynamically adjusts camera views $\mathbf{T}_s$ to provide enhanced refinement in subsequent iterations. The camera trajectory is updated through gradient ascent $\mathbf{T}_{s + 1} = \mathbf{T}_s + \eta_{\mathrm{cam}}\nabla \mathbf{T}\sum_{v = 1}^{V}\mathcal{L}_s^v$ , targeting low-quality regions that require additional attention. + +# 4. Experiments and Evaluation + +To quantify MiDSummer's capability in balancing semantic reasoning with geometric constraints in text-to-scene generation tasks, we evaluate this workflow from two aspects: (1) Layout planning capability through experiments on SUN RGB-D [24] ( $\S 4.1$ ). (2) Overall scene generation quality compared to state-of-the-art methods ( $\S 4.2$ ). We further conducted an ablations on various weighting and self-consistency configurations during guided layout diffusion ( $\S 4.3$ ) to examine how each component contributes to layout planning quality. For all experiments, we use Claude 4.0 [2] as LLM and EchoLayout [3] as pre-trained specialist GDM. We provide a per-stage runtime breakdown and a scalability analysis in Appendix A, as well as additional qualitative results and ablations on the layout-guided assembly and refinement stage in Appendix D. + +# 4.1. Layout Planning Capability + +To evaluate our layout planning capabilities, we conducted experiments on a subset of the SUN RGB-D [101] dataset (KV1-NYU). This dataset provides a broader range of object classes compared to GDM's training set 3D-FRONT [33], while maintaining similarity to photorealistic indoor scenes, enabling assessment of both generalization and layout planning performance. We evaluate two input modalities: (1) Text-to-Layout (Table 1) and (2) SceneGraph-to-Layout (Table 2) generation tasks. Our assessment employs two metric categories: Semantic Understanding measures object size fidelity through Volume Error $(m^3)$ for absolute measurements and pairwise binary volume relationship accuracy (Bi/Sm) for relative size comparisons. Spatial Layout Fidelity evaluates geometric accuracy using three binary spatial relationship metrics between bounding box center pairs: Left/Right (L/R) along $x$ , Front/Behind (F/B) along $z$ , and Up/Down (U/D) along $y$ . For text-to-Layout task, we generate dense textual captions for SUN RGB-D images using LLaVA as input prompts, then evaluate spatial relationship accuracy against input scene graphs. For SG-to-Layout task, we measure the generated layout plans against ground truth 3D bounding box annotations. Both experiments evaluate Volume Error against ground truth bounding box annotations. + +
ConfigurationInputSpatialSemantic
L/R↑F/B↑U/D↑Bi/Sm↑VolErr↓
LLM-onlyText47.558.971.585.164.5
GDM-onlyText88.083.589.076.4255.5
Dual-GuidanceText88.887.687.488.850.8
+ +As shown in Table 1, the LLM-only variation demonstrated superior semantic understanding through better prediction of object volumes, both in absolute and relational senses, while the GDM-only approach showed stronger performance in maintaining spatial relationships. Dual-guidance layout diffusion successfully combines these complementary strengths. To isolate the impact of text-to-scene-graph conversion noise, we conducted an additional experiment using scene graphs derived directly from SUN RGB-D annotations as input (Table 2). Similarly to textual inputs, the dual-guidance approach combines benefits from LLM's semantic reasoning with GDM's spatial fidelity. + +Table 1. Text-to-Layout task performance across model configurations. Results highlight the complementary strengths of base models: LLMs excel in semantic understanding while GDMs demonstrate stronger spatial constraint adherence. Dual-guidance reaps benefits from both guidance signals. + +
ConfigurationInputSpatialSemantic
L/R↑F/B↑U/D↑Bi/Sm↑VolErr↓
LLM-onlySG55.664.266.786.767.4
GDM-onlySG89.582.580.073.3332.7
Dual-GuidanceSG84.081.573.386.764.2
+ +# 4.2. Overall Scene Quality + +We compare MiDSummer's with SoTA scene generation approaches using text or text layout conditioning. Our evaluation employs three metrics that assess different aspects of scene quality: (1) Visual Realism: Kernel Inception Distance $(\mathrm{KID}\downarrow)$ [102] computed against SUN RGB-D [101] images and an indoor subset of Places365 [103] as real image references. (2) Geometric Sharpness: Variance of Laplacian $(\mathrm{VarLap}^{\uparrow})$ measuring image sharpness as a proxy for geometry well-definedness and scene coherence. + +Table 2. SG-to-Layout performance across model configurations. + +
MethodsKID SUN↓KID Places↓VarLap↑
Set-the-scene [18]0.16350.147992.28
ProlificDreamer [104]0.11460.0822142.4
LucidDreamer [10]0.14350.1529322.1
GraphDreamer [26]0.16000.1445542.0
GALA3D [5]0.09730.1127593.9
MiDSummer0.06470.1097633.8
w/o Dual-Guidance Layout0.11980.1175615.4
w/o Layout-Aware Refinement0.05690.1023545.9
+ +Table 3. SoTA text-to-scene approaches using text or text layout prompts. KID [105] is computed against SUN-RGBD [101] and an indoor subset of Places365 [103] as real samples. + +Table 3 shows that MiDSummer demonstrates moderate improvement in overall scene quality compared to SoTA methods, producing realistic compositional immersive 3D scenes with enhanced rendering quality while maintaining stronger prompt-to layout alignment. We also include two ablated variants of MiDSummer: (1) w/o Dual-Guidance Layout, which relies solely on GDM layout proposals in the planning stage, and (2) w/o Layout-Aware Refinement, which incorporates dual guidance layout but omits the layout-guided refinement during assembly. The latter component introduces trade-off between geometric quality and the retention of high-frequency features, which is further discussed in Appendix D. + +# 4.3. Ablation Studies + +We further ablate layout planning configurations to understand how consistency-weighted dual layout diffusion guidance may help improve layout quality. two ablation studies serving these purposes: (1) more thoroughly quantify strengths and weaknesses of GDMs' and LLMs' layout learning paradigms and benefits of dual guidance; (2) measuring how different self-consistency combinations for dual guidance weighting impact results. + +# 4.3.1. Complementary Guidance for Layout Diffusion. + +
WeightBinary Relationships↑Errors↓
GDMLLML/RF/BU/DBi/SmMeanVolErrPosErr
1.00.087.9783.5189.0076.4284.22255.52.81
0.90.185.5181.3986.0379.4483.09242.92.58
0.70.374.1472.6878.8284.2277.46109.52.37
0.50.560.5265.7275.4784.7471.6168.12.34
0.30.755.9059.7775.1784.6468.8763.72.35
0.10.946.5259.8476.4285.6067.1065.42.36
0.01.047.5058.9171.4985.1365.7664.52.35
+ +Table 4 highlights the complementary strengths of the two guidance signals: LLMs excel at functional and semantic aspects such as object volume estimation (achieving the lowest VolErr of 64.5 and PosErr of 2.35), whereas GDM excels at fulfilling prescribed spatial relationships (L/R, F/B, U/D) with consistently higher binary relationship accuracies, matching our intuition in Sec. 3.1.2 and the results in Table 7 and Fig. 6. The lack of a clear overall winner motivates the necessity of self-consistency-weighted guidance to address these limitations and fully exploit their complementary strengths. Our next ablation study attempts to understand how the combination of consistency measures affect the layout quality and how they are correlated. + +# 4.3.2. Effects of Each Self-Consistency Component + +In this ablation study, we exhaust all combinations of Bounding Box Parameter (B), Edge (E) and Clique (C) consistencies and show how every combination is correlated with the quality and stability of the resultant layout. + +Table 4. Performance of various self-consistency combinations. + +
ConsistencyBinary Relationships↑Errors↓
BECL/RF/BU/DBi/SmMeanVolErrPosErr
✓89.9792.9389.3586.6289.7264.22.53
✓88.4280.0088.6182.5584.89175.82.67
✓✓86.4181.8791.9285.1786.34107.32.62
✓91.2888.7987.6487.3688.7750.82.53
✓✓86.7981.8790.8787.2086.6852.32.53
✓✓88.4485.9289.0886.1787.4099.72.63
✓✓✓86.7981.8790.0785.9586.1783.62.59
+ +Table 5. Performance of various self-consistency combinations. + +As shown in Table 5, most consistency term combinations improved layout quality across both spatial relationship fidelity and physical realism metrics, with B and C terms proving particularly effective individually. Distributional + +![](images/1c71bd796f2fcd0e9a4dc8a04bd38a8ac9cdbcb41720e51e5edbf62259961eaa.jpg) +Figure 2. Spatial relationship performance distribution under various consistency configurations. Red dots indicate mean values. B and C help achieve higher mean performance while E elevates performance lower bounds when combined with other terms. + +analysis in Fig. 2 reveals that while E may not have a significant effect on mean performance, it reduces performance variance and elevates the performance lower bound when combined with other terms. Term combinations generally outperform individual approaches, with $\mathrm{B} + \mathrm{C}$ achieving an optimal balance between spatial relationship accuracy and semantic realism. However, diminishing returns when all three terms are activated suggest potential interference between consistency mechanisms, likely due to inherent correlations (see Fig. 5) in the layout reasoning pipeline. + +# 5. Conclusions + +In this paper, we introduced MiDSummer, a two-stage framework for controllable compositional scene generation using multi-guidance diffusion. Our approach combines foundational LLMs and specialist GDMs to leverage their complementary capabilities: LLMs provide semantic reasoning and open-vocabulary understanding, while GDMs enforce geometric constraints and spatial relationships. We propose a multi-level self-consistency mechanism that dynamically weights these guidance signals during layout diffusion based on spatial relationship accuracy, geometric precision, and semantic coherence. The resulting layouts are used for scene assembly and multi-view consistent, diffusion-based refinement to generate immersive scenes with improved geometric quality and prompt adherence. + +Limitations and Future Work. Our current approach has several key constraints with corresponding future work opportunities: (1) The absence of a canonical azimuthal angle interpretation, which may yield unreliable object orientations; future work could investigate into robust pose- or orientation-aware editing. (2) The requirement for backdrop geometry regularity, limiting our analysis to even, uncluttered landscapes due to the need for scene-to-world registration; future work could consider separating irregular areas out of placement location for better robustness; (3) While the proposed self-consistency measures are intuitively motivated by graph structures, they exhibit correlation and have diminishing returns in terms of performance gain as more terms are added; future work may consider more statistically robust and disentangled ways to reformulate and/or gcombine them. + +# Acknowledgements + +We sincerely thank Niall Twomey for his invaluable guidance and mentorship throughout this project. We are also grateful to Kurt Cutajar, Gavin Cheung, Jianhao Yuan, Yangming Li, and Simon Zeng for their insightful feedback and discussions, and to Sara Camplani for her assistance with model evaluation. 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MikuDance consists of two key techniques: Mixed Motion Modeling and Mixed-Control Diffusion, to address the challenges of high-dynamic motion and reference-guidance misalignment in character art animation. Specifically, a Scene Motion Tracking strategy is presented to explicitly model the dynamic camera in pixel-wise space, enabling unified character-scene motion modeling. Building on this, the Mixed-Control Diffusion implicitly aligns the scale and body shape of diverse characters with motion guidance, allowing flexible control of local character motion. Subsequently, a Motion-Adaptive Normalization module is incorporated to effectively inject global scene motion, paving the way for comprehensive character art animation. Through extensive experiments, we demonstrate the effectiveness and generalizability of MikuDance across various character art and motion guidance, consistently producing high-quality animations with remarkable motion dynamics. + +# 1. Introduction + +Character art plays a crucial role in the film, game, and digital design industries. Animating character art, which brings static character images to life, has been an increasingly prominent challenge in computer vision and graphics. Traditional animation software, such as MMD [11], and Live2D [22], requires professional skills, posing significant barriers for non-experts. Recently, image-to-video generation methods [7, 19, 21, 40, 50] have emerged as a promising solution for animation. However, these methods are primarily designed for animating real-world humans and cannot be directly applied to character art due to the following two key challenges. + +The first challenge in animating character art arises from the high-dynamic motion guidance for both the complex + +![](images/b1c50a4043b7150f52d06379ef1b74fb9712df5b031dcb39fa5d33a420e810fe.jpg) + +![](images/22a2c0343f951c8b85bc9bfbab410252e221dfe74d0b03596b7f66f19cda848b.jpg) + +![](images/03383f3f0f7ddfd3a0f64839e36113ecd901e471298761834c9c210761bc8989.jpg) + +![](images/ead57a5e37fab7748a968e5d0f1981e44863f352d5a6e85cccf85a8fde720c02.jpg) +Figure 1. We propose MikuDance, a Diffusion-based pipeline for animating complex and stylized character art with high-dynamic motion guidance. The core insight of MikuDance lies in its Mixed Motion Modeling and Mixed-Control Diffusion capabilities. + +![](images/0eff2940699fbe2b31d682cbbf27c0a3ae10b94bc72ebc20d4f36e166c510afa.jpg) + +![](images/f8a5def724385c58dea93003b31b64c1f8ee58cfc7be4ff9f0e09267cd18e9dd.jpg) + +foreground and background, making unified control and consistently temporal maintaining difficult. For instance, in the second drawing shown in Figure 1, the girl is portrayed in an elegant dress against an artistic background, driven by large-scale dance motion and camera movements. Existing image animation methods, such as Animate Anyone [14] and DISCO [36], are primarily limited to animating humans with a static camera and a clean background. In contrast, animating character art requires the model to handle large-scale motion within complex scenes. As a result, simultaneously modeling the high-dynamic motion of both characters and the backgrounds becomes a critical task. + +The second challenge in animating character art stems from the unique body shapes and diverse scales of characters, which often misalign with motion guidance. For example, anime characters exhibit a large head-to-body ratio, exaggerated poses, and varied artistic styles. As shown in Figure 1, previous methods employ separate networks to process the reference image and motion guidance, oversimplifying the task by assuming a pre-aligned human body [30, 51], or performing alignment through pre-processing [37], which often leads to unnecessarily complex motion control architectures. However, since art images feature distinct characters, explicit alignment becomes impractical. Thus, implicitly aligning the reference and guidance within a unified structure presents a significant task. + +To address these challenges and leverage recent advancements in video generation for character art animation, we propose MikuDance. MikuDance animates in-the-wild character art by utilizing mixed character-scene motion guidance to generate videos with large-scale motion dynamics. It incorporates two key techniques: Mixed Motion Modeling and Mixed-Control Diffusion. + +Mixed Motion Modeling explicitly represents character motions and 3D dynamic camera movements within a unified 2D space, enabling local and global motion guidance of both foreground and background in animations. Unlike previous methods that use camera parameters directly as the control signal [9, 39, 42], we propose a Scene Motion Tracking (SMT) strategy to model the global motion. SMT strategy projects the reference image to a scene point cloud and tracks corresponding points across consecutive camera frames, transforming camera poses into a pixelwise scene motion representation. This scene motion, resembling keypoint-based character motion, establishes the foundational basis of our mixed motion control approach. + +Mixed-Control Diffusion addresses misalignments in scales and body shapes of characters by integrating all reference and motion guidance into a unified Reference UNet [29]. This design is based on our observation that the mixed and implicit alignment approach outperforms other sophisticated control networks while preserving an elegant model architecture. Moreover, as scene motion guides the global dynamics of the animation, we carefully design a Motion-Adaptive Normalization (MAN) module to flexibly inject the scene motion into the Reference UNet, effectively integrating global dynamics and maintaining local consistency in character art animation. + +By leveraging these two techniques and a mixed-source training approach, MikuDance animates diverse character art with mixed motion dynamics. We evaluate MikuDance using a range of reference characters and motion guidance. Both qualitative and quantitative results demonstrate that MikuDance can generate high-quality animation, particularly in maintaining consistency in character local motion and effectively handling large-scale scene motion. + +Contributions of our MikuDance are listed below: + +- Mixed Motion Modeling is proposed to explicitly model character and camera motions within a unified pixel-wise space, enabling the effective representation of high-dynamic motion. +- Mixed-Control Diffusion is exploited to implicitly align character shape, pose, and scale with the motion guidance, enabling cohesive motion control for character art animation. +- Extensive experiments demonstrate the effectiveness and generalizability of our MikuDance, achieving superior animation quality and high-dynamic motion control compared to state-of-the-art methods. + +# 2. Related Work + +Human image animation, which aims to generate human action videos from a reference image, has been studied extensively in recent years. Early methods, such as FOMM [31] and Liquid Warping GAN [20], warped the source human image using affine transformations guided by dense optical flow. Recently, diffusion-based approaches have gained traction due to their strong generalizability [3]. For instance, PIDM [2] introduced a texture diffusion module to model the correspondence between human appearance and poses. DreamPose [16] incorporated an adapter module to integrate both CLIP [27] and VAE [17] features of reference images.Animate Anyone [14] proposed a UNet-based ReferenceNet to extract appearance from reference images, along with a Pose Guider to encode the driving pose sequences, and a temporal module introduced byAnimateDiff [8] to enhance video consistency. + +FollowingAnimate Anyone, many diffusion-based models have been successively proposed, incorporating specific human motion guidance such as dense poses [43], 3D human models [51], and hand sequences [49]. Additionally, DISCO [36] proposed decoupling human subjects from backgrounds, and UniAnimate [37] employed a unified Denoising UNet to generate long-term video. While these methods introduce increasingly stringent human body priors, they do not account for the variable shapes and scales found in anime characters. Moreover,Animate-X [32] generalizes the pipeline to anthropomorphic characters but neglects the broader movements of the entire scene. In contrast, we design the Mixed-Control Diffusion to address the challenges of misalignment and comprehensive motion control in animating character art. + +Controllable video generation builds upon the success of image generation by integrating additional spatial and temporal control signals. For example, VideoCrafter [4] and DynamiCrafter [41] control the first frame of the generated video through an image injection module. DragNUWA [46] integrates motion trajectories to control object movements. Animate Anything [5] introduces area guidance and motion strength guidance to achieve fine-grained motion control. In this work, the central focus is on the unified guidance of both character motion and camera movements. + +Moving forward, existing works on camera control in video generation [9, 42, 45] often use Plücker coordinates [15] as an embedding of camera poses. Recent works such as Human4DiT [30] and HumanVid [39] consider camera movement in human videos by using an independent camera encoder and directly adding this embedding into the Denoising UNet. However, this camera embedding has a significant domain gap compared to the image pixel-wise guidance of character motion, making it difficult to fuse and maintain consistency in animation. In this work, we + +![](images/c1faa4609b29eb734d7145f3adf5e739d89109200b8cfd8b0cfe08077fe73324.jpg) +Figure 2. Illustration of our MikuDance pipeline. Given a reference character art and a driving video, the pixel-wise scene motion is predicted using the Scene Motion Tracking (SMT) strategy, which is combined with the character poses to form the character-scene mixed motion guidance. The Mixed-Control Diffusion subsequently generates the animation in a latent space, guided by the character poses and the scene motion injected through the Motion-Adaptive Normalization (MAN) module. + +explicitly track camera movement in pixel space and integrate it with character motion guidance using the Motion-Adaptive Normalization module, enabling high-dynamic motion modeling in character art animation. + +# 3. Method + +As illustrated in Figure 2, given a character art $\mathcal{I}$ and a driving video $\nu$ , the purpose of our MikuDance is to animate the image $\mathcal{I}$ with reference to the human and camera motion in video $\nu$ . Specifically, we utilize Xpose [44] to separately extract pose sequences of the human body, face, and hand, and employ DROID-SLAM [33] to extract the camera poses $\{\pmb{p}_l^c\}_{l=1}^L$ , $\pmb{p}^c \in \mathbb{R}^{L \times 7}$ from $\nu$ . $L$ indicates the sequence length. The character's initial body pose, which exhibits significant scale and pose differences compared to the driving video, is also extracted from $\mathcal{I}$ . Next, the image $\mathcal{I}$ and all the reference and driving pose images are encoded into the latent space through a VAE Encoder. The camera poses $\pmb{p}^c$ are processed through the Scene Motion Tracking strategy to obtain the pixel-wise scene motion guidance. Then, the Mixed-Control Diffusion is used to animate $\mathcal{I}$ guided by the mixed motion guidance of the character poses and scene motion in the latent space. Finally, the latent output is decoded through the VAE Temporal Decoder to produce the character art animation. + +# 3.1. Preliminaries on Stable Diffusion + +Stable Diffusion (SD) [28] is a popular Latent Diffusion Model for text-to-image generation. SD consists of a VAE [17] for auto-encoding the images, and a UNet [29] for noise estimation to iteratively transform a noise image into a latent image by the reverse diffusion process [12]. Given an input data distribution $\pmb{x}_0$ , the forward process applies a Markov noisng process of $T$ steps on $\pmb{x}_0$ to obtain $\{\pmb{x}_t\}_{t=0}^T$ : + +$$ +q \left(\boldsymbol {x} _ {t} \mid \boldsymbol {x} _ {t - 1}\right) = \mathcal {N} \left(\sqrt {\alpha_ {t}} \boldsymbol {x} _ {t - 1}, (1 - \alpha_ {t}) \boldsymbol {I}\right), \tag {1} +$$ + +where $\alpha_{t} \in (0,1)$ are constant hyper-parameters. When $\alpha_{t}$ is small enough, $\pmb{x}_{T} \sim \mathcal{N}(\pmb{0},\pmb{I})$ . The reverse process takes a noisier data distribution $\pmb{x}_{t}$ and generates a less noisy distribution $\pmb{x}_{t - 1}$ using an UNet, which is trained with the + +simple loss function: + +$$ +\mathcal {L} _ {\text {s i m p l e}} := \mathbb {E} _ {\boldsymbol {\epsilon}, t, c} \left[ \| \boldsymbol {\epsilon} - \boldsymbol {\epsilon} _ {\theta} (\boldsymbol {x} _ {t}, t, c) \| _ {2} ^ {2} \right], \tag {2} +$$ + +where $\epsilon$ is the Gaussian noise. $c$ is the text condition. $\epsilon_{\theta}(\cdot)$ is the trainable noise predictor. In this work, inspired by Animate Anyone [14], we utilize the pre-trained SD-1.5 as our base model to develop our animation pipeline, MikuDance. + +# 3.2. Mixed Motion Modeling + +Following existing human image animation methods [3, 14, 36], we use image-based pose sequences as motion guidance for characters. Unlike previous approaches that directly extract the character's whole-body poses, we separately extract poses for the body, face, and hands, allowing the face and hands to be optional and enabling more flexible motion control. However, character animation often involves high-dynamic motion throughout the entire scene to enhance the visual impact of storytelling. Traditional pose sequences offer only character motion guidance, lacking representations for background dynamics. To address this, we introduce the Scene Motion Tracking strategy. + +Scene Motion Tracking (SMT). As illustrated in Figure 3, given a camera pose $\pmb{p}_l^c$ from the driving video at the $l$ -th frame, a scene point cloud $\phi^l \in \mathbb{R}^{N \times 3}$ of the character art $\mathcal{I}$ is constructed in the $\pmb{p}_l^c$ coordinate system using the depth map of $\mathcal{I}$ . $N$ is the number of points, which depends on the size of the image. Next, $\phi^l$ is transferred into the world coordinate system through the camera-to-world matrix $\mathcal{T}^l \in \mathbb{R}^{N \times 4 \times 4}$ of $\pmb{p}_l^c$ , resulting in the point cloud $\phi^w$ . Subsequently, by applying the world-to-camera matrix $\mathcal{Y}^{l + 1} \in \mathbb{R}^{N \times 4 \times 4}$ of the camera pose $\pmb{p}_{l + 1}^c$ , we obtain the point cloud $\phi^{l + 1}$ for the next frame. Finally, we project $\phi^l$ and $\phi^{l + 1}$ into the image coordinate system using the intrinsic matrices $\mathcal{K} \in \mathbb{R}^{N \times 3 \times 4}$ of $\pmb{p}_l^c$ and $\pmb{p}_{l + 1}^c$ , respectively. The projected images are denoted as $\mathcal{I}^l$ and $\mathcal{I}^{l + 1}$ . Since these two projected images are rendered from the same scene point cloud in the world coordinate system, we can calculate the scene motion $m^s \in \mathbb{R}^{N \times 2}$ in the image space based on the correspondence of the points. This + +![](images/b02f40bfc0e4d6f7fdc4b37646097867b1fe597f34f6ea627994314146c89b57.jpg) +Figure 3. Illustration of the Scene Motion Tracking strategy. To effectively guide global background motion, 3D camera poses extracted from the driving video are transformed into a pixel-wise 2D space through the projection of the scene's point cloud (PC). + +process is formulated as: + +$$ +\left(\boldsymbol {z} ^ {l} - \boldsymbol {z} ^ {l + 1}\right) \left[ \begin{array}{c} \boldsymbol {m} ^ {s} \\ \boldsymbol {1} \end{array} \right] = \mathcal {K} ^ {l} \left[ \begin{array}{c} \phi^ {l} \\ \boldsymbol {1} \end{array} \right] - \mathcal {K} ^ {l + 1} \mathcal {Y} ^ {l + 1} \mathcal {T} ^ {l} \left[ \begin{array}{c} \phi^ {l} \\ \boldsymbol {1} \end{array} \right], \tag {3} +$$ + +where $z$ represents the projected Z-axis coordinates, serving as a scale factor for the scene motion $\boldsymbol{m}^s$ . + +Notably, our SMT strategy diverges from the optical flow commonly used in video generation methods [6, 23] in two key respects: first, the scene motion extracted by SMT is independent of the driving video's content, whereas optical flow is content-dependent. Second, SMT tracks 3D points from the point cloud, while optical flow tracks pixel movements in the image domain, without considering the actual 3D scene. Consequently, our SMT strategy provides decoupled camera dynamic information, which is crucial for continuous background motion in character art animation. + +In the proposed SMT process, we assume that the character and scene are static and standardized in the first camera. However, in real applications of character art animation, the reference scene often misaligns with the camera scale of the driving video, and the character pose varies in each frame. This ambiguity cannot be explicitly eliminated and necessitates the model to be implicitly perception guided by the character pose and the art image. Therefore, we propose Mixed-Control Diffusion in the next section. + +# 3.3. Mixed-Control Diffusion + +The concept of our Mixed-Control Diffusion is to mix and fuse all motion guidance for the character and scene within a unified reference space, thereby achieving aligned motion control over the animation. + +As illustrated in Figure 2, drawing inspiration from Animate Anyone [14], we utilized the pre-trained SD-1.5 as the base Denoising UNet and a copy of it as the Reference UNet to achieve controllable image-to-video generation. Distinct from Animate Anyone and other related work, we eliminate separate encoders for motion guidance and simultaneously encode the reference character art, the reference pose, and all character pose guidance using the VAE Encoder, embedding them into the same latent space. Next, all embedded + +guidance is concatenated along the channel dimension to serve as the input for the Mixed-Control Reference UNet. To accommodate this mixed input, we expand the channel of the input convolution layer in the Reference UNet, initializing the added parameters with zero convolution weights [47]. Additionally, the reference image is embedded using the CLIP image encoder [27] and serves as the key features in the cross-attention operations of both the Denoising UNet and the Reference UNet. This process is commonly used in existing work and is therefore omitted from Figure 2. + +In each denoising step $t$ of the Mixed-Control Diffusion, the self-attention features from the Reference UNet are injected into the Denoising UNet through an addition operation. The Reference UNet requires inference only once, while the denoising process is repeated $T$ times. The experiments demonstrate that our mixed control approach outperforms other control encoding and fusion methods by effectively addressing the misalignments between the reference image and the motion guidance. Furthermore, since scene motion exerts a global influence on the animation frames, it is intuitive to integrate it with character motion using an adaptive normalization method, as introduced below. + +Motion-Adaptive Normalization (MAN) is designed to effectively mix the extracted pixel-wise scene motion, $m^s$ , and enhance the temporal consistency of both foreground and background animations. + +Inspired by SPADE [24], which employs a spatial-aware normalization method to capture semantics for image synthesis, we propose to implement spatial-aware normalization adapted by scene motion, as shown in the right part of Figure 2. Let the mixed motion feature of the $i$ -th block in the Reference UNet be denoted as $\pmb{f}^i$ . We first normalize it using the Instance Normalization operation. Then, the scene motion $\pmb{m}^s$ is processed through three convolutional layers to obtain the motion-adapted standard deviation $\gamma^i \in \mathbb{R}^{C \times H \times W}$ and the mean $\beta^i \in \mathbb{R}^{C \times H \times W}$ . Here, $C$ , $W$ , $H$ represent the channel, height, and width of the feature, respectively. It is important to note that both $\beta^i$ and $\gamma^i$ have spatial dimensions, enabling pixel-wise guidance + +![](images/eabe6b60f84460a03c6765b046dd3bf0e5b79e4f8262890535ff1b8bc304d211.jpg) +Figure 4. The mixed-source training approach. We utilize synthetic stylized video frames and non-character videos in the two training stages, respectively, to enhance generalizability. + +![](images/65853be1b737a26e50b1194ca4d785c66613753faee16b652c1f3aab24c2f957.jpg) + +of the entire scene motion. This process is formulated as: + +$$ +\boldsymbol {f} ^ {i ^ {\prime}} = \gamma_ {C, H, W} ^ {i} \left(\boldsymbol {m} ^ {s}\right) \frac {\boldsymbol {f} _ {C , H , W} ^ {i} - \boldsymbol {\mu} _ {C} ^ {i}}{\boldsymbol {\sigma} _ {C} ^ {i}} + \beta_ {C, H, W} ^ {i} \left(\boldsymbol {m} ^ {s}\right), \tag {4} +$$ + +where $\pmb{\mu}_{C}^{i}$ and $\sigma_{C}^{i}$ are the mean and standard deviation of $\pmb{f}^{i}$ along the channel dimension. + +With the proposed Mixed Motion Modeling and Mixed-Control Diffusion, along with the incorporation of the MAN module after each down-sampling block in the Reference UNet, we outline the complete pipeline of our MikuDance. Furthermore, to enhance MikuDance's ability to accommodate various styles of character art and the dynamics of large-scale camera movements, we present a mixed-source training approach in the next section. + +# 3.4. Mixed-Source Training Approach + +Considering that image animation is a data-intensive task, proposing an effective data and training pipeline is as crucial as the model itself. In our MikuDance, as illustrated in Figure 4, we adopt a mixed-source training approach with two-stage training stages. + +In the first stage, training is conducted using pair-wise video frames, without incorporating the MAN module of the Reference UNet or the temporal module of the Denoising UNet. Different from existing methods [14, 37], we randomly mix stylized pair-wise frames by concatenating the initial frames along the spatial dimension and utilize the depth and edge-controlled anime SDXL model [26, 47], known as SDXL-Neta [18], to transfer the art style while preserving the image content. Additionally, to simulate the inference process in which the reference character art is irrelevant to the driving pose, we randomly select reference frames that are not involved in the target sequence. + +In the second stage, both the MAN module and the temporal module are incorporated into our Mixed-Control Diffusion model, while the other parameters remain frozen during this phase. The training data in this stage consists of mixed MMD video clips and camera movement videos that do not include characters. Importantly, we randomly drop the pose and motion guidance during the two-stage training to enhance the robustness of our MikuDance. + +# 4. Experiments + +Datasets. To train our MikuDance, we collected an MMD video dataset comprising 3,600 animations created by artists, all rendered from 3D models. We split these videos into approximately 120,000 clips, which together include over 10.2 million frames. Additionally, we incorporated around 3,500 non-character camera movement videos in the second training stage. For quantitative evaluation, we used 100 MMD videos that were not included in the training set, with their first frames serving as reference images. We used Xpose [44] for character pose and DROID-SLAM [33] for camera pose extraction. For qualitative evaluation, all character art was randomly generated using SDXL-Neta [18] and the driving videos were unseen during training. + +Implementation details. We implement MikuDance using the SD-1.5 framework [28] and PyTorch [25]. Experiments are conducted on 16 NVIDIA A800 GPUs. In the first training stage, the video frames are center-cropped and resized to a resolution of $768 \times 768$ . Training is conducted for 120,000 steps with a batch size of 128. In the second training stage, we train the MAN module and the temporal module for 60,000 steps using 24-frame video sequences and a batch size of 16. Both learning rates are set to 1e-5, and the dropout ratio for the pose and scene motion guidance is set to 0.2. During inference, we use a DDIM sampler for 20 denoising steps. We adopt the temporal aggregation method described in [34] to generate long videos. + +Evaluation metrics. Following DISCO [36], we evaluate the results from two aspects: image and video. To assess image quality, we report frame-wise FID [10], SSIM [38], LISPIS [48], PSNR [13], and L1. For video quality, we concatenate every consecutive 16 frames to form a sample, from which we report FID-VID [1] and FVD [35]. + +# 4.1. Qualitative Results + +Comparison with the baselines. We compare our Miku-Dance with recent human video generation methods, includingAnimate Anyone (AniAny) [14], DISCO [36], MagicPose [3], and UniAnimate [37], all of which claim the capability to animate anime-style characters in their official reports. Additionally, we implemented AniAny* by fine-tuning the model on our MMD video dataset. + +The results in Figure 5 show that AniAny, MagicPose, and UniAnimate fail to address the misalignment of character shape and scale, resulting in character distortion in their outputs. While DISCO uses independent ControlNets to process background and foreground features, its results suffer from scene collapse when animating character art. Although AniAny* is specifically fine-tuned on the animestyle dataset, its results show limited improvements and blurring in high-dynamic motion, as the pipeline fails to account for background scene motion. Notably, MikuDance + +![](images/ac7273a721da0fd10d608a7591f2ea73257868979d8a819e4b974ed83344a3eb.jpg) +Figure 5. Comparison with the baselines. AniAny* is the fine-tuned version of the AniAny model, trained on our MMD video dataset. + +![](images/9aeb8b3c23250015a77df5e2ff1c3b8b1c5e30e2dd95edc34ec9ebd3ee0a2d9f.jpg) +Figure 6. Experiments on high-dynamic motion guidance. Large camera movements (left) and significant pose variations (right). + +effectively handles complex reference and motion guidance, delivering high-quality and vivid animation results. + +High-dynamic motion. A key highlight of MikuDance is its ability to handle high-dynamic motion guidance in animation, which goes beyond the simple actions used in existing methods. As shown in Figure 6, the character performs large dance movements with a fast-moving camera. Despite these challenging conditions, MikuDance, equipped with our Mixed Motion Modeling approach, demonstrates remarkable robustness, delivering high-fidelity animation results that effectively capture the dramatic visual impact. + +Reference-guidance misalignments. Another key contribution of MikuDance is its implicit alignment of the reference character with motion guidance. As illustrated in Figure 7, two examples show significant spatial and scale misalignments between the guidance and the reference. In such cases, existing methods like AniAny struggle to animate the reference character effectively, whereas MikuDance successfully manages these complexities and generates coherent animations. + +Various shapes and scales. MikuDance effectively handles variations in character shapes and scales. As shown in the left part of Figure 8, characters with distinct body shapes, various poses, and different clothing are precisely driven by the same motion guidance. In the right part of Figure 8, MikuDance demonstrates its ability to implicitly align characters of varying scales, preserving each character's unique features and producing reasonable animation results. + +Generalizability on various art styles. As illustrated in Figure 9, MikuDance, leveraging our mixed-source training approach, can handle a wide range of art styles, including but not limited to celluloid, antiquity, and line sketch. This high level of generalizability opens up broad prospects for real-world applications. + +Ablation study. We conduct ablation experiments to verify the key designs of our MikuDance, as shown in Figure 10, which include the mixed-control architecture (MIX), the MAN module, and the SMT strategy. + +To evaluate the mixed-control design, we implemented a pipeline (w/o MIX) inspired by AniAny, utilizing an in- + +![](images/378c54b8860c7cbed541f31d0956112ff0f02a6ca020bd073f03d54d060593b3.jpg) +Figure 7. Experiments on misalignments between reference images and driving poses. Spatial (left) and scale (right) misalignments. + +![](images/b6b3beadde4bd0acff67b637533df5c835e80b7648a7179636eae0f54e70e134.jpg) + +![](images/d466ac4756df721f3f4d6c9641e93e85a74ad712e1b885e1129f6890b64147b6.jpg) + +![](images/a68bee566d6d29df391460dc31f389df0781fad859a4c0739b0a9e777f7eea1f.jpg) + +![](images/9dc4742a5f97b4b72f8ae24abbdae82de1aacf54fea6cf30438a51a4516f4c0c.jpg) + +![](images/b5e8df38b1d73a92ecb5f65eae6f16c805e75231b04b6206ab494942e4d9e61b.jpg) +Figure 8. Experiments on various shapes (the left part) and scales (the right part) of the reference character art. + +![](images/eca7b2756b3dee0ba71205dcd934e7eb360606822afec559ccd9017733dcfcfb.jpg) + +![](images/f80c681b97df95234dd659eee8b8169df31ad17087355803b93a20a8e68b258b.jpg) + +![](images/ade6c9c7e6d435e5e725a14bec41d35f9eae63f478e59f6e14fee01ab303fce7.jpg) + +![](images/85b2cd997ef7e2724b1fd71a0963ab29af597bc8bb05a6ede7a3bf63b0ea05f5.jpg) + +![](images/a073db781c5e9b65279def11fedb47de6ea2e4c04765ca9c2568b2802deecc03.jpg) + +![](images/cb188e713134f5326af8eb3b17cada4d0a10597b5e434b105b91698922225a9f.jpg) +Figure 9. Experiments on various styles of the reference character art. Please see Appendix for more results. + +![](images/5a9354704f4ae7e4e2c6191b84300c64a5fe937e1bff3ad26fe9e0ede90cea01.jpg) + +![](images/dc276b9ff17ba739d0da4dbbeddd4bac6ad068f61b90c7911b37779a5a447daf.jpg) + +dependent Reference UNet to process the reference image and two ControlNets to separately adapt the character and scene motion guidance. The results indicate that this conventional pipeline fails to account for scale differences between the character art and the driving guidance, leading to a mismatched appearance of the character's face and pose. + +To evaluate the effectiveness of the MAN module, we implemented a pipeline without MAN (w/o MAN) that simply concatenates scene motion with character motion and inputs them together into the Reference UNet. While this approach yields better results than a pipeline without scene motion guidance (w/o SMT), it remains inferior to the results achieved by MikuDance. This is because the MAN module injects global motion through spatial-aware normalization, effectively complementing the local motion. + +To evaluate the SMT strategy, we conducted three experiments: one pipeline without incorporating scene motion + +(w/o SMT), and two pipelines that replaced the scene motion with Plücker embedding (w/ Plücker) and optical flow (w/ Flow), respectively. However, the results from these alternative approaches were inferior to our SMT strategy, showing noticeable artifacts and inconsistencies in the dynamic backgrounds. The pixel-wise scene motion extracted by SMT proved to be a more effective representation for guiding background motion due to its domain consistency with the character motion guidance. + +Compared to the ablative studies introduced above, our MikuDance effectively addresses the misalignment and high-dynamic challenges in animating character art. + +# 4.2. Quantitative Results + +Table 1 presents quantitative comparisons between Miku-Dance and the baseline methods. It is important to note that the metrics reported in our paper are lower than those in + +![](images/3fae6add34916b044495709876ec1306aad418209a57dcb1b4c8bc72779cc7c3.jpg) +Reference +Figure 10. Ablation experiments on the key designs of MikuDance. MIX, SMT, MAN, Plucker, and Flow are defined in Section 4.1. + +![](images/e8afdf93039491e465227fa8b7bb745f3d727365ac0db6cf1de059afb443ed0f.jpg) +MikuDance + +![](images/8e3c1a16e825d1d2ba93e17c20d483acadf3b17fe845a55a2e90c1ce4fd22e8b.jpg) +Ablation for Mixed-Control Diffusion + +![](images/36c5ab065bd1f2b812284fd239a7d1d95b92d5144bc3f9d56e8282cf376f9b76.jpg) +Ablation for Mixed Motion Modeling + +Table 1. Quantitative comparisons with baselines and ablative experiments. AniAny* is the fine-tuned version of the AniAny model. MIX, SMT, MAN, Plücker, and Flow are defined in Section 4.1. The best results are highlighted in bold, and the second-best are underlined. MikuDance achieves superior results across all metrics. + +
MethodsImageVideo
FID↓SSIM↑PSNR↑LISPIS↓L1↓FID-VID↓FVD↓
AniAny [14]43.9450.48812.5300.5487.307E-0538.179846.414
AniAny*28.8330.52613.6100.5176.229E-0526.764575.304
DISCO [36]59.2210.31310.7320.6159.248E-0546.852923.921
MagicPose [3]44.2580.42412.3570.5547.767E-0541.347886.691
UniAnimate [37]47.3280.41712.0740.5717.930E-0540.924882.245
MikuDance w/o MIX27.3150.52314.0040.5285.860E-0524.124541.453
MikuDance w/o MAN24.9850.54214.5010.5055.753E-0523.366509.342
MikuDance w/o SMT25.4720.53414.3120.5125.911E-0523.362517.673
MikuDance w/ Plüc.25.9180.53814.2610.5106.011E-0523.471521.853
MikuDance w/ Flow26.1410.51614.0880.5235.925E-0523.079505.533
MikuDance (Ours)24.5970.57614.5920.4935.726E-0522.868502.380
+ +![](images/f9a2b460890eb2e32de4b868db9e1bdbe10f0c2e7eb0a41fdeead4ea26bc8af5.jpg) +MikuDance + +![](images/c94628050349c0b477b654dbc961d6348569e7049a00f7fa0e2af3a8fa525b67.jpg) + +![](images/e02c50f08a8b75b629bc57e7bb626a7c4d9b3691c5e6fa225497727926510500.jpg) + +![](images/4267c95969672eb979fff5a282a18b283e3ee0f0b24ce5c55155053977269b6d.jpg) +UniAnimate +Figure 11. User Study. The smaller value means the better quality. + +previous studies, as the entire scene in our testing videos is highly dynamic, unlike the static backgrounds used in earlier datasets. Nevertheless, the results demonstrate that MikuDance achieves state-of-the-art performance across all image and video metrics. Additionally, the ablation results confirm the effectiveness of the key design elements in MikuDance. In summary, by incorporating the proposed mixed motion dynamics techniques, MikuDance can animate a wide range of characters and generate high-quality image and video results. + +User study. We invited 50 volunteers and gave them 20 videos to evaluate the performance of our MikuDance against the baseline methods. Each video includes one motion guidance and four anonymous animation results. We + +ask users to rank the four results in overall quality, frame quality, and temporal quality. After excluding abnormal questionnaires, the average rank of the methods is summarized in Figure 11. Our MikuDance outperforms the baseline methods by a large margin, and more than $97\%$ of users prefer the animation generated by our MikuDance. + +# 5. Conclusions + +In this work, we propose MikuDance, a new animation pipeline designed to generate high-dynamic animations for in-the-wild character art. MikuDance incorporates two key techniques: Mixed Motion Modeling and Mixed-Control Diffusion. Mixed Motion Modeling enables the representation of large-scale character and scene motions within a unified reference space, while Mixed-Control Diffusion addresses misalignment between characters and motion guidance. To support diverse art styles, we also employ a mixed-source training approach to enhance generalizability. Extensive experiments demonstrate that MikuDance achieves state-of-the-art performance compared to baseline methods. Limitations. We acknowledge that some generated animations exhibit background distortions and artifacts. This issue stems from the 3D-agnostic challenge in image animation, making scene reconstruction in dynamic cameras an ill-posed problem that requires further investigation. + +Acknowledgements. This work was supported by the Young Scientists Fund of the National Natural Science Foundation of China No. 624B2110, the National Key Research and Development Program of China No. 2024YFC3015600, and the Fundamental Research Funds for Central Universities No.2042023KF0180 & No.2042025KF0053. The numerical calculations are supported by the supercomputing system at the Supercomputing Center of Wuhan University and StepFun. + +# References + +[1] Yogesh Balaji, Martin Renqiang Min, Bing Bai, Rama Chellappa, and Hans Peter Graf. Conditional gan with discriminative filter generation for text-to-video synthesis. In IJCAI, page 2, 2019. 5 +[2] Ankan Kumar Bhunia, Salman Khan, Hisham Cholakkal, Rao Muhammad Anwer, Jorma Laaksonen, Mubarak Shah, and Fahad Shahbaz Khan. Person image synthesis via denoising diffusion model. 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Champ: Controllable and consistent human image animation with 3d parametric guidance. arXiv preprint arXiv:2403.14781, 2024. 1, 2 \ No newline at end of file diff --git a/ICCV/2025/MikuDance_ Animating Character Art with Mixed Motion Dynamics/images.zip b/ICCV/2025/MikuDance_ Animating Character Art with Mixed Motion Dynamics/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8676c562cd4b2b3865248465574ca2e40ac7f2c4 --- /dev/null +++ b/ICCV/2025/MikuDance_ Animating Character Art with Mixed Motion Dynamics/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c4188a38701a0fdeb63958a13edbc1a89294273a24596d8a9267db226253878b +size 1328074 diff --git a/ICCV/2025/MikuDance_ Animating Character Art with Mixed Motion Dynamics/layout.json b/ICCV/2025/MikuDance_ Animating Character Art with Mixed Motion Dynamics/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..beb029f2484c37939860ecc54f06ac56cde8cc81 --- /dev/null +++ b/ICCV/2025/MikuDance_ Animating Character Art with Mixed Motion Dynamics/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5734a2680b9c0aad9a31dde9e703af61770df68c73e8c7656402534ab039d962 +size 397926 diff --git a/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/263d65a0-205e-4c5b-8b91-03badcdf7c38_content_list.json b/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/263d65a0-205e-4c5b-8b91-03badcdf7c38_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..756f38afcfdad44f4088c4074c5682cffab488f6 --- /dev/null +++ b/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/263d65a0-205e-4c5b-8b91-03badcdf7c38_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4f07e79da9603389bed652234661a8c51b665bb49284999ebee47117fad89ea9 +size 83149 diff --git a/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/263d65a0-205e-4c5b-8b91-03badcdf7c38_model.json b/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/263d65a0-205e-4c5b-8b91-03badcdf7c38_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3e4cb3d88f917f5cf7e558c6a51296577b371335 --- /dev/null +++ b/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/263d65a0-205e-4c5b-8b91-03badcdf7c38_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:75f81bf4a9e5009789e77fcb91a48c0d520d981c109268546e157479a6b957a0 +size 99235 diff --git a/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/263d65a0-205e-4c5b-8b91-03badcdf7c38_origin.pdf b/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/263d65a0-205e-4c5b-8b91-03badcdf7c38_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..d11192b0a024a805a5fa0e5d9728364274b7a44d --- /dev/null +++ b/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/263d65a0-205e-4c5b-8b91-03badcdf7c38_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:dd37428aada2847a9bb9d6a59f9c5cd5489fa8abe71230b91e9322f3af37002d +size 4858339 diff --git a/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/full.md b/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/full.md new file mode 100644 index 0000000000000000000000000000000000000000..c9ff6eae1ab73e8ace6e12d425fcbc94d5318e1e --- /dev/null +++ b/ICCV/2025/MinCD-PnP_ Learning 2D-3D Correspondences with Approximate Blind PnP/full.md @@ -0,0 +1,300 @@ +# MinCD-PnP: Learning 2D-3D Correspondences with Approximate Blind PnP + +Pei An $^{1*}$ , Jiaqi Yang $^{2*}$ , Muyao Peng $^{1}$ , You Yang $^{1\dagger}$ , Qiong Liu $^{1}$ , Xiaolin Wu $^{3}$ , Liangliang Nan $^{4}$ $^{1}$ Huazhong University of Science and Technology, China + $^{2}$ Northwestern Polytechnical University, China + $^{3}$ Southwest Jiaotong University, China + +# Abstract + +Image-to-point-cloud (I2P) registration is a fundamental problem in computer vision, focusing on establishing 2D-3D correspondences between an image and a point cloud. Recently, the differentiable perspective-n-point $(PnP)$ has been widely used to supervise I2P registration networks by enforcing projective constraints on 2D-3D correspondences. However, differentiable $PnP$ is highly sensitive to noise and outliers in the predicted correspondences, which hinders the effectiveness of correspondence learning. Inspired by the robustness of blind $PnP$ to noise and outliers in correspondences, we propose an approximate blind $PnP$ -based correspondence learning approach. To mitigate the high computational cost of blind $PnP$ , we reformulate it as a more tractable problem: minimizing the Chamfer distance between learned 2D and 3D keypoints, referred to as MinCD-PnP. To effectively solve MinCD-PnP, we introduce a lightweight multi-task learning module, MinCD-Net, which can be easily integrated into the existing I2P registration architectures. Extensive experiments on 7-Scenes, RGBD-V2, ScanNet, and self-collected datasets demonstrate that MinCD-Net outperforms state-of-the-art methods and achieves higher inlier ratio and registration recall in both cross-scene and cross-dataset settings. The source code: https://github.com/anpei96/mincd-pnp-demo. + +# 1. Introduction + +Image-to-point-cloud (I2P) registration [12] is a fundamental task in computer vision [2], aiming to establish 2D-3D correspondences between images and point clouds [35]. These correspondences are used to estimate the six-degree-of-freedom (6 DoF) camera pose with the perspective-n-point (PnP) algorithm [23], enabling I2P registration by aligning images with point clouds. Thus, I2P registration is + +![](images/587f3ebbf22b94097e44ac99d926438d338cb8f2b7b766eace60b76609df3b24.jpg) +Figure 1. To overcome the limitation of feature-level matching, differentiable PnP employs the projective constraints of 2D-3D correspondences but is highly sensitive to correspondence quality. In this paper, we incorporate blind PnP to enhance I2P registration and achieve a salient improvement compared to other methods. + +widely used in visual localization, navigation, visual odometry, 3D reconstruction, and so on [1, 13, 21, 26, 34]. + +Learning-based approaches have gained significant attention in I2P registration [1, 35]. Deep neural networks (DNNs) help bridge the modality gap between images and point clouds [2, 25] by estimating 2D-3D correspondences through pixel-to-point feature-level matching (i.e., comparing feature distances between each 2D pixel and 3D point) [12]. However, feature-level matching struggles to remove outliers, as it ignores the projective constraints inherent in 2D-3D correspondences, as shown in Fig. 1. + +To utilize the constraints of projective geometry in learning 2D-3D correspondences, the mainstream technique leverages differentiable perspective-n-point (PnP) [4, 6, 42]. The objective is to refine camera pose estimation via differentiable PnP, thereby improving the accuracy of global projective correspondences. However, differentiable PnP is highly sensitive to noise and outliers in the predicted correspondences [37]. This issue makes the estimated camera pose unreliable, thus hindering the effectiveness of differentiable PnP on correspondence learning. + +To overcome the limitations of differentiable PnP, inspired by the robustness of blind PnP against noise and outliers in correspondences [5], we propose an approximate blind PnP based 2D-3D correspondence learning approach. Since blind PnP is computationally expensive [5], we reformulate it as a task of minimizing Chamfer distance between the learned 2D and 3D keypoints, called MinCD-PnP in the sequel. MinCD-PnP ensures the feasibility of learning correspondence with blind PnP and retains the robustness of blind PnP to noise and outliers in correspondences. To effectively solve MinCD-PnP, we propose a lightweight multi-task learning module, denoted by MinCD-Net. Operationally, MinCD-Net can be seamlessly integrated into the existing I2P registration architectures and jointly optimized in an end-to-end manner. Extensive experiments on the 7-Scenes [14], RGBD-V2 [22], ScanNet [8], and self-collected datasets show that MinCD-Net achieves a higher inlier ratio (IR) and registration recall (RR) than state-of-the-art methods in both cross-scene and cross-dataset settings. Our core contributions are: + +- We introduce MinCD-PnP, a formulation that simplifies blind PnP into a more tractable task of minimizing the Chamfer distance between learned 2D and 3D keypoints. +- We design a lightweight, multi-task learning module, MinCD-Net, to effectively solve MinCD-PnP. It can be easily integrated into existing I2P registration pipelines. +- MinCD-Net achieves superior performance across five datasets, outperforming state-of-the-art methods in both cross-scene and cross-dataset generalization. + +# 2. Related Work + +I2P registration. Most I2P registration methods rely on deep learning, as DNNs help bridge the modality gap between images and point clouds. Feng et al. designed the first deep learning based method for I2P registration, training a DNN to learn 3D keypoints descriptors [12]. Li and Lee [24] developed DeepI2P, which enhances the feature representation through global feature interaction. Ren et al. [29] further refined this approach in 2023. Building on the image registration method D2-Net [10], Wang et al. [35] developed P2-Net, which jointly learns 2D-3D keypoints and their descriptors. Circle loss [32] was used to alleviate the extreme imbalance between inliers and outliers. Li et al. [25] followed the point cloud registration architecture GeoTrans [28] to develop 2D3D-MATR, which outperformed P2-Net [35]. This work was further improved by Wu et al. [38] in 2024 by integrating a diffusion model [17] to iteratively denoise correspondence matrix. In 2024, An et al. [2] introduced Proj-ICP, a non-learning algorithm to estimate camera pose by minimizing the 2D-3D contour distances. They also surveyed to summarize the I2P registration methods for LiDAR-camera extrinsic calibration [1]. Wang et al. [36] designed an architecture, FreeReg which + +utilized the pre-trained vision fundamental models to minimize the modality difference between images and point clouds. Based on the above discussions, most current methods follow a pixel-to-point feature-matching paradigm to establish correspondences. + +Learning correspondences with PnP. Recent research has highlighted the absence of the geometrical constraint in I2P registration, leading to the development of differentiable PnP for improved correspondence learning. In 2023, Zhou et al. [42] explored the effect of end-to-end probabilistic PnP (EPro-PnP) [6] on the 2D-3D correspondence learning task. Although EPro-PnP is robust to correspondence noise, its performance becomes unstable in the presence of excessive outliers. In 2024, Wu et al. [38] regarded correspondence learning as a denoising procedure and combined the diffusion model with differentiable PnP to refine 2D-3D correspondences. To make differentiable PnP more robust to correspondence noise and outliers, Campbell et al. [4] were the first to study blind PnP and designed a weighted differentiable blind PnP layer based on a declarative network [15]. In their work [4], RANSAC-based PnP [9] filters correspondences with large noises, and the declarative network computes the loss backward gradient of RANSAC-based PnP layer. Although work [4] is robust to correspondence noise and outliers, the loss gradient from filtered correspondences provides limited benefits to the overall I2P architecture. Thus, an effective differentiable PnP for I2P registration is still an open problem. + +# 3. Problem Formulation and Analysis + +In this section, we revisit I2P registration from an optimization perspective and analyze the bottleneck of 2D-3D correspondence learning (as illustrated in Fig. 2). For a given pixel $q \in \mathcal{I}$ and a point $p \in \mathcal{P}$ , their correspondence $\langle q, p \rangle$ is determined using feature-level matching [25, 35, 36]: + +$$ +d \left(\mathbf {f} _ {q} ^ {\mathrm {2 D}}, \mathbf {f} _ {p} ^ {\mathrm {3 D}}\right) \leq \delta \Rightarrow \langle q, p \rangle \text {i s a c o r r e s p o n d e n c e} \tag {1} +$$ + +$$ +\mathbf {F} _ {\mathrm {I}}, \mathbf {F} _ {\mathrm {P}} = \varphi (\mathcal {I}, \mathcal {P}) \tag {2} +$$ + +where $d(\cdot, \cdot)$ represents the per-feature normalized $L_{2}$ distance, and $\delta$ is a predefined threshold. The features $\mathbf{f}_q^{2\mathrm{D}}$ and $\mathbf{f}_p^{3\mathrm{D}}$ on $q$ and $p$ are extracted from $\mathbf{F}_{\mathrm{I}}$ and $\mathbf{F}_{\mathrm{P}}$ , respectively, and $\varphi$ denotes the neural network used for I2P registration. It is learned by the following optimization problem: + +$$ +\varphi^ {\star} = \arg \min _ {\varphi} \sum_ {p, q} L _ {\text {c o r r}} \left(\mathbf {f} _ {q} ^ {2 \mathrm {D}}, \mathbf {f} _ {p} ^ {3 \mathrm {D}}\right) \tag {3} +$$ + +where $p, q$ are pixel-to-point pair that satisfies Eq. (1). $L_{\mathrm{corr}}$ is the common correspondence loss, such as circle loss [32], because it helps mitigate the severe imbalance between inliers and outliers [25, 35]. + +![](images/0bb78d2266374b397a55d9b3fe143f21c95c837f0abb216c330946109c6d7fad.jpg) +Figure 2. Motivation for the proposed MinCD-PnP. First, we analyze correspondence learning from an optimization perspective and observe that blind PnP is robust to the correspondence quality. To mitigate the complexity of blind PnP, we simplify blind PnP as a new task, MinCD-PnP, using a triple approximation strategy. + +The optimization in Eq. (3) is suboptimal, as it ignores the projective constraint of $\langle q,p\rangle$ . A valid correspondence $\langle q,p\rangle$ must satisfy $q = \pi (\mathbf{T}p)$ , where $\pi (\cdot)$ represents the camera projection operator [40]. $\mathbf{T}$ is the transformation from the point cloud to the camera coordinate system. Differentiable PnP based methods incorporate projective constraints [38, 42] by refining Eq. (3) as: + +$$ +\min _ {\varphi} \left(\sum_ {p, q} L _ {\text {c o r r}} \left(\mathbf {f} _ {q} ^ {2 \mathrm {D}}, \mathbf {f} _ {p} ^ {3 \mathrm {D}}\right) + \alpha \| \hat {\mathbf {T}} - \mathbf {T} \| _ {2} ^ {2}\right) \tag {4} +$$ + +$$ +\hat {\mathbf {T}} = \arg \min _ {\mathbf {T}} \sum_ {p, q} \mathbb {I} \left(d \left(\mathbf {f} _ {q} ^ {\mathrm {2 D}}, \mathbf {f} _ {p} ^ {\mathrm {3 D}}\right) \leq \delta\right) \cdot \| q - \pi (\mathbf {T} p) \| _ {2} ^ {2} \tag {5} +$$ + +where $\| q - \pi (\mathbf{T}p)\| _2$ measures the reprojection error of correspondence $\langle q,p\rangle$ . $\mathbb{I}(x)$ is an indicator function that outputs 1 if $x$ is true, or 0 otherwise. Equations (4) and (5) form a coupled optimization problem, with $\alpha$ controlling the weight of the pose loss. In Eq. (4), the term $\| \hat{\mathbf{T}} -\mathbf{T}\| _2^2$ enforces global geometric consistency and improves the accuracy of estimated correspondences. However, solving Eq. (5) is highly sensitive to noise and outliers in the correspondences [37]. Moreover, since $\varphi$ inevitably predicts outliers and noisy inliers, existing differentiable PnP methods struggle to improve correspondence learning effectively. + +# 4. Proposed Method + +# 4.1. Motivation + +We aim to enhance 2D-3D correspondence learning by leveraging blind PnP. An overview of the proposed ap + +proach is illustrated in Fig. 2. With the blind PnP cost function [5], we revise Eq. (3) as: + +$$ +\min _ {\varphi} \left(\sum_ {p, q} L _ {\mathrm {c o r r}} \left(\mathbf {f} _ {q} ^ {2 \mathrm {D}}, \mathbf {f} _ {p} ^ {3 \mathrm {D}}\right) - \max _ {\mathbf {T}, \mathbf {C}} \kappa (\mathbf {T}, \mathbf {C} | \mathbf {S} _ {\mathrm {I}} (\varphi), \mathbf {S} _ {\mathrm {P}} (\varphi))\right) +$$ + +$$ +\text {s . t .} \mathbf {T} \in \mathbf {S E} (3), \mathbf {C} \in \mathbb {B} ^ {M \times N}, \mathbf {S} _ {\mathrm {I}} = \left\{q _ {i} \right\} _ {i = 1} ^ {M}, \mathbf {S} _ {\mathrm {P}} = \left\{p _ {i} \right\} _ {i = 1} ^ {N} \tag {6} +$$ + +$$ +\kappa (\mathbf {T}, \mathbf {C} | \mathbf {S} _ {\mathrm {I}}, \mathbf {S} _ {\mathrm {P}}) = \sum_ {\langle q, p \rangle \in \mathbf {C}} \mathbb {I} (\| q - \pi (\mathbf {T} p) \| _ {2} ^ {2} \leq \tau) \tag {7} +$$ + +where $\mathbf{S}_{\mathrm{I}}(\varphi)$ and $\mathbf{S}_{\mathrm{P}}(\varphi)$ are pixel and point sets of the candidate correspondences, sampled from $\mathbf{F}_{\mathrm{I}}$ and $\mathbf{F}_{\mathrm{P}}$ via Eq. (1). As $\mathbf{F}_{\mathrm{I}}$ and $\mathbf{F}_{\mathrm{P}}$ are learned from $\varphi$ , $\mathbf{S}_{\mathrm{I}}(\varphi)$ and $\mathbf{S}_{\mathrm{P}}(\varphi)$ can be regarded as functions of $\varphi$ . For the discussion simplicity, $\mathbf{S}_{\mathrm{I}}(\varphi)$ and $\mathbf{S}_{\mathrm{P}}(\varphi)$ are simplified as $\mathbf{S}_{\mathrm{I}}$ and $\mathbf{S}_{\mathrm{P}}$ . $\mathbf{C}$ is a boolean $M\times N$ matrix to denote the correspondences between $\mathbf{S}_{\mathrm{I}}$ and $\mathbf{S}_{\mathrm{P}}$ . $\kappa (\mathbf{T},\mathbf{C}|\mathbf{S}_{\mathrm{I}},\mathbf{S}_{\mathrm{P}})$ denotes the inlier number, and $\tau$ is a pixel threshold to determine whether the correspondence is an inlier. Blind PnP is robust to noise and outliers in correspondences by jointly optimizing $\mathbf{T}$ and $\mathbf{C}$ . However, optimizing $\kappa (\mathbf{T},\mathbf{C}|\mathbf{S}_{\mathrm{I}},\mathbf{S}_{\mathrm{P}})$ is computationally intractable due to its high complexity [31], so blind PnP cannot be directly used for correspondence learning. + +# 4.2. MinCD-PnP formulation + +To address this challenge, we propose MinCD-PnP by simplifying blind PnP with a triple approximation strategy. + +# 4.2.1. Approximation I: from inlier maximization to Chamfer distance minimization + +First, we approximate the inlier maximization cost function $\kappa (\mathbf{T},\mathbf{C}|\mathbf{S}_{\mathrm{I}},\mathbf{S}_{\mathrm{P}})$ as a lightweight Chamfer distance minimization. To reach this goal, we study an inequality: + +$$ +\begin{array}{l} \max _ {\mathbf {T}, \mathbf {C}} \kappa (\mathbf {T}, \mathbf {C} | \mathbf {S} _ {\mathrm {I}}, \mathbf {S} _ {\mathrm {P}}) \leq \max _ {\mathbf {T}} \kappa (\mathbf {T}, \mathbf {C} ^ {\star} | \mathbf {S} _ {\mathrm {I}}, \mathbf {S} _ {\mathrm {P}}) \\ \leq \max _ {\mathbf {T}} \kappa^ {\star} (\mathbf {T} ^ {\star} | \mathbf {S} _ {\mathrm {I}}, \mathbf {S} _ {\mathrm {P}}) \\ \end{array} +$$ + +$$ +\begin{array}{l} \kappa^ {\star} (\mathbf {T} | \mathbf {S} _ {\mathrm {I}}, \mathbf {S} _ {\mathrm {P}}) = \sum_ {q \in \mathbf {S} _ {\mathrm {I}}} \mathbb {I} \left(\min _ {p \in \mathbf {S} _ {\mathrm {P}}} \| q - \pi (\mathbf {T} p) \| _ {2} ^ {2} \leq \tau\right) \\ + \sum_ {p \in \mathbf {S} _ {\mathrm {P}}} \mathbb {I} \left(\min _ {q \in \mathbf {S} _ {\mathrm {I}}} \| q - \pi (\mathbf {T} p) \| _ {2} ^ {2} \leq \tau\right) \tag {9} \\ \end{array} +$$ + +where $\mathbf{C}^{\star}$ is the optimal correspondence matrix and $\kappa (\mathbf{T},\mathbf{C}^{\star}|\mathbf{S}_{\mathrm{I}},\mathbf{S}_{\mathrm{P}})\geq \kappa (\mathbf{T},\mathbf{C}|\mathbf{S}_{\mathrm{I}},\mathbf{S}_{\mathrm{P}})$ . We explain the last term in inequality (8). For a correspondence $\langle q,p\rangle \in$ $\mathbf{C}^{\star}$ , based on the above assumption, we both have $q =$ arg $\min_{q\in \mathbf{S}_1}\| q - \pi (\mathbf{T}p)\| _2^2$ and $p = \arg \min_{p\in \mathbf{S}_{\mathrm{P}}}\| q -$ $\pi (\mathbf{T}p)\| _2^2$ . And $2\kappa (\mathbf{T}^{\star},\mathbf{C}^{\star}|\mathbf{S}_{\mathrm{I}},\mathbf{S}_{\mathrm{P}}) = \kappa^{\star}(\mathbf{T}^{\star}|\mathbf{S}_{\mathrm{I}},\mathbf{S}_{\mathrm{P}}) =$ $2N$ , where $\mathbf{T}^{\star}$ is the optimal pose. It leads to the last term in inequality (8). Based on inequality (8), we reformulate the inlier maximization objective in Eq. (6) as a Chamfer distance minimization cost function: + +$$ +\min _ {\varphi} \left(\sum_ {p, q} L _ {\text {c o r r}} \left(\mathbf {f} _ {q} ^ {2 \mathrm {D}}, \mathbf {f} _ {p} ^ {3 \mathrm {D}}\right) + \min _ {\mathbf {T}} L _ {\text {C h a m f e r}} (\mathbf {T} | \mathbf {S} _ {\mathrm {I}}, \mathbf {S} _ {\mathrm {P}})\right) \tag {10} +$$ + +$$ +\begin{array}{l} L _ {\text {C h a m f e r}} (\mathbf {T} | \mathbf {S} _ {\mathrm {I}}, \mathbf {S} _ {\mathrm {P}}) = \sum_ {q \in \mathbf {S} _ {\mathrm {I}}} \min _ {p \in \mathbf {S} _ {\mathrm {P}}} \| q - \pi (\mathbf {T} p) \| _ {2} ^ {2} \\ + \sum_ {p \in \mathbf {S} _ {\mathrm {P}}} \min _ {q \in \mathbf {S} _ {\mathrm {I}}} \| q - \pi (\mathbf {T} p) \| _ {2} ^ {2} \tag {11} \\ \end{array} +$$ + +Eq. (10) eliminates the $M \times N$ boolean matrix $\mathbf{C}$ in Eq. (6), which significantly reduces computation complexity + +# 4.2.2. Approximation II: reducing complexity in Cham-fer distance optimization with keypoints + +In the second stage, we introduce further refinements to improve the optimization efficiency of Eq. (10). Since images typically contain $10^{6}$ pixels and point clouds $10^{5}$ points, $M \times N$ can exceed $10^{11}$ , leading to a prohibitively expensive Chamfer distance computation. To address this problem, we sample the representative keypoints $\mathbf{K}_{\mathrm{I}} = \{q_{i}\}_{i=1}^{M_{0}}$ and $\mathbf{K}_{\mathrm{P}} = \{p_{i}\}_{i=1}^{N_{0}}$ from $\mathbf{S}_{\mathrm{I}}$ and $\mathbf{S}_{\mathrm{P}}$ , and revise Eq. (10) as: + +$$ +\min _ {\varphi} \left(\sum_ {p, q} L _ {\text {c o r r}} \left(\mathbf {f} _ {q} ^ {2 \mathrm {D}}, \mathbf {f} _ {p} ^ {3 \mathrm {D}}\right) + \min _ {\mathbf {T}} L _ {\text {C h a m f e r}} (\mathbf {T} | \mathbf {K} _ {\mathrm {I}}, \mathbf {K} _ {\mathrm {P}})\right) \tag {12} +$$ + +A key advantage of Eq. (12) is the reduction of the Chamfer distance matrix from $M \times N$ to $M_0 \times N_0$ . As 2D and 3D keypoints number is nearly $10^3$ , the matrix size is smaller than $10^5$ times. Although Eq. (12) improves optimization efficiency, a key challenge remains: how to effectively learn the representative $\mathbf{K}_{\mathrm{I}}$ and $\mathbf{K}_{\mathrm{P}}$ ? To ensure that $L_{\mathrm{Chamfer}}(\mathbf{T}|\mathbf{K}_{\mathrm{I}},\mathbf{K}_{\mathrm{P}})$ contributes effectively to $\varphi$ , $\mathbf{K}_{\mathrm{I}}$ and $\mathbf{K}_{\mathrm{P}}$ should sufficiently represent 2D and 3D spaces. + +# 4.2.3. Approximation III: learning 3D keypoints with the guidance of 2D keypoints + +To deal with the above learning problem of $\mathbf{K}_{\mathrm{I}}$ and $\mathbf{K}_{\mathrm{P}}$ , we design the third approximation that approximates joint 2D and 3D keypoints learning as a single learning task. We aim to learn 3D keypoints that mimic the 2D keypoints distribution, since jointly learning both with sufficient inliers is a challenging task [25]. In this scheme, $\mathbf{K}_{\mathrm{I}}$ is pre-detected using a pre-trained model or a non-learning algorithm. Existing 2D keypoints detectors ensure that $\mathbf{K}_{\mathrm{I}}$ captures representative structures in the image. Then, we design a 2D keypoints guided 3D keypoints learning scheme: + +$$ +\begin{array}{l} \min _ {\varphi} \sum_ {q \in \mathbf {K} _ {1}} \| q - \pi (\mathbf {T} p) \| _ {2} \\ \mathrm {s . t .} p = \underset {p \in \mathcal {P}} {\arg \min} d (\mathbf {f} _ {q} ^ {\mathrm {2 D}}, \mathbf {f} _ {p} ^ {\mathrm {3 D}}), q \in \mathbf {K} _ {\mathrm {I}} \\ \end{array} +$$ + +However, directly learning with Eq. (13) is unreliable, as some 2D keypoints lack salient features, making it difficult to identify corresponding 3D points. It makes the loss in Eq. (13) unstable. So, we approximate Eq. (13) as: + +$$ +\begin{array}{l} \min _ {\varphi} \sum_ {q \in \mathbf {K} _ {1}} L _ {\text {k e y}} (q) \tag {14} \\ = \sum_ {q \in \mathbf {K} _ {\mathrm {I}}} - \mathbb {I} \left(\left\| q - \pi \left(\mathbf {T} _ {\mathrm {g t}} p _ {q} ^ {\star}\right) \right\| _ {2} ^ {2} \leq \tau\right) \cdot \mathbb {I} \left(s _ {q} ^ {\star} \leq s _ {\mathrm {t h}}\right) \\ \end{array} +$$ + +$$ +\begin{array}{l} p _ {q} ^ {\star} = \arg \min _ {p \in \mathcal {P}} \left\{d \left(\mathbf {f} _ {q} ^ {\mathrm {2 D}}, \mathbf {f} _ {1} ^ {\mathrm {3 D}}\right), \dots d \left(\mathbf {f} _ {q} ^ {\mathrm {2 D}}, \mathbf {f} _ {p} ^ {\mathrm {3 D}}\right) \dots , d \left(\mathbf {f} _ {q} ^ {\mathrm {2 D}}, \mathbf {f} _ {N _ {0}} ^ {\mathrm {3 D}}\right) \right\} \\ s _ {q} ^ {\star} = \min _ {p \in \mathcal {P}} \left\{d \left(\mathbf {f} _ {q} ^ {\mathrm {2 D}}, \mathbf {f} _ {1} ^ {\mathrm {3 D}}\right), \dots d \left(\mathbf {f} _ {q} ^ {\mathrm {2 D}}, \mathbf {f} _ {p} ^ {\mathrm {3 D}}\right) \dots , d \left(\mathbf {f} _ {q} ^ {\mathrm {2 D}}, \mathbf {f} _ {N _ {0}} ^ {\mathrm {3 D}}\right) \right\} \tag {15} \\ \end{array} +$$ + +where the term $\min \{d(\mathbf{f}_q^{2\mathrm{D}},\mathbf{f}_1^{3\mathrm{D}}),\dots,d(\mathbf{f}_q^{2\mathrm{D}},\mathbf{f}_{N_0}^{3\mathrm{D}})\}$ approximates $d(\mathbf{f}_q^{2\mathrm{D}},\mathbf{f}_p^{3\mathrm{D}})$ . This implies that Eq. (15) aims to learn a set of 3D keypoints that best approximate the detected 2D keypoints in an error bound of $\tau$ . $s_{\mathrm{th}}$ is a threshold used to filter out low-confidence 3D keypoints. + +![](images/6a86a87e55c62c1a5134f70a6f359af78f60c0d00c9bc0700d1fe034d25d8a5e.jpg) +Figure 3. Proposed 2D-3D correspondence learning module, MinCD-Net. It converts the optimization in Eq. (16) into a multi-task learning mechanism. MinCD-Net can be integrated into existing I2P registration frameworks. + +Following the triple approximation, we formulate the proposed scheme as a new optimization problem that minimizes Chamfer distance and 3D keypoints learning losses: + +$$ +\begin{array}{l} \varphi^ {\star} = \arg \min _ {\varphi} \left(\sum_ {p, q} L _ {\text {c o r r}} \left(\mathbf {f} _ {q} ^ {2 \mathrm {D}}, \mathbf {f} _ {p} ^ {3 \mathrm {D}}\right) + \lambda_ {1} \sum_ {q \in \mathbf {K} _ {\mathrm {I}}} L _ {\text {k e y}} (q) \right. \\ \left. + \lambda_ {2} \min _ {\mathbf {T}} L _ {\text {C h a m f e r}} \left(\mathbf {T} \mid \mathbf {K} _ {\mathrm {I}}, \mathbf {K} _ {\mathrm {P}} (\mathbf {K} _ {\mathrm {I}})\right)\right) \tag {16} \\ \end{array} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are the loss weights. $\mathbf{K}_{\mathrm{P}}(\mathbf{K}_{\mathrm{I}})$ denotes that 3D keypoints are learned from 2D keypoints via Eq. (14). + +# 4.3. Correspondence learning with MinCD-PnP + +In Sec. 4.2, we have modeled the correspondence learning as a MinCD-PnP problem. To address the MinCD-PnP formulation, we introduce MinCD-Net, a lightweight multitask learning module, as shown in Fig. 3. Its core is to predict 3D keypoints and compute multi-task losses in Eq. (16). + +# 4.3.1. General architecture of I2P registration + +Before detailing the proposed MinCD-Net, we briefly review the architecture of the I2P registration network for clarity. As shown in the left part of Fig. 3, the current network incorporates two feature extractors for learning images and point clouds features $\mathbf{F}_{\mathrm{I}}$ and $\mathbf{F}_{\mathrm{P}}$ . The previous work [25] employs ResNet [16] and KPCov [33] as feature extractors for the two modalities. A key step in I2P registration is post-processing. Li et al. [25] designed a two-stage matching scheme inspired by GeoTrans [28]. In the first stage, 2D and 3D patch features (i.e., obtained from extractors) are used for the 2D-3D patches matching. Then, for every matched patch pair, correspondences are determined using Eq. (1). Overall, $\varphi$ in Eq. (2) encompasses two feature extractors, and $L_{\mathrm{corr}}$ is detailed in literature [25, 35]. + +# 4.3.2. Keypoints and Chamfer loss computation + +We provide the computational detail of $L_{\mathrm{key}}(q)$ in Eqs. (13-15). By computing the L2 distance between each 2D keypoint and each 3D point feature, we obtain a $M_0 \times N$ distance matrix $\mathbf{D} = (d_{ij})$ with $d_{ij} = d(\mathbf{f}_i^{2\mathrm{D}}, \mathbf{f}_j^{3\mathrm{D}})$ . Using the Pytorch API function min, elements in Eq. (15) are obtained. To efficiently evaluate $\mathbb{I}(\| q - \pi (\mathbf{T}_{\mathrm{gt}}p_q^\star)\|_2^2 \leq \tau)$ , we precompute an overlap mask in $\mathcal{P}$ , converting $L_{\mathrm{key}}(q)$ into a loss function based on the intersection of union (IoU) of two sets. We empirically set $s_{\mathrm{th}} = e^{-0.4}$ to achieve optimal performance. + +Next, we analyze the Chamfer loss $L_{\mathrm{Chamfer}}(\mathbf{T}|\mathbf{K}_{\mathrm{I}},\mathbf{K}_{\mathrm{P}})$ in Eq. (16). Minimizing this loss during training is computationally expensive. We predict $\mathbf{T}$ from $\mathbf{K}_{\mathrm{I}}$ and $\mathbf{K}_{\mathrm{P}}$ in an end-to-end manner, where $L_{\mathrm{Chamfer}}(\mathbf{T}|\mathbf{K}_{\mathrm{I}},\mathbf{K}_{\mathrm{P}})$ serves as a loss function. MinCD-Net employs the point transformer (PointTf) [41] to encode 2D and 3D keypoint features†, and then compute the global 2D and 3D features. By concatenating these global features, we use a series of multilayer perceptrons (MLPs) to estimate $\mathbf{T}$ [19]. Using $\mathbf{T}$ , we can transform the coordinates of $\mathbf{K}_{\mathrm{P}}$ and then compute the Chamfer loss $L_{\mathrm{Chamfer}}(\mathbf{T}|\mathbf{K}_{\mathrm{I}},\mathbf{K}_{\mathrm{P}})$ . + +# 4.3.3. Summary + +We summarize the impact of MinCD-Net on I2P registration below. First, MinCD-Net is robust to the noise and outliers in the predicted correspondences, because the proposed loss functions (i.e., $L_{\mathrm{key}}(q)$ and $L_{\mathrm{Chamfer}}(\mathbf{T}|\mathbf{K}_{\mathrm{I}},\mathbf{K}_{\mathrm{P}})$ ) are only related to $\mathbf{K}_{\mathrm{I}}$ and $\mathbf{K}_{\mathrm{P}}$ . It addresses the limitations of existing differentiable PnP schemes [4, 38, 42]. Second, MinCD-Net is effective in learning $\varphi$ . Since the pre-detected 2D keypoints can represent the 2D image, $L_{\mathrm{key}}(q)$ ensures that the learned 3D keypoints are + +Table 1. I2P registration performance for cross-scene generalization on the 7-Scenes datasets. Here $\dagger$ represents the average metrics across the unseen scenes. MinCD-Net achieves higher IR and RR than other methods in most scenes. Bold indicates the best performance. + +
IRChess→ChessChess→FireChess→HeadsChess→OfficeChess→PumpkinChess→KitchenChess→StairsAverage†
P2-Net0.5160.4360.3300.4140.4210.4050.2510.376
MATR0.7610.4550.3590.4200.4110.3900.2880.387
+Diff. PnP0.7530.4620.3640.4270.4240.4020.2850.394
+BPnPNet0.7470.4920.3970.4760.4500.3650.3420.420
+MinCD-Net0.8160.5420.4240.5020.4080.4160.3790.445
RRChess→ChessChess→FireChess→HeadsChess→OfficeChess→PumpkinChess→KitchenChess→StairsAverage†
P2-Net0.8750.5360.1620.6720.5610.5630.2930.464
MATR1.0000.5370.1670.7590.5810.6120.2140.478
+Diff. PnP1.0000.5560.1840.7670.5850.6220.2260.490
+BPnPNet1.0000.6650.2240.7780.6600.6010.1420.512
+MinCD-Net0.9850.6710.2500.8690.5740.6190.5710.592
IROffice→OfficeOffice→ChessOffice→FireOffice→HeadsOffice→PumpkinOffice→KitchenOffice→StairsAverage†
P2-Net0.5060.4160.4130.4030.4340.3860.3080.393
MATR0.6450.4980.4910.5210.4420.4480.3380.456
+Diff. PnP0.6530.5020.4970.5320.4390.4570.3510.463
+BPnPNet0.6660.5540.5650.4730.4720.4540.3890.486
+MinCD-Net0.7830.6600.6420.5360.5500.5460.4710.568
RROffice→OfficeOffice→ChessOffice→FireOffice→HeadsOffice→PumpkinOffice→KitchenOffice→StairsAverage†
P2-Net0.7690.5660.6610.2320.5770.5320.2340.510
MATR0.9400.6600.5560.4170.3950.6360.2860.491
+Diff. PnP0.9470.6720.5590.4220.4020.6480.3010.501
+BPnPNet0.8480.7080.7810.1440.6600.7500.4290.578
+MinCD-Net0.9800.7690.7260.2500.6810.8100.6430.647
IRKitchen→KitchenKitchen→ChessKitchen→FireKitchen→OfficeKitchen→HeadsKitchen→PumpkinKitchen→StairsAverage†
P2-Net0.6780.5160.5120.5040.5060.5550.3580.491
MATR0.7170.5710.5940.5370.5380.6120.3700.537
+Diff. PnP0.7230.5760.6020.5450.5460.6270.3820.546
+BPnPNet0.6930.5620.5570.5300.5620.5760.4090.532
+MinCD-Net0.7780.6170.5980.5400.5730.6360.4450.568
RRKitchen→KitchenKitchen→ChessKitchen→FireKitchen→OfficeKitchen→HeadsKitchen→PumpkinKitchen→StairsAverage†
P2-Net0.8510.8570.5830.2500.7690.6110.4290.621
MATR0.9010.8720.7780.6670.7230.6980.5000.706
+Diff. PnP0.9180.8850.7830.6850.7410.7030.5320.722
+BPnPNet0.9230.9540.8490.6500.7170.8300.7140.785
+MinCD-Net0.8750.8460.9040.6830.7980.8720.7860.814
+ +close to the pre-detected 2D keypoints. It ensures that the gradient $\nabla_{\varphi}L_{\mathrm{Chamfer}}(\mathbf{T}|\mathbf{K}_{\mathrm{I}},\mathbf{K}_{\mathrm{P}})$ is closely tied to the pixels and points representing the whole scene. Thus, the backpropagation of $L_{\mathrm{Chamfer}}(\mathbf{T}|\mathbf{K}_{\mathrm{I}},\mathbf{K}_{\mathrm{P}})$ contributes more effectively to $\varphi$ compared to existing differentiable PnP schemes [4, 38, 42]. Third, MinCD-Net is easily integrable with existing I2P registration frameworks, as its inputs are independent of the outputs of I2P registration networks. + +# 5. Experiments and Discussions + +# 5.1. Configurations + +To evaluate the performance of the proposed I2P registration method, we conduct experiments on multiple datasets, including RGBD-V2 [22], 7-Scenes [14], ScanNet [8], and the self-collected dataset captured by an Intel RealSense depth camera. The train-test data split for RGBD-V2 and 7-Scenes follows previous work [25], while ScanNet and self-collected datasets are totally utilized for testing. Inlier rate (IR) and registration rate (RR) are the primary evaluation metrics for I2P registration. Definitions of these metrics are provided in the appendices of [25]. The threshold of + +IR is $0.05\mathrm{m}$ . RR@X represents the RR threshold at X meters, with a default of $0.05\mathrm{m}$ . The implementation details of MinCD-Net are as follows. Its inputs include an RGB image with surface normals and an RGB point cloud with surface normals. Image surface normals are predicted using the pre-trained model DSINE [3]. The extractors in Fig. 3 are ResNet [16] and KPCnv [33], where the extractor networks are similar to those in MATR [25]. The threshold $s_{\mathrm{th}}$ in Eq. (14) is set to $e^{-0.4}$ . Point transformer in Fig. 3 is the single layer of work [41]. Its key, query, and value inputs are the 128 dimensional features which are transformed from pixels and points features. We utilize Shi-Tomasi keypoint detector to extract $\mathbf{K}_{\mathrm{I}}$ that are uniformly distributed in the image. We train MinCD-Net on a single NVIDIA RTX 3080 GPU for 40 epochs. In the first 20 epochs, $\lambda_{1}$ and $\lambda_{2}$ are set to zero. According to the camera model [40], the criterion of $\tau$ is: + +$$ +\tau \leq \left(\frac {\text {T h r e s h o l d o f R R} \cdot \max \left(f _ {u} , f _ {v}\right)}{d _ {\operatorname* {m a x}}}\right) ^ {2} \tag {17} +$$ + +where $f_{u}$ and $f_{v}$ are camera focal lengths, $d_{\mathrm{max}}$ is the maximum depth. On 7-Scenes dataset [22], $f_{u} = f_{v} = 585.0$ + +Table 2. I2P registration performance for cross-dataset generalization on the multiple datasets, including RGBD-V2, ScanNet, and self-collected datasets. The proposed MinCD-Net outperforms other methods in most of the scenes. + +
IRKitchen→Rgbd-S1Kitchen→Rgbd-S2Kitchen→Rgbd-S3Kitchen→Rgbd-S4Kitchen→Rgbd-S5Kitchen→Rgbd-S6Kitchen→Rgbd-S7Average
MATR0.3510.3530.3360.3160.2500.2090.2220.291
+Diff. PnP0.3720.3580.3520.3320.2620.2140.2350.303
+BPnPNet0.3960.3780.3750.3770.2300.1940.2580.315
+MinCD-Net0.4270.4150.4050.4120.3100.2960.3290.371
RR@0.1Kitchen→Rgbd-S1Kitchen→Rgbd-S2Kitchen→Rgbd-S3Kitchen→Rgbd-S4Kitchen→Rgbd-S5Kitchen→Rgbd-S6Kitchen→Rgbd-S7Average
MATR0.9700.8800.8710.7410.4800.4490.4580.692
+Diff. PnP0.9720.9430.8920.7500.4850.4530.4640.708
+BPnPNet0.9650.9740.9540.9420.6100.5070.6460.799
+MinCD-Net0.9740.9850.9680.9630.7070.7250.7110.870
IRKitchen→Scan-S1Kitchen→Scan-S2Kitchen→Scan-S3Kitchen→Scan-S4Kitchen→Scan-S5Kitchen→Scan-S6Kitchen→Scan-S7Average
MATR0.4950.5500.4240.3370.5070.4340.4140.451
+Diff. PnP0.4910.5520.4170.3390.4950.4240.4080.442
+BPnPNet0.5040.5110.4260.3240.5290.4270.4050.446
+MinCD-Net0.5170.5270.4600.3430.5480.4560.4280.468
RR@0.05Kitchen→Scan-S1Kitchen→Scan-S2Kitchen→Scan-S3Kitchen→Scan-S4Kitchen→Scan-S5Kitchen→Scan-S6Kitchen→Scan-S7Average
MATR0.9560.9540.9740.4330.9230.9090.7500.842
+Diff. PnP0.9320.9270.9450.4310.9470.9120.7570.836
+BPnPNet0.9290.9430.9170.4550.9600.9230.7820.844
+MinCD-Net0.9870.9790.9050.7200.9620.9150.8210.898
IRKitchen→Self-S1Kitchen→Self-S2Kitchen→Self-S3Kitchen→Self-S4Kitchen→Self-S5Kitchen→Self-S6Kitchen→Self-S7Average
MATR0.4970.4620.4260.6180.5070.6190.4120.506
+Diff. PnP0.4730.4530.4210.5920.5160.6080.4380.498
+BPnPNet0.4620.4420.4150.5720.5130.5980.4950.499
+MinCD-Net0.4850.4700.4370.5810.5220.6040.5140.516
RR@0.05Kitchen→Self-S1Kitchen→Self-S2Kitchen→Self-S3Kitchen→Self-S4Kitchen→Self-S5Kitchen→Self-S6Kitchen→Self-S7Average
MATR0.5560.3890.3330.9760.5320.9640.2780.575
+Diff. PnP0.5640.3720.3450.9790.5450.9660.3060.582
+BPnPNet0.5020.3620.3520.9810.5840.9480.3340.580
+MinCD-Net0.5120.4050.3890.9840.6110.9520.3890.606
+ +Table 3. Comparison results of current methods on the RGBD-v2 dataset, evaluated with an RMSE threshold of $0.1\mathrm{m}$ . $\dagger$ denotes that the proposed method has been pre-trained on several indoor datasets, including 7-Scene and ScanNet. + +
MethodsP2-NetMATRMATR+SNMATR+DMATR+DinoFCGFPredatorFreeReg+KabschFreeReg+PnPDiff-RegMinCD-NetMinCD-Net†
IR0.1220.3240.4510.4060.4340.0810.1570.3090.3090.3770.4720.581
RR@0.10.3840.5640.7700.6680.7440.3040.3020.3410.5730.8620.8230.914
+ +and $d_{\mathrm{max}} = 10.0m$ . For an RR threshold of $0.05\mathrm{m}$ , $\tau$ is optimally set to 5. Besides, $\lambda_1$ and $\lambda_2$ are empirically set to 0.2 and 0.0001 for the best performance. + +# 5.2. Methods Comparisons + +Cross-scene generalization. First, we conduct the cross-scene experiment on the 7-scenes dataset [14] that contains seven independent indoor scenes. We use the notation $A \to B$ to denote training on scene $A$ and testing on scene $B$ . As the proposed framework falls into the category of differentiable PnP methods, we mainly compare it with two representative methods: Diff. PnP [6] and BPnPNet [4]. BPnPNet [4] is a previous work that used Blind PnP in correspondence learning. For a fair evaluation, all methods are based on the same baseline, $\mathrm{MATR}^{\ddagger}$ [25]. Thus, we refer to them as $\mathrm{MATTR + MinCD - Net}$ (ours), $\mathrm{MATTR + Diff}$ . PnP, and $\mathrm{MATTR + BPnPNet}$ , respectively. Another classic method, P2-Net [35] is also used for comparison. The results are shown in Table 1. $\mathrm{MATTR + MinCD - Net}$ has a significant improvement on both the IR and RR metrics than other methods if the training scene is Office. When the training scene + +is Chess or Kitchen, MATR+MinCD-Net also outperforms other methods, although the improvement in the IR metric is not significant. So, the proposed MinCD-Net achieves both robust and accurate performance compared to existing differentiable PnP based methods in the cross-scene setting. + +Cross-dataset generalization. Next, we evaluate the differentiable PnP based methods in the cross-dataset setting. The results are shown in Table 2. On the RGBD-V2 dataset [22], the IR metric of MinCD-Net outperforms other methods. On the ScanNet dataset [8], all methods exhibit similar performance in the IR metric, but MATR+MinCD-Net learns high-quality correspondences (as seen in the RR metric for Office $\rightarrow$ Scan-s4). The self-collected dataset is the most challenging dataset, leading to poor RR metrics for all methods. Despite the challenges, our method achieves the highest average IR and RR across datasets, indicating its generalization capability. + +Standard comparison. After that, we evaluate the state-of-the-art methods, including P2-Net [35], 2D3D-MATR [25], FCGF [7], Predator [18], FreeReg [36], and Diff-Reg [38] on the RGBD-V2 dataset [22]. Compared models are trained and tested using the same data split of the RGBD-V2 + +![](images/b6dcdf55aee18c7e892ba60d0484830477a4f17494d66319566dab64294ee4b4.jpg) +Figure 4. Visualization of pre-detected 2D keypoints (green dots) and learned 3D keypoints (blue dots). With the proposed sub-optimal learning scheme in Sec. 3.2.3, the learned 3D keypoints exhibit a large overlap with the 2D keypoints. + +Table 4. Additional comparison results on the ScanNet dataset. † indicates that the model was trained on the Kitchen scene with an RR threshold of $0.05\mathrm{m}$ , stricter than $0.3\mathrm{m}$ . + +
MethodsP2-Net†MATR†LCDGlueFreeRegMATR+MinCD-Net†
IR0.3030.4510.3070.1840.5680.468
RR@0.30.7110.842N/A0.0650.7800.898
+ +dataset [22]. Results are provided in Table 3. The notations $+\mathrm{SN}$ , $+\mathrm{D}$ , $+\mathrm{Dino}$ indicate the use of surface normals [3], monocular depth maps [39], and the pre-trained Dino v2 backbone [11], respectively. Similarly, $+\mathrm{Kabsch}$ and $+\mathrm{PnP}$ respectively denote the use of Kabsch [20] and EPnP [23] for outlier removal. Diff-Reg [38] exploits the EPro-PnP [6] in the correspondence learning. MATR+MinCD-Net outperforms existing methods. We include an additional comparison on the ScanNet dataset [8] with other methods, like LCD [27], Superglue (Glue) [30], and FreeReg [36]. Results are shown in Table 4. Even under stricter RR thresholds, MinCD-Net consistently outperforms FreeReg [36]. + +Results analysis. We analyze why MinCD-Net outperforms Diff. PnP [6] and BPnPNet [4]. Diff. PnP estimates the camera pose from the predicted correspondences. However, pose accuracy is highly sensitive to correspondence quality, making the pose loss less reliable during training. Although the declare network [15] in BPnPNet [4] is an effective module in optimizing blind PnP, it requires an accurate pose prior. In BPnPNet [4], the pose loss computed from the filtered correspondences has a limited impact on the I2P registration architecture. MinCD-Net detects and learns 2D-3D keypoints that are uniformly distributed across 2D and 3D spaces, which achieves a higher learning efficiency and is robust to correspondence quality. + +# 5.3. Ablation studies + +We conduct ablation studies to analyze the effects of the hyperparameter $s_{\mathrm{th}}$ and the loss functions. We analyze the relationship between $s_{\mathrm{th}}$ and the quality of learned 3D keypoints. As presented in Table 5, when $s_{\mathrm{th}} \geq e^{-0.1}$ , no 3D keypoints are retained. If $s_{\mathrm{th}}$ is set too low, a large number of redundant 3D keypoints are learned that disturb Chamfer distance minimization. To balance precision and recall, $s_{\mathrm{th}}$ is best set to $e^{-0.4}$ , and the visualization of the learned 3D keypoints is provided in Fig. 4. Using the optimal value of $s_{\mathrm{th}}$ , MinCD-Net achieves the top performance across four + +Table 5. Recall and precision of the learned 3D keypoints. Precision and recall are computed with respect to the pre-detected 2D keypoints (pixel threshold is 3). Avg. Num represents the average number of learned 3D keypoints. + +
Parameter sthe-0.1e-0.2e-0.3e-0.4e-0.5
PrecisionN/A0.5820.5310.4420.308
RecallN/A0.4540.5620.7220.862
Avg. NumN/A≈3.1K≈5.7K≈8.4K≈14.2K
+ +Table 6. Ablation study of different learning schemes. The model was trained on the Office scene and tested on the remaining scenes. + +
SchemesLcorrLcorr + LkeyLcorr + Lkey + LChamferGain
IR0.4730.4890.567↑ 9.4%
RR0.5020.5160.646↑ 14.4%
+ +datasets. This suggests that the chosen $s_{\mathrm{th}}$ generalizes well across different datasets. Then, we study the different loss functions in Table 6. As expected, using the combined loss $L_{\mathrm{corr}} + L_{\mathrm{key}}$ yields only a marginal improvement over $L_{\mathrm{corr}}$ , as $L_{\mathrm{key}}$ supervises only 3D keypoints, which are not incorporated into the network's main branch. $L_{\mathrm{Chamfer}}$ plays a dominant role, as it acts as a global geometrical constraint. + +# 6. Conclusions + +To improve I2P registration accuracy, we incorporate blind PnP into correspondence learning, which is achieved by simplifying blind PnP into MinCD-PnP, a more tractable task of minimizing the Chamfer distance between learned 2D and 3D keypoints. This reformulation enables efficient correspondence learning using blind PnP. To effectively solve MinCD-PnP, we develop MinCD-Net, a lightweight multi-task learning module, which can be seamlessly integrated into I2P registration networks. Extensive experiments on four indoor datasets demonstrate that MinCD-Net achieves superior performance compared to existing methods in both cross-scene and cross-dataset settings. + +# Acknowledgments + +This work is partially supported by the National Key R&D Program of China (2024YFC3015303), National Natural Science Foundation of China (62372377), and China Postdoctoral Science Foundation (2024M761014). + +# References + +[1] Pei An, Junfeng Ding, Siwen Quan, Jiaqi Yang, You Yang, Qiong Liu, and Jie Ma. Survey of extrinsic calibration on lidar-camera system for intelligent vehicle: Challenges, approaches, and trends. IEEE Trans. Intell. Transp. Syst., 25 (11):15342-15366, 2024. 1, 2 +[2] Pei An, Xuzhong Hu, Junfeng Ding, Jun Zhang, Jie Ma, You Yang, and Qiong Liu. 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Differentiable registration of images and lidar point clouds with voxelpoint-to-pixel matching. In Proc. 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Benign Clients May Even Become Accomplices of Backdoor Attack/full.md @@ -0,0 +1,338 @@ +# Mind the Cost of Scaffold! Benign Clients May Even Become Accomplices of Backdoor Attack + +Xingshuo Han $^{1*}$ , Xuanye Zhang $^{2*}$ , Xiang Lan $^{3}$ , Haozhao Wang $^{4**}$ , Shengmin Xu $^{3}$ , Shen Ren $^{5}$ , Jason Zeng $^{6}$ , Ming Wu $^{6}$ , Michael Heinrich $^{6}$ , Tianwei Zhang $^{2}$ + +$^{1}$ Nanjing University of Aeronautics and Astronautics, College of Computer Science and Technology, $^{2}$ Nanyang Technological University, $^{3}$ Fujian Normal University, $^{4}$ Huazhong University of Science and Technology $^{5}$ Continental Automotive Singapore, $^{6}$ Zero Gravity Labs, *Equal Contribution, **Corresponding {xingshuo001, C200212, tianwei.zhang} @ntu.edu.sg, {jason, ming, michaeli} @0g.ai {lanxiang0113, smxu1989} @ gmail.com, hz_wang@hust.edu.cn, shen@shenren.org + +# Abstract + +By using a control variate to calibrate the local gradient of each client, Scaffold has been widely known as a powerful solution to mitigate the impact of data heterogeneity in Federated Learning. Although Scaffold achieves significant performance improvements, we show that this superiority is at the cost of increased security vulnerabilities. Specifically, this paper presents BadSFL, the first backdoor attack targeting Scaffold, which turns benign clients into accomplices to amplify the attack effect. The core idea of BadSFL is to uniquely tamper with the control variate to subtly steer benign clients' local gradient updates towards the attacker's poisoned direction, effectively turning them into unwitting accomplices, significantly enhancing the backdoor persistence. Additionally, BadSFL leverages a GAN-enhanced poisoning strategy to enrich the attacker's dataset, maintaining high accuracy on both benign and backdoored samples while remaining stealthy. Extensive experiments demonstrate that BadSFL achieves superior attack durability, maintaining effectiveness for over 60 global rounds—lasting up to three times longer than existing baselines even after ceasing malicious model injections. + +# 1. Introduction + +Federated Learning (FL) enables distributed model training while preserving client data privacy. However, the effectiveness of FL models heavily depends on the distribution of training data across clients. Two scenarios typically arise: 1) IID data, where training data is uniformly distributed across clients, and 2) non-IID data, a more realistic setting where data characteristics vary significantly across clients. For IID scenarios, FedAvg [27] stands out as the leading FL + +method, setting the standard for server-side model updates by aggregating model parameters from clients. However, its performance deteriorates in non-IID scenarios, where data heterogeneity causes update drifts from individual clients, ultimately degrading convergence [22]. + +To address this challenge, Scaffold [12] was introduced as a robust FL method designed to mitigate client update drift through a correction mechanism based on control variates, thereby enhancing model convergence in non-IID settings. The control variate is essentially an estimate of the difference between a client's local gradient and the global gradient, which helps align the local updates with the global objective. Scaffold reduces variance in the updates caused by data heterogeneity, making it particularly effective for scenarios where clients have diverse data distributions. + +However, Scaffold Federated Learning (SFL) not only changes the way FL models converge but also affects their robustness against adversarial manipulations. In particular, malicious clients in FL can exploit model update mechanisms to introduce backdoor behaviors, embedding hidden misbehavior into the global model [6]. While backdoor attacks have been extensively studied in FL [3, 7, 34, 36, 40], most existing works focus on IID scenarios where attackers have full knowledge of the dataset distribution and can easily craft poisoned updates. In contrast, non-IID data distributions introduce additional constraints, making it harder for attackers to align poisoned models with the global model without significantly degrading overall performance. Although recent studies have explored backdoor attacks in non-IID FL [2, 10, 29, 42], they have largely overlooked the unique security implications introduced by SFL. The question this paper aims to address is: if the new mechanisms of SFL (i.e., control variate for update drift correction) can bring new security threats, and unintentionally facilitate backdoor attacks in non-IID settings? + +![](images/b6230ae4782d6a8fbe00d8bd432fe7dcf7b66a2d0902a5e6e38eb2585c92bb6d.jpg) +Figure 1. Model averaging under IID and non-IID scenarios. + +Our answer to the above question is affirmative. Our new insight is that Scaffold's reliance on control variates introduces a novel attack surface: its correction mechanism, designed to stabilize training by aligning local updates with the global objective, can inadvertently amplify the impact of malicious updates. More critically, this mechanism allows an attacker to influence the control variate itself, effectively co-opting benign clients to "assist in the mischief". Since all clients use the control variate to adjust their local gradients during updates, a tampered variate can subtly steer these honest clients' gradients toward the attacker's poisoned direction. This amplifies the backdoor's reach, making Scaffold more susceptible to sophisticated attacks than standard FL methods like FedAvg, which lack such a correction mechanism. + +To exploit the above insight, we propose BadSFL, a novel backdoor attack specifically targeting Scaffold Federated Learning, to successfully implant a backdoor function into a global model without catastrophically corrupting model performance on benign sample inference. Unlike prior attacks, BadSFL leverages Scaffold's correction dynamics to enhance both the stealth and durability of the backdoor, revealing a critical vulnerability in SFL methods. BadSFL operates as follows: Firstly, as the attacker only has partial knowledge of the dataset distribution in the FL system, he leverages a GAN to generate fake samples that belong to other clients to supplement the dataset, simulating a full knowledge of the dataset distribution. With the supplemented dataset for backdoor training, he gets a backdoor model achieving high accuracy in both backdoor tasks and benign tasks. Secondly, the attacker uses a distinctive feature of a category as the backdoor trigger to maintain the attack stealthiness. Thirdly, the attacker exploits the global control variate, as a reference to predict the global model's convergence direction. This optimization significantly enhances the durability of the embedded backdoor function within the global model. + +We evaluate BadSFL on the MNIST, CIFAR-10, and CIFAR-100 datasets, demonstrating its high accuracy on both backdoor and primary tasks. Moreover, the embedded backdoor function persists in the global model for over 60 rounds and lasts 3 times longer than baseline attacks after the attacker stops injecting malicious updates. Finally, we show that BadSFL remains highly effective when using + +four defense methods simultaneously. + +The main contributions are as follows: + +- We propose BadSFL, the first backdoor attack against SFL on non-IID scenarios. +- We enhance the backdoor durability, ensuring it persists for over 60 rounds and lasts $3 \times$ longer than baselines. +- We conduct extensive experiments on three benchmark datasets, demonstrating high effectiveness of our attack. + +# 2. Background and Related Work + +# 2.1. Non-IID Scenarios in FL + +In FL, non-IID refers to significant differences in data distributions among clients [11, 20, 28]. This discrepancy between local data distributions in non-IID scenarios can lead to inconsistencies between the local optima and the global optima. This inconsistency results in a drift in local model updates, where local models move towards their own local optima which can be far from the global optima [12]. Consequently, averaging these local models may yield a global model far from the true global optima [12, 16, 21, 37, 38], especially with numerous local epochs. As shown in Figure 1, while the global optima aligns with the local optima in IID scenarios, non-IID can cause the global optima to be distant from individual local optima, which is known as the client-drift phenomenon, leading to slow and unstable convergence in the FL training process. + +Scaffold. Several FL algorithms have been proposed to address the above challenges, with Scaffold [12] being the most practical solution. It tackles the client-drift problem through the control variates (variance reduction techniques) for both the server and the clients. These control variates estimate the update direction of the global model and local client models and serve to correct local updates based on the drift, thereby mitigating the divergence between local and global optima (Alg. 1). In this paper, we mainly focus on designing backdoor attacks targeting SFL. + +# 2.2. Backdoor Attacks against FL + +Backdoor attacks pose a significant threat to deep learning models, where malicious clients embed hidden triggers within models that cause misclassification during inference while maintaining normal performance on clean data [23]. In FL, adversaries can deploy backdoor attacks by exploiting compromised clients to manipulate local updates, thereby generating poisoned models that corrupt the global model upon aggregation [3, 19, 34, 36, 40, 45]. + +Backdoor attacks typically involve a combination of model replacement and data poisoning. In model replacement, the adversary substitutes legitimate models with manipulated ones [3], while data poisoning involves injecting poisoned data containing the backdoor trigger into the training datasets of compromised clients. To inject these trig- + +Server Input: local datasets $D^{i}$ , number of total client $N$ , number of sampled client $S$ , number of communication rounds $R$ , number of local epochs $E$ , number of local update steps $K$ + +Client Input: local control variates $c_{i}$ , local step-size $\eta_{l}$ + +Algorithm 1 Scaffold Algorithm in Federated Learning +Server Updates: +$c^t\gets 0$ +for each round $\mathbf{r} = 1,\dots,R$ do: randomly selected clients $S^t\subseteq \{1,\ldots ,N\}$ for $i\in S^t$ in parallel do: send $w^{t},c^{t}\rightarrow i$ $\Delta w_i^t,\Delta c_i^t\gets \mathrm{Local~Update}(i,w^t,c^t)$ +end for $w^{t + 1}\gets w^t -\eta \sum_{i\in S^t}\Delta w_i^t$ $c^{t + 1}\gets c^t +\frac{|S|}{N}\Delta c$ +end on client +local Updates: +Local client $i$ get $w^{t},c^{t}$ from server +for $\mathrm{k} = 1,\dots,\mathrm{K}$ do: training model with $D_{i}$ get gradient $g_{i}(w_{i})$ update local model: $w_{i}\gets w_{i} - \eta_{l}*(g_{i}(w_{i}) - c_{i} + c)$ +end for +update local control variates: $c_{i}^{t + 1}\leftarrow (i)\quad g_{i}(w_{i}),or\quad (ii)\quad c_{i} - c + \frac{1}{K*\eta_{l}} *(w^{t} -$ $\Delta w_i^t\gets w_i - w^t$ $\Delta c_i^t\gets c_i^{t + 1} - c_i$ +return $(\Delta w_i^t,\Delta c_i^t)$ + +gers, the adversary can manipulate the dataset by flipping data labels or adding a unique pixel pattern to the training samples [1, 3, 36]. Afterward, he strategically adjusts training parameters and scales updates to optimize the impact of the attack while evading detection by the anomaly detector deployed at the central aggregation server [5, 30]. + +In this paper, we focus on data poisoning-based backdoor attacks. While most existing backdoor attacks target FL under IID scenarios [9, 25, 31, 40, 43], real-world FL deployments often involve non-IID distributions, posing additional challenges for effective backdoor injection. To the best of our knowledge, no prior research has specifically explored backdoor attacks against FL with the Scaffold aggregation algorithm. We bridge this gap by investigating a novel backdoor attack targeting SFL, leveraging its unique control variate mechanism to enhance the effectiveness, stealthiness, and persistence of the attack. + +# 2.3. Threat Model + +Attack scenarios. We consider an attacker who aims to inject backdoors into SFL, make the final model predict + +![](images/3ec45cce9418169096db9054f7aa4f771e0ed25d078fc6c0162bf96d8cc3385e.jpg) +Figure 2. Left: Primary task accuracy crushed by simple attack; Right: Backdoor accuracy dropped after stop attacking. + +![](images/01f2d06d1b18a78e618c1350231095fceae975785c8b30e13dd266eb35df1930.jpg) + +the desired wrong output over a triggered input. The attacker has partial knowledge of the full dataset in the training stage. Specifically, the attacker trains a local model with a backdoor trigger function and submits poisoned local updates along with the control variate to the server for Scaffold aggregation. During inference, the attacker manipulates predictions to produce the attacker's desired outputs when inputs meet the trigger conditions. + +Attack goal. The attack goal can be summarized as follows: + +- Effectiveness: The attacker must ensure that the backdoor function does not compromise the global model's performance on primary tasks, maintaining high accuracy for both backdoor and benign predictions. +- Robustness: the backdoor should be robust against potential defenses. +- Durability: The backdoor should remain effective in the global model for as long as possible, even after the attacker stops participation in the training process, thereby maximizing the longevity of the attack. + +Attacker's capability. We assume the attacker can compromise at least one client during the training process, thereby allowing him to operate covertly within the system. Additionally, participation in FL provides the attacker with full knowledge of the model structure, facilitated by the consensus among all clients on a common learning objective. This enables the insertion of backdoor triggers, the modification of sample labels, and the manipulation of local training updates. It is essential to note that the attacker cannot control the server or directly manipulate the aggregation procedure or the global model. They also lack access to data and models from non-compromised clients. + +# 3. Challenges with Backdoor Attacks in SFL + +Performing a backdoor attack in SFL presents the following challenges. ① Limited knowledge. In non-IID scenarios, a primary challenge arises from the attacker's lack of knowledge of the dataset distribution across clients. Unlike IID scenarios, where a centralized understanding of the dataset facilitates manipulation, non-IID scenarios involve decentralized and diverse data distributions. This results in three issues: (1) Direct backdoor strategies can cause significant performance degradation on benign samples, leading to the rejection of the global model; (2) The variability in data distributions increases the difference between local and global + +models, making malicious models more detectable; (3) Averaging poisoned models with the global model degrades its performance on the primary task, as shown in Figure 2, where accuracy drops significantly when a poisoned model is aggregated. $②$ Control variate. In SFL, control variate (denoted as $c_{i}$ ) is used to correct the client drift and align local models with the global model. If attackers strictly follow protocols and use the $c_{i}$ to correct their malicious models during the triggering planting process, the effectiveness of the attack can be reduced. Conversely, if an attacker chooses to manipulate the $c_{i}$ inappropriately, introducing a malicious $c$ to the server, it could lead to a potential corruption of the global model. $③$ Backdoor catastrophic forgetting. Catastrophic forgetting [13] occurs when neural networks forget previously learned tasks upon learning new ones. This can cause backdoors to lose effectiveness over time [36]. If attackers stop uploading malicious updates, the backdoor function may eventually be erased by benign updates. As shown in Figure 2, the accuracy of backdoor tasks declines sharply over time, with the backdoor function vanishing around round 65. Although various methods [2, 7, 39, 45] have been proposed to address this issue, none have proven effective in SFL. + +Algorithm 2 BadSFL +Required: local datasets $D^i$ global model $w_{g}$ global control variate $c$ number of local epochs $E$ ,local learning rate $\eta_{l}$ Generator $G$ Discriminator $D$ Update local model with $w_{p}\gets w_{g}$ Initialize Discriminator $D\gets w_{g}$ do: Run G for generating fake samples Evaluate fake sample on D Update G using D until G converges to generate target samples G generates samples into dataset $D_{f}$ $D_{c}\leftarrow D_{f} + D^{i}$ Select backdoor samples from $D_{c}$ and assign them wrong label as $D_{b}$ $D_{p}\gets D_{c} + D_{b}$ for each epoch $\mathbf{e} = 1,\dots,E$ do: $w_{p} = \arg \min_{w_{p}}[L(D_{p},w_{p}) + L(D_{p},P_{j}(w_{p},c))]$ end for $\Delta w_{p} = w_{p} - w_{g}$ $\Delta c_p = \frac{1}{K*\eta_l} *(w_g - w_p) - c$ return $(\Delta w_{p},\Delta c_{p})$ + +# 4. BadSFL + +Overview. To overcome the challenges, we propose BadSFL, as detailed in Algorithm 2. BadSFL mainly consists of 4 steps: Step 1: Initialization. The attacker initiates + +the attack by downloading the global model $w_{g}$ and controlling the variate $c$ from the server. Subsequently, the attacker updates the local model $w_{p}$ and discriminator $D$ using the downloaded global model $w_{g}$ . Step 2: GAN-based Training for Data Supplementation. The attacker performs GAN training on generator $G$ and discriminator $D$ . The training terminates upon the convergence of the generator, signifying its ability to generate realistic fake samples in class $C$ that do not belong to $D^{i}$ but rather originate from other clients' datasets. Then the generator $G$ is utilized to generate a number of samples in class $c$ forming in dataset $D_{f}$ . This dataset $D_{f}$ is then merged with the attacker's original dataset $D^{i}$ to create a new dataset $D_{c}$ . Step 3: Backdoor Sample Selection and Trigger Injection. With dataset $D_{c}$ , the attacker selects specific samples with a characteristic feature to serve as backdoor samples. These samples are then relabeled to a target class $x$ as the backdoor target class that is different from their original labels. The attacker organizes these manipulated samples into a separate dataset $D_{b}$ and merges it with $D_{c}$ to finalize the dataset $D_{p}$ for backdoor training. Step 4: Backdoor Model Training and Optimization. The attacker proceeds to train the local model $w_{p}$ based on the dataset $D_{p}$ . During the training process, the attacker follows the equation 3 to optimize the backdoor objective. Upon convergence, the backdoor model update $\Delta w_{p}$ and the corresponding control variate $\Delta c_{p}$ are obtained and can be uploaded to the server. + +# 4.1. GAN-based Dataset Supplementation + +In non-IID data scenarios, directly injecting backdoor samples into dataset $D^{i}$ for training often leads to a more biased model, deviating significantly from global optima [15, 33]. To mitigate this, inspired by Zhang et al. [44], the attacker can employ GAN to generate synthetic samples that resemble the data held by other clients. This involves training a generator $G$ with local non-IID data to bridge the gap between datasets. The GAN architecture basically consists of a generator $G$ and a discriminator $D$ . In our case, the generator $G$ comprises a series of 'deconvolution' layers that progressively transform random noise into a sample, while the discriminator $D$ closely resembles the global model, except for its output layer, which distinguishes between fake and real samples. The attacker iteratively trains the generator $G$ locally with the constraint of discriminator $D$ until it converges to generate realistic fake samples that do not belong to the attacker. Concurrently, as the SFL procedure progresses, the global model tends to converge. During each server-client communication round, the attacker updates the discriminator $D$ using the latest global model $w_{g}$ downloaded from the server and performs new-round optimization training on the generator $G$ , guiding it to generate more authentic fake samples that closely resemble data from other clients. These high-quality synthetic samples are + +![](images/441a4787045aad45f6e2532a919c77de7eb470042345d4c768da0812a912a2df.jpg) +Figure 3. Left: global optima under non-IID scenario. Right: global optima with data supplementation techniques. + +then integrated into the attacker's original non-IID dataset, effectively supplementing it with additional data classes. + +The attacker synchronously updates the discriminator $D$ during each local training round using the new global model $w_{g}$ downloaded from the server, followed by GAN training to optimize the generator $G$ for improved performance. The output of this process is then merged into the attacker's non-IID dataset for further backdoor training. As the generated samples closely resemble those from other client datasets, the attacker local optima trained by the attacker can converge closer to the global optima than other clients. Figure 3 demonstrates the difference between the aggregated global optima with and without data supplementation techniques. + +# 4.2. Trigger Selection and Injection + +With the prepared dataset $D_{p}$ , containing both original and synthetic data, the attacker proceeds to inject a backdoor into the model. BadSFL leverages three techniques to inject backdoors: (1) Label-flipping [17], in which the ground truth labels of a whole class $a$ in $D_{p}$ are directly altered to another label $b$ . For instance, all the 'dog' labels are altered to 'cat' in CIFAR-10. (2) Pattern trigger [35], which involves poisoning samples with a specific trigger pattern, i.e., a small mosaic cube added in the images to activate the backdoor behavior. The attacker injects these poisoned images into the $D_{p}$ along with a target label, establishing a correlation between the trigger pattern and the desired misclassification. (3) A stealthier backdoor method, known as feature-based backdoor [26], involves selecting a distinctive feature within an image class as the backdoor trigger. This approach eliminates the need to directly manipulate the images, thereby increasing the difficulty of detection. For instance, all the green cars in the 'car' class in CIFAR-10 are designed as the backdoor trigger. During the inference stage, the compromised model outputs the attacker's target label only when the input is an image containing a green car. The selection of a unique feature within a class makes this trigger difficult to detect as it appears as a natural variation within the data. + +# 4.3. Backdoor Training with Control Variate + +As discussed in section 3, the global control variate $c$ is utilized in SFL to correct the client drift. Specifically, the cor + +![](images/4dfdde3d7e0f65c16c9cbcce5620a4e9d15c9680a3fd2f8b6185584d3dc84888.jpg) + +Figure 4. Scaffold correction term on a single client. Rejection value $c - c_{i}$ adjusts the local model point towards the global model, as shown in algorithm 1. During the local model training process, this correction term effectively 'drag' the drifting local model closer to the global model, facilitating convergence towards the global optima, as depicted in Figure 4. In the server aggregation round, the global control variate $c$ is computed by averaging the drift values of all local models, which represents the convergence direction of the global model. + +From the attacker's perspective, allowing the control variate to correct the poisoned model according to SFL rules can reduce the effectiveness of the backdoor attack, as discussed in Section 3. However, the attacker still needs to submit a control variate $c_{p}$ to report the drift of the backdoor model. The key idea is to train a backdoor model that is closer to the global model compared to other local models trained on non-IID data. Since the global control variate $c$ is known to participating clients, it can be used as a reference for the global model's convergence direction, helping to align the poisoned model more closely with the global optimum. This constraint, derived from $c$ , functions similarly to using the future global model for optimization, as suggested by Wen et al.[39]. This constraint can be integrated into the loss function to enhance the backdoor's effectiveness and persistence in the global model. + +Initially, the attacker performs backdoor training and optimizes their backdoor objective as in the Equation 1 [4]: + +$$ +w _ {p} ^ {*} = \underset {w _ {p}} {\operatorname {a r g m i n}} L \left(D _ {p}, w _ {p}\right). \tag {1} +$$ + +where $L$ is the loss function of the backdoor task, $w_{p}$ is the attacker model weights. + +In our BadSFL attack, we modify the standard backdoor objective function by adding a term to ensure that the backdoor updates sent to the server persist in the backdoor function in the global model for more future training rounds. We can simulate an aggregation round and apply the control variate $c$ to obtain a predicted global model for one future round. Here is the modified objective function (Equation 2): + +$$ +P _ {j} \left(w _ {p}, c\right) = \frac {w _ {p} + w _ {g} * (n - 1)}{n} - \eta_ {l} * c * j \tag {2} +$$ + +To summarize, we formalize our attack objective as below: + +$$ +w _ {p} ^ {*} = \underset {w _ {p}} {\operatorname {a r g m i n}} \left[ L \left(D _ {p}, w _ {p}\right) + L \left(D _ {p}, P _ {j} \left(w _ {p}, c\right)\right) \right]. \tag {3} +$$ + +Table 1. Dataset, model structure, and hyperparameter description. + +
DatasetInstancesFeaturesModelBenign \(l_r\)EPoison \(l_r\)Poison ratioBatch Size
FLPTFB
CIFAR-10600001024ResNet-180.001100.050.10.01250.01128
CIFAR-100600001024ResNet-500.00011000.00010.10.01250.01128
MNIST70000784ConvNet0.0120.0010.10.0125-128
+ +where $j$ represents the number of future rounds that $w_{p}$ anticipates. By optimizing the backdoor model to be closer to the global model, the attacker simultaneously optimizes the control variate $c_{p}$ to align it with the expected drift value. This ensures that the attacker's actions conform to the SFL protocol (Algorithm 1). + +# 5. Evaluation + +# 5.1. Setup + +We evaluate BadSFL on a server running Ubuntu 18.04 with an NVIDIA GeForce RTX 2080 Ti GPU. + +Datasets, models, and hyperparameters. We consider the datasets that are commonly used in previous works [25], i.e., MNIST [8], CIFAR-10 [14] and CIFAR-100 [14]. Detailed configurations are summarized in Table 1. + +GAN models. In attacking SFL with CIFAR-10 and CIFAR-100, the discriminator mimics ResNet18 and ResNet50, respectively, differing only in the output layer. The generator consists of five deconvolutional layers to generate synthetic images for supplementing $D_{p}$ in the backdoor attack. For MNIST, the discriminator follows LeNet5, while the generator uses three deconvolutional layers to produce synthetic images resembling those of other clients. + +Attack baselines. We compare BadSFL with 4 backdoor attacks: (1) Black-box Attack [3]. This attack directly poisoned the training dataset through techniques such as label-flipping, pattern trigger, and feature-based trigger. Subsequently, it conducts backdoor training to minimize the classification loss on the dataset $D_{p}$ . (2) Neurotoxin [45]. It incorporates a strategic approach to ensure the durability of the backdoor function within the global model. Specifically, it aims to prevent the malicious model updates from pointing toward coordinates that are frequently updated by benign clients, thereby mitigating the risk of the backdoor being erased. We illustrate it in Figure 9 in the Appendix. (3) Irreversible Backdoor Attack (IBA) [31]. IBA gradually implants a stealthy and durable backdoor into the global model by optimizing trigger imperceptibility and selectively poisoning parameters less likely to be updated. (4) 3DFed [18]. 3DFed is a multi-layered backdoor attack framework that combines constrained loss training, noise masking, and a decoy model to evade detection in a black-box FL setting. + +Attack settings. We run 100 communication rounds in SFL for CIFAR-10, CIFAR-100, and MNIST. In each round, 20 clients participate, with $50\%$ randomly of them selected for + +![](images/b61e16b7df3e91939b2f109552639e7fa4413ddaee6da6edd92cf669d6eea414.jpg) +(a) Generated samples by GAN (CIFAR-10). + +![](images/3f1709d90c9a84456d18d064b33270afa3b01814cc6fe24c50e41e00afb868af.jpg) +(b) Generated samples by GAN (MNIST). + +![](images/e0da59a131a816c16b75f03b00867d23bacb0ec0667890d2dc1dcbefbb706b71.jpg) +(c) PTA on CIFAR-10 and MNIST. +Figure 5. Dataset supplementation on CIFAR-10 and MNIST. + +![](images/19a6194acbefbd1086f0d814cbeebfe57190c2f4a99145c870d967712f563701.jpg) + +training. To ensure a non-IID data distribution, the training dataset is split into 200 label-sorted groups, which are randomly assigned to all the participating clients. + +For BadSFL evaluations on CIFAR-10 and CIFAR-100 datasets, the attacker strategically joins the training process from the 10th round, exiting after the 40th round. Initially, the attacker conducts GAN training to perform data supplementation, employing 10 local epochs, a fixed learning rate of 0.001, and Adam Optimizer with parameters (0.5, 0.999). Subsequently, backdoor training and optimization are carried out with 10 local epochs, a future round $j$ set to 10, a fixed learning rate of 0.05, and an SGD optimizer with a momentum of 0.9 and a weight decay of 0.005. + +To obtain $D_{p}$ , we employ three types of backdoor trigger injections and evaluate the performance of BadSFL based on BTA in each communication round, contrasting it with baseline attacks: (1) Label Flipping. All 'dog' samples in $D_{c}$ are relabeled as 'bird'; (2) Pattern Trigger. A small triangle pattern is added to the right bottom of the image, with all the modified samples labeled as 'cat'; (3) Feature-based trigger. Characteristic features (e.g., car stripe, green car, race car, sunset plane, white horse, red ship, yellow truck) are chosen as backdoor triggers in Dataset $D_{c}$ , with corresponding samples labeled as 'bird'. + +For MNIST, the attacker engages in the training process from the 10th round and quits after the 40th round. Also, GAN training is employed for data supplementation, + +![](images/42de0f06ebb6a270ca84e436c9fe5c3c1eb5f18566736bd20cb79762346e5fa5.jpg) + +![](images/1e5d973649e65ca099a034148a89a54f134150d9a5df2410bd5c664ead664eb1.jpg) +(a) Label Flipping (CIFAR-10) +(e) Plane in Sunset (CIFAR-100) + +![](images/7fe6002a5c824e43cca6f146cb69001d72155eb7bb40c5e491488f86bc16899c.jpg) + +![](images/450e387bae08c0e510cf09713dccf6027f296c79911a5424a08468bb8879c080.jpg) +(b) Pattern Trigger (CIFAR-10) +(f) Yellow Truck (CIFAR-100) + +![](images/7f1bd1bb187966419b611138330a5d7242784cbac4758100020a018455582d8c.jpg) + +![](images/022e3760e32281394d5e56afe4333da5939d307b70b5dc7f3f1a7e6a56856293.jpg) +(c) Plane in Sunset (CIFAR-10) +(g) Label Flipping (MNIST) + +![](images/2f756de0bd00d2c8782e6764a514fa623c3da59c34f6842ca122863a70029a7b.jpg) + +![](images/13af15de7ed29d41975fa2e385bf9f975ecbd1bf40f7fc3a502cbbda2d64c86d.jpg) +(d) Label Flipping (CIFAR-100) +(h) Pattern Trigger (MNIST) + +![](images/db30e220d3a103740191d386ccc3f9f1b9429f255843881da957f6671016ff3b.jpg) +(a) Green Car + +![](images/c29c2322ef144f53d092fa77458e3bda4ebca5751957f530343bf8184b7f47ef.jpg) +Figure 6. Attack comparisons with baselines. +(b) Race Car + +![](images/259b663e2a2c4ade024b89d6a3eaaa1ceff06756ecfa43b5bc5cabefa62692c4.jpg) +(c) White Horse + +![](images/ec2c25fc1a360aa915e868a1c5f53354b1e67b320640c45835dcc935d0e69935.jpg) +(d) Red Ship +Figure 7. Feature-based backdoor attacks on CIFAR-10. + +comprising 2 local epochs, a fixed learning rate of 0.001, and Adam Optimizer with parameters (0.5, 0.999). Subsequently, backdoor training and optimization are performed over 2 local epochs, considering future rounds $j$ as 10, with a fixed learning rate of 0.1 and SGD optimizer. + +To obtain $D_{p}$ , only two types of backdoor trigger injections are used, as MNIST lacks sufficient features for feature-based backdoor attacks. The performance of BadSFL is evaluated based on the BTA in each communication round, compared to two baselines: (1) Label flipping. All samples labeled as '5' in $D_{c}$ are relabeled as '2'; (2) Pattern trigger. A small triangle pattern is added to the right bottom of the image, and the labels of all modified samples are changed to '2'. + +Evaluation metric. We adopt two metrics commonly utilized in FL. (1) Primary Task Accuracy (PTA), which reflects the classification accuracy on clean samples. (2) Backdoor Task Accuracy (BTA), which is the attack success rate, measured by the poisoned model's accuracy on + +poisoned samples. + +# 5.2. Results of GAN + +Figure 5a and Figure 5c illustrate the datasets $D_{f}$ generated by the Generator $G$ for CIFAR-10 and MNIST, respectively. In both cases, $D_{f}$ encompasses nearly all classes of each dataset, demonstrating the successful acquisition of full dataset distribution knowledge within the SFL framework under non-IID scenarios. Utilizing the combined dataset $D_{c}$ , the attacker executes the backdoor attack while maintaining the model's accuracy on the primary task. For CIFAR-10, as shown in Figure 5c, the primary task accuracy remains around $55\%$ with data supplementation, compared to a drop below $25\%$ in the baseline attack. Similarly, for MNIST, Figure 5c reveals that using $D_{c}$ instead of $D_{i}$ , the primary task accuracy stays above $90\%$ , while the baseline attack results in a decline to under $75\%$ . + +# 5.3. Effectiveness of BadSFL + +From Figures 6a to 6f, we present attack comparisons with baselines evaluated on the CIFAR-10 and CIFAR-100 datasets. It is evident that BadSFL outperforms the baseline attacks in terms of both effectiveness and durability. To be specific, BadSFL achieves above $80\%$ backdoor task accuracy across all types of backdoor attacks within the first 10 rounds, while the attacker remains active in the training process for backdoor training and malicious updates to the server. Meanwhile, BadSFL keeps the primary task accuracy at $60\%$ (Figure 5c). Furthermore, even after the attacker exits the training process at the 40th round, the benign clients continue submitting normal updates in subsequent rounds, which could potentially affect the poisoned updates from the attacker in previous attacking rounds thus erasing the backdoor function. Despite this, BadSFL ensures a resilient backdoor function with accuracy exceeding $90\%$ over the entire 100 SFL rounds, which is 3 times + +![](images/997127518b93ad97b675c534d1476afe6c225cbe09f1f19b14a880437771eae3.jpg) +(a) Label Flipping, CIFAR-10, differential privacy $^+$ model pruning. + +![](images/f7b0a1576a430046f808b665f6c648187f0996a1b16a37649db4f7047c40f5ea.jpg) +(b) Pattern Trigger, CIFAR-10, differential privacy $^+$ model pruning. + +![](images/ac94b9f908097337f17fcfd2b83dfb96dc5d974a4e6fe8abc37a034c03ec9081.jpg) +(c) Feature-based Trigger, CIFAR10, differential privacy $^+$ model pruning. + +![](images/84712ba2ad1030ad2392f72c2b1263a76526b21946c9c84187608a47fcb318d7.jpg) +(d) Feature-based Trigger, CIFAR100, differential privacy $^+$ model pruning. + +![](images/e203108bab687d87d93acd769a5313f6a68b80b265a3a6d7daa723e1205faf37.jpg) +(e) Feature-based Trigger, CIFAR100, FLAME. +Figure 8. Defense against backdoor attacks. + +![](images/c22deea6274e24ad0fd92be4175e9b8d9e8cc00ffe3646b9233ce003042970cb.jpg) +(f) Feature-based Trigger, CIFAR100, SparseFED. + +longer than the lifespan achieved by the two baseline attacks, where backdoor task accuracy drops below $50\%$ after the 60th round. Horizontally comparing the effects of different types of backdoor trigger injections (Figures 6a, 6b and 6c), it is observed the feature-based trigger performs the best among them, benefiting from its stealthiness without directly manipulating the images, thereby making its updates less likely to conflict with those from benign updates. We also provide more results available in Figure 7. + +Figures 6g and 6h showcase the results obtained on the MNIST dataset. Similarly, BadSFL outperforms the other baseline attacks, achieving both backdoor task accuracy and primary task accuracy above $85\%$ . After the malicious update injection stops at round 40, in the Label flipping attack, the backdoor task accuracy in two baseline attacks catastrophically drops below $40\%$ within 10 rounds whereas BadSFL maintains a 5 times longer-lasting backdoor function in the global model in future rounds. In the pattern trigger attack, BadSFL also injects a more effective backdoor function into the global model with $10\%$ higher accuracy compared to the baselines. + +Defense. We further conduct multiple defense strategies to demonstrate the superiority of BadSFL. Specifi- + +![](images/33a1ab9b6ed3dae89e6e45417e7be845647170798c258dd3fffca07216bf8a7b.jpg) +Figure 9. Neurotoxin. + +cally, we use differential privacy [41], model pruning [24], FLAME [30] and SparseFed [32] to resist backdoor attacks. Figure 8 shows that BadSFL can still maintain high effectiveness under multiple defense strategies. Taking the label flipping on CIFAR-10 as an example, it can be observed that our method persistently maintains a high attack success rate even under defense strategies, while other baselines fail. + +Analysis on Neurotoxin. Neurotoxin aims to address the durability issue of backdoor attacks in FL settings, which ensures that the backdoor persists in the global model even after the attacker stops uploading poisoned updates. During FL training, Neurotoxin leverages the concept of the L2 norm, a mathematical function that represents the magnitude of a vector. Neurotoxin observes that the majority of the L2 norm of the aggregated benign gradient is contained in a small number of coordinates, which implies that benign updates tend to cluster in a narrow range and consequently, the aggregated gradient direction is likely to point towards this cluster. Therefore, Neurotoxin identifies and targets the parameters that get minimal changes in magnitude during training, as illustrated in Figure 9 in the Appendix. These relatively stable parameters are less likely to be significantly affected by benign updates, thereby mitigating the risk of the backdoor being overwritten by future updates. + +However, our results do not confirm Neurotoxin's expected effectiveness. Despite using this strategy, backdoor accuracy declines similarly to the baseline attack after the attacker exits at round 50. This trend is also observed in BadSFL experiments, warranting further investigation. + +# 6. Conclusion + +This paper introduces BadSFL, a novel backdoor attack specifically tailored for non-IID federated learning environments utilizing the Scaffold aggregation algorithm. By employing a GAN-based data augmentation technique and exploiting the Scaffold's control variate, BadSFL achieves superior effectiveness, stealthiness, and durability compared to existing methods. Our experimental results on multiple benchmark datasets demonstrate the attack's effectiveness, with the backdoor persisting significantly longer than existing approaches. In the future, we hope researchers can design more robust defense mechanisms to safeguard federated learning systems against such attacks. + +# Acknowledgment + +# References + +[1] Manaar Alam, Hithem Lamri, and Michail Maniatakos. Get rid of your trail: Remotely erasing backdoors in federated learning. arXiv preprint arXiv:2304.10638, 2023. 3 +[2] Manaar Alam, Esha Sarkar, and Michail Maniatakos. Perdoor: Persistent backdoors in federated learning using adversarial perturbations. In 2023 IEEE International Conference on Omni-layer Intelligent Systems (COINS), pages 1-6. 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However, previous works have ignored the misalignment when introducing the foundation models into feature matching. The misalignment arises from the discrepancy between the foundation models focusing on single-image understanding and the cross-image understanding requirement of feature matching. Specifically, 1) the embeddings derived from commonly used foundation models exhibit discrepancies with the optimal embeddings required for feature matching; 2) lacking an effective mechanism to leverage the single-image understanding ability into cross-image understanding. A significant consequence of the misalignment is they struggle when addressing multi-instance feature matching problems. To address this, we introduce a simple but effective framework, called IMD (Image feature Matching with a pre-trained Diffusion model) with two parts: 1) Unlike the dominant solutions employing contrastive-learning based foundation models that emphasize global semantics, we integrate the generative-based diffusion models to effectively capture instance-level details. 2) We leverage the prompt mechanism in generative model as a natural tunnel, propose a novel cross-image interaction prompting module to facilitate bidirectional information interaction between image pairs. To more accurately measure the misalignment, we propose a new benchmark called IMIM, which focuses on multi-instance scenarios. Our proposed IMD establishes a new state-of-the-art in commonly evaluated benchmarks, and the superior improvement $12\%$ in IMIM indicates our method efficiently mitigates the misalignment. + +![](images/e657652924d1ec00529160d3b4b5c8635106ddb75525d7f548aa84e449ea1b24.jpg) +(a) Contrastive-Learning based Foundation model for Matching + +![](images/6329539a57e3ee9fe92147485f0fd8772ae342276d2d24aa14094ef857d2f178.jpg) +(b) IMD: Generative based Diffusion model for Matching +Figure 1. The main idea of our proposed IMD. Previous works [15, 28] failed in multi-instance scenarios due to the misalignment. Our IMD leverages the explicit representation of specific instances within the diffusion model with an interaction module, accurately matching the specific instance. + +# 1. Introduction + +Image feature matching serves as the foundation for many computer vision tasks, finds extensive applications in areas as image stitching [25, 33], 3D reconstruction [45, 46] and visual localization [6, 41, 43]. Over the past decade, image feature matching has evolved from hand-crafted approaches [4, 39] to learning-based methods [12, 35, 37]. Recently, numerous learnable image matchers [14, 27, 49, 52] trained on real-world datasets [11, 24] have been proposed achieving ever-improving performance. It has been observed that such methods tend to overfit to a specific training distribution or domain and fail to generalize on unseen data fail to generalize on unseen data [21]. Recent approaches [8, 15, 21] have demonstrated that integrating vision foundation models pre-trained on large-scale datasets can effectively solve this issue, achieving superior generalization ability. However, our investigation identifies a non- + +negligible misalignment when adapting these vision foundational models to image feature matching. + +This misalignment comes from the discrepancy between the vision foundation models focus on understanding the content of the single-image and the cross-image relational understanding requirements for feature matching. The consequence of the misalignment is the poor performance of these methods in multi-instance matching problems as illustrated in Figure 1. In this case, multiple instances of the same object class exist, which impose high requirements on cross-image understanding to locate the correct instance. To address the misalignment issue, this study identifies two critical challenges that need to be confronted: + +Challenge I: Which properties that the foundation model has to equip in order to reduce the misalignment? Previous works leverage contrastive-learning based foundation model [15, 21, 28], which maximum the similarity between features prioritize global semantics. However, as illustrated in Figure 1(a), these foundation models are suboptimal for image feature matching, such contrastive objectives often lose information about specific instances and objects [59], which are crucial for accurate matching. To solve this issue, we argue that generative-based foundation models serve as a more suitable alternative. The reason is that the feature of generative-based models contain various objects and instances each with distinctive appearances and structures [40, 51]. As demonstrated in Figure 1(b), this information is crucial for image feature matching, particularly in multiple instances scenarios. + +Challenge II: How to design a cross-image interaction mechanism aligning with the matching tasks? Although the foundation models have strong single-image understanding ability, they can not lead to cross-image understanding by nature. This paper identifies the condition mechanism of the generative-based model as a natural tunnel for the cross-image information interaction. Inspired by this, we intend to utilize each image as the condition for the other image. + +In this paper, we propose IMD: Image feature Matching with Diffusion models, seamlessly adapt foundation models to matching tasks. The IMD contains two parts: 1) We introduce a novel feature extraction paradigm based on the phenomenal generative-based diffusion models, exploring its ability of self-image understanding while moving toward cross-image understanding. Different from previous works utilizing the progressive denoising process [32, 60], we employ the frozen UNet decoder as a backbone to directly process clean natural images to obtain the explicit representation for every instance. 2) To facilitate interaction between image pairs, we prompt the extraction of diffusion backbone with a novel Cross-image Interaction Prompt Module (CIPM). Specifically, we design a personalized prompt for each image that was conditioned by the image pair to enhance relevance and discriminability. We also propose to + +utilize the cross-attention layers to proceed with explicit interaction and comparison between the image pair. CIPM enforces the model to capture the underlying geometric and semantic relationships between images during the feature extraction process itself, resulting in more correlated and comprehensive image features. + +For a more comprehensive analysis, we construct a new benchmark IMIM based on a recently published video tracking and segmentation dataset [1]. We observe that existing benchmarks predominantly comprise images containing either a single, prominent object, enabling semantic-based approaches to attain high performance. In contrast, our IMIM contains images with multiple instances of the same semantic (e.g., two cars running), which imposes more stringent requirements for preserving instance-level details. We report a significant improvement of $12\%$ in matching accuracy, demonstrating that our method successfully alleviates the misalignment. + +To summarize, we make the following contributions: + +- We identify the misalignment when introducing the foundation models into the feature matching tasks with two challenges for solving the misalignment. +- We propose IMD to achieve seamless alignment with 1) a novel feature extraction pipeline for matching tasks and 2) cross-image interaction prompt module towards cross-image understanding. +- IMD is demonstrated to achieve state-of-the-art results across a wide range of benchmarks. What's more, a new dataset is introduced to evaluate the performance of models in the multi-instance situation. + +# 2. Related Work + +Local Feature Matching. Feature matching methods can be broadly classified into three categories: sparse, semidense, and dense. Traditional sparse feature matching has been tackled through keypoint detection and description, followed by matching the descriptors [3, 5, 12, 30, 39, 42]. More recently, the semi-dense approach [9, 28, 49, 52] has emerged, also known as detector-free methods, replacing keypoint detection with dense matching at a coarse scale, followed by mutual nearest neighbor extraction and subsequent refinement. The dense approach [14, 15, 63] focuses on estimating a dense warp, aiming to identify every potential pixel-level correspondence. However, they are typically much slower than sparse and semi-dense approaches. + +Vision Foundation Models for Matching. There exist prior works leveraging the vision foundation models to improve matching performance. MESA [61] introduced the use of SAM [22] for area matching, narrowing the search space. Nevertheless, the coarse-grained utilization fails to fully leverage the knowledge of foundation models. Another series of works [8, 15, 21, 28] employees vision foun + +![](images/42adb6a3accd79ff29679ee026504c071c8b56cb7659ea885aabde8bf24236cf.jpg) +Figure 2. Pipeline Overview. Given an image pair, we first encode them with the image encoder and employ the cross-attention mechanism to proceed with explicit interaction between images. With the images and its prompt containing interactive information as input, we extract their coarse features $C_A$ , $C_B$ from a frozen text-to-image diffusion UNet. Then, we refine the coarse features for more discriminative by iteratively applying self- and cross-attention mechanisms. The coarse-level matching generates pixel-to-pixel matches $\mathcal{M}_c$ at 1/8 scale. To refine coarse matches, discriminative fine features $\tilde{F}_A$ , $\tilde{F}_B$ are obtained by fusing the transformed coarse features with original fine features from the specialized fine feature encoder. Feature patches are then cropped, centered around each coarse match $\mathcal{M}_c$ . The fine-level matching is followed to obtain sub-pixel matches $\mathcal{M}_f$ . + +dation models as feature extractor directly, significantly improving the performance. However, we identify that they ignored the critical misalignment between foundation models and the matching tasks. Specifically, the commonly used DINo2 [34] often loses information about specific instances. Meanwhile these models lack information interaction between image pairs, leading to failures in multiple instances scenes. In contrast, we propose to integrating the generative-based diffusion models to address the misalignment with a novel cross-image interaction module, achieving excellent performance in multi-instance scenes. + +Building on superior generative performance of diffusion models, recent studies have started investigating the internal representations within diffusion models [40, 57, 58, 62]. DIFT [51] and SD+DINO [59] demonstrated that extracting features from denoising module enables semantic matching between two objects. In addition, DIFT has also shown that the image features from frozen diffusion models can act as powerful descriptors for feature matching tasks. Our work is closely supported by these efforts, but we instead explore the misalignment when adapting the foundation models into feature matching and how to overcome. + +Cross-image Interaction. Mainstream approaches such as RoMa [15] and OmniGlue [21] utilize visual foundation models to process individual images, thereby obtaining in- + +dependent image features. The relationship between the images is obtained through a subsequent attention mechanism. However, we argue that performing matching using image features extracted in this way limited performance through the image features lacking correlation. CroCo [55] and CroCov2 [56] leverage cross-view completion as a pre-training objective to inherently encourage the model to learn correlated features cross images. SD4Match [23] has underscored the importance of the relevance of cross-image in semantic matching, which employ a shared prompt conditioned on the image pairs for diffusion model. Nevertheless, this work faces notable issue: this shared prompt introduces correlation while leading to worse discriminative. In contrast, our proposed CIPM provided the personalized prompts for each image, guiding feature extraction to increase relevance while maintaining discriminancy. Our IMD not only improves information transfer across images but also results in correlated features. + +# 3. Method + +In this section, we present IMD, a new detector-free local feature matching method to overcome the misalignment between vision foundation models and feature matching. IMD adopts a typical two-stage framework, starting with coarse-level correspondences and subsequently refining them to + +sub-pixel positions. Given a pair of images $I_A$ and $I_B$ , the UNet component within diffusion models generates coarse feature maps (1/8) from input images based on the prompt produced by our designed prompting module (Sec. 3.2). Specifically, we propose the cross-image interaction prompt module to explicitly facilitate cross-image interaction. With these extracted features, the self- and cross-attention based coarse matching is performed in coarse-level features (Sec. 3.3). Using the specialized fine features encoder, we extract the fine feature maps (1/2) from image pairs. According to the coarse matches, a subpixel-level refinement module is employed to predict fine-level matches (Sec 3.4). An overview of our approach is illustrated in Figure 2. + +# 3.1. Text-to-Image Diffusion Model + +We begin with a brief overview of the diffusion model and its adaptation for feature extraction. + +Background. Diffusion models [19, 20, 48] are generative models that are designed to transform a normal distribution to an arbitrary data distribution. This model involves two processes: forward and reverse. In the forward process, Gaussian noise of varying magnitudes is added to clean data points to create noisy data samples. A clean image $I_0$ is gradually degraded to a noisy image $I_t$ through a series of Gaussian noise additions, following the equation: + +$$ +I _ {t} = \sqrt {\alpha_ {t}} I _ {0} + (\sqrt {1 - \alpha_ {t}}) \epsilon , \tag {1} +$$ + +where $\epsilon \sim \mathcal{N}(0,1)$ denotes the randomly sampled noise, and $t\in [0,T]$ represents the "time" in the diffusion process with larger time steps corresponding to higher levels of noise. The noise amount is controlled by the pre-defined noise schedule $\{\alpha_t\}_t^T$ . In the reverse process, a neural network $f_{\theta}$ is trained to take $I_{t}$ and the time step $t$ as inputs to predict the added noise $\epsilon$ . For image generation, $f_{\theta}$ is typically parametrized as a UNet [13, 38]. Once trained, $f_{\theta}$ can be utilized to "reverse" the diffusion process. Thus, by sampling from a normal distribution, the corresponding "original image" can be reconstructed through iterative removal of the noise $\epsilon$ . + +Diffusion Model as Feature Extractor. Our framework is built upon the widely used Stable Diffusion (SD) [38] models, which perform the denoising process in a learned latent space using a UNet architecture. SD also exhibits impressive capability to generate high-quality images conditioned on input prompts, such as text or images. Given an input image $I_0$ and a specific timestep $t$ , $I_0$ is first encoded into its latent representation $z_0$ using a VAE encoder $\mathcal{E}$ , which is subsequently corrupted to $z_t$ using Eq. (1). During this noise prediction process, with the latent code $z_t$ at timestep $t$ and the prompt embedding $P$ as inputs, we extract the feature map $F$ from the output of an intermediate layer of denoising UNet. This process can be formally expressed as + +follows: + +$$ +z _ {0} = \mathcal {E} (I _ {0}), +$$ + +$$ +z _ {t} = \sqrt {\alpha_ {t}} z _ {0} + \sqrt {1 - \alpha_ {t}} \epsilon , \tag {2} +$$ + +$$ +F = \operatorname {U N e t} \left(z _ {t}, t, P\right). +$$ + +Another important consideration is the selection of the timestep $t$ and the network layer from which features are extracted. Studies indicate larger $t$ and earlier network layers tend to produce more semantically-aware features, while smaller $t$ and later layers emphasize low-level details [51]. For a detailed overview of the hyper-parameter values utilized in this study, please refer to the Suppl. For simplicity, we omit the VAE encoding step and directly refer to the input to the UNet as the image $I$ rather than its latent representation $z$ in the following sections. + +# 3.2. Cross-image Interaction Prompt Module + +Text-to-image diffusion models pre-trained on extensive image-text pair datasets, exhibit remarkable controllability through customizable prompt mechanisms. During each step of the denoising process, diffusion models perform cross-attention between the text embedding of prompts and UNet features leverage the text input to guide the denoising direction of the noisy image. As shown in Eq.(2), the diffusion model's visual representation $F$ of image $I$ relies on its associated prompt $P$ . This motivated us to explore the possibility of using another image as a prompt to generate interactive image features. + +Recent studies have explored generating the prompts with input images for tasks such as semantic correspondence [23, 59] and image segmentation [57]. In this context, the prompt is generated from the input image itself in single-image task or a shared prompt by concatenating the features from the image pair in tasks involving a pair of images. Although this design has proven effective for the aforementioned tasks, it may be not the optimal choice for facilitating image interaction in feature matching. Our reasons are: + +1. Feature matching requires the model to focus on the local features of the images. Utilizing a shared prompt for feature extraction across image pairs can result in the loss of detailed information from the images. +2. Simply concatenating image features is insufficient to fully capture the relationships between them, as it lacks explicit learning of dependencies and interactive information between the images. + +We therefore propose a novel cross-image interaction prompt module (CIPM) and illustrate its architecture in the bottom of Figure 2. Given a pair of clean images $I_{A}$ and $I_{B}$ , we leverage a pre-trained frozen image encoder $\mathcal{V}$ , e.g., from CLIP [36] to extract the image features $\mathcal{F}^{A}$ and $\mathcal{F}^{B}$ . Then we adopt three $1 \times 1$ convolution layers to encode the input image feature $\mathcal{F}^{A}$ and $\mathcal{F}^{B}$ into features $\phi_{Q,I}$ , + +$\phi_{K,I}, \phi_{V,I}$ . We apply the cross-attention mechanism between features from input images $I_A$ and $I_B$ . We further utilize a learned MLP to transform the image embedding into the prompt embedding $P_A$ and $P_B$ , which is then fed into the text-to-image diffusion UNet, denoted as: + +$$ +P _ {A} = \mathrm {M L P} \circ \operatorname {S o f t m a x} \left(\phi_ {Q, I _ {A}} \phi_ {K, I _ {B}} / \sqrt {d _ {k}}\right) \phi_ {V, I _ {B}}, \tag {3} +$$ + +$$ +P _ {B} = \mathrm {M L P} \circ \operatorname {S o f t m a x} \left(\phi_ {Q, I _ {B}} \phi_ {K, I _ {A}} / \sqrt {d _ {k}}\right) \phi_ {V, I _ {A}}, +$$ + +where $d_{k}$ denote the scale factor. Finally, the UNet of the text-to-image diffusion model, combined with the CIPM, constitutes IMD's feature extractor, which generates the visual representation for the given image pairs. Formally, the coarse features $C_A$ and $C_B$ are computed as: + +$$ +\begin{array}{l} C _ {A} = \operatorname {U N e t} \left(I _ {A}, t, P _ {A}\right), \\ C _ {A} = \operatorname {U N e t} \left(I _ {A}, t, P _ {A}\right) \end{array} \tag {4} +$$ + +$$ +C _ {B} = \operatorname {U N e t} \left(I _ {B}, t, P _ {B}\right). +$$ + +The attention mechanism facilitates interaction between the input images $I_{A}$ and $I_{B}$ within the feature space, thereby capturing correspondence information more explicitly compared to merely concatenating the image pair channel-wise before feeding them into the network [23]. Furthermore, the transformer-based network demonstrates greater robustness when the two input images have significant differences. + +# 3.3. Coarse-Level Matching Module + +We also conduct the attention mechanisms for coarse features to improve discriminativeness and compute coarse-level matches using the transformed coarse feature maps $\tilde{C}_A$ and $\tilde{C}_B$ . These coarse correspondences provide rough matching regions that are refined in the subsequent fine-level refinement module. The score matrix $S$ is generated by computing the pairwise cosine similarity between coarse-level features $\tilde{C}_A$ and $\tilde{C}_B$ . We also apply the dual-softmax of $S$ to obtain the probability of mutual nearest matching, following [8, 9, 49]. The coarse matches $\{\mathcal{M}_c\}$ are determined by selecting matches that exceed a predefined score threshold $\tau$ and satisfy the mutual nearest neighbor (MNN) constraint. + +# 3.4. Subpixel-Level Refinement Module + +As illustrated in Figure 2, with the established coarse matches $\{\mathcal{M}_c\}$ , we refine these matches to achieve subpixel accuracy following [54]. This module consists of a specialized fine feature encoder for generating discriminative fine features, followed by the fine-level refinement to produce the final matches $\{\mathcal{M}_f\}$ . + +Fine Features Encoder. In prior works [9, 49], the FPN [26] is employed for producing a feature pyramid of coarse and fine features used for coarse matching and later refined to a sub-pixel level. This is problematic when using SD features as only coarse features at $1/8$ dimension + +of the original image exist. Hence, we utilize a specialized ConvNet obtained fine features at 1/2 dimension. For efficiency, these fine image features are fusion with the previously transformed coarse features to obtain discriminative fine features $\tilde{F}_A$ , $\tilde{F}_B$ in the original image resolution eliminating the additional transform networks [49]. Then local feature patches are cropped on fine feature maps centered at each coarse match $\{\mathcal{M}_c\}$ . + +Fine-Level Matching. To refine the coarse matches, we first compute the local patch score matrix $S_{l}$ with the fine feature patches. MNN searching is applied on $S_{l}$ to get intermediate pixel-level fine matches. We select the top-1 fine match for each coarse match by ranking the correlation scores. Then the feature of each point in $I_{A}$ is correlated with a $3 \times 3$ feature patch centered around its fine match in $I_{B}$ . The softmax operation is applied to obtain a match distribution matrix, and the final refined match is determined by calculating the expectation. + +# 3.5. Supervision + +The entire pipeline is trained in an end-to-end manner, with separate supervision applied to the coarse and refinement matching modules. + +Coarse-Level Matching Supervision. The coarse-level loss is computed as the focal loss between the matching score matrix and the ground truth matches. The coarse ground truth matches, denoted as $\{\mathcal{M}_c\}_{gt}$ , with a total number of $N$ , are constructed by warping grid-level points from $I_A$ to $I_B$ using depth maps and image poses following [49]. The resulting correlation score matrix $S$ in coarse matching is supervised by minimizing the log-likelihood loss over the locations in $\{\mathcal{M}_c\}_{gt}$ : + +$$ +\mathcal {L} _ {c} = - \frac {1}{N} \sum_ {(\tilde {i}, \tilde {j}) \in \{\mathcal {M} _ {c} \} _ {g t}} \log \mathcal {S} (\tilde {i}, \tilde {j}). \tag {5} +$$ + +Fine-Level Matching Supervision. We train the fine-level matching module by supervising two losses independently. The first fine loss, $\mathcal{L}_{f1}$ , aims to minimize the log-likelihood loss of each fine local score matrix $S_{l}$ based on the pixel-level ground truth fine matches, similar to the coarse loss. The second is optimized using $\mathcal{L}_{f2}$ , which computes the $\ell_2$ loss between the final subpixel matches $\{\mathcal{M}_f\}$ and the ground truth fine matches $\{\mathcal{M}_f\}_{gt}$ . + +The total loss is computed as a weighted sum of all supervision terms: $\mathcal{L} = \mathcal{L}_c + \alpha \mathcal{L}_{f1} + \beta \mathcal{L}_{f2}$ . + +# 4. Experiments + +# 4.1. Implementation Details + +Following DIFT [51], we employ Stable Diffusion (SD) 2-1 [38] pretrained on LAION [47] dataset as the diffusion + +Table 1. Results of multi-instance evaluation on IMIM and two-view pose estimation on the MegaDepth [24], ScanNet [11] datasets. Methods are grouped into 3 groups: 1) methods that are zero-shot and not fine-tuned on the training data, 2) sparse methods, and 3) semi-dense methods. All the IMD results have gray background for easy lookup and annotate best results. The extended version including dense methods, is provided in the Suppl. + +
CategoryMethodMegaDepthScanNetIMIM (%)
AUC@5°AUC@10°AUC@20°AUC@5°AUC@10°AUC@20°
Zero-ShotCLIP [36] ICML'2130.848.163.210.120.631.354.4
DINOv2 [34] Arxiv'2332.550.865.313.028.540.857.9
DIFT [51] NeurIPS'2338.455.970.515.732.045.161.2
SparseSP [12]+NN CVPRW'2331.746.860.17.518.632.155.9
OmniGlue [21] CVPR'2447.465.077.831.350.265.077.6
SP [12]+LG [27] ICCV'2349.967.080.114.830.847.560.5
Semi-DenseLoFTR [49] CVPR'2152.869.281.216.933.650.668.9
RCM [31] ECCV'2453.269.481.517.334.652.1-
Efficient LoFTR [54] CVPR'2456.472.283.519.237.053.670.6
EcoMatcher [10] ECCV'2456.572.083.4----
HomoMatcher [53] AAAI'2557.873.584.422.140.957.5-
TopicFM [16] AAAI'2358.272.883.217.334.550.976.5
MESA_ASpan [61] CVPR'2458.474.184.8----
CasMTR [8] ICCV'2359.174.384.822.640.758.079.2
PRISM [7] ACMMM'2460.074.985.123.941.858.9-
IMD (Ours)61.276.085.829.848.364.288.7
+ +model. We utilize the upsampling block index $n = 2$ of the UNet so the feature map size is 1/8 of the input and the dimension is 640, and we set the time step used for the diffusion process to $t = 0$ . We choose CLIP [36] as the image encoder $\mathcal{V}$ in CIPM. We adopt the ResNet [17] to extract fine image features. The self- and cross-attention are interleaved for $N = 2$ times to transform coarse features. $\tau$ is chosen to 0.2. Our model is trained on the MegaDepth dataset [24], a large-scale outdoor dataset. Following the protocol in [54], the test scenes are strictly separated from the training data. The weights $\alpha$ and $\beta$ in the loss function are set to 1.0 and 0.25, respectively. We employ the AdamW optimizer with an initial learning rate of $4 \times 10^{-3}$ . The training process takes 30 epochs on 8 NVIDIA 3090 GPUs. Both the coarse and fine stages are trained jointly from scratch. The model trained on MegaDepth is subsequently evaluated across all datasets to showcase its generalization capability. + +# 4.2. Evaluation Dataset for Multi-Instances + +Datasets. During the evaluation of IMD on conventional datasets for matching tasks, we observed that most existing datasets primarily have only a single instance per object category. For example, widely used benchmarks like MegeDepth [24] and ScanNet [11] focus on individual landmarks such as buildings, with each category typically representing only one instance. These characteristics make it easier for global semantic-based methods to get accurate matching results, as there are often no objects from the same category but different instances need to distinguish within + +or across images. As a result, comparing instance-based features against current methods on these benchmarks tends to yield similar results, which does not fully showcase the advantages of instance-based approaches. + +To this end, we propose a new benchmark: Image Multi-Instance Matching (IMIM). IMIM is built using the BURST [1] dataset designed for Segmentation and Tracking inspired by [40]. This dataset consists of videos with pixel-level segmentation masks for each unique object track across different object categories. Specifically, we select videos that include at least two instances of the same object class and pick two frames from videos every time, assigning one as the source image and another used for the target image. After filtering, we obtain a total of 100 pairs images from 50 videos across 10 object categories. + +Evaluation Protocol. Ground-truth masks are used to crop instances from source and target images. For every match results $(i,j)$ , we calculate the number $N$ of matching pairs that satisfied $i$ located in the source image instance mask. We report the percentage of $M / N$ that $M$ is the number of matching pairs which satisfied $i$ located in the source image instance mask, while $j$ located in the target image instance mask. + +Results. Table 1 presents the results in IMIM. IMD demonstrates superior performance over methods designed specifically for matching task and zero-shot models including CLIP, DINOv2, DIFT with diffusion, demonstrating our approach's reliable ability when matching the multi instances in the target image. Notably, we observe significant discrep + +Table 2. Results of Homography Estimation on Hpatches Dataset. + +
CategoryMethodHomography est. AUC
@3px@5px10px
SparseR2D2 [37]+NN NeuIPS'1950.663.976.8
OmniGlue [21] CVPR'2455.369.082.5
SP [12]+SG [42] CVPR'2053.968.381.7
Semi-DenseLoFTR [49] CVPR'2165.975.684.6
Efficient LoFTR [54] CVPR'2466.576.485.5
HomoMatcher [53] AAA'2570.279.687.8
SRMatcher [28] ACMMM'2471.279.387.0
CasMTR [8] ICCV'2371.480.287.9
PRISM [7] ACMMM'2471.980.488.3
IMD (Ours)73.982.088.9
+ +ancies between DINOv2 and DIFT. This due to DINOv2 ignoring the information not related to semantics. Qualitative comparisons are shown in Figure 3, demonstrating that our approach consistently and accurately matches the correct instance in the target image. Our experimental results validate the effectiveness of the proposed approach in significantly mitigating the misalignment issue. + +# 4.3. Relative Pose Estimation + +Datasets. We utilize the outdoor MegaDepth [24] dataset and the indoor ScanNet [11] dataset to evaluate relative pose estimation, showcasing the effectiveness of our approach. + +MegaDepth is an extensive outdoor dataset comprising 1 million images across 196 scenes, reconstructed using COLMAP [45]. The key challenges in this dataset include significant viewpoint and illumination variations, along with repetitive patterns. For evaluation, we adopt the test split from [49], using 1500 sampled pairs from the "Sacre Coeur" and "St. Peter's Square" scenes. All images are resized such that the longest edge equals 1152 pixels. + +ScanNet consists of monocular sequences with ground truth annotations and presents challenges due to wide baselines and textureless regions. For evaluation, we use the test pairs sampled in [49], resizing all images to $640 \times 480$ pixels for all methods. + +Evaluation Protocol. Following [49, 54], the recovered relative poses from the matches are evaluated to assess matching accuracy. The pose error is defined as the maximum of the angular errors in rotation and translation. We evaluate the performance by reporting the AUC of pose error at thresholds of $5^{\circ}$ , $10^{\circ}$ , and $20^{\circ}$ . + +Results. We report the accuracy comparison between IMD and other methods in Table 1. Qualitative comparisons are shown in Figure 3. Our proposed IMD sets a new state-of-the-art performance across all evaluation metrics on outdoor benchmarks. Benefiting from the use of pre-trained diffusion backbone, IMD notably improves by $24.6\%$ in AUC@5° on ScanNet compared to the best model trained on MegaDepth PRISM, showing impressive generalization capability. We have the extended version of quantitative re + +Table 3. Results of Visual Localization on InLoc Dataset. + +
MethodDUC1DUC2
(0.25m,2°)/(0.5m,5°)/(1.0m,10°)
SP [12]+SG [42]cvPR2049.0 / 68.7 / 80.853.4 / 77.1 / 82.4
LoFTR [49]cvPR2147.5 / 72.2 / 84.854.2 / 74.8 / 85.5
CasMTR [8] ICCV2353.5 / 76.8 / 85.451.9 / 70.2 / 83.2
AspanFormer [9] ECCV2251.5 / 73.7 / 86.055.0 / 74.0 / 81.7
PRISM [7] ACMMM2453.0 / 77.8 / 87.954.2 / 72.5 / 83.2
IMD (Ours)54.6 / 77.3 / 88.260.3 / 82.7 / 88.5
+ +sults (e.g. dense methods) and more analysis in the Suppl. + +# 4.4. Homography Estimation + +Dataset. Homography is crucial in two-view geometry, facilitating the transformation of perspectives between two images capturing the same scene. We evaluate on the widely used HPatches dataset [2], which includes 57 sequences with significant illumination variations and 59 sequences exhibiting significant viewpoint changes. + +Evaluation Protocol. We present the area under the cumulative curve (AUC) for corner errors at thresholds of 3, 5, and 10 pixels. OpenCV's RANSAC method is used for robust estimation. Following LoFTR [49], all test images are resized so that their shorter dimension equals 480 pixels. + +Results. Table 2 demonstrates that IMD significantly outperforms sparse and semi-dense methods. For the semidense methods, our method notably improves by $2.7\%$ in @3px compared to the best semi-dense methods. We attribute this to the effectiveness of guidance from the diffusion model for generalization and the proposed image interaction module for accuracy improvement. + +# 4.5. Visual Localization + +Datasets and Evaluation Protocols. We evaluate the performance of IMD on the widely-used datasets InLoc [50]. The InLoc dataset includes 9,972 RGBD images with geometric registration and 329 query images with verified poses, posing challenges in textureless or repetitive environments. For testing, we focus on DUC1 and DUC2 following [49]. The candidate image pairs are identified using the pre-trained HLoc [41] system following [7]. The results of Aachen Day-Night v1.1 [44] are provided in Suppl. + +Results. Table 3 presents the result on the InLoc dataset, IMD surpasses all methods on DUC2 and matches the performance of top-tier approaches on DUC1. IMD exhibits robust performances, underscoring the adaptability of our method in diverse task environments. + +# 4.6. Ablation Studies + +Visual Representations. We compare the internal representations of diffusion models with those of other pretrained contrastive learning objective and discriminative objective models. We observe that IMD outperforms the other + +![](images/7e7eaee6f486d8de4a0d90dc6a2709253239a4ba6816997e38c9bf0694b382b1.jpg) +Figure 3. Qualitative comparison of outdoor MegaDepth and IMIM datasets compared with DINOv2 [34], LoFTR [49], CasMTR [8], RoMa [15] and ours IMD. Green indicates the correctly matching results. More visualizations are provided in the Suppl. + +Table 4. Results of Ablation Studies. + +
MethodMegaDepth datasetIMIM
AUC@5°AUC@10°ACU@20°
1) Replace SD to Swin (B) [29]57.573.283.674.0
2) Replace SD to DINOv2 (B) [18]57.873.583.775.5
3) Empty string58.473.884.184.0
4) Individual prompt in CIPM59.674.384.585.2
5) w/o cross attention60.775.085.187.4
6) time step T = 10060.975.785.888.1
Ours Full61.276.085.888.7
+ +models on both datasets. This highlights that internal representations of diffusion models are indeed more efficient for matching tasks, especially in multi-instance scenarios. More comparison results shown in Suppl. + +Cross-image Interaction Prompt Module. We explore the influence of interaction in CIPM on matching accuracy. Specifically, we assess the additional approaches: an empty string and the individual image prompt in Table 4. These evaluations are regarded as does not presuppose any information interaction. These setups yield lower accuracy, further highlighting the benefits of the interaction between image pairs, and facilitates more precise capturing of cross-image relationships. When we replace the cross-attention with a concatenation operation to execute interaction between images which means both images share the same prompt, there is a decline in performance in row 5. + +Different Time Steps. We also investigate which diffusion step(s) are most effective for feature extraction. As the value of $t$ increases, the amount of noise distortion added to the input image also increases. In Stable Diffusion [38], there are a total of 1000 time steps. From the row 6 of Table 4, we observe that all metrics decrease as $t$ increases, with the best results achieved at $t = 0$ (ours). We conduct more ablation studies about timesteps and block-index in Suppl. + +# 4.7. Understanding IMD + +To mitigate potential bias, that the improvement of the model mostly achieved from increased parameters in SD 2-1 (1,300M), we compare with different backbone: (1) DI + +![](images/ba89dd0c573b8d264c14eb16214c9e5cc292ad3f2910354d38a51dd576f3aa86.jpg) +Figure 4. Performance comparison and the circle size indicating parameter count. + +NOv2(G) (1,100M) of similar scale; (2) SD-tiny and SD-small with CIPM, having $75\%$ and $55\%$ fewer parameters respectively. We further compare with RoMa [15] (dense) and SRMatcher [28] (semi-dense) using DINOv2 and its SD 2-1 variant. Figure 4 shows results on MegaDepth and IMIM. All SD-based models achieve strong IMIM performance, indicating capacity alone does not address multi-instance problems. IMD-single-prompt results validate cross-image interaction effectiveness. Discussion on feature behavior analysis and training protocol ablations are detailed in Suppl. + +# 5. Conclusion + +In this work, we present IMD, a novel framework designed to address the misalignment between vision foundation models and feature matching tasks. We identify two challenges for addressing the misalignment: 1) foundation model properties' impact on matching; 2) the disconnect between foundation models and feature matching. We also introduce a new benchmark specifically designed to assess misalignment mitigation. Extensive experiments show that IMD achieves major gains and effectively alleviates misalignment. 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With the Contrastive Language-Image Pre-trained model (CLIP) exhibiting strong capabilities across various downstream tasks, there has been growing interest in leveraging CLIP for continual learning in such scenarios. Most existing works overlook the inherent modality gap in CLIP, a key factor in its generalization and adaptability. In this paper, we analyze the variations in the modality gap during the fine-tuning of vision-language pre-trained models. Our observations reveal that the modality gap effectively reflects the extent to which pre-trained knowledge is preserved. Based on these insights, we propose a simple yet effective method, MG-CLIP, that improves CLIP's performance in class-incremental learning. Our approach leverages modality gap preservation to mitigate forgetting and modality gap compensation to enhance the capacity for new data, introducing a novel modality-gap-based perspective for continual learning. Extensive experiments on multiple benchmarks demonstrate that our method outperforms existing approaches without requiring additional replay data. Our code is available at https://github.com/linlany/MindtheGap. + +# 1. Introduction + +The goal of continual learning is to enable models to continuously acquire new knowledge and adapt to the ever-changing real world [22, 31]. Traditional approaches to continual learning focus on training a model from scratch, aiming to reduce catastrophic forgetting of old task knowledge while maintaining plasticity to adapt to new data [18]. This is often referred to as the stability-plasticity trade-off. However, with the recent development of large-scale pre-trained models, these models offer stronger stability + +![](images/05e97c9165a2e34400f9d09cbe8e72445a9a00cba645b7617a49596577292764.jpg) +Figure 1. Left: In continual learning, we preserve the modality gap to retain CLIP's original knowledge and mitigate forgetting. Right: Due to the modality gap, the text classifier's performance is restricted. We compensate for it through an intra-modal classifier by enhancing its adaptability and refining decision boundaries. + +and generalization capabilities for continual learning [15, 23, 36]. Among pre-trained models, visual language pretrained models such as CLIP demonstrate excellent generalization to downstream tasks, showcasing impressive zero-shot capabilities [16, 17, 26]. Consequently, CLIP-based continual learning (CL) has emerged as a promising new direction, attracting increasing attention from researchers [11, 12, 30, 40]. + +Existing CLIP-based continual learning methods can be broadly categorized into two approaches: one fine-tunes the backbone to modify feature representations [21, 40], while the other freezes the backbone and introduces learnable modules for continual learning [11, 12, 49]. They often treat CLIP as a feature extractor, approximating it to a text-enhanced visual model [21]. Based on this view, they focus on better feature fusion for improved performance [12, 49] or leveraging textual information to guide visual feature adaptation [11]. However, these methods often overlook CLIP's unique cross-modal properties, the modality gap, distinguishing it from unimodal systems. The modality gap is observed in previous work [19]. As shown in Fig. 1 (left), the modality gap is that the intra-modal feature distance is small while the inter-modal distance is large. The feature + +distributions of the two modalities are represented in two distinct cones, with an inherent spacing between them. To fully exploit CLIP's cross-modal properties, it is crucial to explore strategies that preserve the inherent modality gap while addressing its limitations in continual learning. + +In this paper, we investigate CLIP-based class incremental learning from the perspective of the modality gap. In existing studies on multimodal model training and adaptation of downstream tasks, the modality gap is often seen as a source of suboptimal performance. Researchers focus on reducing the modality gap in pre-trained multimodal models [6, 10, 24]. However, in the context of continual learning with CLIP, our objective is to retain the strong generalization capability of the model while learning new data. Thus, how to handle the modality gap in continual learning remains an open question. Our work is based on the assumption that this modality gap reflects the intrinsic knowledge of the pre-trained model. + +Downstream datasets are typically much smaller than pretraining datasets, making them insufficient to fully train the model. As a result, modifying the fundamental properties of a pre-trained model, such as the modality gap, based on the downstream data may disrupt the pre-trained knowledge. It may potentially compromise the performance of continual learning. During training on the current task, the cross-entropy optimization objective tends to expand this gap. This phenomenon intensifies as incremental learning data continue to arrive. Furthermore, directly aligning the two modalities for downstream tasks will also significantly alter the pre-trained knowledge. Therefore, we keep the modality gap relatively stable to maintain the stability of the model. We analyze the changes in modality gap during training and propose a modality gap-aware adjustment strategy. By tracking variations in the modality gap, we regulate the training to maintain a stable modality gap, thereby preserving pre-trained knowledge and mitigating forgetting. + +Additionally, we analyze the impact of preserving the modality gap. As shown in Fig. 1 (right), when text features are used as classifiers, the modality gap may restrict the model's ability to learn new data in continual learning. This limits the adaptability of the model, reducing the plasticity. To compensate modality gap, we propose to build a classifier in the visual space, where the modality gap does not pose a restriction. By integrating its output with that of the text classifier, we compensate for the modality gap and improve the learning capacity of CLIP. + +The main contributions of this paper are as follows: + +- We propose a method to preserve the modality gap that maintains pre-trained knowledge and mitigates forgetting in continual learning. +- We compensate for the limitations of the modality gap by introducing a complementary mechanism, enhancing model plasticity. + +- Our approach achieves state-of-the-art results across multiple datasets without replay or complex structures. + +# 2. Related Work + +# 2.1. Class-Incremental Learning + +Class-incremental learning methods are generally grouped into three types [3]. Regularization methods limit changes to the model. Some methods use distillation to reduce the deviation of model features or penalize changes in model parameters [2, 13, 18, 44, 47]. Dynamic network approaches allow the model structure to evolve as new tasks are introduced [5, 32, 37, 38]. Replay-based methods retain original samples or relevant information from them. When learning a new task, these methods replay original samples [20, 27, 29] or recover old samples from the retained information [11, 33, 41, 43]. The latter often involves techniques such as memory compression or feature replay. Dynamic networks or feature replay methods tend to increase both parameter count and memory storage requirements. With the widespread use of pre-trained models, incremental learning methods for visual pre-trained models have also emerged. Parameter-efficient fine-tuning approaches gradually expand a small number of parameters as tasks increase [28, 34, 35]. Aper [48] maintains stability by training the model only on the first task. SLCA [43] uses a small learning rate fine-tuning backbone for continual learning. They show that preserving the stability of pretrained visual models enhances generalization and benefits class-incremental learning on downstream tasks. + +# 2.2. Class-Incremental Learning with CLIP + +CLIP performs remarkably well in class-incremental learning tasks with downstream data [30]. Continual learning based on CLIP has gained increasing attention. Some approaches add learnable modules to the original CLIP features to modify them for better adaptation to new tasks. PROOF [49] and CLAP [12] add learnable modules to the CLIP output features to facilitate cross-modal interaction. RAPF [11] introduces a linear layer after the CLIP visual encoder for downstream adaptation and uses textual modality information to guide feature replay. Other methods fine-tune CLIP to alter its output features. ZSCL [46] distills additional datasets during training. MOE4CL [40] fine-tunes CLIP with a mixture of experts, introducing a selection mechanism to selectively use the original CLIP model. Magmax [21] sequentially fine-tunes the entire CLIP model, using a task vector algorithm to merge models at inference time. LGVLM [45] trains separate LoRA modules for each task. These methods primarily focus on leveraging the prior knowledge of natural language to assist continual learning, often neglecting the preservation of zero-shot capabilities while emphasizing performance on + +sequential tasks. In contrast, we focus on retaining the model's capabilities while enhancing its continual learning ability, starting from the inherent property of the CLIP. + +# 2.3. Modality Gap + +Liang et al. [19] demonstrated a phenomenon in pre-trained vision language models called the modality gap. In contrastive vision-language models, the modality gap is reflected in the fact that text and image features are located in two separate narrow cones. The features of different modalities exhibit distinct separation, whereas the features within the same modality tend to cluster more closely. Existing studies have explored the impact of the modality gap on tasks such as domain adaptation [10], few-shot classification [39], model pre-training [7] and retrieval task [24]. Reducing the modality gap can improve the model performance in these tasks. However, in continual learning tasks, the stability of pre-trained knowledge is more crucial for downstream tasks over time. Therefore, we propose using the modality gap as an indicator of the changes in the pretrained model's feature space, with the goal of preserving the modality gap in continual tasks. + +# 3. Preliminaries + +Class incremental learning definition. We consider a class-incremental learning setup based on a pre-trained CLIP model $M$ . The objective is to sequentially train the model on a series of classification tasks. Each task $t$ consists of a set of categories $C_t$ , and the categories between tasks do not overlap, $\forall i \neq j, C_i \cap C_j = \emptyset$ . During the training of task $t$ , the model has no access to information related to the previous $t - 1$ tasks. After training in the $t$ -th task, the model $M_t$ is required to correctly classify all previously learned categories, $C_1 \cup C_2 \cup \dots \cup C_t$ , without access to task identifiers. + +Modality gap measure. In the classification task, given $N$ images and $K$ class name of text, we measure the intermodality similarity as the average cosine similarity between all image and text features: $\frac{1}{N}\sum_{i=1}^{N}\frac{1}{K}\sum_{j=1}^{K}\cos(\mathbf{x}_i,\mathbf{t}_j)$ , where $\mathbf{x}_i$ is an image feature and $\mathbf{t}_j$ is a text feature. This captures the overall similarity between the image and text modalities, reflecting the modality gap in the feature space. + +To analyze the impact of image-to-text similarity in more fine-grained, we define the average similarity of positive image-text pairs as: + +$$ +p o s = \frac {1}{N} \sum_ {i} ^ {N} \cos \left(\mathbf {x} _ {i}, \mathbf {t} _ {y i}\right), \tag {1} +$$ + +where $\mathbf{t}_{y_i}$ denotes the corresponding class text feature for the image $\mathbf{x}_i$ . Similarly, we measure the average similarity + +of negative image-text pairs as: + +$$ +n e g = \frac {1}{N} \sum_ {i = 1} ^ {N} \frac {1}{K - 1} \sum_ {j = 1} ^ {K - 1} \cos \left(\mathbf {x} _ {i}, \mathbf {t} _ {j} ^ {n e g}\right), \tag {2} +$$ + +where $\mathbf{t}_j^{neg}$ represents the text features of non-matching classes for the image $\mathbf{x}_i$ . + +# 4. Method + +Our method approaches CLIP-based continual learning from the perspective of the modality gap, recognizing its crucial role in preserving CLIP's generalization capabilities during continual learning. We identify that uncontrolled training can disrupt this inherent modality gap, leading to suboptimal performance in downstream incremental learning. To address this, we propose a two-stage strategy: (1) Preserving the modality gap for model stability. We regulate the training process to ensure a stable modality gap across tasks; (2) Compensating the modality gap for model plasticity. The constraint for the modality gap may limit the model's adaptability, we introduce a complementary classifier that enhances task-specific performance without altering the preserved modality gap. During inference, we integrate both outputs to balance stability and task plasticity. Next, we discuss the motivation (Sec. 4.1) and details of our method (Sec. 4.2 and Sec. 4.3). The pseudo-code can be found in Sec.5 of the supplementary material. + +# 4.1. Effect of Modality Gap in Continual Learning + +In this section, we begin by analyzing the evolution of the modality gap during continual learning. + +Cross-entropy loss expands the modality gap. The optimization objective of cross-entropy is not consistent with the modality gap of the original CLIP. When optimized via cross-entropy loss, the training objective aligns image-text pairs to a cosine similarity of 1 for matches and -1 for non-matches. However, this optimization contradicts the moderate similarity distribution of the original CLIP model, which ranges from approximately 0 to 0.3 reflecting the inherent modality gap. It causes the modality gap of the trained model to expand. Furthermore, downstream classification tasks introduce a structural imbalance absent in CLIP pre-training. Unlike symmetric text-image pairs in pre-training, classification tasks pair multiple images of the same class with a single text embedding. In a $C$ -class dataset, each text forms positive pairs with only $\frac{1}{C}$ of the images while being repelled from the remaining $\frac{C - 1}{C}$ negative pairs. The imbalance leads to the optimization process dominated by repelling non-matching samples, further expanding the modality gap. + +The modality gap implicitly reflects pre-trained knowledge, and expanding it may result in forgetting previous + +![](images/3180576af57301c74352ec58dbd486d80d75849a310607164b7bd2b5cf1c5696.jpg) +(a) Naive fine-tuning reduces cosine (b) The alignment loss increases cosimilarity, widens modality gap, and sine similarity and reduces modalproduces significant forgetting. ity gap, but it disrupts pre-trained knowledge, leading to forgetting. + +knowledge. As shown in Fig. 2a, experimental results confirm this effect: the cosine similarity between image and text representations steadily declines as tasks progress, demonstrating the growing modality gap. This coincides with a continuous drop in accuracy, highlighting its adverse impact on CLIP's pre-trained knowledge and overall performance in class-incremental learning. + +Direct alignment loss reduces modality gap but disrupts pre-trained knowledge. As shown in Fig. 2b, introducing a loss of alignment [7] in downstream tasks can reduce the modality gap by minimizing the Euclidean distance between matched image and text features. The key issue lies in the mismatch of the subspace: downstream datasets span a limited region of the original CLIP feature space, which makes the direct alignment risk of overspecialization. Directly aligning the two modalities can significantly alter pretrained representations, leading to forgetting. + +Sustaining CLIP's lifelong learning capacity. Previous analyses have revealed a phenomenon: naive fine-tuning tends to expand the modality gap, while direct alignment reduces it. As class-incremental learning progresses, this problem becomes increasingly severe, gradually eroding CLIP's pretraining capabilities. Since CLIP's pretraining knowledge plays a crucial role in providing stability for downstream tasks, we need to maintain a relatively stable modality gap. Ensuring this stability is essential for allowing CLIP to incorporate new knowledge without compromising its fundamental vision-language correspondence. + +# 4.2. Adaptive Modality Gap Preservation + +In this section, we characterize the asymmetric evolution of the modality gap in continual learning and propose an adaptive preservation strategy to enhance model stability. + +Asymmetry phenomenon of modality gap change during training. As shown in Fig. 3, we observe an asymmetric + +![](images/702f36cc5df52414a2f8d3d58b5dede8792fbfda71080b27a4ab9b2cb0547b06.jpg) +Figure 2. Average cosine similarity between text and image features, along with accuracy on ImageNet-R during CL. +(a) ImageNet-R + +![](images/4d785e03ac898db03ade92bbd4cbc2961c40167e779e1869108b22827ee2f3c6.jpg) +(b) ImageNet-100 +Figure 3. The variation in the mean of positive and negative cosine within a task during training. The cosine change pattern before and after the green dotted line is different. + +change in cosine similarity between text and image features during single task training. The 'pos' and 'neg' use Eq. 1 and Eq. 2 to calculate. Before training, i.e., epoch 0, the 'pos' is already larger than the 'neg', indicating the zero-shot capability of the model. Even the similarity between an image and its corresponding class text remains relatively low, which is a reflection of the modality gap. During the early phase of training, the output changes are primarily due to an increase in the similarity of positive image-text pairs, indicating the model has learned new knowledge and becomes more confident about the true class. This corresponds to the part before the green dashed line in Fig. 3. As long as the positive output remains larger than the negative outputs, the model can still make correct predictions even if the loss exists. However, in the later stages of training, the positive output stabilizes and the negative outputs begin to decrease. This indicates that the distance between the image and most other text features increases. Therefore, an optimal training stage can retain its learned knowledge while keeping the inter-modal distance relatively stable. + +Adaptive training for preserving modality gap. Based on these observations, we propose determining the number of training epochs by monitoring the mean negative outputs. As shown in Fig. 4, using the first task data of the dataset, we estimate the required number of epochs for subsequent tasks. Specifically, we first compute the mean of the negative outputs using Eq. 2, denoted as $neg^0$ , using the original CLIP model for the first task. Then, we train the model using LoRA, and after the $e$ epoch, we compute the $neg^e$ of the negative outputs for all data. We calculate the relative difference between the current and the original as follows: + +$$ +\Delta = \frac {\left| n e g ^ {e} - n e g ^ {0} \right|}{n e g ^ {0}}. \tag {3} +$$ + +When the difference $\Delta$ exceeds a predefined threshold $\alpha$ , we record the last epoch $e$ where $\Delta$ was still below $\alpha$ . Finally, for all tasks in the downstream dataset, we train the model for the $\max(e, 1)$ epochs. + +![](images/4dfe6d108523543400b27e71e72d0c7964d2d9c0c9db5158875911368236a0e7.jpg) +Figure 4. Our method tackles CLIP-based continual learning through dual mechanisms: (1) Modality Gap Preservation stops training when modality gap deviation exceeds a stability threshold, preventing cross-modal knowledge distortion; (2) Gap Compensation trains a visual-space classifier on frozen features to enhance task-specific plasticity while respecting preserved gap. In inference stage, we combine two different classifier subspaces for prediction. + +![](images/042ecd4b0cd910de5a17d7b02588c4fec76a28333d3fe00663c4a92fa90b9741.jpg) + +# 4.3. Intra-modal Compensation for Modality Gap + +In this section, we explain how the modality gap limits the model's capability, as it must be maintained as discussed in the previous section. Consequently, we construct an intramodal classifier to compensate for the limitations. + +Modal gap restriction on text classifier capability. To achieve minimal cross-entropy loss, an optimal classifier must exist within the image feature space. Specifically, for any classifier that minimizes classification error, there exists an equivalent form $\mathbf{W}_{\mathrm{opt}}$ entirely contained in the span of image features. This follows from the decomposition of any classifier into components parallel and orthogonal to the image space, where the orthogonal component does not contribute to classification. A detailed proof of this claim is provided in the supplementary material 2.1. + +Given this, we analyze the modality gap's impact on text classifiers. The text feature matrix $\mathbf{T}$ decomposes as: $\mathbf{T} = \mathbf{T}_{\parallel} + \mathbf{T}_{\perp}$ where $\mathbf{T}_{\parallel}$ lies in the subspace spanned by visual features $\mathbf{X}$ , and $\mathbf{T}_{\perp}$ is orthogonal to it. Since text features generally do not fully span the image feature space, the best achievable text classifier is restricted to a low-rank subspace, leading to misalignment error. The lower bound of the distance from $\mathbf{T}_{\parallel}$ to the optimal image-space classifier is determined by the singular values $s^2$ outside the text feature subspace: + +$$ +\left\| \mathbf {T} _ {\parallel} - \mathbf {W} _ {\text {o p t}} \right\| _ {F} ^ {2} \geq \sum_ {i = r + 1} ^ {r ^ {\prime}} s _ {i} ^ {2}, \tag {4} +$$ + +where $r'$ is the rank of $\mathbf{W}_{\mathrm{opt}}$ and $r$ is the rank of $\mathbf{T}_{\parallel}$ . The + +formal derivation of this bound is provided in the supplementary material 2.2. + +This result reveals an inherent limitation: unless the text feature space has sufficient capacity to represent the optimal classifier, perfect alignment is unattainable. Due to the modality gap, text classifiers often operate in a lower-rank subspace, restricting their classification effectiveness. + +Modal gap compensation via intra-modal classifier. To compensate the modality gap, we introduce an auxiliary classifier in the visual space. The fine-tuned CLIP model $f_{\mathrm{clip}}(\cdot)$ and the classifier weights for old classes are frozen. For classes introduced in the current task, we initialize their classifier weights within the cosine classifier $\mathbf{W}_v$ using their class prototypes and train them using image features without text. Since the gradients of the classifier remain in the input space, which is the visual space, this ensures that the classifier operates within the visual subspace. + +As shown in Fig. 4, in the model inference stage, we combine the predictions from both the text and visual classifiers. The final predict score is calculated as: + +$$ +\operatorname {p r e} (\mathbf {x}) = f _ {\text {c l i p}} (\mathbf {x}, \mathbf {t}) + \boldsymbol {\beta} \cdot \operatorname {s o f t m a x} \left(\mathbf {W} _ {v} ^ {\top} \mathbf {x}\right), \tag {5} +$$ + +where $\beta$ is a constant hyperparameter. + +# 5. Experiments + +# 5.1. Experimental Setup + +Datasets. We evaluate our method through continual learning tasks on five benchmark datasets: CIFAR-100 [14], + +
MethodExemplarCIFAR-100ImageNet-RImageNet100ImageNet-1KVTAB
AvgLastAvgLastAvgLastAvgLastAvgLast
PROOF [49]DR84.8876.2982.8377.0584.7172.4876.2365.2689.0983.97
CLAP [12]86.1378.2185.7779.9887.7679.1681.7273.1991.3789.67
SLCA [43]FR80.5367.5875.9270.3778.6359.9279.1068.2784.2582.54
RAPF [11]86.1979.0485.5880.2887.5180.2381.7372.5890.8882.31
L2P++ [35]81.9073.0881.6775.9880.5167.2279.3069.6063.2338.37
DualPrompt [34]81.4572.5182.0175.7780.6567.3879.3969.7961.8937.58
CODA [28]NR76.9862.2578.0067.5264.1334.7676.9966.9662.5138.25
Continual-CLIP [30]75.1566.6879.1272.0084.9875.4072.9664.4453.6431.50
Aper-Adapter [48]75.7665.5078.6571.3585.8476.4076.6068.7480.7571.21
MOE4CL [40]85.3678.3785.2880.7786.3976.6681.2972.7368.4961.70
CLAP* [12]74.1963.4581.2275.8081.0772.0075.8567.3682.1180.11
MagMax [21]85.6379.0087.1380.8586.3375.9280.7471.3164.6353.90
MG-CLIP (Ours)NR87.0080.5787.5882.6787.3178.3881.8873.6894.6791.53
+ +Table 1. Comparison of performance with different methods. DR denotes using real data for replay, FR denotes generating old class features for replay, and NR denotes non-replay. The results are mainly obtained from references [11, 12] and reproduced using their publicly available code. The performance of ours is the average over three different class orders. Except for VTAB, which is divided into 5 tasks, the other datasets are divided into 10 tasks. CLAP* represents the replay-free version provided by the paper of CLAP. + +ImageNet-R [8], ImageNet-100 [4], ImageNet-1K [4], and VTAB [42]. All of these datasets except the VTAB are evenly divided into 10 sequential tasks. Following the previous work [48], we extracted a subset from VTAB, including 5 tasks, each with ten categories. For more experimental details, please refer to Sec.4 of the supplementary material. + +Competing methods. Our experiments compare two types of methods: (1) Vision-only approaches that include $\mathrm{L2P + + }$ [35], DualPrompt [34], CODA [28], SLCA [43], and Aper-Adapter [48]; (2) CLIP-based methods that include PROOF [49], CLAP [12], RAPF [11], MOE4CL [40], MagMax [21] and the zero-shot CLIP baseline Continual-CLIP [30]. All methods adopt the ViT-B/16 weights of OpenAI [26] by default. While original MagMax implementations employ enhanced augmentations and optimized text templates, we follow previous works [11, 40, 40] and standardize evaluations using basic image augmentations and a fixed prompt template for fair comparison. + +Evaluation metrics. The average accuracy on the test data after training the t-th task, considering the first through $t$ tasks, is represented as $A_{t}$ . 'Avg' is the average of the accuracies of all tasks, i.e., $\frac{1}{t} \sum_{i=1}^{t} A_{i}$ . 'Last' indicates the average accuracy after the final task $T$ , i.e., $A_{T}$ . + +Implementation detail. We develop our method using PyTorch on an A40 GPU. Unless otherwise specified, we use OpenAI's pre-trained CLIP model, specifically the ViTB/16 version. Results for another version of CLIP can be found in the supplementary materials. During the training of the backbone, we apply LoRA [9] for model adaptation, with the default rank set to 8. Since the focus of our work is + +not on the fine-tuning process itself, we simplify the implementation by applying LoRA only to the key and value parts of the attention module. Different fine-tuning model implementations are left for future work. We use the Adam optimizer with a cosine learning rate scheduler with an initial learning rate of 0.001. The number of epochs is determined by the first part of the method, where the threshold $\alpha$ is set to $10\%$ . In the training stage for the image-space classifier, we train for 3 epochs, with an initial learning rate of 0.0005. The classifier uses a cosine classifier. During inference, the hyperparameter $\beta$ to integrate the two classification results is set by default to 4. Hyperparameter effects are described in the supplementary material. + +# 5.2. Comparison Results + +Table 1 presents a comparison of our approach with other methods. In most datasets, our method outperforms all others, including those relying on replay. Specifically, on CIFAR-100, our method surpasses all competitors in Last accuracy by at least $1.53\%$ . On ImageNet-R, we achieve an improvement of at least $1.82\%$ in Last accuracy. On ImageNet-100, while our approach performs slightly worse than RAPF and CLAP, both of which use replay, we do not rely on replay and still outperform all non-replay methods by at least $1.72\%$ in Last accuracy. Additionally, on ImageNet-100, CLAP* performs significantly worse than CLAP, indicating that much of CLAP's performance gain stems from data replay. On the larger-scale ImageNet-1K dataset, our method achieves comparable or even slightly better results than the best-performing alternatives. + +The VTAB dataset poses a significant challenge to CLIP, as evidenced by the zeroshot accuracy, i.e., Continual_CLIP, which is only $31.5\%$ . On this challenging benchmark, most methods suffer substantial performance drops. Our method outperforms the best replay-based CLAP approach by $1.86\%$ in Last accuracy, significantly outperforming its non-replay version. It shows a clear advantages of our method in this challenging cross-domain scenario. + +# 5.3. Comparison of the Zero-shot Capability + +Continual learning aims to allow models to incrementally acquire new knowledge while retaining existing capabilities. CLIP models, compared to traditional pretrained vision models, demonstrate superior zero-shot generalization. Therefore, continual learning with CLIP should not only minimize forgetting on new downstream tasks but also preserve its original zero-shot abilities. This ensures CLIP based continual learning is more than just a method for task-specific initialization that leads to overfitting, a limitation of previous works in this area. These works often follow traditional evaluation protocols, neglecting the preservation of the model's intrinsic abilities. We propose evaluating zero-shot generalization of CLIP model on independent benchmarks after fine-tuning to address this issue. + +As shown in Tab. 2, we assess zero-shot performance on three standard datasets following continual learning on CIFAR-100. Our approach yields slight improvements over the original CLIP on Food101 [1] and Oxford Pets [25], which are clearly distinct from CIFAR-100, while all baselines show performance degradation. On the more similar ImageNet-1K, three methods outperform the original CLIP, with our method achieving the most substantial improvement (a $2.85\%$ gain). These results suggest that our approach successfully preserves pre-trained knowledge while effectively incorporating new information. + +Notably, replay-based methods (PROOF, RAPF, and CLAP) experience more significant performance declines in zero-shot tasks compared to non-replay methods. This indicates that replay mechanisms may lead to overfitting to downstream tasks, whereas non-replay methods must preserve original representations to prevent forgetting. This further highlights the potential negative impact of replay strategies on pre-trained models. + +# 5.4. Training Cost Analysis. + +Using CIFAR-100 as an example, we analyze the parameter overhead of different methods by comparing the additional learnable parameters introduced by our approach and other baselines, as illustrated in Fig. 5. Our method introduces only 0.54M additional trainable parameters. Although the RAPF method requires fewer learnable parameters, it still necessitates storing a covariance matrix for each class, leading to additional storage consumption proportional to the + +
Food101PetsImageNet-1KAvg
CLIP85.1487.664.4479.06
PROOF9.7522.8111.1814.58
RAPF17.1828.5615.220.31
CLAP80.8274.6856.0470.51
MOE4CL82.8584.0666.0277.64
MagMax81.6785.9666.4478.02
Ours85.7088.1767.2980.39
+ +Table 2. Zero-shot performance of the model on different downstream datasets after completing all class-incremental learning tasks on CIFAR-100. CLIP refers to the original CLIP pre-trained model without any downstream task-specific training. + +![](images/585b11a55bc0627ded7a4563f86124c0285b1c6fdf78115806c59e1e8c7ddfeb.jpg) +Figure 5. Comparison of accuracy and learnable parameters of different methods. + +square of the feature dimension, i.e., $nd^2$ . For instance, with 100 classes, this results in an extra storage overhead of over 26M parameters. In contrast, our method avoids replay entirely, maintaining minimal storage consumption. + +In the training process, the only extra cost in our method occurs after each epoch of the first task, where we perform an additional forward pass on the data of task to evaluate change of the modality gap. However, this step only needs to be done for the first task, does not involve backpropagation, and is minimal compared to the training cost. + +# 5.5. Ablation Study + +Module ablation. Table 3 presents the ablation study of our proposed modules. The baseline setup involves simple fine-tuning of the CLIP model for each task. Following the settings of previous work, we fine-tuned each task for 10 epochs [21] and used the widely adopted cross-entropy loss with the old-class output mask [40]. MGC represents Modality Gap Compensation, while MGP stands for Modality Gap Preservation. As shown in Tab. 3, both components of our method, when used individually, lead to performance improvements, with the modality gap preservation(MGP) providing a more significant boost. The best performance is achieved when both components are used together. + +
MGPMGCAvgLast
XX84.3072.74
X✓85.1074.58
✓X86.7376.86
✓✓87.3178.38
+ +When using MGC alone in the baseline setup, the improvement in last' accuracy is $1.84\%$ , which is larger than the improvement $(1.52\%)$ when adding MGC to MGP. A similar trend is observed for 'Avg' accuracy. This suggests that simple fine-tuning in the baseline setup has expanded the modality gap, and therefore the role of MGC in compensating for the gap becomes more pronounced. + +Image space and classifier space. We investigate the relationships among the linear subspaces spanned by the image features, the text-based classifier, and the learned modality-gap-compensating classifier. To quantify their differences, we apply matrix decomposition to extract the orthonormal bases of each space. For detailed calculations, refer to the supplementary materials Sec.3. $\mathbf{B}_i$ : Orthonormal basis of image feature space; $\mathbf{B}_t$ : Orthonormal basis of text classifier; $\mathbf{B}_{vc}$ : Orthonormal basis of the modality-gap-compensating classifier; $\mathbf{B}_{t + vc}$ : Orthonormal basis of the combined space spanned by both classifiers. To measure how well the text classifier space $\mathbf{B}_t$ covers the image feature space $\mathbf{B}_i$ , we compute the mean norm of the orthogonal component of $\mathbf{B}_i$ with respect to $\mathbf{B}_t$ : + +$$ +d \left(\mathbf {B} _ {i}, \mathbf {B} _ {t}\right) = \frac {1}{\left| \mathbf {B} _ {i} \right|} \sum_ {\mathbf {x} \in \mathbf {B} _ {i}} \| \mathbf {x} - \mathbf {B} _ {t} \mathbf {B} _ {t} ^ {\top} \mathbf {x} \|. \tag {6} +$$ + +This metric reflects how much of $\mathbf{B}_i$ lies outside $\mathbf{B}_t$ : It equals 1 if the spaces are orthogonal and 0 if one is a subspace of the other. Similarly, we compute $d(\mathbf{B}_i,\mathbf{B}_{vc})$ and $d(\mathbf{B}_i,\mathbf{B}_{t + vc})$ . + +As shown in Tab. 4, due to the modality gap, the text classifier space significantly deviates from the image feature space. In contrast, the classifier that compensates for modality gap better aligns with the image space. Combining both classifiers further improves coverage and highlighting their complementary roles. + +Analyzing the impact of our method on the modality gap. We analyze the impact of our method on the modality gap. Tab. 5 presents the mean cosine similarity of the positive and negative for the final task under different experimental settings, along with the last accuracy (Last Acc). The 'Base' refers to the results of naive fine-tuning. It can be observed that the mean of the negative similarity signif- + +Table 3. Ablation study of the modules on ImageNet-100. MGP refers to our adaptive modality gap preservation, and MGC denotes the intra-modal Compensation for Modality Gap. + +
CIFAR-100ImageNet-RImageNet100
d(Bi,Bt)0.77320.71600.7664
d(Bi,Bvc)0.60760.58430.5414
d(Bi,Bt+vc)0.49170.32840.4431
+ +Table 4. Difference measurement of image subspace and subspace of different classifiers on different datasets. + +
CLIPBaseDistillOurs
pos0.31570.30370.31680.3251
neg0.17190.05790.17180.1520
Last Acc75.4072.7475.8578.38
+ +Table 5. Comparison of cosine similarity and last accuracy (Last Acc) across different experimental settings on ImageNet-100. + +icantly decreases compared to the original CLIP. This suggests that the modality gap is expanded, leading to a lower last accuracy. The 'Distill' represents the traditional distillation method, which explicitly limits the output magnitude of the model. It restricts the changes in the modality gap and has some positive effect. However, a complete restriction of the modality gap evidently leads to a decline in the model's learning capability. This leads to suboptimal performance. We can see that its performance is close to the original CLIP. In contrast, our method maintains a relatively stable modality gap, allowing for a moderate increase in the positive similarity and a decrease in the negative similarity. This balance ensures that the model can appropriately learn new knowledge while maintaining pre-trained knowledge, ultimately achieving optimal performance. + +# 6. Conclusion + +This paper investigates the impact of modality gap on the performance of vision-language pre-trained models in class-incremental learning. We find that maintaining a relatively stable modality gap helps preserve pre-trained knowledge and prevents its degradation. Under the condition of a stable modality gap, training a visual space classifier that is not restricted by the modality gap can compensate for some of its negative effects, further enhancing the model's capabilities. The experimental results demonstrate the effectiveness of our approach. + +Limitations and Future Work. Our focus has been on the modality gap, and the model has been fine-tuned simply using LoRA without considering other fine-tuning methods. our current method does not incorporate specially designed loss functions or parameter constraint to mitigate forgetting. Future work will explore the integration of this approach with other continual learning methods and investigate suitable distillation strategies. + +# Acknowledgment + +This work was funded by NSFC (NO. 62206135, 62225604), Young Elite Scientists Sponsorship Program by CAST (2023QNRC001), "Science and Technology Yongjiang 2035" key technology breakthrough plan project (2024Z120), Shenzhen Science and Technology Program (JCYJ20240813114237048), and the Fundamental Research Funds for the Central Universities (Nankai University, 070-63233085). Computation was supported by the Supercomputing Center of Nankai University. + +# References + +[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. 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Despite their impressive capabilities, the robustness of MLLMs under conditions where one or more modalities are missing remains largely unexplored. In this paper, we investigate the extent to which MLLMs can maintain performance when faced with missing modality inputs. Moreover, we propose a novel framework to mitigate the aforementioned issue called retrieval-augmented generation for missing modalities (MISSRAG). It consists of a novel multimodal RAG technique alongside a tailored prompt engineering strategy designed to enhance model robustness by mitigating the impact of absent modalities while preventing the burden of additional instruction tuning. To demonstrate the effectiveness of our techniques, we conduct comprehensive evaluations across five diverse datasets, covering tasks such as audio-visual question answering, audio-visual captioning, and multimodal sentiment analysis. Our source code is available at https://github.com/aimagelab/MissRAG. + +# 1. Introduction + +Multimodal learning, which integrates diverse data types such as text, images, audio, and video, is gaining prominence in Artificial Intelligence research. By leveraging these complementary modalities, multimodal models have achieved remarkable success in tasks like image captioning [2, 5, 16, 29], audio-video question answering [11, 17, 28], and cross-modal retrieval [1, 9, 35, 40]. + +Recently, with the advent of Large Language Models (LLMs), the field has witnessed a trend of aligning + +![](images/4cffea593220e2d9ff6bed13f2e8a949c3ca775aa52aea8f03191d4f0990c06b.jpg) + +![](images/90b693666f42e27f22eb226e52f6a4f6ea30d8aee703b5f9d3e3b08ddc19b392.jpg) + +![](images/881abe1472965f16ca644eceebae50a38e7b78b0429c8fbf9caf0f122ee4fbdd.jpg) +Figure 1. From top to bottom: (i) the complete modality scenario, where the MLLM receives all modality tokens, (ii) the missing modality scenario where one modality is absent, and (iii) our proposed multimodal RAG framework, enhanced with prompt engineering, to mitigate the missing modality problem. + +multimodal information with textual data to harness the strong language generation and zero-shot transfer abilities of LLMs [10, 21, 36, 53]. These models are designed to generate representations of non-textual modalities that are compatible with LLMs. This is achieved by creating token representations for non-textual modalities, which we refer to as modality tokens in this paper. These tokens maintain the same representational depth as textual tokens, allowing them to be fed directly into an LLM as input. Consequently, these modality tokens can be seamlessly incorporated into the LLM input through simple concatenation, enabling the LLM to interpret non-textual data and perform tasks such as + +multimodal captioning and multimodal question answering. + +For example, X-LLM [10] and ChatBridge [53] integrate pre-trained modality-specific image, video, and audio encoders with LLMs by employing separate models such as Q-Former [30] or Perceiver [23]. In contrast, OneLLM [22] addresses the alignment challenge by employing modality-agnostic encoders, enabling direct mapping of inputs from eight modalities into the LLM embedding space. This design makes OneLLM one of the most versatile Multimodal Large Language Models (MLLMs) in terms of supported modalities. However, in real-world applications, multimodal systems often face the challenge of handling cases where certain data modalities are missing or incomplete [31]. This situation arises due to various factors such as sensor malfunctions, hardware limitations, privacy concerns, environmental interference, and data transmission issues. In the literature, these challenges are collectively referred to as the missing modality problem. + +To address the missing modality problem, numerous studies have been conducted over the years [25, 33, 34, 37, 42, 52]. However, these works primarily focus on encoder-only architectures that learn to solve tasks in a closed-form manner by leveraging conventional training methods or fine-tuning existing backbones. In contrast, MLLMs contain billions of parameters, making fine-tuning computationally prohibitive. This has led to increased interest in parameter-efficient alternatives such as zero-shot learning, where models generalize without task-specific training. Recent efforts favor techniques that avoid updating LLM parameters, such as prompt engineering [8, 14, 39, 46], which involves manually modifying the textual prompt of an MLLM to induce a desired behavior, and Retrieval-Augmented Generation (RAG) [6, 26, 41, 49], which integrates a retrieval system to support the MLLM. + +To the best of our knowledge, there are no studies that investigate the robustness of MLLMs under missing modality conditions. Hence, in this paper, we assess the robustness of MLLMs that accept at least two non-textual modalities as input, such as those addressing audio-video tasks [13, 22, 53]. We extend our evaluation by incorporating a textual modality, thereby conducting the first examination of such models on three-modality-input tasks like audio-video-text multimodal sentiment analysis. + +Furthermore, we propose MissRAG, a novel retrieval framework empowered with a tailored prompt engineering strategy that mitigates the missing modality problem in MLLMs without requiring additional fine-tuning. In particular, MissRAG substitutes the missing modality with a candidate retrieved from a prototype pool by querying based on the available modalities. Specifically, our proposed multimodal RAG for addressing missing modalities is the first framework capable of concurrently managing three modalities and retrieving all possible combinations + +of single or multiple modality inputs. Also, the proposed framework is enhanced with tailored prompts to inform the model about the absent modality and condition the text generation process, as illustrated in Fig. 1. We validate the significance of our findings through extensive experiments on five multimodal datasets, covering a broad spectrum of tasks such as, audio-visual question answering (MUSIC-AVQA [27]), audio-visual captioning (VALOR-32K [11], CharadesEgo [43]), and audio-video-text sentiment analysis (MOSI [50], MOSEI [3]). In summary, our contributions are as follows: + +- We are the first to assess the robustness of MLLMs under missing modality conditions across a wide range of tasks involving audio-video, and audio-video-text data; +- This is the first work in which RAG is employed to address the missing modality problem; +- We introduce MissRAG, the first multimodal RAG framework that concurrently operates across three distinct modalities. This framework is capable of retrieving complementary audio-visual-text data for any given combination of audio, visual, and textual inputs; +- Through extensive experiments and ablation studies, we show that our proposed MissRAG enhanced with the proposed prompt engineering strategy effectively mitigates the missing modality problem for MLLMs. + +# 2. Related Work + +Multimodal Learning and Missing Modalities. The integration of heterogeneous data streams in Deep Learning models is a demanding problem in multimodal learning [7, 19, 24, 28]. Among them, the missing modality problem, wherein one or more modalities may be absent during inference or even training, is one of the most challenging. + +Contemporary studies [33, 34, 38, 51, 52] have been directed towards the development of multimodal frameworks capable of handling absent modalities. The SMIL approach [33] has been introduced to infer the latent features of data with incomplete modalities using Bayesian meta-learning. Zeng et al. [51] designed a tag-encoding mechanism that aids the training of Transformer encoders to cope with absent modalities. Ma et al. [34] explored multimodal Transformers under missing modality conditions, improving robustness by automatically learning optimal fusion strategies. However, these studies mainly focus on encoder-only models that are designed to solve tasks in a closed-form manner using standard training techniques or by fine-tuning existing backbones, an experimental setup that differs substantially from that addressed in this paper. + +Multimodal Large Language Models. Early efforts to inject visual cues into LLMs [4, 30, 32] have recently been extended to additional modalities such as audio, video, and point clouds, with the goal of unifying multiple modalities within a single LLM framework. In this context, + +X-LLM [10] pioneered the use of modality-specific Q-Formers and adapters to bridge pre-trained image, audio, and video encoders with frozen LLMs. Follow-up works such as ChatBridge [53] and AnyMAL [36] adopt similar designs but with varying connector modules, including Perceiver and linear layers. VideoLLaMA 2 [13] exploits a pretrained visual encoder in combination with a learnable Spatial-Temporal Convolution Connector to process visual information, while the audio modality is encoded via the BEATs model [12] and aligned to text with an MLP. Qwen2.5-Omni [47] jointly models perception and generation of text and speech across interleaved video and audio inputs, via a thinker-talker architecture and novel positional encoding. VITA [18] enables speech-to-speech dialogue while maintaining remarkable visual-language understanding capabilities. Also, OneLLM [22] removes the need for modality-specific encoders by introducing a universal encoder and projection module, supporting eight modalities. + +In this work, we focus our experiments on three representative MLLMs (i.e., ChatBridge, OneLLM, and VideoLaMA 2) selected for their public availability and demonstrated robustness in audio-visual-text scenarios. + +RAG and Prompt Engineering. Retrieval-Augmented Generation (RAG) [6, 26, 41, 49] has emerged as a powerful paradigm for enriching LLMs and MLLMs with external knowledge. By retrieving relevant snippets from a pre-built knowledge base and incorporating them into the prompt, RAG complements the intrinsic capabilities of generative models with dynamic, context-aware information from external information repositories. In this context, Lewis et al. [26] demonstrated the effectiveness of this approach by conditioning the generation on retrieved textual documents. More recently, Xu et al. [6] introduced VisualRAG, combining image retrieval with text generation for multimodal tasks. Despite these recent advancements, our proposed multimodal RAG-based framework is the first to operate concurrently across three distinct modalities. + +Prompt engineering [8, 14, 39, 46] utilizes task-specific instructions to elicit desired behaviors without modifying model weights. Radford et al. [39] demonstrated that carefully designed prompts enable zero-shot learning, where models perform unseen tasks without labeled examples. Wei et al. [46] further introduced chain-of-thought prompting to encourage step-by-step reasoning. Building on its success, in this work we develop a tailored prompt engineering strategy to handle missing modalities within our multimodal RAG framework. + +# 3. Proposed Method + +This work addresses the challenge of missing modalities in the field of multimodal learning, specifically for MLLMs. Since no previous literature has tackled the missing modality problem for MLLMs, we establish a benchmark to eval + +uate the robustness of these models across a wide range of tasks, including audio-visual question answering, audio-visual captioning, and audio-video-text sentiment analysis. In this setting, we evaluate the robustness of MLLMs under six missing modality scenarios: Missing Audio (MA), Missing Video (MV), Missing Text (MT), Missing Audio-Video (MAV), Missing Audio-Text (MAT), and Missing Video-Text (MVT). Additionally, we consider a Complete (C) scenario in which all modalities are available. Accordingly, in our experimental design, once a specific missing modality scenario is established, we remove the corresponding modalities from all samples in the analyzed dataset to simulate conditions of missing modalities with $100\%$ of missing rate. Thus, we work in the worst-case scenario where all samples strictly adhere to the specified missing modality condition. Consequently, in a hypothetical scenario of lower missing rates, the overall performance would be higher. + +Within this scope, our main contribution is a novel multimodal RAG framework for missing modalities called MissRAG, the first RAG-based solution that simultaneously manages three different modalities, thereby mitigating the missing modality problem. MissRAG exploits pre-trained contrastive backbones to query a pool of prototypes of the same modality as the missing ones, retrieving the corresponding modality tokens to ensure that the model consistently receives complete input pairs or triplets. Moreover, we enhance MissRAG with a specific prompt engineering strategy that informs the model about which modalities are present and which are absent. It also forces the model to infer the likely context of the missing modality through a customized prompt. By integrating both techniques, we reconstruct the input data and induce the model to adapt its behavior in scenarios with missing modalities. + +# 3.1. Preliminaries + +Problem Statement. In our setting, we employ multimodal datasets comprising $M$ modalities, where $M \in \{2,3\}$ . To assess the robustness of our models under missing modality conditions, we omit one or two modalities at a time across all samples within each dataset. Consequently, for a dataset comprising $M$ modalities, there exist $2^{M} - 1$ potential missing modality scenarios, each corresponding to a non-empty subset of the $M$ modalities excluding the case where all modalities are absent. Specifically, for audio-visual question answering and audio-visual captioning datasets, the missing modality scenarios include Missing Audio, Missing Video, and Complete. In the case of audio-video-text sentiment analysis, we consider seven scenarios: Missing Audio, Missing Video, Missing Text, Missing Audio-Video, Missing Video-Text, Missing Audio-Text, and Complete. + +Contrastive Backbone. A contrastive backbone is designed to map data from different modalities into a unified embedding space by pulling together the representa + +![](images/bb0f33171518d3f49710578f0ee2cab004c082c286f740cb7ac1601056915778.jpg) +(a) + +![](images/ab243657c45d4955add7e745d36874e27f94e6915931e2cbf997dda0e41f8cc0.jpg) +(b) + +![](images/74fca62cddf0f9ac29e5b570039030d843da893eba2be729855a12802840c1e7.jpg) +(c) + +![](images/cbedb993a0ffddbcbfa4a977027a0017eb7c46057b0fca52ef449cd0c54e0709.jpg) +Figure 2. Overview of three different scenarios: (a) complete modality scenario where both reference video and reference audio are available; (b) missing video scenario without compensation for the missing modality; (c) missing video scenario where our proposed M1ssRAG+PE approach retrieves a prototype video while employing a designed prompt to mitigate the impact of the missing modality. +(b) +Figure 3. Overview of our MissRAG framework with three modalities. (a) Creation of modality embeddings through a contrastive embedder, pooled for retrieval. (b) Retrieval of the top- $k$ most similar prototypes by computing similarity scores between the embeddings of available modalities (i.e., query) and the stored embeddings of the missing modality via dot product, then aggregated to obtain the missing modality representation. Dashed arrows indicate that the second modality may be unavailable. + +tions of similar data points while pushing apart those of dissimilar ones. This process encourages the formation of distinct clusters in the shared embedding space, where semantically similar instances are grouped closely together. This approach facilitates effective cross-modal retrieval, as it allows for direct similarity computations between data points from disparate modalities. For example, elements with a high dot product are likely to represent similar concepts. + +In our work, we use ImageBind [20] as contrastive backbone. It aligns seven modalities (i.e., audio, image, video, text, IMUs, thermal, and depth) into a shared embedding space, making it useful for retrieval tasks where establishing semantic similarity between modalities is essential. + +MLLM Backbone. For what concerns the MLLM, we select three publicly available models, namely OneLLM [22], VideoLLaMA 2 [13], and ChatBridge [53], due to their broad support to different input modalities and state-of-the-art zero-shot performance on audio-visual question-answering and audio-visual captioning tasks. + +In particular, OneLLM, VideoLLaMA 2, and ChatBridge employ LLaMA-7B [44], Qwen2-7B [48], and Vicuna-13B [15], respectively, as their underlying LLM backbones, alongside a framework that maps non-textual modalities into the LLM embedding space. MLLMs are in + +deed engineered to translate each non-textual modality into a format interpretable by the LLM. Specifically, the LLM processes text input as token embeddings, where each token represents a subcomponent of a sentence and is embedded using an embedding layer that maps the token to a learnable representation of fixed dimension $d_{model}$ . As a result, the input to the LLM has a dimensionality of $(n_{tokens}, d_{model})$ . Moreover, to map each non-textual modality into the input embedding space of the LLM, a token representation must be generated, which we refer to as modality tokens. These modality tokens are created by employing a modality encoder and a projection module, which process the nontextual modality to produce a token representation that can be concatenated with the textual tokens in the LLM input. + +MLLM Prompt Structure. The input prompts for MLLMs adhere to a specific structure designed to enhance model performance. Specifically, each input prompt consists of two primary components: the system message and the user instruction. An example of an input prompt is provided in Fig. 2a. The system message provides contextual information that guides the behavior of the LLM, while the user instruction simulates a human request to the machine, which + +
TaskRetr.Miss.ScenarioPrompt
Audio-VideoXMAThe audio is missing. The assistant must use visual data to infer a probable audio context.
MVThe video is missing. The assistant must use audio data to infer a probable visual context.
CBoth video and audio are present.
✓MAThe assistant receives an approximate audio data and uses it to generate a response as accurately as possible.
MVThe assistant receives an approximate visual data and uses it to generate a response as accurately as possible.
Audio-Video-TextXMAThe audio is missing. The assistant must use visual and textual data to infer a probable audio context.
MVThe video is missing. The assistant must use audio and textual data to infer a probable video context.
MTThe input text is missing. The assistant must use audio and visual data to infer a probable textual context.
MATThe audio and input text are missing. The assistant must use visual data to infer a probable audio and textual context.
MVTThe video and input text are missing. The assistant must use audio to infer a probable video and textual context.
MAVThe video and audio are missing. The assistant must use textual data to infer a probable visual and audio context.
CAudio, visual and textual data are all present.
✓MAThe assistant receives an approximate audio data and uses it to generate a response as accurately as possible.
MVThe assistant receives an approximate visual data and uses it to generate a response as accurately as possible.
MTThe assistant receives an approximate input text data and uses it to generate a response as accurately as possible.
MATThe assistant receives an approximate audio and input text data and uses them to generate a response as accurately as possible.
MVTThe assistant receives an approximate visual and input text data and uses them to generate a response as accurately as possible.
MAVThe assistant receives an approximate visual and audio data and uses them to generate a response as accurately as possible.
+ +Table 1. Prompt Engineering (PE) details for all missing modality scenarios and retrieval modes. + +the LLM must respond to while also considering the information contained in the system message. + +# 3.2. Multimodal RAG for Missing Modalities + +In this study, we propose MISSRAG, the first multimodal RAG-based framework that simultaneously processes three distinct modalities. This framework is capable of retrieving complementary audio, visual, and textual data for any given combination of these input modalities. Specifically, when a modality is absent, we utilize the information from the available modalities to retrieve optimal candidates for substitution. This approach aims to achieve performance comparable to scenarios where all modalities are present, thereby mitigating the missing modality problem. + +To implement this, we require a repository of prototypes for each modality that needs to be retrieved during the testing phase. In practice, we construct this prototype pool using the training set of each respective dataset independently. This approach does not make the proposed prototype retrieval technique restricted or sensitive to the tasks. + +Subsequently, to establish an effective retrieval system, we employ a function that maps the samples of each modality into a shared embedding space where representations of similar concepts are proximally located. Consequently, we expect that within this embedding space, the modality representations of a given sample will exhibit greater similarity to one another than to those of different samples. + +A pre-trained multimodal backbone facilitates this mapping by ensuring that semantically similar samples are closely aligned in the embedding space. Specifically, we use a contrastive backbone to generate key embeddings for each modality in the training set, as shown in Fig. 3, which can then be queried using corresponding embeddings derived from the available modalities in the test set. + +We then calculate the dot product between these queries + +and the embeddings of the missing modality. The resulting similarity scores are concatenated, and the top- $k$ highest scores are selected to retrieve the most relevant samples. If only one modality is available, there is no concatenation of similarity scores, and the process is executed two times to obtain candidates for each of the two missing modalities. Once retrieved, the modality tokens that correspond to the retrieved samples are computed and averaged. It is important to note that there are no modality tokens for the text modality, as it is the native modality of the LLM. Therefore, we concatenate multiple retrieved texts if $k$ is greater than 1. The retrieved information is subsequently used to complete the missing sections of the LLM input prompt, ensuring that the input becomes fully comprehensive. + +# 3.3. Prompt Engineering + +In this work, we leverage Prompt Engineering (PE) techniques to improve the comprehension of our MLLM with respect to its input data, inducing it to cope with cases of missing modalities. In particular, our prompt engineering strategy has two objectives: informing the model about the input modality status and inducing it to mitigate the missing modality problem with a Compensation Strategy for Missing Modalities (CSMM) prompt. + +Specifically, we append to the system message a string that describes the input modality status, composed of a concatenation of input descriptors for each of the possible input modalities of the task defined as: + +{Modality}: {Present/Prototype/Missing}. + +Taking an audio-video task as an example, the string used to indicate that the audio is original and the video is retrieved is "Audio: Present; Video: Prototype". + +Subsequently, we append the compensation strategy, i.e., a handcrafted string designed to induce behavior in the + +LLM that helps the mitigation of the missing modality problem. These prompts are detailed in Table 1 for each missing modality scenario and retrieval mode. Specifically, the handcrafted prompt for the Complete (C) scenario is utilized in both retrieval and non-retrieval modes, as the latter scenario does not require any data retrieval. + +# 3.4. Multimodal RAG and Prompt Engineering + +Our proposal to mitigate the missing modality problem consists in our proposed multimodal RAG for missing modalities, called MissRAG, enhanced with our proposed prompt engineering strategy. Such techniques aim to mitigate the missing modality problem by working on two different and independent levels. The former improves the input quality by substituting missing input with optimal candidates, while the latter is designed to induce the MLLM to change its behavior in front of missing or retrieved modalities. An enhanced visualization of the application of our method is depicted in Fig. 2c. + +# 4. Experimental Results + +We evaluate our proposed methodology in a zero-shot setting by applying it to three baseline models, ChatBridge, OneLLM, and VideoLLaMA 2. The only exception is VideoLLaMA 2 on the MUSIC-AVQA dataset, as it has been exposed to data from this benchmark during training. These baselines use their default system messages and user instructions and, by augmenting them with our proposed MissRAG framework enhanced with the design prompt engineering strategy, we achieve remarkable performance gains. We assess the effectiveness of our methodology across three multimodal downstream tasks: question-answering, captioning, and sentiment analysis. + +Audio-Visual Question Answering. We evaluate our methods on audio-visual question answering on MUSIC-AVQA [27], a dataset which contains 45K question-answer pairs. The problem requires a comprehensive multimodal understanding of both audio and visual cues. + +Audio-Visual Captioning. We evaluate our methods on audio-visual captioning tasks on VALOR-32K [11] and CharadesEgo [43]. VALOR-32K is a large-scale dataset that contains 32K videos with rich audio-visual captions. CharadesEgo contains 7,860 first and third-person videos annotated with textual descriptions, making it suitable for audio-visual captioning. + +Audio-Video-Text Sentiment Analysis. We evaluate our methods on audio-video-text sentiment analysis, testing them on CMU-MOSI [50] and CMU-MOSEI [3], where the goal is to predict the sentiment of the video. CMU-MOSI is a collection of 2,199 opinion video clips, and CMU-MOSEI is an extension of the CMU-MOSI dataset that contains 23,453 annotated video segments. For both datasets, each + +video segment is paired with a text describing spoken words and annotated with a negative, neutral, or positive label. + +Metrics. To assess the performance on these diverse tasks, we employ accuracy for audio-video-text sentiment analysis and audio-visual question answering and the CIDEr metric [45] for the captioning task. + +Evaluation Protocol. For captioning, we compute CIDER using the COCO caption evaluation toolkit,[2] a publicly accessible tool that supports multiple captioning evaluation metrics. To assess the accuracy on the MOSI and MOSEI datasets, we implement a customized evaluation function designed to maximize conservativeness. Specifically, we categorize as missed any prediction that includes multiple labels, and we invert a label polarity if it is preceded by the negation term "not" within the prediction. For further details, please refer to the supplementary material. + +# 4.1. Main Results + +As shown in Table 2, our method, MissRAG+PE, consistently improves ChatBridge in 22 out of 23 experiments, OneLLM in 21 out of 23 experiments, and VideoLLaMA 2 in 17 out of 23 experiments, demonstrating the effectiveness of our approach in missing modality scenarios, especially when the absent modality is the dominant one for the task. In fact, in audio-video tasks such as MUSIC-AVQA, VALOR-32K, and CharadesEgo, our method achieves significant gains over ChatBridge (+15.93, +5.90, +2.86), OneLLM (+7.18, +13.23, +1.30), and VideoLLaMA 2 (+0.54, +3.28, +2.60), in the most challenging scenarios where visual information is absent. + +Regarding MOSI and MOSEI, our methods generally lead to improved performance across all evaluated MLLMs. However, to contextualize these results, it is important to emphasize that the models are assessed in a zero-shot setting and have not been explicitly trained on tasks analogous to sentiment analysis—tasks which demand complex reasoning across textual, visual, and auditory inputs. This leads to two potential issues: (i) a model may lack understanding of the task and thus perform poorly overall (e.g., ChatBridge); or (ii) a model may struggle to reason across multiple modalities, and perform best when prompted exclusively with text—the most natural input for an MLLM (e.g., VideoLLaMA 2 and OneLLM). Furthermore, our approach tries to align the performances of the missing modality scenarios with that of the Complete one, regardless of whether the latter leads to the optimal performance for the MLLM. Consequently, if our method does not yield improvements in every missing modality scenario, we do not attribute this to a shortcoming of the proposed methodology, but rather to inherent limitations of current MLLMs in addressing complex multimodal tasks such as sentiment analysis across au + +
TaskAudio-Video Question AnsweringAudio-Video CaptioningAudio-Video-Text Sentiment Analysis
Dataset MetricMUSIC-AVQA AccuracyVALOR32K CIDErCharadesEgo CIDErMOSI AccuracyMOSEI Accuracy
MethodMAMVCMAMVCMAMVCMAMVMTMAVMATMVTCMAMVMTMAVMATMVTC
ChatBridge [53]41.8027.2543.8718.364.3020.229.471.519.9618.5129.0117.4923.1815.1611.3726.3840.2021.7635.2028.3839.0221.7636.81
MissRAG+PE45.1443.1846.1019.0910.2020.6610.854.3710.2524.7830.0918.2223.7616.1817.9328.1241.2140.9537.0540.4636.1937.3338.94
Improvement+3.34+15.93+2.23+0.73+5.90+0.44+1.38+2.86+0.29+6.27+1.08+0.73+0.58+1.02+6.56+1.74+1.01+19.19+1.85+12.08-2.83+15.57+2.13
OneLLM [22]48.8939.4849.8620.413.3426.402.981.203.7648.5473.9140.2375.8838.3441.6956.4130.8257.7040.2258.7538.1446.1040.09
MissRAG+PE50.8546.6651.3227.1916.5726.424.032.504.1778.5774.2046.6576.6854.0845.4875.5159.1851.6645.1652.3545.8947.6661.56
Improvement+1.96+7.18+1.46+6.78+13.23+0.02+1.05+1.30+0.41+30.03+0.29+6.42+0.80+15.74+3.79+19.10+28.36-6.04+4.94-6.40+7.75+1.56+21.47
VideoLLaMA 2 [13]77.2059.5779.9419.367.0222.4010.170.6912.2046.0643.5910.5074.3410.204.3725.8041.3644.2428.5553.1728.0722.0036.62
MissRAG+PE77.5360.1179.9721.4210.3022.6411.963.2912.6233.3837.7623.7640.5211.0223.3434.6938.6339.4729.2040.1430.3127.1539.17
Improvement+0.33+0.54+0.03+2.06+3.28+0.24+1.79+2.60+0.42-12.68-6.23+13.26-33.82+0.82+18.97+8.89-2.73-4.77+0.65-13.03+2.24+5.15+2.55
+ +Table 2. Main results comparing the baseline versions of ChatBridge, OneLLM, and VideoLLaMA 2 with their enhanced counterparts incorporating our MissRAG+PE method. In this experiment, we assess the robustness of the MLLMs under seven missing modality scenarios: MA (Missing Audio), MV (Missing Video), MT (Missing Text), MAV (Missing Audio-Video), MAT (Missing Audio-Text), MVT (Missing Video-Text), and C (Complete). All experiments are conducted using $k = 1$ retrieved elements. Best results in bold. Gray color indicates that the model has seen the dataset during training. + +dio, video, and text. Notably, the Complete scenario never yields optimal performance for all MLLMs in this task. + +In particular, ChatBridge consistently demonstrates relatively poor performance in this task. Indeed, qualitative analysis shows that its responses are often nonsensical compared to those generated by OneLLM and VideoLLaMA 2, highlighting its limitations. Nevertheless, our method generally contributes to performance improvements. + +Conversely, VideoLLaMA 2 shows discrete performance when operating with text-only inputs, but underperforms in the multimodal setting. This suggests that while its underlying language model possesses the necessary capabilities, the overall multimodal framework struggles to effectively integrate and reason over multimodal inputs. As a result, our methodology encourages the model to behave similarly to the Complete scenario, which, in the case of VideoLLaMA 2, is suboptimal and may lead to a reduction in the final results. + +On the other hand, OneLLM is the only model capable of achieving satisfactory performance in the Complete scenario when prompted and does not exhibit performance degradation in the presence of the audio modality. Consequently, when integrated with our proposed method, it exhibits substantial performance gains in both the Missing Audio and Complete scenarios—achieving improvements of +30.03 and +19.10 on the MOSI dataset, and +28.36 and +21.47 on the MOSEI dataset, respectively. However, similar to the other models, OneLLM experiences performance degradation both when the video modality is present and when the text is absent. Accordingly, as shown in Table 3, when our PE is used alone, yields the highest accuracy under the Missing Video scenario. Hence, by explicitly informing the MLLM of the absence of the video modality, the PE improves its reasoning ability, resulting in a 6.88-point increase in accuracy. Furthermore, a plausible explanation for the performance degradation observed when incorporating the video modality lies in the MLLMs + +visual encoder. Hence, video encoders utilized for sentiment analysis tasks extract highly specific visual features based on facial landmarks, as opposed to general-purpose visual encoders employed by our MLLM backbone. For what concerns the absence of text—the typically worst-case scenario—our method consistently improves OneLLM. + +Finally, although the evaluated models natively struggle with audio-video-text sentiment analysis, these experiments provide valuable insights. They serve to validate existing literature and offer a robust benchmark for assessing the multimodal reasoning capabilities of current MLLMs across three heterogeneous input modalities. + +# 5. Ablation Studies + +Our ablation studies offer a thorough evaluation of the proposed MissRAG framework and prompt engineering strategy. For consistency, experiments are conducted using OneLLM [22], which in general demonstrates greater robustness across various missing modality scenarios. + +MissRAG: on the Effect of the $k$ Parameter. The objective of this ablation study is to investigate the impact of the hyperparameter $k$ in MissRAG, which determines the number of prototypes retrieved by our RAG-based framework. We conduct experiments both with and without isolating the MissRAG from the PE component across all tasks and datasets discussed in this paper. The results, presented in Table 3, indicate that our solution consistently outperforms the baseline in 22 out of 23 cases. Moreover, enhancing our MissRAG with our proposed PE yields performance improvements compared to utilizing the MissRAG alone. These results suggest that the two techniques are complementary, thereby justifying their combined application. However, it is also important to note that if incorporating all modalities does not result in optimal performance for the MLLM, the most effective approach may be to employ only PE. This is because PE is designed to enhance the model behavior regardless of the available input + +
TaskAudio-Video Question AnsweringAudio-Video CaptioningAudio-Video-Text Sentiment Analysis
Dataset MetricMUSIC-AVQA AccuracyVALOR32K CIDErCharadesEgo CIDErMOSI AccuracyMOSEI Accuracy
MethodMAMVCMAMVCMAMVCMAMVMTMAVMATMVTCMAMVMTMAVMATMVTC
OneLLM [22]48.8939.4849.8620.413.3426.402.981.203.7648.5473.9140.2375.8838.3441.6956.4130.8257.7040.2258.7538.1446.1040.09
PE51.7241.8151.3223.793.7726.423.251.224.1768.6679.7444.9076.1139.4842.7275.5148.1264.5849.4347.6931.7941.7361.56
MissRAG (k=1)49.6145.55-25.0015.83-3.932.2-65.6063.4139.5056.7149.9738.78-42.2036.3428.8931.5326.2322.04-
MissRAG (k=3)49.6745.69-22.8717.13-3.992.17-63.7063.8546.7953.3540.9644.46-41.4331.7026.8926.7431.3622.84-
MissRAG (k=5)49.5046.27-21.0117.16-4.222.14-62.6860.5047.5251.6049.5648.98-41.3430.7824.5525.8031.9621.59-
MissRAG+PE (k=1)50.8546.6651.3227.1916.5726.424.032.54.1776.0974.4947.8176.6854.0845.4875.5159.1851.6646.1652.3545.8947.6661.56
MissRAG+PE (k=3)50.8646.8051.3224.8617.3426.424.002.314.1776.3874.0548.6972.0149.7151.0275.5157.6749.0441.2143.7944.4737.4861.56
MissRAG+PE (k=5)50.8347.2951.3223.5017.4926.424.252.604.1776.5372.7449.9870.8549.4250.7375.5157.0747.9137.3342.9141.8331.9061.56
MissRAG+PE (k=1)†50.7146.5751.3226.7316.3726.423.972.464.1778.4373.8548.2572.6854.9645.3475.5155.4249.3348.8952.1645.7846.5161.56
+ +Table 3. Ablation study on the impact of the number $k$ of retrieved prototypes in MissRAG conducted on OneLLM. The symbol $\dagger$ denotes that the prototype pool is constructed by merging the prototype pools from all datasets. + +
Task Dataset MetricQuestion Answering MUSIC-AVQA AccuracyCaptioning VALOR32K CIDEr
MethodMAMVCMAMVC
OneLLM [22]48.8939.4849.8620.413.3426.40
System Message51.7241.8151.3223.793.7726.42
User Instruction48.6841.0249.2723.003.5827.30
+ +modalities, whereas MISSRAG aims to improve the model performance to closely approximate that of the Complete modality scenario. Consequently, when the Complete scenario represents the optimal condition, performance gains are maximized. Otherwise, a performance decline may be observed. Nevertheless, this decline is not attributable to our methodology but rather stems from inherent limitations within the MLLM backbone (i.e., OneLLM). + +Robustness of MISSRAG. We design an experiment to evaluate the robustness of our MISSRAG in a scenario where the prototype pool is generic and not customized for each dataset. To this end, we create a unified pool by merging the prototype pools from all datasets and repeat the experiment with $k = 1$ . The results, presented in the last row of Table 3, indicate that there is no significant deviation compared to the MISSRAG+PE ( $k = 1$ ) case. + +Prompt Engineering: in the System Message vs. in the User Instruction. A key research question is whether our PE technique is more effective when applied to the system message or the user instruction. To explore this, we evaluate both variants on the MUSIC-AVQA and VALOR-32K datasets, as presented in Table 4. The results demonstrate that applying our PE technique to the system message yields superior results compared to applying it to the user instruction across both tasks. This indicates that enhancing the initial system message with the PE method contributes to increased robustness against missing modalities. + +Prompt Engineering: Compensation Strategy. The objective of this ablation study is to demonstrate that incorporating the Compensation Strategy for Missing Modalities (CSMM) immediately following the string indicating + +Table 4. Ablation study on system message vs. user instruction, performed on OneLLM. Best results in bold. + +
Task Dataset MetricQuestion Answering MUSIC-AVQA AccuracyCaptioning VALOR32K CIDEr
MethodMAMVCMAMVC
OneLLM [22]48.8939.4849.8620.413.3426.4
PE51.7241.8151.3223.793.7726.42
PE w/o CSMM49.6840.7951.0123.063.6926.27
+ +Table 5. Ablation study on the prompt engineering compensation strategy, performed on OneLLM. Best results in bold. + +the input modality status within the system message leads to enhanced performance. To isolate the impact of CSMM from that of prototypes, we employ only PE in this setting. Specifically, within the input modality string, the possible values for each modality are Present/Missing, whereas the CSMM prompts, as detailed in Table 1, correspond to prompts without retrieval and are designed to induce the model to infer a plausible context for the missing modality using the available ones. Our results, presented in Table 5, indicate that, across both datasets, adding the instructions to infer missing modalities after the input modality status yields superior performance. + +# 6. Conclusion + +In this work, we have presented the first comprehensive study on the robustness of MLLMs under missing modality conditions. To address this challenge, we have introduced MissRAG, a novel multimodal RAG-based framework, enhanced with a tailored Prompt Engineering (PE) strategy, designed to effectively handle missing modalities. Notably, our approach is the first to jointly manage three distinct modalities within a RAG-based paradigm. Extensive experiments across five diverse datasets spanning audio-visual question answering, audio-visual captioning, and audio-video-text sentiment analysis have demonstrated that the proposed solution significantly outperforms baseline methods. Specifically, MissRAG enhances input quality by substituting missing information with contextually appropriate candidates, while PE improves model robustness to incomplete inputs. Combined, MissRAG+PE consistently yields superior performance in complex multimodal scenarios. + +# Acknowledgments + +This work has been supported by the EU Horizon project "ELLIOT - European Large Open Multi-Modal Foundation Models For Robust Generalization On Arbitrary Data Streams" (GA No. 101214398), by PNRR project "Fit4MedRob - Fit for Medical Robotics" funded by the Italian Ministry of University and Research, and by the University of Modena and Reggio Emilia and Fondazione di Modena through the "Fondo di Ateneo per la Ricerca - FAR 2024" (CUP E93C24002080007) and FARD-2024. The work also received funding from DECIDER, the European Union's Horizon 2020 research and innovation programme under GA No. 965193 and "AIDA: explAinable multImodal Deep learning for personAlized oncology" (Project Code 20228MZFAA). + +# References + +[1] Hassan Akbari, Yin Yuan, Wei Feng, Wei Hu, Yanjun Wang, M Javad Roshtkhari, and Greg Mori. 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While prior research mainly addresses procedural errors that often relate to temporal and ordering information, identifying a broader range of error types is essential for real-world implementation. In this work, we present MistSense, an approach for online mistake identification that includes versatility by considering both procedural errors, which involve incorrect action sequences, and execution errors, such as motor inaccuracies or improper equipment use. Our method integrates RGB and hand pose features to capture fine-grained contextual cues in order to detect a mistake. By jointly modeling spatial and sequential aspects of human actions, our framework enables robust and adaptive error detection in dynamic environments. Once a mistake has been detected, we leverage a large language model (LLM) which provides an error explanation that gives the user further insights into why an action has been identified as a mistake. The evaluation on common mistake detection benchmarks shows the effectiveness of our approach. + +# 1. Introduction + +Recent action detection and recognition approaches [26, 27, 34, 38] enable the accurate perception of human actions from video data while relying on spatiotemporal information to reason about human behavior. An intelligent assistant, however, should have the capability to further reason about the correctness of certain actions, to assist users in accurately performing actions or completing tasks. Such intelligent systems could be applied to daily tasks like cooking or home maintenance, as well as industrial settings such as assembly lines or mechanical repairs. + +In line with recent online mistake detection ap + +![](images/385b12993b73d10cdb9e78d5dfd6c15ca9884fabd80cdcb55760d2557ba7f2c1.jpg) +Figure 1. MistSense framework for mistake detection and explanation: Compared to prior approaches that mainly focus on temporal and ordering relations in the form of procedural mistakes, our approach can consider procedural as well as execution mistakes, that capture how an action is performed, in an online fashion. We further integrate hand pose information during the mistake detection process. Upon detecting an error, an LLM is queried to provide an explanation for why the action is incorrect based on the extracted video features. + +proaches [9, 18, 30], to provide timely feedback, the system should be able to conduct inference in an online setting, enabling it to identify errors from a continuous video stream. This allows the user to respond promptly, preventing further consequences of the mistake. An egocentric perspective offers a valuable advantage by capturing task execution from the user's point of view, circumventing the limitations of static viewpoints that may suffer from occlusions caused by the human body. Furthermore, recent advances in augmented reality enhance the relevance of egocentric systems [2, 5]. The unique egocentric perspective additionally makes it easier to recognize the human hand pose. While this hand-specific information has proven to be helpful for action recognition and detection tasks [11, 32, 37], it can be leveraged for determining the correctness of an executed action and thus used as another modality alongside images. + +While recent methods predominantly focus on procedural errors [9, 18, 28, 30], such as improper sequencing or missed actions, the spectrum of possible errors is broader and application-dependent. Thus, the partial ordering of actions and the successful completion of key steps may only partially represent correct task execution. By additionally considering execution errors that range from motor errors to misusing a piece of equipment, one can get a more holistic interpretation of the successful task completion. Recent datasets further extend to varying error types and consider a mixture of procedural and execution errors [13, 29, 35], which enables a comprehensive evaluation comparable to real-world circumstances. In contrast to anomaly detection methods [22, 36, 39], procedural and execution errors relate to completing a task and its corresponding steps and indicate potential deviations from it in terms of the correctness of ordering or motor execution. As shown by [18] anomaly detection methods struggle to perform procedural and execution error detection in videos. + +Current mistake detection approaches mainly focus on only detecting a mistake [9, 28, 30]. However, to understand why an action is incorrect, additional context is required for the user in order to analyze the executed action. Further information such as the omission of a prerequisite for the current action or the way of executing the action can provide helpful guidance for correcting the behavior. Therefore, drawing inspiration from recent advancements in language and vision-language models [15, 20, 24, 33], we utilize an LLM to generate possible explanations for the detected mistakes. Thus, within our approach, we focus on capturing procedural errors that mainly relate to the relative ordering of actions and depend on temporal relations, as well as execution errors, which refer to how the human is performing certain actions that relate to spatial as well as temporal relations. As a result, our approach can better capture the correct execution of a task while being versatile concerning varying error types. As an additional modality to RGB, we also investigate the use of hand pose data during the mistake detection process. To the best of our knowledge, we are the first to provide a versatile error detection method that further provides textual explanations regarding the detected mistakes. Our contribution is three-fold: + +- We propose MistSense, a versatile online mistake-detection approach that can recognize procedural and execution errors. Thus, our model is capable of evaluating the correct execution of a task in a holistic way compared to only relying on considering temporal ordering. +- Our method also offers explanations for why an action was erroneous, enabling proactive guidance. By providing users with insights into how an error occurred, our approach facilitates easier issue resolution. +- We evaluate our approach on the Epic-tent-O [13] and Holo-Assist [35] datasets, which contain several error + +type variations, where our approach shows strong results and improves over existing methods. + +# 2. Related Work + +# 2.1. Mistake Detection + +Due to the strong semantic reasoning and zero-shot capabilities of Large Language Models (LLMs), recent work has also leveraged these models for online mistake detection. Flaborea et al. [9] and Plini et al. [28] leverage the in-context learning capabilities of LLMs to predict feasible next action while simultaneously detecting actions. Errors are then determined based on discrepancies between the detected and the anticipated action. However, since these approaches first use an action detection method and then pass the recognized events to the LLM, they cannot capture execution errors related to specific object manipulations or other spatial clues that indicate the correctness of the manipulation task. Seminara et al. [30] introduced a differentiable approach for learning task graphs by directly optimizing edge weights via maximum likelihood to perform mistake detection. Lee et al. [18] introduced a framework combining action segmentation with contrastive step prototype learning to detect procedural errors. By leveraging handobject interaction modeling via a Graph Convolutional Network and relying on feature-prototype similarities, offline mistake detection is performed. + +Other methods further investigate the use of additional modalities. Lehmann et al. [19] identified assembly errors by comparing a test image with a correct assembly state, using synthetically generated image pairs to enable controlled change detection. This method is particularly focused on assembly applications as CAD models of objects are required. Wang et al. [35] leveraged a TSFormer [4] while combining RGB and hand pose information. Mazzamuto et al. [25] rely on eye gaze and RGB information while leveraging GLC modules [16], that relate global visual tokens to local embeddings for eye gaze estimation. They detect mistakes by recognizing differences between the predicted and the observed gaze trajectory. + +Compared to previous approaches, we focus on detecting not only procedural errors but also execution errors in order to better evaluate the correctness of an action. Additionally, we integrate hand pose information as an extra modality to consider the correctness of particular hand movements during the execution of an action. + +# 2.2. Language based Reasoning + +The recent progress in Large Language models has enabled a more elaborate and advanced way of reasoning that has been further improved by training on large datasets [8, 15, 33]. Additional work further expanded the reasoning capabilities of LLMs to additional modalities and in particu + +lar vision-based language models (VLMs) [1, 21, 40]. Liet al. [20] proposed BLIP-2, an efficient approach for aligning vision and language representations that can create captions based on the projected embeddings. With VideoLlama, Zhang et al. [40] propose a method that further extends the Q-Former of BLIP-2 to a Video Q-Former that can comprehend temporal dependencies rather than just image-specific features. The resulting representations are projected to a frozen LLM to create captions. Maaz et al. [24] introduced VideoChatGPT, which further considers the temporal relations between the extracted features while supporting multiturn chat interactions. Videollava [21] proposed a unified visual representation space where image and video embeddings are aligned before being passed to the LLM, further enhancing the multimodal reasoning capabilities for visual content. Previous approaches further utilized the reasoning capabilities of LLMs to anticipate future actions [9, 28, 41]. + +In our approach, we also leverage the Q-Former to efficiently encode vision features and an LLM to provide text descriptions. However, instead of generating image content or video descriptions or anticipating actions, the LLM provides explanations of recognized mistakes, offering insights into why an action is incorrect. + +# 2.3. Mistake Detection Datasets + +Various datasets have been proposed to deal with the challenge of mistake detection. The ATA dataset [10] is focused on offline mistake detection for assembly tasks. The Epic-tent-O and Assembly101-O datasets [9] introduce online procedural mistake detection in an industrial and an outdoor environment. The former is based on the Epic-tent [13] dataset and adapted for an online use case under open-set conditions. It captures the outdoor assembly of a tent and introduces execution and procedural errors. The latter is based on Assembly101 [31], which captures toy assembly processes, emphasizing procedural mistakes and their corrections, where the actor reverses the error. + +In addition to procedural errors, the IndustReal [29] dataset captures execution errors, which indicate whether the action has been completed correctly. The HoloAssist dataset [35] is a large-scale dataset that also incorporates procedural and execution errors, along with error explanations, while the user wears a HoloLens headset during various object-centered manipulation tasks. Focusing not only on capturing the temporal and logical dependencies between actions in the form of procedural errors but also on investigating the correct execution of actions, we utilize the HoloAssist and Epic-tent-O datasets, as both contain varying error types. This allows us to assess how effectively our approach integrates spatio-temporal reasoning of action execution and the logical connections between consecutive actions. The egocentric perspective of both datasets further helps to capture hand poses accurately. + +# 3. Methodology + +In this section, we give an overview of our approach and explain the individual components with respect to the mistake detection and error explanation tasks. Additionally, we explain the learning objectives and the overall training strategy that we use to obtain the results of Section 4. + +# 3.1. Mistake Detection + +As depicted in Figure 2 for the online scenario, we expect a continuous video stream as an input, where we process the overall frames in segments up to the current timestep $t$ . The frames get passed through a combination of a visual encoder and a Q-Former, similar to the one proposed in Blip2 [20] in order to extract visual features. The video encoder in our case is a ViT [7]. We denote a segment of features as $v = [v_{t - t_s},\dots,v_t]$ , with $v\in \mathbb{R}^{t_s\times d_1}$ where $t_s$ denotes the number of overall considered timesteps within the segment and $d_{1}$ indicates the feature dimension. In combination with learnable queries $q_{rgb}\in \mathbb{R}^{t_q\times d_2}$ , the features $v$ are input to the Video Q-Former. The learnable queries are trainable token embeddings that guide the model to extract task-relevant information from features with crossattention. Compared to the Q-Former that extracts spatial information within a frame, the Video Q-Former considers the temporal relations between multiple framewise features but retains the overall structure of [20] similarly as shown in [40], meaning that it consists of a BERT encoder [6]. This results in the features $f_{rgb}\in \mathbb{R}^{t_q\times d_2}$ . + +In addition to the RGB-based features, we further extract framewise hand pose representations $h \in \mathbb{R}^{c \times t_s \times v \times m}$ , where $c$ denotes the number of coordinate dimensions, $v$ defines the number of joints and $m$ represents the number of hands. These hand pose representations are forwarded to the hand pose encoder, which we adapt from [32]. It consists of Temporal Convolutional Networks (TCNs) [17] that model the separate joints as well as the wrist individually and subsequently combine them with self-attention into the feature representation $h_1 \in \mathbb{R}^{t_s \times d_h}$ . We do not perform temporal pooling over the features or extract a classification token but directly use these spatiotemporal features for further processing. The features $h_1$ are passed through a projection layer that adjusts the feature dimension to $h_2 \in \mathbb{R}^{t_s \times d_2}$ . Similarly to the RGB processing, a framewise positional embedding is added to these features. The Hand Q-Former, which has the same structure as the Video Q-Former, subsequently processes $h_2$ in combination with the learnable queries $q_{hand} \in \mathbb{R}^{t_q \times d_2}$ , which results in the features $f_{hand} \in \mathbb{R}^{t_q \times d_2}$ . + +The features $f_{rgb}$ and $f_{hand}$ are then added together and passed to the mistake classification layer to obtain the final mistake logits $m \in \mathbb{R}^{t_q}$ . The error explanation generation process is initiated once a mistake is identified based on those logits. + +![](images/3befb83050e2822482651b8e69c3896a9f2f0945da7c79437a245a2ddfd984c0.jpg) +Figure 2. Overview: Based on a continuous RGB stream, a video encoder, and a Q-Former are used to extract framewise visual relations. Within our approach, hand pose information is used as an additional modality during the mistake detection process. Subsequently, a Video Q-Former is leveraged to extract temporal dependencies between the RGB features. The colored squares represent learnable queries, similar to the ones proposed by [20]. The extracted hand pose features are passed to the Hand Q-Former and added to the extracted RGB-based representations. The mistake classification layer then obtains the final predictions. The Video Q-Former features are forwarded through the gate $g_{m}$ and projected to the LLM embeddings space to create the error explanations. The double slashes indicate no backpropagation. + +# 3.2. Error Explanation + +The error explanation aims to provide further reasoning as to why an action is incorrect in the form of a text description. The explanation of our model relates to execution and procedural mistakes observed in the considered segment. In case multiple mistakes appear in the same segment, the corresponding captions are concatenated. To provide a textual explanation regarding recognized mistakes, the aforementioned Video Q-Former features $f_{rgb}$ that are obtained from the mistake detection part are routed through the gating mechanism $g_{m}$ . During the error explanation task, we only consider the RGB-based features to be forwarded to the LLM. This is formulated as + +$$ +g _ {m} (\sigma (m)) = \left\{ \begin{array}{l l} 1, & \text {i f} \sigma (m) \geq \tau \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {1} +$$ + +where $\sigma$ is the sigmoid function. Once the predicted logit reaches a threshold $\tau$ , the features of the video Q-Former are further forwarded to the projection layer. The projection layer is a linear layer that maps the features to the dimension of the LLM embedding space. The resulting features, as well as a prompt, are forwarded to the LLM in order to create the final explanation. Thus, we ensure that our approach generates error explanations once an error is detected. + +# 3.3. Learning Objectives + +MistSense is trained in several stages with respect to mistake detection and explanation generation learning objectives. For mistake detection, during the first stage, we apply a weighted binary cross-entropy loss on the predicted probabilities $\hat{y}_i$ regarding a mistake, defined as + +$$ +\mathcal {L} _ {\text {M i s t}} = - \frac {1}{N} \sum_ {i = 1} ^ {N} \left[ w _ {1} y _ {i} \log \left(\hat {y} _ {i}\right) + w _ {0} \left(1 - y _ {i}\right) \log \left(1 - \hat {y} _ {i}\right) \right] \tag {2} +$$ + +where $y_{i}$ denotes the binary ground truth label, $N$ specifies the number of samples, and $w_{0}, w_{1}$ are the respective weights for a correct and wrong action. The weights are applied in order to mitigate the imbalance between correct and wrong actions, where a correct action is annotated as 0 and a mistake as 1. We finetune all components of the model, besides the LLM projection layer and the LLM, during the mistake detection training while keeping the video encoder and the corresponding Q-Former frozen. + +For the error explanation task, we use a regular cross-entropy loss and annotated explanations as supervision. During this second stage of the training, we first freeze all model components and only fine-tune the projection layer. The resulting features from the Video Q-Former $f_{rgb}$ are processed in segments so that only one given video seg + +
Holo Assist
MethodsModalityF1-ScoreCorrectMistake
PrecRecPrecRec
TSformer [4]RGB35.182.651.812.926.9
TSformer [4][35]RGB + H(GT)36.285.543.19.711.5
GazeCompl [25]RGB + E51.095.092.06.09.0
MistSenseRGB54.895.691.311.421.1
MistSenseRGB+H(P)55.795.985.410.331.6
+ +ment is considered during a training step. In the last stage, we finetune the LLM parameters efficiently with Low-Rank Adaption (LoRA) [12], which is a method that leverages low-rank matrices during the weight updates, while freezing the projection layer. In case of varying errors within the same segment, the ground truth explanations are concatenated during optimization. + +# 4. Experiments + +In this section, we introduce our benchmarking datasets and provide the results of our approach against prior work on mistake detection. We further provide overall qualitative results as well as a quantitative evaluation of the mistake explanation generation capabilities of our approach. The bold scores in the table indicate the best and the underlined ones the second-best result. + +Baselines: In the case of the mistake detection task, as a baseline for Epic-tent-O, we use recent online mistake detection methods. For Holo Assist we use the official baselines of [35] as well as the approaches listed on the benchmarking server. To the best of our knowledge, no existing methods specifically focus on detecting and explaining mistakes; therefore, we compare our results on the error explanation task with recent Vision-Language Models (VLMs) with the same visual encoder and image input dimensions. These methods are fine-tuned by only considering segments with mistakes, as they only focus on the generative task but not on the detection task. + +# 4.1. Datasets and Metrics + +To evaluate the versatility of our approach, we consider two datasets that capture varying scenarios as well as error types. The Epic-tent dataset [13] consists of 7 hours and captures the assembly of a camping tent in an outdoor environment performed by 29 participants with head-mounted cameras, whereas the Epic-tent-O dataset [9] is a subset + +Table 1. Performance comparison on Holo Assist [35]. TSformer [4] + H(GT)[35] denotes the TimeSformer model combined with ground truth hand pose as reported by [35]. E denotes the eye gaze information acquired by the HoloLense device. H(P) refers to the hand pose predicted by Mediapipe [23]. + +
Holo Assist
MethodsBLEUROUGELCIDEr
GT Sampling0.460.500.30
Videollama [40]0.520.570.68
Video-ChatGPT [24]0.550.580.61
MistSense0.530.580.76
+ +Table 2. Performance comparison on the error explanation generation task for the Holo Assist [35] dataset. + +of this dataset, designed for open-set online mistake detection, that only captures certain procedural mistakes. The Holo Assist dataset [35] is an egocentric human interaction dataset capturing 169 hours of collaborative physical manipulation tasks from 350 unique performer-instructor combinations, where a task performer wearing a mixed-reality headset follows real-time verbal guidance from an instructor. As our approach relies on supervision in the form of labeled errors, we use the entire original Epic-tent dataset during training. + +For online mistake detection on both datasets, we report the precision and recall values of the correct and mistaken actions. For Epic-tent-O and Holo Assist, we report the F1-Score, where in the latter case, results are obtained from the official benchmark server1. For the mistake explanation generation task, we report the BLEU, which is based on the precision of n-grams with a brevity penalty, ROUGEL, which is computed concerning the longest common subsequence between prediction and ground truth explanation, and CIDEr scores, which captures similarities based on tfidf weighted n-grams. As the error explanations for the Holo Assist test set are not publicly available, we report the results on the validation set with annotated explanations. + +
MethodsEpic-tent-O
ModalityF1-ScoreCorrectMistake
F1PrecRecF1PrecRec
Count-Based [3]RGB40.459.242.995.521.680.012.5
PREGO [9]RGB29.241.697.926.417.29.593.3
MSG² [14]RGB45.267.552.495.122.973.313.6
DO [30]RGB46.569.354.495.223.773.314.1
MistSenseRGB59.889.784.296.229.855.020.4
MistSenseRGB+H(P)63.388.285.690.938.345.433.1
+ +Table 3. Performance comparison on Epic-tent-O [9]. H(P) refers to the hand pose predicted by Mediapipe [23]. We evaluate our approach concerning different modality combinations. + +
Epic-tent
MethodsBLEUROUGELCIDEr
GT Sampling0.500.541.58
Videoillama [40]0.530.571.78
Video-ChatGPT [24]0.430.612.61
MistSense0.620.663.09
+ +Table 4. Performance comparison on the error explanation generation task for Epic-tent [13]. + +# 4.2. Mistake Detection + +For both datasets, we report the results of our approach only based on RGB data as well as the combination of RGB and predicted hand pose data. For the hand pose extraction, we use Mediapipe [23]. For evaluating the mistake detection performance on Epic-tent-O, we use consistent evaluation with [9], where mainly procedural errors are considered. While DO [30] and $\mathrm{MSG}^2$ [14] consider supervision in the form of key-steps in order to access the procedural correctness of activities, our approach is supervised directly based on the error annotations, which is why the training set of our method is extended by incorrect action sequences from the unmodified Epic-tent dataset. From Table 3 we can observe that our approach based only on the RGB features outperforms DO [30] by $13.3\%$ in terms of the overall F1-Score and by $6.1\%$ concerning the F1-Score when only considering the faulty actions. Additionally, integrating the Hand Q-Former and utilizing the hand pose modality further improves the performance by $3.5\%$ . This further indicates that hand-specific information can help to identify a particular mistake within a sequence. The overall evaluation shows that our model is suitable for detecting mistakes in a procedural assembly scenario. + +For the Holo Assist dataset, in line with prior work, + +we report the results of our approach based on the official competition server, as the test set annotations are not publicly available. Based on the results displayed in Table 1 we can observe that our method significantly improves upon the RGB-only TSformer [4] results reported by [35]. MistSense further improves upon the GLC-based method of [25] abbreviated as GazeCompl by $3.8\%$ , without using the additional eye gaze modality. When utilizing the hand pose information in addition to RGB data, the resulting F1-Score is further increased to 55.7. Compared to Epic-tent-O, the videos of Holo Assist frequently contain background classes without particular meaningful actions which makes the extraction of interaction dependencies more challenging. Additionally, this dataset contains procedural and execution error types, which indicates that our method is also applicable to such challenging conditions and can identify varying mistake types. + +# 4.3. Error Explanation + +In Table 4 we provide the error explanation generation results for the Epic-tent [13] dataset. We provide the explanations for the whole test set and evaluate our approach with respect to the aforementioned captioning metrics. As the original Epic-tent dataset does not contain text explanations, we generate them based on the underlying action and the error type, which results in explanations such as 'Place guyline was done in the wrong order', where further qualitative examples are shown in Section 4.5. All other referenced approaches are also finetuned with the same explanations. For the GT Sampling method, we randomly sample an explanation from the ground truth test set. From the results, we can observe that our approach outperforms other methods that solely focus on caption generation without mistake detection components. Due to the inherent structure of the action and mistake type, the resulting explanations have a similar structure, which is also partially reflected by the higher BLEU and ROUGEL scores. In partic + +ular the high CIDEr, however, further indicates that the semantic similarity of the generated explanations is improved by our method compared to the other approaches. + +Additionally, we evaluate the error explanation capabilities of our approach on the Holo Assist [35] dataset. This dataset provides explanations such as "The battery is upside down" or "The person accidentally turned on the GoPro", which give more detailed information to the user about why a particular action is a mistake. The variety and structure of the explanations are thus more diverse as compared to Epic-tent. Based on the results in Table 2 one can see that our approach performs on par or better than other baseline methods. The explanation quality regarding semantic similarity is particularly improved as indicated by the CIDEr score. + +# 4.4. Multimodal fusion strategies + +In order to evaluate, how to integrate the hand pose information into the mistake detection process we conducted an ablation study on different feature combinations. Handonly denotes omitting RGB features and only passing the hand pose features through the Hand Q-Former for mistake detection. Late-Fusion describes the summation of the RGB-based Video Q-Former features and the features resulting from the hand pose encoder without the Hand Q-Former, thus considering a smaller temporal segment. Shared Q-Former is the setting, where the RGB and hand pose features are summed and passed through the same shared Video Q-Former. Sep Q-Former results in the configuration with a separate Video and Hand Q-Former. + +From the results in Table 5 we can observe that only considering the hand modality can achieve an F1-Score of $49.1\%$ which is approximately $10\%$ below the RGB only score. When considering the late fusion, without a separate Hand Q-Former, the results are on par with the RGB-only case. Considering separate Q-Formers for each modality over a shared Q-Former further increases the F1-Score of the combined RGB and hand pose detection performance by $2.5\%$ . + +# 4.5. Qualitative Results + +In Figure 3 we display cutouts of videos from the Epicent and the Holo Assist dataset. It displays the confidence scores regarding the detected mistake in green over the time axis and the corresponding binary ground truth in blue, where 1 indicates an error and 0 indicates a correct action. The color of the textual explanation denotes its semantic correctness, where red denotes semantically wrong and green denotes semantically right explanations. + +In the upper example from the Epic-tent dataset, we can observe that generally, our method yields confidence values that align with the ground truth. However, very short mistakes and brief temporal segments of correct actions be + +
Epictent-O
MethodsF1-ScoreCorr. F1Mist. F1
Hand-Only49.188.010.1
Late-Fusion57.883.132.6
Shared Q-Former60.883.437.8
Sep Q-Former63.388.238.3
+ +Table 5. Ablation on different fusion strategies for the RGB and hand pose features. Sep-Qformer denotes separate Q-Formers for each modality. Hand-Only denotes only using the Hand Q-Former without RGB information. + +tween errors cannot always be perfectly retrieved. We further compare our model's mistake explanations with the ground truth, observing that while the overall structure of the explanations is preserved, misclassifications of error types and certain action components can occur. + +In the second row of the figure, an example of the Holo Assist dataset is displayed. The display of confidence values and ground truth remains the same, however, we can also observe in this sample that Holo Assist annotations generally have more mistakes, that are just 1.5 to 2 seconds long. This seems also particularly challenging for our model as such short mistake spikes in the ground truth sometimes do not correspond to higher confidence values. We can observe, however, that our model can detect execution mistakes such as the student grabbing the wrong piece or aligning the base frame incorrectly as shown in the Holo Assist example. + +# 4.6. Implementation Settings + +For our MistSense architecture, a ViT-L is used as a video encoder, a Llama2-7B as the LLM, and the Video and Hand Q-Former are based on the same BLIP2 structure [20]. For our evaluation the approach is trained for 12 epochs on 2 RTX A6000 GPUs with an AdamW optimizer, a batch size of 16 for Epic-tent and a batch size of 32 for Holo Assist, and a cosine learning rate scheduler with an initial learning rate $(lr)$ of $3e^{-5}$ , a weight decay of $5e^{-3}$ and a linear warmup starting from a learning rate of $1e^{-6}$ . The features are extracted based on 2 fps for both datasets. For the Epic-tent-O dataset, we use $w_{1} = 1$ , $w_{0} = 1$ , and for Holo Assist, we use $w_{1} = 4$ , $w_{0} = 1$ . For the hand pose encoder, we adapt the hyperparameters of [32] and use a learning rate of $2.5e^{-2}$ without weight decay. For training the baselines, we retain the same hyperparameters as proposed in the original approaches. During inference, the model requires 20.5 GB of VRAM, while a single run on an RTXA6000 takes approximately 4 seconds when considering the mistake detection as well as the explanation generation. + +![](images/5fd6c1c9627902943676c7113068a26c5c2f9f02852717c29f7dead52dcfdd3a.jpg) +Figure 3. Qualitative results on a video cutout of the Epic-tent dataset, where exemplary frames are sampled from the indicated segments. The confidence scores indicating the mistake detection probabilities $\hat{y}$ and the ground truth indicating the mistake annotations are visualized over time. + +# 5. Conclusion + +In this work, we propose MistSense, an approach capable of versatile online mistake detection that can further provide explanations regarding mistakes. This is enabled by projecting the extracted features used for mistake detection to the LLM embedding space upon recognizing an error. As our approach captures the spatial information of how an action is executed and the temporal dependencies between actions, it recognizes execution and procedural mistakes. In addition to utilizing RGB features, it further integrates hand pose features to improve mistake detection performance. The experimental results on the public benchmarks Epicent-O and Holo Assist show the overall strong performance of MistSense on the mistake detection and the explanation generation tasks. Our approach is leading the benchmark on the official evaluation server at the time of writing. + +Limitations and future work As the error variety and scale of Epic-tent is limited, additional datasets similar to the size of Holo Assist with mistake annotations would be helpful to cover a broader range of actions and frequent mistakes which would help to further improve the performance of our approach. In particular, variations regarding mistake explanation annotations and a focus on reliable and consistent mistake explanation annotations would further strengthen the performance with respect to the provided explanations. + +Future work could define approaches to deal with very short mistakes robustly, as these mistakes seem particularly challenging as discussed in Section 4.5. Additionally, one could investigate the use of additional modalities like eye gaze or depth to strengthen mistake detection. + +# 6. Acknowledgement + +We gratefully acknowledge the funding of the Lighthouse Initiative Geriatronics by StMWi Bayern (Project X, grant no. 5140951) and LongLeif GaPa GmbH (Project Y, grant no. 5140953). + +# References + +[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. Advances in neural information processing systems, 35:23716-23736, 2022. 3 +[2] Fabio Arena, Mario Collotta, Giovanni Pau, and Francesco Termine. An overview of augmented reality. Computers, 11 (2):28, 2022. 1 +[3] Kumar Ashutosh, Santhosh Kumar Ramakrishnan, Triantafyllos Afouras, and Kristen Grauman. Video-mined task graphs for keystep recognition in instructional videos. Advances in Neural Information Processing Systems, 36, 2024. 6 +[4] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. Is space-time attention all you need for video understanding? 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Antgpt: Can large language models help long-term action anticipation from videos? 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However, FAT suffers from Catastrophic Overfitting (CO), where models' robust accuracy against multi-step attacks plummets to zero during training. Recent studies indicate that CO occurs because single-step adversarial perturbations contain label information that models exploit for prediction, leading to overfitting and diminished robustness against more complex attacks. In this paper, we discover that after CO occurs, the label information of certain samples can transfer across different samples, significantly increasing the likelihood of modified images being classified as the intended label. This discovery offers a new perspective on why various adversarial initialization strategies are effective. To address this issue, we introduce an innovative FAT strategy that leverages special samples to capture transferable label information and proactively removes potential label information during training, complemented by a non-uniform label smoothing technique to further eliminate label information. Experimental results across three datasets demonstrate that our method maintains competitive robustness against several attacks compared to other FAT approaches, with ablation studies confirming the effectiveness of our methodology. The code is available at https://github.com/fzjcdt/LIET. + +# 1. Introduction + +Fast Adversarial Training (FAT) has gained popularity in adversarial machine learning as an efficient alternative to traditional methods. By generating Adversarial Examples + +![](images/812049fd7745b06f84e6e3bacea3f88a0e384fde4e297d4f9d51367f82a582b0.jpg) +Figure 1. Label information transferability post-catastrophic overfitting. A ResNet18 model, FAT-trained on CIFAR10 and experiencing CO, was tested. A single-step perturbation targeting "cat" $(y_{\text{cat}})$ , generated from a gray image (value 0.5), was applied to 10,000 test images. "Cat" classification surged from $10.23\%$ to $53.89\%$ . This highlights that single-step perturbations after CO encode transferable label information. + +(AEs) using single-step gradient propagation, FAT significantly reduces computational costs compared to multi-step approaches [3, 7, 14, 28]. However, this efficiency comes at a cost: FAT is highly susceptible to Catastrophic Overfitting (CO), a phenomenon where the model suddenly loses its robustness against multi-step adversarial attacks, such as those generated by the Projected Gradient Descent (PGD) method [7, 16, 18, 24, 28]. The contrast between increasing single-step robust accuracy and the sudden drop to zero of multi-step robust accuracy exposes a critical vulnerability in FAT. + +Recent investigations into the nature of adversarial examples generated during CO have led to a pivotal discovery: the decoupling of single-step adversarial perturbations into data-information and self-information components [11]. This study reveals that the label information embedded within single-step perturbations plays a dominant role in guiding model predictions post-CO, thus facilitating the network's unintended learning focus on self-information. Consequently, models tend to rely solely on the label information present in single-step AEs for making predictions, thereby compromising their defense capability against multi-step AEs. + +In this study, we observed that after experiencing CO, the transferability of label information is remarkably effective across different samples. Utilizing a ResNet18 [10] model trained on the CIFAR10 [15] dataset with standard FAT and subjected to CO, we generated a single-step adversarial perturbation $\delta$ targeting the label $y_{cat}$ for a uniform gray image (value 0.5) using the Fast Gradient Sign Method (FGSM) [7]. Initially, among 10,000 original test images, only $10.23\%$ were classified as "cat". However, after applying $\delta$ , a striking $53.89\%$ of the samples were recognized as "cat", marking an $84.84\%$ increase in the likelihood of such classification. This significant shift in classification, as illustrated in Figure 1, underscores the strong transferability of label information embedded within single-step perturbations across a diverse set of images. + +Building on this new discovery, we propose a novel perspective to understand why various adversarial initialization strategies [13, 20] within the FAT method are effective. Adversarial initialization, in essence, inadvertently eliminates the label information contained within single-step adversarial perturbations, thereby aiding in the mitigation of CO. The experiments we conducted further validate this viewpoint, demonstrating that the strategic removal of label information at the initialization phase significantly contributes to the robustness and effectiveness of the FAT method against adversarial attacks. + +The discovery that label information plays a crucial role in the phenomenon of CO and its notable transferability across different samples has inspired us to introduce a novel FAT strategy. Our method, LIET: Label Information Elimination Training, is designed to proactively eliminate label information from adversarial perturbations during the training process, thereby tackling the underlying cause of CO directly. By implementing non-uniform label smoothing, we further enhance the process of removing label information, establishing a more effective defense mechanism against adversarial attacks. + +This work makes several contributions to fast adversarial training: + +1. We empirically demonstrate that label information embedded within single-step adversarial perturbations ex + +hibits remarkable transferability across different samples post-CO. This insight sheds light on the intrinsic properties of single-step adversarial perturbations and their impact on model classification behaviors. + +2. Building upon this discovery, we propose a novel explanation of why adversarial initialization strategies, commonly employed in FAT, are effective. Through rigorous experimentation, we demonstrate that adversarial initialization inadvertently facilitates the removal of label information from single-step adversarial perturbations, thereby mitigating the risk of CO. +3. Leveraging the above insights, we introduce a new FAT methodology, LIET: Label Information Elimination Training, specifically designed to proactively eliminate label information from adversarial perturbations during the training process. We validate the competitiveness of our approach across three datasets, with ablation studies further corroborating the efficacy of our strategy. + +# 2. Related Work + +# 2.1. Adversarial Attack and Training + +Adversarial attacks aim at crafting examples that lead to incorrect model predictions by adding perturbations to the input data [8, 9, 19, 21, 23]. The objective is to find a perturbation within a specified range $S$ that maximizes the loss function, thereby increasing the likelihood of misclassification. This process can be formulated as an optimization problem, expressed as: + +$$ +\delta^ {*} = \arg \max _ {\delta \in S} \mathcal {L} (f (\boldsymbol {x} + \delta ; \boldsymbol {\theta}), y), \tag {1} +$$ + +where $\delta^{*}$ represents the optimal perturbation aimed at maximizing the loss $\mathcal{L}$ , with $\theta$ denoting the model parameters, and $y$ the true label of $x$ . + +Adversarial Training (AT) seeks to improve model robustness by incorporating adversarial examples into the training process, formulated as a min-max optimization problem [16, 22]: + +$$ +\min _ {\boldsymbol {\theta}} \mathbb {E} _ {(\boldsymbol {x}, y) \sim \mathcal {D}} \left[ \max _ {\boldsymbol {\delta} \in \boldsymbol {S}} \mathcal {L} (f (\boldsymbol {x} + \boldsymbol {\delta}; \boldsymbol {\theta}), y) \right]. \tag {2} +$$ + +# 2.2. Fast Adversarial Training and Catastrophic Overfitting + +Fast adversarial training employs single-step attack methods, such as the FGSM, to generate adversarial examples [7]. However, FAT is vulnerable to catastrophic overfitting, a sudden drop in robust accuracy against adversarial examples generated by multiple adversarial attacks, primarily due to overfitting on specific adversarial patterns generated in early training phases [28]. + +# 2.2.1. Random Initialization + +To counter CO, random initialization introduces variability in the adversarial examples by starting the perturbation process with a random noise. This approach, including methods like Random Start FGSM (FGSM-RS) and Noise-FGSM (N-FGSM), has shown effectiveness in enhancing model robustness and preventing CO [3, 28]. + +# 2.2.2. Adversarial Initialization + +Adversarial initialization strategies, including Adversarial Training with Transferable Adversarial Examples (ATTA) [30], Prior-Guided Initialization (PGI) [13], and Universal Adversarial Perturbation (FGSM-UAP) [20], are designed to commence the adversarial example generation process using inputs that are inherently adversarial. + +# 2.2.3. Regularization + +Regularization techniques, like Gradient Alignment Regularization [1] and Nuclear-Norm regularization [27], are employed to stabilize the model's response to adversarial perturbations by aligning gradients and regularizing the output space, thereby enhancing the smoothness of the decision boundary and mitigating CO. + +# 3. Proposed Strategy for Label Information Elimination + +This section explores the transferability of label information post-CO, introduces a novel understanding of adversarial initialization, proposes a new FAT method, and discusses the implementation of non-uniform label smoothing as a defense mechanism. + +# 3.1. Transferability of Label Information after Catastrophic Overfitting + +This section aims to demonstrate a critical characteristic of single-step adversarial perturbations generated after CO: the transferability of label information. It is important to distinguish this concept from adversarial example transferability, where a single adversarial example can fool multiple models. Here, label information transferability refers to the ability of the label information embedded within one carefully crafted perturbation to influence the classification of different input samples. + +To empirically verify this phenomenon, we conducted an experimental study following the settings of He et al. [11]. We trained a ResNet18 [10] model on the CIFAR10 [15] dataset using FGSM-AT. + +After obtaining models that had undergone CO, we generated single-step perturbations for various inputs, including uniform gray images with all values set to 0 and 0.5, the training data mean, uniformly distributed noise, and the first sample from the test data. The perturbation for a given class $c$ was computed using the formula: + +$$ +\boldsymbol {\delta} _ {c} = \epsilon \cdot \operatorname {s i g n} \left(\nabla_ {\boldsymbol {x}} \mathcal {L} (f (\boldsymbol {x}; \boldsymbol {\theta}), c)\right), \tag {3} +$$ + +where $\pmb{x}$ represents the input, $c$ the class, and $\epsilon$ the perturbation magnitude. + +In order to evaluate the ability of these single-step perturbations to be transferred across different samples, we applied the perturbation $\delta_{c}$ to $N$ samples from the test set and observed the model's responses. To quantify the transferability of these perturbations, we introduced two specific metrics: $P_{abnormal}$ and $P_{dominate}$ . These metrics are defined as follows: + +$$ +P _ {a b n o r m a l} = \frac {1}{N C} \sum_ {i = 1} ^ {N} \sum_ {c = 1} ^ {C} \mathbb {1} \left(f \left(\boldsymbol {x} _ {\boldsymbol {i}} + \boldsymbol {\delta} _ {\boldsymbol {c}}\right) _ {c} > f \left(\boldsymbol {x} _ {\boldsymbol {i}}\right) _ {c}\right), \tag {4} +$$ + +$$ +P _ {\text {d o m i n a t e}} = \frac {1}{N C} \sum_ {i = 1} ^ {N} \sum_ {c = 1} ^ {C} \mathbb {1} \left(\operatorname {a r g m a x} f \left(\boldsymbol {x} _ {i} + \boldsymbol {\delta} _ {c}\right) = c\right). \tag {5} +$$ + +$P_{abnormal}$ is designed to measure the frequency with which the application of perturbation $\delta_c$ to an input $\pmb{x}_i$ increases the model's confidence in class $c$ . $P_{dominate}$ evaluates the proportion of instances where the perturbation $\delta_c$ not only increases the model's confidence in class $c$ but also makes class $c$ the most probable class. Together, these metrics quantify the effectiveness of transferring label information across samples, with higher values indicating stronger transferability of the adversarial features associated with specific classes after CO. + +
Input xPabnormal (%)Pdominate (%)
Uniform Gray (0)42.2 ± 32.5520.29 ± 28.62
Uniform Gray (0.5)81.81 ± 20.0044.47 ± 27.44
Training Mean81.36 ± 20.4745.45 ± 28.42
Uniform Noise50.70 ± 2.3511.08 ± 1.72
Test Sample 073.08 ± 18.9526.06 ± 15.03
+ +Table 1. Transferability of label information for different inputs on the CIFAR-10 dataset with a perturbation size of 16/255. + +As evidenced in Table 1, our experiments reveal that single-step perturbations crafted from uniform gray images (value 0.5) and the training data mean exhibit remarkable transferability. This is notable because these inputs are devoid of specific object features. Perturbations from a neutral gray image (0.5) likely capture more generalizable label information, as the model is forced to rely on more fundamental features rather than image-specific details. Similarly, the training data mean, representing a central point in the data distribution, generates perturbations that effectively exploit the model's learned feature space. Consequently, these perturbations are more likely to transfer and mislead the model across diverse inputs compared to those generated from more specific or noisy inputs. + +![](images/8f3887c21ef542a6859aa6ddb6d2f00ec9f98d7427a95bab7053cddb7bcb8373.jpg) +Figure 2. Transferability of label information for uniform gray image (value 0.5) on the CIFAR10 dataset with a perturbation size of 16/255 and 8/255. The shaded regions represent the standard deviation across five experiments. + +![](images/c08e378d51119037d345a6e08b31c617490ae91f25684e1aca3600462c1cdb9e.jpg) + +Additionally, we analyzed the progression of $P_{abnormal}$ and $P_{dominate}$ , along with PGD accuracy for uniformly gray images (values set to 0.5). As shown in Figure 2, for $\epsilon = 16 / 255$ , the PGD accuracy declines, signaling CO, is closely linked to a concurrent rise in $P_{abnormal}$ and $P_{dominate}$ . This temporal relationship strongly indicates that transferable label information emerges alongside CO and is embedded within single-step adversarial perturbations. For $\epsilon = 8 / 255$ , while $P_{abnormal}$ increases, $P_{dominate}$ remains low, likely due to the perturbation's limited strength in dominating the output. These observations reveal that transferable label information is a byproduct of CO, residing in single-step perturbations. Therefore, developing methods to prevent or remove this label information from single-step perturbations is essential for FAT methods. + +Due to page limitations, we provide detailed experimental settings, results for perturbation size 8/255 in Table 1, and results across five seeds in Figure 2 in Appendix A. + +# 3.2. Revisiting Adversarial Initialization: A Novel Understanding + +Building upon the observation that transferable label information, a byproduct of CO, resides within single-step adversarial perturbations, this section explores adversarial initialization strategies in FAT. We propose a novel understanding: their effectiveness stems not merely from enhanced adversarial example quality, but from their unintentional removal of label information. + +Adversarial initialization strategies play a pivotal role in FAT, significantly mitigating the risk of CO. These strategies aim to begin the adversarial example generation process with inputs that are already adversarial in nature. + +FGSM-PGI [13] employs a momentum mechanism, accumulating historical gradients to guide perturbation generation. Specifically, in epoch $t + 1$ , the perturbation $\delta_{x}^{t + 1}$ for + +sample $x$ is updated based on momentum $m_{x}^{t + 1}$ : + +$$ +\boldsymbol {m} _ {\boldsymbol {x}} ^ {t + 1} = \mu \cdot \boldsymbol {m} _ {\boldsymbol {x}} ^ {t} + \operatorname {s i g n} \left(\nabla_ {\boldsymbol {x}} \mathcal {L} \left(f \left(\boldsymbol {x} + \delta_ {\boldsymbol {x}} ^ {t}; \boldsymbol {\theta}\right), y\right)\right), \tag {6} +$$ + +$$ +\delta_ {x} ^ {t + 1} = \Pi_ {S} \left(\delta_ {x} ^ {t} + \alpha \cdot \operatorname {s i g n} \left(m _ {x} ^ {t + 1}\right)\right). \tag {7} +$$ + +Here, $\delta_x^t$ from the previous epoch serves as adversarial initialization, incorporating historical gradient information via momentum $m_{x}$ + +Similarly, class-based FGSM-UAP [20] initializes each class $y$ with a unique Universal Adversarial Perturbation (UAP) $\delta_y$ . The update rule for $\delta_y$ is: + +$$ +\boldsymbol {m} _ {\boldsymbol {y}} = \mu \cdot \boldsymbol {m} _ {\boldsymbol {y}} + \operatorname {s i g n} \left(\nabla_ {\boldsymbol {x}} \mathcal {L} \left(f \left(\boldsymbol {x} + \delta_ {\boldsymbol {y}}; \boldsymbol {\theta}\right), y\right)\right), \tag {8} +$$ + +$$ +\delta_ {\boldsymbol {y}} = \Pi_ {S} \left(\delta_ {\boldsymbol {y}} + \alpha \cdot \operatorname {s i g n} \left(\boldsymbol {m} _ {\boldsymbol {y}}\right)\right). \tag {9} +$$ + +In this case, $\delta_y$ acts as a class-specific adversarial initialization. + +Both FGSM-PGI and FGSM-UAP employ adversarial initialization derived from single-step attacks targeting the true label $y$ . Consequently, the adversarial initializations $\delta_x^t$ and $\delta_y$ inherently contain label information. + +A conventional understanding might suggest that adversarial initialization's effectiveness stems from generating higher quality single-step adversarial examples [13, 20]. If this were the sole mechanism, removing adversarial initialization should diminish or even negate its benefits, potentially leading to a degradation in adversarial example quality. + +However, our findings, illustrated in Figure 3, challenge this perspective. We observe that both adding and subtracting adversarial initialization prove beneficial. As depicted in the bottom-left panel of Figure 3, subtracting adversarial initialization ensures that regardless of the subsequent FGSM attack direction, the final adversarial example is unlikely to retain label information that contributes to CO. + +![](images/bea1caa4b04616d47914a3f480a99f169e9e99c156df12632efffa1531cd2857.jpg) +Final AE: 0 probability in Label Info State + +![](images/be1cec9d123a64be85910796a7ea3198e99d1d675344b6f9c8e30f7277cc4812.jpg) +Figure 3. Impact of adversarial initialization (added and subtracted) on the label information component of adversarial examples generated by FGSM attacks. +Figure 4. Comparison of robust accuracy between models trained using FGSM-PGI and FGSM-UAP, under plus and minus adversarial initialization scenarios. + +Conversely, as shown in the top-right panel of Figure 3, adding adversarial initialization, while starting from a point containing label information, forces the subsequent FGSM attack to move away from this region. This drastically reduces the probability of the final adversarial example still encoding label information, theoretically to $1 / 2^{n}$ where $n$ is the number of pixels. + +To empirically validate this, we conducted experiments comparing the robust accuracy of models trained with FGSM-PGI [13] and FGSM-UAP [20] under both "plus" and "minus" adversarial initialization conditions. These results, presented in Figure 4 alongside benchmarks against PGD50 [16] and AutoAttack (AA) [2], demonstrate negligible differences in robust accuracy between the "plus" and "minus" initialization scenarios. + +This outcome provides compelling evidence that the effectiveness of adversarial initialization goes beyond simply improving single-step AE quality. Instead, we propose a novel interpretation: adversarial initialization's efficacy is + +significantly attributed to its unintentional removal of label information from single-step adversarial perturbations, offering a fresh perspective on its role in mitigating CO. + +# 3.3. LIE: Label Information Elimination Training + +To effectively counteract CO in FAT, leveraging the transferability of label information presents a novel pathway. This approach is predicated on the observation that single-step perturbations generated from a gray image with all values set to 0.5 contain substantial label information, which can be transferred across different samples. By strategically manipulating these perturbations during the training process, it is possible to preemptively eliminate the embedded label information, thereby mitigating the risk of CO. + +The process begins with the generation of class-specific, single-step adversarial perturbations, $LI_{c}$ , from a gray image, $x_{gray}$ , which inherently carry transferable label information. These perturbations are formulated as follows: + +$$ +\boldsymbol {L} \boldsymbol {I} _ {c} = \epsilon \cdot \operatorname {s i g n} \left(\nabla_ {\boldsymbol {x} _ {\text {g r a y}}} \mathcal {L} \left(f \left(\boldsymbol {x} _ {\text {g r a y}}; \boldsymbol {\theta}\right), c\right)\right), \tag {10} +$$ + +where $\epsilon$ is the perturbation magnitude, $\nabla_{x_{gray}}$ denotes the gradient with respect to $x_{gray}$ , $\mathcal{L}$ is the loss function, $f$ represents the model parameterized by $\theta$ , and $c$ is the class label. + +In the context of FAT, where adversarial examples are generated through single-step attacks, as we demonstrated in the previous section, initializing the training samples, $\mathbf{x}$ , by either subtracting or adding $LI_{c}$ effectively removes the label information of $y$ from the generated perturbation. + +The adversarial perturbation $\delta_{x}$ is then defined as: + +$$ +\boldsymbol {\delta} _ {\boldsymbol {x}} = \epsilon \cdot \operatorname {s i g n} \left(\nabla_ {\boldsymbol {x}} \mathcal {L} \left(f \left(\boldsymbol {x} \pm \boldsymbol {L} \boldsymbol {I} _ {\boldsymbol {y}}; \boldsymbol {\theta}\right), y\right)\right). \tag {11} +$$ + +To enhance the effectiveness of model training with generated adversarial examples and to ensure a smoother loss surface, we adopt a dual approach. Drawing inspiration from the regularization-based FAT method, we incorporate Jensen-Shannon divergence to promote a smoother loss landscape [1, 27]. This approach systematically minimizes the discrepancy between predictions for $x$ and its adversarially perturbed counterpart $x + \delta_x$ , using the Jensen-Shannon divergence [17]. + +The training process is guided by two loss components. The first component, $\text{loss}_1$ , focuses on the standard training objective, ensuring accurate predictions on perturbed inputs: + +$$ +\left. \operatorname {l o s s} _ {1} = \mathcal {L} \left(f \left(\boldsymbol {x} + \boldsymbol {\delta} _ {\boldsymbol {x}}; \boldsymbol {\theta}\right), y\right). \right. \tag {12} +$$ + +The second component, $\text{loss}_2$ , employs the Jensen-Shannon divergence to minimize the discrepancy between the model's predictions on the original and the perturbed inputs, thus encouraging prediction consistency: + +$$ +\left. \operatorname {l o s s} _ {2} = \lambda \cdot \mathcal {L} _ {J S D} (f (\boldsymbol {x}; \boldsymbol {\theta}), f (\boldsymbol {x} + \boldsymbol {\delta} _ {\boldsymbol {x}}; \boldsymbol {\theta})) \right). \tag {13} +$$ + +
Method TypeMethod NamePGD-10 (%) ↑PGD-20 (%) ↑PGD-50 (%) ↑AA (%) ↑Training Cost
Multi-step ATPGD-AT [16]53.76 ± 0.1852.83 ± 0.1152.60 ± 0.1348.68 ± 0.12353.70 min
37.10 ± 0.2528.41 ± 0.0925.80 ± 0.3620.07 ± 0.0559.87 PFLOPs
PGD-AT-WA [24]54.90 ± 0.1554.21 ± 0.1554.08 ± 0.1250.26 ± 0.14358.21 min
41.09 ± 0.0733.22 ± 0.2531.17 ± 0.2125.09 ± 0.2159.87 PFLOPs
Random Initialization-based FATN-FGSM [3]53.78 ± 0.1353.28 ± 0.0753.17 ± 0.0947.97 ± 0.1274.15 min
39.29 ± 0.4533.00 ± 1.0531.65 ± 1.3622.50 ± 1.3310.89 PFLOPs
FGSM-RS [28]48.22 ± 7.6447.77 ± 7.4647.68 ± 7.4642.82 ± 6.7074.36 min
15.11 ± 5.159.33 ± 6.205.42 ± 5.120.00 ± 0.0010.89 PFLOPs
Adversarial Initialization-based FATFGSM-PGI [13]56.36 ± 0.1955.81 ± 0.1355.70 ± 0.1049.73 ± 0.1799.71 min
19.02 ± 0.3412.96 ± 0.388.78 ± 0.280.11 ± 0.0010.89 PFLOPs
FGSM-UAP [20]56.60 ± 0.0356.10 ± 0.0455.89 ± 0.0249.36 ± 0.11108.71 min
15.56 ± 1.359.72 ± 1.116.03 ± 0.910.03 ± 0.0016.33 PFLOPs
Regularization -based FATNuAT [27]55.43 ± 0.0854.79 ± 0.0454.64 ± 0.0550.04 ± 0.13127.81 min
14.93 ± 0.617.29 ± 0.633.51 ± 0.370.13 ± 0.0216.33 PFLOPs
Grad-Align [1]53.52 ± 0.1652.99 ± 0.2052.93 ± 0.2047.99 ± 0.15228.64 min
27.72 ± 12.5323.09 ± 9.2821.82 ± 8.4215.43 ± 3.9416.33 PFLOPs
Other FAT MethodsFGSM-AT [7]38.66 ± 1.9228.91 ± 1.3619.47 ± 1.650.00 ± 0.0074.14 min
15.15 ± 2.4910.13 ± 2.895.98 ± 2.410.00 ± 0.0010.89 PFLOPs
Free-AT [25]52.23 ± 0.1551.60 ± 0.0951.42 ± 0.0847.43 ± 0.1470.53 min
31.91 ± 2.1721.66 ± 1.9812.47 ± 0.500.00 ± 0.0010.89 PFLOPs
COAT [14]53.10 ± 0.2252.38 ± 0.1752.33 ± 0.0937.99 ± 0.3190.03 min
36.27 ± 6.4424.64 ± 6.9418.17 ± 1.524.58 ± 3.2413.61 PFLOPs
GAT [26]55.03 ± 0.0554.23 ± 0.2054.05 ± 0.2149.39 ± 0.22126.75 min
9.48 ± 0.795.98 ± 2.884.44 ± 3.943.14 ± 4.4116.33 PFLOPs
OursLIET56.70 ± 0.0656.14 ± 0.0556.08 ± 0.0750.01 ± 0.09101.29 min
37.17 ± 2.1133.55 ± 1.5933.10 ± 1.4425.22 ± 0.4110.93 PFLOPs
+ +Table 2. Comparison of robust accuracy and training cost (time in minutes and computation in PFLOPs) on CIFAR-10 using ResNet-18. Each method is evaluated with perturbation sizes of 8/255 (first row) and 16/255 (second row). The best results of the FAT method are highlighted in bold. + +The overall objective combines these two terms, with $\lambda$ serving as a balancing parameter between the standard training loss and the loss aimed at ensuring prediction consistency across perturbed and unperturbed inputs. We provide the pseudocode of the LIEF algorithm in Appendix B. + +# 3.4. Non-uniform Label Smoothing + +As discussed in the preceding sections, label information is a crucial factor contributing to CO. To further mitigate CO by reducing this label information, we explore Non-uniform Label Smoothing (NLS) as a practical trick. Building upon the idea of standard label smoothing, NLS aims to more effectively obscure label information. + +Traditional label smoothing enhances adversarial robustness by softening the target distribution [5, 6]. Given a one-hot encoded label vector $\mathbf{y}$ , standard label smoothing produces a smoothed label vector $\hat{\mathbf{y}}$ using the formula: + +$$ +\hat {y} _ {i} = y _ {i} (1 - \alpha) + \frac {\alpha}{K}, \tag {14} +$$ + +where $\hat{y}_i$ is the $i$ -th element of the smoothed label vector + +$\hat{\mathbf{y}}$ $y_{i}$ is the $i$ -th element of the original one-hot label vector $\mathbf{y}$ $\alpha$ is the smoothing parameter, and $K$ is the number of classes. + +Non-uniform Label Smoothing (NLS) is a simple modification to further reduce label information. Instead of uniformly distributing the smoothing probability $\alpha$ across incorrect classes, NLS distributes it non-uniformly. Specifically, for the correct class $y$ , the smoothed probability remains $1 - \alpha$ . For the incorrect classes, we assign random probabilities $r_i$ such that they sum to $\alpha$ . The non-uniform smoothed label vector $\hat{\mathbf{y}}$ is then defined as: + +$$ +\hat {y} _ {i} = \left\{ \begin{array}{l l} 1 - \alpha & \text {i f} i = y \\ r _ {i} & \text {i f} i \neq y \end{array} , \right. \tag {15} +$$ + +where $\sum_{i\neq y}r_i = \alpha$ and $y$ is the index of the correct class in the one-hot label vector $\mathbf{y}$ . + +This trick of non-uniform distribution introduces additional randomness and uncertainty into the label smoothing process, making it harder for adversarial perturbations to + +exploit label information and thus further preventing CO. + +# 4. Experimental Study + +# 4.1. Experimental Setup + +Our research conducted experiments on three widely used datasets to evaluate the robustness against adversarial attacks, namely CIFAR-10, CIFAR-100 [15], and Tiny ImageNet [4]. + +Each experiment was replicated three times under different random seeds to improve the reliability of our results. To evaluate the robustness of our model, we subjected it to several adversarial attack methods, including PGD [16] and AutoAttack (AA) [2]. Due to page limitations, detailed experimental configurations can be found in Appendix C. + +We have fine-tuned the comparison algorithms, incorporating techniques such as weight averaging [12] and label smoothing [6], among others, to ensure a fair comparison. + +# 4.2. Results and Performance Analysis + +In this section, we present the results of our experiments conducted on CIFAR-10, CIFAR-100 [15], and Tiny ImageNet [4] datasets. We compare the performance of our proposed FAT method with existing state-of-the-art FAT methods under various attack scenarios. The complete experimental results across the three datasets, as well as results on other architectures [29], are provided in Appendix D. + +The average results and standard deviations of three runs are shown in Table 2 and Table 3, respectively. Compared to other FAT methods, our approach demonstrates superior robust accuracy under both PGD [16] and Auto Attack [2] scenarios, even reaching levels close to the multi-step adversarial training method PGD-AT [16] and PGD-AT-WA [12]. This indicates the effectiveness of our method in enhancing the robustness of neural networks. + +Our model's training time is approximately 1.25 times faster than the best previous FAT methods, including GAT [26] and NuAT [27], and 2.3 times faster than Grad-Align [1]. Furthermore, our training time is comparable to FGSM-PGI [13], yet our performance surpasses it. Notably, FGSM-PGI requires additional memory equivalent to the size of all training data, whereas our method only needs extra memory proportional to the number of classes. + +# 4.3. Loss Landscape Analysis + +Figure 5 illustrates the loss landscape of different FAT methods, including FGSM-AT [7], FGSM-RS [28], PGD-AT-WA [12, 16], and our proposed method. + +We utilized the first 500 samples from the CIFAR-10 test dataset to plot their cross-entropy loss, as it varies in two dimensions: randomly and along the gradient direction of PGD50. It was observed that for FGSM-AT and FGSM-RS, their loss surfaces are not smooth and exhibit significant + +![](images/8fd05a2560d031b170a0d0e6275e21cafbc93f7f09d06e077421da67f8158bfa.jpg) +(a) FGSM-AT + +![](images/f7c927e509b1cc148be33983c1acac626553d085f996c86637fe448226769e33.jpg) +(b) FGSM-RS + +![](images/c02c3592ddfb72e25a5a967d833611304c1c2380589824e94b1f589f58b58028.jpg) +(c) PGD-AT-WA + +![](images/acfd6482fb72130acd934d72983995a770a621410c20778b128ac5da8c5185a9.jpg) +(d) LIET (Ours) +Figure 5. Loss landscape comparison of FGSM-AT, FGSM-RS, PGD-AT, and our LIET method by using 500 CIFAR10 test samples, showcasing variations in cross-entropy loss across a random and the PGD50 gradient direction. + +variations along the gradient direction, making them still susceptible to attacks. In contrast, PGD-AT-WA and our LIET method demonstrate more linear loss landscapes with minimal variations in loss, indicating that our approach better preserves the local linearity of the target model, thereby enhancing its robustness. + +# 4.4. Ablation Experiment + +We conducted ablation experiments to validate the effectiveness of our proposed method. As observed from Table 4, initializing with perturbations that contain label information significantly outperforms the initialization using uniform [28] or Bernoulli [27] distributions. Moreover, applying non-uniform label smoothing further enhances the robust accuracy under AutoAttack. + +# 5. Conclusion + +In conclusion, our study contributes to the understanding and advancement of fast adversarial training by uncovering the transferability of label information. We not only reveal why adversarial initialization strategies are effective but also introduce a novel FAT methodology, LIET, which proactively eliminates label information from single-step adversarial perturbations to mitigate the risk of CO. Our experimental validations across multiple datasets underscore the effectiveness and competitiveness of our approach. + +
Method NameCIFAR100Tiny-ImageNet
PGD-50 (%)↑AA (%)↑Training CostPGD-50 (%)↑AA (%)↑Training Cost
PGD-AT [16]28.87 ± 0.2725.48 ± 0.11353.65 min19.86 ± 1.2316.00 ± 1.022432.63 min
11.56 ± 0.169.17 ± 0.1259.88 PFLOPs13.15 ± 0.009.54 ± 0.19479.01 PFLOPs
PGD-AT-WA [12]32.22 ± 0.2526.84 ± 0.28358.80 min26.06 ± 0.3419.62 ± 0.242439.34 min
17.45 ± 0.2712.66 ± 0.1559.88 PFLOPs18.43 ± 0.1412.31 ± 0.02479.01 PFLOPs
N-FGSM [3]30.41 ± 0.2925.31 ± 0.2874.62 min25.10 ± 0.2318.76 ± 0.24498.95 min
15.95 ± 0.1811.18 ± 0.2110.89 PFLOPs16.64 ± 0.1411.11 ± 0.1887.09 PFLOPs
FGSM-RS [28]20.84 ± 9.5516.70 ± 7.8474.62 min22.70 ± 1.2716.28 ± 1.03493.77 min
1.61 ± 0.321.05 ± 0.2110.89 PFLOPs2.25 ± 0.011.33 ± 0.0187.09 PFLOPs
FGSM-PGI [13]32.31 ± 0.1126.76 ± 0.0799.85 min26.39 ± 0.1719.52 ± 0.07652.09 min
1.50 ± 1.330.57 ± 0.7010.89 PFLOPs4.02 ± 0.141.33 ± 0.2787.09 PFLOPs
FGSM-UAP [20]31.81 ± 0.0526.29 ± 0.03114.03 min25.84 ± 0.0419.45 ± 0.14717.30 min
1.35 ± 0.470.55 ± 0.6716.33 PFLOPs1.89 ± 0.400.71 ± 0.59130.64 PFLOPs
NuAT [27]21.62 ± 0.5813.77 ± 0.58131.49 min26.37 ± 0.1419.55 ± 0.12865.64 min
4.07 ± 0.111.94 ± 0.1216.33 PFLOPs10.59 ± 4.585.47 ± 3.37130.64 PFLOPs
Grad-Align [1]31.54 ± 0.2326.18 ± 0.07229.34 min24.21 ± 0.4117.65 ± 0.281514.23 min
9.50 ± 5.476.43 ± 3.9316.33 PFLOPs14.22 ± 0.728.71 ± 0.59130.64 PFLOPs
FGSM-AT [7]1.88 ± 0.320.19 ± 0.0374.17 min16.84 ± 8.5516.60 ± 0.36492.96 min
0.82 ± 0.170.51 ± 0.4910.89 PFLOPs1.58 ± 0.210.84 ± 0.2987.09 PFLOPs
Free-AT [25]29.96 ± 0.2024.34 ± 0.4271.97 min23.58 ± 0.2616.34 ± 0.32474.87 min
9.79 ± 2.215.84 ± 1.5610.89 PFLOPs13.99 ± 0.738.42 ± 0.5887.09 PFLOPs
COAT [14]22.70 ± 0.3318.93 ± 0.0788.85 min17.25 ± 0.2211.56 ± 0.02578.07 min
4.45 ± 0.612.75 ± 0.3813.61 PFLOPs7.38 ± 0.863.71 ± 0.60108.87 PFLOPs
GAT [26]26.54 ± 0.1621.97 ± 0.15126.85 min17.01 ± 0.2811.53 ± 0.15851.30 min
0.57 ± 0.060.06 ± 0.0316.33 PFLOPs0.60 ± 0.020.20 ± 0.01130.64 PFLOPs
LIET (Ours)32.74 ± 0.1427.05 ± 0.09103.74 min26.54 ± 0.1119.79 ± 0.04682.47 min
17.22 ± 0.4212.04 ± 0.3011.11 PFLOPs17.31 ± 0.1911.29 ± 0.1590.56 PFLOPs
+ +Table 3. Comparisons of robust accuracy, training time (minutes), and computation (PFLOPs) on CIFAR-100 (using ResNet-18) and TinyImageNet (using PreResNet-18). For each method, the first row shows results with perturbation $\epsilon = 8 / 255$ , while the second row uses $\epsilon = 16 / 255$ for CIFAR-100 and $\epsilon = 12 / 255$ for Tiny-ImageNet. The best results of the FAT method are highlighted in bold. + +
MethodConfiguration
Config 1Config 2Config 3Config 4
Initialization Methods:
Uniform✓
Bernoulli✓
Label Information (Ours)✓✓
Label Smoothing Methods:
Uniform Label Smoothing✓
Non-uniform Label Smoothing (Ours)✓✓✓
Performance Metrics:
Robust Accuracy (%) at ε = 8/2555.6048.2949.6450.01
Robust Accuracy (%) at ε = 16/25521.5220.3124.5925.22
+ +Table 4. Comparison of robust accuracy under AutoAttack for different initialization methods and the impact of applying non-uniform label smoothing at various perturbation budgets (ε). Best results are highlighted in bold. + +# 6. Acknowledgments + +We thank the anonymous reviewers for their insightful comments. This work was supported by the National Natural Science Foundation of China under Grant 62250710682, Guangdong Provincial Key Laboratory under Grant 2020B121201001, and the Program for Guangdong Introducing Innovative and Entrepreneurial Teams under Grant 2017ZT07X386. This project has been supported by the Hong Kong Research Grants Council under General Research Fund (project no. 15200023) as well as Research Impact Fund (project no. R1015-23). + +# References + +[1] Maksym Andriushchenko and Nicolas Flammarion. Understanding and improving fast adversarial training. 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However, it incurs significant computational overhead, severely impacting the model's inference efficiency. Random sampling or grid sampling is considered faster downsampling methods; however, these fast downsampling methods may lead to the loss of geometric information during the downsampling process due to their overly simplistic and fixed rules, which can negatively affect model performance. To address this issue, we propose FastAdapter, which aggregates local contextual information through a small number of anchor points and facilitates interactions across spatial and layer dimensions, ultimately feeding this information back into the downsampled point cloud to mitigate the information degradation caused by fast downsampling methods. In addition to using FastAdapter to enhance model performance in methods that already employ fast downsampling, we aim to explore a more challenging yet valuable application scenario. Specifically, we focus on pre-trained models that utilize FPS, embedding FastAdapter and replacing FPS with random sampling for lightweight fine-tuning. This approach aims to significantly improve inference speed while maintaining relatively unchanged performance. Experimental results on ScanNet, S3DIS, and SemanticKITTI demonstrate that our method effectively mitigates the geometric information degradation issues caused by fast downSampling. + +# 1. Introduction + +With the advancement of deep learning models and sensor technology, there is a growing interest among researchers in using neural networks to recognize point cloud data [7, 8, 25, 26, 31, 32]. One important issue is that some practical 3D applications, such as autonomous driving and augmented reality, demand high inference speeds from neural networks. However, due to the unordered and irregular na + +![](images/f7286ffd3af62cd43451482b845225c7698fb077e9205921760b130163640740.jpg) +Figure 1. Model Comparison by Size, mIoU and Throughput(inference). We visualized the size, mIoU, and throughput of different models on ScanNet. First, for most point-based models that use FPS, it is evident that FPS generally results in slower inference speeds. However, while replacing FPS with random sampling significantly improves inference speed, it leads to severe performance degradation. By embedding our FastAdapter (FA+XXXX), we can effectively mitigate this performance degradation issue. Secondly, incorporating FastAdapter into models that already utilize the fast downSample (like RandLA with random-sample and PTV3 with gridsample) method results in a significant performance improvement. + +ture of point cloud data, point-based models typically use custom sampling and grouping operators instead of traditional convolutional neural networks to extract local features, which often incurs significant computational overhead. + +The downsampling method is a part of the computational resource overhead. Farthest point sampling (FPS) is the most commonly used downsampling method, which involves selecting the point in the point cloud that is farthest from the already selected points as the new sampling point. This ensures a relatively regular density distribution and preserves the integrity of local structures during the down-sampling process. However, the need to compute the distance matrix between points incurs significant computational overhead $(O(N^{2}))$ , which results in slow in + +ference speed, which affects its application on large-scale point clouds. + +In contrast, random sampling is highly efficient, with constant time complexity, making it suitable for large-scale point cloud scenarios. Similarly, GridSample was proposed in PTV2 [40] as a replacement for FPS. It adopts a voxel-based downsampling approach, which also brings about a significant increase in inference speed. For convenience, we collectively refer to these simple and efficient downsampling methods as fast downSampling. However, due to their straightforward and fixed rules, these fast down-Sampling methods are likely to lose geometric information during the downsampling process in complex point cloud scenarios, compromising the integrity of the geometric structure (We will provide detailed explanations in the supplementary materials). This issue of information degradation limits the application of fast downSampling, particularly the simplest and most efficient random sampling approach. An example, as shown in Fig. 1, illustrates that both classic models like PointNet++ and state-of-the-art models such as PointMetaBase-L/XL experience significant performance degradation when FPS is replaced with random sampling.. Some methods have attempted to address the issues arising from random sampling. RandLA [11] introduces a multi-layer local aggregation module to expand the receptive field and supplement more local information. APPNet [20] uses anchor points to aggregate local information and propagates features to the input point cloud. However, it lacks refinement of the features from the anchor points, which can lead to errors in the simply aggregated local features. More importantly, previous methods require the design of unique network architectures to address the issues brought about by random sampling, making them not universally applicable to other models. + +Therefore, in this paper, we propose FastAdapter, a universal adapter mechanism designed to mitigate the information degradation issues associated with fast downsampling methods. Specifically, FastAdapter consists of the P2A (Point2Anchor) Aggregator and the A2P (Anchor2Point) Adapter. For P2A Aggregation, we first establish fixed anchor points in the scene. Each point in the point cloud is then assigned to the nearest anchor point, and its features are injected into the anchor point to aggregate local contextual information. To refine the features aggregated at the anchor points, we facilitate information exchange between the anchor points across both spatial dimensions and different layers. Then, in the A2P Adapter, the features of the anchor points are adaptively sent back to the downsampled point cloud based on geometric relationships. This process helps to supplement the lost local features and mitigates the information degradation problem. + +We want to emphasize that our method is independent of the model and sampling method, allowing it to be uni- + +versally embedded into existing approaches. An intuitive idea for utilizing FastAdapter is to embed it into models designed for fast downSampling (like RandLA with randomsample or PTV3 [41] with GridSample). By doing so, FastAdapter can further alleviate the issues of geometric information degradation, effectively enhancing the overall performance of the model. However, a more practical challenge is that most currently trained point-based models are designed for FPS, such as the widely used PointNet++. Therefore, we propose to fix the weights of these models and embed FastAdapter, simultaneously replacing FPS with random sampling for fine-tuning. This approach aims to preserve the original knowledge learned by the model while effectively mitigating the geometric information degradation issues brought about by random sampling and improve inference speed several times. Some examples are shown in Fig. 1. We primarily focus on the point cloud segmentation task and conducted experiments on ScanNet, S3DIS, and SemanticKITTI. We simultaneously tested various point-based models, including those utilizing Fast DownSampling (RandLA with randomsaple and PTV3 with gridsample) and those designed with FPS (PointNet++ with FPS and PointMetaBase-L/XL with FPS). In summary, FastAdapter is a universal method that can effectively address the issue of key information loss associated with fast downSampling. We hope that this work will encourage researchers to focus on random sampling or other fast downsampling methods in order to achieve faster point cloud analysis. + +Our contributions can be summarized as follows: + +1. We propose FastAdapter, an adapter mechanism designed to mitigate the information degradation problem associated with Fast DownSampling methods, which can be universally embedded into existing point-based models. +2. We propose the P2A Aggregator and A2P Adapter. The former gradually injects the features of the input point cloud into the anchor points to aggregate local information, while the latter propagates the local information from the anchor points back to the input point cloud to supplement the local structural features lost due to fast downsampling methods. +3. FastAdapter is tested on multiple segmentation datasets and models, and the results verify its effectiveness. + +# 2. Related Work + +Voxel-based Methods. Due to the irregularity of points, CNN is difficult to be directly applied to point cloud data. Therefore, some works [6, 8, 21, 22, 42, 43, 46] voxelize point clouds into regular grids, and then mature 2D networks can be used to identify point clouds. However, due to the voxelization of point clouds, many empty voxels are present in the scene. Traditional 3DCNN processes these empty voxels, leading to unnecessary computational over + +head. Therefore, to accelerate voxel-based models, sparse convolution [4, 9, 24] is introduced, which is applied only to non-empty voxels, significantly improving the inference speed. + +Point-based Methods. Point-based models operate directly on the point cloud data, which prevents missing information caused by operations such as voxelization or projection. PointNet [25] first proposes to use symmetric aggregation function to solve the disorder problem of point cloud, and then PointNet++ [26] replaces CNN to capture local features on irregular point cloud by custom downsampling and grouping operator. Many subsequent works [11, 16, 20, 30, 31, 34, 35, 40, 41, 44] design more complex local feature extraction modules based on PointNet++. However, with the development of models, more and more people pay attention to how to identify point clouds more efficiently. PTV2 [40] designs grouped vector attention, which greatly reduces the computational overhead of the attention mechanism through the grouping strategy. APPNet [20] designs the push-pull operator, which assigns each point to only one neighborhood, reducing the overhead of repeated feature extraction. RandLANet [11] uses random sampling and a specialized architecture. + +Transfer Learning. Transfer learning refers to the process of adapting a model to a new data distribution. Full fine-tuning updates all parameters of the model without the need for carefully designed tuning methods. While this approach is simpler, it carries the risk of losing the knowledge that was acquired during the initial training. Prompt Tuning [12, 19, 36, 37, 45] guides the fine-tuning of a model by augmenting the input with additional prompt information. In contrast, Adapter Tuning [3, 10, 13-15, 45, 47] adjusts the model's output features by inserting lightweight Adapter modules into the model, making them more aligned with the target distribution. + +# 3. Proposed Method + +In this section, we first outline FastAdapter's task in 3.1, which is how to achieve faster point cloud segmentation by using FastAdapter and fast downSampling. Then, we introduce the P2A Aggregator and A2P Adapter in 3.2 and 3.3, respectively. Finally, we present the overall training loss in 3.4. The overall framework of FastAdapter can be seen in Figure 2. + +# 3.1. Preliminary + +1) Background: Existing point-based models generally follow the steps below when extracting local features from points: + +$$ +p ^ {c}, f ^ {c} = \phi_ {d} (p, f) \tag {1} +$$ + +$$ +p _ {\mathcal {N}}, f _ {\mathcal {N}} = \phi_ {t} \left(\phi_ {g} \left(p ^ {c}, f ^ {c}, p, f\right)\right) \tag {2} +$$ + +$$ +\hat {p}, \hat {f} = \phi_ {r} \left(p _ {\mathcal {N}}, f _ {\mathcal {N}}\right) \tag {3} +$$ + +where $p \in R^{n \times 3}$ and $f \in R^{n \times C}$ represents the coordinates and features of $n$ points. Then, $\phi_d$ means the downsampling methods, which then selects $m$ center points $\{(p^c \in R^{m \times 3}, f^c \in R^{m \times C})\}$ from $p$ and $f$ . After that, the point-based model uses $\phi_g$ to construct local neighborhoods for each center point and extracts the features of each neighboring point using $\phi_t$ . Finally, it aggregates the local features into the center points using $\phi_r$ . + +2) Problem Statement: FPS is widely used in most point-based models; however, its computational overhead is significant, impacting the model's inference efficiency. In contrast, methods like random sampling and gridsample, which have simple and fixed rules, offer higher efficiency. We refer to these sampling methods as fast downSampling. + +Above all, existing point-based models can be classified into two categories: one is $\phi_d = FPS$ , and the other is $\phi_d \in \{\text{RandomSample}, \text{GridSample}\}$ . Therefore, FastAdapter has two main tasks: (1) For pretrained-models that $\phi_d = FPS$ , since they are not designed with architectures for fast downSampling, directly replacing FPS with fast downSampling methods, such as random sampling, can lead to severe performance degradation. Our goal is to embed FastAdapter and fine-tune the pre-trained model so that it can adapt to random sampling, significantly improving inference speed while maintaining performance relatively unchanged. The reason for choosing random sampling is that it presents greater challenges and can better demonstrate the effectiveness of our method. (2) For models that have already utilized fast downSampling ( $\phi_d \in \{\text{RandomSample}, \text{GridSample}\}$ ), their architectural design can somewhat mitigate the information loss caused by fast downSampling. Therefore, we aim to embed FastAdapter and train from scratch to demonstrate that FastAdapter can complement such models effectively. + +It is important to emphasize that for the first task, we do not train from scratch but instead fine-tune the pre-trained models. This is because these models are designed for FPS, and training with FPS yields better results. By simply using FastAdapter and random sampling for lightweight fine-tuning, we can inherit competitive performance. And the second task can be regarded as a special case of the first task, where we fine-tune the weights of all the models. To this end, we will subsequently introduce the method based on the settings of the first task, including the process shown in Fig. 2. Therefore, we define the original model that uses FPS as $M_{FPS}$ , and the model that incorporates FastAdapter and undergoes fine-tuning with random sampling as $M_{FA}$ . + +# 3.2. P2A Aggregator + +The purpose of P2A Aggregator is to gradually aggregate local features into anchor points and obtain well-represented local structures through feature refinement so that the A2P Adapter can supplement the structural features + +![](images/d3d5d45bdaedf823df9108a011f9590d96a638dcf803e555b2d15370db580c20.jpg) +Figure 2. Illustration of FastAdapter. FastAdapter can fine-tune any trained point-based model using FPS to adapt it to random sampling. To achieve this, we freeze all parts of the model except for the classification head, and we insert the P2A Aggregator for aggregating local features and the A2P Adapter for supplementing local information. + +lost in the random sampling of the input points. Specifically, P2A first introduces a geometry-aware aggregation to extract the local feature. Then, to further refine the local structural features, we designed the Cross-Layer Aggregator and the Spatial Aggregator. The former primarily fuses the features of anchor points across different layers, effectively combining high-level and low-level semantic information, while the latter employs an attention mechanism to merge spatial information between different anchor points, thereby expanding the receptive field. + +Geometry-aware Aggregator. We first select $L$ anchor points $q \in R^{L \times 3}$ in the initial scene using FPS, where $L$ is much smaller than the number of input points. Anchor points are fixed throughout the entire forward process of the model. In simple terms, the positions of the anchor points inputted into each layer of FastAdapter remain the same, which facilitates the subsequent cross-layer interaction of information between the anchor points. In our implementation, $L = 100$ . At the same time, for the $l$ -th layer of the model $M_{FA}$ , its output $(\hat{p}^l, \hat{f}^l)$ are obtained from Eq. 3. For convenience, we define the output as $(p^l, f^l)$ to serve as the input for FastAdapter. + +Next, we inject the point cloud features into the anchor points. To achieve this, we first define the corresponding anchor point index of the $i$ -th point as $j = \arg \min_{j} \| p_i^l - q_j \|$ , + +which means that we have $p_i^l \in \mathcal{N}_{q_j}$ . Then, we calculate the weights for aggregating local features based on the geometric distance from each point to the anchor point. + +$$ +z _ {i} = M L P \left(p _ {i} - q _ {j}\right) \tag {4} +$$ + +$$ +z _ {j} ^ {q} = \frac {1}{\operatorname {L e n} \left(\mathcal {N} _ {q _ {j}}\right)} \sum_ {i \in \mathcal {N} _ {q _ {j}}} z _ {i} \tag {5} +$$ + +where $z_{i}$ represents the geometric relationship between $i - th$ point and its corresponding anchor point, while $z_{j}^{q}$ represents the local geometric structure information of the $j - th$ anchor point. Then, we calculate the weights for each point. + +$$ +w _ {i} = M L P \left(\left[ z _ {i}, z _ {j} ^ {q} \right]\right) \tag {6} +$$ + +Finally, we inject the point features into the corresponding anchor points based on the calculated weights. + +$$ +A _ {l j} = \frac {1}{L e n \left(\mathcal {N} _ {q _ {j}}\right)} \sum_ {i \in \mathcal {N} _ {q _ {j}}} w _ {i} f _ {i} ^ {l} \tag {7} +$$ + +where $A_{lj}$ means the feature of $j - th$ anchor points in $l - th$ layer. + +Cross-Layer Aggregator. In this part, we fuse the anchor points' features of the current layer with those of the previous layer and introduce a residual connection. We believe that this approach effectively combines the low-level and high-level semantic features of anchor points, which can enhance the semantic feature representation capability of the anchor points. More importantly, the anchor features from the previous layer can effectively prevent certain local features from being completely discarded during the down-sampling process of the current layer.. + +$$ +A _ {l j} ^ {(1)} = M L P \left(\left[ A _ {l j}, A _ {(l - 1) j} \right]\right) + A _ {l j} \tag {8} +$$ + +It is important to note that in the first layer, the Cross-Layer Aggregator will not be applied since there are no features from a previous layer. + +Spatial Aggregator. However, since each point only injects features into the corresponding anchor point, this limits the ability of anchor points to fuse richer features and restricts their receptive field. To address this, we propose the + +Table 1. Segmentation results on S3DIS [1] 6-fold, Area-5 and ScanNet [5]. We test our RandPoint on different point-based models and report the mIoU, mAcc, OA, the Throughput (TP) and the GFLOPs (G). Then, FPS means Farthest Point Sample, RS means Random Sample and GS means GridSample. + +
MethodsSamplingS3DIS 6-foldS3DIS Area5ScanNet mIoUTP(ins./sec.)GFLOPs
mIoUOAmIoUOA
KPConv [34]70.6-67.1-69.2--
PointTransformer [44]73.590.270.490.870.6-5.6
RepSurf [31]74.390.868.990.270.0-1.04
ASSANet [27]FPS--65.888.9--2.5
PointVector-L [7]77.491.471.290.8--10.7
Pix4Point [29]69.689.9-----
PointNeXt-L [28]73.989.869.590.169.4-15.2
PointNet++ [26]FPS54.581.053.583.053.57.730.6
RS51.6↓2.979.7↓1.350.8↓2.781.3↓1.751.1↓2.42330.6
+FastAdapterRS54.0↓0.580.6↓0.453.1↓0.482.7↓0.352.9↓0.620↑259%31.8
PointMetaBase-L [18]FPS75.690.669.890.671.07.38.48
RS73.8↓1.889.6↓1.068.2↓1.689.9↓0.767.6↓3.4278.48
+FastAdapterRS75.2↓0.490.3↓0.369.2↓0.690.1↓0.570.4↓0.623↑315%9.55
PointMetaBase-XL [18]FPS76.391.071.591.071.86.539.28
RS74.6↓1.790.2↓0.869.4↓2.189.8↓1.268.9↓2.91939.28
+FastAdapterRS75.8↓0.590.7↓0.371.2↓0.390.9↓0.171.3↓0.515↑230%41.80
RandLA [11]RS70.287.068.587.469.02332.0
+FastAdapterRS71.0↑0.888.1↑1.169.2↑0.788.0↑0.670.0↑1.02133.1
PTV3 [41]GS77.7-73.4-77.525150
+FastAdapterGS78.2↑0.5-73.8↑0.4-78.0↑0.523155
+ +Spatial Aggregator, which aims to use attention to merge features from different anchor points to expand the receptive field. Additionally, we introduce residual connections to stabilize the training process. + +$$ +A _ {l j} ^ {(2)} = A _ {l j} ^ {(1)} + \text {A t t e n t i o n} \left(A _ {l j} ^ {(1)}, A _ {l j} ^ {(1)}\right) \tag {9} +$$ + +where Attention represents self-attention, which fuses features between different anchor points. Then $A_{lj}^{(2)}$ will be used for the A2P Adapter and as input for the $l + 1$ layer's Cross-Layer Aggregator. + +# 3.3. A2P Adapter + +A2P aims to propagate the aggregated local structural features from the anchor points back to the downsampled point cloud in order to supplement the local information lost during random sampling. + +Offset Embedding. However, directly backpropagating the same anchor features to different points is suboptimal, as features at different positions should exhibit differences. To address this, we designed Offset Embedding, which predicts the feature offsets based on the positional offsets between the anchors and the points. + +$$ +O _ {l j} ^ {i} = M L P \left(p _ {i} - q _ {j}\right) \tag {10} +$$ + +Then, the features propagated from the superpoint to the $i$ -th point are given by: + +$$ +A _ {l j} ^ {i} = A _ {l j} ^ {(2)} + O _ {l j} ^ {i} \tag {11} +$$ + +Geometric Weight. However, the randomness of random sampling may result in varying degrees of local information loss across different regions. We believe that anchor point features should primarily supplement information in regions with significant loss rather than in areas with minimal loss. This approach can help preserve the knowledge initialized by $M_{FPS}$ as much as possible, leading to superior performance. Therefore, we utilize $z_{i}$ and $z_{j}^{q}$ obtained from Eq. 4 and Eq. 5 to calculate the intensity of the superpoint feature propagation to the $i - th$ point. It is important to note that this is different from the meaning of Eq. 6; therefore, we need a new MLP for learning. + +$$ +S _ {i} ^ {l} = M L P \left(\left[ z _ {i}, z _ {j} ^ {q} \right]\right) \tag {12} +$$ + +Finally, we supplement the corresponding points with anchor point features based on the calculated weights. + +$$ +\hat {f} _ {i} ^ {l} = f _ {i} ^ {l} + S _ {i} ^ {l} A _ {l j} ^ {i} \tag {13} +$$ + +Then $\hat{f}_i^l$ will be used as the input of the $l + 1$ layer. + +Table 2. Segmentation results on SemanticKITTI [2]. We report the mIoU and inference speed throughput (TP). + +
MethodsSamplingSizemIoUTP (ins./sec.)
PointNet [25]FPS50K pts14.6-
PointNet++ [26]20.1-
TangentConv [33]40.9-
SqueezeSeg [38]-64*2048 pixels29.5-
SqueezeSegV2 [39]-39.7-
RangeNet++ [23]-52.2-
RandLA [11]RS50K pts52.932
+FastAdapter53.828
PointMetaBase-LFPS50K pts71.87.0
RS69.218
+FastAdapterRS71.316.7
+ +# 3.4. Overall Loss + +For the input $(X,Y) = \{(x_{1},y_{1}),(x_{2},y_{2}),\dots,(x_{n},y_{n})\}$ , where $x_{i}$ and $y_{i}$ means the $i - th$ point and corresponding label, $M_{FA}$ output the point-wise feature $\bar{f}_{FA}$ and the class predictions $P_{FA}$ . + +$$ +f _ {F A} ^ {-}, P _ {F A} = M _ {F A} (X) \tag {14} +$$ + +Then, the segmentation loss is defined as: + +$$ +L _ {s e g} = \text {C r o s s E n t r o p y} \left(P _ {F A}, Y\right) \tag {15} +$$ + +Furthermore, to improve the performance of $M_{FA}$ , we additionally introduce feature distillation. + +$$ +f _ {F P S, -} = M _ {F P S} (X) \tag {16} +$$ + +$$ +L _ {\text {d i s t i l l}} = 1 - \operatorname {C o s} \left(f _ {F A} ^ {-}, f _ {F P S} ^ {-}\right) \tag {17} +$$ + +where $Cos$ computes the cosine similarity between the inputs. + +Finally, the overall loss can be defined as: + +$$ +L _ {\text {o v e r a l l}} = L _ {\text {s e g}} + \lambda L _ {\text {d i s t i l l}} \tag {18} +$$ + +It is worth noting that when FastAdapter is embedded into models that already utilize Fast Downsampling methods, we do not use distillation loss; instead, we retain only the segmentation loss. + +# 4. Experiments + +# 4.1. Experimental Setups + +We primarily conducted experiments on the indoor datasets S3DIS [1] and ScanNet [5], as well as the large-scale outdoor dataset SemanticKITTI [2], and integrated multiple point-based models to demonstrate the effectiveness of RandPo. + +S3DIS. S3DIS is a 3D point cloud dataset for indoor scene understanding. The S3DIS dataset contains large-scale RGB-D data collected from six indoor areas at Stanford + +Table 3. Performance Variance Under Different Random Seeds. We used PointMetaBase-XL as the backbone and conducted tests on the S3DIS Area-5 dataset under three different random seeds (1, 42, 1000). + +
BackboneFPSBackboneRSFastAdaptertrainFastAdapterinfer
mIoU±0.4±1.1±0.3±0.1
+ +Table 4. Ablation Study of Fine-tuning Setups. We used PointMetaBase-XL and conducted tests on S3DIS Area-5 dataset. + +
SetupmIoU (%)mACC (%)OA (%)
Baseline69.4775.8189.87
Head69.9975.8390.43
Decoder+Head69.5375.4590.25
Encoder+Head70.0975.8890.63
Full Fine-tuning69.4275.3890.16
FastAdapter71.2277.3490.86
+ +University, covering a total of 272 rooms with 13 categories of objects. + +ScanNet. ScanNet is a large-scale 3D indoor space dataset. It contains 2.5 million views from the indoor environment, and each view has the corresponding camera pose, depth map, and high-quality 3D reconstruction data. In addition, it includes semantic annotations of over 1500 unique scenes covering 20 common indoor categories. + +SemanticKITTI. SemanticKITTI is a large-scale outdoor dataset that includes LIDAR scans from 21 sequences, with a total of 43,552 densely annotated scans, each containing $10^{5}$ points. Following common practice, we use sequences 00 to 07 as the training set and sequence 08 as the evaluation set. + +# 4.2. Main Results + +Indoor Segmentation. For indoor segmentation tasks, we conducted experiments on S3DIS and ScanNet, integrating FastAdapter into the classic PointNet++ and RandLA as well as state-of-the-art models PointMetaBase-L/XL and PTV3 for testing. In terms of performance, we report mIoU and OA, while for efficiency, we report Throughput (ins./sec) and GFLOPs (G). The efficiency tests were conducted on an NVIDIA GeForce RTX 4090 and two Intel(R) Xeon(R) Gold 6442Y CPUs. The results can be seen in the Table 1, + +First, for models PointNet++ and PointMetaBase-L/XL, their original versions use FPS during both training and inference, which significantly hampers inference speed. To address this, we embed FastAdapter into the pre-trained models and replace FPS with random sampling, followed by simple fine-tuning. For each method, we report three types of results: the first is the performance of the pre-trained model using FPS, the second is the result of directly replac + +Table 5. Ablation Study of P2A Aggregator and A2P Adapter. We used PointMetaBase-XL and conducted tests on S3DIS Area-5 dataset. + +
P2A AggregatorA2P AdaptermIoU
Geometric-awareCross-LayerSpatialOffsetGeometric-weight
✓✓70.12
✓✓✓70.48
✓✓✓✓70.85
✓✓✓✓✓71.22
✓✓✓69.83
✓✓✓✓70.68
✓✓✓✓70.47
+ +ing FPS with random sampling in the pre-trained model, and the third is the outcome of embedding FastAdapter into the pre-trained model and using random sampling to fine-tune. By comparing the first and the second result, we can observe that models using random sampling achieve computation speeds that are several times faster than those using FPS, demonstrating the significant efficiency advantage of random sampling in fast point cloud segmentation. However, due to the limitations of random sampling, its use leads to a substantial decrease in performance. Then, by comparing the second and the third result, we can find that FastAdapter significantly reduces the performance degradation while ensuring superior inference speed, effectively alleviating the issues related to geometric information degradation. Taking the results on ScanNet as an example, when using random sampling, embedding FastAdapter allows PointNet++, PointMetaBase-L, and PointMetaBase-XL to achieve improvements of $1.8\%$ , $2.8\%$ , and $2.4\%$ mIoU, respectively. In comparison to using FPS, this approach only results in a decrease of $0.6\%$ , $0.6\%$ and $0.5\%$ mIoU while significantly enhancing inference speeds by $259\%$ , $315\%$ , and $230\%$ , respectively. More importantly, these models were not specifically designed with architectures for random sampling. By freezing the model parameters and only training FastAdapter, we were able to adapt these models to random sampling. This demonstrates the versatility and effectiveness of FastAdapter. We have included additional information regarding the training overhead (in terms of epochs and additional parameter) in the supplementary materials. + +Furthermore, for RandLA and PTV3, which are specifically designed with architectures corresponding to their respective fast downSampling methods, embedding FastAdapter during training can further enhance model performance. For example, on ScanNet, FastAdapter improved the mIoU by $1.0\%$ and $0.5\%$ for RandLA and PTV3, respectively. This indicates that FastAdapter is complementary to these specialized architectures and can further address the information loss issues associated with fast downSampling. Outdoor Segmentation We also conducted experiments on the large-scale outdoor dataset SemanticKITTI, testing RandLA and PointMetaBase-L to demonstrate the ef + +Table 6. Ablation Study of Training Setups. We used PointMetaBase-XL and conducted tests on S3DIS Area-5 dataset. + +
AnchorPoints Number50100150200250
mIoU70.8771.2271.2071.1370.92
λ0151020100
mIoU70.5171.0470.9271.2270.9470.51
+ +fectiveness of FastAdapter. The results are shown in Table 2. For RandLA, embedding FastAdapter allows us to achieve an improvement of $0.9\%$ mIoU. In the case of PointMetaBase-L, by replacing FPS with random sampling and integrating FastAdapter for fine-tuning, we can achieve an improvement of $2.1\%$ mIoU compared to directly using random sampling. Furthermore, compared to using FPS, this approach enhances inference speed by $238\%$ while only resulting in a decrease of $0.5\%$ mIoU. + +Performance Variance Under Different Random Seeds. Although Tabel 1 and Table 2 demonstrate that FastAdapter can effectively assist point-based models in adapting to random sampling, it is important to note that random sampling may yield significantly different results under different random seeds. Here, we aim to explore the stability of FastAdapter across various random seeds. We conducted experiments using PointMetaBase-XL on S3DIS Area 5, with the results shown in Table 3. We selected three different random seeds (1,42,1000) and tested the performance variance of the models under various conditions. First, we reported the variance of the baseline trained from scratch using both FPS (Backbone $FPS$ ) and RS (Backbone $RS$ ). The results indicate that, due to the lack of a fixed rule in random sampling, the performance exhibits a considerable variance. Then, we reported FastAdapter $train$ , which presents the variance from training FastAdapter under three random seeds. It is evident that, because we fine-tuned a pre-trained model and the FastAdapter effectively compensated for the geometric information lost during the downsampling process, the randomness of random sampling was significantly reduced, resulting in more stable model performance like using FPS. Finally, we reported FastAdapter $infer$ , which fixed the random seed to 42 when training model and performed multiple inferences using different random seeds, reporting the performance variance. The results show that the local features captured through anchor point aggregation effectively compensated for the information lost due to random sampling, resulting in stable outcomes. + +# 4.3. Ablation Study + +Fine-tuning Setups. Replacing FPS with Random Sample can be considered a distribution shift problem. Therefore, fine-tuning can partially mitigate this issue. Here, we tested different fine-tuning strategies to demonstrate the ef + +![](images/4b30e298d873fa8db651badd7af649515db8f6c410ce7d599358b9ed566cba13.jpg) +Figure 3. Visualization results on the S3DIS Area 5 dataset. The first row shows the model's predicted results, while the second row displays the ground truth. + +fectiveness of FastAdapter, and the results are shown in Table 4. We conducted experiments using PointMetaBase-XL on S3DIS Area-5 dataset. Firstly, the first row represents the performance of the model during inference when directly replacing FPS with random sampling without any fine-tuning. It is evident that the performance significantly deteriorates due to the geometric information degradation caused by random sampling. Then, we tested the performance of finetuning different parts of the model without FastAdapter. The results indicate that over-fine-tuning multiple modules (The rest modules of $M_{FPS}$ except for A2P and P2A) led to suboptimal performance, with full fine-tuning yielding the worst results. In contrast, finetuning the classification head achieved good performance with a smaller computational overhead. We believe this is because freezing most of the parameters helps preserve the knowledge learned during FPS training, thus avoiding the training collapse caused by random sampling. Finally, since FastAdapter continuously aggregates local features through anchor points to supplement information, training only FastAdapter while freezing the weights of the model except for the head can achieve the best results. This indicates that FastAdapter can effectively assist the model in adapting to the distribution resulting from the use of random sampling. + +P2A Aggregator and A2P Adapter. Here, we tested the design strategy of the P2A Aggregator and A2P Adapter using PointMetaBase-XL on S3DIS Area-5 dataset, and the results are shown in Table 5. The first four rows are used to test the effect of P2A Aggregator, while the last three rows are used to evaluate the performance of A2P Adapter. First, in the first row, we simply averaged the point features into anchor point without Geometric-aware aggregation. In the second row, we employed a geometry-aware aggregation module that dynamically assigns aggregation weights based on geometric information. As a result, we observed a noticeable performance improvement. Then, by adding the Cross-Layer Aggregator and Spatial Aggregator, the perfor + +mance gradually improved, which demonstrates the effectiveness of the P2A design. Further, In the fifth row, we directly added the anchor point features to the corresponding point cloud without any processing. It can be observed that due to the lack of correction and weighting for the anchor features, the inherent characteristics of the point cloud may be compromised, resulting in a significant decline in performance. In the sixth row, by incorporating Offset Embedding, we can effectively correct the anchor features, preventing biased information from being propagated. + +Training Setups. In this section, we primarily tested the impact of the number of superpoints and the distillation loss weight $\lambda$ on the performance of PointMetaBase-XL on S3DIS Area-5. As shown in Table 6, regarding the number of anchor points, we can see that setting the count to 100 and 150 yields the best performance. Further increasing the number of anchor points does not lead to additional performance improvements; instead, it increases costs. Regarding the weight of the distillation loss, it can be observed that when the weight is set to 0, there is a significant decline in performance. + +Visualizations. In Figure 3, we visualized the segmentation results of FastAdapter. It can be observed that FastAdapter can help the model achieve accurate segmentation results under random sampling conditions. + +# 5. Acknowledgement + +This work was supported by the National Natural Science Foundation of China under Grant 62376032. + +# 6. Conclusion + +In this paper, we introduce FastAdapter, which continuously aggregates local features through anchor points to supplement the information lost during downsampling. This approach effectively alleviates the geometric degradation issues associated with fast downsampling methods. + +# References + +[1] I Armeni, S Sax, AR Zamir, S Savarese, A Sax, AR Zamir, and S Savarese. 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Existing hallucination mitigation methods either incur prohibitive computational costs or introduce distribution mismatches between training data and model outputs. We identify a critical insight: hallucinations predominantly emerge at the early stages of text generation and propagate through subsequent outputs. To address this, we propose SENTINEL (Sentence-level Early iNtervention Through IN-domain prEference Learning), a framework that eliminates dependency on human annotations. Specifically, we first bootstrap high-quality in-domain preference pairs by iteratively sampling model outputs, validating object existence through cross-checking with two open-vocabulary detectors, and classifying sentences into hallucinated/non-hallucinated categories. Subsequently, we use context-coherent positive samples and hallucinated negative samples to build context-aware preference data iteratively. Finally, we train models using a context-aware preference loss (C-DPO) that emphasizes discriminative learning at the sentence level where hallucinations initially manifest. Experimental results show that SENTINEL can reduce hallucinations by over $90\%$ compared to the original model and outperforms the previous state-of-the-art method on both hallucination benchmarks and general capabilities benchmarks, demonstrating its superiority and generalization ability. The models, datasets, and code are available at https://github.com/pspdada/SENTINEL. + +# 1. Introduction + +Recent advancements in multimodal large language models (MLLMs) have demonstrated significant progress in aligning visual and textual representations through cross-modal feature integration, marking a pivotal step toward + +![](images/dd145140512598c94801ca6722334f96a56d82fed3c03900ee626a91e377d422.jpg) +(c) SENTINEL (Ours) +Figure 1. Comparative analysis of data construction strategies for hallucination mitigation in MLLMs. Our proposed approach demonstrates superior efficiency and effectiveness in generating high-quality, domain-specific preference learning datasets, offering a robust solution for reducing hallucination in MLLMs. + +the development of general-purpose AI systems [2, 9, 33-35, 44, 65, 87]. However, a critical challenge persists in multimodal settings: the phenomenon of hallucinations [4, 36, 53], wherein models generate factually inconsistent or fabricated information that deviates from the image content provided by users. This issue not only degrades user trust and experience but also poses substantial risks in real-world applications of MLLMs, thereby impeding the realization of trustworthy general AI systems [5, 18, 68]. + +To address this challenge, recent work has explored enhanced decoding strategies [8, 19, 27] as a means to mitigate hallucinations. While these approaches show promise, they often introduce trade-offs, including increased computational overhead during inference, higher latency, and re + +liaence on specific dependencies, which may limit their scalability and practicality in resource-constrained scenarios. + +On the other hand, preference alignment methods [31, 51, 60] avoid additional inference costs but face other challenges. As shown in Fig. 1a, many of them rely on large proprietary models (e.g., GPT [1]) [21, 69, 75, 80, 82, 86] or human annotators [13, 76], incurring high costs. Additionally, Fig. 1b highlights that output rewriting [69, 82, 86] can create distributional discrepancies, while Lai et al. [25] and our experiments in Tab. 2 show that out-of-domain training data harms generalization. Therefore, the high costs and the distribution disparities inherent in the curated training data may compromise hallucination mitigation efforts. + +Key observations. To address hallucination with greater efficacy and efficiency, we investigate the dynamics of hallucination within the model's output. Our analysis reveals that hallucination intensity escalates with the length of generated text, while mitigating hallucinations at specific sentences significantly reduces their prevalence in subsequent outputs, as detailed in Figs. 2a and 2b. These findings suggest that early intervention—targeting hallucinations at their initial occurrence—is crucial to preventing their propagation in later generations. This raises a key question: How can we effectively implement an early intervention strategy to address hallucinations of MLLMs as they arise? + +Our solution. In this work, we propose SENTINEL (Sentence-level Early iNtervention Through IN-domain prEference Learning), which provides early intervention for the initial occurrence of hallucinations during generation. Unlike existing methods, SENTINEL operates without relying on external large language models for rewriting, ensuring that the learning targets remain strictly within the domain of the model's original outputs. This approach preserves the model's intrinsic distribution and expression patterns while effectively curbing hallucination propagation. + +Specifically, SENTINEL first employs an in-domain candidate bootstrapping strategy, which performs multiple sampling rounds on the current model, extracts objects from the outputs, and applies consistency cross-checking to classify objects as hallucinated, uncertain, or factual. This is followed by a context-aware preference data generation process, which constructs preference pairs using non-hallucinated positive samples and hallucinated negative ones, enhanced by iterative contextual bootstrapping. Finally, context-aware preference learning is performed using the modified context-aware DPO loss, maximizing the likelihood of generating context-coherent positive samples while minimizing hallucinated negative ones. By focusing on captions where hallucinations first emerge, SENTINEL effectively halts their propagation in subsequent outputs. + +Experimental results across various benchmarks demonstrate that SENTINEL effectively mitigates object hallucination while preserving the generalization capabilities of + +MLLMs. Specifically, on Object Halbench [55] and AMBER [63], hallucinations are reduced by about $92\%$ and $65\%$ , respectively, with consistent improvements on HallusionBench [12]. Furthermore, SENTINEL preserves its performance on VQAv2 [10] and TextVQA [59], and achieving decent gains on both ScienceQA [41] and MM-Vet [78]. + +To summarize, our contributions are as follows: + +- We demonstrate that early intervention at the first occurrence of hallucination is crucial for preventing its propagation in subsequent model outputs of MLLMs. +- We propose SENTINEL, which effectively and efficiently mitigates hallucinations without requiring extensive external resources or manual effort. +- The model-agnostic SENTINEL achieves state-of-the-art performance on hallucination benchmarks without compromising MLLMs' general capabilities. + +# 2. Background and Motivation + +In this section, we briefly introduce the foundational concepts and methods relevant to this study in Sec. 2.1, establishing the necessary background. Following this, in Sec. 2.2, we outline our key insights and elucidate the motivations behind our proposed designs. + +# 2.1. Related Work and Preliminaries + +Object Hallucination (OH) in Multimodal Large Language Models (MLLMs) is characterized by the generation of text that is semantically coherent yet inconsistent with the visual content of the provided image [4, 53]. To mitigate this issue, recent advancements have focused on innovative decoding strategies, which aim to reduce the prevalence of OH by refining the generation process of MLLMs [6, 8, 19, 27]. + +Concurrently, preference learning has emerged as an alternative approach for addressing OH, leveraging its capacity to align MLLMs with human expectations for truthfulness and traceability [13, 28, 32]. Notably, the Proximal Policy Optimization algorithm (PPO) [57] enhances model reliability by training an auxiliary reward model to assess response quality and then guide the model in optimizing its outputs based on the reward signals. Moreover, Direct Preference Optimization (DPO) [51] has emerged as a simpler alternative, learning directly from pre-collected feedback without requiring a reward model. The DPO loss is: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {D P O}} (\boldsymbol {\theta}) = - \mathbb {E} _ {(\boldsymbol {x}, \boldsymbol {y} _ {w}, \boldsymbol {y} _ {l}) \sim D} \left[ \log \sigma \left(\beta \log \frac {\pi_ {\boldsymbol {\theta}} (\boldsymbol {y} _ {w} | \boldsymbol {x})}{\pi_ {\mathrm {r e f}} (\boldsymbol {y} _ {w} | \boldsymbol {x})} \right. \right. \\ \left. - \beta \log \frac {\pi_ {\boldsymbol {\theta}} (\boldsymbol {y} _ {l} | \boldsymbol {x})}{\pi_ {\mathrm {r e f}} (\boldsymbol {y} _ {l} | \boldsymbol {x})}\right) \Bigg ], \tag {1} \\ \end{array} +$$ + +where $\pmb {x} = [\pmb {v},\pmb {q}]$ + +Here, $D$ represents the preference dataset for learning, $\sigma$ denotes the sigmoid function, $\pi_{\theta}$ indicates the policy + +![](images/df9b03541e2604be6b532ffe7f47980fa7d61044648c8a075e55bd9f40721b2a.jpg) +(a) +Figure 2. Object position distribution in MLLM hallucination analysis. (a) illustrates the progressive deterioration of hallucination effects in Multimodal Large Language Models (MLLMs) with increasing description length in the image captioning task, while (b) demonstrates the effectiveness of early-stage intervention in mitigating the propagation of hallucination. + +![](images/c8ce4736ae66e247cff5725d7e893bce64878a126002868d706783381b640dce.jpg) +(b) + +model under training, $\pi_{\mathrm{ref}}$ represents the unchanged reference model, $y_w$ stands for the positive sample, and $y_l$ represents the negative sample, both based on the input $x$ , which includes the image $v$ and prompt $q$ . The hyperparameter $\beta$ governs the separation between the policy model and the reference model. Many recent methods [16, 69, 77, 82, 86] leverage DPO to mitigate hallucinations by curating preference data to guide the models. More related works of this study are discussed in Sec. F. + +# 2.2. Motivation + +This section outlines the motivations behind this work. The implementation details of related experiments are provided in Sec. A. + +Hallucination grows with text length. To better understand the causes of Object Hallucination (OH), we analyze the distributions of hallucinated and factual objects in image captions generated by MLLMs. Specifically, as shown in Fig. 2a, where the horizontal axis represents the normalized position of an object in the caption (as a percentage), while the vertical axis denotes the normalized frequency (probability density), the blue curve represents hallucinated objects, and the orange curve corresponds to objects present in the image. The comparison reveals that as caption length increases, the model becomes more prone to hallucinations, with fewer factual objects described and more hallucinated ones introduced. This trend is further corroborated by sentence-level analysis in Fig. 2b. These findings lead us to hypothesize that intervening at the initial occurrence of hallucination could be critical in reducing its recurrence in subsequent model outputs. + +Early intervention mitigates hallucinations. To evaluate the effectiveness of early intervention in curbing hallucination propagation, we analyze the impact of addressing hallucinations at the sentence level in image captioning tasks. + +Specifically, as illustrated in Fig. 2b, eliminating hallucinated objects in the second sentence—compared to vanilla greedy decoding—significantly reduces the likelihood of hallucinated objects in subsequent sentences while increasing the probability of factual objects present in the image. Similar results are observed when addressing hallucinations in the third sentence, as shown in Sec. A.2. These findings underscore the necessity of early intervention to mitigate hallucinations effectively. + +To enable early intervention, an open-vocabulary object detector [7, 37] could be employed during inference to verify the presence of the objects generated by the model within the image. While this method effectively reduces hallucinations without sacrificing caption diversity, as demonstrated in Sec. A.2, it is time-consuming; despite the object detector being efficient, the model's sampling process incurs significant computational overhead. + +Consequently, we opt for a preference learning strategy during model training, which mitigates hallucinations without compromising the original inference efficiency. + +# 3. Method + +# 3.1. Overview + +Existing preference learning methods may use an external model to rewrite sentences or rely on model-generated responses as training data. However, these methods may introduce discrepancies in distribution and expression patterns between the training data and the model's original output. Hence, we propose SENTINEL, which performs sentence-level early intervention to mitigate object hallucinations through preference learning with in-domain data, without manual effort or dependence on extensive LLMs. + +As shown in Fig. 3, the proposed SENTINEL method takes six essential steps. Specifically, Sec. 3.2 presents the process of generating the in-domain candidates containing the factual and hallucinated objects. Subsequently, Sec. 3.3 introduces the construction of preference data pairs derived from these in-domain candidates. These two steps can be integrated into the In-domain Preference Data Construction phase (shown in Algorithm 1). Finally, in Sec. 3.4 we elaborate on how SENTINEL leverages the curated preference data to achieve preference learning. + +# 3.2. In-domain Candidate Bootstrapping + +To construct positive and negative preference data pairs without relying on external models for rewriting, we perform multiple sampling rounds on the current model and extract objects from the outputs. We then apply a consistency cross-checking method to classify the model's output objects into three categories: hallucinated, uncertain, and factual, which are used to construct preference data in subsequent steps. This process is termed In-domain Candidate + +![](images/d5a60153740100c57023d2512e809d04c41deaf132918fbe708d32be40c6b22e.jpg) +Figure 3. The overview of SENTINEL. The proposed SENTINEL takes six essential steps: (1) Generate multiple in-domain responses conditioned on the input image, prompt, and context $c$ . (2) Identify and extract all mentioned objects from each generated sentence. (3) Utilizing two object detectors to validate the existence of extracted objects through cross-referencing. (4) Categorize generated sentences into hallucinated and non-hallucinated groups based on detection results. (5) Extend the generation context with verified non-hallucinated sentences to guide subsequent outputs. (6) Fine-tune the model using the context-aware DPO (C-DPO) loss with the in-domain, style-consistent, and context-varying preference data. + +Booststrapping, as illustrated in Fig. 3 (1)-(3). + +In-domain candidate sampling. In our approach, we use sampling-based decoding to obtain $n$ candidate samples. This ensures that the positive $(\pmb{y}_w)$ and negative $(\pmb{y}_l)$ samples are drawn from the same distribution as the current model, preserving consistency in textual styles and linguistic structures. The generation halts upon sentence completion (e.g., detection of a period), at which point sentences are automatically segmented for subsequent discrimination. + +Object extraction. After generating candidate sentences, we extract the mentioned objects from the text for hallucination detection. To achieve this, we utilize the SceneGraphParser [30] model to transform the textual descriptions into a series of triplet-based scene graphs. By parsing these scene graphs, we identify specific noun entities from the subjects and objects, which are subsequently used as candidate objects for existence verification. + +Object presence validation. Following object extraction, we apply cross-checking to validate the presence of candidate objects in the image. Specifically, we utilize two open-vocabulary object detectors, GroundingDINO [37] and Yolo World [7], for cross-validation. This approach demonstrates superior performance compared to using a single detector, as shown in Fig. 8 of the ablation study. + +The cross-checking results are categorized into three + +types: (1) hallucinated (both models confirm absence), (2) factual (both models confirm presence), and (3) uncertain (conflicting results). Sentences containing hallucinated objects are tagged as "hallucinated", whereas those only containing factual objects are tagged as "non-hallucinated", forming positive-negative sample pairs for preference learning. To ensure data quality and minimize detector bias, we ignore uncertain objects. + +# Algorithm 1 In-domain Preference Data Construction + +Input: Image $\pmb{v}$ , prompt $\pmb{q}$ , context $\pmb{c}$ (initially empty) + +Output: Training samples $(\pmb {v},\pmb {q},\pmb {c},\pmb{y}_{w}^{+},\pmb{y}_{l})$ + +1: while Model $M$ does not generate $\langle /s\rangle$ do +2: Sample $n$ in-domain candidates $s_i$ using $\mathbf{v}$ , $\mathbf{q}$ , and $c$ +3: for each sample $s_i$ do +4: Extract entities from the sample +5: Validate the presence of entities using object detectors +6: Select $\pmb{y}_{w}^{+}$ as context-coherent non-hallucinated sample +7: Select $\pmb{y}_l$ as hallucinated sample +8: Construct preference samples $(\pmb{v},\pmb{q},\pmb{c},\pmb{y}_w^+, \pmb{y}_l)$ +9: Append a non-hallucinated sample $\pmb{y}_w^+$ to the context $\pmb{c}$ + +# 3.3. Context-aware Preference Data Generation + +With sentences labeled as "hallucinated" or "nonhallucinated" from Sec. 3.2, this section introduces context-aware preference data generation. As illustrated in Fig. 3 + +![](images/47334f26ee5e4d724137d8b41e8e34f99555e8ccbbf0c1ea790ceca9758ab43b.jpg) +Figure 4. Categories of in-domain candidates. The in-domain candidates fall into three types. Employing non-hallucinated, context-coherent descriptions $(\pmb{y}_w^+)$ as positive samples, paired with hallucinated descriptions $(\pmb{y}_l)$ , enhances the model's generalization performance and robustness. + +(4)-(5), this process extracts contextually relevant data, ensuring the training data better represents the model's output distribution. The specifics are elaborated below. + +Preference data construction. The preference data is typically composed of the image, the corresponding prompt, the positive sample, the negative sample, and the context (i.e., all generated sentences excluding the current one). In the construction of sample pairs, positive samples $\mathbf{y}_w$ are selected from the non-hallucinated sentences, while negative samples $\mathbf{y}_l$ are derived from the hallucinated sentences. + +Subsequently, we partition the positive samples $\mathbf{y}_w$ into two categories: (1) the context-coherent positive sample $\mathbf{y}_w^+$ , wherein some of the described objects are explicitly referenced in the context, and (2) the context-agnostic positive sample $\mathbf{y}_w^-$ , where none of the objects are mentioned in the context. In essence, the objects described in $\mathbf{y}_w^+$ exhibit a strong correlation with the context, while those in $\mathbf{y}_w^-$ display a weaker or negligible correlation. Illustrative examples are provided in Figs. 3 and 4. + +We observe that the context-coherent sample $\mathbf{y}_w^+$ can effectively mitigate hallucinations without compromising the model's generalization capabilities, and incorporating $\mathbf{y}_w^-$ as the positive samples results in performance reduction, as shown in Tab. 3. This observation underscores the importance of contextual signals in guiding the model's generation process. Specifically, the richer contextual information in $\mathbf{y}_w^+$ samples appears to enhance the model's ability to preserve contextual coherence and prioritize salient content, resulting in performance improvements [15]. + +Iterative Contextual Bootstrapping (ICB). The proposed SENTINEL framework is designed to enable early intervention for mitigating hallucinations in generative models. Given the context $c$ , which represents the hallucination-free content preceding the current output, the model is trained to distinguish between a non-hallucinated positive sample $y_w^+$ and a hallucinated negative sample $y_l$ . To enhance robust- + +![](images/0d1535b9f019a3792bb8c906f18b33c1cf87c9f3c3ca8d3ee5acbfd716546f13.jpg) +Figure 5. Visualization of the Iterative Contextual Bootstrapping (ICB) framework. Given an input image and corresponding question, this pipeline iteratively generates diverse contextual samples, enabling robust hallucination mitigation across varying contexts and significantly improving model generalization. + +![](images/3db3bcc5a175ad4f57e2493cd44b7a81921061a063e79aceaf508148d844a92c.jpg) + +ness across diverse contexts, we introduce the Iterative Contextual Bootstrapping (ICB) strategy, as depicted in Fig. 5. + +Specifically, given the query $\pmb{q}$ , the input image $\pmb{v}$ , and the current context $\pmb{c}_i$ , we generate multiple candidate outputs by repeatedly sampling from the MLLM. These candidates are then processed through a structured pipeline consisting of (2) object extraction, (3) object presence validation, and (4) preference data construction, as illustrated in Fig. 3. This pipeline is designed to identify a non-hallucinated positive sample $\pmb{y}_w^+$ and a hallucinated negative sample $\pmb{y}_l$ . By aggregating $\pmb{v}, \pmb{q}, \pmb{c}_i, \pmb{y}_w^+$ and $\pmb{y}_l$ , we construct a preference data pair $(\pmb{v}, \pmb{q}, \pmb{c}_i, \pmb{y}_w^+, \pmb{y}_l)$ , which is subsequently appended to the dataset for preference learning. + +Furthermore, to bootstrap the preference data with different hallucination-free contexts, we construct $c_{i+1} = c_i + y_w^+$ for the next iteration by appending the positive sample $y_w^+$ to the current context $c_i$ . The updated context $c_{i+1}$ is then processed through the same procedure as described above to generate a new preference data pair. This iterative approach ensures that the preference data is enriched with progressively more complex and varied contexts, enabling the model to generalize its hallucination mitigation capabilities across different scenarios. The effectiveness of this pipeline is validated and discussed in Sec. B.2. + +# 3.4. Context-aware Preference Learning + +The preference data generated through the processes outlined in Sec. 3.2 and Sec. 3.3 can be formally represented as $(\pmb{x},\pmb{c},\pmb{y}_w^+, \pmb{y}_l)$ , where $\pmb{x}$ is the input, including the image $\pmb{v}$ and the prompt $\pmb{q}$ , $\pmb{c}$ denotes the context, $\pmb{y}_w^+$ is the context- + +
ModelMethodHallucination benchmarksGeneral benchmarks
Object HalBench [55]AMBER [63]HallusionBench [12]VQAv2 [10]TextVQA [59]ScienceQA [41]MM-Vet [78]
Resp. ↓Ment. ↓CHAIR ↓Hal. ↓Cog. ↓Question Acc. ↑Acc. ↑Acc. ↑Image Acc. ↑Overall ↑
LLaVA-v1.5-7Bbaseline52.728.08.435.54.046.8678.558.266.831.0
VCD [27]51.325.99.139.84.2-77.056.168.729.8
OPERA [19]45.322.96.528.53.1-78.258.268.230.3
DoLa [8]44.025.16.227.72.9-76.356.667.530.8
EFUF [70]39.322.65.828.23.147.0378.157.266.431.2
HA-DPO [82]37.020.96.730.93.347.7477.656.769.730.6
POVID [86]33.416.65.328.73.046.5977.256.668.831.8
CLIP-DPO [45]--3.716.61.3--56.467.6-
RLAIF-V [77]7.84.22.815.70.935.4375.255.168.229.9
TPO [16]5.63.23.620.51.640.1275.955.367.125.7
Ours4.32.62.914.61.247.5678.458.269.232.6
LLaVA-v1.5-13Bbaseline46.023.06.931.93.346.4380.061.271.636.0
VCD [27]43.721.67.836.23.7-78.559.572.033.7
vanilla-DPO [69]6.73.62.815.51.646.4179.260.471.835.0
HSA-DPO [69]5.33.22.113.41.246.1478.360.071.333.7
Ours3.31.92.711.70.946.7779.961.072.836.2
+ +Table 1. Comparison of hallucination mitigation methods in MLLMs: effectiveness and general capabilities. This evaluation highlights the best and second-best results in bold and underlined, respectively. All comparisons are performed under identical model size constraints. "Resp." and "Ment." denote response-level and mention-level hallucination rates, while "Hal." and "Cog." represent the Hallucination Score and Cognitive Score, respectively. More evaluation details are provided in Sec. D. + +coherent positive sample, and $\pmb{y}_l$ is the negative sample. + +The learning objective is to guide the model, conditioned on the input $\mathbf{x}$ and the context $c$ , to maximize the likelihood of generating the contextually coherent positive sample $\mathbf{y}_w^+$ while minimizing the likelihood of producing the negative sample $\mathbf{y}_l$ . To achieve this, we adapt the Direct Preference Optimization (DPO) loss by incorporating the context $c$ as part of the input. We term this modified loss as context-aware DPO (C-DPO), which is formulated as follows: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {C - D P O}} (\boldsymbol {\theta}) = - \mathbb {E} _ {(\boldsymbol {x} ^ {\prime}, \boldsymbol {y} _ {w} ^ {+}, \boldsymbol {y} _ {l}) \sim D} \left[ \log \sigma \left(\beta \log \frac {\pi_ {\boldsymbol {\theta}} \left(\boldsymbol {y} _ {w} ^ {+} \mid \boldsymbol {x} ^ {\prime}\right)}{\pi_ {\mathrm {r e f}} \left(\boldsymbol {y} _ {w} ^ {+} \mid \boldsymbol {x} ^ {\prime}\right)} \right. \right. \\ \left. - \beta \log \left. \frac {\pi_ {\boldsymbol {\theta}} \left(\boldsymbol {y} _ {l} \mid \boldsymbol {x} ^ {\prime}\right)}{\pi_ {\mathrm {r e f}} \left(\boldsymbol {y} _ {l} \mid \boldsymbol {x} ^ {\prime}\right)}\right) \right], \\ \end{array} +$$ + +where $\pmb{x}^{\prime} = [\pmb {x},\pmb {c}] = [\pmb {v},\pmb {q},\pmb {c}]$ (2) + +In C-DPO, the context $c$ is excluded from the loss computation, and gradients are only derived from the discrimination between $\mathbf{y}_w^+$ and $\mathbf{y}_l$ . This design ensures that the model focuses on learning the contextual coherence of the positive sample without being directly influenced by the context during gradient updates. Further discussions and comparisons between the proposed C-DPO and the standard DPO are provided in Sec. C.3. + +# 4. Experiments + +In this section, we conduct comprehensive experiments to evaluate the effectiveness of our SENTINEL in reducing hallucinations while improving the general abilities of the model. We first introduce the experimental setup in Sec. 4.1, then present the main results in Sec. 4.2, and finally conduct ablation studies in Sec. 4.3 to analyze our method's effectiveness. More results are in Secs. C and D. + +# 4.1. Experimental Setup + +Training. To ensure a fair comparison, we follow the settings of prior works [16, 19, 26, 27, 34, 45, 56, 66, 69, 69, 70, 77, 79, 82, 86], using LLaVA-v1.5 as the reference model across all experiments. For data collection, we prompt the model with detailed image descriptions [76] to generate training data, with images sourced from the Visual Genome dataset [23]. Model training is conducted using C-DPO (Eq. (2)) in combination with LoRA [17], and optimized with AdamW [40]. The 7B and 13B models are trained for one epoch on $8.6\mathrm{K}$ and $7.0\mathrm{K}$ samples, respectively, with learning rates of $2\times 10^{-7}$ and $3\times 10^{-7}$ . Additional training details are provided in Sec. C. + +Evaluation benchmarks. We evaluate the hallucination extent and general capabilities of our SENTINEL method across multiple benchmarks. For hallucination evaluation, we use widely adopted benchmarks, including Object HalBench [55], AMBER [63], and HallusionBench [12]. To assess general capabilities, we employ VQAv2 [10], TextVQA [59], ScienceQA [41], and MM-Vet [78]. Further details of these benchmarks are provided in Sec. D.1. + +Baselines. To show the effectiveness of our method, we compare SENTINEL with several state-of-the-art (SOTA) methods. Specifically, VCD [27], OPERA [19], and DoLa [8] focus on enhanced decoding strategies, while HADPO [82], POVID [86], CLIP-DPO [45], RLAIF-V [77], and TPO [16] leverage preference training. Additionally, Vanilla DPO applies the original DPO objective Eq. (1) using training data from HSA-DPO, while EFUF [70] is an unlearning-based approach. Details are in Sec. D.2. + +# 4.2. Main Results + +Comparison with recent SOTAs. As shown in Tab. 1, we compare our method with baseline methods across several + +![](images/7935b52c16d2fd9bb784bfd22b59c41dd69173a06905c2f3c92c8defc70744ea.jpg) +Figure 6. Impact on different hallucination types. Comparison between multiple methods shows that our method reduces hallucination in all six hallucination types. +Figure 7. Qualitative results of SENTINEL. Our method can effectively eliminate hallucinations in MLLMs while enhancing the model's general capabilities. + +benchmarks. The results demonstrate that SENTINEL significantly reduces the models' hallucination rate. Specifically, for the 7B model, our method achieves a 4.3 response-level (Resp.) and a 2.6 mention-level (Ment.) hallucination rate. Compared to the previous SOTA method, TPO [16], which achieves a 5.6 response-level and 3.2 mention-level hallucination rate, our proposed SENTINEL surpasses it by further reducing hallucinations by a total of $24\%$ on Object Halbench. Furthermore, even on the 13B model, compared to the baseline, which achieves 6.9 CHAIR, 31.9 Hallucination score (Hal), and 4.0 Cognitive score (Cog), our proposed SENTINEL significantly improves performance, achieving 2.7 CHAIR, 11.7 Hal score, and 0.9 Cog score, respectively. These results demonstrate that our method is also effective on larger models. + +Comprehensive hallucination mitigation. To further evaluate the effect of our method on various hallucination types, we conducted experiments on the discriminative part of the AMBER [63] benchmark and report the F1 scores for each hallucination type. As shown in Fig. 6, LLaVA-v1.5 with SENTINEL outperforms the baseline across all six hallucination types, demonstrating the effectiveness of our method in mitigating various hallucination issues. Notably, for the Existence hallucination type, our method improves the 7B model by 6.3 and the 13B model by 7.6 compared to the baseline. Detailed results are provided in Sec. D.4. + +Improved general capabilities. As shown in Tab. 1, SENTINEL enhances the general capabilities of the model on multiple benchmarks. Specifically, SENTINEL demonstrates stable performance on VQAv2 and TextVQA, whereas previous methods designed for hallucination mitigation suffer from significant performance degradation. Moreover, on ScienceQA and MM-Vet, our method not only surpasses previous hallucination mitigation methods but also outperforms the vanilla LLaVA-v1.5. These results show that SENTINEL not only significantly mitigates hal + +![](images/87983806c994b417cf5fe3a4849d2997bdd6d522bdab4f954f6c822028e3b3e8.jpg) +图 + +![](images/f2ffdc719a3f26dafd23c1bb85f973c6304f9ff9a61a53a24e8a98c89a7fc5ee.jpg) + +# LLaVA-v1.5-7B + +Yes, the persons in the image are likely to be living in the house, as they are walking through the hallway and interacting with each other. The presence of chairs, a dining table, and other furniture in the room suggests that it is a living space. The people in the image are dressed in period clothing, which indicates that they might be attending a special event or gathering in the house. The fact that they are walking together and engaging in conversation further supports the idea that they are residents of the house. + +![](images/391d46f024de452ffe3d049e2b58e71259ffaf27fc9230283945e90046cd7e0f.jpg) +Do the persons live in this house? Answer it and give the rationale. +Required capabilities: Recognition, Knowledge and Language generation + +# LLaVA-v1.5-7B + SENTINEL (Ours) + +No, the persons in the image do not live in the house. They are dressed in period costumes and are walking through the hallway of a large, ornate mansion. This suggests that they are likely actors or performers participating in a historical reenactment, a theatrical performance, or a film set. The presence of the costumes and the grand setting indicate that the scene is staged and not a typical everyday living situation. + +
MethodObject HalBenchAMBERMM-Vet
Resp. ↓Ment. ↓Acc ↑F1 ↑Overall ↑
LLaVA-v1.5-7B52.727.971.574.131.1
Ours (8.6K (\( y_w^+ \), \( y_l \))4.32.676.179.332.6
Ours (8.6K Rewrited (\( y_w^+ \), \( y_l \))4.8↑0.52.9↑0.375.0↓1.178.0↓1.331.3↓1.3
+ +Table 2. Effects of rewritten samples. Rewriting the preference training samples $(\pmb{y}_w^+, \pmb{y}_l)$ results in performance reduction. + +lucinations but also improves general capability. + +Qualitative results. To further demonstrate the effectiveness of our method, we conduct case studies. As shown in Fig. 7, the baseline model misinterprets the image content, leading to an incorrect conclusion. In contrast, our model effectively understands image content and provides a more detailed and precise description. This example highlights how our approach effectively reduces hallucinations while simultaneously enhancing the model's overall capability. We conduct more case studies in Sec. G. + +# 4.3. Ablation Studies + +In this section, we conduct a series of ablation experiments to further analyze the effectiveness of SENTINEL. More discussions can be found in Sec. D.5. + +Effectiveness of data style consistency. To analyze the effect of preference data style, we train the model using rewritten data for comparison. Specifically, we instructed GPT-4 [1] to rewrite $(\pmb{y}_w^+, \pmb{y}_l)$ while ensuring coherence with the context $c$ . As shown in Tab. 2, the rewriting results show performance degradation in reducing hallucinations and general ability. This highlights the advantage of our approach in preserving data style consistency. Furthermore, we conduct a detailed analysis in Sec. D.5, which shows that models trained on in-domain data converge to a lower preference optimization loss and achieve better differentiation between positive and negative samples, whereas training with rewritten data provides less improvements. + +Effectiveness of cross-checking. To validate the effectiveness of cross-checking for object presence, we conduct experiments using only the Grounding DINO or YOLO World for detection. In this setting, if the model determines that an + +
MethodData ScaleObject HalBenchTextVQAScienceQAMM-Vet
Resp. ↓Ment. ↓AccI-Acc↑Overall ↑
LLaVA-v1.5-7B-52.727.958.266.831.1
y+w100%8.6K4.32.658.269.232.6
y+w50% + yw50%10.0K↑1.4K4.8↑0.52.9↑0.358.1↓0.169.0↓0.232.0↓0.6
yw-100%14.0K↑5.4K4.6↑0.33.0↑0.458.1↓0.168.7↓0.531.6↓1.0
+ +Table 3. Comparison between context-coherent samples $y_w^+$ and context-agnostic samples $y_w^-$ . This table reveals that incorporating context-coherent samples $y_w^+$ yields better performance. + +
MethodObject HalBench[55]AMBER[63]
Resp. ↓Ment. ↓CHAIR ↓Hal ↓Cog ↓
LLaVA-v1.5-7B52.727.98.435.54.0
Non-hallucinated context4.32.62.914.61.2
Natural context8.64.73.315.61.5
Hallucinated context14.37.13.918.61.8
+ +Table 4. Comparison between different new context formation strategies during the iterative contextual bootstrapping pipeline. Appending non-hallucinated sample $\boldsymbol{y}_w^+$ to the existing context $c_i$ yields superior performance compared to incorporating hallucinated samples $\boldsymbol{y}_l$ or greedy decoding contexts, highlighting the effectiveness of our proposed approach. + +object is absent, it is directly classified as hallucinated. As shown in Fig. 8, leveraging two object detectors for cross-validation significantly outperforms using a single model, effectively reducing the hallucination rate. + +Effect of different $y_{w}$ types on model performance. As shown in Tab. 3, we conduct a detailed study on the impact of different types and proportions of the positive data $y_{w}$ on model performance. The results show that $y_{w}^{+}$ samples, which contain richer contextual information, enhance the model's generalization ability while achieving similar hallucination reduction with less data. + +Effect of non-hallucinated sentences as context $c$ . To analyze the impact of using non-hallucinated sentences as context $c$ , we evaluate three different settings for generating new context: selecting a hallucinated sentence, selecting a non-hallucinated sentence, or directly using a model-generated sentence from greedy decoding. As shown in Tab. 4, using a non-hallucinated sentence as context improves the model's ability to distinguish hallucinations and significantly reduces their occurrence in the output. This further demonstrates that intervening at the first instance of hallucination is critical for minimizing its recurrence. + +Effect of data scale. To analyze the impact of the training data scale on our method, we train the model using different dataset sizes (1k/2k/4k/6k/8k) and evaluate its performance on Object Halbench. As shown in Fig. 8, our method further mitigates model hallucinations as data scale up. This demonstrates the potential and scalability of SENTINEL. Furthermore, since our method does not rely on ultra-large proprietary models or human annotators for dataset construction, it can efficiently collect more training data. + +Integrating with existing preference learning methods. + +![](images/f7dc54fe08c3d22d1f1528605fabc75d63ff9ab3dd32aaada5245b10f6b32a22.jpg) +Figure 8. Impact of training data quantity on hallucination rate in Object Halbench [55]. The results show that SENTINEL demonstrates better efficiency, effectiveness, and scalability, while effectively reducing hallucination rates across varying data scales. + +![](images/854ad8f49fc4ba391362713e9788600e33081bfaa146b490d6e834d647a7d755.jpg) + +
MethodObject HallBench [55]AMBER [63]HallusionBench [12]TextVQA [59]MM-Vet [78]
Resp. ↓Ment. ↓Acc↑Fi↑Question Acc↑Acc↑Overall ↑
LLaVA-v1.5-7B52.728.072.174.146.8658.231.0
HA-DPO [82]37.0,29.8%20.9,25.4%74.2,27.778.0,3.947.74,8.8856.7,1.530.6,0.4
HA-DPO + Ours (6K)8.0,78.4%4.6,78.0%76.6,2484.2,6.248.72,9.9857.1,10.433.5,7.2.9
+ +Table 5. Effectiveness of combining the proposed SENTINEL with HA-DPO. Only a subset of our training data is needed to reduce hallucinations while enhancing generalization effectively. + +To further demonstrate SENTINEL's generalization, we explore integrating with previous hallucination mitigation approaches. As shown in Tab. 5, incorporating a subset of our data into the GPT-generated dataset collected by HA-DPO [82] effectively mitigates hallucinations while significantly enhancing the model's generalization. This highlights SENTINEL's complementarity with other preference learning methods and its potential for broader applicability. + +# 5. Concluding Remarks + +Summary. In this work, we address the critical challenge of hallucinations in multimodal large language models (MLLMs). While prior methods have shown promise, they often introduce significant computational overhead, rely on costly resources, or create distributional discrepancies. To tackle these issues, we propose SENTINEL, a framework that intervenes early at the onset of hallucinations by leveraging in-domain preference learning. SENTINEL employs an in-domain candidate bootstrapping strategy, context-aware preference data generation, and a context-aware DPO (C-DPO) loss to effectively curb the propagation of hallucinations while preserving the model's intrinsic distribution. Experimental results across multiple benchmarks demonstrate the superiority of SENTINEL, establishing it as a scalable, efficient, and model-agnostic solution for enhancing the reliability of MLLMs. + +Limitation. Currently, as SENTINEL lacks the capability to incorporate spatiotemporal information, it might not be able to effectively address the hallucination issues that require long-term reasoning in video MLLMs. This limitation highlights the need for further research in this area. + +Acknowledgments. 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For a given uniform-bit quantization configuration, MixA-Q separates the batched window computations within Swin blocks and assigns a lower bit width to the activations of less important windows, improving the trade-off between model performance and efficiency. We introduce a Two-Branch Swin Block that processes activations separately in high- and low-bit precision, enabling seamless integration of our method with most quantization-aware training (QAT) and post-training quantization (PTQ) methods, or with simple modifications. Our experimental evaluations over the COCO dataset demonstrate that MixA-Q achieves a training-free $1.35 \times$ computational speedup without accuracy loss in PTQ configuration. With QAT, MixA-Q achieves a lossless $1.25 \times$ speedup and a $1.53 \times$ speedup with only a $1\%$ mAP drop by incorporating activation pruning. Notably, by reducing the quantization error in important regions, our sparsity-aware quantization adaptation improves the mAP of the quantized W4A4 model (with both weights and activations in 4-bit precision) by $0.7\%$ , reducing quantization degradation by $24\%$ . + +# 1. Introduction + +Swin Transformer [22] is a representative vision transformer that generalizes well across different visual perception tasks, particularly dense prediction tasks such as object detection and segmentation [3]. While it improves upon the quadratic complexity of conventional ViT [8] by introducing a hierarchical structure and shifting window mechanisms, the self-attention operation remains computationally intensive. + +With recent advancements in high-resolution imaging, + +models process richer visual information, improving performance on dense tasks. However, this comes with increased computational overhead that results in latency bottlenecks for real-time applications like autonomous driving. Thus, reducing the computational cost associated with activations has become increasingly important. To tackle these computational challenges that arise from vision transformers and high-resolution inputs, activation pruning and quantization are two effective methods that improve efficiency with acceptable performance degradation. + +Real-world images exhibit natural sparsity because not all pixels within an image are important. Activation pruning is a group of methods that exploits this activation sparsity to improve latency performance by selecting less important tokens [21] or windows of transformers at runtime and skipping the computations associated with them. SparseViT [2] is a representative work for window-based ViTs like Swin Transformer and has achieved good latency improvement with negligible loss of accuracy. However, activation pruning methods have several limitations: + +- Require retraining to adapt the model for the pruned activations. +- Significant accuracy degradation at high pruning ratios. +- Performance is largely dependent on accurate window selections, which can't be guaranteed for Out-Of-Distribution (OOD) inputs. This could limit their deployment on safety-critical applications. + +On the other hand, quantization is an effective and prevalent compression approach that reduces a model's computational cost by decreasing the representation precision of weights and activations. While most quantization methods use uniform-bit precision across the whole network, modern hardware increasingly supports the multi-bit precision, giving rise to mixed-precision quantization (MPQ) methods. The key insight in most prior MPQ methods is that different layers within the machine learning model don't have the same contribution to the final output and don't have the same robustness to quantization noise. However, they often overlook the intra-layer activation sparsity and focus on the inter-layer bit-width allocation. This offers another dimen + +![](images/2038fc6eb9d2948a1328edfd3f64095830b17d797fe9b6cab30a4bf8c4b268a9.jpg) +Figure 1. Example for how MixA-Q leverages activation sparsity for efficient inference. + +![](images/d553a4237bf9243a7fd60101d72a7933545abe87e90ddc4d74f70d495d23fc39.jpg) +(a) Example image from the COCO dataset [17] +higher bit width lower bit width +(b) MixA-Q assigns lower bit width to the activation windows from less important regions to reduce computational cost. + +sion to exploit activation sparsity from a mixed-precision quantization perspective: instead of skipping computations for less important regions, we can quantize them with lower bit width. + +In this paper, we bring the activation sparsity awareness from activation pruning to the quantization world and propose a novel mixed-precision activation quantization framework for Swin Transformer called MixA-Q. The key feature of Swin Transformer is that the feature map is separated into several local windows for batched multi-head attention [22]. Fig. 1 illustrates how we leverage this feature of the Swin Transformer and the spatial sparsity of activations across local windows to reduce the computational cost. Using the L2 norm of the feature map, MixA-Q assigns high bit width to important foreground windows and keeps the rest in low bit width. We use an evolutionary search to optimize layerwise compression ratios, accounting for varying computational costs and activation compression sensitivities. In the case of a high computation savings target, MixA-Q can incorporate activation pruning to achieve better performance than pure mixed-precision or pruning method. Our main contributions are summarized as follows: + +1. We propose a novel mixed-precision activation quantization framework for window-based ViTs that investigates the intra-layer activation sparsity for efficient inference of quantized models. +2. We introduce a Two-Branch Swin Block architecture to replace the Swin blocks in Swin Transformer that enables mixed-precision execution of window-based attention. With this architecture, MixA-Q can be integrated with most quantization-aware training (QAT) and posttraining quantization (PTQ) methods with minor modification, making it flexible in terms of application. +3. We adopt sparsity-aware quantization adaptation (adapted from SpraseViT [2]) to adapt the model for mixed-precision activation sparsity. By improving the sampling algorithm with our uniform-sum compression ratio sampling, we improve the sampling efficiency and + +reduce the fine-tuning time required. + +4. When integrated with QAT methods, we show that MixA-Q reduces the quantization error of important areas during the sparsity-aware quantization adaptation through dynamic activation distillation. +5. Compared to directly applying activation pruning on the quantized model, our mixed-precision approach can be applied without training and is more robust to Out-Of-Distribution (OOD) inputs where the window selection is inaccurate. + +We evaluate MixA-Q on the COCO [17] dataset by integrating it with QAT and PTQ methods. MixA-Q achieves a lossless $1.35 \times$ computational speedup without training in PTQ configuration. On ultra-low bit width (4-bit), we integrate MixA-Q with the QAT method and achieve a lossless $1.25 \times$ speedup and a $1.53 \times$ speedup with only $1\%$ mAP drop by incorporating activation pruning. Additionally, through dynamic activation distillation (detailed in Sec. 4.1.2), our sparsity-aware quantization adaptation improves the mAP of the quantized W4A4 model (weights and activations both in 4-bit precision) by $0.7\%$ , reducing quantization degradation by $24\%$ . + +# 2. Related Work + +# 2.1. Vision Transformers + +Vision Transformers (ViTs) adapt the self-attention mechanism from NLP [29] to image processing [8]. While ViT showed impressive performance on image classification, it faced challenges with dense prediction tasks like object detection. Swin Transformer [22] introduces a hierarchical structure and shifted windowing to efficiently handle high-resolution images. Its linear computational complexity to image size and strong performance on dense tasks like detection and segmentation have made it particularly effective for a wide range of computer vision applications and has become the backbone for many vision models [3, 33]. + +# 2.2. Model Quantization + +Model quantization aims to reduce the computational and memory requirements of machine learning models by lowering the precision of weights and activations. By retraining the network and allowing the model to compensate for the quantization error, QAT methods can achieve very competitive quantization performance. For the image classification task, state-of-the-art QAT methods [14, 19] have achieved higher accuracy than the original floating-point model in ultra-low-bit precision (4 bits). Due to the high resource and time usage required by QAT methods, PTQ methods are favored for dense prediction tasks [15, 20] and LLMs [18]. Many prior PTQ methods [25, 26] have achieved impressive results on CNNs. Recently, many works have also investigated PTQ methods for ViTs in image classification and + +Figure 2. Overview of how our MixA-Q replaces the window pruning in SparseViT [2] to mixed-precision execution. Note that the LN and FFN following the window attention are omitted here. +![](images/6596503affca2c99d834bcfd0334fa684dcd136a737bd3406c2c94fa9508c7f2.jpg) +(a) Our mixed-precision activation quantization attention block, which replaces the pruning block in SparseViT [2]. Instead of skipping the computation of less important patches and copying the features from the last computation like Fig. 2b, we keep the computations in low precision. + +![](images/9d7702f220805f64f95c0865b45f6f56f8ff3037a23a83d458e82fbf683afff1.jpg) +(b) The window attention with activation pruning from SparseViT [2]. The computations on less important windows are skipped, and the latest features are forwarded. + +object detection tasks, such as RepQ [15] and EQR [34]. + +# 2.3. Mixed-precision Quantization + +Unlike uniform-bit quantization that aims to reduce the quantization error, mixed-precision quantization (MPQ) aims to achieve better precision and performance tradeoff by assigning different bit widths to activations and/or weights. Existing mixed-precision quantization methods can be classified into search-based approaches [31] and criterion-based approaches [6, 7, 28]. Most of these works focus on the mixed-precision quantization of weights, with some [5, 23] still using uniform bits for activation. For the mixed-precision quantization of activations, Kim et al. [12] found that the activation instability due to bit selection can affect the performance largely and propose to train a metanetwork for the bit selection of activations for different layers. PMQ[32] saves the computation of MLPs following attention layers by adapting the bit allocation of tokens according to the attention scores. Granular-DQ[30] dynamically quantizes different patches based on their information density in super-resolution tasks. + +# 2.4. Activation Pruning + +Pruning the computation on less important areas can improve latency and memory consumption without apparent accuracy loss. Due to the sparse nature of the attention mechanism, token pruning methods for ViTs have been well investigated, including using gating networks [13, 27], attention scores [9, 16], etc. SparseViT [2] prunes local windows of Swin Transformer on dense prediction tasks and achieves competitive performance. In activation pruning, the selected windows or tokens considered less important are pruned, meaning that the computations over these windows or tokens are skipped for certain layers, and the features from previous layers are simply forwarded. + +# 3. Mixed-Precision Activation Quantization + +In this section, we present the overall MixA-Q framework. Within the framework, we explore the adaptation of activation pruning to mixed-precision activation quantization. Instead of pruning the less important windows or tokens, we process them with the low-precision branch, thus saving the computation complexity without losing too much information. + +# 3.1. From Pruning to Mixed-Precision + +Before going into the details of our framework, we first answer this question: + +Why do we need mixed-precision activation quantization if we can directly apply the activation pruning method on the quantized model to further optimize it? + +It is because instead of skipping the computation of less important regions, retaining them in lower precision has several advantages: + +- Mixed-precision activation quantization doesn't change the computation flow of the network and thus can be integrated with PTQ methods without training. +- At high pruning ratios, most activation pruning methods suffer from obvious accuracy degradation due to drastic information loss. In this case, retaining some less important but relevant windows at low precision is beneficial. More details are discussed in Sec. 3.4 and Sec. 4.1.1. +- The robustness of activation pruning methods relies on simple window-token selection criteria [2] or light-weight layers [21]. In the case of out-of-distribution inputs, e.g. street in foggy weather, where window-token selection is inaccurate, activation pruning methods may suffer from drastic performance degradation due to pruning important patches. On the other hand, the performance of MixA-Q in the worst case is bounded below by the low-precision branch. We will further investigate this claim in + +# Sec. 4.1.3. + +- By updating the model only with important activations, MixA-Q can reduce the model's overall quantization error other than the latency improvement through dynamic activation distillation (more details are in Sec. 4.1.2). + +Hence, we adapt the window-level activation pruning proposed in SparseViT [2] to a mixed-precision activation quantization framework for Swin Transformers [22]. + +Replace Pruning with MP Execution Swin Transformer separates the feature map into non-overlapping image windows (e.g. $7 \times 7$ ) and performs multi-head self-attention (MHA) upon them to extract local features. Each MHA is followed by a layer normalization (LN) and a feed-forward network (FFN) layer. Taking advantage of this window-based attention design of Swin Transformer, SparseViT first gathers the features from the windows with the highest importance scores, then runs computations on the selected windows, and finally scatters them back to the original feature map. As shown in Fig. 2b, after certain windows are pruned at some point, the features stop being further processed, e.g. "D1" is only forwarded after being pruned at the second block. + +Instead of skipping the computations on less important windows, MixA-Q compresses them by assigning a lower bit width to them (annotated as "Attn Low" in Fig. 2a). In this way, the network's original computations upon those windows are still kept, but their computational cost is reduced. + +# 3.2. Two-Branch Swin Block + +To support the separated computation on high- and low-precision windows, we introduce the Two-Branch Swin Block in Fig. 3 that replaces the original swim blocks within Swin Transformer. Each two-branch swin block takes as input a sequence of activation windows. As in SparseViT, the importance score of each window is defined as its L2 norm. For each stage, the importance score is only computed once before the execution of the first swim block and then shared across the whole stage. We call the layers that perform computation on high-precision windows high-precision branch and the layers that perform computation on low-precision windows low-precision branch. Given a compression ratio (detailed in Sec. 3.3), we gather those windows with the highest importance scores, feed them to the high-precision branch, and then feed the rest of the windows to the low-precision branch. + +The layer normalizations are duplicated for the high- and low-branches to address the distribution shift after the separation. After the duplication, parameters within layer normalizations can be updated independently during fin-tuning (in QAT) or reparameterization (in PTQ). On the other hand, multi-head attention layers (MHA) and feed + +forward networks (FFN) are created as shadow layers that share the same underlying weights and bias while independent step sizes and zero points can be kept for the high- and low-precision branches. During training, the gradients of shadow layers from high- and low-precision branches will flow through the same set of parameters and be accumulated by the autograd engine of Pytorch. + +# 3.3. Evolutionary Search of Compression Ratios + +Following the design of SparseViT [2], each two consecutive swim blocks (one with shifted windows and one without) are assigned a fixed compression ratio, which is the proportion of windows that should be processed by the low-precision branch. The compression ratios are hyperparameters that can be optimized with an evolutionary search (detailed in Sec. 3.3). The search for optimal compression ratios can be formed as a bi-objective optimization problem: + +- Objectives: computational savings, mAP (mean average precision) +- Variables: compression ratios for each stage + +The computational saving is computed as the proportion of bit operations that are saved by applying the compression ratios. mAP is the mean average precision on the COCO val dataset. In the case of Swin-Tiny, there are 6 compression ratios for the 12 swim blocks in the model. To narrow the search space, we discretize the compression ratios to $\{0\%, 10\%, \dots, 80\}$ . We use the NSGA-II [4] algorithm implemented in pymoo [1] to search for the optimal ratios iteratively. + +Sparsity-aware Quantization Adaptation For PTQ methods, the same quantized model is used for evaluation during the evolutionary search. However, for QAT methods, the model needs to be fine-tuned after changing the compression ratios, which makes searching compression ratios inapplicable. Thus, we adopt a sparsity-aware quantization adaptation (SAQA), which is similar to the sparsity-aware adaptation (SAA) introduced in SparseViT [2]. At first, we quantize the model with uniform-bit QAT method on the high precision. Then, we perform the SAQA by training the model while randomly sampling a set of compression ratios at each iteration, i.e., a random proportion of activations is assigned to the low-precision branch. After SAQA, the model achieves a good estimated performance for different compression ratio configurations without re-training. + +Uniform-sum Compression Ratio Sampling To make evolutionary search and SAQA more sample efficient, we propose an algorithm called uniform-sum compression ratio sampling. SparseViT uses a naive sampling algorithm, where the ratios for each layer are uniformly sampled from $\{0\%, 10\%, \dots, 80\% \}$ . This causes the averaged pruning ratio of the model to have a scaled Irwin-Hall distribution + +![](images/e465e57b350bd58bfd13e1ada62c086fd5096f402b94ee57a357a31f54e1fb8b.jpg) +Figure 3. Two-branch swim block that replaces the original swim blocks in Swin Transformer. The windows are gathered into high- and low-precision windows according to the importance score. They go through the high- and low-precision branches separately and then are scattered back to the feature map. + +(uniform sum distribution), a bell-shaped distribution centered at $40\%$ . This makes the sampling of evolutionary search inefficient. Furthermore, the adapted model shows inaccurate estimations on compression ratios that have an average far away from the center. In our uniform-sum ratio sampling, we begin by randomly sampling a scalar value $S$ from a predefined range, representing the target sum of compression ratios across all blocks. Given $S$ , we then sample the individual compression ratios $\{r_0, r_1, \ldots, r_n\}$ using a Dirichlet distribution, ensuring that their sum is constrained to $S$ . To enforce an upper bound on each ratio, we apply a rejection sampling criterion: if any $r_i$ exceeds 0.8, the sampled set is discarded, and the process is repeated until a valid set is obtained. More details can be found in Appendix 6.1. + +# 3.4. Activation Pruning Incorporation + +Activation pruning and mixed-precision quantization are not mutually exclusive. Compared to mixed-precision activation quantization, pruning-based methods have higher efficiency in terms of activation sparsity exploitation at the cost of more information loss. For each less important window, the pruning-based method saves $100\%$ of its computations by skipping them. On the other hand, mixed-precision activation quantization saves $50\%$ of computations by downgrading the precision to half of the bit widths. In the case of a high computation savings target, pruning the most unimportant windows while keeping the less important but still relevant windows in lower precision can leverage the activation sparsity efficiently while avoiding drastic information loss due to aggressive pruning. + +With this insight, we also incorporate activation pruning in MixA-Q that can be activated when integrating with QAT methods. When activation pruning is adopted, each two + +consecutive swim blocks are assigned an additional pruning ratio, apart from the compression ratio. In the window selection phase, the windows with the lowest importance scores will be pruned, and the computations upon them will be skipped as in Fig. 2b. Then, MixA-Q continues separating the rest of the windows and processing them in two precisions. + +# 4. Experiments + +In this section, we evaluate MixA-Q by integrating it with QAT and PTQ methods respectively. We evaluate our method's computation savings with relative computation cost or speedup in terms of bit operations (BOPs) of the backbone, as our method is only applied to the backbone. + +# 4.1. QAT Result on COCO + +Setup We integrate our method with a QAT method, OFQ [19], to quantize a Mask R-CNN [11] with SwinTiny [22] backbone. The COCO [17] dataset is used for training and evaluation. We first quantize the floating-point model with OFQ on W4A4 (weight and activations both in 4-bit precision). This W4A4 OFQ model serves as a baseline model for evaluating our mixed-precision activation quantization method, MixA-Q, and the activation pruning method, SparseViT [2]. When applying MixA-Q, the less important windows are assigned a bit width of 2. + +For all the metrics of SparseViT reported in this section on the W4A4 OFQ model, we follow the procedure reported in the SparseViT [2] paper. We first train the sparsity-aware adapted model and use evolutionary search to search for the optimal pruning ratios, and finally fine-tune the model. The optimal pruning ratios that we found on the W4A4 OFQ model and the performance degradation after applying the pruning align with the metrics reported in [2]. + +![](images/17e83a5a2b444a2c36744f29f180030ac2abcc704481d5ebcf007e7b6b0f4c2d.jpg) +Figure 4. Pareto fronts of different methods. The x-axis is the relative computation cost in terms of bit operations (BOPs) to the baseline model (W4A4 OFQ model). "MixA-Q+Act.Prun." represents MixA-Q incorporated with $30\%$ activation pruning. + +# 4.1.1. Analyses and Comparisons + +First, we present the Pareto fronts of different methods in Fig. 4 to offer insight into their performance variations at different relative computational costs (abbreviated as relative cost) in terms of bit operations (BOPs). It can be observed from the figure that the precision and performance trade-off of MixA-Q and SparseViT is better than the uniform-bit OFQ. At higher relative costs $(\geq 0.8)$ , MixA-Q outperforms other works in terms of mAP. Notably, MixA-Q shows higher mAP than the OFQ model in W4A4. The reason behind this will be further investigated in Sec. 4.1.2. However, at relative costs $\leq 0.75$ , we can observe that SparseViT starts to have higher mAP than MixA-Q due to its higher efficiency in terms of sparsity utilization, as discussed in Sec. 3.4. To leverage this advantage of activation pruning while avoiding the drastic information loss, we incorporate MixA-Q with $30\%$ overall activation pruning. As shown by the purple dots in Fig. 4, the MixA-Q incorporated with activation pruning outperforms the pure activation pruning method, SparseViT, at relative costs $(\leq 0.7)$ . + +We also report numerical results in Tab. 1 for high relative costs ( $\geq 0.75$ ) and Tab. 2 for low relative costs ( $\leq 0.7$ ). As shown in Tab. 1, MixA-Q achieves $1.24 \times$ speed up with slightly better mAP than the W4A4 OFQ model. Compared with the W4A3 OFQ model where precision of activations are uniformly downgraded to 3 bits, we achieve a higher $1.35 \times$ speed up with less than $1\%$ mAP loss ( $1.7\%$ for W4A3 OFQ). From Tab. 2, it can be noticed that by incorporating activation pruning, MixA-Q achieves a $1.53 \times$ speedup with only $1\%$ mAP loss. For even higher speedups of $1.66 \times$ and $1.82 \times$ , MixA-Q with activation pruning continuously achieves higher mAP than SparseViT at the same relative costs. This shows that retaining less important but still relevant windows in lower precision helps recover some + +
MethodAct Bit#BOPs (T)mAP
Full-Precision3288.4246.0
OFQ [19]411.0543.1
38.29 (1.33×)41.4
SparseViT [2]3.2*8.92 (1.24×)43.1
2.96*8.28 (1.33×)42.7
MixA-Q (Ours)411.0543.8
3.2*8.92 (1.24×)43.2
2.94*8.21 (1.35×)42.3
+ +Table 1. Quantization results of different methods on the COCO dataset. mAP is the bounding box average precision for object detection. Act Bit represents the activations' equivalent bit width. * indicates that the bit width is a computationally weighted average. #BOPs (T) is the number of bit operations in trillion scale. The scale shown after #BOPs indicates the computational speedup compared to the W4A4 OFQ model. MixA-Q and SparseViT are both applied to the model quantized with OFQ in W4A4 precision. + +
MethodAct Bit#BOPs (T)mAP
OFQ [19]411.0543.1
SparseViT [2]2.6*7.24 (1.53×)41.4
2.4*6.63 (1.66×)40.8
2.2*6.08 (1.82×)40.1
MixA-Q2.6*7.24 (1.53×)42.1
+Act.Prun.2.4*6.63 (1.66×)41.5
2.2*6.08 (1.82×)40.5
+ +Table 2. Results of SparseViT and MixA-Q with activation pruning (denoted as MixA-Q+Act.Prun.) at high speedups. + +performance degradation caused by aggressive pruning and can achieve better mAP at a comparable relative cost. + +# 4.1.2. Dynamic Activation Distillation + +After applying SAQA on the W4A4 OFQ model, our MixA-Q model shows a mAP enhancement as observed in Fig. 4 and Tab. 1. In this section, we explore the reason behind it. We confirm that this is a benefit brought by our SAQA because the mAP enhancement can't be observed by continuing training the W4A4 OFQ model or applying the pruning-based SAA from SparseViT. + +From Tab. 3, we can observe that after applying SAQA, the model has a higher mean signal-to-quantization-noise ratio (mSQNR $\uparrow$ ) at later stages but lower mSQNR at early stages. We attribute this phenomenon to the fact that during SAQA, only gradients from important windows can flow through the high-precision (4-bit) branch. This process guides the model to focus on reducing the quantization error of important windows during training. We call this process dynamic activation distillation as it selects important parts from activations to better update the quantization-related parameters. + +In Fig. 5, we visualize the SQNR changes after applying SAQA, which aligns with our explanation and the results in Tab. 3. At early stages (Stage 0 and Stage 1), quantization + +noise is reduced (red windows) for foreground windows but increases (blue windows) for background windows, leading to lower overall SQNR due to the abundance of background windows. At stage 2 and 3, the quantization noise of more windows is reduced because the important windows from early stages contribute more to the high-level features at later stages, corresponding to the mSQNR increase at later stages in Tab. 3. In general, SAQA guides the model to reduce quantization noise of important windows and thus improve the mAP. + +
mean SQNR↑
before SAQAafter SAQA
Stage 013.7013.60
Stage 19.709.50
Stage 26.906.96
Stage 37.818.14
+ +# 4.1.3. Robustness of Pure Activation Pruning + +Performance on the test dataset is not the only criterion for evaluating the quality of a method. The ability to detect objects regardless of image distortions or weather conditions is crucial for safety-critical systems like autonomous driving. SparseViT relies on the L2 norm of features to effectively decide the windows' importance. However, for the first stage, the feature map is only dependent on the local patch embedding layer, which lacks the global view and can be largely affected by natural image shift. Applying activation pruning with inaccurate window selection will result in the pruning of important parts, which leads to catastrophic performance degradation. On the other hand, although our MixA-Q is also affected negatively by inaccurate window selection, the computations of the wrongly compressed windows are not skipped but kept in low precision. In the worst case, where only important windows are computed with low precision, the model's performance is still guaranteed by the low precision branch. + +We use the weather scenario from the COCO-O [24] dataset for evaluating the model's robustness on out-of-distribution inputs, which consists of real-world images that contain objects in challenging weather conditions, e.g. rain, snow, and fog. + +From Tab. 4, it can be observed that although SparseViT and MixA-Q both cause a higher decay rate on OOD inputs than the uniform-bit quantized model, but the model pruned by SparseViT has a worse degradation rate than MixA-Q. This is consistent with our claims in Sec. 3.1. In Fig. 6, the windows selection of the SparseViT model on the OOD sample is visualized. It can be observed that compared + +Table 3. Mean SQNR at different stages before and after the SAQA over 1000 samples. The SQNR is computed between the different stages' output features of the quantized model and those of the floating-point model. + +
mAPmAPoro↓mAPwrw↓
OFQ, W4A443.134.220.6//
MixA-Q,1.4×41.530.526.528.830.6
SparseViT, 1.4×42.429.630.224.043.4
+ +Table 4. mAP on COCO [17], COCO-O [24] $(\mathrm{mAP}_o)$ dataset, and on COCO with worst window selection $(\mathrm{mAP}_w)$ . The worst window selection is achieved by calculating the importance score in reverse order. $1.4\times$ means the model is compressed by MixA-Q or pruned by SparseViT to reach the speedup of $1.4\times$ in terms of computations. $r_d^o$ and $r_d^w$ is the degradation rate of $\mathrm{mAP}_o$ and $\mathrm{mAP}_w$ with respect to the mAP. + +to Fig. 1, the window selection of SparseViT is distracted largely by the fog. As a result, many important windows are wrongly pruned, causing the performance degradation we observe. In the worst case, SparseViT has an even higher $43.4\%$ degradation rate compared to MixA-Q $(30.6\%)$ . + +# 4.2. QAT Result on COCO Panoptic Segmentation + +We further evaluate MixA-Q on the COCO panoptic segmentation dataset. We use Mask2former with Swin-Tiny backbone, and the QAT settings are the same as in Sec. 4.1. As shown in Fig. 7a, the performance enhancement (as in Sec. 4.1.2) after SAQA can still be observed, and $1.25 \times$ speedup is achieved with $\leq 1\%$ PQ drop. Compared to the object detection task, the relative performance of MixA-Q versus SparseViT improves on the segmentation task. MixA-Q surpasses SparseViT by large at relative cost $\geq 0.8$ . We speculate that this is because panoptic segmentation requires classifying every pixel (80 "things" and 53 "stuff"), worsening performance degradation caused by pruning. + +# 4.3. PTQ Result on COCO + +Setup We integrate MixA-Q with a representative PTQ method, RepQ [15]. As in QAT, we use Mask R-CNN with Swin-Tiny backbone and the COCO dataset for evaluation. The baseline model is quantized to W4A8. One random sample from the training set is used for calibration. When applying MixA-Q, the less important windows are assigned a bit width of 4. + +RepQ makes post-training updates to the weights and bias of the QKV layer and the first layer of FFN. To be compatible with our sharing weights setup, we use the full feature map as calibration data to initialize the step sizes of high- and low-precision branches so that the updates to the two branches' weights will be the same. As for the bias, we make them independent in PTQ. Note that during the evolutionary search, we evaluate different compression ratios without recalibrating the model. + +In Fig. 7b, we compare applying MixA-Q on the baseline model with uniformly reducing the activation bit widths of it from 8 to 5. We show the result on two different random calibration sets. It can be observed that MixA-Q + +![](images/8a50cc666f92051cfb5a1f56c20e02b1c3fb019a70b4f4855230e91cad5b99b2.jpg) +Input Image + +![](images/23bfc67d2c0b30c917a4a3ee18a6dce81a52b8978705c13822328d5e7dc6e3c8.jpg) +Stage 0 +Figure 5. Signal-to-quantization-noise ratio (SQNR↑) changes across different stages before and after SAQA. Red implies higher SQNR after SAQA, and blue implies lower SQNR. At early stages, the model learns to decrease the quantization noise of important areas, which leads to an increase in overall SQNR at later stages. + +![](images/a4a1a337a9cbe38ff2a9b439cf8b63cdb88d62273796ee12b9d0555f584a8da6.jpg) +Stage 1 + +![](images/d27bcd828a65748ef66d7842fb397c4c68c761ed94b443438f82b611fd3c8fce.jpg) +Stage 2 + +![](images/0dfb6b108f3646f4eb6b706c5a129806938ec87f98ab4c2e9772e150dfdcf3a8.jpg) +Stage 3 + +![](images/f6ece3fa073a127fdf20133c286d8c94e467ae6eeba72442eeafcbef7b7c4bac.jpg) +(a) Foggy weather + +![](images/8a1cf687f7ac7998a44e1c607a32983415f9e67aaf185a129972d36288c388a9.jpg) +(b) Window selection of SparseViT at stage 0. Red windows are important windows selected to be kept and orange windows are pruned. + +![](images/d9efdbaf0f0e86ac5181c9312b671630dc4f3f3bda914eebbdd17cfdc08e682f.jpg) +Figure 6. Visualization of the window selection of SparseViT over an OOD sample from COCO-O +(a) QAT Pareto front of MixA-Q and SparseViT on COCO Panoptic Segmentation dataset. Compared to the object detection task, the relative performance of MixA-Q versus SparseViT improves on the segmentation task. +Figure 7. Further evaluation result on panoptic segmentation task and post-training quantization. + +![](images/04637d5bad921b045423e55cb16da698ef630e237983b1cb046ffb4af08ac5e9.jpg) +(b) PTQ Pareto front of MixA-Q and RepQ on two different calibration sets. MixA-Q consistently has better computation cost and performance trade-off compared to the uniform-bit RepQ. + +constantly has better computational cost and performance trade-off compared to RepQ. Another benefit brought by MixA-Q is that bit widths from 5 to 7 are not supported by most of the general-purpose computing hardware, while our solution is based on a mixed 4-bit and 8-bit precision. + +# 4.4. Ablation Study + +SAQA from scratch In our experiments in Sec. 4.1, we quantize the model into W4A4 before adding the low-precision branch and starting the SAQA. In this section, we explore whether directly adding a low-precision branch to the floating-point model and starting the SAQA has impact. + +
Act bitmAP
SAQA3.36*43.4
3*42.4
SAQA from fp3.36*42.8
3*42.1
+ +Table 5. mAP comparison of SAQA based on model already quantized and SAQA from floating-point model + +From Tab. 5, it can be observed that starting SAQA directly from the floating-point model results in worse mAP compared to starting SAQA based on the model that has been quantized on W4A4. Given that the loss landscape of ViT quantization is highly non-smooth [10], we speculate that jointly training the two aggressively quantized branches makes the model converge sub-optimally. + +Windows Elevation: In MixA-Q, since less important windows are not pruned but instead kept in lower precision, it may make sense to elevate some windows to high precision again in later blocks. However, according to our experiments, allowing the elevation of previously compressed activation gives slightly worse $(-0.1\%)$ or the same mAP. We speculate that the consistent computation precision of windows within one stage is important. + +# 5. Conclusion + +In this work, we introduced MixA-Q, a mixed-precision activation quantization method that revisits activation sparsity from a mixed-precision perspective to improve efficiency in window-based vision transformers. MixA-Q dynamically assigns high and low bit widths to different windows, effectively leveraging intra-layer activation sparsity. Compared to activation pruning methods that discard computations on less important windows, MixA-Q retains them in lower precision. This enables MixA-Q to be integrated training-free and gives greater robustness against out-of-distribution (OOD) inputs. On the COCO dataset, MixA-Q achieves a $1.35 \times$ speedup in W4A8 PTQ settings and a $1.25 \times$ speedup in W4A4 QAT settings without accuracy loss. By incorporating activation pruning, MixA-Q further achieves $1.5 \times$ with a $1\%$ mAP drop. + +# References + +[1] Julian Blank and Kalyanmoy Deb. Pymoo: Multi-objective optimization in python. 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While recent State Space Models (SSMs) like Mamba have shown promise through input-dependent selectivity on three key parameters, the critical forget-gate (A matrix) controlling temporal memory remains static. We address this limitation by introducing a mixture of experts approach that dynamically selects contextually relevant A matrices based on input features, enhancing representational capacity without sacrificing computational efficiency. Extensive experiments on the 50Salads, Breakfast, and Assembly101 datasets demonstrate that MixANT consistently outperforms state-of-the-art methods across all evaluation settings. Our results highlight the importance of input-dependent forget-gate mechanisms for reliable prediction of human behavior in diverse real-world scenarios. The project page is available at https://talalwasim.github.io/MixANT/. + +# 1. Introduction + +Human activity anticipation represents a fundamental challenge in computer vision, requiring models to predict future human actions from partial observations. This capability is crucial for applications ranging from assistive technologies to autonomous driving systems, where timely intervention depends on accurate forecasting of human intentions and behaviors. In particular, long-term dense action anticipation [1, 2, 11] presents a particularly challenging problem: generating multiple and continuous, frame-by-frame predictions of future activities, often extending several minutes ahead. In order to handle the uncertainty for this task, stochastic approaches have been proposed [8, 35, 36, 43] that predict multiple plausible future samples. While recent approaches [35, 36, 43] use a diffusion model to generate multiple predictions for the same observations, these approaches differ in the architecture that is used within the diffusion model, including gated temporal convolutions [35] + +![](images/5f9e442a4a127e34749e6dd3c5e8d1823e9ce0df6f1cbed12b6496af0e0b77e7.jpg) + +![](images/f0ba613ec7caee568df5c0569f73bd53423dea362099bb15adf2742ea9987988.jpg) +Figure 1. The current state-of-the-art method [36] employs standard Mamba blocks for stochastic dense action anticipation. In contrast, we introduce the MixMamba block, where each block dynamically selects an appropriate $\mathbf{A}$ matrix based on the input sequence. + +and Transformers [43]. While Transformers have shown impressive capabilities in modeling long-range dependencies, their quadratic computational complexity with respect to sequence length limits their practical application to extended temporal horizons as they occur in long-term dense anticipation. MANTA [36] thus utilizes the Mamba architecture [12] due to its remarkable capabilities in handling long sequences with near-linear computational complexity. + +The standard Mamba model [12] applies input-dependent selectivity to three of its four key parameters, dynamically adapting the model's behavior based on contextual cues within the observed sequence. Specifically, these parameters include the input gate, output gate, and time-step parameter. However, one critical parameter—the forget-gate (the A matrix) that controls how the hidden state evolves over time—lacks this input dependence. This forget-gate parameter determines how much past information is remembered or forgotten. While [36] demonstrated that input dependence on the input, output and time-step parameters is particularly important for long-term dense action anticipation, the fourth parameter, the matrix A, is independent of the input as illustrated in Fig. 1. + +This raises a particularly important research question, as + +![](images/26a48b8c7ac457d043038ee7b4c2d480254083ebba1e0ac8934bba805ebdc143.jpg) +Figure 2. Our architecture and its components. In the MixANT architecture (a), the first $K_{0}$ blocks are standard Mamba blocks and the rest $(K - K_{0})$ are MixMamba blocks (b). Each MixMamba block contains a bi-directional MixMamba layer (c). In contrast to the standard Mamba unit (e) where $\mathbf{A}$ is fixed for all input sequences, the MixMamba unit (d) contains a router that selects the relevant $\mathbf{A}$ matrix depending on the input sequence. + +the A matrix's role in controlling temporal memory is particularly relevant for anticipation tasks. Depending on the specific input context, sometimes past information is critically important, while in other contexts, it may be less relevant. Moreover, in the stochastic long-term dense anticipation task, the input sequence consists of observed data and padded zeros representing future unknown labels. In this scenario, it is also desirable to have selectivity on the hidden state through forget-gates such that it selectively ignores the padded zero sequence. Therefore, any form of input dependence on this matrix, that controls the evolution of the hidden state, is important. However, introducing input dependence to the A matrix presents substantial technical challenges. Direct computation would either require query-key like multiplication, which diminishes the sub-quadratic complexity advantage Mamba models, or a large MLP, which adds significant computational overhead. + +In this work, we address this challenge by introducing MixANT, a mixture of $\mathbf{A}$ for ANTicipation, which enhances the network's representational capacity with minimal computational overhead. As shown in Fig. 2, our method employs layers called MixMamba that dynamically select the most contextually relevant $\mathbf{A}$ matrix based on input features. This approach introduces input dependence without sacrificing computational efficiency. To the best of our knowledge, we propose the first mixture of experts ap + +proach specifically for the $\mathbf{A}$ matrix in Mamba-based architectures. + +We demonstrate that this novel architecture achieves state-of-the-art performance on stochastic long-term dense anticipation task through extensive experimentation on three benchmark datasets: 50Salads [32], Breakfast [18], and Assembly101 [29]. Our approach consistently outperforms existing methods across all evaluation settings, and our results highlight the potential of our approach to advance the field of stochastic dense action anticipation and enable reliable prediction of human behavior in diverse real-world scenarios. + +# 2. Related Work + +Action anticipation research [41] is divided into different branches, but mainly consists of short-term approaches (predicting actions within seconds) [9, 10, 24, 28, 33, 34, 38, 39, 42] and long-term approaches (forecasting multiple actions over minutes). Our work focuses on long-term dense anticipation, which requires predicting both action sequences and their durations across specified future frames. Unlike methods that treat anticipation as ordered [7, 23, 24, 38] or unordered [26, 38, 43] transcript prediction without temporal boundaries, our work focuses on long-term dense anticipation. This application requires pre + +dicting both action sequences and their durations across specified future frames. + +Dense anticipation approaches further split into deterministic models [1, 11, 17, 28] that generate single predictions, and stochastic methods [8, 37] — including ours — that produce multiple plausible futures for each observation. Other methods, e.g. [35, 43], can generate predictions in both stochastic and deterministic settings. [8] pioneered stochastic dense anticipation by extending RNN architecture to generate multiple samples. [37] enhanced this framework using adversarial learning to improve prediction diversity. Recent approaches [35, 43] have advanced beyond requiring ground-truth actions by performing simultaneous past classification and future forecasting. Specifically, [43] combined a diffusion model with the FUTR encoder [11] to model uncertainty in future actions, while [35] introduced a gated temporal diffusion network that models uncertainty in both past and future actions, achieving state-of-the-art results. + +Traditional attention-based architectures face efficiency challenges due to quadratic complexity with sequence length, inspiring the development of State Space Models [13, 30] that offer linear scaling with sequence length. Mamba [12] enhances this framework through selective state space modeling with input-dependent selection mechanisms, making it particularly effective for long sequence processing. This efficiency has led to Mamba's adaptation across various fields including anticipation [36], vision [19, 22], and as backbones for diffusion models in generative tasks [14, 25]. Recently, [36] also utilized bi-directional Mamba blocks similar to [19] for stochastic long-term anticipation. Our work uniquely leverages Mamba's capabilities by introducing a novel "mixture of $\mathbf{A}$ " matrices approach that addresses the shortcomings of [12] mentioned in the introduction. + +The Mixture of Experts (MoE) architectures allow for significant scaling of model parameters with minimal computational overhead. First proposed by [15, 16], MoE leverages conditional computation, i.e., activating only specialized "expert" sub-networks for specific inputs. By implementing this sparse activation strategy, MoE-based models can substantially increase model parameters with reasonable computational demands. The MoE technique has been successfully applied to both transformer-based and, more recently, Mamba-based architectures. Similar to our architecture in spirit are Mamba-based methods leveraging a mixture of experts (MoE) [3, 20, 27]. However, these approaches differ from our method in key ways. Both [3] and [27] utilize standard Mamba blocks [12] while employing MoE only to MLPs outside the Mamba block. Meanwhile, [20] employs a mixture-based architecture for modality-aware selection but unlike our method it uses a shared A matrix (of Mamba block) constraining the expres + +sivity of the network. + +# 3. Observation-dependent Memory Propagation in Mamba + +The work [36] showed that state-space models outperform transformer and other architectures for stochastic long-term dense action anticipation. The approach utilizes the bidirectional Mamba layer [12, 19] for modeling temporal relations between past observations and future actions. A key feature of this block compared to previous state-space models are the input-dependent parameters, as we will discuss in Sec. 3.1. The temporal memory propagation, however, which is steered by the matrix $\mathbf{A}$ , remains input-independent as it is illustrated in Fig. 1, i.e., the learned matrices $\mathbf{A}$ for each block do not change for different observations. This poses a major limitation for action anticipation since the way how temporal memory should be propagated between observations and future actions depends on the context of the observation. Indeed, we will show that the matrices $\mathbf{A}$ vary depending on the semantic context, see Fig. 6. + +We will first describe the Mamba layer [12, 19] in Sec. 3.1 and our extension in Sec. 3.2. The entire approach for stochastic long-term dense action anticipation is then described in Sec. 4. + +# 3.1. Mamba Layer + +State-space models define a mapping from an input sequence $x_{t}$ to an output sequence $y_{t}$ through a latent state $h_{t}$ using a first-order ordinary differential equation discretized with a time-step parameter $\Delta$ : + +$$ +h _ {t} = \overline {{\mathbf {A}}} h _ {t - 1} + \overline {{\mathbf {B}}} x _ {t}, \tag {1} +$$ + +$$ +y _ {t} = \mathbf {C h} _ {t}, \tag {2} +$$ + +$$ +\bar {\mathbf {A}} = \exp (\Delta \mathbf {A}), \tag {3} +$$ + +$$ +\bar {\mathbf {B}} = (\Delta \mathbf {A}) ^ {- 1} \left(\exp (\Delta \mathbf {A}) - I) \Delta \mathbf {B}. \right. \tag {4} +$$ + +Mamba [12] enhances this framework by making most parameters input-dependent, i.e., $\mathbf{B}(x) \in \mathbb{R}^{B \times T \times N}$ , $\mathbf{C}(x) \in \mathbb{R}^{B \times T \times N}$ , and $\Delta(x) \in \mathbb{R}^{B \times T \times D}$ are computed as functions of the input $x \in \mathbb{R}^{B \times T \times D}$ where $B$ is batch-size, $T$ is sequence length, $N$ is latent state dimension, and $D$ is channel dimension. $\Delta$ controls the flow of information from the input $x_{t}$ to the hidden state $h_{t}$ . $\bar{\mathbf{B}}$ modulates the input. $\bar{\mathbf{A}}$ serves as a forget-gate, determining which information persists from previous states and how quickly past information decays, effectively controlling the model's memory duration. Finally, the $\mathbf{C}$ parameter filters state information for outputs, determining which aspects of the internal state are expressed in the output signal. While [12] made the hypothesis that it is sufficient to make $\Delta$ input-dependent and keep $\mathbf{A}$ input-independent, we demonstrate that this is not true + +for the task of long-term dense action anticipation, where very long sequences are processed. + +# 3.2. MixMamba Layer + +Making the A matrix input-dependent presents substantial computational challenges. A straightforward implementation would either require query-key multiplication, which would negate Mamba's sub-quadratic complexity advantage for long sequences, or necessitate a very large MLP, which would introduce significant computational overhead and parameter inefficiency. For dense anticipation tasks specifically, where models must effectively reason over both observed and unobserved regions of input sequences, this limitation is particularly restrictive. An input-dependent A matrix would enable more nuanced control over how past information is selectively retained or forgotten based on the content of observed tokens. + +To address these challenges while maintaining computational efficiency, we propose a mixture-of-experts approach for the $\mathbf{A}$ matrix. Rather than computing a single input-dependent $\mathbf{A}$ matrix directly, we maintain multiple expert $\mathbf{A}$ matrices and employ a softmax gating mechanism to select the appropriate combination based on input characteristics. + +Building upon the S6 algorithm [12], we propose $\mathrm{S6^{+}}$ which enhances the selection mechanism by implementing a mixture approach for the $\mathbf{A}$ matrix. Instead of using a single fixed $\mathbf{A}$ matrix, we define a set of $E$ expert matrices $\{\mathbf{A}_1,\mathbf{A}_2,\dots,\mathbf{A}_E\} \in \mathbb{R}^{E\times D\times N}$ . For a given input sequence, we compute a gating vector $\gamma (x)\in \mathbb{R}^{B\times E}$ based on the projected mean of the input tokens $\gamma$ : + +$$ +\gamma (x) = \operatorname {s o f t m a x} \left(W _ {g} \cdot \operatorname {m e a n} (x)\right), \tag {5} +$$ + +where $W_{g}\in \mathbb{R}^{D\times E}$ is a learnable projection matrix. The matrix $\mathbf{A}$ is then selected by: + +$$ +\mathbf {A} (x) = \mathbf {A} _ {\hat {e}}, \quad \hat {e} = \underset {e} {\arg \max } \gamma_ {e} (x), \tag {6} +$$ + +where $\gamma_{e}(x)$ is the $e$ -th element of the routing vector $\gamma(x)$ . Note that during training, both $\{\mathbf{A}_1, \mathbf{A}_2, \dots, \mathbf{A}_E\}$ and $\gamma(x)$ are learned, but it requires an additional loss term as we will discuss in Sec. 4.3. + +The general structure of our MixMamba layer follows the bi-directional approach [19] with the $\mathrm{S6^{+}}$ algorithm as illustrated in Fig. 2(c). The processing flow for both paths is given by + +$$ +\hat {F} _ {\mathrm {F w d}} = \sigma \left(H ^ {K} * \operatorname {F F} \left(F _ {t} ^ {l}\right)\right), \quad \hat {F} _ {\mathrm {B w d}} = \sigma \left(H ^ {K} * \operatorname {F F} \left(\overleftarrow {F _ {t} ^ {l}}\right)\right), \tag {7} +$$ + +where $H^{K}$ is a 1D convolutional filter with size $K$ , flipping across the temporal dimension is denoted as $\leftarrow$ , and * represents the convolution operator. For both forward and backward paths, we apply our mixture-of-experts approach: + +$$ +W _ {t} ^ {l} = \mathrm {S} 6 ^ {+} \left(\hat {F} _ {\mathrm {F w d}}\right), \quad B _ {t} ^ {l} = \mathrm {S} 6 ^ {+} \left(\hat {F} _ {\mathrm {B w d}}\right). \tag {8} +$$ + +Similar to the Mamba layer, we apply a residual gating mechanism and combine the outputs: + +$$ +W _ {t} ^ {l} = W _ {t} ^ {l} \odot R _ {t} ^ {l}, \quad B _ {t} ^ {l} = \overleftarrow {B _ {t} ^ {l}} \odot R _ {t} ^ {l}, \tag {9} +$$ + +$$ +O _ {t} ^ {l} = \operatorname {F F} \left(W _ {t} ^ {l} + B _ {t} ^ {l}\right) \tag {10} +$$ + +where $R_{t}^{l} = \sigma (\mathrm{FF}(F_{t}^{l}))$ and $\odot$ represents element-wise multiplication. + +This mixture-of-experts approach for the $\mathbf{A}$ matrix enhances the model's ability to selectively process temporal information, which is crucial for tasks involving long sequences with varying temporal dependencies. By dynamically weighting different expert $\mathbf{A}$ matrices based on input characteristics, the $\mathrm{S6^{+}}$ algorithm can adapt its temporal processing strategy to the specific patterns present in the data, enabling more effective modeling of complex sequential relationships. + +# 4. MixANT Architecture for Stochastic Long-Term Dense Action Anticipation + +In this section, we present our approach for long-term stochastic dense action anticipation that is based on the bidirectional MixMamba layer described above in Sec. 3.2. For a fair comparison, we follow the diffusion architecture [36], which we discuss in Sec. 4.1. In Sec. 4.2, we describe the proposed MixANT architecture, which is illustrated in Fig. 2(a). In Sec. 4.3, we finally describe the loss functions. Our final loss includes a novel load balancing loss, which encourages that the router in the MixMamba unit (Fig. 2(d)) utilizes and learns all matrices and not only a subset during training. + +# 4.1. Diffusion for Stochastic Long-Term Dense Action Anticipation + +Following [35], we employ a diffusion model framework for stochastic long-term dense action anticipation. The diffusion model learns the distribution of per-frame actions given a set of observed frames: + +$$ +\tilde {Y} _ {1: P + F} \sim p \left(Y _ {1: P + F} \mid \mathbf {x} _ {1: P}\right), \tag {11} +$$ + +where $P$ is the number of observed frames, $F$ is the number of future frames to predict, $\mathbf{x}_{1:P}$ is the sequence of observed frames, $Y_{1:P + F}$ represents the random variables for each frame of the entire sequence, and $\tilde{Y}_{1:P + F}$ represents the sampled action label for each frame. To condition the anticipation on the observed visual frames, a conditioning vector $\mathcal{X}$ is created by extending the observed visual features with zeros for future frames: + +$$ +\mathcal {X} = \left\{\phi \left(x _ {1}\right), \dots , \phi \left(x _ {P}\right), \underbrace {0 , \dots , 0} _ {F} \right\} \tag {12} +$$ + +where $\phi (x_{i})$ represents visual features extracted from the $i$ -th observed frame. For a fair comparison, we use the same features that have been used in previous works. After sampling $\hat{Y}_T\sim \mathcal{N}(\mathbf{0},\mathbf{I})$ , the diffusion model gradually generates a sample $\hat{Y}_{1:P + F} = \hat{Y}_0$ after $T$ iterations + +$$ +\hat {Y} _ {t - 1} = G _ {\theta} \left(\hat {Y} _ {t}, \mathcal {X}, t\right), \tag {13} +$$ + +based on an anticipation generator $G_{\theta}$ with learnable parameters $\theta$ . The index $t$ denotes the diffusion step. While [35] uses gated temporal convolutions and [36] a Mamba architecture for the generator $G_{\theta}$ , we harness our proposed MixANT architecture, which we will describe in Sec. 4.2. During inference, multiple predictions are sampled using DDIM [31] for a single set of input frames $\mathbf{x}_{1:P}$ . For more details regarding the diffusion model, we refer the reader to [35]. + +# 4.2. MixANT Architecture + +Our proposed MixANT architecture consists of a sequence of state-space model blocks, where we utilize a hybrid approach combining standard Mamba blocks and our proposed MixMamba blocks. This design allows the model to extract basic features in the earlier layers and benefit from the enhanced selective capabilities in the later layers. + +The overall architecture processes the input to predict future actions through a sequence of $K$ total blocks. Among these, the first $K_{0}$ blocks utilize standard Mamba blocks, while the remaining $K_{E} = K - K_{0}$ blocks employ our proposed MixMamba blocks, as illustrated in Fig. 2(a). Each block follows a similar structure to transformer blocks, with normalization, state-space processing, and MLP components, as illustrated in Fig. 2(b). + +Given pre-extracted observed frame features, we first create the conditioning vector $\mathcal{X}$ as described in Eq. (12). This vector is then concatenated with the latent variables $\hat{Y}_t$ along the channel dimension to form $F_t \in \mathbb{R}^{(P + F) \times (n_c + n_d)}$ , where $n_c$ is the number of classes and $n_d$ is the number of feature channels. For the $k^{th}$ block, the processing flow is as follows: + +$$ +\hat {F} _ {t} ^ {k} = \left\{ \begin{array}{l l} \operatorname {M a m b a} \left(\operatorname {L N} \left(F _ {t} ^ {k - 1}\right)\right), & \text {i f} k \leq K _ {0} \\ \operatorname {M i x M a m b a} \left(\operatorname {L N} \left(F _ {t} ^ {k - 1}\right)\right), & \text {i f} k > K _ {0}, \end{array} \right. \tag {14} +$$ + +where LN represents Layer Normalization [4]. It needs to be emphasized that $\gamma (F_{t,1:P}^{k - 1})$ in Eq. (5) is only conditioned on the features of the observed frames. Ablation on conditioning MixMamba on both observed and future frames is provided in the suppl. material. After the state-space processing, an MLP layer is applied, followed by a residual connection: + +$$ +F _ {t} ^ {k} = \operatorname {M L P} \left(\hat {F} _ {t} ^ {k}\right) + F _ {t} ^ {k - 1} \tag {15} +$$ + +After processing through all $K$ blocks, we generate the final prediction $\hat{Y}_{t - 1}\in \mathbb{R}^{(P + F)\times n_c}$ using an MLP layer, representing the per-frame action predictions for both observed and future frames. + +# 4.3. Training + +We train our MixANT model using the established diffusion training approach [35] with an additional load balancing mechanism to ensure effective utilization of all expert matrices $\{\mathbf{A}_1, \mathbf{A}_2, \dots, \mathbf{A}_E\}$ in our mixture approach. + +For each training step, we sample a diffusion step $t$ uniformly at random and obtain the corresponding noisy action sequence $\tilde{Y}_t$ using the forward diffusion process. We then pass $\tilde{Y}_t$ alongside the conditioning vector $\mathcal{X}$ to our Mix-ANT model to obtain a reconstruction $\hat{Y}_0$ of the ground-truth action sequence $Y$ . The primary reconstruction loss is the $\mathcal{L}_2$ -loss between the predicted and the one-hot-encoded ground-truth action sequences: + +$$ +\mathcal {L} _ {r e c} = \left| \left| Y - \hat {Y} _ {0} \right| \right| ^ {2}. \tag {16} +$$ + +To ensure balanced utilization of the expert matrices in our mixture approach, we propose a load-balancing mechanism. During training, we track the usage of each expert by computing: + +$$ +C _ {e} ^ {k} = \sum_ {b = 1} ^ {B} \gamma_ {e} ^ {k} \left(F _ {t, 1: P} ^ {k - 1} (b)\right) \tag {17} +$$ + +where $C_e^k$ represents the weight for expert $e$ in layer $k$ in the batch of size $B$ . The load balancing loss then encourages uniform expert utilization by minimizing: + +$$ +\mathcal {L} _ {l b} = \sum_ {k = K _ {0} + 1} ^ {K} \mathrm {K L} \left(\frac {C ^ {k}}{\sum_ {e} C _ {e} ^ {k}} \| \mathcal {U} (E)\right) \tag {18} +$$ + +where $\mathcal{U}(E)$ represents a uniform distribution over $E$ experts, and KL denotes the Kullback-Leibler divergence. + +Our combined training objective is then given by + +$$ +\mathcal {L} _ {\text {t o t a l}} = \left(1 - \lambda_ {l b}\right) \mathcal {L} _ {\text {r e c}} + \lambda_ {l b} \cdot \mathcal {L} _ {l b}, \tag {19} +$$ + +where $\lambda_{lb}$ controls the contribution of the load balancing loss. The impact of $\lambda_{lb}$ is evaluated in the suppl. material. + +# 5. Experiments + +Evaluation Settings: We evaluate our proposed MixANT model using the stochastic long-term dense action anticipation protocol introduced by Farha et al. [8]. In this protocol, the observation length and anticipation horizon are specified as proportions of the total video duration. For a video $v$ with $n_v$ frames, the model observes the first + +$P = \alpha n_{v}$ frames and predicts action labels for the subsequent $F = \beta n_{v}$ frames, where $\alpha$ and $\beta$ represent the observation and anticipation ratios. For each observed video segment, we generate $S = 25$ prediction samples from our model. We report two key metrics: Mean MoC (Mean over Classes) accuracy and Top-1 MoC accuracy. Mean MoC measures the average accuracy across all $S$ generated samples, while Top-1 MoC reflects the accuracy of the best-matching sample. Consistent with previous works, we evaluate with observation ratios $\alpha \in \{0.2, 0.3\}$ and anticipation horizons $\beta \in \{0.1, 0.2, 0.3, 0.5\}$ . Our experiments utilize three standard datasets for action anticipation: + +Breakfast [18] comprises 1,712 cooking videos showing 10 different breakfast meal preparations across various kitchen environments. The videos are annotated with 48 action classes and vary in length, with the longest sequence requiring anticipation of up to 5.4 minutes. We evaluate using the established 4-fold cross-validation and report average performance across these splits. + +Assembly101 [29] is a large-scale dataset containing 4,321 videos of toy assembly tasks from multiple viewpoints. The videos are densely annotated with 202 coarse action classes, with the longest sequences extending beyond 25 minutes and requiring anticipation up to 12.5 minutes into the future. Following standard protocol, we train on the training set and evaluate on the validation set. + +50Salads [32] consists of 50 videos showing salad preparation, annotated with 17 action classes. The mean video duration is 6.4 minutes, with the longest sequence requiring anticipation of up to 5.1 minutes. We report results averaged over the 5 standard cross-validation splits. + +For a fair comparison with previous methods, we use identical pre-extracted frame features. Specifically, we utilize I3D features from [2] and [11] for Breakfast and 50Salads datasets, while for Assembly101 we employ TSM-features [21] provided by [29]. + +Implementation Details: Our MixANT architecture consists of $K = 15$ sequential processing blocks. To balance computational efficiency with the benefits of our mixture approach, we implement a hybrid design where the first $K_{0} = 3$ blocks use standard bidirectional Mamba operations without mixtures, while the remaining $K_{E} = 12$ blocks incorporate our proposed mixture mechanism with $E = 5$ experts. This configuration allows the model to establish foundational representations in the initial layers while leveraging the enhanced selective capabilities of the mixture approach in the deeper layers. Additional implementation details are provided in the suppl. material. + +# 5.1. Comparison to State of the Art + +Tab. 1 presents a comparison of our MixANT approach against previous methods across all three datasets. Our model consistently outperforms existing techniques, estab + +
MoCMethodβ (α = 0.2)β (α = 0.3)
0.10.20.30.50.10.20.30.5
Breakfast
MeanTri-gram [8]15.413.712.911.919.316.615.813.9
UAAA [8]15.714.013.313.019.117.217.415.0
DiffAnt [43]24.722.922.122.330.930.228.927.5
GTDA [35]24.022.021.420.629.126.825.324.2
MANTA [36]27.725.324.623.834.230.929.127.7
MixANT29.626.325.92536.232.831.228.7
Top-1Tri-gram [8]--------
UAAA [8]28.928.427.628.032.431.632.830.8
DiffAnt [43]31.329.829.430.137.437.036.334.8
GTDA [35]51.247.345.645.054.050.449.647.8
MANTA [36]55.551.047.946.959.655.053.751.9
MixANT57.152.049.148.460.756.355.553.5
Assembly101
MeanTri-gram [35]2.82.21.91.53.52.72.31.8
UAAA [8]2.72.11.91.72.42.11.91.7
GTDA [35]6.44.53.52.85.94.23.52.9
MANTA [36]6.75.34.23.56.64.74.23.5
MixANT8.07.06.24.48.76.65.64.6
Top-1Tri-gram [35]9.08.07.25.69.58.27.85.9
UAAA* [8]6.95.95.65.15.95.55.24.9
GTDA [35]18.012.89.97.716.011.910.27.7
MANTA [36]16.913.310.28.815.612.011.18.4
MixANT20.314.711.39.818.213.813.110.2
50Salads
MeanTri-gram [8]21.416.413.39.424.615.611.78.6
UAAA [8]23.619.518.012.828.018.014.812.1
GTDA [35]28.322.117.811.729.918.514.210.6
MANTA [36]28.622.819.513.631.321.917.613.0
MixANT30.325.020.915.233.423.719.714.6
Top-1Tri-gram [8]--------
UAAA* [8]53.543.040.533.756.442.835.830.2
GTDA [35]69.655.845.228.166.244.939.231.0
MANTA [36]68.351.541.731.371.753.343.831.1
MixANT71.556.946.535.072.954.644.932.4
+ +Table 1. Comparison of MixANT to state-of-the-art methods on Breakfast, Assembly101, and 50Salads. + +lishing new state-of-the-art results across virtually all evaluation settings and metrics. + +On the Breakfast dataset, MixANT demonstrates substantial improvements over prior approaches, including MANTA [36] and GTDA [35]. For both Mean MoC and Top-1 MoC metrics, our method shows consistent gains across all anticipation horizons. Notably, for Mean MoC with $\alpha = 0.3$ and $\beta = 0.1$ , MixANT achieves $36.2\%$ , compared to MANTA's $34.2\%$ , while for Top-1 MoC, we achieve $60.7\%$ versus $59.6\%$ . The challenging Assembly101 dataset, with its 202 action classes, presents a more complex anticipation scenario where MixANT demonstrates even more substantial improvements. For Mean MoC, our approach shows relative gains of up to $32\%$ over MANTA at longer anticipation horizons. For Top-1 MoC, MixANT surpasses the previous state-of-the-art GTDA in most settings, achieving $20.3\%$ with $\alpha = 0.2$ and $\beta = 0.1$ . + +On the 50Salads dataset, MixANT again establishes new state-of-the-art results. Our method achieves the highest performance for both Mean MoC across all settings and Top-1 MoC for nearly all configurations, with particularly + +![](images/469d4b8368e8503866b7f94e852527a4fa4105dfa9b1652676c7f206a2b47b86.jpg) +Figure 3. (a) Impact of number of experts in each layer. (b) Effect of the number of initial static blocks $(K_0)$ . + +strong performance at shorter anticipation horizons. These consistent improvements across diverse datasets demonstrate the effectiveness of our mixture-based approach for the state-transition matrix. By enabling adaptive temporal memory processing through expert specialization, MixANT significantly enhances the model's capacity to generate accurate and contextually relevant action predictions across varying time scales. + +# 5.2. Analysis + +In this section, we discuss a series of analysis and ablation experiments that we performed to explore individual components of our proposed MixANT model. All experiments use the Breakfast dataset with $\alpha = 0.2$ and $\beta = 0.1$ . + +Number of experts per block: A design choice in our work is the number of experts per block. MixANT allows for flexibility in this parameter, starting from a single expert (equivalent to a standard Mamba block) and scaling up as needed. We conducted a systematic experiment, increasing the number of experts from 1 to 8. As shown in Fig. 3(a), the model performance improves significantly as we increase the number of experts from the baseline (i.e. 1 expert), reaching optimal results at approximately 5 experts per block. Beyond this point, we observe a performance decline as additional experts are introduced. This pattern reveals important insights about expert-based architectures. The initial performance gains can be attributed to two mechanisms: (1) increased model capacity and expressiveness through parallel processing pathways, and (2) expert specialization across diverse input patterns. Each expert effectively learns to handle a distinct subset of the data distribution, collectively enabling more nuanced representations than a single expert. However, the performance degradation beyond 5 experts highlights a fundamental training challenge in mixture-of-experts architectures. With a fixed training budget, models with excessive experts suffer from sparse gradient updates. Each expert receives fewer training signals, creating an effective data starvation that impedes further gains in performance. This observation suggests that scaling expert count should be proportional to available training data and computational resources. + +Number of initial static blocks: Another design parameter in our architecture is the number of initial static blocks. These blocks implement standard Mamba processing with a single expert, before transitioning to our proposed mixture-of-experts configuration. To determine the optimal setup, we systematically investigated the number of initial static blocks from 0 to 6, as shown in Fig. 3(b). Our results reveal a clear pattern: performance improves significantly as we increase the number of initial static blocks up to 3, after which we observe a consistent decline. This finding demonstrates that expert routing is most effective when applied to intermediate and higher-level representations rather than raw input features. The information processing hierarchy within the network can explain this behavior. Early layers typically extract general, low-level features that benefit from consistent processing across all inputs. Introducing input-dependent routing too early forces premature specialization before the model has extracted meaningful features to guide expert selection. The initial static blocks provide a foundation of general feature extraction, allowing subsequent expert layers to make more informed routing decisions based on these refined representations. Conversely, having too many static blocks (beyond 3) constrains the network's expressiveness by limiting the layers that can benefit from adaptive, input-dependent processing. Each expert block adds capacity and flexibility to the model, so reducing their number effectively caps the model's ability to specialize across diverse input patterns. These results also highlight the importance of making the A matrix input-dependent since not introducing enough A matrices or experts hinders the model's performance. + +Router configuration: In the MixMamba layer (Fig. 2(c)), there are two MixSSM units. One processes the input in the forward direction and the other one in the backward direction. Each of these MixSSM units has its own mixture of A matrices. In this case, the routing can be done separately (independent case) or collectively for both units (unified case). In separate routing, there are two learnable projection matrices $W_{g}^{1}$ and $W_{g}^{2}$ from which two gating vectors $\gamma^{1}$ and $\gamma^{2}$ are computed. In this case, the A matrix chosen for the forward and backward units depends on the index of the maximum values of $\gamma^{1}$ and $\gamma^{2}$ after the softmax operation, respectively. In the unified case, we compute only one gating vector $\gamma$ which is then used for both forward and backward units. Our results in Fig. 4(b), show that the unified router configuration performs better than the independent one. This is intuitive since in independent configuration, bi-directionality of the SSM is sacrificed because the forward and backward units are learning two different A matrices instead of learning the $\vec{A}$ matrix for the forward direction and its counterpart $\vec{A}$ for the backward direction. + +Load balancing and expert usage: The load balancing mechanism explicitly encourages uniform utilization of all + +![](images/857fba9eabb04fb525a258b8b5d0e3699559aac357508d3cf8d9538a26eb0184.jpg) +Figure 4. (a) Comparison of router configurations: unified (same experts in forward and backward passes) versus independent (different experts selected in forward and backward passes). (b) Impact of load balancing loss. + +![](images/55ae37e4ca99c89a498a6966440b9d2abe15be72cacb9195146bef096568e426.jpg) +Figure 5. Utilization of the 5 experts across all layers on Breakfast. + +experts during training as detailed in Sec. 4.3. This constraint is removed during inference. As demonstrated in Fig. 4(b), even without load balancing, our expert-based architecture outperforms the baseline due to its expanded representational capacity. However, these gains are significantly enhanced when load balancing is applied, as it ensures all experts receive adequate training signals to develop specialized functionality as shown in Fig. 5. Without load balancing, the second expert is selected in nearly $50\%$ of the cases, while E1 and E4 are barely selected. The optimal utilization of the available expert capacity with loadbalancing translates directly to improved performance metrics, validating the importance of balanced expert training in the MixANT architecture. + +Additional ablations: In the suppl. material, we provide additional ablation experiments regarding the conditioning of the gating vector $\gamma$ in (17), impact of $\lambda_{lb}$ in (19), and a comparison of the proposed mixture-of-experts approach to a query-key approach or a very large MLP for making A input-dependent. + +# 5.3. MixANT's Expert Selection Patterns + +To understand MixANT's operational dynamics, we analyze expert selection patterns using the test split 1 of Breakfast with $\alpha = 0.2$ and $\beta = 0.1$ . For each testing instance, we initialize a selection matrix $S \in \mathbb{R}^{(K_E \times E)}$ , where $K_E$ represents the total number of mixture blocks and $E$ is the number of experts per block. As input sequences propagate through the network, we track which expert $\mathbf{A}$ matrix is selected at each block. For each block row in $S$ , we set a value of 1 in the column corresponding to the chosen expert while other columns remain zero. After processing each in + +![](images/4f4dd2a45dddccad3257fa045308a89a2da5ae251946f9f37b2719e10c8da376.jpg) +Figure 6. The t-SNE plot shows that using only a binary vector of the selected experts for each input sequence separates high-level activities. This shows that the selection of the experts in the Mix-ANT model depends on the semantic context of the video. + +stance, we flatten these matrices and visualize them using t-SNE dimensionality reduction in Fig. 6. + +The results reveal a striking emergent property: despite being trained only on atomic actions (cutting, stirring, pouring) rather than complete activity categories (making salad, preparing tea), MixANT implicitly learns to contextualize these actions within broader activities. The t-SNE visualization shows a clear clustering of expert selection patterns according to high-level activity categories, even without explicit training on these umbrella categories. This organization indicates that MixANT's expert matrices develop specialized functions aligned with semantic activity structures, enabling more nuanced temporal reasoning. + +# 6. Conclusion + +In this work, we presented MixANT, a novel architecture that enhances Mamba-based models for stochastic long-term dense action anticipation by introducing input-dependent selectivity to the forget-gate (A matrix). Our mixture of experts approach dynamically selects the most contextually relevant A matrix based on input features, providing crucial temporal memory control without sacrificing computational efficiency. Extensive experiments on the 50Salads, Breakfast, and Assembly101 datasets demonstrate that MixANT consistently outperforms existing state-of-the-art methods across all evaluation settings. These results confirm our hypothesis that input-dependent control of the hidden state evolution is particularly beneficial for anticipation tasks where the relevance of past information varies greatly across contexts. + +# Acknowledgement + +The work has been supported by the ERC Consolidator Grant FORHUE (101044724), the Federal Ministry of Education and Research (BMBF) under grant no. 01IS22094A WEST-AI, the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) GA 1927/4-2 (FOR 2535 Anticipating Human Behavior), and the project iBehave (receiving funding from the programme "Netzwerke 2021", an initiative of the Ministry of Culture and Science of the State of North Rhine-Westphalia). For the computations involved in this research, we acknowledge EuroHPC Joint Undertaking for awarding us access to Leonardo at CINECA, Italy, through EuroHPC Regular Access Call - proposal No. EHPC-REG-2025R01-218. + +# References + +[1] Y. Abu Farha, A. Richard, and J. Gall. 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However, deploying ViTs on edge devices remains a persistent challenge due to their high computational demands primarily caused by the over use of self-attention layers with quadratic complexity together with the resource-intensive softmax operation. To resolve this challenge, linear self-attention approach has emerged as an efficient alternative. Nonetheless, current linear attention methods experience considerable performance degradation compared to the softmax-based quadratic attention. Hence, we propose MixA, a novel mixed attention approach that enhances efficiency of ViT models while maintaining comparable performance to softmax-based quadratic attention. MixA takes a pretrained ViT model and analyzes the significance of each attention layer, and selectively apply ReLU-based quadratic attention in the critical layers to ensure high model performance. To enhance efficiency, MixA selects the less critical layers and replaces them with our novel ReLU-based linear attention module called Stable Lightweight Linear Attention (SteLLA). SteLLA utilizes theoretically motivated normalization terms that improve stability of prior ReLU-based linear attention, resulting in better performance (see Figure 1) while achieving significant speedup compared to softmax based quadratic attention (see Figure 2). Experiments conducted on three benchmark vision tasks show that MixA can significantly improve efficiency of ViT models with competitive performance. Notably, MixA can improve inference speed of DeiT-T model by $22\%$ on Apple M1 chip with only $\sim 0.1\%$ accuracy loss. + +# 1. Introduction + +Vision Transformers (ViTs) have gained significant popularity and demonstrated state-of-the-art performance across a variety of computer vision tasks, including image classification [8, 28], object detection [3, 4] and semantic seg + +![](images/a1317e4e4b587d788cbbdc79af9ff4ab8b2b63595037e7c711b6fdb2b92f29a3.jpg) +Figure 1. ReLU-based linear attention faces stability challenges due to the prior normalization technique [2, 23], which normalizes each row of the attention matrix by its row sum. In contrast, our proposed SteLLA utilizes theoretically motivated normalization terms to prevent variance explosion, resulting in more stable and superior performance. + +mentation [4, 38]. Despite their strong performance, ViTs come with a substantial computational demand, often resulting in slower runtimes compared to competitive convolutional neural networks (CNNs). For example, [20] shows that DeiT-T [28] is more than $10 \times$ slower compared to MobileNetV2 [25] on edge inference. Hence, deployment of ViTs remains a significant challenge in resource-constrained edge devices, where inference speed is a critical concern [20, 22]. + +A key factor limiting the inference speed of ViTs is their self-attention mechanism [2, 10, 15]. In particular, the current self-attention mechanism in ViTs introduces two major issues. First, it results in quadratic computational complexity, $\mathcal{O}(N^2)$ , with respect to the sequence length $N$ in all attention layer. Second, the self-attention mechanism heavily utilizes Softmax operations, which involve a large number of exponential function calls during inference. These operations are especially resource-intensive on edge devices [15, 27, 30], where exponential functions require significantly more resources than the basic arithmetic operations, such as multiplication or addition [15]. + +Previous studies have attempted to address the challenge of heavy computational burden associated with self + +attention by limiting the global receptive field to a smaller region, such as designing sparse global attention patterns [31, 34] or applying smaller attention windows [11, 17]. While these strategies are effective, they still rely on expensive Softmax operation and often compromise the model's ability to capture critical information from other regions. + +Recently, linear attention designs have emerged as a viable alternative that reduces computational burden of ViTs by decreasing overall complexity. Existing linear attention approaches leverages either complex activation functions [13] or specially designed mapping functions [10, 19] and apply them to queries and keys separately. This separation enables a computational reordering from (query·key)·value to query·(key·value) in self-attention computation, effectively reducing the complexity from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ . However, despite this efficiency aspect, current works that solely rely on using linear attention methods either exhibit less expressiveness compared to Softmax-based quadratic attention or introduce additional computational overhead due to the complexity of the adopted kernel functions [19], which limits their appeal for real-world application. + +In this paper, we address the limitations of current attention mechanisms by introducing a novel mixed attention approach called MixA. Our proposed MixA takes a pretrained ViT model and modifies its attention mechanism to improve efficiency while ensuring high performance. In particular, MixA consists of two key components. The first component, Targeted Quadratic Attention, takes the pretrained ViT model and analyzes the significance of each attention layer for model performance based on a novel importance score. It applies ReLU activation based quadratic attention in the critical layers to ensure high expressiveness. To enhance efficiency, MixA selects the less critical layers and modify them with our second novel component called Stable Lightweight Linear Attention (StLLA). SteLLA applies light ReLU activation function to queries and keys separately enabling the computation reordering from (query·key)·value to query·(key·value) to improve computational complexity and achieve significant speedup over Softmax-based quadratic attention (see Figure 2). However, applying normalization in ReLU based linear attention to mimic Softmax like behavior (i.e., ensuring each row of Attention matrix sums to one) as used in prior works [2, 23] leads to stability challenges and inferior performance. To resolve these challenges, we propose a theoretically motivated normalization technique that ensures stability and improves performance (see Figure 1). Overall, our contributions can be summarized as follows: + +- We introduce a novel mixed attention approach, namely MixA, that strategically applies different attention mechanisms. Performance-critical layers utilize ReLU-based + +![](images/6f15a1a31aeb1eacc3d8ce74109d49f8f9a04053ad02a71c07c3ad280bfd11ac.jpg) +Figure 2. Execution time comparison between Softmax attention (quadratic complexity) and SteLLA (linear complexity) for a single attention layer. SteLLA achieves significant speedup over Softmax attention ( $>5 \times$ at sequence length $N = 1024$ ) through its linear complexity and elimination of the computationally expensive Softmax operation. Execution time is measured on Apple M1 chip. + +quadratic attention, while less critical layers employ ReLU-based linear attention, resulting in a balanced trade-off between efficiency and performance. + +- To determine which layers are performance-critical, we propose a novel importance scoring mechanism that assesses the significance of each attention layer. +- To improve overall efficiency of proposed MixA, we propose SteLLA, a novel ReLU-based linear attention module with theoretically motivated normalization terms that successfully resolves stability challenges in prior ReLU linear attention (see Figure 1) with improved performance and significant speedup over Softmax quadratic attention (see Figure 2). +- We empirically validate the effectiveness of our proposed MixA on image classification, object detection and semantic segmentation tasks using two popular ViT models. The results demonstrate significant improvement in terms of execution time over Softmax-based counterpart while ensuring comparable performance. + +# 2. Related Work + +# 2.1. Vision Transformers + +Transformers [29] were initially developed for natural language processing (NLP) tasks, where they quickly became dominant due to their attention mechanism which effectively captures long-range dependencies. Later, Vision Transformers (ViTs) [8] have shown that applying pure transformer architectures directly to sequences of image patches can yield impressive results on various image classification benchmarks, especially with large-scale pretraining. This success has led to a surge in transformer-based models for computer vision. For instance, DeiT [28] introduced advanced training techniques and a novel distillation approach to reduce ViT's dependence on large datasets, surpassing the original ViT in performance. Models like + +PVT [31] and Swin Transformer [17] later integrated pyramid structures to produce multi-scale feature maps, making transformers a versatile backbone for diverse vision tasks. Building on this progress, numerous vision transformers have emerged [9, 33], delivering remarkable results across various benchmarks. Despite their success, ViTs suffer from significant latency that makes them unsuitable for real-world applications, particularly in edge devices. + +# 2.2. Efficient Attention Design + +A prime contributor to this high execution time of ViTs is their existing design of self-attention mechanism. To mitigate this, several research efforts have been made targeting efficient attention design. One of the popular approaches involves gradually lowering feature resolution and employing specialized attention patterns to limit the number of tokens being attended to. For example, PVT [31] employs a sparse attention mechanism, selecting tokens for attention from a global perspective. Following this direction, DAT [34] introduces a deformable attention module to create a data-dependent attention pattern. Meanwhile, Swin Transformer [17] takes a different approach by selecting tokens locally, dividing the input into isolated windows. Similarly, NAT [11] adopts a query-centric approach, designing independent tokens for each query. Despite these advancements, many of these approaches still rely on expensive Softmax operator and often compromise the model's ability to capture critical information from other regions. + +In addition to the previously discussed methods, another promising research direction focuses on reducing computational complexity through linear attention mechanisms [5, 13, 15, 35]. Linear attention addresses the inefficiencies of traditional self-attention by replacing the Softmax function with kernel functions, which removes the need to compute the pairwise similarity between queries and keys, $\mathbf{Q}\mathbf{K}^T$ . As shown in Figure 4, by leveraging the associative property of matrix multiplication, linear attention can reorder computations by first calculating $\mathbf{K}^T\mathbf{V}$ , reducing the complexity from $O(N^{2}d)$ to $O(Nd^{2})$ . + +Although this approach offers computational benefits, designing a linear attention module that matches the effectiveness of Softmax-based attention has remained a persistent challenge. Performer [5] attempts to approximate the Softmax operation using orthogonal random features, while Efficient Attention [13] applies the Softmax function to both queries and keys individually, ensuring that each row of $\mathbf{Q}\mathbf{K}^T$ sums to one. Other methods such as Nystromformer [35] and SOFT [19] approximate the full self-attention matrix using matrix decomposition techniques. Hydra Attention [1], however, replaces Softmax with cosine similarity and introduces the hydra trick, which further reduces complexity to $O(Nd)$ . + +Nevertheless, current linear attention designs either lack + +the expressive power needed to match Softmax attention or introduce additional computational overhead due to the complexity of the kernel functions used. In this work, we address the limitations of these efficient attention design and propose a novel approach called MixA which employs dual attention based strategy while completely eliminating the need for costly Softmax operation. + +# 3. Preliminaries and Notation + +Consider an input of $N$ tokens, where the queries, keys, and values are represented by matrices $\mathbf{Q},\mathbf{K},\mathbf{V}\in \mathbb{R}^{N\times d}$ . The self-attention mechanism within each head of the Multi-Head Self-Attention block is expressed as: + +$$ +\mathbf {O} = \mathbf {A} \cdot \mathbf {V}, \tag {1} +$$ + +where $\mathbf{A}$ denotes the attention matrix, calculated by measuring the similarity between the queries and keys as follows: + +$$ +\mathbf {A} = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q K} ^ {T}}{\sqrt {d}}\right), \tag {2} +$$ + +where $d$ represents the head dimension. + +This self-attention mechanism in (2) computes the similarity between all pairs of queries and keys resulting in a computational complexity of $\mathcal{O}(N^2 d)$ . The number of tokens $N$ is higher than the head dimension $d$ . As a result, applying global self-attention becomes computationally expensive. + +# 4. Inefficiency of Attention Mechanism + +Before introducing the details of our proposed method, in this section, we first demonstrate the problem that our work aims to address. Here, we empirically demonstrate the execution time bottlenecks in existing self attention mechanisms. + +Observations. The experimental results of our timing analysis are illustrated in Table 1 and Figure 3, which show the breakdown of computation times for different components of ViT model. This leads to our first observation: + +Observation I. The attention layer consumes the majority of the inference time in ViT models, making it a critical bottleneck for efficient edge inference. + +Table 1. Comparison of cumulative execution time measurements between Attention and MLP layers. Measurements are taken on the DeiT-S backbone with a 448x448 input resolution, tested on an Apple M1 chip. + +
LayerTime (ms)PercentageParameters per layer
Attention121.775.37%0.59M
MLP39.824.63%1.18M (2×)
+ +![](images/9b1733d877be6bcf974fd337fa21d167261946995456a67bc49e74de32ba341f.jpg) +(a) Computational Pipeline of Attention Layer +Figure 3. (a) Computational pipeline of a self-attention layer. (b) Latency profile of the self-attention layer, illustrating the percentage of time allocated to each operation within the attention layers. Latency measurements are taken using the DeiT-S backbone with a 448x448 input resolution, tested on an Apple M1 chip. + +![](images/332afbf6dd35fa13d16b9b9007a8678451e8e1bbcacd6087b0cb954573ba94be.jpg) +(b) Attention Layer Latency Profile + +As shown in Table 1, although attention layers have only half the parameters of MLP layers, they consume more than $3 \times$ the computational time. This significant disparity highlights the need for optimizing attention operations for edge devices with limited computational capabilities. + +To identify the sources of this computational overhead, we performed a detailed profiling of various operations within the attention mechanism, as illustrated in Figure 3. This profiling reveals our second observation: + +Observation II. Within the attention layer, the quadratic attention operation along with the Softmax operation consume a disproportionate amount of time compared to other operations. + +The $\mathbf{Q}\mathbf{K}^T$ matrix multiplication alone accounts for $44.81\%$ of the total attention time, while the Softmax operation takes up $18.82\%$ of total time even though Softmax contributes to $< 0.5\%$ FLOPs in attention layer. Together, these two operations constitute more than $63\%$ of the attention layer's computation time. In contrast, the $QKV$ linear transformation and Output linear projection operations consume only $10.24\%$ and $3.41\%$ of the total time in the attention layer, respectively. + +These observations confirm the latency bottleneck in current attention mechanisms, primarily driven by the quadratic complexity of attention and the computational demands of Softmax operations. + +# 5. Proposed MixA Method + +To address the inefficiencies of attention mechanisms in Vision Transformers (ViTs), we introduce a novel approach called MixA, comprising two key components. The first component is called Targeted Quadratic Attention, which takes a pretrained Vision Transformer and evaluates the significance of each attention layer through a novel importance score. The importance score quantifies the contribution of each attention layer to model performance. Based on this + +score, we selectively modify the Softmax-based quadratic attention in critical layers with efficient ReLU activation based quadratic attention [32]. This modification in critical layers ensures that the overhead associated with Softmax function is eliminated while having minimal impact to model performance. To further enhance efficiency, we modify the attention of less significant layers using our second component called Stable Lightweight Linear Attention (SteLLA). SteLLA applies pointwise ReLU activation function independently to keys and queries, enabling a reordering of matrix multiplication from $(\mathbf{Q}\mathbf{K}^T)\mathbf{V}$ to $\mathbf{Q}(\mathbf{K}^T\mathbf{V})$ . Since $N$ is often much larger than $d$ (i.e. $d$ is 64 in DeiT, $N$ is 1024 for image resolution of $448 \times 448$ with a patch size of 14), this reordering reduces the computational complexity of these layers from $\mathcal{O}(N^2)$ to $\mathcal{O}(N)$ , as illustrated in Figure 4. + +# 5.1. Targeted Quadratic Attention + +The first component of our proposed MixA selects critical attention layers and modifies them with an efficient ReLU activation-based quadratic attention mechanism. To quantify the significance of each attention layer, we introduce an importance score that leverages two critical properties: (1) the impact of attention modifications on the model performance, and (2) the sensitivity of the attention scores to the modification. + +To compute the importance score, we begin by performing a forward pass of the input images $\mathbf{x}$ through the pretrained ViT model, recording the original attention scores $\mathbf{A}$ and the corresponding loss $\mathcal{L}$ . Next, we perform backpropagation to calculate the gradient of the loss with respect to each attention head, denoted as $\nabla_{\mathbf{A}_i} \mathcal{L}$ . The gradient for the $i$ -th attention head indicates how sensitive the loss function is to small changes in $\mathbf{A}_i$ , capturing the impact of attention modifications on model performance. + +Next, we modify the attention layer to replace the Softmax-based quadratic attention layers with linear attenuate + +![](images/64a26b16d52bd56695cc94a658b2d9c131227c20901f5134982b91e52708d1bc.jpg) + +![](images/4d7c6111148446051140ced13bc7b5b62883fea054dc8d48b6478abdd54f7580.jpg) + +![](images/a10d828cf1d06f6fa5bd763d47ba141f3b05b30035181e305636279d6d518ab0.jpg) +Quadratic Attention +Complexity: $O(N^2 d)$ +Figure 4. Comparison of attention mechanisms with quadratic and linear computational complexity. $\mathbf{Q},\mathbf{K},\mathbf{V}\in \mathbb{R}^{N\times d}$ denote the query, key, and value matrices, respectively. Traditional Softmax-based attention in (2) requires pairwise similarity computation between queries and keys, resulting in a complexity of $\mathcal{O}(N^2 d)$ . Linear attention, on the other hand, applies activation function or mapping functions to $\mathbf{Q}$ and $\mathbf{K}$ separately enabling calculation of $\mathbf{K}^T\mathbf{V}$ first, reducing complexity to $\mathcal{O}(Nd^2)$ . $N$ is higher than $d$ in ViTs [17, 28]. + +![](images/60007cd514c0d43412bdfca72c5040f1bf4358d31031d09e244e8695c41cd0ea.jpg) +Linear Attention +Complexity: $O(\mathrm{Nd}^2)$ + +tion in (7) and perform another forward pass using the same input $\mathbf{x}$ to obtain the modified attention scores $\mathbf{A}'$ and compute the perturbation in the attention scores for each head as $\Delta \mathbf{A}_i = \mathbf{A}_i' - \mathbf{A}_i$ . This perturbation reflects the sensitivity of the attention layer to the applied modification. + +The proposed importance score $\mathcal{I}_A$ is then calculated as: + +$$ +\mathcal {I} _ {A} = \frac {1}{H} \sum_ {i = 1} ^ {H} \left| \operatorname {T r} \left(\left(\nabla_ {\mathbf {A} _ {i}} \mathcal {L}\right) ^ {\top} \Delta \mathbf {A} _ {i}\right) \right|, \tag {3} +$$ + +where $H$ denotes the total number of attention heads in the layer and $\mathrm{Tr}(\cdot)$ denotes the trace operator. By taking the absolute value and averaging across all heads, we obtain a scalar importance score that reflects the overall significance of the attention layer. A higher value of the importance score $\mathcal{I}_A$ indicates that the corresponding attention layer is critical for maintaining the model's performance. + +After computing the importance scores for each attention layer, we select the layers with the highest importance scores for quadratic attention placement. To formalize, let $\mathcal{L}_A = \{l_1,l_2,\dots ,l_L\}$ denote the set of all attention layers in the model. We select a subset of layers $S\subset \mathcal{L}_A$ as follows + +$$ +\mathcal {S} = \left\{l _ {i} \mid l _ {i} \in \mathcal {L} _ {A} \text {a n d} \mathcal {I} _ {A} ^ {l _ {i}} \in \operatorname {t o p - k} (\mathcal {I} _ {A}) \right\} +$$ + +where $k$ is a hyperparameter representing the number of layers chosen for quadratic attention. + +Even though placing quadratic attention in some layers incurs computational cost, we ensure that the quadratic attention is Softmax-free. To ensure this, we utilize ReLU as activation function for computing this quadratic self attention which is formulated as follows + +$$ +\mathbf {O} = \frac {1}{\alpha_ {Q}} \cdot \mathbf {A} _ {Q} \cdot \mathbf {V}, \tag {4} +$$ + +where the ReLU-based quadratic attention matrix $\mathbf{A}_Q$ in (4) is calculated as: + +$$ +\mathbf {A} _ {Q} = \operatorname {R e L U} \left(\frac {\mathbf {Q} \mathbf {K} ^ {T}}{\beta_ {Q}}\right), \tag {5} +$$ + +where $\beta_{Q}$ in (5) and $\alpha_{Q}$ in (4) are normalization terms following Theorem 5.1 and Theorem 5.2. + +Theorem 5.1. Consider the query and key matrices $\mathbf{Q},\mathbf{K}\in$ $\mathbb{R}^{N\times d}$ and assume that the components of query $\mathbf{Q}_i\in \mathbb{R}^d$ and key $\mathbf{K}_j\in \mathbb{R}^d$ are independent random variables following standard normal distribution. Then the variance of dot-product between $\mathbf{Q}_i$ and $\mathbf{K}_j$ follows + +$$ +\operatorname {V a r} \left(\mathbf {Q} _ {i} ^ {T} \mathbf {K} _ {j}\right) \in \mathcal {O} (d) +$$ + +where $d$ is the dimension of the attention head. + +Here, the independent assumption is followed by [29] and the proof is provided in the supplementary material. According to Theorem 5.1, we propose a scaling factor $\beta_{Q} = \beta_{Q}^{\prime}\sqrt{d}$ in dot-product attention computation in (5) to counteract the variance explosion, where $\beta_{Q}^{\prime}$ is a learnable parameter initialized as 1. + +Theorem 5.2. Consider an attention matrix $\mathbf{A} \in \mathbb{R}^{N \times N}$ and value matrix $\mathbf{V} \in \mathbb{R}^{N \times d}$ . Assume that the variance of product of elements $A_{ij}$ and $V_{jk}$ is bounded, i.e., $\text{Var}(\mathbf{A}_{ij} \mathbf{V}_{jk}) \leq C$ for some constant $C$ . Then the variance of elements of the resultant matrix, i.e., $\mathbf{O}_{ik} = \sum_{j=1}^{N} \mathbf{A}_{ij} \mathbf{V}_{jk}$ has the following growth rate + +$$ +\operatorname {V a r} \left(\mathbf {O} _ {i k}\right) \in \mathcal {O} \left(N ^ {2}\right) +$$ + +where $N$ is the number of tokens in the sequence. + +The proof of Theorem 5.2 is provided in the supplementary material. According to Theorem 5.2, we use a scaling factor $\alpha_{Q} = \alpha_{Q}^{\prime}N$ in (4) to counteract the variance explosion when Attention matrix $\mathbf{A}_Q$ is multiplied by the Values matrix $\mathbf{V}$ , and $\alpha_{Q}^{\prime}$ is a learnable parameter initialized as 1. + +Overall, by leveraging the proposed importance score, we effectively identify and select the most critical layers for ReLU-based quadratic attention and avoid the overhead associated with the Softmax operation. However, applying quadratic attention to less critical layers is unnecessary. Therefore, to enhance overall efficiency, we propose to utilize linear attention mechanism in these less critical layers. + +Table 2. Performance comparison of different ViT models [17, 28] for classification task on ImageNet-1K dataset [7] with Softmax-based quadratic attention [29] and proposed MixA. + +
Method#ParamsFLOPsAccuracy (%)Execution Time (ms)
Apple M1Speedup Gain (%)Raspberry PiSpeedup Gain (%)
DeiT-T [28]5.7M3.40G74.6612.57-346.76-
MixA-DeiT-T5.7M3.17G74.5410.3022.04299.9015.63
DeiT-S [28]22M12.25G80.7631.00-863.38-
MixA-DeiT-S22M11.79G80.5927.0714.52778.0710.96
Swin-T [17]29M9.79G81.7649.74-940.46-
MixA-Swin-T29M9.24G81.2840.6622.33819.9714.69
Swin-S [17]51M18.83G83.5979.06-1674.12-
MixA-Swin-S51M17.89G82.8861.6728.201408.7018.84
+ +# 5.2. Stable Lightweight Linear Attention + +The second component of our proposed MixA is a novel lightweight attention mechanism with linear computational complexity. Here, we apply lightweight ReLU activation function to queries and keys separately enabling the computation reordering from $(\mathbf{Q}\mathbf{K}^T)\mathbf{V}$ to $\mathbf{Q}(\mathbf{K}^T\mathbf{V})$ in the less critical layers to reduce their computational complexity from quadratic to linear (see Figure 4). However, applying normalization in ReLU-based linear attention to mimic Softmax-like behavior (i.e., ensuring each row of Attention matrix sums to one) as used in prior works [2, 23] leads to instability and degraded performance (see Figure 1). To resolve this, we propose a theoretically motivated normalization technique that ensures stability and improved performance which we formulate as follows + +$$ +\mathbf {O} = \frac {1}{\alpha_ {L}} \cdot \mathbf {A} _ {L} \cdot \mathbf {V}, \tag {6} +$$ + +where the linear attention matrix $\mathbf{A}_L$ is calculated as: + +$$ +\mathbf {A} _ {L} = \frac {\operatorname {R e L U} (\mathbf {Q}) \operatorname {R e L U} (\mathbf {K}) ^ {T}}{\beta_ {L}} \tag {7} +$$ + +where $\alpha_{L}$ in (6) and $\beta_{L}$ in (7) are our proposed normalization terms derived in Theorem 5.2 and Theorem 5.3. + +Theorem 5.3. Consider the query and key matrices $\mathbf{Q},\mathbf{K}\in$ $\mathbb{R}^{N\times d}$ and assume that the components of query $\mathbf{Q}_i\in \mathbb{R}^d$ and key $\mathbf{K}_j\in \mathbb{R}^d$ are independent random variables following standard normal distribution. Then the variance of dot-product between $ReLU(\mathbf{Q}_i)$ and $ReLU(\mathbf{K}_j)$ vectors follows + +$$ +\operatorname {V a r} \left(\operatorname {R e L U} \left(\mathbf {Q} _ {i}\right) ^ {T} \operatorname {R e L U} \left(\mathbf {K} _ {j}\right)\right) \in \mathcal {O} (d) +$$ + +where $d$ is the dimension of the attention head. + +Here, the independent assumption is followed by [29] and the proof is provided in the supplementary material. According to Theorem 5.3, we propose a scaling factor $\beta_{L} = \beta_{L}^{\prime}\sqrt{d}$ in (7) to counteract the variance explosion, where $\beta_{L}^{\prime}$ is a learnable parameter initialized as 1. And + +according to Theorem 5.2, we propose a scaling factor $\alpha_{L} = \alpha_{L}^{\prime}N$ in (6) to mitigate variance explosion when attention matrix $\mathbf{A}_L$ is multiplied by the values matrix $\mathbf{V}$ , where $\alpha_{L}^{\prime}$ is also a learnable parameter initialized as 1. + +# 6. Experimental Results + +In this section, we evaluate the performance of proposed MixA on image classification, object detection and semantic segmentation tasks using two popular ViT architectures: DeiT [28] and Swin [17]. We consider primarily "small" and "tiny" variants as we focus on accelerating edge inference. + +# 6.1. Datasets and Implementation Details + +Datasets. We evaluate our approach on several benchmark datasets across multiple tasks. For image classification, we use the widely adopted ImageNet-1K dataset [7], which includes 1.28 million training images and 50,000 validation images spanning 1,000 classes. For object detection, we utilize the COCO dataset [16], consisting of 118,000 training images and 5,000 validation images. For semantic segmentation, we conduct experiments on the ADE20K dataset [40] with 20,000 training images and 2,000 validation images. + +Experimental Settings and Execution Times. For classification task, we take pretrained ViT models [17, 28] and fine-tune them after applying MixA. For finetuning the models, we utilize the cross-entropy loss and standard knowledge distillation loss [12], using pretrained models as teachers. This fine-tuning process is conducted over 150 epochs with the AdamW optimizer [18] and a cosine learning rate schedule, including 10 warm-up epochs with a base learning rate of $1 \times 10^{-4}$ . To avoid overfitting, we apply the augmentations used in DeiT [28]. In addition, a weight decay of 0.05 is also used. For fair comparison, we carry out exact fine-tuning process and finetune the pretrained ViT models with Softmax-based quadratic attention under the same settings and report their results. Similarly, we carry out the same fine-tuning process to report performance of existing linear attention mechanisms [13, 15, 23]. + +For object detection and semantic segmentation tasks, we use ViT backbones with their respective classification + +Table 3. Performance comparison of different ViT backbones [17, 28] for semantic segmentation tasks on ADE20k dataset [40] with Softmax-based quadratic attention [29] and proposed MixA. + +
Method#ParamsFLOPsmIoU (%)Execution Time (ms)
Apple M1Speedup Gain (%)Raspberry PiSpeedup Gain (%)
DeiT-Adapter-T [4]12M29.12G34.7211.54-3798.57-
MixA-DeiT-Adapter-T12M26.48G33.8187.6712.723539.817.31
Swin-T [17]32M39.17G35.3148.93-3299.54-
MixA-Swin-T32M36.97G35.8115.7028.722935.7012.39
+ +Table 4. Performance comparison of different ViT backbones [17, 28] for object detection task on COCO dataset [7] with Softmax-based quadratic attention [29] and proposed MixA. + +
Method#ParamsFLOPsmAP (%)Execution Time (ms)
Apple M1Speedup Gain (%)Raspberry PiSpeedup Gain (%)
DeiT-Adapter-T [4]14M29.12G33.9208.62-3807.66-
MixA-DeiT-Adapter-T14M26.48G33.5185.2312.623514.728.33
Swin-T [17]34M39.17G34.6146.49-3315.01-
MixA-Swin-T34M36.97G32.6112.2230.532945.7912.53
+ +checkpoints, integrating them with Faster-RCNN [24] and SemanticFPN [14] models. For object detection, we train the object detection model for 36 epochs, and for semantic segmentation, we train for 40k iterations and use a batch size of 16 across both tasks. For additional implementation details and more ablation studies (e.g., effect of different k), we direct the reader to the Supplementary section. + +We use Raspberry Pi 4 Model B and MacBook Pro with Apple M1 Max chip to report the execution times. Following the standard approach in [15, 20], we measure execution time on these devices by first performing five warm-up runs. We then record the execution time across 100 inference runs and report the average execution time. For object detection and semantic segmentation tasks, we report the execution times and FLOPs of the backbone networks for direct comparison between different ViT backbones. + +# 6.2. Main Results + +Image Classification. Table 2 presents performance comparison between Softmax-based quadratic attention and our proposed MixA on the ImageNet-1K dataset. As shown in the table, with MixA, each model variant shows a reduction in FLOPs and execution times on both Apple M1 and Raspberry Pi devices, while maintaining similar accuracy levels. Notably, MixA achieves over $20\%$ speedup in DeiT-T and Swin-T, with only a minor accuracy drop of approximately $0.1\%$ and $0.5\%$ , respectively. The most significant gains are seen in Swin-S, where MixA improves execution speed by up to $28.20\%$ on Apple M1 and $18.84\%$ on Raspberry Pi, demonstrating effectiveness of proposed approach for improving execution time. + +Semantic Segmentation. Table 3 presents performance comparison between Softmax-based quadratic attention and MixA-based backbones for DeiT-Adapter-T and Swin-T, integrated with the Semantic FPN model, on the ADE20K + +dataset. Similar to object detection, we adopt an edge friendly resolution of $448 \times 448$ to report the model performance. And similar to object detection, MixA provides comparable mean Intersection over Union (mIoU) values in semantic segmentation while reducing FLOPs and achieving significant execution time speedups of ViT backbones. For example, MixA-DeiT-Adapter-T reduces FLOPs from 29.12G to 26.48G, with a minor mIoU degradation $< 1\%$ , and achieves a speedup of $12.39\%$ on Apple M1 and $7.31\%$ on Raspberry Pi. Notably, MixA-Swin-T improves its segmentation performance with an mIoU improvement to $35.8\%$ and reduces FLOPs and gains speedup of over $28\%$ on Apple M1 and $12\%$ on Raspberry Pi. + +Object Detection. Table 4 presents performance comparison of Softmax-based quadratic attention and MixA based backbones for DeiT-Adapter-T and Swin-T with the Faster R-CNN model as object detection head on the COCO dataset. We use DeiT-Adapter since DeiT itself does not perform well for dense vision tasks for its lacking vision-specific inductive bias [4]. We use an edge-friendly resolution of $448 \times 448$ to evaluate model performance. From the results, we find that, for each model variant, MixA provides a notable reduction in both FLOPs and execution times (12 - 30% speedup gain) across Apple M1 and Raspberry Pi devices for ViT backbones, while maintaining comparable mean Average Precision (mAP). + +Table 5. Comparison with Other Linear Attentions with DeiT-T on ImageNet-1K. + +
Linear Attention#ParamsFLOPsAccuracy (%)
CosFormer [23]5.7M2.94G69.05
Efficient Attn [26]5.7M2.94G71.80
SimA [15]5.7M2.94G72.73
StELA (Ours)5.7M2.94G73.71
+ +# 6.3. Ablation Study + +Comparison with Other Linear Attentions. On the DeiT-T model, we compare our proposed SteLLA module with three established linear attention methods: CosFormer [23], Efficient Attention [26], and SimA [15]. As shown in Table 5, SteLLA outperforms the prior linear attention approaches. Notably, our normalization technique enables SteLLA to achieve a $4.66\%$ improvement over CosFormer [23], which uses similar ReLU-based linear attention but with a different normalization approach (normalizes each row of Attention matrix by corresponding row sum). This improved performance highlights the effectiveness of the proposed normalization technique in SteLLA. + +Effect of different components of MixA. Next, we assess the impact of each component of our proposed MixA by progressively incorporating them. Starting from the proposed SteLLA, we observe that adding targeted quadratic attention results in an accuracy improvement of $+0.83\%$ , as shown in Table 6. + +Table 6. Effect of different components of MixA. + +
Method#ParamsFLOPsAccuracy (%)
SteLLA5.7M2.94G73.71
SteLLA + TQA (k=6)5.7M3.17G74.54
+ +Impact of Targeted Quadratic Attention. Table 7 compares the effect of targeted quadratic attention and applying quadratic attention to randomly chosen layers. As shown in Table 7, placing quadratic attention on random layers achieves an accuracy of $73.98\%$ . In contrast, applying targeted quadratic attention boosts accuracy to $74.54\%$ without increasing FLOPs. This demonstrates that selecting layers based on their importance score significantly enhances model performance, confirming the effectiveness of importance score-based layer selection. + +Table 7. Impact of Targeted Quadratic Attention on MixA. + +
Method#ParamsFLOPsAccuracy (%)
StELLA + QA (k=6)5.7M3.17G73.98
StELLA + TQA (k=6)5.7M3.17G74.54
+ +Impact of scaling parameters $(\alpha_{L}^{\prime},\beta_{L}^{\prime},\alpha_{Q}^{\prime},\beta_{Q}^{\prime})$ . Table 8 shows that incorporating learnable scaling parameters in MixA improves accuracy on DeiT-T [28] from $74.44\%$ to $74.54\%$ . This suggests they help prevent variance explosion and enhance the Attention mechanism. + +Table 8. Impact of learnable scaling parameters $(\alpha_{L}^{\prime},\beta_{L}^{\prime},\alpha_{Q}^{\prime},\beta_{Q}^{\prime})$ on proposed MixA evaluated on DeiT-T. + +
Method#ParamsFLOPsAccuracy (%)
MixA (wo learnable params)5.7M3.17G74.44
MixA5.7M3.17G74.54
+ +![](images/2a2b10766d8a866c30afdcf3b250121a33ddae438ce9530ec9386184443348d1.jpg) +Figure 5. Normalized importance scores of DeiT-T. + +Impact of different $k$ . Table 9 illustrates the effect of varying $k$ on MixA's performance using DeiT-T. While the parameter count remains constant at 5.7M, FLOPs increase from 3.05G to 3.28G as $k$ grows from 3 to 9. Accuracy peaks at $74.54\%$ for $k = 6$ but shows no further gains at $k = 9$ , indicating that $k = 6$ balances computational cost and performance, justifying its selection. + +Table 9. Impact of different k on MixA, evaluated on DeiT-T. + +
Method#ParamsFLOPsAccuracy (%)
MixA (k=3)5.7M3.05G74.28
MixA (k=6)5.7M3.17G74.54
MixA (k=9)5.7M3.28G74.54
+ +Layerwise Importance Score. Figure 5 visualizes the distribution of importance scores across the layers of DeiT. The distribution of scores indicate that the attention of earlier layers are more sensitive and contribute more significantly to model performance compared to the later layers. This pattern may arise because the earlier layers are primarily responsible for local feature extraction, making them better suited to benefit from the enhanced capacity of quadratic attention. In contrast, the later layers, which focus on capturing global context, may perform adequately with linear attention. + +# 7. Conclusion + +In this work, we propose MixA, a novel and efficient attention approach that enhances the efficiency of Vision Transformer models while achieving performance comparable to traditional, resource-intensive Softmax-based quadratic attention. 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It can be instantly applied to a novel object at test time without finetuning. We design our network to meet the demands of real-world applications, emphasizing reduced memory requirements and fast inference time. Unlike existing works that utilize many reference images and have large network parameters, we directly match points based on the multi-view information between the query and reference images with a lightweight network. Thanks to our reference image fusion strategy, we significantly decrease the number of reference images, thus decreasing the time needed to process these images and the memory required to store them. Furthermore, with our lightweight network, our method requires less inference time. Though with fewer reference images, experiments on seven core datasets in the BOP challenge show that our method achieves comparable results with other methods that require more reference images and larger network parameters1. + +# 1. Introduction + +Six degrees-of-freedom (6DoF) object pose estimation predicts the orientation and location of a target object in 3D space. This is crucial for embodied AI, as intelligent agents must comprehend and interact with their environments to perform tasks such as robotic manipulation and augmented reality applications [13, 54]. In recent years, 6DoF object pose estimation accuracy has been significantly improved with deep learning [3, 28, 36, 37, 41, 43, 46, 63, 65, 69, 76, 84, 87, 88]. However, these methods require the same object during training and test time and rely on generating abundant synthetic data for each object during the training stage, which is tedious to deploy in practical situations. + +![](images/9c979872e984604ba46f6b56f3f38d52f99850d0c68470b09fcbba26d65ab8e2.jpg) +Figure 1. Comparison of different methods. The area of each bubble is proportional to the size of the network parameters, and the color indicates the number of reference images used. The detection[58] stage was removed in all speed evaluations. MixRI achieves competitive results while using fewer reference images, a smaller network, and providing shorter inference time. + +To satisfy the practical need in industrial and daily life, CAD-based novel object pose estimation (During the training stage, the specific object to be inferred at test time is unknown.) was introduced [32] and more and more methods [1, 5, 10, 33, 38, 56, 57, 59, 61, 64, 68, 79, 83, 89] arise. + +To enable methods to adapt to different objects without retraining, recent works utilize reference images. These images are typically rendered offline and stored in memory [1, 5, 10, 38, 56, 59, 61]. For edge AI and efficient deployment on edge devices in practical embodied AI applications, a compact memory cache for both reference images and network parameters is essential, along with the need for fast inference time [40]. However, as shown in Fig. 1, although recent works have successfully pursued high pose estimation accuracy, they do so at the cost of requiring extensive reference images, large network parameters, and slow inference time. As shown in Fig. 2 (a), existing meth + +![](images/ba80e8792fe68afa5f4ad332ca9f01323945e675124e0b157aafc2700af6ca62.jpg) +(a): The Pipeline of Previous Methods + +![](images/edb094ce7e9b119438e229b08cc7d1ad1d7418519f8ebfed5419b78bc29d0cfe.jpg) +Step 1: Find Corresponding Points in All Reference Images + +![](images/9f7cea332a0d70e6b8f2b7044710b5ee5060e58c720cd0c8d1fdc560dbc935c9.jpg) +Step 2: Find Corresponding Points on Query Image +(b): The Overview of Our Pipeline +Figure 2. Comparison between our pipeline and previous methods. Unlike existing two-stage methods [1, 38, 59, 61] that first retrieve the closest reference image from abundant reference images, we directly predict the location of sampled 3D object points on the query image from their projections on all reference images. It constructs the 2D-3D correspondence and can solve the 6DoF pose. Hollow points indicate invisibility, while solid points indicate visibility. + +![](images/545a9508390f5c8070d3ad97a3d50ebff6f2c8afe38911e5d9fed72ef98d855f.jpg) +Step 3: Solve Pose + +ods [1, 38, 56, 59, 61, 68] usually divide the pose estimation into two stages: a view selection stage to retrieve the closest reference image and a pose estimation stage to estimate the 6DoF pose of the query image by comparing it with the selected reference image. As the number of reference images for each object increases, this restricts the algorithm's ability to scale to a larger number of objects, as each object requires rendering a substantial number of reference images to be stored in memory [61]. Besides, these works mainly rely on networks with a large number of parameters. The large number of rendered reference images and extensive network parameters present a significant challenge for devices with limited computing power and memory. Additionally, some previous works [59, 61] require the pre-extraction of image features, which are stored in memory as well. These limitations restrict their practical application in edge AI and limit the number of unseen objects whose poses can be estimated, as algorithms typically run in real time on edge devices with limited memory. + +In this paper, we aim to solve the novel pose estimation problem using a lightweight network with a minimal number of reference images, designed to support edge AI [40]. Additionally, our approach eliminates the need for pre-extraction of features. Inspired by previous work that utilizes matching to compute the pose [1, 59, 61], we also try to build our method in a matching framework. However, when the number of reference images is significantly reduced, the closest reference image may still suffer from wide rotation with the query image, known as a wide baseline in matching, which is challenging to address [34]. To effectively solve the matching problem, we design our method from the following observation: 1) Given that multi-view geometry can provide more information [23], we can use multi-view information + +to enhance the matching procedures. 2) When the reference images are few, the views become sparse, and occlusion becomes more common. This makes matching more necessary to integrate multi-view information and handle occlusion scenarios. Based on the above two observations, we design our network by aggregating all the reference image features and propose MixRI (Mix Reference Images), which is a lightweight network and requires only few reference images as input to solve the novel object pose estimation. + +As shown in Fig. 2 (b), we gather all the 2D information belonging to the same 3D object points in all reference images and mix their features. We train a lightweight network to fully fuse the feature of all reference images and enhance the query image feature with the reference images, which makes the matching more stable and accurate. We also design the occlusion detection as part of the network's output, making our network handle the occlusion automatically. In contrast to the usual feature matching problem [14, 70, 85, 86] between paired images, our method requires establishing correspondences from multiple reference images to a single query image. Specifically, the objective is to determine the position and occlusion flag of each 3D object point on the query image, based on its projections on all the reference images. Upon establishing these correspondences, the corresponding 2D points for the 3D object points are then derived. With a sufficient number of 2D-3D correspondences, the object pose can subsequently be computed using the PnP algorithm [72] within the RANSAC [21] framework. + +Our experiments demonstrate that, under the setting without refinement, our method achieves comparable results despite utilizing $33 \times$ fewer reference images than the most accurate method [61] and being $2 \times$ faster than the fastest method [59]. This suggests that a heavy reliance on a large + +number of reference images and large network parameters may not be the only way for achieving high performance. + +In summary, our contributions can be summarized as: + +- We present MixRI, a lightweight network for RGB-based novel object pose estimation. It requires only 12 reference images and does not necessitate the offline pre-extraction of image features. +- We propose a View-Aggregated Point Matching module that can find correspondences on the query image based on multiple reference images simultaneously and give occlusion prediction. +- MixRI achieves comparable performance to state-of-the-art approaches while using significantly fewer reference images, significantly fewer network parameters, shorter preparation time for reference images, and faster inference speed, making it more suitable for practical applications. + +# 2. Related Work + +Pose Estimation of Known Objects or Categories. 6DoF object pose estimation has been widely studied for decades as a fundamental vision problem [49, 50], solved from the traditional methods [12, 18, 49, 50] to deep learning methods [28, 43, 46, 63, 65, 69, 81, 84, 88]. Early deep learning-based methods for pose estimation focused on the seen object pose estimation problem either based on template matching [36] or feature matching followed by PnP [3, 9] for 2D-3D correspondences [3, 43, 63, 65, 69, 88] or least squares fitting for 3D-3D correspondences [7, 27, 28, 46, 76]. To compensate for the expensive retraining required for a new object in seen object scenario, one approach involves making the trained network generalize to known categories [11, 39, 42, 45, 53, 73, 77]. While these approaches can estimate unseen objects, they assume all objects belong to the same category, which still limits their application. In contrast, our work can be generalized to arbitrary objects. + +Pose Estimation of Unseen Categories. Recently, some works have focused on novel object pose estimation, where the target category is not seen during the training stage. This can be addressed when an object model is available [1, 5, 10, 33, 38, 56, 57, 59, 59, 61, 64, 68, 79, 83, 89] or with reference images [4, 26, 29, 48, 62, 71, 82, 83]. These works either use RGB images [1, 26, 38, 48, 56, 59, 62, 68, 71, 79, 90] or RGB-D images [5, 10, 33, 38, 44, 56, 60, 68, 83] as input. For scenes with available object models, methods can be divided into feature-matching methods [1, 5, 10, 33, 59, 61, 64] and template matching methods [1, 38, 56, 57, 59, 61, 68, 79, 83, 89]. However, for those feature-matching methods, they primarily use a retrieval-based strategy, which actually applies a template matching method to get the closest reference image and build the correspondence between the closest reference image and the query image [1, 10, 56, 59, 61]. Unlike those works, our method is pure feature-matching. We directly build the cor + +respondences across all the reference images and the query image, which significantly reduce the number of reference images needed. This reduces the time needed to render reference images and avoids caching pre-computed features for view selection, saving substantial memory. + +Local Feature Matching & Point Tracking. Local feature matching establishes precise correspondences between images, typically in paired image scenarios. Early works use a detector-based approach first employing some well-established handcrafted features such as SIFT [51] and ORB [67] followed by a feature matching algorithm like nearest-neighbor searches. With the help of deep learning, more complex methods [14, 20, 47, 55, 66] arise. Recently, more works [8, 70, 85, 86] are detector-free methods, and they can efficiently handle extreme circumstances such as texture-less regions or substantial viewpoint changes. Our work focuses on feature matching, but we build the correspondences between the query image and multiple reference images of the same 3D object points, which differs from the matching between two images. Those methods struggle to handle occlusion and massive changes in viewpoint, which can not predict the occlusion information as well. + +Besides, some works focus on tracking points across continuous frames [15, 22, 52, 75, 78]. In those works, adjacent frames, along with the initial points to be tracked, are input into the network. The network will then output the points' trajectories across the sequence, along with occlusion information. As with works in point tracking, we also build the correspondence along all the images and output the occlusion information. However, in our method, the reference images are unordered and not consecutive. Furthermore, we have the locations of the query 3D object points on all reference images, which are the projections of the same 3D object points onto each reference image, and some can be occluded. While in point tracking work, query points usually belong to a single frame and must be visible. + +# 3. Method + +Our method is built on finding the correspondences between the 2D pixel locations and 3D object point locations, followed by a RANSAC-based PnP framework to compute the 6DoF pose. We break down the pose estimation problem to a matching problem. However, different from the previous matching-based pose estimation, we neither directly find 2D-3D correspondences between the query image and 3D object points [26, 63, 71, 88] nor find 2D-2D correspondences between paired images as is done in classic local feature matching [1, 59, 70, 86]. Instead, we focus on finding correspondences between multiple reference images and the query image. Given multiple projections of one 3D object point, some of which may be occluded, we aim to find its projection coordinate and occlusion flag on the query image. + +![](images/f87318c86f67c1a66bc9f71ac8f42cda010a58fae904f00cebc7d64cc6580557.jpg) +Figure 3. Overview of our network. Unlike existing methods [1, 38, 59, 61], which use two stages to compute the pose, we directly input all reference images into our network without a view selection stage. After obtaining all features of the projection belonging to one 3D object point $\mathbf{p}_k$ , we use Dual-Attention Based Feature Mixer to fuse their features with the query image feature. Then, we build the cost volume followed by two separate heads to predicate the projection of $\mathbf{p}_k$ on the query image, including the occlusion flag as well as the coordinate. + +# 3.1. Preliminary + +Our task is CAD-based novel object pose estimation with RGB images, where the primary goal is to estimate the pose $\mathbf{T}_0$ of the query image $I_0$ . It is worth noting that the objects observed in $I_0$ used for testing are unseen in the training dataset, i.e., $\mathcal{O}_{train} \cap \mathcal{O}_{test} = \emptyset$ [90]. After detecting and segmenting the object in the query image, we can estimate the pose of the novel object using a series of reference images and depths rendered by the corresponding object model. In other words, given $S$ reference images $\{I_1, I_2, \ldots, I_S\}$ showing the same object under various viewpoints, for which the object pose $\mathbf{T}_i = (\mathbf{R}_i, \mathbf{t}_i) \in SE(3)$ , intrinsic matrix $\mathbf{K}_i \in \mathbb{R}^{3 \times 3}$ and depth $\mathbf{D}_i$ are known, we focus on estimating the novel object pose in the query image. + +# 3.2. Correspondences between Reference Images + +Before training and testing, to find the projections of each 3D object point across all reference images, we first sample on each reference image $i$ to obtain 2D pixel coordinates $\mathbf{u}_{i,k} \in \mathbb{R}^{2 \times 1}$ . Using the given ground truth pose $\mathbf{T}_i$ and depth $d_{i,k}$ , we can then recover the corresponding 3D object point in the object model coordinate: + +$$ +\mathbf {p} _ {k} = d _ {i, k} \mathbf {T} _ {i} ^ {- 1} \mathbf {K} _ {i} ^ {- 1} \tilde {\mathbf {u}} _ {i, k}, \tag {1} +$$ + +where, $\tilde{\mathbf{u}}_{i,k}$ is homogeneous coordinate, $1\leq k\leq N$ and $N$ is the total number of sampled points. Besides, we can calculate new 2D coordinates on other reference image $j$ by projecting the 3D object points: + +$$ +\tilde {\mathbf {u}} _ {j, k} = \frac {1}{\tilde {d} _ {j , k}} \mathbf {K} _ {j} \mathbf {T} _ {j} \mathbf {p} _ {k}, \tag {2} +$$ + +where, $\tilde{d}_{j,k}$ is the depth of point $\mathbf{p}_k$ transformed to the $j$ -th camera coordinate. In this manner, we can obtain the 2D pixel coordinates $\{\mathbf{u}_{i,k}\}$ of the $N$ sampled points on $S$ reference images and their 3D object coordinates $\{\mathbf{p}_k\}$ . However, since each point may be occluded by the object itself or other objects, we set the occlusion flag $O_{i,k} \in \{0,1\}$ for each $\mathbf{u}_{i,k}$ . Similar to the Z-buffer algorithm [6], we mark points that are projected outside the image or occluded, i.e., $\left|\tilde{d}_{j,k} - d_{j,k}\right| > \tau$ , as occlusion $(O_{j,k} = 1)$ . + +Next, we aim to compute the corresponding point on the query image. Supposing among $S$ reference images, for a given 3D object point $\mathbf{p}_k$ , $S_o$ of all its projections are occluded and $S_v$ are visible (where $S_v + S_o = S$ ), one approach is to use $S_v$ reference images to match pairwise with it, and finally merge all the matching results to get $\mathbf{u}_{0,k}$ which is the projection of $\mathbf{p}_k$ on the query image $I_0$ . However, this approach can not handle the situation when $\mathbf{u}_{0,k}$ is occluded and fails to fully utilize the multi-view information. To address this, for a 3D object points $\mathbf{p}_k$ , we develop a network to directly fuse all the projections' information around $\mathbf{u}_{i,k}, 1 \leq i \leq S$ in the feature space and locate the corresponding 2D pixel coordinate $\mathbf{u}_{0,k}$ on the query image, as shown in Section 3.3. + +# 3.3. View-Aggregated Point Matching + +Fig. 3 shows an overview of our network architecture. The query image, along with the reference images, are sent to the encoder $f_{enc}$ together. $f_{enc}$ is a ResNet-like backbone [24] sharing the same weights between the query and reference images. Since objects in images may have various poses + +![](images/6e88e60ab7a5cbfb514b732b5900646c5d6b8aa9afe05ebddbbab209f48da588.jpg) + +![](images/a5cafaeda199dbcb32f607c24a60eda4c39ff7cd31dcde1cd44174b10dc4e90a.jpg) + +![](images/18903df575f2c4db4c213a5895b3496f6c0b5f20afe4f02563b148185a4b9a5d.jpg) + +![](images/8346f5284f563eef10a8192063d3add1272ca3379b4db5344b7acba6f770dd39.jpg) +Figure 4. Overview of the Dual-Attention Based Feature Mixer. The mixer consists of three modules: SAP (Self-Attention between Points), SAF (Self-Attention between Frames), and MARQ (Mix-Attention between Reference & Query). These modules perform attention operations between N points within one reference image, between S frames, and between reference images and the query image, respectively. + +and the features of the matching points are independent of the poses, we utilize [80] in the encoder to ensure that the extracted features are rotation-invariant. After feature extraction, we obtain $S + 1$ feature maps: + +$$ +\mathbf {F} _ {i} = f _ {e n c} \left(I _ {i}\right) \in \mathbb {R} ^ {H ^ {\prime} \times W ^ {\prime} \times D}, 0 \leq i \leq S, \tag {3} +$$ + +where $H' = H/8$ , $W' = W/8$ . With pre-sampled 2D projections $\{\mathbf{u}_{i,k}\}_{i=1}^{S}$ and occlusion flags $\{O_{i,k}\}_{i=1}^{S}$ on reference images, we retrieve the feature tokens $\{\hat{\mathbf{F}}_i \in \mathbb{R}^{N \times D}\}_{i=1}^{S}$ using bilinear interpolation. Next, for all 3D object points $\{\mathbf{p}_k\}_{k=1}^N$ , we gather all feature tokens in the feature space and fuse them with the query image feature $\mathbf{F}_0$ using attention mechanism (see Section 3.4 for details). We denote the final gathered feature and fused query image feature as $\bar{\mathbf{F}} \in \mathbb{R}^{N \times D}$ , $\tilde{\mathbf{F}}_0 \in \mathbb{R}^{H' \times W' \times D}$ , respectively. Then we can build the cost volume $\mathbf{C} \in \mathbb{R}^{H' \times W' \times N}$ with the query image feature $\tilde{\mathbf{F}}_0$ . + +For the given cost volume $\mathbf{C}$ , we first extract the information with a Conv3D backbone. After that, we use two separate heads to predict the corresponding 2D heatmap of the 3D object points and the associated occlusion flags. To convert the heatmap to valid 2D coordinates, we use "spatial soft argmax" [15], which computes the argmax of the heatmap and then estimates the spatial average position within a radius around the argmax location. Lastly, we calculate the 6DoF pose directly using RANSAC-based SQ-PnP [72] algorithm. Note that we only use the 2D location where the predicted occlusion flag is False, i.e., where $O_{0,k} \leq \tau_{\mathrm{occ}}$ . + +# 3.4. Dual-Attention Based Feature Mixer + +Previous methods [1, 59, 61] select the reference image closest to the query image for matching. Unlike them, we fuse the feature tokens extracted from all reference images to obtain the final tokens that contain more viewpoint information. We design the Dual-Attention module, an overview of which is illustrated in Fig. 4. Referring to [16], we first initialize the fused feature tokens $\bar{\mathbf{F}}$ as learnable parameters, then input the feature tokens $\hat{\mathbf{F}} \in \mathbb{R}^{N \times S \times D}$ of all reference images, occlusion flags $\mathbf{O} \in \mathbb{R}^{S \times N}$ of these tokens, and the feature map $\mathbf{F}_0$ of the query image. + +Firstly, in order to integrate the spatial location information of $N$ points, we permute $\hat{\mathbf{F}}$ as $\hat{\mathbf{F}}^N = g_N(\hat{\mathbf{F}}) \in \mathbb{R}^{S \times N \times D}$ . Then we input $\hat{\mathbf{F}}^N$ into the SAP (Self-Attention between Points) module for spatial dimension mixing after adding position encoding [70]. Secondly, the features mixed on $N$ -dim are permuted into frame-first form, i.e., $\hat{\mathbf{F}}^S = g_S(\hat{\mathbf{F}}) \in \mathbb{R}^{N \times S \times D}$ , and then sent to SAF (Self-Attention between Frames) module to perform Self-Attention calculation with learnable fused tokens $\bar{\mathbf{F}}$ on $S$ -dim. These permutations enable the first dimension to be merged with the batch size dimension, thereby accelerating computation when multiple objects are predicted concurrently. Finally, the adjusted tokens $\hat{\mathbf{F}}$ are input for the next iteration. To further augment the features, we fuse $\bar{\mathbf{F}}$ with the permuted query image feature $\mathbf{F}_0 \in \mathbb{R}^{(H'W') \times D}$ using MARQ (Mix-Attention between Reference & Query) module, which consists of two Self-Attention and two Cross-Attention layers. It performs the Self-Attention separately on the query image feature $\mathbf{F}_0$ and the learnable fused token $\bar{\mathbf{F}}$ , and Cross-Attention between + +the two [70]. The Dual-Attention module can be written as: + +$$ +\left\{ \begin{array}{l} \hat {\mathbf {F}} = \operatorname {S e l f} _ {\mathrm {N}} \left(g _ {N} (\hat {\mathbf {F}}), \mathbf {O}\right), \text {f o r n 1 i t e r s} \\ \hat {\mathbf {F}}, \bar {\mathbf {F}} = \operatorname {S e l f} _ {\mathrm {S}} \left(g _ {S} (\hat {\mathbf {F}}), \bar {\mathbf {F}}, \mathbf {O}\right), \text {f o r n 2 i t e r s , (4)} \\ \bar {\mathbf {F}}, \mathbf {F} _ {0} = \operatorname {M i x} (\bar {\mathbf {F}}, \mathbf {F} _ {0}, \mathbf {O}), \text {f o r n 3 i t e r s} \end{array} \right. +$$ + +where $\mathrm{Self}_N$ , $\mathrm{Self}_S$ , Mix denote Self-Attention on $N$ -dim, Self-Attention on $S$ -dim, and Mix-Attention, respectively. Mask $\mathbf{O}$ is used in masked attention mechanism, introduced to correct the weight matrices of attention, which avoids fusing erroneous features corresponding to occluded points. Iterate Equation (4) for $n_0$ times and take the obtained $\bar{\mathbf{F}}$ and $\bar{\mathbf{F}}_0$ as the final fused results. By combining Self/Cross-Attention, Self-Attention on $N/S$ -dim, our Dual-Attention module can automatically perform fusion based on the degree of similarity between point-to-point, frame-to-frame and reference-to-query during feature mixing. This module is crucial to accomplishing the view-aggregated point matching task, as we will show in Section 4.4. + +# 3.5. Training Losses + +The total loss for each 3D object point consists of two components: occlusion supervision and location supervision. The occlusion loss is supervised using a BCE loss: + +$$ +L _ {\text {o c c}} = \mathrm {B C E} \left(O _ {g t, k}, O _ {0, k}\right), \tag {5} +$$ + +where $O_{0,k}$ is network output for the $k^{th}$ 3D object point and $O_{gt,k}$ is the corresponding ground truth occlusion flag. + +For location supervision, we use the Huber loss to regress the 2D coordinates of the projection of the 3D object points when the occlusion flag is False: + +$$ +L _ {\text {l o c}} = \operatorname {H u b e r} \left(\mathbf {U} _ {g t, k}, \mathbf {U} _ {0, k}\right) \cdot 1 \left\{O _ {g t, k} = 0 \right\}, \tag {6} +$$ + +where $\mathbf{U}_{gt,k}$ and $\mathbf{U}_{0,k}$ is the ground truth 2D coordinate and predicted 2D coordinate for $k^{th}$ 3D object point. $1\{\cdot\}$ is the indicator function. The total loss is a weighted sum of the occlusion and location losses: + +$$ +L = L _ {\text {o c c}} + \lambda L _ {\text {l o c}}, \tag {7} +$$ + +with $\lambda = 100$ . The final loss is the mean of the losses across $N$ sampled points. + +# 4. Experiments + +In this section, we first present the experiment setup. Then, we compare our method with the state-of-the-art methods for novel object pose estimation on seven core datasets of the BOP challenge [32]. We also provide further ablation studies to evaluate our method. + +# 4.1. Datasets + +We train our network entirely with synthetic images from the GSO-Dataset [38]. Following previous work [38, 56, 59, 61], + +we evaluate our method on seven core BOP datasets [32], including LM-O [2], YCB-V [84], T-LESS [30], TUD-L [31], IC-BIN [17], HomebrewedDB(HB) [35] and ITODD [19]. Detailed information is explained in the supplementary material. We follow the official test splits of each dataset and use the off-the-shelf object detector CNOS [58]. In practical situations, this detector can be replaced by any other lightweight tracking method or an object-specific segmentation network. + +# 4.2. Evaluation Metrics + +For all experiments, we use the standard evaluation protocol in the BOP challenge [31], including Visible Surface Discrepancy (VSD), Maximum Symmetry-Aware Surface Distance (MSSD), and Maximum Symmetry-Aware Projection Distance (MSPD). The final average recall (AR) is calculated by averaging the individual average recall scores of these three metrics across a range of error thresholds. For a more detailed explanation, refer to the BOP challenge [32]. + +# 4.3. Comparison with the State of the Art + +We compare our method with OSOP [68], MegaPose [38], ZS6D [1], GigaPose [59], Genflow [56] and FoundPose [61] as shown in Table 1. In a setting without refinement, our method achieves promising results. Specifically, compared to FoundPose, our method achieves similar performance while utilizing $33 \times$ fewer reference images, with fewer network parameters and shorter inference time. When compared to GigaPose, which uses the second fewest reference images, our method improves accuracy by approximately $10\%$ on the challenging IC-BIN and HB datasets, and by around $25\%$ on the challenging YCB-V dataset. We also achieve comparable results on LM-O, T-LESS, and TUD-L. However, the performance on ITODD is not as good as GigaPose. This might be because it is a dataset with grayscale images, whereas our training is based on RGB images. In addition, it has severe occlusions, reflections, and surfaces with weak textures, which increases the difficulty of matching. However, we still improve the mean AR of all seven core datasets by $6.5\%$ compared with GigaPose. When it comes to MegaPose, our method achieves better results across all seven core datasets and improves around $15\%$ on average. Genflow utilizes a network similar to MegaPose, and our method achieves better results on most datasets, except for ITODD, where performance is impacted due to differences in color modes. ZS6D is a method that first retrieves the closest reference image from 300 reference images and matches the query image with the closest one. However, our method uses far fewer reference images but achieves better results. This demonstrates that our multi-view fusion strategy can improve matching accuracy and increase the AR score. Fig. 5 shows qualitative results, which illustrate the accurate pose estimation results. More qualitative results and comparisons with other methods + +
MethodParm sizeRef NumDetectionLM-OT-LESSTUD-LIC-BINITODDHBYCB-VMEANTIME
OSOP [68]-90 kOSOP [68]27.4----46.429.6--
MegaPose [38]21.6 M520Mask R-CNN [25]18.719.720.515.38.018.613.916.4-
ZS6D [1]21.7 M300CNOS [58]29.821.0----32.4--
MegaPose [38]21.6 M520CNOS [58]22.917.725.815.210.825.128.120.815.5 s
GigaPose [59]316.3 M162CNOS [58]29.927.330.223.118.834.829.027.60.8 s
Genflow [56]21.7 M208CNOS [58]25.021.530.016.815.428.327.723.53.8 s1
FoundPose [61]302.9 M798CNOS [58]39.633.846.723.920.450.845.237.21.6 s
MixRI (ours)5.3 M12CNOS [58]27.025.429.329.710.944.952.831.40.5 s
MixRI (ours)5.3 M24CNOS [58]30.427.433.630.811.650.254.634.10.7 s
+ +Table 1. Results on the seven core BOP datasets. The table compares methods in Average Recall (AR), network parameter size, reference image count, and inference time. Bold denotes the best, and underline the second best. + +
Ref NumsMethodYCB-VLM-OTUD-LMEAN
4GigaPose [59]8.1109.19.1
MixRI (ours)28.611.213.817.9
6GigaPose [59]7.91213.111.0
MixRI (ours)46.522.125.731.4
8GigaPose [59]15.415.612.314.4
MixRI (ours)51.826.228.535.5
12GigaPose [59]14.913.915.314.7
MixRI (ours)52.827.029.336.4
24GigaPose [59]15.918.220.818.3
MixRI (ours)54.630.433.639.5
+ +are provided in the supplementary material. + +Limited Number of Reference Images. Since GigaPose uses the fewest reference images among existing works, we compare it when using only a limited number of reference images. We conduct experiments with various settings by changing the reference image number $S$ and report the results in Table 2. GigaPose experiences a significant performance decrease when there are fewer reference images. Because it's a two-stage approach, which highly relies on the closest reference image. When there are few reference images, selecting a reference image with similar viewpoint becomes difficult, and it is also challenging to provide sufficient information for estimating the pose in their second stage. It is worth noting that other methods [1, 38, 56, 61], which are also based on the retrieval mechanism, can encounter the similar issue when using a limited number of reference images. In contrast, our method is designed specifically for limited reference images and achieve a better AR score when using the same number of reference images. + +Runtime & Memory. We report the average inference timings for each method in Table 1, measured using a single 4090 GPU. It is worth noting that the detection time included in CNOS [58] is also taken into account, and each image may contain multiple objects for pose estimation. In addition + +![](images/2fbfe5fe5b9a36e1400f66395674c8833b468573fc55898c96e0fd1f9f1ff1e1.jpg) +Figure 5. Qualitative results on YCB-V. We present the pose estimation results obtained using MixRI. All the results are visualized in error heatmap [74] which darker blue indicates lower error with respect to the ground truth pose (legend: $0\mathrm{cm}$ 5 cm). to reducing inference time, our method significantly saves time in rendering the reference images and does not require pre-extraction of features. However, GigaPose and Found- Pose need pre-extracting all the reference image features [59, 61], which also waste memory due to the need to cache them. Compared to MegaPose, which also does not require pre-extracting features, our method outperforms it, as we eliminate the need for image rendering during inference [38]. + +![](images/a565b60b29f6790b263757884eb1e069aef8559f78936f0b8d232fbe94a390a0.jpg) + +We also report the network parameters compared with others in Table 1. The parameter count of our network is significantly smaller than that of all other methods. In particular, we have over $50 \times$ fewer parameters than GigaPose. Combined with fewer reference images and no feature cache needed, MixRI is very friendly for deployment on devices with limited memory space. More discussions are shown in A.7 in the supplementary material. + +# 4.4. Ablation Study + +Effectiveness of the Attention Module. Our main innovation is to fuse the multiple reference points in the feature + +Table 2. Comparison with a limited number of reference images. We compare our method with GigaPose in different number of reference images. + +
SAPMARQYCB-VLM-OTUD-LMEAN
XX2.92.82.22.6
✓X19.27.88.711.9
X✓33.213.421.922.8
✓✓54.630.433.639.5
+ +Table 3. Effectiveness of the attention module. We analyze the impact of our different modules. Here SAP stands for Self-Attention between Points in Section 3.4 and MARQ stands for Mix-Attention between Reference & Query in Section 3.4. + +
MethodRef NumDetectionRefinementLM-OT-LESSTUD-LIC-BINITODDHBYCB-VMEANTIME
MixRI+ (ours)162CNOS [58]-42.636.041.833.922.256.056.941.31.0 s
MegaPose [38]520CNOS [58]MegaPose [38]49.947.765.336.731.565.460.150.917.0 s
GigaPose [59]162CNOS [58]MegaPose [38]55.654.657.844.337.869.363.454.72.3 s
FoundPose [61]798CNOS [58]MegaPose [38]55.451.063.343.034.669.566.154.74.4 s
MixRI (ours)12CNOS [58]MegaPose [38]40.845.044.644.421.661.461.145.61.5 s
MixRI (ours)24CNOS [58]MegaPose [38]44.846.148.244.621.361.462.046.91.7 s
MixRI+ (ours)162CNOS [58]MegaPose [38]52.150.457.544.534.367.164.853.02.1 s
+ +![](images/41447d7739d4289978b26c4eb562f53911d5d5fb9d3be0de0bc5e689dc93c080.jpg) +(a) Number of Correspondences + +![](images/0e8cfc7925daeb008c777aa4cc48ffea8a8762f0633fc3b21861244f93fee703.jpg) +(b) Number of Reference Images +Figure 6. Impact of the number of correspondences and reference images. We report the AR score on LM-O, TUD-L, and YCB-V, along with the average. + +space. To demonstrate the effectiveness of the fusing strategy, we conduct several ablation studies. As shown in Table 3, through row 1 and row 2, adding SAP brings a $9.3\%$ increase in AR score. The considerable increase comes with MARQ, which results in a $20.2\%$ increase in AR score. Finally, with both modules, we get the final AR score shown in row 4, which has a $36.9\%$ increase compared to row 1. + +Number of Correspondences. Fig. 6 (a) shows the results of different correspondences used in matching. Our method is robust to correspondence, and increasing the correspondences can increase the AR score until around 2400. It is worth mentioning that, although there are only 60 correspondences, for the YCB-V dataset, there is already an AR score of $45\%$ . When the number of correspondences reaches 240, it is already comparable to other methods. + +Number of Reference Images. Fig. 6 (b) ablates the number of reference images. Our network is trained using 12 reference images, but it does not require the same number of reference images during inference. Therefore, we only alter the number of reference images during the test stage. However, we observe a performance degradation when the number of reference images increases significantly, particularly when it exceeds 60. This is expected because our lightweight network is less capable of handling the feature fusion from a large number of reference images. As previous work [38, 59, 61], more reference images need a larger network with more parameters to handle. + +Effectiveness of Occlusion Flags. Table 5 demonstrates the effectiveness of incorporating occlusion flags. It is worth noting that when $\tau_{\mathrm{occ}} = 1$ , the occlusion flag mechanism is + +Table 4. Results on the seven core BOP datasets with refinement. The table shows Average Recall (AR) scores per dataset, the time and the number of reference images. We also present MixRI+, the same structure but trained for more reference images available. + +
τoccLM-OT-LESSTUD-LIC-BINITODDHBYCB-VMEAN
1.027.624.130.928.510.444.149.430.7
0.830.427.433.630.811.650.254.634.1
0.527.826.728.428.610.246.853.831.8
+ +Table 5. The effectiveness of occlusion flags. We compare different occlusion flag settings. + +effectively disabled. The results validate the robustness of the method when occlusion prediction is enabled. + +Refinement. While refinement can lead to improved pose accuracy, it does so at the expense of speed, which goes against our initial intention. However, to demonstrate the potential of our lightweight network, we also present the results after refinement in Table 4. For this, we use MegaPose [38] to further refine our initial pose estimates. Additionally, we include another MixRI variant (MixRI+) having the same structure but trained for more reference images available. To optimize the use of reference images, we follow the approach in [59], which retrieves the reference image with the closest out-of-plane rotation. However, in our method, we also select three additional reference images as input to the network. Detailed information on this process is provided in the supplementary material. Notably, with more reference images available, the initial poses achieve an AR score of 41.3, surpassing FoundPose which is 37.2. Additionally, the refinement performance is comparable, even we use fewer network parameters and achieve faster processing speed. + +# 5. Conclusion + +In this paper, we proposed MixRI, a novel approach for CAD-based novel object pose estimation using RGB images. Designed with practical applications in mind, our method features a lightweight network and requires far fewer reference images than existing approaches, eliminating the need for feature caching. This reduces both pose inference time and reference image preparation time while avoiding preprocessing. Despite its simplicity, MixRI achieves performance comparable with more complex networks that rely on numerous reference images. 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Six samples of the scenes in the dataset. The different agent's LiDAR point clouds are colored as follows: electric vehicle-001 (EV-1) in purple, electric vehicle-002 (EV-2) in red, urban vehicle (Laser) in yellow, and the RSU DOME and TOP LiDARs in green and blue, respectively. We also draw the annotated bounding boxes within the scene. Best viewed in color. + +# Abstract + +Vehicle-to-everything (V2X) collaborative perception has emerged as a promising solution to address the limitations of single-vehicle perception systems. However, existing V2X datasets are limited in scope, diversity, and quality. To address these gaps, we present Mixed Signals, a comprehensive V2X dataset featuring 45.1k point clouds and 240.6k bounding boxes collected from three connected autonomous vehicles (CAVs) equipped with two different configurations of LiDAR sensors, plus a roadside unit with dual LiDARs. Our dataset provides point clouds and bounding box annotations across 10 classes, ensuring reliable data for perception training. We provide detailed statistical analysis on the quality of our dataset and extensively benchmark existing V2X methods on it. Mixed Signals is ready-to-use, with precise alignment and consistent annotations across time and viewpoints. We hope our work advances research + +in the emerging, impactful field of V2X perception. Dataset details at https://mixedsignalsdataset.cs.cornell.edu/. + +# 1. Introduction + +In recent years, driver assistance [19, 29] and autonomous driving [1, 47] technologies have advanced significantly, equipping vehicles with promising capabilities in perception [20, 44], planning [13, 15], and control [2, 8]. Most of these developments focus on single autonomous vehicle scenarios. Despite the advancements, such settings still face challenges in complex or unpredictable situations [42]. For instance, important traffic participants can be occluded from view, or sensors can fail unexpectedly. As autonomous vehicle deployment increases, new possibilities emerge to address these issues: multiple vehicles can communicate with each other and nearby infrastructure, enabling each vehicle to reliably detect road users even when its own sensors miss them by leveraging shared information. This approach is commonly referred as vehicle-to-everything (V2X) collaborative perception. + +
DatasetHetero. FleetLocationDriving Side#Roadside LiDARs# CAV# Point Clouds (K)# 3D Boxes (K)# Classes# Vulnerable ClassesTrack ID
V2X-Sim [23]✘CARLA (Sim.)Right1510.026.610✓
OPV2V [42]✘Right02-711.4232.910✘
V2X-Set [41]✘Right2-72-733.0230.010✘
DAIR-V2X-C‡ [45]✘ChinaRight2139.0464.0104✘
V2X-Seq (SPD)‡ [46]✘ChinaRight2115.010.4104✓
RCooper‡ [12]✘ChinaRight3030.0N/A103✘
HoloVIC‡ [26]✘ChinaRight21100.0180032✓
Open Mars [24]✘USARight02-315.00N/AN/A✘
V2V4Real [43]HeightUSARight0220.0240.050✓
V2X-Real [38]HeightUSARight2233.01200.0102✓
TUMTrafV2X [48]✘GermanyRight212.030.083✓
Mixed SignalsHeight, TiltAUSLeft2345.1240.6104✓
+ +Table 1. Comparison of Mixed Signals and existing V2X datasets. To our best knowledge, Mixed Signals is the first dataset to include heterogeneous CAV LiDAR configurations, and also the first one that is collected in a left-hand driving country. It captures complex, real-world traffic scenarios and features a diverse range of traffic participants. Those marked with $\ddagger$ are valuable datasets, but are only accessible from certain geographical regions. + +While single-vehicle perception datasets are abundant across diverse driving conditions [4, 5, 9, 11, 16, 18, 27, 28, 30, 33, 39], real-world V2X datasets remain limited in availability, diversity, and quality. Only a handful of publicly available V2X datasets exist [24, 38, 43, 48], with some of them accessible only within specific geographical regions [12, 26, 45, 46]. These data are collected exclusively from three right-hand traffic locations, overlooking the unique traffic dynamics in left-hand traffic countries which make up about a third of the world [40]. Furthermore, as collaborative perception becomes more widespread, it is valuable for vehicles equipped with different sensor configurations to communicate. However, in prior datasets, the connected autonomous vehicles (CAVs) share identical or very similar LiDAR configurations. Finally, as the V2X setting involves multiple agents and sensors, data collection and alignment present additional challenges. Often times, difficulty with pose estimation and faulty localization systems result in poor alignment (Figure 4). Such inaccuracies can lead to suboptimal performance for detector training [41]. + +To address these limitations, we introduce the Mixed Signals dataset, designed to support diverse real-world V2X research scenarios with clean, high-quality data. Notably, Mixed Signals is the first V2X dataset that provides heterogeneous CAV LiDAR configurations in both position and orientation, and features a left-handing traffic country, Australia. The dataset includes 45.1k point clouds and 240.6k bounding boxes, collected from three CAVs equipped with two configurations of LiDAR sensors, along with a roadside unit with two LiDARs. It captures a diverse range of traffic participants across 10 different classes, including 4 vulnerable road user categories. Furthermore, compared to existing datasets, Mixed Signals offers significantly more pre + +cise alignment and consistent annotations across time and viewpoints. We emphasize that our dataset is ready-to-use; a subset is provided in the supplementary materials, along with the corresponding video visualization showcasing the quality of our collected data and annotations. To summarize, our contributions are: + +- We introduce the Mixed Signals dataset, a high quality, large-scale, publicly available V2X dataset created through careful processing and precise annotations. +- To the best of our knowledge, we are the first real-world V2X dataset that encompasses CAV LiDAR configurations that differ in both position and orientation, as well as left-hand traffic scenarios. +- We provide detailed analysis of the dataset's statistics, and conduct comprehensive benchmarking of existing V2X methods across various settings. + +# 2. Related Works + +While existing collaborative perception datasets have the same sensor setup for their CAVs, our dataset contains three vehicles with two different sensor configurations, including the height and tilt of LiDAR and the type of vehicle. This difference introduces heterogeneity to our fleet of vehicles, thus making our data more closely resemble the real-world collaboration deployment. To the best of our knowledge, we have the largest fleet of CAVs with the most diverse sensors of any prior works. + +Vehicle-to-Everything Communication. One of V2X's objectives is to enhance the perception capabilities of CAVs, facilitating their deployment in urban environments. These areas usually have a high presence of Vulnerable Road Users (VRUs), which are defined as people not inside vehicles [32]. Despite this, VRUs are under represented in prior + +![](images/717450d3f72599f9171b7c6c44574e4d1fa34a75986e00fa5f84cf46fe299dfe.jpg) +(a) Electric vehicle (EV). + +![](images/bb5ef9436c46944f46094a6af2ede911eef52a30abdc97816452ea7d0e185a2b.jpg) +(b) Urban vehicle with a OS1-128 beams LiDAR. + +![](images/06d25efb6ad2e87ab9ad47a5e09cd5963b2d177902c329d50b47113c46745127.jpg) +(c) Roadside Unit (RSU). + +works. The three synthetic datasets made with CARLA [10] and the real-world dataset V2V4Real [43] do not have VRUs. DAIR-V2X-C [45] and its extension V2X-Seq (SPD) [46] provide annotations for 4 VRU classes (pedestrian, bicyclist, tricyclist, and motorcyclist). However, the absence of details on class distribution in their publications make it hard to judge their VRU coverage. Additionally, restricted access to these datasets outside China limits their usability. TUMTrafV2X [48] annotates 3 VRU classes including pedestrian, bicycle, and motorcycle, which together account for only $24.6\%$ of the total annotations. Such underrepresentation causes VRU detection to be overlooked in several collaborative perception studies [22, 36, 41, 42]. + +Real World Vehicle-to-Everything Datasets. The recent V2X-Real [38] has a large number pedestrian annotations, which is higher than annotations of the class car, and 3 other VRU classes (scooter, motorcycle, and bicycle). A drawback of this dataset for VRU detection evaluation is that its benchmark only accounts for pedestrians. Our dataset contains the highest number of VRU classes, including pedestrian, bicycle, portable personal mobility, and motorcycle. More importantly, these classes account for $50.3\%$ of our dataset's total bounding boxes. Instead of selecting certain VRU classes for benchmarking, we group 4 VRU classes into 2 detection classes as in Section 3.4 to provide a better understanding of how different collaboration methods perform in detecting VRUs. We provide a detailed comparison of our dataset, Mixed Signals, with prior works in Table 1. + +# 3. Mixed Signals Dataset + +In this section, we describe the data collection process of the Mixed Signals dataset. We provide a devkit and our full dataset for download on our website: https://mixedsignalsdataset.cs.cornell.edu/. + +# 3.1. Hardware + +The data collection was carried out using three vehicles and a roadside unit. + +![](images/b118da62626dd037f8a46e061edce7fe12f2bf72d249c27df532ca410821c30f.jpg) +Figure 2. Vehicles used for data collection. (a) is a small electric vehicle outfitted with an OS1-128 beams LiDAR system. The LiDAR is mounted at a $15^{\circ}$ angle relative to the vehicle's body and stands at a height of 1.63 meters. (b) is an urban vehicle equipped with an OS1-128 beam LiDAR system located at a height of 1.9 meters. (c) is the RSU which consists of two LiDARs: an OS1-64 beam (TOP) and an OSDome-128 (DOME) LiDAR mounted on a pole at the intersection at a height of 2.5 meters. +Figure 3. Geographical location of the roadside unit. + +**Vehicles.** The three vehicles included two small electric vehicles (EVs) and one urban vehicle, each equipped with OS1 128-beam LiDARs, as shown in Figure 2. The LiDAR on the urban vehicle is located horizontally with respect to the ground, while for the EV, the LiDAR is tilted downwards 15 degrees. We transformed both EVs' point clouds to have a horizontal reference frame as shown in Figure 2a. Although all the vehicles are equipped with the same type of LiDAR sensor, their configurations differ in terms of sensor position and orientation. This variation introduces additional complexity, creating a domain gap between the data collected from different vehicles. + +Roadside Unit. The roadside unit is equipped with two different LiDAR sensors: an OS-Dome 128-beam for long-range detection and an OS1 64-beam LiDAR for detecting nearby objects. It was located at a fixed geographical position, 2.5 meters above the ground. The intersection where the roadside unit was installed experiences moderate vehicular traffic and features pedestrian crosswalks along with a bike lane that crosses the intersection. This setup allows us to capture diverse agents during data collection. The placement of the roadside unit is illustrated in Figure 3. + +# 3.2. Data Acquisition + +The data collection took place at the intersection between Abercrombie Street and Myrtle Street in Sydney, Austria, + +where the roadside unit is located. The vehicles recorded LiDAR data for two hours during peak rush hour. Throughout this period, the three vehicles repeatedly passed through the intersection. This allowed them to capture interactions between the vehicles and other agents on the road, such as pedestrians, cyclists, and other vehicles. + +# 3.2.1. Synchronization and Localization + +Synchronization and localization are crucial for cross-sensor point cloud alignment. Our dataset employs proven techniques from robotics to achieve precise sensor synchronization and agent localization. The end result is superior point cloud alignment compared to previous V2X datasets (Figure 4). We describe the details below. + +Synchronization refers to the temporal alignment of data streams, ensuring that synchronized sensors capture the same events simultaneously within their overlapping fields of view (FOV). We use GPS time to timestamp point clouds captured by our LiDARs at a frequency of $10\mathrm{Hz}$ . Even if two vehicles are GPS-synchronized, cross-sensor synchronization still needs to be considered. For example, since the LiDAR scans the environment in a rotating fashion, the data collected at different spatial locations are captured at slightly different moments. We defined data samples by setting a time window to match the closest available timestamps from each LiDARs. A maximum timestamp mismatch of 50 milliseconds between point clouds was set to achieve minimal spatial discrepancies. For additional details, refer to Appendix C.1. + +Localization, i.e., estimating vehicle position relative to a global reference frame, is one of the most critical tasks for CAV. To overcome inherent problems of Global Navigation Satellite System (GNSS) in urban environments, we use dense and accurate point cloud maps [31] as references for our localization algorithm. Both the vehicles and the roadside units are localized within a common reference frame, referred to as the map_frame, which serves as the origin of our map. The localization algorithm employs a scan-matching technique [3] to estimate the vehicles' poses within this map, achieving a maximum positioning error of $15\mathrm{cm}$ and a heading error of 0.4 degrees. This allows for consistent spatial alignment between the vehicles and the roadside infrastructure. The vehicles' localization estimates their positions within the map_frame, while the roadside unit is static. We leave details about map construction and usage in Appendix C.2. + +# 3.2.2. Scene Selection + +In total, 37 scenes – each consisting of a 30-second snippet—were carefully selected for inclusion in the dataset due to their rich diversity of vehicles, pedestrians, and cyclists. The primary goal was to capture various vehicles and vulnerable road users. These scenes encompass a broad spec + +![](images/80710939dbf9b32c1257e56a201c404f77583a0fc995dd6225db84f353c9752d.jpg) +Figure 4. Localization and synchronization quality of Mixed Signals and existing datasets. Different colors correspond to different sensors. In the lateral view, existing datasets visually exhibit vertical inconsistencies, where one point cloud is tilted due to localization errors. In contrast, point clouds in Mixed Signals are all accurately aligned. + +trum of interactions, including between different types of vehicles and between vehicles and vulnerable road users. The selected scenes feature intersections of the FOV of the LiDARs of 3 vehicles and the RSU. Among 37 scenes of our dataset, we select 33 scenes for training and 4 scenes of testing. The size of the training set and test set are 9553 and 1164 data samples, respectively. Our selection ensures that there is no temporal overlap between the training set and test set and among scenes of the test set. + +# 3.3. Dataset Annotation + +The task of 3D object detection for autonomous vehicles requires annotations in the form of 3D bounding boxes, usually parameterized by the center location, three dimensions (length, width, height), and rotation (represented as a quaternion). To generate such annotations for each data sample, we first aggregate the point clouds of every agent in the coordinate of the roadside unit's top (TOP) LiDAR to focus the annotators' attention to the intersection of interest. Then, professional annotators from FlipSideAI [34] employ the SegmentsAI [35] annotation tool to label objects and localize them with a 3D bounding box. Classes labeled belong to 10 categories, consisting of: car, truck, pedestrians, bus, electric vehicle, trailer, motorcycle/bike, bicycle, portable personal mobility, and emergency vehicle. Figure 1 depicts the annotations applied to the dataset, where each object is enclosed within a cuboid. + +Annotations. Our annotation process involved cycles of monitoring, reviewing, and adjusting labels to meet defined quality objectives. This allows Mixed Signals dataset to extend the quality of the pioneering datasets in the field, which are generally labeled by lay annotators, as shown in Figure 5. Here, we reproject the bounding box of a vehicle, as + +![](images/80fe360ca94858f82566ccf96cc02f2bbb10d499b8fff04de645c2dce09d2a70.jpg) +Figure 5. Label quality of Mixed Signals and existing datasets. We aggregate labels of an object across a entire snippet. Labels in Mixed Signals are consistent across time steps and viewpoints. + +observed from other sensors, back onto its coordinate frame to visualize label consistency. Details of the class descriptions and labeling instructions are presented in Appendix Sec. B. While agents in our dataset are synchronized at 10 Hz, we sample keyframes at 1 Hz for manual annotation. To obtain annotations in a non-key frame, we linearly interpolate the pose of annotations of its closest preceding and succeeding keyframes based on their timestamp. + +Category Labels. The Mixed Signals dataset categories consist of road agents in 10 categories of vehicle types and pedestrians including: Car, Truck, Emergency Vehicle, Bus, Motorcycle, Motorized Bike, Portable Personal Mobility Vehicle, (traditional) Bicycle, Electric Vehicle, Trailer, and Pedestrian. Detailed definition of each category can be found in the appendix. + +# 3.4. Dataset Analysis + +Statistics. In our benchmark, we group 10 categories into 3 detection classes according to Table 2. Figure 7 shows the distribution of annotations of three classes with respect to their polar coordinate in the coordinate system of TOP. Figure 8 shows the distribution of dimensions and yaw angle of annotations of three classes. Figure 6 shows the number of annotations of each class in the training set and test set. Figure 9 analyzes track lengths in the training and test set. For both splits, most tracks are under 10 seconds. This is due to the dynamic and typical speeds at the intersection environment. A sharp peak at 30 seconds indicates the presence of static objects detected primarily by the RSU for the entire sequence duration. Figure 10 depicts the aggregation of point clouds from 5 agents and ground truth annotations in the coordinate system of TOP during a 4-second time span, which amounts to 40 time steps. The consistent pose of static objects and the smooth trajectory of dynamic objects visually demonstrate the quality of our annotation. + +# 4. Proposed Tasks and Benchmarks + +Our dataset includes multiple agents and annotations in the form of 3D bounding boxes with track IDs. This enables + +
Detection ClassAnnotation Classes
Vehiclecar, truck, emergency vehicle, bus, electric vehicle, trailer
Bikemotorbike, bicycle, portable personal mobility
Pedestrianpedestrian
+ +Table 2. Definition of detection classes. The Mixed Signals dataset includes 10 fine-grained annotation classes for traffic participants, organized into 3 broader detection classes. + +![](images/016278d100378cf0884b04acd871ddc0ddb25df44de84728d799ef1b7221cf86.jpg) +Figure 6. Number of objects by class. The y-axis is in log scale. + +the development of methods for various collaborative perception tasks, such as object detection, tracking, and motion forecasting. Given the importance of object detection in autonomous driving, we focus on collaborative detection tasks in the main text and report preliminary tracking benchmark results in Appendix B.2. + +# 4.1. Definition of Tasks + +We define two tasks that are distinguished by the collaboration setting: Collaborative Object Detection and Single-Vehicle Object Detection enhanced by communication to RSU, which we describe in the following sections. + +Collaborative Object Detection. This is the classical collaborative object detection task [22, 36], where every connected agent (i.e., vehicles and RSUs) uses a shared model to (i) extract features from their point clouds, (ii) generate messages to send to other agents, and (iii) fuse the features of their point clouds with messages received from others. The goal is to detect every visible object in a region of interest. We define visibility by comparing the number of LiDAR points contained within an object's bounding box to a threshold. In this task, these LiDAR points are sourced from any agents present within the region of interest. + +Object Detection Enhanced by Communication to RSU. This task assumes that the RSU model is designed and trained by a different provider than the one responsible for the CAVs' models. In this task, the RSU model is pretrained in the single-vehicle detection setting to detect objects visible to its LiDARs. After the pre-training process, the RSU model is fixed. CAVs in the proximity of the RSU + +![](images/6903c23e05707adfee6a50cef1acb12b8dad68679431662be75940fdce8b2be3.jpg) +(a) Vehicle + +![](images/be4dae8f5508f11f513345f60db83884c4e1774dde44e2eb9a0e888f5967a0e5.jpg) +(b) Bike + +![](images/6cfaac11fa5073925b15a6023ac0f9199c417b0a22bf660f3c4c3f842d8fddb6.jpg) +(c) Pedestrian + +![](images/786f3c375ef7df954d3574fe0a0acf293dee49c2af9fb7caaeb726c2db170d2f.jpg) +Figure 8. Distribution of bounding box dimensions and yaw angles. Vehicles exhibit a wide range of sizes. + +![](images/985d91a425238ad604f1dff6a63a8af3297623b7c6cc4eb0ad4de6e3265d04bd.jpg) + +![](images/5c2b58fd9727db937fd7b028832df7e3ba438b882708e6b651c631084708bae3.jpg) + +![](images/6d608235495113c00936c11cb30afaa89c8625a59319e0fbef50b61bb33a04e7.jpg) +Figure 7. Distribution of annotated object locations. Locations are shown in polar coordinates relative to the RSU TOP sensor. + +![](images/5ddb751596f709643d6771efb0aef57572adcbad2f203abef89eb9d225de84c6.jpg) +Figure 9. Distribution of track lengths. The peak at 30 seconds corresponds to static objects. + +receive messages from the RSU to enhance their detection capabilities. The objective is to detect all objects in a region of interest that are visible to either the CAV or the RSU. + +The differences between this task and Collaborative Object Detection are twofold. First, there is no communication among connected vehicles in this task, making it similar to Vehicle-to-Infrastructure (V2I) detection [38, 45, 48]. Second, instead of having a single model shared among all connected agents like prior works on V2I collaboration, we have one model for the CAVs and another independent model for the RSU. This introduces a different challenge, as the CAV's model must adapt to messages from the RSU, which may contain domain gaps due to differences in model architecture, types of LiDAR, and viewpoints. + +![](images/3943d8bc344090721392e5435904de39c23fb949954c8b72b9d15995870989b9.jpg) +Figure 10. Visualization of object tracks in Mixed Signals. Dynamic objects display smooth trajectories, while static objects maintain consistent poses over time, highlighting the high quality of our annotations. + +
Vehicle AP@Bike AP@Pedestrian AP@Avg. Bandwidth (MB)
IOU 0.5IOU 0.7IOU 0.5IOU 0.7IOU 0.3IOU 0.5
No Fusion0.420.420.190.190.470.410.00
Early Fusion (Adapting [43])0.240.24----7.79
Early Fusion0.650.650.650.650.740.677.79
Attentive Fusion [42]0.820.820.710.710.740.685.26
V2V-Net [36]0.720.720.690.690.420.324.19
F-Cooper [6]0.750.750.680.680.720.6515.31
V2X-ViT [41]0.840.840.710.700.770.7019.36
V2V-AM [21]0.830.830.790.790.690.6016.78
where2comm [14]0.770.770.740.740.310.1816.78
Laly Fusion [7]0.610.610.680.680.690.620.11
Late Fusion (Adapting [43])0.120.12----0.11
Late Fusion0.430.430.560.560.570.480.11
+ +Table 3. Benchmarking results for the Collaborative Object Detection task. All fusion methods outperform the No Fusion baseline, highlighting the advantage of collaborative perception. Each fusion method involves trade-offs between detection performance and communication bandwidth overhead. Models adapted from a premier R.H.S. V2V dataset [43] are shown in gray. + +
Vehicle AP@Bike AP@Pedestrian AP@
IOU 0.5IOU 0.7IOU 0.5IOU 0.7IOU 0.3IOU 0.5
EV-1 + RSUNo Fusion (EV-1 only)0.330.330.280.280.370.30
No Fusion (RSU only)0.220.220.200.190.260.22
Attentive Fusion0.530.530.600.590.570.45
V2V-Net0.460.460.470.470.320.21
Late Fusion0.290.290.430.430.520.41
EV-2 + RSUNo Fusion (EV-2 only)0.330.330.160.160.080.05
No Fusion (RSU only)0.240.240.200.190.260.23
Attentive Fusion0.560.560.560.560.400.27
V2V-Net0.520.520.490.480.270.18
Late Fusion0.410.410.490.490.430.31
Laser + RSUNo Fusion (Laser only)0.300.300.320.320.460.44
No Fusion (RSU only)0.170.170.180.180.250.22
Attentive Fusion0.710.710.660.650.580.50
V2V-Net0.630.630.550.540.370.27
Late Fusion0.460.460.520.510.660.57
+ +Table 4. Benchmarking results for the Object Detection Enhanced by Communication to RSU task. Communication between the agent and RSU generally improves performance compared to single-agent perception. Performance varies across agents with different sensor configurations, suggesting future research opportunities to develop methods that work effectively with diverse sensor types. + +# 4.2. Benchmark + +Evaluation Settings. Since the annotations are made in the coordinate system of TOP, we define the region of interest for the two detection tasks as the range $[-51.2, 51.2]$ meters along both the x and y axes of this coordinate system. For evaluation, we transform objects detected by each agent into this coordinate system. The visibility threshold is + +set to 5 points. Since timestamp mismatches and localization errors are inherent in real-world applications and consequently present in our dataset, we do not artificially introduce them into the messages exchanged among connected agents (something that is often done in synthetic datasets [41, 42]). We measure object detection performance using Average Precision (AP). Detected objects are matched with ground truth based on their Intersection over Union (IoU) + +in the bird's-eye view plane. A detection and a ground truth object are considered a match if their IoU exceeds thresholds of 0.3, 0.5, or 0.7. In addition to AP, we measure the bandwidth consumption of each collaborative method to gauge their practicality. The total bandwidth consumption is calculated by multiplying the number of agents in the collaboration network by the size of the message each agent sends. While the number of agents is not dependent on the collaboration method of choice, the message size is. We report the bandwidth consumption by averaging the size of the messages that agents send, measured in Megabytes (MB). While some intermediate collaboration methods [22, 36, 41] employ specialized compressing algorithms to reduce the message size, other methods [7, 25, 42] do not. For fair comparison, we report uncompressed sizes. + +Methods. Our benchmark covers three conventional collaboration frameworks, namely Early fusion, Intermediate fusion [6, 14, 21, 36, 41, 42], and Late fusion, and the recent Laly fusion [7]. We detail the benchmarking methodology specifics in the appendix. + +# 4.3. Results + +# 4.3.1. Collaborative Object Detection + +We show the benchmark of the Collaborative Object Detection task in Table 3. The results in this table clearly demonstrate the advantage of collaboration perception over single-agent perception, as all fusion methods largely outperform No Fusion on every class. The comparison of three conventional fusion methods, including Early, Intermediate, and Late, shows that a higher precision is attained at the cost of a larger bandwidth consumption. In contrast, Laly fusion achieves comparable precision on Bike and Pedestrian compared to Early Fusion and Intermediate Fusion while consuming an order magnitude less bandwidth. The high performance at less bandwidth of Laly fusion coupled with its simplicity make this method a strong candidate for real-world deployment. However, we note that there is still ample room for improvement, particularly among the VRUs, suggesting the need for future algorithm design. + +Domain Gap from prior R.H.T. Datasets. To illustrate the domain gap covered by Mixed Signals, we directly adapt an early-fusion and a late-fusion model trained on the right-hand traffic (R.H.T.) dataset, V2V4Real [43], onto our dataset (grayed-out rows in Table 3). Performance degraded significantly, with vehicle headings predicted incorrectly, indicating a learned prior from traffic flow (Figure 11). This highlights a substantial domain gap due to left-hand traffic and sensor modality differences, underscoring Mixed Signals' unique contribution to the V2X perception landscape. + +# 4.3.2. Detection via Communication to RSU + +Table 4 presents the performance of different fusion methods on Object Detection Enhanced by Communication to + +![](images/f13625ba9743f0b872dbdff773fd30f1798b2b75cfa22d3f52e0f5788c646d60.jpg) +Figure 11. Detection visualization from adapting models trained on V2V4Real [43] into Mixed Signals. Ground truth bounding boxes are shown in green and predicted detections in blue, with heading indicated by the triangle. Observe that predicted heading directions are often aligned to priors learned in R.H.T. driving. + +RSU task. In this setting, detector training is more challenging, as each vehicle-centric detector must adapt to a frozen RSU detector. Nevertheless, results show that communication with RSU is still advantageous, as evidenced by the substantial performance improvement over the No Fusion baselines. Furthermore, the performance of the Laser car is better than the performance of the two EVs. This is because the LiDAR of the Laser car has a 360-degree coverage of its surroundings. On the other hand, the tilted angle of the LiDAR on the two EVs makes the region behind them unobservable. The LiDARs on the two EVs do not capture the intensity information, resulting in a domain gap between their features and those from the RSU. These observations point to future research directions for developing methods that could work well with diverse sensor configurations. + +# 5. Discussion and Conclusion + +Our work presents the Mixed Signals V2X dataset, created through careful data selection, sensor synchronization and localization, and a strong investment in high quality annotations. To the best of our knowledge, our dataset is the first to support heterogeneous sensor configurations with varying positions and orientations, collected in an out-of-domain left-hand traffic country, Australia, providing a diverse dataset addition to the field. We hope that the release of our dataset will facilitate research into complex and realistic settings for V2X perception. Future directions of research include studying communication protocols that ensure both fast transmission and directed communication that targets salient information. + +# Acknowledgement + +We thank Runsheng Xu and Hao Xiang for their insightful discussions and support throughout the early stage of this project. This research is funded by University of Sydney – Cornell University Ignition Grants/Global Strategic Collaboration Awards, National Science Foundation (IIS-2107161), and the New York Presbyterian Hospital. MinhQuan Dao is funded by ANNAPOLIS project managed by the French National Agency for Research (ANR-21-CE22-0014), and Katie Luo by AAUW American Dissertation Fellowship. + +# References + +[1] National Highway Traffic Safety Administration. Research on connected vehicle technology. In online. https://www.nhtsa.gov/sites/nhtsa.gov/files/2024-02/research-connected-vehicle-technology-report-to-Congress-021524.pdf, accessed 29/09/2024.1 +[2] Alexander Amini, Igor Gilitschenski, Jacob Phillips, Julia Moseyko, Rohan Banerjee, Sertac Karaman, and Daniela Rus. Learning robust control policies for end-to-end autonomous driving from data-driven simulation. IEEE Robotics and Automation Letters, 5(2):1143-1150, 2020. 1 +[3] P. Biber and W. Strasser. 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Code: https://github.com/snehashismajhi/GS-MoE + +# Abstract + +Video Anomaly Detection (VAD) is a challenging task due to the variability of anomalous events and the limited availability of labeled data. Under the Weakly-Supervised VAD (WSVAD) paradigm, only video-level labels are provided during training, while predictions are made at the frame level. Although state-of-the-art models perform well on simple anomalies (e.g., explosions), they struggle with complex real-world events (e.g., shoplifting). This difficulty stems from two key issues: (1) the inability of current models to address the diversity of anomaly types, as they process all categories with a shared model, overlooking category-specific features; and (2) the weak supervision signal, which lacks precise temporal information, limiting the ability to capture nuanced anomalous patterns blended with normal events. To address these challenges, we propose Gaussian Splatting-guided Mixture of Experts (GS-MoE), a novel framework that employs a set of expert models, each specialized in capturing specific anomaly types. These experts are guided by a temporal Gaussian splatting loss, enabling the model to leverage temporal consistency and enhance weak supervision. The Gaussian splatting approach encourages a more precise and comprehensive representation of anomalies by focusing on temporal segments most likely to contain abnormal events. The predictions from these specialized experts are integrated through a mixture-of-experts mechanism to model complex relationships across diverse anomaly patterns. Our approach achieves state-of-the-art performance, with a $91.58\%$ AUC on the UCF-Crime dataset, and demonstrates superior results on XD-Violence and MSAD datasets. By leveraging category-specific expertise and temporal guidance, GS-MoE sets a new benchmark for VAD under weak supervision. + +# 1. Introduction + +Video Anomaly Detection (VAD) in surveillance videos is one of the most challenging tasks in the field of Computer + +Vision. With the increasing capabilities of deep-learning models, there have been various approaches to tackle this task. The main focus of recent research in the field of VAD has been to model spatio-temporal dependencies in videos, obtaining meaningful representations of the motion of relevant agents in the scene. In this sense, the transformer architecture has proved to be very effective, forming the backbone of multiple works. While the current state-of-the-art models have achieved reasonable results on publicly available datasets, they still fail to capture subtle anomalies and to detect the temporal window in which they happen. + +We identify one of the main reasons for these issues in the formulation of the WSVAD task [31, 36]. Multi-instance learning (MIL) strikes a balance between fully supervised methods, which exhibit good performance but require costly data annotation, and unsupervised methods, which do not require manual annotations but generally result in worse performance. The core idea of MIL is to create bags containing positive and negative data samples (i.e., normal and abnormal videos), labeled only at the video-level. During training, the model assigns a score between 0 and 1 to each snippet, with 0 indicating a normal snippet and 1 indicating an abnormal snippet. The highest-scoring samples in the normal bag are guided towards 0, allowing the model to learn most normal scenarios correctly. On the other hand, the highest-scoring negative samples are pushed towards 1. This leads the model to be supervised, and therefore learn, few and specific instances of anomalous events, ignoring useful information contained in neighboring snippets. Over time, this approach has proved to be powerful but insufficient to train a model to correctly capture the secondary and specific attributes of different anomalous classes. In recent works [8, 38, 40], different auxiliary objectives are identified as priors for the VAD task to optimize the training process. + +To address this issue, we propose to model the anomalies in a video as Gaussian distributions, rendering multiple Gaussian kernels in correspondence with peaks detected along the temporal dimension of the scores estimated for + +![](images/24125f303306114fdb0cd216c902cb9ef6e74e506a1220a9c13f031fb489591f.jpg) +Figure 1. While SoTA methods address the task of WSVAD via the most normal and abnormal snippets in a video, the approach proposed in this paper focuses on learning a more complete representation of anomalous events via Gaussian kernels. + +abnormal videos. This technique, called Temporal Gaussian Splitting (TGS), creates a more complete representation of an anomalous event over time, including snippets of the anomaly with lower abnormal scores in the training objective. A side-by-side comparison of the MIL task and the TGS task is shown in Figure 1. The Gaussian kernels are extracted from the abnormal scores produced by the model. An additional challenge is related to the intrinsic differences between abnormal classes. Under the MIL paradigm, the models are trained to learn the difference between normal and abnormal videos, while the specific differences between anomalous classes are overlooked. As a result, these methods mainly focus on coarse-level representations of anomalies that allow us to distinguish between normal and abnormal events, but ignore the fine-grained category-specific cues. Therefore, the more salient anomalies (i.e., such as an explosion) are likely to be easily detected, while subtle anomalies (i.e., shoplifting) are more likely to be confused with normal events. This constitutes a major limitation of most recent methods based on WSVAD. We address this issue via a Mixture-of-Expert (MoE) architecture, in which each expert is trained to model a single anomaly class, enhancing the specific attributes of each anomaly class that are often overlooked. To further leverage the correlations and differences between anomalies, a gate model mediates between the predictions of each expert and the more coarse-level anomalous features to learn potential interactions between anomalies. + +The contributions of this paper are complementary: learning specific representations of anomalous classes allows for more accurate Gaussian kernels, and the Gaussian splatting enables the experts to learn from more subtle anomalous events that would be overlooked otherwise. To summarize, this paper presents: + +- A novel formulation of the WSVAD task based on Gaussian kernels extracted from the estimated abnormal scores to generate a more expressive and complete representation of anomalous events. Splitting the kernels along the + +temporal dimension allows the model to learn more precise temporal dependencies between snippets and highlight more subtle anomalies; + +- A Mixture-of-Expert (MoE) architecture that focuses on individual anomaly types via dedicated class-expert models, allowing a gate model to leverage similarities and diversities between them; +- The impact of the proposed contributions is measured via an extensive set of experiments on the challenging UCF-Crime [30], XD-Violence [35] and MSAD [51] datasets, showing notable improvements in performance w.r.t. previous SoTA methods. + +# 2. Related Work + +Weakly-Supervised VAD: In the WSVAD task, anomalous events encompass various classes, each exhibiting distinct characteristics across the spatial and temporal dimensions. The task of WSVAD was introduced in a seminal work by [31]. In the following years, there have been multiple different approaches that addressed the trade-off between the ease of data collection and the performance exhibited by models trained in this task. The limitation of weak labels was addressed by [48] using a graph convolutional network to correct noisy labels and supervise traditional anomaly classifiers. Further, [33] proposed to learn a function of the magnitude of features to improve the classification of normal snippets and, therefore, the detection of abnormal events. The model is based on attention modules and pyramidal convolutions. The idea of improving the quality of weak labels was also explored by [18], which designed a transformer-based method trained to predict abnormal scores both at the snippet and video levels. The video-level predictions are then used to improve the performance of the model at the snippet level. More recently, [43] designed a multi-head classification model that leveraged uncertainty and completeness to produce and refine its own pseudo-labels. [24] proposed a two-stage transformer-based model that generates anomaly-aware position embeddings and then models the short and long-range relationships of anomalous events. Inspired by point-supervision [1], [44] introduced Glance annotations. These annotations enhance the common weak labels by localizing a single frame in which an anomalous event is happening. While reporting very good performance, these annotations require an additional manual-labelling procedure. Recently, [25] proposed a method to include additional data modalities in the anomaly detection process. + +Under the MIL paradigm, these variations complicate the model's ability to effectively differentiate between them. By focusing on the $\mathrm{top}_k$ most abnormal snippets of a video, the model is guided towards specific and evident anomalous events, without properly considering the sequence of actions that lead to them and follow them. In fact, some + +anomalies occur within short time windows, while others unfold over longer periods; moreover in both cases, the MIL paradigm selects the same amount of abnormal snippets. + +Mixture of Experts: This architecture has been introduced by [5] and has since been improved and employed for diverse tasks, from image classification to action recognition [10]. The original MoE design proposed a series of small experts and a separate gate network, all receiving the same input data. Each expert predicts an output, while the gate network assigns a score of importance to them. Since then, this architecture has been improved upon by various works. A common idea across domains is to let a routing network select which portions of the input data, or input tokens, to pass to each expert [6, 14, 26, 29]. A recent work by [27] proposed to weight the input tokens in a different way for each expert. + +Gaussian Splatting: It has received a lot of attention in recent years, proving to be very efficient in fields like 3D scene reconstruction [12, 13]. The main idea of Gaussian Splatting is to represent each 3-dimensional point in a scene as a multivariate normal distribution, which allows to render the scene as the sum of the contributions of all the 3-dimensional areas. Gaussian splatting has since been extended to incorporate the temporal dimension in multiple domains, for example, dynamic scene rendering [15, 19] and medical imaging [46]. + +Our approach utilizes Mixture-of-Experts (MoE) by assigning each expert to a specific anomaly class, enabling fine-grained, category-specific learning often missed in traditional designs. A gate model bridges class-specific experts and coarse features, leveraging anomaly correlations while ensuring balanced utilization. We extend Gaussian Splatting into the temporal domain with Temporal Gaussian Splatting (TGS), capturing nuanced dependencies and integrating subtle, low-scoring snippets into training. Anchored to temporal peaks, TGS mitigates noise, enhances weak supervision, and preserves sharp transitions, avoiding over-smoothing while delivering precise anomaly detection. + +# 3. Methodology + +Our novel Gaussian Splatter-guided Mixture-of-Experts (GS-MoE) framework aims to accurately detect complex anomalies using weakly-labeled training videos. GS-MoE leverages two key techniques: (I) Temporal Gaussian Splatting loss, to ensure superior separability between normal and anomalous instances under weak-supervision; (II) Mixture-of-Experts (MoE) architecture, that learns class-specific representations and detects complex anomalies with high confidence. + +# 3.1. Temporal Gaussian Splitting (TGS) + +Our Temporal Gaussian Splitting (TGS) technique provides a novel formulation of the MIL optimization paradigm by + +![](images/1abf1b1b8275b3cdecb11f5a59dfbabcac2a3e6ddfa1276b5c18276d450d18b1.jpg) +Figure 2. The abnormal scores obtained from the backbone model on a training video at the end of training. The $top_{k}$ snippets used in the MIL paradigm lead the model to focus on the first and last of the three anomalous events present in the video, overlooking the second anomaly. However, the second anomaly, while not scoring as high as the others, is still detected. + +![](images/0777f0099ffbbfde6b97ccd096a3ffbeeb3de377549c29aafc2471ac0e0798b5.jpg) +Figure 3. The Gaussian kernels extracted from the abnormal scores shown in Figure 2 are splatted across the width of the detected peaks. This allows the model to learn a more complete representation of the anomalous events in the video. + +leveraging Gaussian kernels. The core idea of TGS is to reduce the over-dependency on the most abnormal snippets that is often the result of the classical MIL. An example of such over-dependency is shown in Figure 2. The top $k$ abnormal scores are the ones that would normally be used in the loss function in the MIL paradigm: + +$$ +\operatorname {t o p} _ {k} (S) = \left\{s c o r e _ {1}, s c o r e _ {2}, \dots , s c o r e _ {k} \right\} \tag {1} +$$ + +such that + +$$ +\begin{array}{l} L _ {\operatorname {t o p} _ {k}} = - \underbrace {\frac {1}{N ^ {+}} \sum_ {i = 1} ^ {N ^ {+}} \frac {1}{k} \sum_ {j \in \operatorname {t o p} _ {k} (\mathbf {S} ^ {+})} \log \sigma \left(\operatorname {s c o r e} _ {i j}\right)} _ {L _ {\operatorname {t o p} _ {k} - \operatorname {a b n}}} + \\ \underbrace {- \frac {1}{N ^ {-}} \sum_ {i = 1} ^ {N ^ {-}} \frac {1}{k} \sum_ {j \in \operatorname {t o p} _ {k} (\mathbf {S} ^ {-})} \log \left(1 - \sigma \left(\operatorname {s c o r e} _ {i j}\right)\right)} _ {L _ {\operatorname {t o p} _ {k} - \operatorname {n o r m}}} (2) \\ \end{array} +$$ + +where $S \in S^{+}, S^{-}$ and $\mathrm{score}_1 \geq \mathrm{score}_2 \geq \dots \geq \mathrm{score}_k$ . Here, $S^{-}$ and $S^{+}$ denote the set of scores derived from an abnormal and normal video, and $\mathrm{score}_i$ , $i \in \{1, \ldots, k\}$ represents the score of the $i$ -th highest-ranked snippet. Similarly, $N^{+}$ and $N^{-}$ are the number of videos in the abnormal and normal classes and $\sigma$ is the sigmoid function. + +At the end of the training, the task encoder is able to detect two out of three anomalies contained in the video as + +![](images/8a5466c8b60442c30fbfb481dc6a0564f1c85de9e928c59b5ee82432981e8d9a.jpg) +Figure 4. Overview of the GS-MoE architecture: First, in the feature extraction stage, the video encoder extracts snippet-level features from the video, and the task encoder refines them in the anomaly-detection latent space. In the second stage, each class-expert is trained only on refined features belonging to its assigned class and to the normal class. In the final stage, the gate model collects the scores assigned by each expert and compares them with the refined features of the task encoder, producing the final abnormal score. + +in Figure 2, assigning a very high abnormal score to most snippets in the first and third anomalies time window. The model is not as confident about the snippets belonging to the second anomaly, due to the fact that during training, it has never been supervised specifically on them, but it assigns them an anomalous score higher than the normal snippets of the video. Additionally, the snippets between anomalies are still considered partially anomalous. We conjecture that it is possible to leverage those situations to generate pseudo-labels that allow a model to be trained on more information, while remaining in the data-annotation boundaries of the WSVAD paradigm. Following [44], we propose a technique called Temporal Gaussian Splitting (TGS) that leverages the peaks in the abnormal scores predicted by the model to represent precisely the temporal windows in which an anomalous event is happening. + +Peak detection: Gaussian kernels are extracted in correspondence with local maxima, called "peaks", in the temporal axis of the abnormal scores predicted by a model. The peaks are detected by thresholding the local maxima, selecting only the ones that are above a minimum prominence threshold over the previous two scores and the subsequent two. The width $W_{i}$ of each peak $P_{i}$ is determined by minimum $(v_{1}, v_{2})$ , where $v_{1}$ is the number of preceding snippets with monotonically increasing scores, and $v_{2}$ is the number of following snippets with monotonically decreasing scores. + +The set of peaks $P$ , detected for a given video, contains the position of the snippet with the highest abnormal score for each peak in the video. This may lead to the detection of spurious peaks, meaning peaks in the abnormal scores of a video that do not belong to an anomalous event. To mitigate this, the model can be trained for a few iterations with the $L_{topk - norm}$ component of the standard MIL training objective. + +This allows us to identify subtle anomalies that are usually not included in the top $k$ snippets described in Equation 2. The kernels obtained from the detected peaks are then rendered over the length of anomalous videos to obtain a more accurate representation of the anomalies along the temporal dimension. + +Gaussian kernels $G_{i}$ are then initialized with a unitary value for the snippets corresponding to each peak $P_{i}$ detected in the abnormal scores of the video. To further represent the duration of the anomaly, the kernel values corresponding to snippets that are within the width $W_{i}$ of the respective peak are also set to 1 if their abnormal score is higher than the difference between the peak score and the standard deviation of the normal distribution centered in the peak: + +$$ +G _ {i, t} = \left\{ \begin{array}{l l} 1, & i f t = P _ {i}, \\ 1, & i f s _ {t} \geq s _ {P _ {i}} - \sigma_ {i} \wedge t \in W _ {i}, \forall t \in [ 1, T ] \\ 0, & o t h e r w i s e \end{array} \right. \tag {3} +$$ + +where $s_t$ is the abnormal score assigned to snippet $t$ and $\sigma_i$ is the standard deviation of the normal distribution centered in peak $i$ . This allows to treat each anomaly separately, which is beneficial for the WSVAD task due to the fact that different anomalies have different characteristics along the temporal dimension. Computing the Gaussian kernels in this way represents an improvement upon the top $k$ formulation, allowing the model to learn from the entirety of an anomalous event instead of its most abnormal snippets. Each kernel is splatted via: + +$$ +f _ {i} (t) = G _ {i, t} \cdot \exp \left(- \frac {\| t - P _ {i} \| ^ {2}}{2 \sigma_ {i} ^ {2}}\right), \forall t \in [ 1, T ] \tag {4} +$$ + +where $T$ is the length of the video and $\sigma_{i}$ is the standard deviation of the scores around the peak centered in $P_{i}$ within the width $W_{i}$ . Finally, the pseudo-labels $\hat{y}$ are generated by rendering each of the $K$ extracted kernels over the + +length of the video: + +$$ +\hat {y} = \left\| \left(\sum_ {i = 1} ^ {k} f _ {i} (t)\right) \right\| \tag {5} +$$ + +An example of such pseudo-label (Temporal Gaussian Splitting) is shown in Figure 3. The generated pseudolabels contain a target abnormal score between 0 and 1 for each snippet in the video, allowing the model to learn the severity of each abnormal snippet. This represents a relevant improvement over the standard MIL training objective, where only the $\mathrm{top}_k$ snippets are pushed towards 1 in the training objective, as in Equation 2. Instead, the TGS loss function used to train the experts and the MoE is formulated as: + +$$ +L _ {T G S} = L _ {\text {t o p k - n o r m}} + B C E (y, \hat {y}) \tag {6} +$$ + +# 3.2. Mixture of Experts (MoE) + +Our Mixture-of-Experts (MoE) architecture, illustrated in Figure 4, combines three stages. The first is task-agnostic and task-aware feature extraction, the second has class-specific expertise, and the third provides a novel gate mechanism. This multi-stage framework directly addresses the challenges of weak supervision and anomaly diversity, enabling precise detection of complex anomalous patterns through enriched representations and specialized models. + +Stage 1: Enhanced Temporal-Spatial Feature Extraction. The synergy of I3D and UR-DMU forms the backbone of feature extraction. The widely-used I3D model provides task-agnostic general features, capturing basic video dynamics. However, these features lack the specificity needed for detecting intricate spatial and temporal anomalies. To address this, UR-DMU [50] acts as a task-aware feature extractor tailored to anomaly detection. Trained initially with the standard MIL loss [49] and fine-tuned using our novel Temporal Gaussian Splitting (TGS) loss (Equation 6), UR-DMU extracts highly informative features by leveraging temporal consistency. These richer features filter motion dynamics and fine-grained temporal patterns crucial for distinguishing between normal and abnormal events. While UR-DMU can coarsely differentiate normal and abnormal events, it cannot fully address the complexities of different anomaly types. + +Stage 2: Class-Specific Anomaly Detection with Expert Models. To overcome the limitations of coarse anomaly detection, our framework incorporates multiple expert models optimized with our TGS loss (Equation 6), each dedicated to identifying specific types of anomalies. This design introduces a crucial level of specialization, allowing the framework to capture the unique attributes of individual anomaly classes. Each expert model is composed of a transformer block with four self-attention heads and a MLP with + +GELU activation [9], which maps the extracted features to an anomaly score for its respective class. These expert models leverage the enriched UR-DMU features, expanding the boundaries of the latent anomaly space. These fine-grained, specialized experts enable the model to detect subtle or complex anomalies that may blend seamlessly with normal events, a feat that generic models fail to achieve. + +In the final stage of the framework, the scores generated by the expert models are passed to the gate model, which acts as collaborative integration mechanism. This step ensures that the individual strengths of the experts are harnessed to create a unified representation capable of robust anomaly detection. The gate model comprises of three components: (a) Score Refinement: The expert scores are concatenated and projected into a higher-dimensional space, enriching the representation of class-specific anomaly logits. This projection enables the gate model to handle the intricate variations across anomaly classes effectively. (b) Bi-Directional Cross-Attention Module: To bridge the gap between fine-grained class-specific logits and coarse abnormal logits from the task encoder, the gate model incorporates a bi-directional cross-attention mechanism. This module learns the correlations and contrasts between the expert predictions and the coarse anomaly-aware features, allowing the gate model to leverage detailed, class-specific insights as well as the more general anomaly-aware features. (c) Final Prediction: The refined and integrated features are processed through a transformer block followed by a four-layer MLP, similar to the architecture of the experts, to produce the final anomaly scores. This step ensures that the latent space representation is expressive and well-suited for capturing diverse anomaly patterns. + +# 4. Experiments + +Datasets. We conduct our experiments on two widely-used Weakly-Supervised Video Anomaly Detection (WSVAD) datasets, namely UCF-Crime [30] and XD-Violence [35]. We further experiment on the recent MSAD dataset [51]. Importantly, for all datasets, the training videos are annotated with only video-level labels, without access to frame-level annotations. + +Evaluation Metrics. We adhere to the evaluation protocols established in prior works [22, 30, 35, 37]. To ensure comprehensive evaluation, we utilize multiple indicators, such as frame-level Average Precision (AP), Abnormal AP $(\mathrm{AP}_{\mathrm{A}})$ for XD-Violence and Area Under the Curve (AUC), Abnormal AUC $(\mathrm{AUC}_{\mathrm{A}})$ for UCF-Crime dataset. The AP and AUC metrics show the method robustness towards both normal and anomaly videos. However, $\mathrm{AP}_{\mathrm{A}}$ and $\mathrm{AUC}_{\mathrm{A}}$ allows to exclude normal videos where all snippets are labeled as normal and retain only the abnormal videos + +
ModelEncoderUCF-CrimeXD-Violence
AUCAUCAAPAPA
SoTA Methods With Multi-modal Features
M.A. [52]C3D79.1062.18--
HL-Net [35]I3D82.44---
HSN [23]I3D85.45---
MACIL-SD [41]I3D+audio--83.40-
UR-DMU [49]I3D+audio--81.77-
TPWNG [39]CLIP87.79-83.68-
VadCLIP [37]CLIP88.0270.2384.15-
SoTA Methods With RGB only Features
MIL [30]C3D75.4154.2575.6878.61
I3D77.42---
TCN [45]C3D78.66---
GCN [47]TSN82.1259.0278.64-
MIST [7]I3D82.30---
Dance-SA [28]TRN85.00---
RTFM [32]I3D84.3062.9677.8178.57
CLAV [4]I3D86.10---
UR-DMU [49]I3D86.9770.8181.6683.94
SSRL [16]I3D87.43---
MSL [17]V-Swin85.30-78.28-
WSAL [21]I3D85.3867.38--
ECU [42]V-Swin86.22---
MGFN [3]V-Swin86.67---
UMIL [22]CLIP86.7568.68--
TSA [11]CLIP87.58-82.17-
GS-MoE (Ours) I3D91.58 (+3.56%)83.86 (+13.63%)82.8985.74
+ +Table 1. State-of-the-art comparisons on UCF-Crime and XD-Violence datasets. The best results are written in bold. + +
ModelMSAD
AUCAUCAAPAPA
RTFM[32]86.65---
MGFN[3]84.96---
TEVAD[2]86.82---
UR-DMU[49]85.02---
UR-DMU*85.7867.9567.3575.30
GS-MoE87.7269.5468.2676.68
+ +containing both normal and anomalous snippets. This poses a more meaningful challenge to the model's ability to accurately localize anomalies. + +# 4.1. State-of-the-art Comparison + +In our experiments, the proposed GS-MoE model outperforms prior state-of-the-art (SoTA) approaches across multiple metrics, as summarized in Table 1. On the challenging UCF-Crime dataset, GS-MoE achieves an AUC of + +Table 2. State-of-the-art comparisons on MSAD. * indicates our own implementation. The best results are written in bold. + +
BaselineTGSMoE Experts GateAUC(%) UCF XD-VAPA(%) UCF XD-V
✓---86.97 94.0745.65 82.91
✓✓--87.84 94.1346.01 83.39
✓✓✓-89.53 94.2947.17 84.16
✓✓✓✓91.58 94.5251.63 85.74
+ +Table 3. Impact of each component in GS-MoE framework on UCF-Crime and XD-Violence datasets. + +![](images/58990e9e010d0f0fb1b5fb5a875439a10941d931f96faa8730255bbabb24b73e.jpg) +Figure 5. Category-wise performance comparison with UR-DMU. + +91.58%, surpassing the previous best model, VadCLIP [37], by 3.56%. This significant improvement illustrates the effectiveness of our model in detecting complex video anomalies in real-world datasets. Additionally, when considering the performance on the abnormal videos $(\mathrm{AUC}_{\mathrm{A}})$ only, GS-MoE achieves a score of 83.86%, which constitutes a remarkable 13.63% improvement over the second-best approach, UR-DMU [49], at 70.81%. This result supports one key hypothesis of our work: different types of anomalies require class-specific fine-representations for more effective detection. UR-DMU performance remains limited due to feature-magnitude based optimization which overlooks the subtle cues and enhances the sharp cues. However, the proposed TGS loss promotes both subtle and sharp cues to take part in the separability optimization. Further, the mixture-of-experts architecture is capable of capturing these class-specific representations, leading to substantial performance gains, especially on complex anomalies. + +On the XD-Violence dataset, GS-MoE achieves an AP score of $82.89\%$ , which is competitive with the best-performing TSA [11] model $(82.89\%)$ . Moreover, when focusing on anomalous videos only, GS-MoE achieves an $\mathrm{AP}_{\mathrm{A}}$ score of $85.74\%$ , outperforming the second-best approach, UR-DMU [49], which achieved an $\mathrm{AP}_{\mathrm{A}}$ score of $83.94\%$ . Since the AP metric considers both normal and anomaly videos for evaluation, the performance gets elevated by accurately predicting many normal videos. + +As a result, methods performing well on the AP metric may still struggle in anomaly detection. The proposed method outperforms previous SoTA in the $\mathrm{AP_A}$ metric, reinforcing its utility in real-world scenarios. On the recently released MSAD, GS-MoE surpasses the available baseline models by up to $2.74\%$ on the AUC metric and establishes a new SoTA on the dataset. We report the other metrics as well, in order to provide a baseline for subsequent works. + +
ExpertAbuseArrestArsonAssaultBurglaryExplosionFightingRoadAcc.RobberyShootingShopliftingStealingVandalism
Mask50.0250.5149.2750.7249.4949.9249.9549.9150.0449.2049.3950.5249.87
W/o Mask86.3755.4861.7363.1253.6557.0465.1465.2272.3760.8954.7377.6257.43
+ +![](images/1cc0f347aebf94e162074bc3c9d856748acfc519255e109b0209e9a3e778251a.jpg) +(a) UR-DMU features. + +![](images/822920c82b65127d63bf1cb6d17a1adfade209899ff7d72e05a1ece95a79e378.jpg) +(b) GS-MoE features. +Figure 6. Category-wise t-SNE feature distribution comparison between the baseline, the experts and the gate model. + +Category-Wise Performance Analysis: To bring additional analytical insights on the complex anomaly performance, Figure 5 provides an anomaly category-wise performance comparison between GS-MoE and the baseline UR-DMU method on the UCF-Crime dataset. Notably, significant performance boosts are recorded for complex categories like "Arson", "Assault", "Fighting", "Stealing" and "Burglary", up to $+24.3\%$ . These performance gains corroborate the benefits of GS-MoE in detecting complex video anomalies. Figure 6 shows the t-SNE plot [34] of the logits obtained at the first and third stages of GS-MoE for the anomalous videos in the test set. The plot in Figure 6a, obtained from the baseline UR-DMU, shows a low degree of separability. The class diversification performed by the experts and shown in Figure 6b demonstrates the capability of GS-MoE to learn enhanced class representations. + +# 4.2. Qualitative Results + +As shown in Figure 7, the Gaussian kernels extracted from the abnormal score contain a precise representation of the anomalous events present in videos of the UCF-Crime dataset. The kernel temporal activation (heatmaps) demonstrate the capabilities of this approach. By correctly distinguishing the peaks of the anomalous events and from the spurious peaks, the model is trained to predict high anomaly scores for the associated anomalous snippets. In the "Assault-010" video sample, two peaks are detected in the abnormal score and the TGS finds a small variance for both, leading to a steep normal distribution for each of them. On the other hand, in the "Arson-011" and "Explosion-033" samples, the TGS creates much longer distributions by lead + +ing the model to estimate a large variance and producing a long time-window for the anomaly. + +# 4.3. Ablation Studies + +Component Impact: Extensive ablation studies are conducted to evaluate the impact of each contribution to the final performance of GS-MoE, as shown in Table 3. Finetuning the baseline UR-DMU model with the TGS loss in Equation 6 leads to a performance increase of $+1.77\%$ on the AUC metric of UCF-Crime, while the $\mathrm{AP_A}$ of XD-Violence increases by $+0.48\%$ . These results show that the new formulation of the WSVAD task is beneficial to existing methods as well. The class-experts outperform the fine-tuned baseline by $+0.79\%$ on UCF-Crime. Notably, the $\mathrm{AP_A}$ increases on both datasets, leading to $+1.16\%$ for UCF-Crime and $+0.76\%$ on XD-Violence, further supporting the idea that different classes of anomaly should be treated separately. Adding the gate model to the framework brings the largest performance increment. For UCF-Crime, the AUC increases by $+2.05\%$ and the $\mathrm{AP_A}$ by $+4.46\%$ . On XD-Violence, we observe relatively smaller improvements, increasing AUC by $+0.23\%$ and $\mathrm{AP_A}$ by $+1.68\%$ . + +Table 4. Category-wise performance comparison on UCF-Crime dataset between the UR-DMU baseline model and GS-MoE without the expert model for a given class. Masking the relevant experts results in an almost random output from the gate model. + +
DatasetsW. TA featuresW/o. TA features
UCF-Crime (AUC)91.5890.98
XD-Violence (AP_A)85.7481.45
+ +Table 5. Evaluation of the importance of the task-aware (TA) features for the gate model on the key metrics of the UCF-Crime and XD-Violence datasets. + +![](images/0f1a4c10532b76159ace191824e6c5fd46aeefcb8198d15ef1b00c97843642be.jpg) +Figure 7. Visualization of sample frames and ground truth (green shed) vs. prediction scores (red shed) for various cases in Row-1 and Row-2. For each plot in Row-2, the X and Y axis denotes the number of frames and corresponding anomaly scores. Row-3 shows the temporal activation (heatmaps) learned by Gaussian splatter (GS). + +Task-Aware Features: In order to further analyze this performance increment, the gate model was trained with and without the task-aware features. The results of this experiment are shown in Table 5. The task-aware features seem to have a key role in the performance on the $\mathrm{AP_A}$ metric of XD-Violence. In fact, the Gate model trained with the task-aware features outperforms the other configuration by $4.29\%$ on this setting, and by $0.6\%$ on UCF-Crime. + +Class-Experts Impact: The relevance of the expert models on the performance of the gate model is measured with the class-wise AUC score obtained by masking the respective class expert on the UCF-Crime dataset. The results of this experiment are shown in Table 4. By masking the experts, the measured AUC hovers around $50\%$ for each class. On the other hand, the gate model predictions are much improved when the relevant expert score is included, leading to a significant performance boost. + +Class experts vs cluster experts: In practical applications, anomalies often span multiple classes, making it challenging to train a predefined set of specialized experts. To address this issue, we trained GS-MoE using cluster-based experts rather than class-specific experts. To form the data clusters, we calculated the average task-aware features for each anomalous video in the UCF-Crime training set and applied the K-Means algorithm [20] to group them. Each expert was then trained using videos from a single cluster combined with normal videos, resulting in $k$ specialized expert models. This approach enabled us to evaluate the model's performance in real-world scenarios where the number of classes is undefined. The results are reported in Table 6. In this setting, GS-MoE is able to outperform current SoTA models by $0.56\%$ clustering the anomalous training videos in 7 clusters and using 7 experts while performing on par with other SoTA models using fewer experts. These results highlight the capabilities of GS-MoE in a real-world use case where the number of anomalous events is not predefined. + +
ModelAUC
UR-DMU [49]86.97
TSA [11]87.58
TPWNG [39]87.79
VadCLIP [37]88.02
GS-MoE (5 clusters / 5 experts)87.35
GS-MoE (6 clusters / 6 experts)88.03
GS-MoE (7 clusters / 7 experts)88.58
GS-MoE (class experts)91.58
+ +Table 6. Comparison between the performance of GS-MoE with varying number of experts. + +# 5. Conclusion + +We proposed GS-MoE to provide a novel formulation for weakly-supervised video anomaly detection by leveraging Temporal Gaussian Splatting to overcome the limitations of previous methods. More specifically, we address the overdependency on the most abnormal snippets for separability optimization. Our framework utilizes a mixture-of-experts architecture that learns category-specific fine-grained representations. building a correlation between coarse abnormal cues and fine-grained cues to learn a more compact representation for each category. Extensive experiments on challenging datasets across various metrics show GS-MoE consistently outperforms SoTA methods with significant performance gains. 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Most metrics currently use off-the-shelf models, like CLIP-Score, to score pairs based on feature similarity. However, we find that different scoring models often produce inconsistent quality scores for the same data. This disparity impacts data processing results, leading to variations in datasets and, consequently, in model performance when trained on these datasets. Notably, no single quality score excels across all tasks, as each has biases toward specific concepts, resulting in complementary effects on model performance. This complicates the selection of scoring models. In this paper, we analyze these disparities and propose a method called Mixture-of-Scores (MoS). This approach integrates various quality scores into a robust ensemble score, effectively mitigating biases. It can be implemented easily in just three lines of code. Our extensive experiments show that MoS outperforms existing single quality scores across multiple vision-language tasks and benchmarks. We aim to offer new insights and practical tools to help the community navigate the challenges of scoring model selection. + +# 1. Introduction + +Large-scale web image-text datasets [17, 36, 38, 41, 47, 48] have greatly promoted the breakthroughs in vision-language representation learning and driven the development of vision-language foundation models [1, 20, 49]. Nevertheless, these web-crawled datasets are generally noisy [1, 9, 36], e.g., the text description does not precisely match the visual content of its corresponding image. Recently, more and more works found that data quality plays a crucial role in model + +learning [1, 25, 53]. Noisy image-text data with poor alignment will seriously hinder the representation learning and may lead to training instability [1, 9, 40]. Therefore, evaluating the quality of image-text data is becoming a critical and valuable research topic, that serves as an essential tool for various data processing strategies [4, 14, 36, 42, 52, 64] to mitigate the negative impact on vision-language representation learning caused by noisy and low-quality data [1, 9]. + +Early works relied on manual criteria to evaluate the quality of image-text pairs, for example, human judgement [65] and invalid text detection [17, 47]. Since the emergence of CLIP [20], model-based quality score has become the most widely-used metric [1, 36, 38, 48], which is formulated as the similarity between image and text embedding extracted from an off-the-shelf vision-language model (VLM), such as CLIP [20], BLIP [1] and their follow-up works [7, 59]. Related works are discussed in Sec.3 of supplementary material. + +Observation and Motivation. However, we observe a prevalent phenomenon, that is, for the same data, there are significant differences between the quality scores derived from different scoring models (quality score disparity). As depicted in Figure 1(a), the standard deviations of these quality scores are quite substantial (between 0.01 and 0.29), reaching around $60\%$ of its upper-bound1. + +Consequently, this quality score disparity has a direct impact on the data processing result, leading to the discrepancy between datasets processed using different quality scores. Taking the example of data filtering that removes $\rho \%$ data with the lowest quality scores, it is noteworthy that there is almost no intersection between the filtered subsets under different quality scores when $0 < \rho \leqslant 50$ (refer to Figure 1(b)). This can be attributed to the fact that the quality rank of each data fluctuates significantly (ranging from $4\%$ to $46\%$ ) when sorting the whole dataset by different quality scores, as shown in Figure 1(c). + +![](images/43bdefb823a41884d47763b3047717888f4c84ea2d2b78b7314f94e8466093be.jpg) +Figure 1. Illustration of the disparity phenomenon in quality score, processed dataset and model performance, and the relationship between them. Quality Score Disparity: The histogram in (a) shows the standard deviations between different quality scores of each data over the entire dataset. Processed Dataset Disparity: Such quality score disparity will directly result in discrepancies between datasets processed using different scores. As an example, we separately filter out a subset with the lowest quality $\rho \%$ data based on the quality score from each scoring model, and (b) presents the intersection ratio between these subsets under different $\rho$ . The histogram in (c) shows the standard deviations of each data's quality ranks obtained by sorting the entire dataset based on distinct quality scores. Model Performance Disparity: Such dataset disparity will further lead to differences in the performance of models separately trained on each of the processed datasets. (d-f) compare the performance on various evaluation tasks under three data processing strategies, data filtering1, sample weighting2 and image re-captioning3, respectively. The experiments are conducted on the CC3M dataset [47] and trained on CLIP ViT-B/32 model [20]. The scoring models involved comprise various variants of CLIP [20], EVACLIP [7], BLIP [1], and BLIP2 [59]. “pt” and “ft” denote ‘the model with pre-trained and fine-tuned weights, respectively. + +As a result, such processed dataset disparity will further propagate to the performance disparity in models individually trained on each of datasets processed by distinct quality scores. Figure 1(d-f) illustrate the model performance disparity under three commonly-used data processing strategies. It is worth noting that no quality score performs best on all evaluation tasks, and different quality scores have complementary effects on the model performance across various tasks. For example, scores from CLIP series model [7, 20] outperforms in fine-grained recognition task (e.g., ImageNet [65]), while scores from BLIP series model [1, 59] excels in retrieval task (e.g., COCO [66] and Flickr [67]) and common category recognition task (e.g., CIFAR [68] and VOC [69]). It indicates that each individual quality score exhibits bias towards certain concepts or tasks, stemming from differences in the training data, model architecture, model capacity and training objective of its scoring model (explained in Sec.2.3). This brings great confusion for the community to choose the scoring model. This motivates us to extract the essence and + +eliminate the bias of each quality score and construct a more robust image-text data quality metric that performs best on all tasks. + +Our Approach. In this paper, we propose a simple yet effective method, named Mixture-of-Scores (MoS), which integrates multiple existing quality scores into a more robust one through a data-adaptive ensemble strategy. For each data, we consider a set of existing quality scores derived from diverse scoring models, and assign an individual ensemble weight to each quality score. In our design, the ensemble weight is related to two factors: (1) Consensus of this score among all scoring models. Different scoring models give quality assessment from different angles. We treat it as complementarity. + +If the scores are highly consensual, it indicates that this is a high-quality data. Thus, the score with higher consensus is assigned a larger ensemble weight. (2) Quality uncertainty of this data. The data with higher quality uncertainty tend to own a smoother distribution of ensemble weights. + +Specifically, we first utilize the density of each quality score as a measure of its consensus among the scoring models. The density of a score is defined as the average distance between it and other scores, indicating the concentration degree around that score. Second, we compute the standard deviation of different quality scores for each data, which serves as a quantification of the quality uncertainty. Next, we formulate the ensemble weight for each given quality score as the softmax-normalized density with a temperature coefficient. Each data point has its unique temperature, which aims to incorporate the awareness of its quality uncertainty. This temperature is designed to be proportional to the above standard deviation of multiple scores. Finally, our MoS metric is obtained by calculating the weighted sum of all the given quality scores using the aforementioned ensemble weights. + +To evaluate the effectiveness and robustness of our MoS, we thoroughly compare the performance of models trained separately on the dataset processed by different quality scores under three kinds of data processing strategies. As shown in Figure 1(d-f), compared with any single quality score that is biased in performance, our MoS is more robust and performs best on all vision-language tasks and benchmarks. For example, our MoS has an advantage of +4.3 on Flickr30K I2T retrieval compared with the average performance of baseline scores. + +We summarize our main contributions as follows: + +- We are the first to discover and investigate the quality score disparity problem for image-text data and its subsequent serious impact on vision-language pre-training. +- We propose a cost-effective solution, named Mixture-of-Scores (MoS), which leverages a data-adaptive ensemble strategy to harness the strengths of various existing quality scores while mitigating their inherent biases. Particularly, our MoS can be easily implemented with only three lines of code. +- Experimentally, our MoS is the first one to perform best in all evaluation settings. + +# 2. Problem Investigation + +# 2.1. Preliminary + +In this sub-section, we introduce the principle and formulation of the current popular model-based image-text quality score. Specifically, given a well-trained dual-encoder vision-language model $\Phi$ (comprising an image encoder $\Phi_{\mathrm{img}}$ and a text encoder $\Phi_{\mathrm{text}}$ ), the paired image $\mathbf{x}^I$ and text $\mathbf{x}^{\tilde{T}}$ are first passed through $\Phi_{\mathrm{img}}$ and $\Phi_{\mathrm{text}}$ respectively to extract the + +corresponding image embedding $\mathbf{I}$ and text embedding $\mathbf{T}$ . Then, $\mathbf{I}$ and $\mathbf{T}$ are normalized separately followed by an inner product operation $\langle \cdot ,\cdot \rangle$ to calculate their cosine similarity $S$ . The above process can be formulated as follows: + +$$ +\mathbf {I} = \Phi_ {\operatorname {i m g}} \left(\mathbf {x} ^ {I}\right), \quad \mathbf {T} = \Phi_ {\text {t e x t}} \left(\mathbf {x} ^ {T}\right), \quad S = \langle \mathbf {I}, \mathbf {T} \rangle \tag {1} +$$ + +This similarity reflects the consistency between the visual information in the image and its text description, which has the same meaning as the quality of the image-text pair data. Therefore, the model-based quality score $S$ of an image-text pair can be defined as the cosine similarity between its image embedding and text embedding. + +Theoretically, for a VLM, as long as it has a dual-encoder architecture and its visual and linguistic embedding space have been well aligned with each other, then it can be regarded as a quality scoring model for image-text pair data. In practice, the CLIP model [20] is most commonly used, followed by its subsequent works BLIP [1], BLIP2 [59], EVACLIP [7], etc. + +# 2.2. Problem Discovery + +Quality score disparity. As mentioned in Sec.2.1, for an image-text pair, its quality can be assessed by various dual-encoder VLMs. However, considering a variety of scoring models that cover different architectures [1, 7, 20, 59] and varying model sizes (from base-level to giant-level), we observe significant differences between the quality scores they generate. We name this phenomenon "Quality Score Disparity". + +Specifically, for a dataset $\mathcal{D} = \{(\mathbf{x}_i^I,\mathbf{x}_i^T)\}_{i = 1}^N$ with $N$ image-text pairs and a series of scoring models $\{\Phi^1,\dots,\Phi^M\}$ , each image-text pair $(\mathbf{x}_i^I,\mathbf{x}_i^T)$ is passed through these scoring models separately to calculate the corresponding quality scores $\{S_i^1,\dots,S_i^M\}$ as Eq. (2) below, which has the same principle as Eq. (1) with only additional subscripts $i\in \{1,\dots,N\}$ and $k\in \{1,\dots,M\}$ to distinguish different data and scoring models, respectively. + +$$ +\mathbf {I} _ {i} ^ {k} = \Phi_ {\mathrm {i m g}} ^ {k} \left(\mathbf {x} _ {i} ^ {I}\right), \quad \mathbf {T} _ {i} ^ {k} = \Phi_ {\mathrm {t e x t}} ^ {k} \left(\mathbf {x} _ {i} ^ {T}\right), \quad S _ {i} ^ {k} = \left\langle \mathbf {I} _ {i} ^ {k}, \mathbf {T} _ {i} ^ {k} \right\rangle \tag {2} +$$ + +To quantify the disparity between these quality scores $\{S_i^1,\dots,S_i^M\}$ , we then compute the standard deviation $\sigma_{i}^{\mathrm{score}} = \sqrt{\frac{1}{M}\sum_{k = 1}^{M}(S_{i}^{k} - \overline{S}_{i})^{2}}$ of them, where $\overline{S}_i = \frac{1}{M}\sum_{k = 1}^{M}S_{i}^{k}$ denotes the mean value. Figure 1(a) shows the distribution of the standard deviations $\{\sigma_{i}^{\mathrm{score}}\}_{i = 1}^{N}$ over the entire dataset. Notably, the standard deviations approximately follow a normal distribution, with a mean value of around 0.15 and a maximum value of 0.29, which has reached $60\%$ of its upper-bound (e.g. 0.5, proved in Sec.2 of supplementary material). + +Processed dataset disparity. To mitigate the negative effects of noisy data, pre-processing the image-text pairs before training has become an indispensable step for various visual-language models [1, 7, 9, 20, 49]. Many commonly-used data + +![](images/15bb78cb0c6bcf63b2f06ae16755e6884ae6b70ca1e33d51ee853f035eac74d3.jpg) +Figure 2. The relationship between performance and the size of the quality scoring model. Each evaluation benchmark corresponds to an individual color. Each bubble denotes a distinct scoring model (bigger bubble means larger model size). + +![](images/9d8abf6b21924c940447fae208653b98cf7daf3f2145187317d2ed0901e68460.jpg) +Figure 3. The relationship between the quality score disparity and the level of data quality (see Sec.2.3 for more analysis). The standard deviation is calculated among all the models listed in Figure 1. + +![](images/3ca387adbb26d5fe362b02f5a49ef553b04d67bd17d9b7f698a13c68d174f505.jpg) +Figure 4. The relationship between the quality score disparity and scene complexity of data (detailed in Sec.2.3). The standard deviation is calculated among all the models listed in Figure 1. + +processing strategies are closely associated with the data quality score. For example, data filtering [36, 52] removes part of low-quality data from the training set, image re-captioning [14, 64] replaces the original web text of partial low-quality data with a better text description generated by a professional caption model, and sample weighting [4, 42, 70, 71] assigns each data its own weight according to its quality, enforcing the model over-fit less on the noise in data. As a result, the data quality score has a direct impact on the results of data processing. + +Our quantitative experiments demonstrate that "quality score disparity" can further lead to significant differences in the processed datasets. Taking data filtering as an example, given multiple quality scores $\{S_i^1\}_{i = 1}^N,\dots,\{S_i^M\}_{i = 1}^N$ obtained from $M$ different scoring models for an image-text pair dataset $\mathcal{D} = \{(x_i^I,x_i^T)\}_{i = 1}^N$ , we first perform filtering based on the score from each scoring model respectively, and then compare the differences between the filtered subsets. Specifically, for $k$ -th scoring model, the entire dataset is sorted by its quality scores $\{S_i^k\}_{i = 1}^N$ , resulting in the rank $R_{i}^{k}$ (ranges from 1 to $N$ ) of each data. The larger $S_{i}^{k}$ the smaller $R_{i}^{k}$ . We further normalize the rank to $\mathcal{R}_i^k = \frac{100}{N} R_i^k$ to make its range fixed within [1, 100] regardless of the data amount $N$ . Then, we select a subset $\tilde{\mathcal{D}}^k$ including the data with the higher $\rho \%$ ranks. This selection process can be formulated as the following Eq. (3), + +$$ +\widetilde {\mathcal {D}} ^ {k} = \left\{\left(\mathbf {x} _ {j} ^ {I}, \mathbf {x} _ {j} ^ {T}\right) \right\} _ {\forall_ {j} \delta_ {j} ^ {k} = 1}, \text {w i t h} \delta_ {j} ^ {k} = \left\{ \begin{array}{l l} 1 & \text {i f} \mathcal {R} _ {j} ^ {k} \geqslant \rho \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {3} +$$ + +where $j = \{1,2,\dots,N\}$ . The subset $\widetilde{\mathcal{D}}^k$ contains the $\rho \%$ lowest quality data of the entire dataset, thus it is finally removed from the training set under the data filtering strategy. + +We quantify the subsequent impact of quality score disparity on data processing from the following two aspects: + +(1) Difference between the quality ranks $\{\mathcal{R}_i^1,\dots,\mathcal{R}_i^M\}$ under different quality scores. We calculate the standard deviation $\sigma_{i}^{\mathrm{rank}} = \sqrt{\frac{1}{M}\sum_{k = 1}^{M}(\mathcal{R}_{i}^{k} - \overline{\mathcal{R}}_{i})^{2}}$ between the ranks + +for each data individually, where $\overline{\mathcal{R}}_i = \frac{1}{M}\sum_{k=1}^{M}\mathcal{R}_i^k$ is the mean value. Figure 1(b) shows the distribution of standard deviations $\{\sigma_i^{\mathrm{rank}}\}_{i=1}^N$ over the entire dataset. Notably, the quality rank of each data fluctuates significantly when sorting the whole dataset by different quality scores, ranging from $4\%$ to $46\%$ . + +(2) Intersection size between the filtered data subsets $\{\widetilde{\mathcal{D}}_i^1,\dots,\widetilde{\mathcal{D}}_i^M\}$ under different quality scores. Figure 1(c) shows the ratio of intersection size to subset size under different filtering ratios $\rho \%$ . Surprisingly, when $0 < \rho \leqslant 50$ , there is almost no intersection between the subsets selected using different quality scores, which demonstrates that the disparity between quality scores calculated by different scoring models is enough to cause significant differences in the training data after data processing. + +Model performance disparity. We further train a model individually on each of datasets processed via different quality scores, and compare their performance on various evaluation tasks. The results show that the processed datasets disparity can further lead to differences in the performance of models trained with each of them. Figure 1(d-f) show the comparison under three data processing strategies respectively. Notably, different quality scores show different ability preferences for certain concepts and tasks. For example, quality scores derived from CLIP series models [7, 20] show stronger generalization and perform better on fine-grained recognition tasks (e.g., ImageNet [65]), while quality scores calculated via BLIP series models [1, 59] excel in common category recognition (e.g., CIFAR [68] and VOC [69]) and retrieval tasks (e.g., COCO [66] and Flickr [67]). However, no quality score performs best on all evaluation tasks. The performance is not directly related to the size of scoring model (as Figure 2), which means that a larger scoring model will not exactly result in a better quality score. This brings great trouble to the community in choosing which model for scoring the quality. + +![](images/c32df4c3938b91bd7473bf3429b0801f5d5315de53e5b62a4bce010fa2422db5.jpg) +(a) + +![](images/0b166927020790cbe74a79b7f45196b876b94597773b0556a10df4543e68047d.jpg) +(b) +Figure 5. The relationship between quality score disparity and the concepts involved in data. In (a) and (b), the scatter points show the standard deviation of scores for each data, and the curve presents the average standard deviation of all data in each cluster or including each type of object. The word cloud in (c) and (d) illustrate the 20 concepts with the lowest and highest standard deviation, respectively. + +![](images/87c2f68cb92a2d851253607d88739191d3925c9cd74580ff5d482a1766d880e2.jpg) +(c) + +![](images/f4887002651e28974c218fd911eaae8155e370485e73e23811883b01b31cc56e.jpg) +(d) + +# 2.3. Reason Analysis + +What causes disparity in quality scores derived from different models? As can be observed from Figure 1(a), the disparity level of quality scores is not consistent for all data. Furthermore, we find that this disparity level is related to the following three factors: + +(1) Level of data quality. As shown in Figure 3, quality score disparity for the lowest and highest quality data is significantly smaller than that of medium-quality data. This may be because poor-aligned (low-quality) image-text pair and well-aligned (high-quality) image-text pair are easier to identify, so the quality scores predicted by most models for them are relatively consistent. While, the quality score of partial-aligned image-text pair is more controversial between different models because it is generally more difficult to identify and quantify. +(2) Concepts involved in the data. We divide all the data into multiple groups according to different concepts, and compare the degree of data quality score disparity (measured by standard deviation) across these groups. Specifically, we consider two kinds of concepts with different granularities as follows: + +The first one is coarse-grained concept, e.g., the comprehensive visual content in the image. We perform clustering on all data into 1000 clusters based on the image embedding extracted by CLIP ViT-L/14 [20]. Data in each cluster have similar scenes and can also be regarded as containing similar concepts. Figure 5(a) shows the standard deviation between multiple quality scores for each data involved in each cluster. It can be seen that the standard deviation exhibits obvious differences across clusters. + +The second one is more fine-grained concept, that is, the object categories involved in the data. For each image-text pair, We strive to extract comprehensive concepts by gathering object categories from both image and text, respectively. In particular, we utilize the off-the-shelf Recognize Anything model [72] to identify objects in the image, and employ the Scene Graph Parser tool [73] to extract object information from the text description. The concept set of the entire dataset + +is naturally defined as the union of concepts collected from all image-text pairs. For each concept in this set, we calculate the standard deviation between quality scores for each data containing it. As shown in Figure 5(b), the standard deviations vary with different concepts, which demonstrates that the quality score disparity of an image-text pair is related to the concepts it contains. Figure 5(c) and (d) visualize the word cloud of the 20 concepts with the lowest and highest standard deviations, respectively. One can observe that the concepts presented in (c) are more prevalent, whereas those in (d) exhibit a bias towards rarer categories. This reveals that quality scoring models are more likely to diverge for the image-text pairs that contain uncommon categories. + +(3) Scene complexity of the data. We divide the entire dataset into 50 groups according to the level of scene complexity, and calculate the standard deviation between quality scores of the data in each group. The scene complexity is assessed only based on the visual information of the image, since the image tends to contain more complete information than its web-crawled text counterpart. Specifically, given an image, we first apply the Recognize Anything model [72] to extract the object categories inside it. These categories are then sent into the Grounded-SAM model to predict the number of instances. Subsequently, the scene complexity of an image is defined as the summation of the number of categories and the number of instances. As shown in Figure 4, data with a more complex scene is more likely to obtain disparate quality scores from various scoring modes. + +Why different quality scores exhibit performance bias? As mentioned in Sec.2.2, the quality score inherits the ability preference of its scoring model to some extent. Empirically, we find that this fact may be attributed to two aspects: (1) training data of scoring model. The pre-training data of the BLIP series models is generally less than that of CLIP series models, thus they may perform worse on fine-grained recognition tasks due to the omission of concepts involved. In addition, some BLIP variants are finetuned on datasets that mainly focus on common categories (such as COCO [66]), so they perform better on the data with common concepts. (2) model architecture and training objectives of scoring model. + +Algorithm 1: Code of MoS calculation in PyTorch-like style +```python +def mixture_of Scores(s, M): + s: baseline scores for the entire dataset, shape=[N, M], N is the number of data + M: number of baseline scores + "" + # compute density + density = (s:, None).repeat(1, 1, M) - s:, None).repeat(1, M, 1)).abs().sum(-1) / (M - 1) + # compute temperature + temp = ((temp_max - temp_min) * s.std(-1) + (temp_min * s.std(-1).max() - temp_max * s.std(-1).min())) / (s. + std(-1).max() - s.std(-1).min()) + # ensemble + mos = (((density / temp).exp() / (density / temp).exp().sum(-1)[:, None]) * s).sum(-1) + return mos +``` + +For example, the Qformer module and image-text matching loss in the BLIP series models [1, 59] make them better at retrieval task than the CLIP series, and the quality scores derived from BLIP series models also exhibit this preference. + +# 3. Mixture-of-Scores + +To mitigate the confusion caused by disparate quality scores, we propose Mixture-of-Scores (MoS), which integrates multiple existing quality scores into a more robust one via a data-adaptive ensemble strategy. In this section, we first demonstrate our motivation for using this ensemble-based solution in Sec.3.1, and then detail the approach in Sec.3.2. + +# 3.1. Motivation + +Although each existing quality score exhibits performance bias on certain concepts or tasks as discussed in Sec.2.2, we still observe an interesting phenomenon: different quality scores have complementary effects on the model performance across various tasks. Some scores perform well on partial benchmarks or tasks and poorly on others, while some scores do the opposite. This complementarity provides us with a unique opportunity to potentially derive a more robust quality score by combining these existing scores. Inspired by the powerful ensemble learning, we aim to design an ensemble-based solution that can effectively exploit the complementarity of these quality scores to eliminate the negative impact caused by their inherent bias. We hope that our work can provide the community with new perspectives and tools to avoid confusion when choosing the quality scoring model. + +# 3.2. Method + +Given a set of quality scores $\{S_i^1,\dots,S_i^M\}$ for $i$ -th image-text pair, they can be regarded as a discrete one-dimensional distribution. Firstly, we calculate the density for each quality score. In particular, for the $k$ -th score $S_{i}^{k}$ , its density $d_{i}^{k}$ is defined as the average distance between it and other scores, formulated as follows: + +$$ +d _ {i} ^ {k} = - \frac {1}{M - 1} \sum_ {j = 1 (j \neq k)} ^ {M} D \left(S _ {i} ^ {k}, S _ {i} ^ {j}\right), \tag {4} +$$ + +where $D(\cdot, \cdot)$ denotes a distance function, instantiated as L1 distance by default (ablated in Table 4). Obviously, density $d_i^k$ reflects the concentration degree of these scores near $S_i^k$ . The larger $d_i^k$ implies that $S_i^k$ is more of a consensus among most scoring models. Conversely, the smaller $d_i^k$ indicates that $S_i^k$ is more likely to be an outlier. + +Then, we assign a weight to each quality score according to its consensus and the quality uncertainty of this data. Specifically, the weight of $k$ -th quality score is defined as + +$$ +w _ {i} ^ {k} = \frac {\exp \left(d _ {i} ^ {k} / \tau_ {i}\right)}{\sum_ {j = 1} ^ {M} \exp \left(d _ {i} ^ {j} / \tau_ {i}\right)}, \tag {5} +$$ + +where softmax normalization is used to ensure the summation of all the weights equals 1. $\tau_{i}$ is the temperature coefficient that controls the smoothness of weight distribution. We set $\tau_{i}$ to be proportional to the standard deviation of scores, e.g., $\tau_{i} = h(\sigma_{i})$ , where $h(\cdot)$ is a monotonically increasing function. We simply instantiate it as a linear function as follows: + +$$ +\tau_ {i} = \frac {\tau_ {\operatorname* {m a x}} - \tau_ {\operatorname* {m i n}}}{\sigma_ {\operatorname* {m a x}} - \sigma_ {\operatorname* {m i n}}} \cdot \sigma_ {i} + \frac {\tau_ {\operatorname* {m i n}} \sigma_ {\operatorname* {m a x}} - \tau_ {\operatorname* {m a x}} \sigma_ {\operatorname* {m i n}}}{\sigma_ {\operatorname* {m a x}} - \sigma_ {\operatorname* {m i n}}} \tag {6} +$$ + +where $\sigma_{i} = \sqrt{\frac{1}{M}\sum_{k = 1}^{M}(S_{i}^{k} - \frac{1}{M}\sum_{k = 1}^{M}S_{i}^{k})^{2}}$ is standard deviations of different quality scores. $\tau_{\mathrm{min}}$ and $\tau_{\mathrm{max}}$ are two pre-defined hyper-parameters determining the bound of temperature. $\sigma_{\mathrm{min}}$ and $\sigma_{\mathrm{max}}$ are the minimum and maximum values of standard deviation $\sigma_{i}$ over the entire dataset, respectively. + +To sum up, in our design, the weight of score is related to two factors: (1) consensus of various scoring models, which is indicated by the density of score. Scores with higher consensus have higher weights because they have higher confidence. (2) uncertainty of the data quality, measured by the standard deviation of multiple scores. Data with higher quality uncertainty require more comprehensive consideration of the scores from various scoring models. Accordingly, we take the quality uncertainty into account by introducing the temperature coefficient, enabling a smoother weight distribution for data with higher quality uncertainty. + +
Data ProcessingQuality ScoreFlickr30KMSCOCOImageNet-1K Acc@1ImageNet-R Acc@1CIFAR100 Acc@1VOC2007 Acc@1
I2T R@1T2I R@1I2T R@1T2I R@1
--19.013.69.27.513.916.028.938.1
Data FilteringPerformance of Best Baseline Score23.516.711.58.214.316.529.539.0
Average Performance of All Baseline Scores22.315.510.88.014.316.428.638.5
MoS (ensemble all baseline scores)24.317.412.49.315.618.831.140.1
Sample WeightingPerformance of Best Baseline Score23.916.111.08.413.216.029.839.0
Average Performance of All Baseline Scores22.415.310.67.913.916.028.838.5
MoS (ensemble all baseline scores)24.716.711.89.115.318.230.539.8
Image Re-captioningPerformance of Best Baseline Score40.027.621.614.915.220.024.036.4
Average Performance of All Baseline Scores39.026.421.014.115.520.322.735.7
MoS (ensemble all baseline scores)43.229.623.116.017.622.726.537.3
+ +Table 1. Comparison on the performance of CLIP ViT-B/32 model trained on CC3M dataset [47] processed by three strategies under different quality scores. The first line in this table denotes the performance of model trained on full CC3M dataset without any data filtering. We consider 18 baseline scores listed in Table 1 of supplementary material. Here, we show the MoS that ensembles all 18 baseline scores to demonstrate its robustness (note that MoS can achieve better performance when ensembling fewer and critical scores, see Table 3). + +
ModelCLIP R50CLIP ViT-B/32CLIP ViT-L/14EVACLIP ViT-L/14EVACLIP ViT-G/14
Time2.5 min2.3 min5 min5 min6.4 min
ModelBLIP ViT-B/16BLIP ViT-L/16BLIP2 ViT-L/14BLIP2 ViT-G/14
Time4.3 min5.7 min6 min8.1 min
+ +Table 2. The detailed time cost of baseline quality score calculation under different scoring models for 1M image-text pairs. + +Finally, we simply ensemble the given quality scores via weighted summation as Eq. (7), resulting in our Mixture-of-Scores (MoS). Therefore, MoS can be regarded as a data-adaptive ensemble of multiple existing quality scores. + +$$ +S _ {i} ^ {\mathrm {M o S}} = \sum_ {k = 1} ^ {M} w _ {i} ^ {k} S _ {i} ^ {k}. \tag {7} +$$ + +Notably, our MoS is easy to implement, requiring only three lines of code. We provide a PyTorch-style code in Algorithm 1. + +# 4. Experiments + +Dataset. Experiments are conducted on two image-text pair datasets (CC3M [47] and LAION [36]) with different sizes. + +Baseline quality score. We consider a variety of popular baseline quality scores generated from diverse scoring models, including different variants of CLIP [20], EVACLIP [7], BLIP [1], and BLIP2 [59] models. + +More details are shown in Sec.5 of supplementary material. + +# 4.1. Efficiency of MoS + +The computational cost of our MoS comes from the following two aspects: + +- Calculate the baseline quality scores: This step is relatively fast. We list the time consumption of calculating different baseline quality scores in Table 2. +- MoS ensemble calculation: Our MoS can be implemented using only three lines of code (as Algorithm 1). Given the pre-calculated baseline quality scores, the ensemble progress of our MoS can be quickly completed in a few minutes. For example, ensembling 18 baseline scores only takes around 2 minutes on 1 NVIDIA A800 GPU. + +![](images/9b09b7ebd7c9280cd1b716cf74645c6a753f01699c6b4243f0b8b8ef959109b4.jpg) +Figure 6. The Correlation between human rating and different quality scores. + +Thus, our method is cost-efficient, taking around several minutes per 1M data on NVIDIA A800. This makes it easy to scale up to large-scale datasets. In addition, these computational costs are one-time, and the resulting score and processed dataset can be reused multiple times. + +# 4.2. Comparison with Baseline Quality Scores + +Human Evaluation. We first randomly select 100 image-text pairs from CC3M with images containing different numbers of objects balanced, and then ask human to rate their image-text alignment. As Figure 6, our MoS shows a higher correlation with human rating than other baseline quality scores. + +Effect on Vision-language Pre-training. The main use of image-text quality score is to process the image-text dataset before vision-language pre-training based on their quality. For comprehensiveness, we consider three image-text processing strategies, including data filtering [36, 52], sample weighting [4, 42] and image re-captioning [14], whose pipelines are detailed in Sec.4 of supplementary material. Specifically, we first process the same dataset based on each of these different quality scores respectively, and then conduct a thorough comparison of the performance of models trained separately on each processed dataset. For fairness, the training settings remain consistent across the compared experiments. + +Table 1 shows the superiority of our MoS compared with various baseline scores. As Table 4 in supplementary, no baseline score is winning in all evaluation settings. For example, CLIP(ViT-B/32) score performs best on ImageNet-1K, but ranks in the middle on COCO retrieval. In contrast, our method is the first one to perform best in all evaluation settings. Due to space limitations, the comparison on LAION + +
Quality ScoreFlickr30KMSCOCOImageNet-1K Acc@1ImageNet-R Acc@1CIFAR100 Acc@1VOC2007 Acc@1
I2T R@1T2I R@1I2T R@1T2I R@1
MoS (ensemble all 18 baseline scores)24.317.412.49.315.618.831.140.1
MoS (ensemble top-2 top-performing scores)24.517.313.110.116.418.030.640.1
MoS (ensemble top-3 top-performing scores)24.917.513.810.517.017.730.740.3
MoS (ensemble top-4 top-performing scores)25.017.914.211.017.318.531.040.5
MoS (ensemble top-5 top-performing scores)24.718.014.011.017.418.631.240.6
MoS (ensemble top-2 bottom-performing scores)23.516.512.08.914.617.430.138.4
MoS (ensemble top-4 bottom-performing scores)24.017.111.89.014.817.730.539.0
MoS (random ensemble 4 baseline scores)24.017.212.59.815.918.831.440.0
MoS (ensemble 4 scores: CLIP-ViT-L/14, EVACLIP-ViT-L/14, BLIP-ViT-L/16-pt, BLIP2-ViT-L/14-pt)24.417.313.010.115.518.330.940.1
MoS (ensemble 4 scores: CLIP-R50, EVACLIP-ViT-L/14, BLIP-ViT-B/16-pt, BLIP2-ViT-G/14-pt)24.717.513.810.617.818.731.240.7
+ +dataset are shown in supplementary Table 5, the results for other models (BLIP and LLaVA) are shown in supplementary Table 3 and 1. Table 2 in supplementary demonstrates the robustness of MoS on different data filtering ratios. + +# 4.3. Discussion + +Number of ensembled scores in MoS: more is not always better. It is not necessary to ensemble as many baseline scores for our MoS. As Table 3, ensembling less but critical baseline quality scores can be superior to ensembling all the scores. This demonstrates that our MoS does not rely on ensembling so many baseline quality scores, which is beneficial to its efficiency in practical applications. + +No need to get entangled in choosing which scores to ensemble when using MoS. Although ensembling different scores for MoS lead to differences in performance (Table 3, they are still much better than using a single score. Our MoS shows great robustness to the number of ensembled scores. Therefore, there is no need to struggle with choosing which scores to be ensembled when using our MoS. And one of the original intentions of our work is to free the community from the entanglement of choosing the scoring model. + +Recipes for choosing less but key scores for MoS ensembling. Considering that some users may want to pursue the best tradeoff between efficiency and performance, we provide two heuristic recipes for choosing less but key ensembled scores when using our MoS. + +- If the performance preference of each baseline score is known in advance, you can directly ensemble these well-performing scores. This helps reduce the interference of inaccurate scores, save computational cost, and achieve better performance. As line 2-5 in Table 3, only ensembling several top-performing baseline quality scores can achieve better performance than ensembling all baseline scores because there are fewer negative interferences in the top-performing scores. +- If the performance preference of each baseline score is unknown in advance, you are recommended to select scoring models with diverse model architecture and varying model sizes. This helps to increase the diversity of scores and + +is more likely to obtain complementary effects from each baseline score, because different types of scoring models give quality assessment from different angles. Please refer to line 1,8-10 in Table 3 for the effectiveness of this recipe. + +# 4.4. Ablation Study + +Ensemble strategy. As Table 4 (line 1&2), simply averaging all the baseline quality scores will not achieve the best performance on all benchmarks, thus cannot eliminate the bias of these baseline scores. This demonstrates the vital necessity of the data-adaptive ensemble strategy in our MoS. + +Softmax temperature. Table 4 (line 1&3) compares our uncertainty-awareness temperature in Eq. (6) and the fixed temperature. We can observe some penalty on performance with a fixed temperature coefficient independent of the quality uncertainty. Table 4 (line 1&4-6) ablates the effect on the value of $\tau_{\mathrm{min}}$ and $\tau_{\mathrm{max}}$ in Eq. (6). We employ the best setting $\tau_{\mathrm{min}} = 0.5$ and $\tau_{\mathrm{max}} = 1.5$ by default. + +Distance function. The $D(\cdot, \cdot)$ in Eq. (4) can be instantiated as any distance function. Table 4 (line 1&7) shows that L1 distance is slightly better than L2 distance, thus we use L1 distance by default. + +Table 3. Comparison on different number and recipes of ensembled scores in our MoS. The experiments are conducted on CLIP (ViT-B/32) model and trained on CC3M dataset [47]. Note: We use the average performance of 8 evaluation datasets as the criterion for the superiority of the performance of the scoring models. + +
Ensemble StrategySoftmax typeTemperature τminτmaxDistance FunctionFlickr30KMSCOCOImageNet-1K Acc@1
I2T R@1T21 R@1I2T R@1T21 R@1
1oursEq.(6)0.51.5L124.317.412.49.315.6
2averageEq.(6)---22.7 (-1.6)15.0 (-2.4)10.6 (-1.8)7.9 (-1.4)14.5 (-1.1)
3oursfixed (τ = 1)--L123.5 (-0.8)16.8 (-0.6)11.7 (-0.7)8.9 (-0.4)15.1 (-0.5)
4oursEq.(6)0.51.0L123.9 (-0.4)17.1 (-0.3)12.2 (-0.2)9.1 (-0.2)15.3 (-0.3)
5oursEq.(6)0.52.0L124.2 (-0.1)17.5 (+0.1)12.2 (-0.2)9.3 (-0.0)15.4 (-0.2)
6oursEq.(6)1.01.5L123.6 (-0.7)17.0 (-0.4)12.0 (-0.4)9.2 (-0.1)15.1 (-0.5)
7oursEq.(6)0.51.5L223.2 (-1.1)17.0 (-0.4)11.7 (-0.7)8.8 (-0.5)15.2 (-0.4)
+ +Table 4. Ablation study on ensemble strategy and softmax temperature coefficient. The comparison is conducted on CLIP ViT-B/32 model trained on the filtered CC3M dataset. + +# 5. Conclusion + +In this work, we first expose and investigate the quality score disparity problem and its subsequent impact on data processing and model learning. Then, we propose a simple but powerful ensemble-based solution to integrate multiple existing quality scores into a more robust score. Extensive experiments show the effectiveness of our method. + +# Acknowledgements + +This work was supported in part by the Research Grants Council under the Areas of Excellence scheme grant AoE/E-601/22-R, Hong Kong Research Grant Council - Early Career Scheme (Grant No. 27209621), General Research Fund Scheme (Grant No. 17202422, 17212923, 17215025), Theme-based Research (Grant No. T45-701/22-R) and Shenzhen Science and Technology Innovation Commission (SGDX20220530111405040). 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While existing methods focus on detecting face retouching, how to accurately recover the original faces from the retouched ones has yet to be answered. This paper introduces Face Retouching Restoration (FRR), a novel computer vision task aimed at restoring original faces from their retouched counterparts. FRR differs from traditional image restoration tasks by addressing the complex retouching operations with various types and degrees, which focuses more on the restoration of the low-frequency information of the faces. To tackle this challenge, we propose MoFRR, Mixture of Diffusion Models for FRR. Inspired by DeepSeek's expert isolation strategy, the MoFRR uses sparse activation of specialized experts handling distinct retouching types and the engagement of a shared expert dealing with universal retouching traces. Each specialized expert follows a dual-branch structure with a DDIM-based low-frequency branch guided by an Iterative Distortion Evaluation Module (IDEM) and a Cross-Attention-based High-Frequency branch (HFCAM) for detail refinement. Extensive experiments on a newly constructed face retouching dataset, RetouchingFFHQ++, demonstrate the effectiveness of MoFRR for FRR. + +# 1. Introduction + +Retouched face images, produced through various techniques such as face lifting, eye enlargement, whitening, and smoothing, are pervasive on social platforms. Most users acquire these images through straightforward and convenient methods to improve their appearance. Despite amusement and fun, the abuse of face retouching causes a lot of serious problems, including aesthetic degradation, commercial deception [2] and identity fraud [3]. To address these problems, many retouching detection schemes and regulatory countermeasures have been proposed. For instance, Norway [14] has enacted strict disclosure requirements for + +![](images/f3ecd4e023e484f96fa15e3f9574c63c185fc22faeb682e70765a28b79915842.jpg) +Figure 1. Application scenario of the proposed scheme (MoFRR). (a) People use face retouching in various applications, (b) face retouching poses risks such as fraud, societal security, and cultural psychological issues, (c) existing work for face retouching detection, (d) our proposed MoFRR method recovers the original image from the retouched version, thereby offering an additional layer of protection against face retouching fraud. + +edited promotional content. US and Israel also have labeling requirements for retouched faces [9, 30]. Researchers have developed dedicated datasets and neural networks to auto-detect the presence of retouching within a digital image [7, 11, 42]. In application, once exaggerated retouching is detected, the corresponding images can be automatically removed, or the livestreams closed. + +In the literature, researchers have focused mainly on the accurate detection of face retouching [20, 31, 42]. It has yet to be answered regarding how we could near-faithfully recover the original face image from the retouched one, which is important to trace back to the real identity of the severely retouched faces. + +In this paper, we consider a new computer vision task, Face Retouching Restoration (FRR), to restore the original faces from the retouched ones, which serves as a further step for fighting against the misuse of face retouching. In literature, researchers have dedicated their efforts to dealing with similar tasks, including makeup removal [37] and image restoration (IR) [23, 27, 41]. The former transfers the style of a reference face to a makeup face for face restora + +tion. The latter tries to restore high-quality textural details from low-quality images. These schemes work well in recovering textural features. However, in face retouching, it may not be sufficient to change only the textural features of the face image. Usually, the face structure has to be modified in order to have distinct differences in appearance. Consequently, noticeable structural changes can be made during face retouching, such as enlarged eyes, more prominent noses, and thinner face shapes. Thus, directly applying existing makeup removal or image restoration schemes may not be appropriate for FRR. + +We believe that a good and appropriate FRR scheme should focus more on the restoration of low-frequency information of the faces, which significantly differs from the existing approaches for the IR and makeup removal tasks. FRR is a challenging task as the faces might be operated in a complex setting of face retouching with various types and degrees, including whitening, smoothing, eye enlargement, and face lifting. The logic among different touching types varies and the goals are also different. Thus, it might not be appropriate to perform the FRR using a single model. We also notice that the impact of different face retouching operations is independent in the face images. + +Inspired by the Mixture of Experts (MoE) [4, 21], we propose MoFRR that restores the face images in a divide-and-conquer manner using an MoE framework with specialized and shared experts. A specialized expert is trained to explicitly restore the faces for a certain type of face retouching. The design of the shared expert is inspired by the recent success of DeepSeek [28], which aims to deal with universal retouching traces in different types of face retouching. We propose a novel wavelet DDIM [34] model, denoted as WaveFRR, for the design of specialized experts. Each WaveFRR contains a dual-branch structure including a DDIM-based low-frequency branch and a cross-attention-based high-frequency branch. The former contains an Iterative Distortion Evaluation Module (IDEM) that restores the wavelet low-frequency sub-band of the faces. The latter contains a High-Frequency Cross-Attention Module (HF-CAM) that recovers the wavelet high-frequency sub-bands. For the shared expert, we adopt the ordinary DDIM architecture to make it general for various retouching conditions. + +For training and evaluation, we newly construct a dataset named RetouchingFFHQ++, which contains over a million retouched face images from four commercial face retouching APIs. We have conducted comprehensive experiments including intra-API and cross-API tests, both demonstrate the effectiveness of our MoFRR for face retouching restoration. To summarize, our contributions are as follows. + +- We are the first to consider the task of face retouching restoration, and we propose MoFRR, an MoE framework with both specialized and shared experts, to address this challenging problem. + +- We propose a wavelet-based DDIM model for face restoration from a specific retouching type, where an IDEM module and an HFCAM moule are designed to recover the low-frequency and high-frequency sub-bands of the face, respectively. +- We extend the large-scale face retouching dataset, RetouchingFFHQ [42], into RetouchingFFHQ++ to make it more suitable for training and evaluation of FRR schemes. + +# 2. Related Works + +# 2.1. Makeup Transfer and Removal + +Over the past year, makeup removal [8, 37] has garnered significant attention in research, often explored in conjunction with makeup transfer [15]. PairedCycleGAN [6] utilizes an asymmetric framework that includes an additional sub-network specifically for makeup removal. PSGAN++ [29] employs a makeup distillation network and an identity extraction network to facilitate makeup transfer and removal. SSAT [35] is proposed for simultaneous makeup transfer and removal, utilizing a Symmetric Semantic Corresponding Feature Transfer module for accurate semantic alignment. Recently, CSD-MT [36] introduces an unsupervised framework to achieve robust performance by adaptively combining high-frequency content details and low-frequency style features. Nevertheless, face retouching differs from making-up in that the former often involves changes to the facial structure while the latter does not. + +# 2.2. Image Restoration + +Many methods are proposed to utilize facial component dictionaries [26] or codebooks [16, 39] derived from high-quality images to guide the restoration process. DR2 [40] uses a DDPM to transform degraded images into coarse, degradation-invariant predictions, which are then enhanced to high-quality images. Restormer [43] uses an efficient Transformer to achieve superior performance on several image restoration tasks. ResDiff [33] proposes a DDPM to predict residuals, using frequency-domain loss and guided diffusion to improve generation speed and sample quality. However, image restoration primarily focuses on recovering high-frequency texture details for image quality improvement, while FRR often aims to restore a face image more semantically. + +# 3. Method + +# 3.1. FRR: Goals, Evaluations and Our Dataset + +Goals and Evaluations. The goal of FRR is defined to blindly, i.e., with no other reference of template, reconstruct the original face images given the retouched ones via computer vision algorithms or deep learning methods. + +![](images/7156ffa925274d1e0e65624bc5bc7a3c3ab16e7593676a60b33a3a8f8751e9e9.jpg) +Figure 2. Examples from the RetouchingFFHQ++ dataset, where original faces are retouched by different retouching APIs. In each row, the applied retouching types and degrees are kept same. + +
PortraitMegviiTencentAlibabaTotal
Ori----57910
Single1082676669220010029483404542
Multi206655232641173590-612886
Total314922299333373690294831075338
+ +Table 1. Summary of RetouchingFFHQ++. The "Multi" column includes a mixture of $2+$ face retouching operations. + +Our evaluation framework prioritizes forensic admissibility over perceptual quality, explicitly discouraging methods that synthesize plausible but inauthentic facial features. We adopt a dual-metric approach: pixel-level fidelity is quantified through standard PSNR and SSIM [38] to measure spatial and structural reconstruction accuracy, while biometric veracity is assessed via feature-space cosine similarity using state-of-the-art face recognition models like AdaFace [24] and ArcFace [12], etc. This dual evaluation mechanism ensures FRR methods meet both visual reconstruction benchmarks and evidentiary standards required for judicial applications, where synthetic enhancements could render biometric evidence legally inadmissible. + +The RetouchingFFHQ++ Dataset. In order to train networks for FRR, we prepare our first dedicated dataset for FRR based on RetouchingFFHQ [42], a recently proposed large-scale face retouching detection dataset that includes high-quality, fine-grained annotated retouched face images from commercial APIs such as Tencent, Megvii, and Alibaba. The original face images are from the famous FFHQ dataset [22], and the retouched subsets include thousands of retouched images, covering whitening, smoothing, face lifting, eye enlarging, or combined operations of the above. + +But the dataset is originally proposed for face retouching detection, so in order to better cater to our FRR task, we extend this dataset as RetouchingFFHQ++ in the following two aspects. + +First, we expand the dataset using the widely-adopted PortraitPro 24 API [1], increasing the total number of images to over a million, as shown in Tab. 1. We show examples of the dataset in Fig. 2, and we include more details and statistics of the dataset in the supplement. From the examples images, we see that retouched images by the PortraitPro API can have noticeable visual differences compared to the existing images from other APIs, thus further diversifying the dataset. + +Second, we propose a more reasonable criteria on the degree definition of each retouching. While RetouchingFFHQ directly defines the degrees according to the argument passed on generating the images, it could less reflect the actual degree due to API-level algorithmic discrepancy. To mitigate this, we redefine the degree of modification of each operation within images via statistically analyzing the PSNR distribution of all retouched face images. We re-categorize them into five groups with proportions of $15\%$ , $25\%$ , $25\%$ , $25\%$ , and $10\%$ , based on ascending PSNR values, and labeled from 5 to 1 accordingly. + +# 3.2. FRR Model with Multi Experts + +The overall pipeline of our proposed MoFRR, as depicted in Fig. 3, is a Mixture of Diffusion Models for FRR. We explicitly decompose the task into several steps. First, given a targeted image, we first predict which types of face retouching operations are performed. Second, we employ several expert networks, where apart from a reserved shared expert as inspired by DeepSeek, the rest of experts (denoted as specialized experts) are respectively specialized in removing one certain type of face retouching in the given image. As a result, the experts provide several versions of intermediate recovered images. Third, with the intermediate images from all the activated experts, we merge these images with the original image through the Combine Module to obtain the final restored image. + +Concretely, we train a router to identify which face retouching operations have been applied to the images and to activate the following expert networks. We implement it by the ResNet-MAM [42], which is adapted for multi-label classification and outputs an $N$ -dimensional binary label vector. Here in our paper, we focus on the most typical types of face retouching operations, which are whitening, smoothing, face lifting, and eye enlarging, so $N = 4$ . + +$$ +\left[ b _ {w}, b _ {s}, b _ {f}, b _ {e} \right] = \mathbb {1} (\operatorname {R o u t e r} (X) > \text {t h}), \tag {1} +$$ + +where $X\in \mathbb{R}^{H\times W\times C}$ represents the input retouched face image. $b_{M}$ for $M\in \{w,s,f,e\}$ denotes the prediction result of whether the input image contains the correspond + +![](images/5ab48fd3f88ca39aa112d4a2bea72afc6eaa5e4278b0a93b2d793c768b6ac37e.jpg) +Figure 3. Left: Overview of MoFRR, where input image is processed by the router and selectively sent into the specialized experts for different retouching types. A shared expert is continuously engaged inspired by Deepseek, and the result images from the experts are jointly sent to a lightweight Combine Module to produce the final restored image. Right: the WaveFRR design, where the image is decomposed using DWT, and the DDIM process works on low-frequency subband restoration guided by the transformed degree estimation result (by IDEM). Then HFCAM module restores the high-frequency sub-bands via cross-attending the restored lower sub-bands. + +ing face retouching operation $M$ . $\mathbb{1}(\cdot >\mathrm{th})$ represents if the prediction exceeds a given threshold (here 0.5 by default). + +Next, four $(N)$ independent experts, named WaveFRR models, process the image once activated by the router. The design of a WaveFRR model is illustrated in Fig. 3. Each expert is specialized in estimating and restoring a particular face retouching operation. It begins with predicting the degree of the specific face retouching operation, which is trained ahead and guides the subsequent restoration process. Then, considering that face retouching primarily emphasizes content modifications, such as cheeks and eyes, rather than global high-frequency details, we first perform the discrete wavelet transformation (DWT) that decomposes the input image into lower and higher frequencies. For lower frequencies, we propose sampling a retouching-free version via conditional DDIM [18, 34], guided by the predicted retouching degree and the original lower frequencies. For higher frequencies, we modify them by cross-attending [13] the generated lower frequencies for more refined retouching removal. The modified frequencies are then combined via Inverse Discrete Wavelet Transform (IDWT) to produce the restored image $\hat{Y}_M$ , which removes only the specific face retouching operation $M$ . + +For the shared expert, we adopt a baseline DDIM architecture without wavelet decomposition, where we hope the architectural divergence from WaveFRR explicitly could promote complementary functional specialization. While WaveFRR experts focus on frequency-aware sub-band recovery, the shared expert captures global retouching patterns across spectral domains, denoted as $\hat{Y}_{se}$ . + +Finally, we gather all restored outputs of the activated experts and design a lightweight Combine Module to give the final retouching-free image $\hat{Y}$ . The Combine Module employs a UNet [32], which leverages all images and the re + +touched image to generate results while preserving fidelity to the input image, as follows: + +$$ +\hat {Y} = \text {C o m b i n e} _ {-} \text {M o d u l e} ([ X, \hat {Y} _ {s e}, \hat {Y} _ {M _ {0}}, \hat {Y} _ {M _ {1}}, \dots ]). \tag {2} +$$ + +# 3.3. WaveFRR Model + +Degree Estimator and DWT. Each expert begins with estimating the degree of its specialized face retouching operation. Afterward, we train a ResNet50 [17] as Degree Estimators, using our newly defined degree labels as supervision. It predicts the global retouching degree $z = \mathrm{DE}_M(X)$ for the face retouching operation $M$ . Besides the estimator, we apply the DWT to decompose it into low-frequency and high-frequency sub-bands, denoted as $\{x_{LL}, x_H\}$ , where $x_{LL} \in \mathbb{R}^{\frac{H}{2} \times \frac{W}{2} \times C}$ and $x_H \in \mathbb{R}^{\frac{H}{2} \times \frac{W}{2} \times 3C}$ represent one low-frequency sub-band, i.e., LL, and three high-frequency sub-bands, i.e., HH, LH and HL. + +Low-Frequency Branch. The LL sub-band of DWT contains major information of $X$ . We propose to sample a retouching-free LL sub-band of $X$ via conditional DDIM, guided by the predicted retouching degree and the original LL sub-band. For denoised image $\hat{y}_t$ at timestamp $t$ , our IDEM module utilizes the multi-scale channel attention network [10], denoted as MCA( $\cdot$ ), which produces the pixel-wise condition $\tilde{x} \in \mathbb{R}^{\frac{H}{2} \times \frac{W}{2} \times 2C}$ given $\hat{y}_t$ , $x_{LL}$ and $z$ as: + +$$ +F = \operatorname {M C A} (z + x _ {L L}) \otimes x _ {L L} + (1 - \operatorname {M C A} (z + x _ {L L})) \otimes z, \tag {3} +$$ + +$$ +\hat {R} = \operatorname {M C A} \left(F + \hat {y} _ {t}\right) \otimes \hat {y} _ {t} + \left(1 - \operatorname {M C A} \left(F + \hat {y} _ {t}\right)\right) \otimes F, \tag {4} +$$ + +$$ +\tilde {x} = \operatorname {I D E M} \left(\hat {y} _ {t}, x _ {L L}, z\right) = \operatorname {C o n c a t} \left(x _ {L L}, \hat {R}\right), \tag {5} +$$ + +where $\hat{R} \in \mathbb{R}^{\frac{H}{2} \times \frac{W}{2} \times C}$ is the pixel-wise distortion map. + +The DDPM [18] uses a Markov chain to restore the image step by step from Gaussian noise. The forward diffusion process progressively transforms the ground truth + +$y_{0}$ into noise data in $T$ steps with a variance schedule $\{\beta_1,\beta_2,\dots ,\beta_T\}$ , which can be formulated as: + +$$ +q \left(y _ {t} \mid y _ {t - 1}\right) = \mathcal {N} \left(y _ {t}; \sqrt {1 - \beta_ {t}} y _ {t - 1}, \beta_ {t} \mathbf {I}\right), \tag {6} +$$ + +where $\mathcal{N}$ denotes the Gaussian distribution. The denoising process gradually removes noise from a randomly sampled Gaussian noise $\hat{y}_T\sim \mathcal{N}(0,\mathbf{I})$ . We use conditional denoising process with the condition $\tilde{x}$ , i.e, + +$$ +p _ {\theta} \left(\hat {y} _ {0: T} \mid \tilde {x}\right) = p \left(\hat {y} _ {T}\right) \prod_ {t = 1} ^ {T} p _ {\theta} \left(\hat {y} _ {t - 1} \mid \hat {y} _ {t}, \tilde {x}\right). \tag {7} +$$ + +The sampled lower-frequent subband at the last times- tamp is denoted as $\hat{y}_0$ , which is regarded as the retouchingfree lower frequency of $X$ . To accelerate inference, we take DDIM [34] as the sampling scheme. + +High-Frequency Branch and IDWT. We further introduce the HFCAM module to adjust the high-frequency sub-bands for refined retouching removal. The famous visual patchwise Cross-Attention [13] mechanism is efficient in providing large receptive field only with several layers' effort. Thus, we propose to patchify $\hat{y}_0$ , $x_H$ , and apply a lightweight one-layer CA and a three-layered convolution network to modify the higher-frequency bands. + +$$ +\hat {y} _ {H} = x _ {H} + \operatorname {C o n v} \left(\mathrm {C A} \left(\hat {y} _ {0}, x _ {H}\right)\right). \tag {8} +$$ + +Finally, we combine the restored frequencies via the inverse wavelet transformation, i.e., $\hat{Y}_M = \mathrm{IDWT}(\hat{y}_0,\hat{y}_H)$ + +# 3.4. Objective Functions and Training Details + +To train the proposed method, we first separately train the router and the Degree Estimators ahead of the rest modules for restoration. Next, these models are fixed and we train the low- and high-frequency branches within WaveFRR. Once the experts are prepared, we train the Combine Module that gets the intermediate images and produces the final result. Note that while we train MoFRR based on hybrid face images that have come through 0-4 face retouching operations, we only train WaveFRR models using single-operated images since they only remove their selected type, and train the shared expert on subset B for capturing global retouching patterns. + +The objective functions of the proposed method include three categories, namely, frequency loss $\mathcal{L}_{\text{freq}}$ , spacial loss $\mathcal{L}_{\text{space}}$ , and classification loss $\mathcal{L}_{\text{class}}$ . The total loss for the WaveFRR is given by $\mathcal{L} = \mathcal{L}_{\text{freq}} + \mathcal{L}_{\text{space}} + \mathcal{L}_{\text{class}}$ . + +The frequency loss $\mathcal{L}_{\text{freq}}$ includes three parts, namely, IDEM loss $\mathcal{L}_{\text{IDEM}}$ , diffusion loss $\mathcal{L}_{\text{simple}}$ , and high-frequency loss $\mathcal{L}_{\text{high}}$ . i.e., $\mathcal{L}_{\text{freq}} = \mathcal{L}_{\text{IDEM}} + \mathcal{L}_{\text{simple}} + \mathcal{L}_{\text{high}}$ . The IDEM loss uses the $\ell_2$ loss to quantify the difference between the pixel-wise distortion and the true residual of the low-frequency sub-band, which is given by $\mathcal{L}_{\text{IDEM}} = \| \hat{R} -$ + +$(y_{LL} - x_{LL})\|^{2}$ , where $y_{LL}$ is the LL sub-band of the ground truth image. The training objective for diffusion models is $\mathcal{L}_{simple} = \mathbb{E}_{y_0,t,\epsilon_t\sim \mathcal{N}(0,\mathbf{I})}\left[\| \epsilon_t - \epsilon_\theta (y_t,\tilde{x},t)\| ^2\right]$ . We utilize the $\ell_2$ loss and Total Variation (TV) [5] loss to optimize the HFCAM, defined as: $\mathcal{L}_{high} = \lambda_1\parallel \hat{y}_H - y_H\parallel^2 +\lambda_2\mathrm{TV}(\hat{y}_H)$ where $\lambda_{1}$ and $\lambda_{2}$ are set as 0.1 and 0.01, respectively. + +The spatial loss $\mathcal{L}_{space}$ is to maximize the PSNR between restored and original image. We use a hybrid $\ell_1$ & SSIM [38] loss, defined as $\mathcal{L}_{hyb}(\cdot ,\hat{\cdot}) = \| \cdot -\hat{\cdot}\| _1 + (1-$ SSIM(.,)) where the symbol $\cdot$ denotes the ground-truth value of the symbol $\hat{\cdot}$ , to minimize the difference between the restored face image and the ground truth image for both WaveFRR and Combine Module, i.e., $\mathcal{L}_{space} = \mathcal{L}_{hyb}(Y,\hat{Y}) +$ $\sum_{M}\mathcal{L}_{hyb}(Y,\hat{Y}_M)$ . + +As for the router and Degree Estimator, we respectively train them based on cross-entropy loss $\mathcal{L}_{\text{class}}$ , i.e., $\mathcal{L}_{\text{class}} = -\sum_{i=1}^{5} c_i \log(\hat{c}_i)$ , where $c$ and $\hat{c}$ respectively denote the true label and the predicted probability for class $i$ . + +# 4. Experiments + +# 4.1. Experimental Setups + +Implementation Details We use Adam [25] as the optimizer with a learning rate of $1 \times 10^{-4}$ . The WaveFRR model is trained till convergence for about $2 \times 10^{5}$ iterations on eight NVIDIA A100 GPUs with a default batch size of 16, and the overall pipeline is trained for 50 epoch to converge. Input and output images have a resolution of $1024 \times 1024$ . More details can be found in the supplement. + +Test Cases and Baseline Preparations. We employ two test cases, namely, intra-API tests, and cross-API tests. For intra-API tests, we train and test the models with a mixture of data from all APIs. For cross-API tests, we train our MoFRR and all comparing models on a mixture of subsets except Portrait and test on the Portrait subset, additionally validating the generalizability of models. In both test cases, the according dataset material is divided evenly into 8:1:1 as training/evaluation/test set. + +There are no FRR methods available in the literature. We select a list of representative work from several relevant fields as baselines, including reference-free makeup removal method PairedCycleGAN [6] (PCGAN for short), as well as image restoration methods containing Pix2pix [19], Restormer [43], DR2 [40], and ResDiff [33]. The comparison methods cover a variety of mainstream architectures, including GAN, Transformer, and diffusion models. For fair comparison, we retrain them on our RetouchingFFHQ++ dataset for fair comparisons. + +# 4.2. Intra-API Performance + +In Fig. 4, we provide a visual comparison with other methods for FRR on the RetouchingFFHQ++ dataset. The images are randomly chosen from the subset that contains + +![](images/be0d067cc8dd8f5087211d335d8cb87086e24baec90132447c70dfcbebfe40fc.jpg) +Figure 4. Qualitative comparison of the restored faces using different methods. The images are retouched through multiple operations, and our method achieves higher restoration quality with fewer artifacts. Zoom in for best view. + +
MethodsWhiteSmoothFaceEyeMulti
PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑PSNR↑SSIM↑
Input29.140.94035.590.93429.550.90335.820.95228.030.887
Pix2pix (CVPR17)27.720.88328.550.85827.340.85628.410.87028.730.897
PCGAN (CVPR18)22.470.68423.530.63923.040.62723.630.63422.170.581
Restormer (CVPR22)29.890.91837.590.94329.830.90333.750.94228.190.888
DR2 (CVPR23)24.330.72325.970.71924.390.71225.710.71923.870.711
ResDiff (AAAI24)26.210.89135.940.93529.860.89735.840.93728.980.889
MoFRR33.110.94938.060.94331.260.91338.050.95834.470.959
+ +Table 2. Quantitative comparison of face retouching restoration. All compared models are retrained on our RetouchingFFHQ++ dataset for fair comparison. For each column, all the models are trained and tested on the same single-operated images, or all images for "Multi". + +face images retouched by multiple operations. As can be seen in the figures, methods like Pix2pix [19] and ResDiff [33] can recover the facial structure to some extent, but fail to generate high-quality face images without artifacts. Restormer [43] and PCGAN [6] perform better in restoring facial skin color, but struggle with structural restoration. In contrast, it can be observed that our MoFRR restores the original images more faithfully with fewer artifacts, particularly around the face and eyes. Besides, we also interestingly find that the baseline methods that apply the diffusion network generally provides better results compared to + +the non-diffusion ones. The reason might be that diffusion models also accept the "divide and conquer" methodology in nature, and therefore the image qualities are generally better, as aligned with many recent findings. However, the fidelity of their results are noticeably worse compared to ours, especially from the view that ResDiff in many cases would apply wrong type of retouching. + +Table 2 shows the quantitative comparison of FRR w.r.t. overall PSNR and SSIM. To better investigate the model performance against different retouching types as well as combined retouching, in the leading four groups we report + +![](images/d872004c19368bb3a71c68f64232c0f6e65edc4a070df0400ebba0bc9003c6a6.jpg) +(a) + +![](images/3d9500e8d759c2a042e649d7c1f3c9728e1c63bdd36a8a23ceb11460f98b2572.jpg) +Figure 5. Visualization of images generated by five specific experts. (a) shared expert, (b) face lifting expert, (c) eye enlarging expert, (d) smoothing expert, and (e) whitening expert. +Figure 6. Probability density distribution of facial feature similarity among retouched/restored and original face images. + +the performance on images that only has the specific retouching, and in the last group (named "Multi"), the per + +
MethodsSingleMulti
PSNR↑SSIM↑PSNR↑SSIM↑
Input34.450.95626.410.879
Pix2pix28.180.88126.680.886
PCGAN23.180.62621.300.569
Restormer34.830.95426.500.882
DR224.720.70922.630.676
ResDiff34.930.96126.790.885
MoFRR36.650.97131.280.938
+ +Table 3. Cross-API performance. Models trained on all other datasets are tested on the Portrait subset to evaluate their generalization ability. + +
MethodsSingleMulti
PSNR↑SSIM↑PSNR↑SSIM↑
Input32.730.93428.030.887
WaveFRR35.180.93931.090.904
w/o IDEM34.340.93632.940.915
w/o Degree34.430.93732.950.921
w/o HFCAM34.690.93733.040.926
w/o shared expert35.370.94132.420.913
w/o router35.630.94234.190.947
MoFRR36.120.94334.470.959
+ +Table 4. Ablation study over different model modules w.r.t. the ground truth. We fine-tune the models in partial settings till convergence. Test: intra-API. + +formance on images with two or more retouching operations. From the results, our method outperforms other methods on the four single-operated subdatasets. Although PCGAN [6] exhibits excellent performance on the makeup transfer task, it struggles on the novel task of FRR with PSNR of around 23 dB. DR2 [40] performs well on face restoration but struggles with FRR due to the addition of excessive detail noise, resulting in higher image quality but lower fidelity. Other baselines have their own advantages in different subsets but do not perform as well and as comprehensively as MoFRR, particularly on the whitening subset where MoFRR achieves 3.97 dB improvement in PSNR. Particularly, our proposed MoFRR demonstrates superior performance compared to all baselines on the multi-operated subset. The distortion effects of multi-operated images are more pronounced. MoFRR effectively restores retouched face images, which surpasses the second-best method by 5.49 dB, achieving the highest improvement of 6.44 dB in PSNR. Multi-operated images better represent actual application scenarios, indicating that our method has significant advantages in practical use. The significant improvement observed in the multi-operated subset further validates effectiveness of our MoE framework. + +Figure 5 provides the visual results generated by specific experts. To facilitate a clearer visual observation, we pro + +![](images/47a46d8b135bf516f780a9e87efc62de0d64088fa2b4c57f5a019baa800a2db3.jpg) +Original +Ours +w/o shared expert +w/o IDEM +Figure 7. Qualitative comparison of the ablation studies, which proves the necessity of employing shared expert like DeepSeek and the IDEM design. + +vide a sub-figure in each row as a zoom-in on some region-of-interest areas. It can be observed that four operation-specific experts perform well in restoring the targeted retouching operation, where we indeed see that the corresponding retouching is successfully reverted while other types of retouching operations that the expert is not specialized in are kept unchanged. We also see that the shared expert is able to do multiple types of retouching removal in parallel, but the generated result is not close to the ground-truth images. This finding is generally in line with our hypothesis that though one expert is not enough yet could steadily contribute to the overall quality improvement via seeing more retouched samples compared to the specialized experts. + +Impact on Face Recognition. Figure 6 illustrates the probability density distributions of facial feature similarity between retouched/restored and original images. Each curve represents the cosine similarity distribution of a specific method's results compared to the original faces, where a value closer to 1.0 indicates near-perfect feature alignment. The blue curve of MoFRR exhibits a sharp peak near 1.0 across both AdaFace [24] and ArcFace [12], which means the faces recovered by using our proposed method are more similar to the original faces at the feature level. The narrow width of the blue curve's peak further highlights its high confidence in restoring identity features. While existing methods ResDiff [33] and Restormer [43] improve over retouched images, their curves show flatter distribution and lower peak values than ours. The curve of Pix2pix [19] has the lowest peak value and the flattest distribution, implying feature misalignment which may be caused by the heavy artifacts. Besides, the long left tail of the red curve indicates some retouched images are extremely processed with severe identity degradation. All methods can restore the extreme cases to some extent, while our MoFFR suppress the left-tail density more effectively. + +# 4.3. Cross-API Performance + +In a real-world scenario, training data and testing data are likely to come from different sources, so cross-API performance analysis helps us probe into the estimated performance of models in real-world conditions. From the results shown in Tab. 3, we observe that while there is a modest degradation in overall PSNR, MoFRR consistently delivers commendable restoration outcomes. Compared to the baselines, which achieve poor performance on both single- and multi-operated images, MoFRR demonstrates a notable advantage with improvements of $1.2\mathrm{dB}$ and $3.87\mathrm{dB}$ . This substantial performance gain, particularly for multi-operation images, can be attributed to the specialized expertise of multiple expert networks within MoFRR. + +# 4.4. Ablation Study + +Architectural analysis. The results are shown in Tab. 4. It can be observed that removing any one of modules in WaveFRR degrades performance compared to the full model. Both the Degree Estimator and IDEM handle distortion predictions, with the former focusing on global predictions and the latter on pixel-level predictions. The removal of IDEM results in significant performance degradation due to its refined iterative predictions. The combination of the two modules makes the prediction more effective by indicating the location and extent of retouching, as well as HF-CAM demonstrates unique effectiveness in artifact removal. The performance degradation of removing the shared expert mainly occurs in multi-operated cases due to its effect on global structural restoration. In contrast, removing the router has minimal impact on performance, as the Degree Estimator can reduce the impact of false activation while the router contributes positively to enhancing efficiency. + +Comparison with Single-Expert Mode. We also test the performance where we use one single WaveFRR as the whole MoFRR. Results show that it performs well on single-operated images, but limited when restoring all operations simultaneously. The multi-expert mechanism also offers flexibility that once novel types of face retouching appear, a plug-in of corresponding expert networks would mitigate the huge cost of fully retraining the model. + +# 5. Conclusion + +We propose face retouching restoration, a novel task of recovering the original faces from retouched ones. We propose a Mixture of Diffusion Models for FRR, including specialized WaveFRR models that uses a dual-branch structure, i.e., a low-frequency recovery using DDIM, and a high-frequency refinement guided by the restored lower subbands. 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Black $^{4}$ Andreas Geiger $^{2}$ + +$^{1}$ ETH Zürich $^{2}$ University of Tübingen, Tübingen AI Center + +$^{3}$ HKUST(GZ)&HKUST $^{4}$ Max Planck Institute for Intelligent Systems, Tübingen + +![](images/321533efdee9ebd286a7750ae0b85c1206afdb426bb6204afcffe8373d9f00d3.jpg) +Input + +![](images/6d3b2a2c45f0b1d09c9f4f6b89101bcd55d652b24aa95b3a7a1a191468398b9c.jpg) + +![](images/c29d446f5663a281c7f0949470de562cf1719f5e0e0faa0deeb6ce50862c978e.jpg) +GaussianAvatar + +![](images/2c0c4885199e5c53de898ca6dff71d0e29c31463f13b4312b10a26c33d860f26.jpg) +Rendered Novel Views + +![](images/cc7a64bcf9f27249a6f86874714097dd35fd1791423659641bf3d9787a300823.jpg) + +![](images/df103a91ee64a12a3d42ec1da373dd0deee722077fd09898ec2c3ed14db6e63c.jpg) +Animation +Figure 1. We propose MoGA, a method to generate high-fidelity Gaussian avatars from a single image. Left: A challenging in-the-wild example. Middle: Unlike previous methods that struggle with such cases (Fig. 4), MoGA enables 3D-consistent full-body novel view synthesis and detailed geometry extraction. Right: Our reconstructed Gaussian avatar supports animation without any post-processing. + +# Abstract + +We present MoGA, a novel method to reconstruct high-fidelity 3D Gaussian avatars from a single-view image. The main challenge lies in inferring unseen appearance and geometric details while ensuring 3D consistency and realism. Most previous methods rely on 2D diffusion models to synthesize unseen views; however, these generated views are sparse and inconsistent, resulting in unrealistic 3D artifacts and blurred appearance. To address these limitations, we leverage a generative avatar model, that can generate diverse 3D avatars by sampling deformed Gaussians from a learned prior distribution. Due to limited 3D training data, such a 3D model alone cannot capture all image details of unseen identities. Consequently, we integrate it as a prior, ensuring 3D consistency by projecting input images into its latent space and enforcing additional 3D appearance and geometric constraints. Our novel approach formulates Gaussian avatar creation as model inversion by fitting the generative avatar to synthetic views from 2D diffusion models. The generative avatar provides an initialization for model fitting, enforces 3D regularization, and helps in refining pose. Experiments show that our method surpasses state-of-the-art techniques and generalizes well to real-world scenarios. Our Gaussian avatars are also inherently animatable. For code, see https://zj-dong.github.io/MoGA/ + +# 1. Introduction + +Animatable and realistic avatar creation enables many applications in AR/VR, movies, and the gaming industry. It is hard to scale up this process since previous traditional approaches [22] require expensive multi-view systems and highly-specialized expertise to craft the avatar. To make digital avatars widely available and consumer-friendly, it is essential to develop methods for creating an avatar from in-the-wild images. However, this problem is very challenging due to the ill-posed nature of the monocular setting, which causes ambiguities in the appearance, depth, and body poses. + +Embracing the challenging problem, previous methods [41, 42, 52] learn a large network to predict explicit or implicit 3D representations from 2D pixel-aligned features. These methods are trained on small-scale datasets due to the limited amount of available 3D data; this greatly restricts their generalization to diverse human poses and clothing styles. More recently, to enable more powerful generalization ability, some methods [14, 26, 53, 59] leverage a multi-view diffusion model to hallucinate back and side views. Despite impressive performance, most existing multi-view diffusion models can only generate very sparse views with high resolution due to memory constraints during training [23]. The sparsity of generated views leads to artifacts in self-occluded regions or unobserved side views. Furthermore, since such methods rely heavily on 2D priors + +from 2D diffusion, the generated multi-view imagery often lacks 3D consistency [27, 38], which results in blurry appearance in 3D. To prevent the reconstruction of unnatural bodies, some methods [8, 14, 20, 26, 59] leverage parametric body models like SMPL [29] as full-body priors. Although this helps avoid abnormal shapes, it is restricted by the fixed topology and minimally-clothed SMPL body shape and cannot provide a 3D appearance prior. + +To address these limitations, we propose a novel method, MoGA (Monocular Gaussian Avatar), that reconstructs a high-fidelity 3D Gaussian avatar from a single-view image (Fig. 1). At its core, our approach leverages a generative 3D avatar model as a powerful human body prior. Unlike the SMPL body prior, our model captures not only detailed geometry but also realistic human appearance, including hair and clothing, using deformed Gaussians. We harness multi-view diffusion to infer unseen views while ensuring 3D consistency and realism. This is achieved by projecting the synthetic images back to the learned latent space of the generative avatar and applying additional constraints. The creation of the Gaussian avatar is then formulated by fitting the generative avatar to these generated views. During this process, our generative avatar model plays a pivotal role in three ways: (i) Initialization: Sampling from the learned avatar prior enables a meaningful initialization of geometry and appearance for fitting, helping avoid local minima in few-shot reconstruction. (ii) Regularization: Rather than relying solely on inconsistent synthetic images, the avatar prior enforces strong 3D constraints, ensuring view consistency and preventing unrealistic artifacts. (iii) Pose Optimization: This avatar prior enables us to refine human and camera poses through an effective photometric rendering loss, improving alignment accuracy and reconstruction fidelity over baselines. + +More specifically, we represent human bodies and clothing in canonical space using 2D Gaussian Splatting [19], anchored to a parametric body template [35], and integrate it with an efficient deformation module [11]. To enable generation, we model every human subject via a per-subject latent code and a shared decoder to interpret the latent code into Gaussian features. This generative avatar prior is learned through a single-stage pipeline [7] that jointly optimizes the latent code, the shared decoder, and a latent diffusion model in the latent space. At test time, we first employ image-guided sampling [7] to obtain a meaningful latent code. Given this initialization, we perform model inversion to compute the latent code for a novel target identity while freezing the decoder and learned diffusion model. During this process, the diffusion model serves as a constraint in the latent space via a score distillation sampling loss [37]. Throughout the fitting procedure, both the avatar model and camera/human pose parameters are optimized in an alternating manner to correct abnormal poses. + +We experimentally demonstrate that our method significantly outperforms previous state-of-the-art methods both quantitatively and qualitatively (Table 1 and Fig. 3). The resulting Gaussian avatar has better 3D consistency and realism (Fig. 3), and adapts better to model complex structures like hair (Fig. 5). In summary, we contribute: + +- An optimization-based model fitting framework to reconstruct a Gaussian avatar from a single image, by fitting a 3D generative avatar to synthetic images generated by 2D multi-view diffusion. +- A generative 3D Gaussian avatar prior that enables reconstructing a deformed Gaussian avatar from sparse and inconsistent generated images, by providing crucial support for meaningful initialization, regularization, and pose refinement during model fitting. +- Generalization to in-the-wild outdoor images with challenging pose and clothing. The resulting avatar can be animated without post-processing. + +Code and models are available at https://zj-dong.github.io/ MoGA/. + +# 2. Related Work + +# 2.1. Single-view Human Reconstruction + +Creating realistic avatars from a single RGB image is a challenging problem. PIFu [41] pioneered a data-driven pipeline to learn a mapping from 2D pixel-aligned features to 3D implicit functions. More recent work builds upon this idea and improves the geometry by leveraging normal guidance and parametric human body models [3, 27, 28, 42, 52]. However, given only a frontal view, these methods struggle to reconstruct realistic full-body texture because of the unobserved back side. More recently, methods use 2D diffusion models to hallucinate the back view and incorporate this into the reconstruction pipeline [14, 59]. However, with only two observations, these methods suffer from strong artifacts in side-views. Several methods go further by leveraging a modified multi-view diffusion process to generate more views, improving rendering quality and geometry [26, 53, 59]. Unfortunately, 2D diffusion often produces synthetic images that are inconsistent in 3D. To address this, PSHuman [26] and SIFU [59] leverage SMPL [29, 35] as a 3D template to regularize the reconstruction. However, since SMPL does not provide an appearance prior and only has a minimally clothed body shape, the methods struggle when the clothing and hair differ from the SMPL body topology. Human3Diffusion [53] uses a 3D diffusion model to guide sampling of a multi-view diffusion model, but is limited by the low resolution of the diffusion model. In contrast to the prior work, we combine an expressive generative 3D avatar model with synthetic 2D images generated from a multi-view diffusion model, achieving better reconstruction quality and robustness to self-occlusion. + +# 2.2.3DAvatar Generation + +Several methods [1, 11, 16, 32] leverage 3D-aware GANs [5, 6, 44] to generate 3D humans from 2D image collections. The main idea is to leverage 3D human models [29, 35] to learn a 3D human GAN with an adversarial loss. Several techniques are then developed to improve geometric quality [11], the face region [11, 16], deformation [11] and efficiency [1]. Despite impressive results, these methods are all trained with 2D image discriminators that are unable to reason about cross-view relationships [7], making it challenging to exploit multi-view data. Recent 3D diffusion models [7, 15, 46, 48] show better generation capabilities due to their more expressive and high-dimensional latent space. Leveraging this, recent work [9, 18, 58] parameterizes the human via primitives [9] or a structured latent code [18] and learns a diffusion model in the latent space for unconditional generation. By leveraging multi-view data, these methods achieve 3D consistency in appearance generation. Unlike these methods we leverage a 3D generative avatar model for single-view avatar reconstruction. Although reconstruction from single images is possible through GAN inversion [6], the quality is limited by the expressiveness of the latent space, making it hard to apply to in-the-wild images. Rodin [50] and its extensions [57] employ an image-conditioned diffusion model for few-shot face reconstruction. These are trained on synthetic images and struggle to generalize to the real-world. We address the more challenging problem of reconstructing full-body avatars with diverse poses and clothing styles from in-the-wild images. + +# 2.3. Gaussian Avatar + +Representations for 3D avatars include 3D meshes [2, 29, 35], implicit functions [10, 12, 21, 30, 36, 51], and point clouds [49, 62]. Recently, 3D Gaussian Splatting [19, 24] has gained attention due to its high rendering quality and efficiency. Many methods [17, 31, 39, 56, 60] learn 3D Gaussian avatars from monocular videos. Despite strong performance, these methods typically fail when the number of observations becomes sparse. GPS-Gaussian [61] proposes a generalizable multi-view human Gaussian model with high-quality rendering, but it needs relatively dense views (16) and accurate camera poses. Concurrent methods [8, 33] leverage a pre-trained transformer to predict the 3D Gaussians from a single-view image, but struggle to reconstruct details and tend to generate artifacts on faces. In contrast, our method achieves a more detailed and realistic Gaussian avatar from only a single-view image. A detailed comparison with [8, 33] is not possible since the models or code have not been released at the time of writing. + +# 3. Method + +Given a single-view image, our goal is to reconstruct a high fidelity 3D Gaussian avatar. To address this ill-posed problem, our key idea is to leverage a generative 3D avatar model as a human prior and fit this generative model to synthetic images generated by multi-view diffusion. An overview of our method is shown in Fig. 2. + +We first introduce an efficient and articulation-aware 3D human generator (Section 3.1 and Fig. 2(a)), which generates the appearance and shape in canonical space and leverages a deformation module to deform these into posed space. To learn this generator, we utilize a single-stage training pipeline [7] that jointly optimizes a Gaussian autodecoder and a latent diffusion model. + +At test time, we fit the learned generative avatar model to 6 synthetic images generated using a pre-trained multi-view diffusion model (Section 3.2 and Fig. 2(b)). We show that the learned generative prior improves the performance by providing a good initialization and regularization for fitting to handle the inconsistency between synthetic views. During the fitting process, we optimize both the avatar model and the camera/human pose parameters alternately to correct abnormal poses. + +# 3.1. Generative Avatar Prior Training + +# 3.1.1. Canonical Gaussian Representation + +To achieve high quality reconstruction of both appearance and geometry, we employ 2D Gaussian splatting [19] to represent the appearance and geometry of the avatar generated in the canonical space. Motivated by GGHead [25] and Relightable Gaussian Codec Avatars [43], we parameterize 2D Gaussians $\mathcal{G}$ on a UV map $U$ of a template mesh [35]. Here, each Gaussian primitive $\mathcal{G}_k$ is parameterized by five attributes: an opacity $\sigma_k \in \mathbb{R}$ , a Gaussian center $\mu_k \in \mathbb{R}^3$ , RGB color $c_k \in \mathbb{R}^3$ for simplicity, a scale vector $s_k \in \mathbb{R}^2$ for 2D Gaussian Splatting, and a rotation matrix $R_k$ represented by the axis angle vector $r_k \in \mathbb{R}^3$ . Finally, based on the UV mapping, we can represent the Gaussian attributes $\mathcal{G}$ with a 2D UV map $U \in \mathbb{R}^{256 \times 256 \times 12}$ . + +To better leverage the template body prior, we model the Gaussian center $\mu_{k}$ , the scale vector $s_k$ , and the rotation $r_k$ as a residual from the canonical SMPL-X body [35]: + +$$ +\begin{array}{l} \mu_ {k} = \hat {\mu} _ {k} + \delta_ {\mu k} \\ s _ {k} = \hat {s} _ {k} \cdot \delta_ {s k} \tag {1} \\ r _ {k} = \hat {r} _ {k} \cdot \delta_ {r k}. \\ \end{array} +$$ + +Here, $\hat{\mu}_k$ , $\hat{s}_k$ , and $\hat{r}_k$ are the initial center, scale, and rotation of the Gaussian primitives, which are obtained from the SMPL-X mesh; for more details, see Sup. Mat. Finally, we predict the offset value $\delta_{\mu k}$ , $\delta_{sk}$ , $\delta_{rk}$ to represent Gaussian attributes. + +![](images/bfadb9878f6133ffb10c64af511ca5d20c65b0fdaad3f7e761ecdad893e9e75a.jpg) + +![](images/cc2d2706783d2fe9003ad3c08ab4380ecab45e8b7598f5c594637719fd1f9fa4.jpg) +Figure 2. Method Overview. Generative Avatar Prior Learning: Our 3D human generator creates the appearance and geometry in canonical space represented by 3D Gaussians and leverages an efficient deformation module to deform these into posed space for Gaussian rasterization. To learn this generative avatar model from a 3D human dataset, we utilize a single-stage training pipeline that jointly optimizes a Gaussian auto-decoder (including a per-subject latent code and a shared decoder) and a latent diffusion model. Model Fitting: At test time, we fit the learned generative avatar to synthetic images generated from a pretrained multi-view diffusion model. During this process, we first initialize the latent code by image-guided sampling and perform model inversion to compute the latent code while freezing the decoder and learned diffusion model. Both the avatar model and camera/human pose parameters are optimized in an alternating manner to correct abnormal poses. + +To make our model generalize to various people, we learn a shared auto-decoder across all the training people. For each identity, we model each person by a small compressed latent code $X_{i} \in \mathbb{R}^{64 \times 64 \times 32}$ and then decode the latent code to final UV map $U_{i}$ using the shared CNN decoder. More details of the decoder can be found in Sup. Mat. + +# 3.1.2. Deformer + +To enable animation and learn from posed images, we use a deformer to transform the avatar $\mathcal{G}$ from the canonical space into posed space. For each Gaussian primitive $\mathcal{G}_k$ , the deformed Gaussian center and rotation matrix $\mu_k'$ and $R_k'$ are computed as: + +$$ +\mu_ {k} ^ {\prime} = T \mu_ {k}, R _ {k} ^ {\prime} = T R _ {k}, \text {w h e r e} T = \sum_ {i = 1} ^ {n _ {b}} w _ {i} B _ {i}. \tag {2} +$$ + +Here $n_b$ is the number of joints, $B_i$ is the bone transformation matrix for joint $i \in \{1, \dots, n_b\}$ , and $w_i$ is the skin- + +ning weight, which determines the influence of the motion of each joint on $\mu_{k}$ . Following AG3D [11], the skinning weight is represented as a low-resolution voxel grid. More details can be found in Sup. Mat. + +# 3.1.3. Rendering + +After we obtain the deformed Gaussian attributes, we perform 2D Gaussian splatting as in [19]. For each pixel $\mathbf{x} = (x,y)$ , the pixel color is obtained by: + +$$ +c (\mathbf {x}) = \sum_ {i = 1} ^ {N} c _ {i} \mathcal {G} _ {i} (\mathbf {x}) \sigma_ {i} \prod_ {j = 1} ^ {i - 1} (1 - \sigma_ {j} \mathcal {G} _ {j} (\mathbf {x})) \tag {3} +$$ + +where $c_{i}$ is the color of the $i$ -th projected 2D Gaussian primitive sorted by depth. To render normal maps, we replace the color $c_{i}$ with the normal of the Gaussian primitives. $\sigma_{i}$ represents the opacity values. $\mathcal{G}(\mathbf{x})$ is the evaluated 2D Gaussian value. More details of the evaluation of $\mathcal{G}(\mathbf{x})$ can be seen in [19]. + +# 3.1.4. Generative Avatar Training + +Fig. 2(a) illustrates the training process of this generative avatar model. We leverage the latent diffusion model (LDM) [40] to learn the generative prior in the latent space. Following SSDNeRF [7], we adopt a single-stage training pipeline to jointly optimize our auto-decoder and LDM. The training objective is: + +$$ +\mathcal {L} = \lambda_ {\text {r e n d}} \mathcal {L} _ {\text {r e n d}} \left(\left\{X _ {i} \right\}, \psi\right) + \lambda_ {\text {d i f f}} \mathcal {L} _ {\text {d i f f}} \left(\left\{X _ {i} \right\}, \phi\right). \tag {4} +$$ + +Here $X_{i}$ is the latent feature code and $\psi$ and $\phi$ denote the parameters of the decoder and denoising U-Net respectively. $\lambda_{*}$ are the loss weights. $\mathcal{L}_{\mathrm{rend}}$ and $\mathcal{L}_{\mathrm{diff}}$ are the training objectives for the rendering and diffusion process. Compared to two-stage training [46, 50], the resulting learned latent space is smoother due to end-to-end optimization of the diffusion and decoder weights. The rendering loss is: + +$$ +\mathcal {L} _ {\text {r e n d}} \left(\left\{X _ {i} \right\}, \psi\right) = \lambda_ {1 2} \mathcal {L} _ {1 2} + \lambda_ {\mathrm {v g g}} \mathcal {L} _ {\mathrm {v g g}} + \lambda_ {\mathrm {r e g}} \mathcal {L} _ {\mathrm {r e g}}. \tag {5} +$$ + +$\mathcal{L}_{\mathrm{l2}}$ is the L2 reconstruction loss between rendering and observations. Unlike [7], we compute the reconstruction loss on both RGB and normal images to improve the geometry quality. $\mathcal{L}_{\mathrm{vgg}}$ is a perceptual loss based on the difference between the feature maps obtained from [47] and the rendered image. We define $\mathcal{L}_{\mathrm{reg}} = \|\delta_{\mu k}\|$ to prevent the predicted offset from being too large. + +To train the diffusion model, similar to [7], we compute $\mathcal{L}_{\mathrm{diff}}$ as: + +$$ +\mathcal {L} _ {\text {d i f f}} \left(\left\{X _ {i} \right\}, \phi\right) = \underset {i, t, \epsilon} {\mathbb {E}} \left[ \frac {1}{2} w ^ {(t)} \left\| \hat {X} _ {i} - X _ {i} \right\| ^ {2} \right] \tag {6} +$$ + +where $\hat{X}_i$ is the denoised latent code with time step $t \sim \mathcal{U}(0, T)$ , $w^{(t)}$ is an empirical time-dependent weighting function, and $\epsilon$ is the added noise. More details can be found in Sup. Mat. + +# 3.2. Model Fitting + +Equipped with the learned generative avatar prior, we reconstruct a personalized avatar by fitting the generative model to synthetic views generated from multi-view diffusion. + +# 3.2.1. Multi-view Hallucination and Pose Estimation + +Since a single image is not enough for Gaussian reconstruction, we leverage a pre-trained multi-view diffusion model [26] to hallucinate 6 synthetic human images from a single image. After obtaining synthetic views, similar to [45], we leverage a human pose estimator to obtain the initial SMPL-X parameters. More details of preprocessing can be found in Sup. Mat. + +# 3.2.2. Rendering Objective + +To optimize the latent feature map, we define the rendering loss $\mathcal{L}'_{\mathrm{rend}}$ during inference as: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {r e n d}} ^ {\prime} \left(\left\{X _ {i} \right\}, \psi\right) = \lambda_ {\mathrm {l} 2} \mathcal {L} _ {\mathrm {l} 2} + \lambda_ {\mathrm {v g g}} \mathcal {L} _ {\mathrm {v g g}} + \lambda_ {\mathrm {r e g}} \mathcal {L} _ {\mathrm {r e g}} \tag {7} \\ + \lambda_ {\mathrm {n c}} \mathcal {L} _ {\mathrm {n c}} + \lambda_ {\mathrm {d}} \mathcal {L} _ {\mathrm {d}}. \\ \end{array} +$$ + +Here we use the same equation as in Eq. (4) to calculate the L2 reconstruction loss $\mathcal{L}_{\mathrm{l2}}$ and perceptual loss $\mathcal{L}_{\mathrm{vgg}}$ between predicted images (normals) and generated synthetic images (normals). To improve the geometry of the avatar, we additionally add the normal consistency loss $\mathcal{L}_{\mathrm{nc}}$ and the depth distortion loss $\mathcal{L}_{\mathrm{d}}$ from [19]. More details can be found in the Sup. Mat. + +# 3.2.3. Prior-guided Optimization + +Since the multi-view diffusion model generates sparse and inconsistent images, solely relying on the rendering loss makes the result blurry and unrealistic. Here, we tackle the problem by leveraging our pretrained generative avatar prior as a powerful human prior of 3D appearance and geometry. More concretely, this prior mainly contributes to three aspects including: + +Initialization. Random initialization of the latent code can sometimes cause the optimization to converge to a bad local minimum. To solve this problem, we leverage our learned generative model to provide a good starting point for model fitting. To make our model generalizable to unseen test images, we follow [7] to use image-guided sampling. More specifically, for a noisy code $X^{(t)}$ at every denoising step $t$ , we additionally compute an approximated rendering gradient $g$ based on testing rendering loss $\mathcal{L}_{\mathrm{rend}}'(X^{(t)})$ and add it to the denoised output $\hat{X}^{(t)}$ as an image-guided correction. More details of this computation can be found in Sup. Mat. + +Regularization. Image-guided sampling provides a good initialization, but still cannot reconstruct all the details of test images. To solve this, we refine the sampled latent code by solving: + +$$ +\min _ {X} \lambda_ {\text {r e n d}} \mathcal {L} _ {\text {r e n d}} ^ {\prime} (X) + \lambda_ {\text {d i f f}} ^ {\prime} \mathcal {L} _ {\text {d i f f}} (X). \tag {8} +$$ + +Here we optimize the diffusion loss defined in Eq. (6) jointly with the rendering loss, while freezing the weights of the diffusion and decoder models. Unlike [37], the diffusion model trained in UV feature space serves as a prior to regularize and inpaint the noisy and incomplete latent code during optimization. + +Pose Optimization. The generated synthetic images from multi-view diffusion models are inconsistent, and this results in inaccurate camera and body pose estimation. Instead of using noisy 2D joint estimates [4, 34], we optimize pose parameters via a more effective photometric loss: + +$$ +\mathcal {L} _ {\text {p o s e}} = \lambda_ {1 2} \mathcal {L} _ {1 2} + \lambda_ {\mathrm {v g g}} \mathcal {L} _ {\mathrm {v g g}} + \lambda_ {\text {m a s k}} \mathcal {L} _ {\text {m a s k}} \tag {9} +$$ + +where we combine a mask loss $\mathcal{L}_{\mathrm{mask}}$ with predefined L2 loss $\mathcal{L}_{12}$ and a perceptual loss. Here we optimize both SMPL + +![](images/86e82dd648f6701a05d9947d2117841285e6150c9bf43f4780bc11e357c467f2.jpg) + +![](images/6388b0e389268099c940276529ee16bc1bd3fc1fa8d2c5d1cd731218fffb3cdb.jpg) +Input Image + +![](images/3cd21cddf09a1960e51e54c795b98dd6742f5f6fe3c4eebca50efa72777b34bf.jpg) + +![](images/d22e74e8585fc7c37a34468d4f555e881b39136d9c9d2111f3088c2ba629df23.jpg) + +![](images/5406e691f2be74d0aa594344474c615afba9677fc2d7eff4e02a7fa838c8eca9.jpg) + +![](images/b7313c5acc16eb164f088867e76ab94c44aae034497380e0d8fdfef890bcf057.jpg) +Human3Diffusion + +![](images/9ef6e49804827e8e15ce65477c0219227b3e53e238ab13b69724d762210e08a2.jpg) + +![](images/2f07b162e45aa22dd23458362dd57480ea9312011f5486dacd26ed380561e7df.jpg) + +![](images/dff6fc6c0d7ad96071d4f1ecc4135b8646c638482db75dc345f05390e12c3a45.jpg) + +![](images/11c6cad0fa3f7f114f39f5f7d9be9acacc084c0501cc6136206fe87384a3b2f4.jpg) +SIFU + +![](images/2eb940879e4bdba72a902621edeb3ca92056ad8ee6c69d90096ef1be6757efd3.jpg) + +![](images/180d4a2057bfd2e16b61e1c13997a69ccc374f7537fa1d624d7c3ad0f20e15f6.jpg) + +![](images/b21c707f357a9e048fa6a256dcddc880f1448ae5d38c16e504e8f0a4e40904ae.jpg) + +![](images/1a677c950dd71a9c93202c6fe5cbbb15447124870093bc7d8c2ff65c92cbb524.jpg) +SITH +Figure 3. Qualitative comparison to SotA methods on CustomHuman. Our method achieves better image and shape quality, enables 3D consistency in side views, and avoids unrealistic reconstruction due to self-occlusion. + +![](images/ee5d513a8d9a27fdac3469cd97f5be1e8d655dfdc49c048446b957f51a7ad492.jpg) + +![](images/624668981577bea4dd24300d50ca78d17cfc3a5a48224a7a737c83dda54064e2.jpg) + +![](images/c085eb1d3ab18364af37ac257557a8a52846219db0e4ebb1d1c51c9a74f6a487.jpg) + +![](images/fe420ae93abfcda0eddd264cebfd3ba2872ac920cd1b8cf068942783040dc3c3.jpg) +PSHuman + +![](images/57aad0e3f61253ab4830e0a77cad9442969cb37cd8b39704b99d152f8373ef21.jpg) + +![](images/25da9e232d595974587f0902be5075a36cfa51b9925a54125de2d9294fc1df49.jpg) + +![](images/6df148f26190488504db14b91ebc4692690aeaf0c2c0245c910e9df5d0493e11.jpg) + +![](images/5b1456f77cef0a5f354afc12737ba80ebc7dbe58c488735bd51c768b0a1bab1b.jpg) +Ours + +![](images/3957340dbab298f562259f85b24c309c8309458e96d73fdfdba3169592c176ce.jpg) + +![](images/c0200a647c3b570290b4b7b49f1307184a3eb0a96329e7c727228b0ccfdeae37.jpg) + +![](images/ea4fdc23c24338ed1b1f03e2ff63237bc67849009b8beb955ca26216d3fc955f.jpg) + +![](images/be5251b40b20f3b1582b06b053868c0224c63739a5ffaecd8603f03516f71d8b.jpg) +GT + +parameters and camera poses by back-propagation. We optimize the latent code, camera and human poses in an alternating manner to avoid falling into locally suboptimal results. More details can be found in Sup. Mat. + +# 4. Experiments + +In our experiments, we first compare our method to state-of-the-art (SotA) baselines on two public datasets and then test the generalization capability of our method on in-the-wild images. In addition, we provide an ablation study to investigate the importance of each component in our model. + +Datasets. We evaluate our proposed method on THuman2 [55] and CustomHumans [13]. To test the generalization ability, we also collect some in-the-wild images from the Internet for qualitative comparison. For details see Sup. Mat. + +Metrics. Following previous methods [14, 26], we evaluate appearance using peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and perceptual similarity (LPIPS). For geometry comparison, we compute Chamfer Distance (CD), Point to Surface (P2S) distance, and normal consistency (NC). For details see Sup. Mat. + +Baselines. We conduct experiments on current state-of-the-art methods for single-view human reconstruction, including Human3Diffusion [54], SIFU [59], SiTH [14], and a concurrent method, PSHuman [26]. More details about baselines can be found in Sup. Mat. + +# 4.1. Comparison to SotA. + +Table 1 summarizes our quantitative comparisons. Since Human3Diffusion [54] only supports low-resolution rendering, we mainly compare it qualitatively in Fig. 3. Table 1 shows that our method largely outperforms other baselines in appearance, especially in PSNR. As shown in Fig. 3, our method generates overall sharper images with more details. Our method also reconstructs better geometry both quantitatively and qualitatively with better local geometric detail. Here, we discuss the main reason for the improvements: + +Side views. The improvements of appearance and geometry are particularly pronounced for side views. This is because most baselines rely on 2D multi-view diffusion models to hallucinate side views, which are not 3D consistent. In contrast, our learned generative avatar model provides additional appearance and geometry constraints on multi-view consistency, yielding better results. + +Self-occlusion. With a single input view, self-occlusion inevitably happens in the arm and hand regions due to the articulated nature of the human body as illustrated in Fig. 3. In the first example, despite the use of the SMPL body prior, all previous methods fail to accurately reconstruct the left hand and arm. This is because these baselines tend to overfit to the input view, leading to incomplete reconstructions in occluded regions. In contrast, our method effectively reconstructs occluded arms and hands by leveraging the 3D + +![](images/251bc47041ed6acf84b0fba43244aca0c1836c4a1693634bdd286241ce1eba82.jpg) + +![](images/614450a98ffa03e483498b6e0f54f8fc66edb70f22b6347ebca28ade526f0ad6.jpg) +Figure 4. Qualitative comparison to SotA methods on in-the-wild images: Ours outperforms baselines on in-the-wild images by generating more plausible back/side views, reconstructing finer details such as fingers and hats, and avoids artifacts due to self-occlusion. + +![](images/bf8107f95ce0f63208c0c8c018dc9f04c5a236c3a6ff5b86302863dc7bb81dc3.jpg) + +![](images/4432a60c1e9345025a2ac99a21d64d212f7c56f9e6673802e3d65b658030ebda.jpg) + +![](images/f547d301260a615de59cd6359e3c0a5216ad0002e544089b98ad9bc30682560c.jpg) + +![](images/28689ef11a60a1edb79c39305643b840c9c2851e4163827dad899f84c13b3bff.jpg) + +![](images/20565f6705bcee3d7121adad11874c6b01029ea4bca54396b3f62c3525403855.jpg) + +![](images/2eebedc39fe0742621889fa3ca8edcbdaebab7d3c0c5c02d25c0bc765e54b04a.jpg) + +![](images/e773a22465e420073e0bef7e6e2a4cc0d192eceb0966078807ff654deabeb655.jpg) + +![](images/92c2935aed687a64661c5ef8a46c34999709b5bfa8f106fb99261e08113cac1f.jpg) + +![](images/db5e130b5b1455939c8c52d5a08e2395a06322ab2416c26177e3cce97d181fb1.jpg) +Figure 5. Qualitative comparison to PSHuman on fine-sclae structures. Our method reconstructs complex topologies, like a ponytail, that deviate from the body topology. + +appearance prior from our model. In the second example, the baselines exhibit artifacts on the clothing due to color misalignment from the arm, which is exacerbated by self-occlusion and depth ambiguity. Instead, our method reconstructs both the arm and clothing, despite the occlusion. + +Topology changes. Figure 5 compares our method with the concurrent PSHuman [26] on two more challenging subjects. Due to fixed topology of the template mesh, PSHuman fails to model areas between the arm and face, as well as the ponytail. These artifacts are present in other SMPL-based methods [59]. In contrast, our method reconstructs 3D Gaussians and this flexible representation allows it to reconstruct more complex structures. + +# 4.2. In-the-wild Performance + +Figure 6(a) shows qualitative results on in-the-wild images. MoGA generalizes to loose clothing and challenging poses. The reconstructed Gaussian avatar can be posed or animated (Fig. 6(b)), because it is based on SMPL-X. Figure 4 compares results of SotA methods on in-the-wild images. Both + +![](images/4b36df9869d103f1b482e21634f1bdf67b6f1bc2770108bb4005e582e272c340.jpg) +(a) + +![](images/628d1cc81c3bfe6a4147e346cfcdcadba7a891e4e51f3533a41e05aa5762fd55.jpg) +Figure 6. Qualitative results on in-the-wild images. (a) From an in-the-wild image with challenging poses and clothing, our method reconstructs a high-quality Gaussian avatar, that enables realistic novel view synthesis and detailed geometry reconstruction. (b) The resulting avatar can be animated with SMPL-X poses. + +SiTH and SIFU struggle to produce reasonable reconstructions, often generating blurry back views and unrealistic appearance. PSHuman works better, but fails to capture fine details such as fingers and hats, while also introducing artifacts on clothing. In contrast, by leveraging the learned + +
MethodTHuman2.1CustomHuman
PSNR↑SSIM↑LPIPS↓CD↓P2S↓NC↑PSNR↑SSIM↑LPIPS↓CD↓P2S↓NC↑
SIFU[59]17.52710.92190.10192.62202.44500.78716.01980.90560.11462.37172.22060.809
SiTH [14]19.40200.93440.07962.23701.84590.80817.79860.92110.09212.91422.04260.788
PSHuman [26]19.95950.93500.07781.41281.23200.83718.67040.92230.08501.91971.46950.828
Ours24.09260.94550.07321.36081.22260.85023.43830.93510.07911.80861.48210.834
+ +generative avatar prior, our MoGA model faithfully reconstructs Gaussian avatars in this challenging setting. + +# 4.3. Ablation Study + +Since the generative avatar prior is the key to our method, we focus on ablations that evaluate its effectiveness. An analysis of pose optimization, unconditional generation, and robustness to the number of views appears in Sup. Mat. All experiments are conducted on the CustomHuman Dataset. + +Table 1. Quantitative comparison with SotA Methods on Thuman2.1 and CustomHuman. Our method outperforms other baselines by a large margin on appearance and also demonstrates a clear improvement in geometry. + +
MethodPSNR ↑SSIM ↑LPIPS ↓
w/o Initialization22.69960.92780.0891
w/o Avatar Prior22.58380.92880.0863
Full Model23.43830.93510.0791
+ +Table 2. Ablation. We compare our method with ablated baselines in which we remove the generative avatar prior for initialization and regularization. + +Effect of initialization. Our generative avatar plays a crucial role in initializing the fitting process. We compare our method against ablated versions where the latent code is initialized randomly. As shown in Table 2, MoGA improves all appearance metrics. Furthermore, qualitative results in Fig. 7 demonstrate that, without proper initialization, the reconstructed appearance becomes blurry, particularly in the face region. This degradation occurs because the optimization process converges to a poor local minimum. In contrast, our method produces sharper and more accurate facial reconstructions, highlighting the importance of a well-initialized latent code. + +Effect of generative avatar prior. To evaluate the effect of the generative avatar prior, we create an ablated version of our method that directly optimizes SMPL-anchored Gaussians without using the learned decoder and latent diffusion model. Table 2 shows that the generative avatar prior is important. In the first example of Fig. 8, removing the generative avatar prior results in a blurry side view and introduces a visible white crack between the front and back. This artifact arises due to the 3D inconsistency of images gener + +![](images/1e40f30a30500275bcbe1847fc58e9ba19a702417711bdfec3da2fde5e791625.jpg) +Figure 7. Ablation of Initialization. The good initialization provided by our generative avatar model enhances appearance quality, reducing blurriness and producing a more detailed face + +![](images/a8fe9ad02d188ef989ecf4a248bc1fae51bd13cee000734c9292afa1484b3268.jpg) + +![](images/ac69183e55d39b31287d6464caafa685e8baf99f7bfbd423d46a633b38f12f87.jpg) + +![](images/17fb585753cc86fe56864325b7602fdb17ec3e648e09fd2b6a80ed252f92314f.jpg) + +![](images/86746d0dbd1df14c9aac6f3c4e5aabf90b64c76d8e623e11af8fca97161682ac.jpg) + +![](images/03908205ca99e83f9cf845334a327a69c9ca2ffda77465614324d9c8b4e83271.jpg) + +![](images/153633a07665db157677c909df994ca4434e81eaec7f8881e5ee4de16ea3a122.jpg) +GT + +![](images/3a6d973633895cb6095e5d4cdd2823b72a4db20e11e879dc1e6e798ff9e4b9e2.jpg) +w/o Prior + +![](images/5ac2765f8d4a0951b71a25ee25b200766740a848c6672e00ba2f7630fa8f0825.jpg) +with Prior + +![](images/2f0d7a3f96991a8db18bf9f7508524d146995aa6f46c8c5bdd991a256f67697f.jpg) +GT + +![](images/37f147ea3346cea40a30f3064b6e843d88ecaa30cfd3e590d28c38d8c27966d5.jpg) +w/o Prior +Figure 8. Ablation of generative avatar prior. The generative avatar model serves as an important 3D regularization to ensure 3D consistency and inpaint missing regions. + +![](images/2303ceb7947ac1de13a6373bf999c4bbb1b9e93155c98db68305d65e3c564e1d.jpg) +with Prior + +ated by the multi-view diffusion model. In contrast, our method enforces better 3D consistency. The second example in Fig. 8 highlights another issue without our model. The ablated baseline tends to produce artifacts in occluded regions. In comparison, incorporating the generative prior enables our model to inpaint the missing areas effectively, resulting in a more natural and complete appearance. + +# 5. Conclusion + +In this paper, we propose MoGA, a novel approach for reconstructing Gaussian avatars from a monocular image. Unlike previous methods that rely solely on multi-view diffusion, we integrate a 3D generative avatar model as a complementary prior, ensuring 3D consistency by projecting images into its latent space and enforcing both 3D appearance and geometry constraints. We formulate Gaussian avatar creation as model inversion by fitting the generative avatar model to synthetic images from 2D diffusion models. Our method sets a new state-of-the-art in reconstruction quality and 3D consistency, generalizing well to in-the-wild images while producing animatable avatars without post-processing. Limitations and discussions appear in Sup. Mat. + +Acknowledgements: Andreas Geiger was supported by the ERC Starting Grant LEGO-3D (850533) and the DFG EXC number 2064/1 - project number 390727645. While MJB is a co-founder and Chief Scientist at Meshcapade, his research in this project was performed solely at, and funded solely by, the Max Planck Society. 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0000000000000000000000000000000000000000..0377b582316d514013f3934171e25e004dabaedc --- /dev/null +++ b/ICCV/2025/MoMa-Kitchen_ A 100K+ Benchmark for Affordance-Grounded Last-Mile Navigation in Mobile Manipulation/full.md @@ -0,0 +1,426 @@ +# MoMa-Kitchen: A 100K+ Benchmark for Affordance-Grounded Last-Mile Navigation in Mobile Manipulation + +Pingrui Zhang $^{1,2*}$ Xianqiang Gao $^{2,3*}$ Yuhan Wu $^{3}$ Kehui Liu $^{2,4}$ + +Dong Wang² Zhigang Wang² Bin Zhao²,⁴ Yan Ding²† Xuelong Li⁵† + +$^{1}$ Fudan University $^{2}$ Shanghai AI Laboratory $^{3}$ University of Science and Technology of China + +$^{4}$ Northwestern Polytechnical University $^{5}$ TeleAI, China Telecom Corp Ltd + +{zhangpingrui, dingyan}@pjlab.org.cn, xuelong.li@ieee.org + +# Conventional Navigation Agent without Navigation Affordance Grounding + +![](images/cfd278da6df5f012344f508e50a2191935a38120d0d1eb4635cbef31fb4cb5e2.jpg) + +![](images/a811368a3e2f23b21de0ddec7d27ac4151a04c07b64a42d922e5c24b5a0d1d88.jpg) + +# Agent with Navigation Affordance Grounding + +![](images/b6fe27a7658965b48abb2cb76438da0909fe6c2a5eb0904d571ad838a5226323.jpg) + +![](images/b9fb1c21bfee3e35b433e9204d2f9b407c10d75855f91adb29e01756b9830a3f.jpg) +User + +# Give me the bottle on the counter. + +Turn to the nearest position A. + +![](images/121b91dc7f8eec7f918b657932df44f73f54874a70c1c2634d33e43904c5f42f.jpg) +Figure 1. Conventional navigation methods typically prioritize reaching a target location but do not account for constraints affecting manipulation feasibility. Left: Position A prioritizes proximity but is obstructed by chairs, preventing stable execution. Middle: Position B places the robot in a spacious and stable area for operation but beyond its effective reach. Right: Our approach, leveraging navigation affordance grounding, identifies Position C as the optimal stance, ensuring both reachability and task feasibility. + +Too narrow to stand for grasping! + +![](images/db2a6a743dfb76527836ca11b730df0859324ffc683e3d9be908daae00a5faad.jpg) +Navigation Agent + +![](images/1e3d451eea91a29f529e34e6b1127fd26e66377ca41292a362f864052f9593dc.jpg) + +# Give me the bottle on the counter. + +User Turn to the position B that in front of the target. + +Out of the grasp range! + +![](images/6943be5ea67fbe544f8bf90170d9862de870ffe48c12d0bd02339d260a363535.jpg) +Navigation Agent + +![](images/6a6b8f3a0c23ba553b094c1dee773c98725ca2749b80799b96eff73604b038df.jpg) + +# Give me the bottle on the counter. + +User + +Do navigation affordance grounding. Stop at the best grasp position C! + +![](images/6d7ac9aed0e6f5cd71a85dbf88c37d01b0722d62caccffad625bfd5ae36ceba1.jpg) +NavAff Agent + +![](images/c3c2f455e5c297dfcfbe848e1aa09d933d2043a9b83680f3758899e807e75170.jpg) + +# Abstract + +In mobile manipulation, navigation and manipulation are often treated as separate problems, resulting in a significant gap between merely approaching an object and engaging with it effectively. Many navigation approaches primarily define success by proximity to the target, often overlooking the necessity for optimal positioning that facilitates subsequent manipulation. To address this, we introduce MoMa-Kitchen, a benchmark dataset comprising over 100k samples that provide training data for models to learn optimal final navigation positions for seamless transition to manipulation. Our dataset includes affordance-grounded floor labels collected from diverse kitchen environments, in which robotic mobile manipulators of different models attempt to + +grasp target objects amidst clutter. Using a fully automated pipeline, we simulate diverse real-world scenarios and generate affordance labels for optimal manipulation positions. Visual data are collected from RGB-D inputs captured by a first-person view camera mounted on the robotic arm, ensuring consistency in viewpoint during data collection. We also develop a lightweight baseline model, NavAff, for navigation affordance grounding that demonstrates promising performance on the MoMa-Kitchen benchmark. Our approach enables models to learn affordance-based final positioning that accommodates different arm types and platform heights, thereby paving the way for more robust and generalizable integration of navigation and manipulation in embodied AI. Project page: https://momakitchen.github.io/. + +# 1. Introduction + +Most existing navigation algorithms define success in terms of reaching a location near the target [40]. However, in household environments, navigation is an intermediate step preceding task-specific manipulation. As a result, such navigation strategies are inadequate for mobile manipulation tasks that requires precise end-effector positioning. In practice, navigation and manipulation are tightly integrated. For instance, when tasked with retrieving an object from a kitchen counter, a robot typically navigates toward the target using conventional policies before attempting manipulation. While existing navigation algorithms reliably guide robots across rooms, they often fail in proximity to the target. The robot may stop beyond the manipulator's reachable workspace or be obstructed by spatial constraints, rendering manipulation infeasible (as shown in Fig. 1). Additionally, obstacles such as furniture, bins, or containers in cluttered environments are seldom accounted for in existing navigation policies, further complicating the selection of feasible grasping positions. As a result, reliance solely on these navigation algorithms, without incorporating the demands of manipulation, limits their efficacy in addressing complex tasks in household settings. + +This limitation highlights the disconnect between object localization (navigation) and physical interaction (manipulation) in mobile robotics. In particular, optimizing final positioning in the "last mile" remains a fundamental challenge, yet existing datasets and benchmarks provide limited supervision for this aspect. While recent efforts have employed large language models (LLMs) to assist in selecting optimal navigation positions, these approaches fall short when transitioning to the manipulation phase [37, 79, 81]. Training-free LLMs struggle to accurately predict the requirements of robotic arm interactions. Additionally, they cannot dynamically adjust positioning strategies based on different robotic arm models or base morphology [64, 80]. + +To bridge this gap, we introduce MoMa-Kitchen, a large-scale benchmark with over 100k samples designed to train models for affordance-grounded final positioning in mobile manipulation tasks. Our dataset comprises 127,343 episodes spanning 569 diverse kitchen scenes, where each episode involves predicting floor affordances that enable a robot to approach a target while avoiding collisions with obstacles. We collect large-scale floor affordance data by creating kitchen scenes with various layouts—in which target objects are either randomly placed or selected from common appliances (e.g., refrigerators and cabinets) and obstacles are strategically positioned to generate distinct scenarios. In the simulator, various mobile manipulators attempt to grasp target objects from multiple positions, and success rates are recorded to obtain ground truth affordance labels for each floor position. The collected visual data, consisting of RGB-D and point cloud inputs from a first- + +person view camera mounted on the robotic arm, along with robot-related information, are subsequently used to train our lightweight baseline model, NavAff, which identifies the optimal floor affordance region for subsequent manipulation. To enhance generalization, we employ various robotic arms (e.g., Flexiv and Franka) and varied mobile bases during grasping, enabling the model to learn that floor affordance predictions depend on arm height and operational range. This approach is intended to develop a model that can be used on heterogeneous devices [52]. In summary, our contributions are as follows: + +- We propose MoMa-Kitchen, the first large-scale dataset with over 100k samples that bridges the gap between navigation and manipulation in mobile manipulation tasks by enabling models to optimize final positioning near target objects. +- We develop a fully automated data collection pipeline – including scene generation, affordance labeling, and object placement – to simulate diverse real-world scenarios and enhance model generalizability. +- We design a lightweight baseline model, NavAff that employs RGB-D and point cloud inputs for navigation affordance grounding, achieving promising results on the MoMa-Kitchen benchmark. + +# 2. Dataset Generation + +Task Definition. MoMa-Kitchen focuses on determining feasible final navigation positions that enable successful manipulation in cluttered environments. Given RGB-D inputs from a first-person camera and robot-specific parameters (e.g., arm reach, base height), the goal is to produce an affordance map over the floor. This map indicates where the robot can position itself to reliably manipulate the target while accounting for obstacles, bridging navigation and manipulation within a unified pipeline. + +MoMa-Kitchen includes diverse kitchen environments with multiple types of robotic mobile manipulators, first-person view visual data, and navigation-specific affordance ground truth. As illustrated in Fig. 2, we first construct large-scale kitchen environments that contain different targets, obstacles, and furniture. Mobile manipulators are then placed in these environments to obtain navigation affordance labels through robotic manipulation. For each labeled scene, we collect first-person view visual data from multiple randomly sampled robot viewpoints, including RGB-D images of the scene. The position of each viewpoint is also recorded to generate and transform both the global and floor point clouds. Additionally, floor-level affordance ground truth is collected near the target. + +# 2.1. Scene Setup + +To construct diverse kitchen environments for affordance annotation, we employ BestMan [66], a PyBullet-based + +![](images/86cf80081e781e6dd860f46bedb9353c0d9ef5e1b417f3a6fcb688eb4d3d272f.jpg) +Figure 2. Overview of scene setup and data generation pipeline. Each scene features unique base furniture and layout, with randomly placed obstacles surrounding the target object to enhance scene complexity. Discrete navigation affordance values are collected by moving the mobile manipulator and interacting with the target objects in the scene. View transformation and Gaussian interpolation are then applied to generate a dense affordance map, along with corresponding RGBD data. + +simulation platform that integrates assets from PartNet-Mobility [7, 33, 63]. The generation process begins with a rectangular kitchen layout, where common kitchen furniture and appliances (e.g., sinks, cabinets, dishwashers, and fridges) are procedurally arranged along one wall. To ensure scene diversity, we randomize both the placement order of object categories and the specific instance selection within each category. We further augment each scene with both rigid and articulated objects as manipulation targets, and introduce additional obstacles around them to increase scene complexity. Once the scene assets are ready, we randomly select a manipulator from various types and place it into the scene to collect navigation affordance labels. + +# 2.2. Visual Data Collection + +To comprehensively capture the target and its surroundings from the robot's perspective, we sample ten distinct camera poses $\left[\mathbf{R}_{\mathbf{c}}\mid \mathbf{T}_{\mathbf{c}}\right] \in \mathbb{R}^{4 \times 4}$ around each target. These viewpoints are strategically selected to cover the target object, its surrounding environment, and the floor. For viewpoint selection, we alternate the positions to the left and right of the target object, gradually increasing the distance from it. After placing the robot at the selected position, we check whether the target object is within the observation range. If not, we randomly generate a new position. This process continues until the target object is within the line of sight, + +at which point we stop and record the viewpoint. For each camera pose, we collect RGB images $\mathbf{I}$ , depth maps $\mathbf{D}$ , and floor point clouds $\mathbf{P}_{\mathrm{floor}} \in \mathbb{R}^{n \times 3}$ , where $n$ denotes the number of points in the point cloud. + +# 2.3. Affordance Labeling + +We gather mobile manipulators with various robotic arms to collect floor-level navigation affordance ground truth data for target objects. For each target object, we define the affordance sampling area $\mathcal{A}$ as a semicircular region on the floor, centered at the target's position with a radius equal to the maximum reach of the robotic arm. At each sampling position $\mathbf{p} \in \mathcal{A}$ , we place the robot base and initialize the manipulator configuration, then align the end-effector orientation $\mathbf{R} \in \mathrm{SO}(3)$ with the surface normal of either the target object (for rigid objects) or its functional link (for articulated objects). Here, $\mathrm{SO}(3)$ denotes the Special Orthogonal Group, representing the set of all rotation matrices that describe rotations in three-dimensional space. + +For each configuration $(\mathbf{p},\mathbf{R})$ , we attempt a manipulation and record a binary affordance outcome $\nu_{p}\in 0,1$ at position $\mathbf{p}$ . Success is determined by the outcome of the manipulation attempt: for robots equipped with two-finger parallel grippers (e.g., Panda, Flexiv, and xArm6), success is defined by a successful grasp of the target object; for the robot employing a suction-based end-effector (e.g., UR5e), success is determined by a valid suction-and-move action. To associate these affordance values with the previously collected floor point cloud $\mathbf{P}_{\mathrm{floor}}$ , we first transform $\nu_{p}$ from the world coordinate system to the robot base frame. This transformation yields $\nu_{pb}$ through: + +$$ +v _ {p b} = \mathbf {T} _ {b c} \mathbf {T} _ {c w} v _ {p}, \tag {1} +$$ + +where $\mathbf{T}_{bc}$ and $\mathbf{T}_{cw} \in \mathbb{R}^{4 \times 4}$ are the transformations from the camera to the base and from the world to the camera, respectively. We then match each transformed affordance value $v_{pb}$ to its nearest neighbor in $\mathbf{P}_{\mathrm{floor}}$ . This association process can be formally expressed as: + +$$ +\mathbf {V} _ {\text {a f f}} \left(p _ {j}\right) = \left\{ \begin{array}{l l} v _ {p b} & \text {i f} \min _ {p \in \mathcal {A}} \| p - p _ {j} \| < \theta , \forall p _ {j} \in \mathbf {P} _ {\text {f l o o r}}, \\ 0 & \text {o t h e r w i s e}, \end{array} \right. \tag {2} +$$ + +where $\theta$ is a distance threshold. This yields sparse affordance values $\mathbf{V}_{\mathrm{aff}}\in \mathbb{R}^{n\times 1}$ . To produce dense and continuous floor-level affordance maps, we employ Gaussian interpolation with k-nearest neighbors. This process produces interpolated affordance values $\hat{\mathbf{V}}_{\mathrm{aff}} = \{\hat{v}_i\in [0,1]\mid i = 1,\dots ,n\}$ through the following formulation: + +$$ +\hat {v} _ {i} = \frac {\sum_ {j = 1} ^ {k} w _ {i j} v _ {j}}{\sum_ {j = 1} ^ {k} w _ {i j}} \tag {3} +$$ + +where the Gaussian weights $w_{ij}$ are computed as follows. + +$$ +w _ {i j} = \exp \left(- \frac {\| p _ {i} - p _ {j} \| ^ {2}}{2 \sigma^ {2}}\right), \quad \forall i, j \tag {4} +$$ + +![](images/712bb9764f51b77c0f4e2415842cfdba81151e183a9dd1ed61cece1a29a4df51.jpg) +Figure 3. (a) Robot arms used in MoMa-Kitchen. The end-effectors of the Panda, Flexiv, Elephant, Realman and xArm6 robots are grippers, while the end-effector of the UR5e is a suction cup. (b) Object categories utilized in MoMa-Kitchen. Each category consists of multiple object instances. Rigid and articulated objects serve as manipulation targets, while obstacle objects are strategically placed around the target to enhance scene complexity. (c) Examples of affordance maps in MoMa-Kitchen. Discrete affordance values are first collected (left) by moving the mobile manipulator and allowing it to interact with the target. Gaussian interpolation is then applied to obtain a smooth affordance map (right). + +![](images/d17d5ed9159776f92a10ee8814609d3006fc0e3b42072a322a06b2f329a12c4d.jpg) + +![](images/a9631b3c2c8a826a2c51a2430f7d6064e8bc69494b46d0cce197744bb6d31e03.jpg) + +Here, $\| p_i - p_j\|$ is the Euclidean distance between the interpolation target $p_i$ and the sparse point $p_j$ , $\sigma$ controls the width of the Gaussian kernel, and $s_j$ is the affordance value at $p_j$ . This weighting scheme ensures that points closer to $p_i$ have a larger influence, resulting in a smooth, continuous affordance map that captures the spatial distribution of potential manipulation outcomes. + +# 2.4. Generated Dataset Statistics + +As summarized in Table 1, MoMa-Kitchen spans 569 kitchen scenes, each with procedural variations in objects and obstacles. These configurations yield over $127\mathrm{k}$ episodes, each capturing an RGB-D view and the resulting affordance map. Six robot arms (Flexiv, Panda, UR5e, xArm6, Realman, Elephant) are deployed to ensure diverse reachability constraints and end-effector types. (see Fig. 3(a)) The dataset covers 137 kitchen-relevant assets (65 rigid, 48 articulated, and 24 obstacle types), providing a broad spectrum of layouts and manipulation targets. (see Fig. 3(b)) (Details in Supp.) During data collection, each configuration is labeled via discrete success/failure outcomes for different robot placements. These discrete labels are then interpolated to produce dense affordance maps (see Fig. 3(c)). Collectively, MoMa-Kitchen provides largescale supervision for end-to-end training of navigation-to-manipulation models that generalize across varying hardware and scene complexity. + +# 3. Baseline Model + +In this section, we introduce our baseline model, NavAff, which is designed for optimal manipulation positioning and + +Table 1. Dataset Split Statistics. + +
SplitScenesConfigurationsEpisodes
Train45611,408102,687
Test (Unseen Scenes)1132,74724,656
+ +obstacle interaction in complex mobile manipulation tasks. As shown in Fig. 4, Our baseline method consists of two main components: Visual Alignment Module (VAM) and Navigation Affordance Grounding Module (NAG). This two-part structure is designed to process visual and spatial information sequentially, facilitating effective affordance prediction for mobile manipulation tasks. + +# 3.1. Visual Alignment + +VAM extracts and projects features of target object $\mathbf{T}$ and obstacles $\{\mathbf{O}_1,\mathbf{O}_2,\dots ,\mathbf{O}_n\}$ onto the global point cloud $\mathbf{P}_{global}\in \mathbb{R}^{3\times N_{global}}$ to ensure accurate 3D representation of them. As illustrated in Fig. 4(a), VAM processes an image $\mathbf{I}\in \mathbb{R}^{3\times H\times W}$ captured by the robot's camera along with its corresponding depth $\mathbf{D}\in \mathbb{R}^{H\times W}$ , extracting target and obstacle masks using BestMan[66], where $H,W$ denotes the height and width of the camera observation. The global point cloud $\mathbf{P}_{global}$ is then generated via inverse projection. To enhance feature representation, we leverage PointNet++ [34], which supports additional feature channels in the point cloud input. Pixels from the target mask are projected into the 3D space to form a target channel, with values at target locations set to 1, while obstacle mask pixels create an obstacle channel, assigned related values of -1 [18]. This process enriches the global point cloud by + +![](images/81ed4e6f1b3a594a36ef1195cc8b8d784ce20f4b63437104982e67a02544ded5.jpg) +(a) Visual Align + +![](images/2d9f3208919b2a2ff9650c67502b9df6f373b39bc6c1b97cf62903ad5b4c0806.jpg) +(b) Navigation Affordance Gounding +Figure 4. NavAff Baseline. (a) Visual Alignment Module: Projects object masks to align 2D visual features with 3D spatial representations. (b) Navigation Affordance Grounding Module: Fuses global point cloud, floor point cloud, and robot-specific features to predict navigation affordance maps. + +embedding 2D visual cues (e.g., target and obstacle features) into the 3D spatial structure. The resulting feature-enhanced point cloud $\bar{\mathbf{P}}_{global}$ serves as input for the next stage, aligning visual perception with spatial information for improved downstream processing. + +# 3.2. Navigation Affordance Grounding + +NAG uses the robot's relevant information and the visually aligned global point cloud to interact with the reference floor, generating a robot-specific affordance prediction for optimal positioning. As illustrated in Fig. 4(b), NAG takes as input the feature-enhanced global point cloud $\bar{\mathbf{P}}_{global}$ from VAM, the floor point cloud $\mathbf{P}_{floor}$ , and the robot-related information $\mathbf{R}_I$ . To extract features from the point cloud data, PointNet++ processes $\bar{\mathbf{P}}_{global}$ and $\mathbf{P}_{floor}$ , yielding feature representations $\mathbf{F}_{pcg}$ and $\mathbf{F}_{pcf}$ , respectively. These features are then tokenized using a multi-layer perceptron (MLP) in preparation for multi-head cross-attention [48]: + +$$ +\bar {\mathbf {F}} _ {p c g} = \operatorname {T o k e n i z e r} \left(\mathbf {F} _ {p c g}\right), \tag {5} +$$ + +$$ +\bar {\mathbf {F}} _ {p c f} = \operatorname {T o k e n i z e r} \left(\mathbf {F} _ {p c f}\right), \tag {6} +$$ + +where $\bar{\mathbf{F}}_{pcg} \in \mathbb{R}^{n_{global} \times dim}$ and $\bar{\mathbf{F}}_{pf} \in \mathbb{R}^{n_{floor} \times dim}$ . + +For the mobile manipulator, $\mathbf{R}_I$ encodes the base platform height and the operational radius of the robotic arm. This information is also processed by an MLP to produce the robot-specific tokens $\mathbf{F}_r$ , which are then concatenated with $\bar{\mathbf{F}}_{pcg}$ , forming a combined key and value for crossattention fusion with $\bar{\mathbf{F}}_{pcf}$ . The process is defined as follows: + +$$ +\mathbf {F} _ {r} = \operatorname {T o k e n i z e r} (\mathrm {M L P} (\mathbf {R} _ {I})) \tag {7} +$$ + +$$ +\mathbf {F} _ {\text {o u t}} = \operatorname {M C A} \left(\bar {\mathbf {F}} _ {p c f} \mathbf {W} _ {q}, \left[ \bar {\mathbf {F}} _ {p c g}, \mathbf {F} _ {r} \right] \mathbf {W} _ {k}, \left[ \bar {\mathbf {F}} _ {p c g}, \mathbf {F} _ {r} \right] \mathbf {W} _ {v}\right) \tag {8} +$$ + +where $\mathbf{F}_r\in \mathbb{R}^{n_{robot}\times dim}$ , $\mathbf{F}_{out}\in \mathbb{R}^{n_{floor}\times dim}$ . Finally, $\mathbf{F}_{out}$ is passed through a decoder $f_{d}$ to predict the navigation affordance grounding $\mathbf{P}_{out}$ . + +# 3.3. Loss Function + +Following standard practices in affordance grounding, we utilize the mean squared error (MSE) loss as the primary objective function to align the model's predictions $\mathbf{P}_{out}$ with the ground truth affordance labels $\mathbf{P}_{label}$ . In our experiments, we observed that zero-valued elements constitute a large proportion of the ground truth floor affordance labels, leading to an imbalance between zero-valued elements and those with non-zero values. To address this issue, we apply a weighted mask to perform a weighted average on the MSE loss (Weighted MSE). The Weighted MSE loss is computed by adjusting the weight for zero-valued elements in the ground truth. Specifically, for elements in the ground truth that are zero, we apply a weight of $\lambda$ with a probability of 0.5, while other elements are assigned a weight of 1. This ensures the model places adequate emphasis on nonzero affordance areas. The formula for the Weighted MSE loss is as follows: + +$$ +\mathcal {L} _ {\text {W e i g h t M S E}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \mathbf {W} _ {i} \cdot \left(\mathbf {P} _ {\text {o u t}, i} - \mathbf {P} _ {\text {l a b e l}, i}\right) ^ {2} \tag {9} +$$ + +where + +$$ +\mathbf {W} _ {i} = \left\{ \begin{array}{l l} \lambda & \text {i f} \mathbf {P} _ {\text {l a b e l}, i} = 0 \text {a n d w i t h p r o b .} 0. 5 \\ 1 & \text {o t h e r w i s e .} \end{array} \right. \tag {10} +$$ + +Table 2. Main results. Quantitative evaluation of navigation affordance grounding performance of NavAff. + +
MethodRMSE ↓logMSE ↓PCC ↑SIM ↑
PointNet++ [34]0.1640.01420.5650.589
VoteNet [35]0.1670.01430.5430.570
H3DNet [76]0.1740.01560.5030.522
NavAff0.1470.01150.6800.696
+ +Here, $N$ represents the total number of elements, $\mathbf{W}_i$ is the weight applied to each element based on the corresponding floor ground truth, and $\lambda \in (0,1)$ is a hyperparameter that assigns a reduced weight to samples with a zero ground truth value, applied with a probability of 0.5. + +# 4. Experiments + +In this section, we benchmark NavAff on the MoMaKitchen. We introduce baseline results for NavAff, conduct a comprehensive performance analysis across both simulated and real-world environments, and identify emerging challenges in complex mobile manipulation scenarios that are uniquely highlighted through our benchmark. + +# 4.1. Experimental Settings + +Given that this is a newly proposed task, no existing methods provide a direct basis for comparison. To establish an evaluation, we adapt three well-established models from point cloud learning: PointNet++[34], VoteNet [35], and H3DNet [76]. Specifically, PointNet++ serves as a foundational backbone model widely used in point cloud processing tasks; VoteNet and H3DNet, both originally designed for 3D object detection, are suited for adaptation to navigation affordance grounding on our benchmark. By leveraging these models, we aim to establish strong baselines and gain insights into how existing point cloud techniques perform when applied to this new challenge. + +For evaluation, we employ standard and diversity metrics tailored for the MoMa-Kitchen benchmark. Each metric provides a distinct perspective on navigation affordance grounding performance: Root Mean Squared Error (RMSE), facilitating understanding the magnitude of prediction error; Logarithmic Mean Squared Error (logMSE) focuses more on relative differences rather than absolute differences; Pearson Correlation Coefficient (PCC) helping to gauge the model's ability to maintain consistent patterns with the ground truth data across various affordance regions; Cosine Similarity (SIM) compares the structural or shape similarity between predicted and ground truth. + +All the above experiments are trained on a single NVIDIA A100 GPU with a batch size of 64, using the Adam optimizer with a learning rate of 8e-4. Further experimental details are available in the Appendix. + +Table 3. Manipulation Success Rate (MSR). + +
MSRRandomH3DNetVoteNetPointNet++NavAff
Top10.0800.540.560.600.72
Top50.0460.470.530.580.66
+ +# 4.2. Quantitative Analysis + +# 4.2.1. Main Results + +Tab. 2 reports the metrics of the proposed method NavAff compared with other methods on the MoMa-Kitchen benchmark. The results highlight that NavAff achieves superior performance in navigation affordance grounding, outperforming transferred methods across all evaluated metrics. Specifically, NavAff achieves an RMSE of 0.147 and a logMSE of 0.0115, demonstrating a marked improvement in prediction accuracy compared to the second-best method, PointNet++. In terms of correlation and similarity measures, NavAff achieves the highest scores with a PCC of 0.680 and SIM of 0.696, highlighting its robustness in capturing affordance patterns even in cluttered environments. Notably, VoteNet and H3DNet fall short of NavAff's accuracy and consistency across the various metrics, showcasing the effectiveness of our approach. + +For further analysis, while VoteNet and H3DNet are effective in point cloud detection and proposal classification tasks, they are less suited to the fine-grained requirements of navigation affordance grounding, resulting in slightly lower performance. All methods are trained for the same number of epochs, but H3DNet converges more slowly due to its larger parameter count. Consequently, within the same training duration, H3DNet demonstrates the weakest performance. These findings suggest that a lightweight model capable of fine-grained feature prediction may achieve superior results on our MoMa-Kitchen benchmark. + +# 4.2.2. Manipulation Success Rate + +To more intuitively demonstrate the improvement of our method and benchmark its performance in mobile manipulation, we introduce the manipulation success rate (MSR) (See Tab. 3). The Top1 MSR refers to moving the robot to the location with the highest affordance score and recording the MSR in the test scenes. The Top5 MSR refers to recording the average MSR across the top 5 locations. + +As quantitatively shown in Tab. 3 using the MSR metric, our navigation affordance prediction paradigm shows significant practical advantages. A comparison between the "Random" baseline and other methods reveals that approaches trained on MoMa-Kitchen benchmark significantly outperform those relying on randomly sampled points within the robot's operational radius, thereby validating the effectiveness of our benchmark. Among all the trained methods, NavAff sets a new state-of-the-art performance, achieving an impressive Top1 MSR of $72\%$ + +![](images/450a51ef2572d28f43bcaee90a0a4eea2c6f3008adb077a8d6b75ed5d2593080.jpg) +GT + +![](images/d56e7771512e6b64352e53f9ad07345411df5bb58fddd5734e59b5d93cffb1c9.jpg) +H3dNet + +![](images/ed6f77b4b13be64ee1b863c466a928376f904ecb4d15df82b747296073454738.jpg) +VoteNet + +![](images/e8138a4cdd1a380941f6f9f3009878ec18e5f175013c149fcef8c53e8a1ff9f5.jpg) +PointNet++ + +![](images/420a851d8899d865c6346b612a72217dbfbef66b3bd2c1f946b9eb33ef4a3b45.jpg) +NavAff + +![](images/82965b59742132b912dd7be6120e276575b387e5ac4abafcada8044c9ba4e18f.jpg) + +![](images/78e3e47f43961d14d230f6a18bd7311b0e0baddf4435d03b55c21fadc7498da2.jpg) + +![](images/843d5a035ee98622a9069c4c269264cb22e74df274166904c1484bfaf55d303d.jpg) + +![](images/de6e5b490a882e6c04b972abe49aae6dc16761f9a6d2d366d9c363ff40c16638.jpg) + +![](images/84eb2fd1e08b581c5840fd508c992ca82ead17f515f5c032bfa150680af63de3.jpg) + +![](images/213787f4132f7657612aa0110d413cb03b04c526214156e4c15b306e4d6d662a.jpg) + +![](images/65af7a5f9372c859071421efd91d4c646b281d1798fb1c6ce6903cc501e592a5.jpg) + +![](images/56578ca3a50e2050991fb9728a6360c0d7ea1bcf658a6240e26373111c3d0a0a.jpg) + +![](images/d08ccc85190d47272b690964a08086ddd49d6f9596b9eba9409b8a7268de318e.jpg) + +![](images/76b15a3214f787bdfe24e63f99367b004f2c0d59fd7f077ff618fc46029a7625.jpg) + +![](images/b38a560dc7764db59b9226c8409aeee9c0377cd5a635ad153c3e4db83dbedade.jpg) +Figure 5. Qualitative comparison of navigation affordance between all methods and ground truth. Blue to red regions indicate affordance values ranging from 0 to 1, while void areas represent obstacle-occupied spaces. + +![](images/90a6e094e953133ea13f4521036cc661e41d7352ac11d713c4febd1136f36315.jpg) + +![](images/26cda744308067c5114e6b1efc43ec47888be21e21fbc44ed0530422f8df7804.jpg) + +![](images/061a2f3bfad708f44389e414e6cd00029dcc259cea65ddcedde9a9c0c200933f.jpg) + +![](images/2f9ec99af22234d9e4f19e9b6086fb6564ce33017a474930242bddde6c4663d0.jpg) + +and Top5 MSR of $66\%$ . Notably, when expanding the candidate point selection from Top1 to Top5, the model demonstrates strong generalization with minimal performance degradation, suggesting its robust adaptability to varying operational conditions. + +Additionally, by comparing the MSR values of all models, we observe a strong positive correlation between MSR and the accuracy of navigation affordance prediction (see Tab. 2 and Tab. 3), indicating that accurate navigation affordance prediction indeed contributes to higher manipulation success rates in mobile manipulation tasks. + +# 4.3. Qualitative Results + +We show the qualitative results of NavAff and compared methods for navigation affordance grounding in Fig. 5. As illustrated, our model successfully predicts floor-level affordance maps that closely align with the ground truth patterns. The visualization clearly reveals distinct void regions in both predicted and ground truth maps, which correspond to areas occupied by obstacles, effectively demonstrating our model's ability to recognize spatial constraints. Compared to other methods, NavAff exhibits a more accurate representation of these void regions, indicating its superior capability in handling complex spatial relationships and navigating cluttered environments. + +# 4.4. Ablation Study + +To understand the impact of each module in our proposed NavAff model, we conduct an ablation study on the MoMa-Kitchen benchmark. Tab. 4 shows the results of this study, where we assess the model variations by excluding robot information, the Visual Alignment Module (VAM), and the global point cloud. Below, we analyze the role and impact of each component in detail. + +Table 4. Ablation study results of NavAff. + +
RMSE ↓logMSE ↓PCC ↑SIM ↑
NavAff0.1470.01150.6800.696
w/o robot information0.1480.01150.6700.688
w/o VAM0.1650.01400.5620.589
w/o global point cloud0.1680.01440.5340.568
+ +- w/o robot information. Removing robot-specific parameters (e.g., base height and arm reach) leads to moderate performance degradation, particularly in RMSE and logMSE. The limited impact may be attributed to the simplified representation of robot information in NavAff, which only considers two parameters. For instance, only xArm6 has a unique base height, while other platforms share identical base configurations. +- $w / o$ VAM. Excluding the Visual Alignment Module significantly reduces performance, particularly in PCC and SIM metrics, underscoring the importance of integrating 2D visual cues for accurate navigation affordance prediction. This demonstrates that aligning visual data with spatial information is essential for accurate and robust navigation affordance grounding. +- $w/o$ global point cloud. Without the global point cloud, the model's performance drops across all metrics, with the largest degradation in PCC. This indicates that global spatial context is crucial for capturing the layout of objects and obstacles in the scene. + +# 4.5. Real World Application + +As shown in Fig. 6, we validate our method by conducting experiments in a real-world setting. A D435i camera is mounted on the head of a mobile manipulator to capture data. Using Grounded-Sam [39], we obtain open-vocabulary object masks, while Depth Anything v2 [68] + +![](images/d47be6dfd753336b852c281d5b080aacea5dc68a386f6021b007e1e91f2319c8.jpg) +Figure 6. Pipeline of real-world application with simulator trained NavAff. The D435i camera mounted on the mobile manipulator captures image, and our model predicts optimal navigation affordances on the floor based on this data. + +provided the depth images. We generate the global point cloud through back projection and segmented the object's local point cloud based on the mask. Then, we apply our model—trained on simulation data—to predict navigation affordances on the floor. + +The prediction results, shown in Fig. 6, demonstrate that our model performs well in real-world scenarios, validating the strong generalization capability of our benchmark. This success highlights the robustness of our method, which was specifically designed to minimize the visual gap between simulation and reality. By addressing this challenge, our model can effectively adapt to real-world settings, showing that our approach is not only effective in controlled environments but also highly reliable in real-world situations. + +# 5. Related Work + +Mobile Manipulation. Such tasks have been extensively studied by researchers in both simulated and real-world settings [14, 15, 32, 41, 42, 59, 60, 70]. More recently, approaches that integrate visual and linguistic information have emerged as promising methods for achieving unified reasoning in mobile manipulation [29, 37, 50, 69, 78]. However, most existing methods still lack the versatility required to seamlessly combine coarse and fine motions for both navigation and manipulation. Prior mobile manipulation approaches often assume obstacle-free or easily navigable environments. While interactive navigation techniques [62] attempt to tackle scenarios in which obstacles must be moved or manipulated—such as shifting boxes or pressing buttons—they typically rely solely on geometric reasoning [24, 43, 47, 53, 55, 72]. In contrast, our proposed benchmark is specifically designed to address these limitations. + +tions by integrating both semantic and geometric reasoning for optimal positioning and manipulation. This benchmark provides a robust and cohesive foundation for advancing mobile manipulation tasks in complex environments. + +Embodied Dataset. In recent years, large-scale embodied datasets have become essential for advancing both navigation and manipulation tasks in robotics. On navigation, several datasets have been proposed to tackle challenges in object-goal navigation [6, 21, 38, 61], rearrangement [4, 31, 57], vision-language navigation [3, 22, 23, 36], and question answering [9, 10, 58, 71, 75]. In contrast, manipulation-focused works leverage large-scale proprioceptive and visual data (e.g., RGB images or 3D point clouds) to simulate real-world dexterous hand operations [28, 30, 49, 54, 65], while other datasets provide object affordance labels to facilitate interaction learning [5, 8, 13, 16, 19, 44, 67, 73]. In parallel to simulation-based approaches, several real-world datasets have emerged to address the gap between simulated and physical environments. Like FastUMI [77] propose a scalable hardware-independent robotic manipulation data collection system. More recently, research has increasingly focused on integrating manipulation capabilities with navigation for everyday tasks. Recent frameworks like BEHAVIOR Robot Suite [20] enable whole-body manipulation with bimanual coordination in household environments, while AgiBot World Colosseo [1] offers over one million trajectories across 217 tasks. Moreover, some approaches use vision-language models or procedural methods to autonomously generate scalable language annotations in simulated environments [2, 11, 12, 17, 25–27, 45, 46, 51, 56, 74]. Despite these advances, navigation datasets often offer rich spatial information yet lack guidance for optimal positioning during subsequent manipulation, whereas manipulation datasets—despite providing valuable interaction data—do not fully capture the complexities of achieving optimal grasping positions via navigation. + +# 6. Conclusion + +Our work addresses the "last mile" challenge in mobile manipulation by introducing MoMa-Kitchen, the first large-scale dataset (127k+ episodes across 569 kitchen scenes) featuring comprehensive, high-quality ground truth affordance maps to guide optimal positioning for manipulation tasks. We resolve the navigation-manipulation disconnect through automated cross-platform data collection and a unified framework compatible with diverse robotic systems, ensuring generalizability. Experimental results demonstrate that our baseline model NavAff achieves robust affordance prediction, validating the approach's efficacy. This dataset and methodology not only advance integrated navigation-manipulation systems for real-world deployment. + +Acknowledgment. This work is supported by the Shanghai AI Laboratory, the National Natural Science Foundation of China (62376222), and Young Elite Scientists Sponsorship Program by CAST (2023QNRC001). + +# References + +[1] AgiBot-World-Contributors, Qingwen Bu, Jisong Cai, Li Chen, Xiuqi Cui, Yan Ding, Siyuan Feng, Shenyuan Gao, Xindong He, Xu Huang, Shu Jiang, Yuxin Jiang, Cheng Jing, Hongyang Li, Jialun Li, Chiming Liu, Yi Liu, Yuxiang Lu, Jianlan Luo, Ping Luo, Yao Mu, Yuehan Niu, Yixuan Pan, Jiangmiao Pang, Yu Qiao, Guanghui Ren, Cheng-Xing Ruan, Jiaqi Shan, Yongjian Shen, Chengshi Shi, Mi Shi, Modi Shi, Chonghao Sima, Jianheng Song, Huijie Wang, Wenhao Wang, Dafeng Wei, Chengen Xie, Guo-Liang Xu, Junchi Yan, Cunbiao Yang, Lei Yang, Shukai Yang, Maoqing Yao, Jia Zeng, Chi Zhang, Qingli Zhang, Bin Zhao, Chengyu Zhao, Jiaqi Zhao, and Jianchao Zhu. 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(A) Given the first time frame color and segmentation image and a text prompt, our model generates the future dynamic 3D scene. (B) 3D dynamic scenes as pixel-aligned curve/trajectory images, re-purposing an image diffusion model for 4D generation. + +![](images/d053450f8c482ddac19dbc691602cbec8de66cb21b002d2cc0d3eff8c92bae25.jpg) + +![](images/b06c166856723fff169902f2c0328d53d85eaa0768f87023004c9c7f45b91c62.jpg) +Time + +![](images/66007f2611bacaca0a035a327359c94a0b6386f03f6b875a79700c766e18840d.jpg) +(B) Representation: Motion Map + +![](images/2311a3a728ecf8ef3698dbc77c6f74b686edbc74aa60b23e40c7e34788f043d8.jpg) + +![](images/037c5ff98a6733eb26f018a1e5e6c9137bf4e2ab663057e4f145768d369e4341.jpg) +Time + +# Abstract + +This paper addresses the challenge of learning semantically and functionally meaningful 3D motion priors from real-world videos, in order to enable prediction of future 3D scene motion from a single input image. We propose a novel pixel-aligned Motion Map (MoMap) representation for 3D scene motion, which can be generated from existing generative image models to facilitate efficient and effective motion prediction. To learn meaningful distributions over motion, we create a large-scale database of MoMaps from over 50,000 real videos and train a diffusion model on these representations. Our motion generation not only synthesizes trajectories in 3D but also suggests a new pipeline for 2D video synthesis: first generate a MoMap, then warp an image accordingly and complete the warped point-based renderings. Experimental results demonstrate that our approach generates plausible and semantically consistent 3D scene motion. + +# 1. Introduction + +Motion is ubiquitous in the visual world. Understanding, reconstructing, forecasting, and interrogating how objects and entities move in 3D is an important task for computer vision and is critical for applications that involve interaction with physical environments such as augmented reality, autonomous driving, or robotics. Of special interest to us is motion forecasting, prediction, and generation, as required by an agent operating in a 3D environment. Despite its importance, there is a lack of approaches that learn 3D generative motion priors at scale. Existing methods either treat dynamic scene priors as a 2D video generation problem, focus on localized object-centric priors from large-scale object databases, or handle only very short 3D trajectories in constrained, small-scale setups. + +In this work, we aim to learn semantically and functionally meaningful 3D motion priors from real-world videos at scale, and to use these priors for semantics-aware 3D motion generation. Recent generative motion methods either consider 2D motions (e.g., TAPIR [10]) or treat 3D trajectories as sets of very short curves, using PointNet or Transformer architectures over them (e.g., GeneralFlow [41], Track2Act [4]). In contrast, we represent motion in a video through a set of pixel-aligned 3D motion snippets we call Motion Maps, or MoMaps for short (Fig. 2-A). Each MoMap is a motion snapshot—a view of the evolving scene from a fixed camera over a time interval (typically about 50 frames at 3 FPS). The pixels of each MoMap frame encode (in RGB channels) the XYZ 3D locations of points seen by that camera in the fixed reference camera coordinate system, and the entire MoMap records their spatial evolution during the time interval captured by the MoMap. + +MoMaps facilitate motion learning in two ways. First, they disentangle camera motion from object motion, reducing the dimensionality of the problem (only dynamic foreground changes over time). Second, their image-like structure allows us to build upon diffusion-based image generative models, such as Stable Diffusion [30, 32], that have been trained on vast amounts of data—effectively repurposing them from the task of dense photometric generation to that of dense position and motion prediction, considering the full context (both foreground and background) of the scene. Such repurposing has been used, for example, in depth prediction by the Marigold method [18]. Additionally, pixel-aligned motion images can directly bind with powerful 2D segmentation masks such as SAM [19, 31], enabling us to exploit semantic and instance information when predicting motion, as motion and semantics are often strongly correlated. + +Prior motion prediction methods typically rely on syn + +thetic data (e.g., Kubric [13]) for training, where the motions involved do not capture the richness of the physical world. In contrast, our goal is to learn semantically meaningful real-world motions. Leveraging recent advances in point tracking and 4D reconstruction, our work presents a large dataset of 3D motions extracted from real-world videos and represented as MoMaps. Towards this goal, we developed a full-stack data pipeline based on video depth models [7, 16, 36], 3D point tracking [28, 38], video object segmentation [8, 31] and the MoSca 4D reconstruction system [22] to generate 3D tracks and semantic maps for more than 50K real videos taken from the HOI4D [25] (egocentric) and BRIDGE [35] (robotics) datasets. + +Learning a 3D motion prior from large-scale real videos and building a generative model to predict future 3D trajectories from a single initial frame has proven valuable for various tasks, including robotics [41] and video model prompting [12]. As the first work to explore dense 3D trajectory generation, we showcase another novel downstream application: 2D video frame synthesis. Once a MoMap is generated, we can render the dense 3D trajectories frame by frame into target cameras, resulting in a partial video. A lightweight image diffusion model with flattencross-attention can then complete these partially warped 2D frames, directly synthesizing 2D RGB and semantic videos. This pipeline highlights a new direction for video generation that explicitly embeds dynamic 3D bias and 3D motion consistency into the video formation process. Because MoMap retains an image-like structure, most techniques that operate with 2D image diffusion models can be adapted to MoMaps, offering increased flexibility and opening up a broad range of future enhancements for 3D motion generation, for example, more fine-grained motion generation control through vision-language models. + +In summary, our key contributions are: (1) A general framework for representing 3D motion in dynamic scenes that can be used for encoding real videos as well as generating plausible future motions conditioned by scene view semantics and language. (2) An image-like representation of motions, MoMaps, that disentangles camera and object motions and allows the use of large pre-trained image diffusion models for motion prediction. (3) A large database of MoMaps derived from open-source datasets. (4) An application of MoMaps to a new paradigm for generating future video frames from an image by first generating MoMaps and then completing renderings of warped point clouds. + +# 2. Related Work + +Motion Generation in 2D and 3D The closest related work to ours typically focuses on predicting 2D or 3D point trajectories, often within robotics settings [3, 29, 37, 39, 41]: TAPIR [10] uses a U-Net and Fourier encodings of 2D tracks to predict future 2D trajectories from large-scale + +real videos. *GeneralFlow* [41] adopts a PointNeXT geometric backbone to process a point cloud from the first video frame, and employs a trajectory-conditioned VAE to predict future 3D trajectories for queried object points. *Im2Flow2Act* [39] leverages Animatediff [15] to predict 2D tracks and visibilities obtained from TAPIR [10], focusing on object manipulation tasks. *Track2Act* [3] uses a transformer-based diffusion model over sets of 2D object tracks; it generates these tracks from the first frame and then estimates a rigid SE(3) transformation to manipulate the object. Similarly, ATM [37] learns policies on top of a comparable transformer-based diffusion model for 2D track generation. In a concurrent effort, ARM4R [29] pre-trains a causal transformer to predict future 3D tracks (at a coarser resolution in an egocentric coordinate system) on EPIC-Kitchens, later fine-tuning on robot joint trajectories for policy learning. Zhang et al. [43] address action-conditioned 3D future prediction for specific non-rigid objects reconstructed from visual data. In contrast to these works, our model focuses on long-term, dense, and camera-disentangled 3D motion generation. It also exploits priors from pre-trained image diffusion models, extending beyond the robotics domain and offering a more general-purpose solution. + +Video Generation The field of video generation has advanced rapidly with models such as SORA [26], Veo [33], CogVideo [40], and COSMOS [1], etc., which primarily capture priors over pixel sequences across multiple frames. Their approaches often rely on diffusion-based methods applied to stacks of frames [6, 11, 23, 27] or autoregressive models that predict future frames [9, 21, 24]. Some works [20, 34] first generate future 2D video frames and then extract 3D motion for downstream tasks such as object manipulation. However, in all these methods, motion priors are implicitly learned through pixel-level color changes rather than explicit 3D trajectories. By contrast, our approach learns a prior directly on dense 3D tracks, which reside on a simpler and smoother manifold compared to pixel-space motion representations. Additionally, recent works [5, 12, 14] demonstrate that 3D tracks reconstructed from reference videos or obtained via user prompts can improve controllability in video generation. Yet these methods still rely on reconstructing 3D motion from existing sequences, whereas we focus on generating new 3D motions outright. + +4D Reconstruction Reconstructing real-world, semantically meaningful 3D motion from video is a key step in learning 3D motion priors. Modern vision foundation models such as video depth estimators [7, 16, 36], 2D/3D point trackers [10, 17, 28, 38], and the induced 4D reconstruction systems [2, 22, 36, 42] play a crucial role in this pro + +![](images/1b50fc9da83a224702ae56c5cf963caa35c51fd2da5e45001ffe349d81d39a64.jpg) +(A) Represent Dynamic 3D Scene with Motion Maps +Figure 2. Motion Maps: (A) Dynamic 3D scenes can be represented as one or more Motion Maps - curve/trajectory images. (B) We develop a full-stack data pipeline to recover a large dataset of MoMaps from many real videos. + +![](images/2b9bf48219b5fefc0b34f47cc964beeadc0099554f3eb7af1cfb6ebc37c9057e.jpg) +Data Pipeline + +![](images/da58929793e3da46dbef8cbedf70f12c10e197bf7cbfaf210966715fc72b26a6.jpg) + +![](images/6e54a2233b7767f83e250f6b631cec1b541210f8125b5a9f7158fa71b10750b5.jpg) + +![](images/75785431a6e790d2f38b96c96fab408e3ef6cb611a94d6539780edb3f4ea0cb3.jpg) +(B) Build Motion Maps Database from Real Videos + +![](images/66e02de98a2888fade3d3d3f53560a54be88d51497b8872fc818bec9455a5f08.jpg) + +![](images/157736ac3ebb06427b9d1a6f089d3328a72dc3224b28c861426f39ff06db1f50.jpg) + +![](images/596228f43914b65d30da645b6e5a1cbe2e0e8329fc74f831827780575bac6661.jpg) + +![](images/2e8ff6dbba8a36cb5197b83654ab2c3853ee67a9996c2a9643be0a13dea46609.jpg) + +![](images/a016259365b05194dc8ef822df3f2ee031ef8a8ef828610027e092820f85b515.jpg) +HO14D (3K) Egocentric Videos + +![](images/65ecf6fbd08efaadb7426bf3cf4c93e1e56d5a3320c2a856a7ff70c6e9124030.jpg) +BRIDGE (60K) Robot Videos + +cess. They enable camera pose estimation, geometry reconstruction, and the establishment of dense 3D correspondences, which collectively encode the 3D motion present in a scene. These recent advances in 4D reconstruction serve as the foundation for constructing large-scale databases, facilitating the learning of predictive and generative motion priors. + +# 3. Method + +# 3.1. Motion Map Representation + +The first challenge is to represent real-world dynamic 3D scenes in a way that neural networks can easily output or predict. It is crucial to capture motion in 3D space rather than in 2D. Most prior methods model motion as 2D tracks—either for reconstruction tasks (e.g., BootsTAPIR) or for generating 2D tracks (e.g., TAPIR [10], ATM [37], and Track2Act [3]). However, 2D tracks require the model to handle complexities like occlusion. Therefore, we aim to represent the dynamic scene directly as 3D trajectories. A prior method, General-Flow [41], attempts to model individual 3D trajectories as a set of polylines, using a PointNet-like structure to build a VAE that generates short-term 3D trajectories. However, this unstructured set representation cannot handle dense predictions for every pixel and has limited network capacity. Inspired by recent work repurposing image diffusion models for depth prediction (e.g., Marigold), we propose a novel scene representation, called Motion Maps, that is pixel-aligned and can be produced by a repurposed image diffusion model. As shown in Fig. 2(A), a Motion Map (MoMap) is an image of 3D trajectories/curves, or intuitively, is a list of XYZ position maps aligned onto the single-view reference image. Given a reference time (e.g., $t = 1$ ), we store the 3D trajectory of each pixel observed at this reference time in the corresponding pixel location. All 3D locations are defined with respect to the fixed reference frame at this time, which separates the egocentric (camera) motion from scene object motion. Other ways to see it are that MoMap forms a "3D trajectory image" of all pixels anchored at the reference time; or that + +MoMap is an XYZ recoloring across time of the same reference XYZ point map. The MoMap representation offers several advantages: + +- Pixel-aligned: MoMap shares the same underlying structure as a standard image, making it straightforward to generate using large 2D models and allowing us to leverage pretrained image priors. +- Dense: Unlike a set of sparse trajectories, MoMap is dense and stores information for every pixel at the reference time, thus capturing both background and foreground elements critical for understanding motion. +- Smooth and Compressible: Because MoMap stores 3D trajectories, which are often smooth and low-rank, it can be further compressed into compact latent maps. +- Camera Motion Disentanglement: By "freezing" the reference frame, MoMap isolates only the meaningful (foreground) motion, removing the camera's egocentric motion. + +Note that one MoMap only captures the content of pixels observed at the reference time, a more complete dynamic 3D scene can be represented by the union of multiple MoMaps anchored at different reference frames with camera poses. This paper only studies the generation of one MoMap and leaves the complete multi-MoMap joint generation as future work (Sec. 5). + +# 3.2. MoMap Database from Real Videos + +A non-trivial question arises: where do we learn meaningful motion priors? Many previous works rely on synthetic data (e.g., Kubric and PointOdyssey) to train 2D/3D tracking models that reconstruct trajectories from real observations, or they use manually/semi-automatically labeled small datasets (e.g., General-Flow) to generate short 3D trajectories. However, synthetic data often contains random, semantically/functionally meaningless motion that is only suitable for low-level vision tasks such as tracking or flow, while manual or semi-automatic labeling does not scale well to large video datasets. Instead, we leverage recent advances in 4D reconstruction (MoSca [22]) to reconstruct many real-world 4D scenes, and then convert them into our + +![](images/b890ad18ebbfe4920e77e8f7b1444b67a3208f7fab2d0bf26d8d80ba7640a7ec.jpg) +(B) MoMap Latent Diffusion +Figure 3. Method Overview: (A) A MoMap can be compressed to compact latent via initializing and finetuning a Stable-Diffusion VAE. (B) Given a starting frame and language condition, MoMap can be generated by finetuning the SD UNet. + +MoMap representation. + +Specifically, as shown in Fig. 2(B), the data preparation stage processes all frames of a raw 2D real video with several steps: + +1. We first apply an off-the-shelf video depth model, DepthCrafter, to infer the depth of each frame. +2. We then query a 3D tracker (SpaTracker) densely on every pixel of a target reference time frame (randomly sampled for each video) to build the corresponding MoMap. +3. For videos captured by a moving camera, we run a tracklet-based bundle adjustment to solve for camera poses. +4. Because no current 3D tracker can reliably predict 3D locations under occlusions, we must run an optimization procedure to address occluded intervals in each 3D trajectory. We adapt the geometric optimization stage from MoSca [22] to optimize the dense foreground 3D trajectories. +5. Finally, we fill in the MoMaps at the reference time using these optimized dense 3D trajectories. +6. In addition to this geometric reconstruction process, we also apply a VOS model (DEVA [8]) for dense instance-level video object segmentation, allowing us to incorporate semantic information into the later 3D motion generation. + +We applied this data processing pipeline to 3K HOI4D [25] videos (human-object, egocentric camera) and 60K BRIDGE [35] videos (robotics, static camera) as shown in Fig. 2(B). + +# 3.3. MoMap Generation + +# 3.3.1. Task Definition + +Given a large database of MoMaps, we aim to learn a prior for 3D motions. As shown in Fig. 1(A), the task is as follows: given a single RGB image (the first frame) and optionally a text prompt, the model should generate the 3D dense motion of every pixel in that frame, from the input time step into the future time steps. + +We also aim to leverage semantic information from instance segmentation, since points belonging to the same instance typically share a similar motion pattern. Additionally, we assume access to a reliable monocular depth model so that the system does not need to learn 2D-to-3D lifting from scratch. Consequently, the first-frame RGB image can be augmented with an instance segmentation map and an XYZ map derived from the monocular depth model. + +# 3.3.2. MoMap Compression + +Thanks to the pixel-aligned property of the MoMap representation, our approach is to exploit existing 2D image diffusion models (e.g., StableDiffusion) to generate MoMaps. However, these image models generally operate on inputs and outputs of shape $H \times W \times 3$ , while MoMaps have shape $H \times W \times T \times 3$ , where $T$ is the number of frames. Notably, $T$ is typically large (e.g., 50 or 60) in our setting, as we want to generate semantically and functionally meaningful long-term 3D motions. The key question, therefore, is how to adapt these powerful 2D diffusion models to generate MoMaps. We found that it is necessary to encode the $H \times W \times 3$ MoMaps into compact latent feature maps of shape $H_{L} \times W_{L} \times C_{L}$ . The underlying insight is that + +real-world motion is often smooth and low-rank, making it compressible in both space and time. Concretely, we set $H_{L} = H / 8$ and $W_{L} = W / 8$ for the spatial dimensions, and compress the temporal dimension $T = 50$ (times the 3 spatial channels) into $C_L = 32$ channels. As illustrated in Fig. 3, we increase the input, output, and latent dimensions of the 2D VAE. By carefully initializing the network at the input, intermediate, and output layers, we can effectively transfer weights from a pre-trained VAE, and then finetune with MoMap data. This design allows the architecture to function similarly to the standard 3-channel RGB (as averaging across time of XYZs), leveraging the pre-trained knowledge acquired from large-scale image datasets. + +# 3.3.3. MoMap Diffusion + +We exploit the pixel-aligned nature of MoMap by repurposing a large pre-trained image generation model (e.g., Stable Diffusion) to generate these "trajectory images". Once the MoMap compression networks are trained, we can convert the ground-truth MoMap into a compact latent representation and use the U-Net to perform generation. Concretely, as shown in Fig. 3(B), we modify the input and output layers of a pre-trained U-Net from Stable Diffusion while initializing the remaining layers with weights from SD. The input conditions—the first-frame RGB image, the instance segmentation image (encoded as random RGB colors per patch), and the first-frame XYZ map—are all encoded by 2D VAE encoders into low-resolution latents, which are concatenated with noise and fed into the U-Net. Language prompts are incorporated in exactly the same manner as in standard Stable Diffusion. Note that such a lightweight (equivalent to one single image generation) diffusion process can efficiently generate long ( $T = 50$ ) frames in a single sampling process, exploiting the pixel aligned nature of the MoMap representation. + +# 3.4. Application + +# 3.4.1. Video Synthesis + +MoMap captures the future 3D motion of every pixel, which is inherently related to predicting future 2D video frames (commonly approached as a video generation problem). We further explore how to transform the 3D MoMap into a complete 2D video, as illustrated in Fig. 4(A). Given a generated MoMap and target camera intrinsics and extrinsics, we render the MoMap using 3D Gaussian Splatting to obtain a partial 2D RGB and semantic video (top row). This rendering is partial because a single MoMap contains only the pixels visible in the first frame, resulting in holes (shown in black). We then finetune another Stable Diffusion single-image model to complete these partial videos using a simple cross-view flattening attention module (similar to CAT3D), ultimately reconstructing the full video (bottom row). + +At a high level, this approach explicitly embeds a dy + +![](images/1f98b7851e8641635bb970f1872831a49e2c1ca4a1746ec3a4c046f77d46b54d.jpg) + +![](images/44cc4b4fc65b46013c176edc59451a32450afcb780a4e45cf4a79c90561052e3.jpg) +Figure 4. Application: (A) 2D video generation via render MoMap and then complete; (B-1) motion DSL representation. (B-2) Infer motion DSL with VLM for finer generation control. + +namic 3D inductive bias into video generation. Unlike most video models, which focus on memorizing pixel-level color changes and tend to be computationally heavy, we directly learn how objects move in 3D and form the images using a dedicated renderer (Gaussian Splatting). A separate diffusion model subsequently corrects artifacts and fills in missing regions. As a result, the video generation is handled by two relatively lightweight image models. + +# 3.4.2. VLM Control + +Real-world motion often spans long time periods, making effective conditioning challenging. Relying solely on global text conditions (as in Stable Diffusion) may be insufficient and would require highly accurate text annotations in the dataset (Fig. 6-B). Consequently, there is a need for alternative or augmented conditioning strategies to achieve robust and contextually aligned control over motion generation. We propose leveraging Vision-Language Models (VLMs), which possess strong semantic understanding and commonsense reasoning. To connect high-level VLM outputs with low-level MoMap diffusion, we introduce a domain-specific language (DSL), illustrated in Fig. 4-(B-1). The centroid of each semantic patch is quantized into nine directional flags (e.g., "left", "right", "stay") and converted into a structured language format (e.g., JSON) for each patch. Alternatively, these patch-level directional flags can be grounded + +at the pixel level, forming 2D conditions. Thus, this DSL seamlessly combines both a structured language format and pixel-grounded information. + +Rather than inserting text prompts directly into the MoMap diffusion network, we remove the text condition and instead rely on pixel-based DSL (2D pixel conditions) to guide generation. During inference, we let a VLM (e.g., Gemini) generate the DSL from the input's first frame as well as the global text prompt via in-context learning, using a few ground-truth examples from the training videos (Fig. 4-B-2). In this setup, VLM's strong reasoning and language capabilities allow it to interpret flexible prompts—even those substantially different from the training dataset—and determine what moves and how. The DSL it produces is then converted into pixel-form conditions for the diffusion model's U-Net (trained without global text conditioning) as an input condition, enabling fine-grained, semantically informed control over 3D motion generation. + +# 4. Experiment + +# 4.1. Baselines Comparison + +We compare our 3D motion generation approach with several baselines that also generate 3D trajectories. The closest related work is GeneralFlow [41], which produces short 3D trajectories (typically $T = 4$ frames) from an input-colored point cloud. We train three variants of the G-Flow-large model on our BRIDGE robot dataset: + +- GFlow-Original: Uses the same configuration as the original GeneralFlow [41] but extends the trajectory prediction length from 4 to 50. +- GFlow-Rollout: Keeps the original configuration without changing the prediction length. To achieve $T = 50$ , it performs iterative "roll-outs" by taking the last generated frame as the new first-frame input for each subsequent generation round. +- GFlow-Extend: An upgraded version of GeneralFlow that increases the querying chunk size from 128 to 20,000 and the scene point cloud samples from 4,096 to 10,000. The network also takes semantic colors as additional point features. Furthermore, the trajectory VAE latent dimension is increased from 16 to 32, and more layers are added to boost overall capacity. + +We also built another baseline, MoMap-VAE, which uses the same overall architecture but omits the diffusion U-Net in the middle. Instead, it is trained as a conditional VAE that directly generates the MoMap. + +Generating a long motion (T=50) from a single starting frame is highly ill-posed, so the most direct and arguably maybe the most accurate way to assess performance is via side-by-side qualitative comparisons of the generated 3D motions as in Fig. 5. From the comparisons, we observe: GFlow-Original: Tends to produce diverging trajectories in long-term predictions. Objects often lose their + +original rigid shape at later time steps. GFlow-Rollout: Performs poorly in this setting because it can only generate very short time spans (T=4) and must roll out repeatedly to reach T=50. This causes even more severe divergence over time. GFlow-Extend: Benefiting from a larger query chunk size and more network capacity, it generates smoother and more consistent motion. However, due to limited semantic and contextual understanding of Point-NeXT, it misidentifies which objects should move. For instance, in the second-to-last row, it moves two blocks when only one should be moving. MoMap-VAE vs. Ours (MoMap Diffusion): While MoMap-VAE can produce reasonable long-term motions, our diffusion-based approach generates more natural-looking hand and object motions, reflecting a richer learned prior over realistic 3D trajectories. + +# 4.2. Metrics and Quantitative Comparison + +Evaluating the generated results quantitatively is challenging because the problem is highly ill-posed and many plausible generations can be consistent with the provided initial conditions. For each starting frame, there is only one ground-truth observed trajectory, but many plausible solutions exist. We follow the previous work (GeneralFlow [41]) which generates $\mathrm{N} = 10$ samples per input, but computing the metric by comparing the closest of the generated samples with the ground truth. Beside detailed reconstruction errors, we introduce several additional coarse metrics that capture various aspects of the motion: + +1. Foreground Mask IoU (fg_mask_iou ↑): Measures whether the generated motion correctly identifies the moving regions. A “moving mas” is constructed by identifying pixels with significant 3D trajectory displacement. The Intersection over Union (IoU) between the ground truth and generated moving masks is then computed. +2. Foreground Absolute Trajectory Error under Dynamic Time Warping (ate_dtw $\downarrow$ ): Computing ATE (reported in GeneralFlow) after optimizing temporal alignment with Dynamic-Time-Warping (DTW), capturing scenarios where the timing of motions differs but the overall trajectory is correct. +3. Foreground Curve Distance-Matrix Signature Error $(\mathbf{D\_sig}^{\downarrow})$ : Creates a translation and rotation-invariant signature by computing a T x T distance matrix between positions at any two-time steps. The difference between ground truth and generated matrices measures SE(3) invariant curve similarity. +4. Foreground Local Distance Difference (local_dist_diff $\downarrow$ ): Evaluates the preservation of local structure by computing distances between K-nearest neighbors in the ground truth and generated 3D trajectories. Measures whether the generated motion preserves local rigidity and avoids collapsing into noise. + +![](images/0af99c67e593ecfd1ab4e0c2c7d20ade49e7ffb76136c8de49ed2356eb41ba65.jpg) + +![](images/7dd23ba9924e0dff72757e32f83d7cfb715f5396f87ba15facf830211a9587e2.jpg) +Figure 5. Qualitative Results: (A) comparison with baselines. (B) More generation results. (C) Diverse generations from the same condition with different random seeds. + +5. Foreground Patches Nearest Patch Accuracy (cross.patchnearest_acc↓) tracks which patch is closest (centroid-wise) to each moving foreground patch at each time step. Accuracy measures whether the generated motion maintains the same nearest-patch relationships as the ground truth. +6. Foreground dT Quantized Direction Accuracy (quantize_acc_dT↑): Coarsely evaluates motion direction by quantizing a 3D trajectory over a delta time interval (dT) into 9 directions (left-stay-right, forward-stay-backward, up-stay-down). Measures the accuracy between ground truth and generated motion directions for each pixel in the foreground mask. + +These metrics capture a variety of aspects, ranging from fine-grained reconstruction errors to coarse object-level motion directions and proximities, enabling a more comprehensive evaluation of 3D trajectories. The metrics of Ours and the baselines on a small testset are reported in Tab. 1. + +We observe that our method outperforms the baselines in most metrics, especially in quantized directional accu + +racy and the D_sig_fg $\downarrow$ metric. From both qualitative and quantitative findings, we note that our generated trajectories exhibit stronger semantic coherence and greater internal consistency, particularly in capturing aggregate motion. In contrast, GFlow appears to have lower noise in individual point trajectories (reflected by higher reconstruction metrics) but exhibits inconsistent noise across adjacent points belonging to the same object, leading to visually detectable "object breakdowns." + +# 4.3. Application + +Video synthesis. We present our video synthesis results in Fig.6-A, following the approach in Sec.3.4.1, showing that our lightweight model achieves decent performance. + +VLM control. In Fig.6-B, we showcase VLM-controlled generation, described in Sec.3.4.2. Notably, the VLM-controlled approach produces more accurate motion than relying solely on a global text condition, which can fail in certain scenarios. + +
DatasetBRIDGEHOI4D
Metric\MethodGFlow-Ori.GFlow-Roll.GFlow-Ext.MoMap VAEOursGFlow-Ori.GFlow-Roll.GFlow-Ext.MoMap VAEOurs
fg_mask_iou↑0.80440.56590.75970.82710.81280.06670.00000.06670.34000.4492
ate_dtw↓0.07470.11640.08120.07510.06891.61190.12410.72810.12650.1112
D_sig↓0.05360.08730.05910.05380.04631.38880.11930.29220.10300.0886
local_dist_diff↓0.01240.01540.00730.00730.00580.01540.00860.00920.00940.0092
patchnearest_acc↑0.83870.76490.82440.83980.86910.69260.76310.75540.74950.7923
quantize_acc_1↑0.67580.62710.66230.68560.72120.21160.60140.32790.60150.6157
quantize_acc_4↑0.58900.47020.55680.61480.65540.36530.27100.36560.30000.4278
quantize_acc_16↑0.72940.45030.70490.72930.77520.43190.13470.40680.39800.4610
+ +![](images/8c5593ce17be645d6046c2055ed9cc40dfc8639fc87ceb0ffa2db98ac47f219c.jpg) + +![](images/9d941d0133eca3ea1a6d161b85ff247d329debeadb361d4366385c18e61db47d.jpg) +Figure 6. Application Results: (A) 2D video generation results. (B) VLM finer control can generate reasonable results even when global text condition fails. + +# 4.4. Ablation Study + +We validate the design of our MoMap diffusion by ablating various components in its architecture: (1) remove the input XYZ condition; (2) remove the input semantic image condition; (3) remove the VAE compression of the MoMaps and let the UNet work on the original MoMap space instead of the latent space; (4) train the diffusion from scratch without initialization from stable-diffusion pre-trained weights; and (5) train both the MoMap VAE and UNet from scratch. Tab. 2 presents the results of these ablation experiments, illustrating that our full model achieves the best performance. + +Table 1. Quantitative comparison on BRIDGE and HOI4D testset. + +
Metric\AblationFullno xyzno semno vaeno unet initno unet&vae init
fg_mask_iou↑0.81280.79620.80790.13050.79740.7450
ate_dtw↓0.06890.07380.06890.17590.07920.0992
D_sig↓0.04630.04840.04680.10820.05200.0579
local_dist_diff↓0.00580.00600.00560.13480.00550.0094
patchnearest_acc↑0.86910.86050.86590.75330.85100.8306
quantize_acc_1↑0.72120.71420.71870.19400.70850.6566
quantize_acc_4↑0.65540.64150.65220.39770.62600.5925
quantize_acc_16↑0.77520.75890.77190.53110.74340.7267
+ +Table 2. Ablation comparison on BRIDGE dataset. + +# 5. Limitations and Conclusion + +In this paper, we explored a new problem: learning to generate future 3D motion for an entire scene using large-scale real-world videos. We introduced an image-like MoMap representation, which enables the repurposing of established 2D image diffusion models for 3D motion generation. By assembling a large database of MoMaps from real videos, we demonstrated the feasibility of synthesizing semantically and functionally meaningful 3D scene motion, also highlighting its potential impact on 2D video synthesis. + +Despite these promising results, our work represents an initial step in the realm of dense 3D motion generation at scale, and several challenges and directions remain: + +1. Multiview MoMap joint generation. This paper primarily focuses on generating a single MoMap anchored at the first frame, which only partially captures the scene. A key future direction lies in jointly and consistently generating multiple MoMaps anchored at different frames or viewpoints to aggregate a more complete scene. +2. Enhanced motion control and VLMs. Currently, the language prompts are integrated similarly to Stable Diffusion, providing limited motion control. Achieving more fine-grained and semantically meaningful motion control using advanced vision-language models is a promising area of future research. +3. Scaling to larger and more diverse data. Our current datasets, though sizable, are domain-specific (e.g., handobject or robotics). Extending these techniques to largescale, general-purpose videos presents an important avenue for broader impact. + +# References + +[1] Niket Agarwal, Arslan Ali, Maciej Bala, Yogesh Balaji, Erik Barker, Tiffany Cai, Prithvijit Chattopadhyay, Yongxin Chen, Yin Cui, Yifan Ding, et al. 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M. Snoek, $^{1}$ Yuki M Asano $^{3}$ VIS Lab, UvA $^{2}$ Valeo.ai $^{3}$ Fundamental AI Lab, UTN + +# Abstract + +Dense self-supervised learning has shown great promise for learning pixel- and patch-level representations, but extending it to videos remains challenging due to the complexity of motion dynamics. Existing approaches struggle as they rely on static augmentations that fail under object deformations, occlusions, and camera movement, leading to inconsistent feature learning over time. We propose a motion-guided self-supervised learning framework that clusters dense point tracks to learn spatiotemporally consistent representations. By leveraging an off-the-shelf point tracker, we extract long-range motion trajectories and optimize feature clustering through a momentum-encoder-based optimal transport mechanism. To ensure temporal coherence, we propagate cluster assignments along tracked points, enforcing feature consistency across views despite viewpoint changes. Integrating motion as an implicit supervisory signal, our method learns representations that generalize across frames, improving robustness in dynamic scenes and challenging occlusion scenarios. By initializing from strong image-pretrained models and leveraging video data for training, we improve state-of-the-art by $1\%$ to $6\%$ on six image and video datasets and four evaluation benchmarks. The implementation is publicly available at our GitHub repository: github.com/SMSD75/MoSic + +# 1. Introduction + +Dense self-supervised learning has emerged as a powerful paradigm for learning rich pixel- and patch-level representations without reliance on labeled data [24, 59, 71]. While significant progress has been made in the image domain, leveraging videos for self-supervised learning presents an even greater opportunity. Videos not only provide vast amounts of readily available data but also introduce a natural temporal dimension, which could be crucial for learning representations that extend beyond static imagery. However, directly applying image-based self-supervised learning techniques to + +![](images/b7ff07cec9da1b4aaaac5b95e86f530eb9804afe63aeb14c6af3e2ccc041263a.jpg) +Figure 1. We introduce MoSiC, a self-supervised framework that uses optimal transport (OT) to enforce spatio-temporal consistency in dense visual representations. By tracking points across frames and clustering their motion trajectories, MoSiC encourages features of points that move together to be temporally coherent. + +videos proves ineffective [4, 57]. In images, correspondences are often implicitly encoded by data augmentations—for instance, color transformations preserve pixel-wise associations. In contrast, videos exhibit complex motion patterns caused by object movement, camera shifts, and dynamic backgrounds, breaking such pixel-level correspondences. + +In this work, we aim to learn temporally coherent dense representations by leveraging motion as an implicit supervisory signal. Rather than treating frames independently, we enforce feature consistency over time by clustering points that move together. This encourages representations that are not only spatially meaningful but also temporally stable, improving robustness to occlusions and viewpoint changes. Prior works have explored various strategies for learning dense representations in videos, including architectural modifications to track multiple objects in ViTs [61], joint-embedding architectures with specialized masking strategies [4, 7], and temporally coherent clustering [50]. In this work, we propose a new approach inspired by the Gestalt principle of "what moves together belongs together" [32]. We bring this principle to a much finer level of granularity and introduce MoSiC in Figure 1, a self-supervised Motion-based Sinkhorn Clustering framework that clusters points along motion tracks to learn spatiotemporally consistent representations. + +Our approach begins by extracting dense point tracks that + +![](images/df508e97e1afb77c0a267114354494152628c56c8db7458e6c2275700ad1428e.jpg) +Figure 2. In-context scene understanding on Pascal VOC MoSiC improves DINOv2's dense representations on unlabeled videos, resulting in precise segmentation boundaries and better object identification. + +capture long-range motion trajectories across frames. These tracked points are then clustered using a momentum-encoder-based optimal transport mechanism, ensuring feature consistency while applying the loss only to visible points. By enforcing temporal coherence along motion trajectories, our model captures object permanence despite occlusions and viewpoint changes, resulting in more stable and semantically meaningful representations. Extensive evaluations across six image and video datasets demonstrate the effectiveness of MoSiC, showcasing its ability to learn robust and transferable dense features for tasks such as semantic segmentation and scene understanding. Notably, by leveraging the strong vision foundation model DINOv2 [42], MoSiC consistently improves its dense representations, as demonstrated qualitatively in Figure 2. This improvement is further validated quantitatively, achieving a $1\%$ to $6\%$ gain across four benchmarks—solely through training on video data. + +# 2. Related Works + +Video-to-Image self-supervised learning Video data provides rich temporal signals that naturally supervise learning by capturing object transformations and scene dynamics over time. Unlike static images, videos encode motion patterns and object persistence, offering essential cues for robust visual understanding. Early approaches explored various pretext tasks, including egomotion prediction [1, 26], pose estimation [13], dense prediction [37, 47], optical flow [39, 64], and visual correspondence learning [63]. + +Traditional self-supervised learning (SSL) methods, primarily developed on ImageNet, rely on augmentations for contrastive or predictive objectives [10, 14]. While extended to video [19, 45, 58, 62], direct transfer often leads to performance drops due to distribution shifts [45]. Recent works instead learn directly from videos, avoiding augmentation-based supervision. Carreira et al. [12] process continuous video streams without mini-batches, while DoRA [61] uses a single, long, unlabelled video to train strong image encoders without relying on traditional data augmentation techniques. MooG [60] models dynamic scene elements for improved motion tracking, and [11] scales SSL to larger models via + +masked autoencoding for spatiotemporal learning. + +Closest to our work, TimeTuning [50] leverages temporal cues but struggles with occlusions and long-range tracking under rapid camera motion. Unlike existing SSL methods, we incorporate dense point tracking to ensure robust temporal correspondences, improving performance on real-world video and image datasets. + +Unsupervised object segmentation Unsupervised object segmentation has been widely studied, with many methods [2, 6, 22, 35, 53, 68] segmenting objects in images without labeled data. These approaches often use pretrained models to extract information and train another model for segmentation. Seitzer et al. [52] use slot attention to reconstruct DINO-pretrained features, clustering image regions into object slots. CroC [54] aligns cluster centers across views using a dense self-supervised loss, while Leopart [71] enhances representations with dense clustering. Hummingbird [5] leverages attention mechanisms within and across images for in-context scene understanding. CrIBo [36] enforces cross-image nearest-neighbor consistency, while NeCo [44] enforces patch-level nearest-neighbor consistency generating high-quality dense representations. + +While these methods demonstrate the effectiveness of clustering and feature alignment for object segmentation, they primarily focus on static images, lacking the temporal consistency crucial for videos. In contrast, our method extends these ideas to the video domain by leveraging motion trajectories as signal. By propagating cluster assignments along tracked points, we ensure spatiotemporally coherent representations, bridging the gap between object-centric clustering and motion-aware learning. Tracktention [34] is another work that uses point trackers, which guides the attention for video prediction tasks to improve temporal consistency for depth. In contrast, we use point tracks to enforce temporal consistency for object segmentation across time. + +# 3. MoSiC: Motion-Based Sinkhorn Clustering + +We introduce $MoSiC$ in Figure 3, a novel approach to dense self-supervised learning in videos that leverages motion as an implicit supervisory signal. Our method first extracts long-range motion trajectories using an off-the-shelf point tracker, ensuring robustness to occlusions and object permanence. To enforce spatiotemporal coherence, we perform clustering over these motion trajectories, aligning feature representations across frames. Unlike prior methods that rely purely on mask propagation or local frame-based learning, our approach establishes long-range correspondences, leading to spatiotemporally consistent features, considerably improving the quality of the learned representations. + +![](images/cc4fdbe437a8b75c85566f9ff5b1db0320257a67302d1b8b8e0f23f3c2c595b1.jpg) +Figure 3. MoSiC: Motion-based Sinkhorn Clustering for dense self-supervised pretraining. A video clip is patchified, with masked patches passed through the student network to obtain $Z^{\mathrm{stu}} \in \mathbb{R}^{n_s \times d \times T}$ , while the teacher network processes the patches from raw clip to produce $Z^{\mathrm{teach}} \in \mathbb{R}^{n \times d \times T}$ . Features are clustered using Sinkhorn-Knopp [15] into prototypes $P$ . The cluster assignments $Q_{t_0}^{\mathrm{teach}}$ (eq. (6)) and $Q_{t_0}^{\mathrm{stu}}$ (eq. (7)) are computed for the first frame ( $t = t_0$ ). These assignments are then propagated along motion trajectories $\mathrm{Traj}_{t,i}$ computed using CoTracker-v3 [29] to obtain $Q_{t}^{\mathrm{teach}}$ (eq. (8)). Finally, a cross-entropy loss is applied between $Q_{t_0}^{\mathrm{stu}}$ and $Q_{t}^{\mathrm{teach}}$ (eq. (10)) for frames where $\mathrm{Traj}_{t,i}$ remains visible, ensuring temporal consistency by clustering points along motion paths and preserving object identity over time. + +# 3.1. Preliminaries + +Given a video clip $X \in \mathbb{R}^{h \times w \times c \times T}$ , where $T$ is the number of frames, $h \times w$ is the spatial resolution, and $c$ is the number of channels, we first divide each frame into $n = \frac{h \times w}{p^2}$ patches of size $p \times p$ . These patches are then linearly projected into $d$ -dimensional embeddings and passed through an encoder. We apply a binary mask $M \in \{0,1\}^{n \times T}$ uniformly across all frames, randomly masking a fraction $m$ of the tokens. Following Moutakanni et al. [41], we demonstrate that simple augmentations, such as cropping and masking, are sufficient for learning effective representations, eliminating the need for more complex augmentations like color jitter, grayscale, or blurring. We use a Vision Transformer (ViT) [17] in a teacher-student framework, where the student and teacher models are $f_{\theta}$ and $g_{\theta}$ . The representations are given by $Z^{\mathrm{teach}} = g_{\theta}(X_t) \in \mathbb{R}^{n \times d}$ for the teacher and $Z^{\mathrm{stu}} = f_{\theta}((1 - M) \odot X_t) \in \mathbb{R}^{n_s \times d}$ for the student networks, where $\odot$ denotes the Hadamard product and $n_s$ denotes the number of unmasked tokens. + +# 3.2. Clustering Motion Trajectories + +A major challenge in learning from real videos is the transient nature of objects due to occlusions, camera movement, and object permanence. Unlike images, video frames un + +dergo temporal deformations, making feature consistency difficult. Prior methods [50] propagate object masks across frames but struggle when objects temporarily disappear, leading to propagation errors. Additionally, long-range tracking suffers from drift accumulation, which compounds over time and degrades feature representations—an issue that worsens with longer sequences. + +Motion Trajectories From a Point Tracker To address these challenges, we utilize an off-the-shelf point tracker capable of long-range tracking and robust to object permanence. The tracker samples points from a regular grid in the first frame and updates their positions across subsequent frames. Given our video clip $X$ , we sample $N$ points from the initial frame, forming a grid $= (x_{i},y_{i})_{i=1}^{N}$ , where $(x_{i},y_{i})$ are the coordinates of the $i^{\text{th}}$ point. Using the video clip $X$ and the grid, the tracker predicts the trajectories of these points across all frames as: + +$$ +\operatorname {T r a j} _ {t, i} := \operatorname {T r a c k e r} \left(X _ {t}, \left(x _ {i}, y _ {i}\right)\right) \in \mathbb {R} ^ {T \times N \times 2}. \tag {1} +$$ + +$\operatorname{Traj}_{t,i}$ represents the trajectory of the $i^{\text{th}}$ point across $T$ frames, with each element encoding its coordinates at time $t$ . + +Optimal-Transport Based Clustering Although motion trajectories provide a strong signal for motion-based group + +ing, relying solely on them can be a challenge especially for objects with subtle or ambiguous motion. To address this, we perform clustering to enforce temporal coherence, ensuring that points belonging to the same object or part remain consistently clustered over time. Given motion trajectories from the point tracker, we incorporate semantic clustering to obtain a more discriminative representation of objects. + +We first cluster the features from the student and teacher networks $Z^{\mathrm{stu}} \in \mathbb{R}^{n_s \times d \times T}$ , $Z^{\mathrm{teach}} \in \mathbb{R}^{n \times d \times T}$ for the first frame using the Sinkhorn-Knopp algorithm [15]. This clustering solves an entropy-regularized optimal transport problem, iteratively refining the assignment of feature tokens to cluster prototypes while maintaining marginal constraints and has been used in various self-supervised works [3, 9, 42, 51]. + +Let $P^{\mathrm{stu}}$ , $P^{\mathrm{teach}} \in \mathbb{R}^{K \times d}$ denote $K$ cluster prototypes and $Z_{t_0}^{\mathrm{stu}} \in \mathbb{R}^{n_s \times d}$ , $Z_{t_0}^{\mathrm{teach}} \in \mathbb{R}^{n \times d}$ represent the features extracted from the initial frame $t = t_0$ . The transport cost between the patch features and the cluster prototypes $C^{\mathrm{stu}} \in \mathbb{R}^{n_s \times K}$ , $C^{\mathrm{teach}} \in \mathbb{R}^{n \times K}$ are: + +$$ +C ^ {\mathrm {s t u}} = - Z _ {t _ {0}} ^ {\mathrm {s t u}} P ^ {\mathrm {s t u} ^ {\top}} \in \mathbb {R} ^ {n _ {s} \times K} \tag {2} +$$ + +$$ +C ^ {\text {t e a c h}} = - Z _ {t _ {0}} ^ {\text {t e a c h}} P ^ {\text {t e a c h} ^ {\top}} \in \mathbb {R} ^ {n \times K} \tag {3} +$$ + +which denote the negative cosine similarity between the normalized patch features and normalized prototypes. The optimal transport plans $M^{\mathrm{stu*}}$ and $M^{\mathrm{teach*}}$ using eq. (2) and eq. (3) are obtained by solving: + +$$ +M ^ {\mathrm {s t u} *} = \arg \min _ {M ^ {\mathrm {s t u}} \in \mathcal {M} ^ {\mathrm {s t u}}} \left\langle M ^ {\mathrm {s t u}}, C ^ {\mathrm {s t u}} \right\rangle - \frac {\epsilon}{\lambda} H \left(M ^ {\mathrm {s t u}}\right) \tag {4} +$$ + +$$ +M ^ {\text {t e a c h *}} = \arg \min _ {M ^ {\text {t e a c h}} \in \mathcal {M} ^ {\text {t e a c h}}} \left\langle M ^ {\text {t e a c h}}, C ^ {\text {t e a c h}} \right\rangle - \frac {\epsilon}{\lambda} H \left(M ^ {\text {t e a c h}}\right) \tag {5} +$$ + +where $M^{\mathrm{stu}} \in \mathbb{R}^{n_s \times K}, M^{\mathrm{teach}} \in \mathbb{R}^{n \times K}$ are the assignment matrices, $H(M)$ is an entropy regularization, and $\epsilon$ is the regularization coefficient that controls the smoothness of the assignment enforcing uniform marginal constraints + +$$ +M ^ {\mathrm {s t u}} \mathbf {1} _ {K} = \mathbf {1} _ {n _ {s}} / n _ {s}, \quad M ^ {\mathrm {s t u}} ^ {\top} \mathbf {1} _ {n _ {s}} = \mathbf {1} _ {K} / K \text {a n d} +$$ + +$$ +M ^ {\text {t e a c h}} \mathbf {1} _ {K} = \mathbf {1} _ {n} / n, \quad M ^ {\text {t e a c h} ^ {\top}} \mathbf {1} _ {n} = \mathbf {1} _ {K} / K. +$$ + +# 3.3. Cluster Propagation using Motion Trajectories + +After clustering the initial frame, we propagate these assignments across frames using the tracked motion trajectories from eq. (1). This allows us to maintain consistent object representations over time, even when objects undergo deformation. Given the tracked trajectories from eq. (1), we sample features from the student and teacher embeddings $Z^{\mathrm{stu}}$ , $Z^{\mathrm{teach}}$ at these locations. + +To extract features at the tracked locations, we interpolate values from the feature maps using the continuous trajectory coordinates. Since these points do not always align with discrete pixel locations, we apply bilinear interpolation for the teacher network, computing feature values as a weighted sum of the four nearest neighbors. For the student network, we use nearest-neighbor interpolation, since the points are sampled along a simple uniformly spaced grid. + +![](images/69f76a2f119b0606eeec740e04fccc6810376986434aece26aeb50c8e06fc32b.jpg) +Figure 4. Previous methods such as TimeT lose precise object mapping after occlusions (e.g., a tree), rapid camera and object motion – resulting in degraded and coarse segmentation targets over long-range video clips. In contrast, MoSiC leverages stable point tracks, preserving consistency despite occlusions and motion via our trajectory based clustering loss eq. (10). + +Cluster Propagation First, we compute the cluster assignment for the features from the teacher and the student networks using $M^{\mathrm{stu*}}$ and $M^{\mathrm{teach*}}$ computed in eq. (4) and eq. (5) as follows: + +$$ +\mathcal {Q} _ {t _ {0}} ^ {\mathrm {s t u}} = \arg \max _ {K} M ^ {\mathrm {s t u} ^ {*}} \cdot Z _ {t _ {0}} ^ {\mathrm {s t u}} \tag {6} +$$ + +$$ +\mathcal {Q} _ {t _ {0}} ^ {\text {t e a c h}} = \arg \max _ {K} M ^ {\text {t e a c h} ^ {*}} \cdot Z _ {t _ {0}} ^ {\text {t e a c h}} \tag {7} +$$ + +where the optimal transport plans assigns each feature to its nearest cluster prototype. We guide the cluster assignments $\mathcal{Q}_{t_0}^{\mathrm{teach}}$ using the motion trajectories $\mathrm{Traj}_{t,i}$ obtained from eq. (1), where each tracked point retains its original cluster assignment as it moves along the trajectory: + +$$ +\mathcal {Q} _ {t} ^ {\text {t e a c h}, i} = \mathcal {Q} _ {t _ {0}} ^ {\text {t e a c h}, i}, \quad \forall (x _ {i, t}, y _ {i, t}) = \operatorname {T r a j} _ {t, i} \tag {8} +$$ + +# 3.4. Training Objective + +To ensure temporal consistency, we aim to align features of different views of the same object over time. Although motion trajectories provide the correspondence of object locations across frames, relying solely on trackers may not guarantee that features from different views are assigned to the same cluster. For each frame $t \in T$ , let $Q_{t_0}^{\mathrm{stu},i}$ denote the cluster assignment for the $i$ -th point in the initial frame $t_0$ from the student network, and $Q_t^{\mathrm{teach},i}$ denote the propagated cluster assignment for the $i$ -th point in frame $t$ from the teacher network, as defined in eq (8). + +We compute the cluster scores $S_{t_0}^{\mathrm{stu},k,i}$ for each cluster $k$ and point $i$ in the frame $t$ applying a softmax on the similarity between the $Z_{t_0}^{\mathrm{stu},i}$ and the cluster prototypes $M^{\mathrm{stu*}}$ : + +$$ +S _ {t _ {0}} ^ {\mathrm {s t u}, k, i} = \frac {\exp \left(M ^ {\mathrm {s t u} *} \cdot Z _ {t _ {0}} ^ {\mathrm {s t u} , i}\right)}{\sum_ {k ^ {\prime}} \exp \left(M ^ {\mathrm {s t u} *} \cdot Z _ {t _ {0}} ^ {\mathrm {s t u} , i}\right)} \tag {9} +$$ + +The teacher's assignments are one-hot vectors, where $\delta(\mathcal{Q}_t^{\mathrm{teach},i} = k)$ equals 1 if the assigned cluster is $k$ and 0 otherwise. The clustering loss is formulated as a cross-entropy loss, averaged over all visible trajectories and frames: + +$$ +\mathcal {L} _ {\text {c l u s t}} (i) = - \sum_ {t = 1} ^ {T} \sum_ {k = 1} ^ {K} v _ {t, i} \cdot \delta \left(\mathcal {Q} _ {t} ^ {\text {t e a c h}, i} = k\right) \cdot \log \left(S _ {t _ {0}} ^ {\text {s t u}, k, i}\right) \tag {10} +$$ + +where $v$ is a visibility flag indicating whether the $i$ -th point is visible in frame $t$ . This ensures that the loss is computed only for points that are visible in each frame, thereby enhancing the robustness of our model to occlusions. Therefore, as shown in Figure 4 we enforce that all patches along a trajectory, representing the same object or part as observed, are consistently clustered over time. This approach extends beyond individual images by maintaining consistency across pixel trajectories throughout the video sequence. + +# 4. Experiments + +# 4.1. Experimental setup + +We follow TimeTuning [50] and initialize MoSiC with a pretrained DINOv2 [42] backbone and a frozen CoTracker v3 [29] for point tracking. Training is conducted on YouTube-VOS [65], one of the largest video segmentation datasets. For evaluation, we discard the projection head and use the teacher network as the feature extractor, following DINO [10]. Unless specified, mean intersection over union (mIoU) serves as the primary metric. + +We assess linear segmentation on Pascal VOC [18], COCO-Things [8], and ADE20K [69] by training a segmentation head on frozen spatial features, and perform end-to-end segmentation using the Segmenter head [55]. For frozen clustering-based evaluations, we apply $K$ -Means to spatial tokens, setting $K$ to both the number of ground-truth objects and larger values (300, 500), then match cluster maps to ground truth using Hungarian matching [33]. Dense nearest-neighbor retrieval is used to evaluate on-context scene understanding [5] for ADE20K and Pascal VOC. For unsupervised video semantic segmentation, we perform clustering and overclustering on YouTube-VOS and DAVIS [48], aligning clusters with ground truth via Hungarian matching. + +We evaluate MoSiC across four dense benchmarks spanning images and videos, assessing unsupervised semantic segmentation across time and space, visual scene understanding, and feature transferability via linear segmentation. Additional experiments, including end-to-end finetuning results for object detection and segmentation, scaling to the large variant, image classification performance and pretraining with DINO, can be found in Appendix 6.1 + +# 4.2. Unsupervised Video Object Segmentation + +To assess temporal coherence in MoSiC, we evaluate the clustering performance on DAVIS [48] and YouTubeVOS [65]. Following [50], clusters are aligned with groundtruth object masks using the Hungarian algorithm [33]. We also evaluate performance under Over-Clustering, where a + +larger number of clusters is used. This is particularly relevant in dense self-supervised learning, as representations serve as feature descriptors for downstream tasks such as semantic segmentation and object detection. + +From Table 2, MoSiC-S14 outperforms TimeT [50] by $8.7\%$ and $9.4\%$ mIoU on DAVIS and YouTube-VOS, respectively. Additionally, MoSiC surpasses both DINOv2 and DINOv2-R by $4.3\%$ and $3.7\%$ on average across clustering and overclustering evaluations. These results highlight MoSiC's ability to produce temporally consistent segmentations and generalize across diverse video datasets. + +# 4.3. Visual In-Context learning + +We compare MoSiC on the Hummingbird Benchmark [5], which evaluates in-context reasoning in vision models. Unlike traditional segmentation approaches, this task does not involve fine-tuning; instead, segmentation maps are generated by matching patch-level feature similarities between validation (query) and training (key) images. As shown in Table 1, MoSiC consistently outperforms SOTA on PascalVOC [18] and ADE20K [69], particularly in low-data settings. On Pascal VOC, MoSiC-S14 outperforms DINOv2 by $6\%$ and DINOv2-R by nearly $10\%$ with 1/128th of the data and persists across all data regimes, with MoSiC-S14 surpassing DINOv2 by $1\%$ even with full data. The larger variant, MoSiC-B14, further improves performance, outperforming DINOv2-R by $10\%$ in the lowest-data setting and exceeding DINOv2 by $3\%$ with full data. + +Similarly, on ADE20K, MoSiC outperforms DINOv2 by $2\%$ across both variants. These results demonstrate MoSiC's ability to learn robust and transferable representations, especially in data-scarce scenarios where it significantly outperforms prior methods. + +# 4.4. Frozen Clustering + +We assess the quality of learned representations by clustering features and evaluating their ability to differentiate objects within datasets. Ideally, the patch features corresponding to the same object should be assigned to a single cluster. If representations capture finer details (e.g., hands or faces rather than entire persons), they should remain consistent across images. To analyze this, we extract dense features and apply $K$ -Means clustering with varying $K$ values. Cluster maps are then aligned with ground truth using Hungarian matching [33]. We evaluate performance when $K$ matches the number of ground-truth objects, as well as under Over-Clustering, similar to subsection 4.2. + +From Table 3a and Table 3b, MoSiC achieves the highest mIoU across all clustering granularities. For $K = 300$ , it outperforms DINOv2 by $3.7\%$ on Pascal VOC and $1.6\%$ on COCO-Things, indicating its ability to learn structured, discriminative representations. Under Over-Clustering ( $K = 500$ ), MoSiC surpasses CrIBo by $5.7\%$ on Pascal VOC and $6.6\%$ on COCO-Things, demonstrating its capacity to + +Table 1. In-context scene understanding benchmark. We evaluate dense nearest neighbor retrieval performance across various training data proportions on ADE20K [69] and Pascal VOC [18]. Retrieved cluster maps are compared with the ground truth via Hungarian matching [33]. We report mIoU; higher is better. + +
METHODBACKBONEPARAMSADE20KPASCAL VOC
1/1281/641/81/11/1281/641/81/1
TRAINED ON IMAGES
DINO [10]ViT-S/1621M9.511.015.017.926.430.541.348.7
CrOC [54]ViT-S/1621M8.710.815.217.334.041.853.860.5
SelfPatch [66]ViT-S/1621M10.010.914.717.728.432.643.250.8
Leopart [71]ViT-S/1621M12.914.819.623.944.649.758.464.5
CrlBo [36]ViT-S/1621M14.617.322.726.653.959.966.972.4
DINOv2 [42]ViT-S/1421M22.826.433.538.856.062.472.377.0
FINETUNED ON VIDEOS
TimeT [50]ViT-S/1621M12.114.118.923.238.143.855.262.3
MoSiCViT-S/1421M23.827.435.740.762.566.674.778.2
TRAINED ON IMAGES
MAE [23]ViT-B/1685M10.011.315.418.63.54.15.67.0
DINO [10]ViT-B/1685M11.513.518.221.533.137.749.857.3
Leopart [71]ViT-B/1685M14.616.821.826.750.154.763.169.5
Hummingbird [5]ViT-B/1685M11.715.122.329.650.557.264.371.8
CrlBo [36]ViT-B/1685M15.918.424.428.455.961.869.274.2
DINOv2 [42]ViT-B/1485M24.227.634.739.955.761.872.477.1
FINETUNED ON VIDEOS
MoSiCViT-B/1485M25.429.337.342.665.569.876.980.5
+ +Table 2. Unsupervised video semantic segmentation results for clustering and over-clustering on DAVIS [48] and Youtube-VOS (YTVOS) [65]. For clustering, the Hungarian algorithm [33] matches clusters (K) to ground truth (GT) per frame (F), clip (C), or dataset (D). For over-clustering: K=10 (F, C), K=200 (D, DAVIS), K=500 (D, YTVOS). All the models are ViT-S16, except for DINOv2 variants and MoSiC, which are ViT-S14. We report mIoU and, unlike [50], do not use CBFE for any method to ensure consistency; higher is better. + +
CLUSTERINGOVER-CLUSTERING
YTVOSDAVISYTVOSDAVIS
FCDFCDFCDFCD
TRAINED ON IMAGES
DINO [10]39.137.91.930.231.01.666.265.44.056.954.917.9
Leopart [71]39.237.911.730.330.216.564.562.815.554.954.426.7
DINOv2 [42]56.355.512.857.457.413.662.862.517.357.958.525.5
DINOv2R [16]56.855.414.757.357.814.364.063.521.558.159.527.2
FINETUNED ON VIDEOS
STEGO [22]41.540.32.031.931.03.258.154.35.147.646.310.4
DINO [10]37.236.11.229.329.22.453.150.91.345.444.08.6
Leopart [71]41.540.57.737.536.512.660.859.86.853.753.116.8
TimeT [50]50.251.412.849.549.212.860.659.418.155.957.622.0
MoSiC60.659.618.458.960.823.466.865.624.458.459.829.0
+ +encode fine-grained object structures. These results show MoSiC's effectiveness in distinguishing objects and their components, making it suitable for dense prediction tasks. + +# 4.5. Linear Segmentation + +We further evaluate MoSiC for supervised semantic segmentation, keeping the pretrained backbone frozen while training a linear layer on top. Output features are upsampled via bilinear interpolation to match input dimensions, allowing for pixel-wise cross-entropy loss. Unlike fine-tuning, this setup provides a more reliable measure of the backbone's learned representations. As shown in Table 4, MoSiC consistently + +outperforms SOTA segmentation models, including CrIBo, and surpasses DINOV2-R by up to $4\%$ on Pascal VOC and $3.3\%$ on ADE20K. Additionally, MoSiC outperforms DINOV2 across all datasets, underscoring its ability to capture semantically meaningful features that enable strong segmentation performance with just a linear probe. + +# 4.6. Generalization to Diverse Vision Encoders + +We explore the generalization of MoSiC to a diverse set of vision foundation models. We observe in Table 5, that MoSiC enhances both in-context scene understanding and linear classification for vision models, as well as vision-language + +Table 3. Frozen clustering-based evaluations. (a) We evaluate the models using $K$ -means with various clustering granularities $K$ on the features of Pascal VOC [18] and COCO-Things [8]. Cluster maps are matched to the ground-truth via Hungarian matching [33], We report mIoU; higher is better. (b) We post-process these maps for unsupervised semantic segmentation on Pascal VOC. All the models are ViT-S16, except for DINOv2 variants and MoSiC, which are ViT-S14. + +(a) Clustering + +
METHODPASCAL VOCCOCO-THINGS
K=100K=300K=500K=100K=300K=500
TRAINED ON IMAGES
DINO [10]10.113.917.314.418.819.2
CrOC [54]10.216.420.022.414.718.1
iBOT [70]16.523.831.115.526.628.0
EVA-CLIP [56]31.737.441.430.538.039.8
DINOv2R [16]34.846.749.532.038.941.2
Leopart [71]39.246.551.238.347.853.2
CrIBo [36]40.351.354.540.246.048.3
DINOv2 [42]43.255.158.643.851.653.1
FINETUNED ON VIDEOS
TimeT [50]†34.643.646.234.942.744.6
MoSiC50.058.860.245.853.254.9
+ +(b) Semantic segmentation + +
METHODMIOU
TRAINED ON IMAGES
MaskConstrast [59]35.1
DINOv2R [16]35.1
DINOv2 [42]37.5
DeepSpectral [40]37.2
DINOSAUR [52]37.2
Leopart [71]41.7
COMUS [67]50.0
FINETUNED ON VIDEOS
TimeT [50]41.1
MoSiC51.2
+ +Table 4. Linear segmentation performance. A linear segmentation head is trained on top of frozen spatial features. We report mIoU scores on 4 validation datasets. + +
METHODARCH.COCO-THINGSCOCO-STUFFPASCAL VOCADE20K
TRAINED ON IMAGES
DINO [10]ViT-S/1643.945.950.217.5
iBOT [70]ViT-S/1658.951.566.121.8
CrOC [54]ViT-S/1664.351.267.423.1
CrBo [36]ViT-S/1664.349.171.622.7
DINOv2 [42]ViT-S/1481.458.378.937.9
FINETUNED ON VIDEOS
TimeT [50]ViT-S/1658.248.766.320.7
MoSiCViT-S/1482.361.079.739.6
TRAINED ON IMAGES
DINO [10]ViT-B/1655.851.262.723.6
MAE [23]ViT-B/1638.038.632.95.8
iBOT [70]ViT-B/1669.455.973.130.1
CrIb [36]ViT-B/1669.653.073.925.7
EVA-CLIP [56]ViT-B/1675.948.070.434.6
DINOv2 [42]ViT-B/1484.058.980.342.6
FINETUNED ON VVideos
MoSiCViT-B/1485.861.481.543.6
+ +models such as EVA-CLIP [56], achieving improvements of $2\%$ and $3\%$ on average, respectively, using only video-based training. This demonstrates that videos can serve as a complementary source of information to further enrich image and language datasets. + +Table 5. Performance on In-context visual scene understanding (IC) and linear classification (LC) benchmarks with and without MoSiC. MoSiC improves various baselines across segmentation datasets. + +
METHODIC(1/1)LC
ADE20KPASCAL VOCADE20KPASCAL VOC
DINO-S1617.948.717.550.2
+MoSiC24.964.522.367.3
EVA-CLIP-B14 [56]32.969.034.670.4
+MoSiC35.070.040.173.4
DINOv2R-B1439.578.843.080.2
+MoSiC43.779.344.481.1
+ +# 4.7. End-to-end Full Fine-tuning + +In Table 6 and Table 10, we evaluate the performance of MoSiC when used as the backbone for object detection and semantic segmentation in the full finetuning setting. For object detection ViT-Det [38] and for semantic segmentation Segmenter [55] frameworks are used. As shown, our method consistently outperforms DINOv2 across all datasets and evaluation protocols, setting a new state-of-the-art—despite being fine-tuned solely on video data that differs in distribution from the evaluation datasets. Since full finetuning updates all model parameters, the superior performance of MoSiC indicates that learning a more structured, object-aware feature space is achievable even without any image dataset, by finetuning on videos alone. + +Table 6. MoSiC vs. DINOv2 on object detection. We use ViTDet [38] on COCO [8] and report Average Precision (AP) on bounding-box object detection $(\mathrm{AP}^{\mathrm{box}})$ and instance segmentation $(\mathrm{AP}^{\mathrm{mask}})$ . + +
MethodBackboneParamsAPboxAPmask
DINOv2ViT-S/1421M42.536.7
MoSiCViT-S/1421M42.536.8
DINOv2ViT-B/1485M46.141.9
MoSiCViT-B/1485M46.442.0
DINOv2ViT-L/14307M51.645.9
MoSiCViT-L/14307M51.846.0
+ +# 4.8. Ablations + +We conduct ablations on key parameters of MoSiC using the DINO [10] backbone trained on YouTube-VOS for 50 epochs with an image resolution of 224. We evaluate visual in-context learning on Pascal VOC12 and ADE20K, using a + +Table 7. Ablating the key parameters of MoSiC by training a linear layer on top of the frozen representations (Lin.) or using the in-context (IC) evaluation [5] on the validation images of Pascal VOC (PVOC) and ADE20K. +(a) Mask Ratio + +
RATIOPVOCADE20K
No Mask51.118.2
10%51.518.6
20%51.318.8
40%49.918.5
+ +(b) EMA Teacher + +
TEACHERPVOCADE20K
×50.518.2
✓51.518.6
+ +(e) Number of Prototypes + +
PROTOTYPESPVOCADE20K
5046.515.3
10051.518.6
20051.018.7
30050.118.1
+ +(f) Optimized points + +
BATCHPVOCADE20K
All50.518.0
Visible51.518.6
+ +(c) Grid Size + +
GRIDPVOCADE20K
8 × 849.217.5
16 × 1651.518.6
32 × 3250.518.2
+ +(d) Crop Scale + +
INTERVALPVOCADE20K
No crop49.118.0
[0.2, 1]50.818.5
[0.4, 1]51.518.6
[0.6, 1]50.518.4
+ +(g) Clip length in second + +
TPVOCADE20K
0.547.616.2
150.518.2
1.651.018.2
3.251.518.6
+ +(h) Number of frames. + +
#FRAMESPVOCADE20K
239.313.1
448.016.4
850.418.2
1251.518.6
+ +reduced memory size of 1/100 of the original setting in our primary experiments. + +Masking ratio. We analyze the effect of different masking ratios in Table 7a. Moderate masking enhances semantic learning by preventing reliance on a limited set of patches. However, excessively high masking (e.g., $40\%$ ) degrades performance by reducing available input information. We select a $10\%$ masking ratio due to its superior training stability over $20\%$ , despite both achieving similar performance. + +Crop scale. Table 7d evaluates the impact of different cropping scales in augmentations. Moderate cropping yields the highest improvements, particularly due to the non-object-centric nature of YouTube-VOS, where aggressive cropping can make it difficult to extract meaningful regions consistently across frames. This differs from static-image datasets [71]. + +EMA teacher. We assess the impact of an Exponential Moving Average (EMA) teacher in Table 7b. Incorporating a teacher network improves performance by $1\%$ on Pascal VOC and $0.4\%$ on ADE20K, aligning with findings from [10], where EMA stabilization led to improved training consistency in self-supervised frameworks. + +Number of prototypes. Table 7e shows that increasing the number of prototypes significantly enhances performance up to a threshold. The best results are achieved with 100 prototypes, beyond which improvements plateau. MoSiC remains robust across a wide range (100-300 prototypes), indicating insensitivity to fine-tuning this parameter. + +Grid size. Table 7c shows the effect of different grid sizes for tracking initialized points. Denser grids improve performance, peaking at $16 \times 16$ , after which performance slightly drops at $32 \times 32$ . This decline is likely due to an incompatibility between patch-based feature extraction and point-wise tracking, where excessive density leads to misleading correspondences during training. + +Clip length. We evaluate the effect of clip length in Table 7g, considering sequences of 12 frames. Longer clips improve performance by exposing the model to richer motion cues and diverse object transformations. We select a 3.2-second clip length as the optimal setting for all + +Number of clip frames. Table 7h explores the impact of clip frame count while keeping the time step per frame fixed at $3.2 / 12$ seconds. Increasing the frame count consistently improves performance, as it provides richer spatial and temporal signals during training. We use 12 frames as the optimal setting. + +Optimized points. To improve tracking accuracy, we apply loss only to points that remain visible throughout the sequence. As shown in Table 7f, this approach reduces false similarity enforcement, improving performance by up to 1 + +# 5. Conclusion + +In this paper, we introduced MoSiC, a motion-based self-supervised learning approach that leverages dense point tracking to enforce temporal consistency in feature learning. By propagating cluster assignments along motion trajectories, our method effectively mitigates occlusions and long-range tracking drift, enhancing representation quality for dense prediction tasks. Extensive evaluations across unsupervised video-object segmentation, in-context learning, frozen clustering, and linear segmentation demonstrate that MoSiC achieves state-of-the-art performance across both image and video benchmarks. Our results highlight the importance of motion cues in self-supervised representation learning and suggest that point tracking can serve as a powerful supervisory signal—enabling robust feature learning without requiring dense annotations. + +# Acknowledgements + +Shashanka was supported by HPC resources from GENCI-IDRIS Grant 2024-AD011016023. + +# References + +[1] Pulkit Agrawal, Joao Carreira, and Jitendra Malik. Learning to see by moving. In ICCV, 2015. 2 +[2] Nikita Araslanov, Simone Schaub-Meyer, and Stefan Roth. Dense unsupervised learning for video segmentation. NeurIPS, 2021. 2 +[3] Yuki Markus Asano, Christian Rupprecht, and Andrea Vedaldi. Self-labelling via simultaneous clustering and representation learning. In ICLR, 2020. 4 +[4] Mahmoud Assran, Quentin Duval, Ishan Misra, Piotr Bojanowski, Pascal Vincent, Michael Rabbat, Yann LeCun, and Nicolas Ballas. Self-supervised learning from images with a joint-embedding predictive architecture. 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This paper introduces the first mobile-optimized image-to-video diffusion model. Starting from a spatio-temporal UNet from Stable Video Diffusion (SVD), we reduce the computational cost by reducing the frame resolution, incorporating multi-scale temporal representations, and introducing two novel pruning schemas to reduce the number of channels and temporal blocks. Furthermore, we employ adversarial finetuning to reduce the denoising to a single step. Our model, coined as MobileVD, can generate latents for a $14 \times 512 \times 256$ px clip in 1.7 seconds on a Xiaomi-14 Pro, with negligible quality loss. Our results are available at https://qualcomm-ai-research.github.io/mobile-video-diffusion + +# 1. Introduction + +Video diffusion models are making significant progress in terms of realism, controllability, resolution, and duration of the generated videos. Starting from zero-shot video models [11, 26, 30, 36], which deploy pretrained image diffusion models to generate consistent frames, e.g., through cross-frame attention, modern video diffusion models rely on spatio-temporal denoising architectures, i.e., 3D UNets [2, 3, 16] or 3D DiTs [33, 68, 74]. This involves inflating image denoising models by adding temporal transformers and convolutions to denoise multiple frames simultaneously. Despite their impressive generation qualities, spatiotemporal denoising architectures demand high memory and computational power, which limits their usage to clouds with high-end GPUs. This hinders the wide adoption of video + +generation technology for many applications that require generating content locally on mobile devices. + +Prior work on accelerating video diffusion models has mostly focused on reducing the number of sampling steps [62, 72]. By extending the consistency models [58] and adversarial distillation [54] to video diffusion models, they managed to reduce the number of denoising steps from 25 to only 4 [62] and 1 step [72], which tremendously accelerates video generation. However, step distillation alone does not reduce the memory usage of the model, which is the key setback in deploying video diffusion models on mobile devices. + +This paper is the first attempt to build image-to-video diffusion models for mobile. Starting from model of Stable Video Diffusion (SVD) [2, 3], as a representative for video diffusion models, we conduct a series of optimizations on its spatio-temporal UNet to build a mobile-friendly UNet: driven by the lower resolution needs for user-generated content on phones, we first opt for using a smaller latent resolution for generating $512 \times 256$ px frames. Additionally, instead of preserving the number of frames throughout the denoising UNet, we introduce additional temporal down- and up-sampling operations to extend the multi-scale representation both in space and time, which reduces the memory and computational cost with minimal loss in quality. Moreover, we discuss how naive visual conditioning through crossattention leads to significant computational overhead that can be avoided without damaging visual quality. + +We further accelerate the mobile-friendly UNet by reducing its parameters using a novel channel compression schema, coined channel funneling, and a novel technique to prune the temporal transformers and temporal residual blocks from the UNet. Finally, following Zhang et al. [72], we reduce the number of denoising steps to a single step using adversarial finetuning. This results in the first mobile video diffusion model called MobileVD, which is able to generate 14 latent frames of resolution $512 \times 256$ in 1.7 seconds on a Xiaomi 14-Pro smartphone at a slightly worse quality in terms of FVD, 149 vs. 171. + +# 2. Related work + +Video generation. Fueled by advancements in generative image modeling using diffusion models, there has been notable progress in the development of generative video models [2, 3, 13, 14, 21, 25, 32, 45, 52, 75]. These video models generally evolve from image models by incorporating additional temporal layers atop spatial blocks or by transforming existing 2D blocks into 3D blocks to effectively capture motion dynamics within videos. Although these advancements have paved the way for the generation of high-resolution videos, the significant computational demands make them impractical for use on low-end devices. In this work, we address this by optimizing a representative of video generative model, SVD [2], to make it accessible to a broader range of consumer-graded devices. + +Diffusion optimization. The problem of making diffusion models efficient naturally consists of the following two parts: (i) reducing the number of denoising steps and (ii) decreasing the latency and memory footprint of each of those steps. Reducing number of steps is achieved by using higher-order solvers [39, 40, 69], distilling steps to a reduced set using progressive step distillation [34, 41, 53], straightening the ODE trajectories using Rectified Flows [35, 37, 76], mapping noise directly to data with consistency models [38, 57, 58], and using adversarial training [54, 55, 63, 72]. To decrease computational cost of each step, research has been done in weight quantization [19, 46, 56] and pruning [8, 34] as well as architectural optimization of the denoiser [9, 17, 31, 49, 66]. In this work, following Zhang et al. [72] we reduce number of steps to one using adversarial training and optimize the UNet denoiser using multiple novel techniques. + +On-device generation. On-device generation has attracted interest due to its ability to address privacy concerns associated with cloud-based approaches. There have been advancements in running text-to-image generation on mobile devices and NPUs [5, 7, 8, 22, 34, 73]. Although there has been progress in the video domain with fast zero-shot video editing models [27, 28, 64, 71], by now the only reported deployment of a video generative model to a device is concurrent work of SnapGen-V [65]. However, unlike SnapGen-V, we finetune a publicly released image-to-video SVD [2] checkpoint rather than train from scratch, which makes our method suitable for low-compute practitioners. It is noteworthy that, while most state-of-the-art generative models pivoted to a DiT-based transformer architecture [48], deploying DiT to device is more challenging due to its quadratic memory need. Therefore, all the mentioned mobile-targeting approaches stick with UNet-based architecture. + +# 3. Mobile Video Diffusion + +In this section, we propose a series of optimizations to obtain a fast and lightweight version of an off-the-shelf image-to- + +
ModelNFEFVD ↓TFLOPs ↓Latency (ms) ↓
GPUPhone
Resolution 1024 × 576
SVD5014945.43376OOM
AnimateLCM*828145.43376OOM
UFOGen*1191745.43376OOM
LADD*1189445.43376OOM
SF-V*118145.43376OOM
MobileVD-HD (ours)118423.63227OOM
Resolution 512 × 256
SVD (original)504768.6082OOM
SVD (finetuned)501968.6082OOM
SF-V (our implement.)11688.24763630
MobileVD (ours)11714.34451780
+ +Table 1. Comparison with recent models. FLOPs and latency are provided for a single function evaluation (NFE) with batch size of 1. For rows marked with asterisk* FVD measurements were taken from Zhang et al. [72], while performance metrics are based on our measurements for UNet used by SVD. For consistency with these results, FVD for SVD and our MobileVD model was measured on UCF-101 dataset at 7 frames per second. + +video diffusion model [2], suitable for on-device deployment. + +# 3.1. Preliminaries + +Stable Video Diffusion. We adopt Stable Video Diffusion (SVD) [2] as the base model for optimization. The SVD released checkpoint1 is an image-to-video model that by default generates 14 frames at the resolution $1024 \times 576$ with 25 sampling steps. To generate a video from an image, the input image is first mapped into a latent code of resolution $128 \times 72$ using a Variational Auto-Encoder (VAE). Then it is duplicated 14 times and concatenated with a noise latent of spatiotemporal resolution $14 \times 128 \times 72$ . The combined latent is then denoised by a conditional UNet through an iterative process. Additionally, the input image is encoded with a CLIP image embedding for use in cross-attention layers [50]. The UNet denoiser consists of four downsampling blocks, one middle block and four upsampling blocks. To handle the dynamics of video sequences, the model employs temporal blocks after spatial blocks. Notably, up- and downsampling is conducted across spatial axes only, and temporal resolution of the latent is kept constant to 14 throughout the UNet. The UNet denoiser as-is is too resource-intensive for on-device use, requiring 45.43 TFLOPs and 376 ms per denoising step on a high-end A100 GPU. Using FLOPs and latency as proxy metrics, we propose a series of optimizations to make the model suitable for on-device deployment. + +Baseline model. We observe that the original high-resolution SVD can not be compiled for on-device usage. The main reason is that Android NPU has extremely low memory (only 8 MB) and restricted set of instructions and + +![](images/bb5f19eb3afafb0e32306bcfdbab1367703353898d3019c5657d7d7ea97560c5.jpg) +Figure 1. Effect of optimized cross-attention for a mobile device. We show the number of cycles of the top-4 operations on mobile hardware for an input resolution of $128 \times 128$ . Note that removing the no-op similarity map computation in cross-attention layers reduces cycles on softmax operations by roughly $80\%$ . + +operations (no 5D operations, sub-optimal batch inference, slow scalar processing required for activation functions and softmax). To satisfy the memory constraints, we decrease the spatial resolution of the model to $512 \times 256$ , resulting in latent size of $14 \times 64 \times 32$ . This decreased resolution leads to $4.5 \times$ smaller feature maps and reduced peak memory. While the released SVD checkpoint supports multiple resolutions, we found out that the original model demonstrates deteriorated quality for our target spatial resolution as reported in Tab. 1. Therefore, we finetuned the diffusion denoiser at our target spatial size. With this optimization, computational cost and GPU latency is reduced to 8.60 TFLOPS and 82 ms respectively. We consider this low resolution, finetuned model as the baseline in our work. + +Adversarial finetuning. In addition to the high cost of the UNet, the iterative sampling process in video diffusion models further slows them down. For example, with the conventional 25-step sampling it takes 11 seconds to generate a video on a high-end A100 GPU. Also, due to the usage of classifier-free guidance, each step results in two UNet forward passes on a device leading to the total number of UNet evaluations (NFE) of 50 [20]. To reduce the cost, we follow SF-V framework [72] and use adversarial finetuning, enabling our models to generate videos in a single forward pass. Namely, we initialize the discriminator feature extractor with an encoder part of the denoising UNet and do not train it. After each block of this backbone, the extracted feature maps are passed to the two projection discriminator heads, one spatial and one temporal [43]. The heads also use the frame index and the CLIP embedding of the conditional image as input. At each training step, we apply the pseudo-Huber (Charbonnier) [6] and non-saturating adversarial loss [15] to the generator output to update its weights. To regularize the discriminator, the $R_{1}$ penalty is used [42]. For further details please refer to the original SF-V work. + +# 3.2. Mobile-friendly UNet + +Our first modification to SVD architecture regards the feature resolution that affects both GPU and mobile latency. Then we highlight some lossless optimizations that have a large effect on mobile latency. These are the first optimizations that allow us to run the UNet on device. + +Temporal multiscaling. To further reduce computational burden, one might lower the input resolution more heavily. However, this significantly degrades visual quality. Instead, we can additionally downscale the feature maps by a factor of 2 along either spatial or temporal axis after the first downsampling block of the UNet. To maintain the same output shape, this is accompanied by the corresponding nearest-neighbor upscaling operation before the last upsampling block. We refer to these two additions as multiscaling. In terms of computational cost, spatial multiscaling results in a $51\%$ reduction in FLOPs and $33\%$ in GPU latency, while temporal multiscaling reduces FLOPs and GPU latency by $34\%$ and $22\%$ , respectively. For our final deployed model, we use temporal multiscaling as it offers a better trade-off between quality and efficiency, as reported in Sec. 4.3.1. + +Optimizing cross-attention. In SVD, each cross-attention layer integrates information from the conditioning image into the generation process. The attention scores are computed similarly to self-attention layers, $\mathrm{Attn}(Q,K,V) = \mathrm{softmax}\left(QK^T / \sqrt{d}\right)V$ , but the key and value pair $(K,V)$ comes from the context tokens. However, the context in the cross-attention blocks always consists of a single token, namely, the CLIP embedding vector of the conditional image. Consequently, each query token attends to only a single key token. Therefore, computation of a similarity map $QK^T$ and softmax becomes a no-op, and query and key projection matrices can be removed without any difference in results. While this loss-less optimization reduces GPU latency only by $7\%$ , we found that it significantly impacts on-device behavior. In detail, at target resolution of $512 \times 256$ , the model runs out of memory (OOM) on the device without the described modification of cross-attention. And at a smaller resolution of $128 \times 128$ this optimization reduces mobile latency by $32\%$ . The gain is attributed to the time-consuming nature of softmax operation on device, as shown in Fig. 1. + +# 3.3. Channel funnels + +Channel size, which refers to the width of neural network layers, is crucial for scaling models. Increasing channel size generally enhances model capacity but also increases the number of parameters and computational cost. Research has focused on compressing the number of channels by either discarding less informative channels through channel pruning [12, 44] or representing weight matrices as low-rank products of matrices using truncated singular decomposition [70]. However, these could have sub-optimal tradeoffs + +![](images/0d579127ecc2aa089a65cee472b2204bb6949fd89e4c6a4253fb13348c80eb44.jpg) +Figure 2. Channel funnels. We show an example of channel funnels applied to a couple of layers within the model. At training time, funnels serve as adaptors reducing model width. At inference, they are merged with corresponding weight matrices without loss of quality. + +in quality and efficiency when deployed on device. While low-rank decomposition is relatively straightforward to implement, it only reduces the number of parameters and computational complexity if the rank is reduced by more than half for feed forward layers. Additionally, not all layers of neural network types benefit equally from low-rank factorization. Moreover, this method does not reduce the size of output feature maps, which can cause significant memory overhead on mobile devices. In this part, we propose channel funnels, a straightforward method to reduce the number of channels at inference time, with negligible quality degradation. Intuitively, a channel funnel is placed between two affine layers, reducing the intermediate channel dimensionality to save computation. Consider two consecutive linear layers $y = W_{2}\sigma (W_{1}x)$ and the non-linear function $\sigma$ in between, where $W_{1} \in \mathbb{R}^{c_{\mathrm{inner}} \times c_{\mathrm{in}}}$ , $W_{2} \in \mathbb{R}^{c_{\mathrm{out}} \times c_{\mathrm{inner}}}$ . We introduce two funnel matrices, $F_{1} \in \mathbb{R}^{c' \times c_{\mathrm{inner}}}$ and $F_{2} \in \mathbb{R}^{c_{\mathrm{inner}} \times c'}$ , where $c' < c_{\mathrm{inner}}$ , and rewrite our network as $y' = W_{2}F_{2}\sigma (F_{1}W_{1}x)$ . The $F$ -weights, having fewer channels, can be merged during inference with their associated $W$ -weights, resulting a weight matrix with smaller inner dimension $c'$ , see Fig. 2. We refer to the reducing factor of the inner rank of the layers, i.e. $c'/c_{\mathrm{inner}}$ , as the fun-factor. + +Initialization. We propose to use coupled singular initialization (CSI) for funnel matrices $F_{1}$ and $F_{2}$ that improves the model results, as demonstrated below. In this method we make a simplifying assumption by ignoring the non-linearity, and consider the effective weight matrix $W_{2}F_{2}F_{1}W_{1}$ which in practice has rank of $c^{\prime}$ . For that reason, we aim to use such an initialization which mimics the best $c^{\prime}$ -rank approximation of the original effective matrix. As Eckart-Young-Mirsky theorem implies, this can be achieved by means of truncated singular decomposition [10]. Let $W_{2}W_{1} = U\Sigma V^{T}$ be the singular vector decomposition, and $U_{c^{\prime}}\Sigma_{c^{\prime}}V_{c^{\prime}}^{T}$ to be its truncated $c^{\prime}$ -rank version. Then it suffices to set $F_{2} = W_{2}^{\dagger}U_{c^{\prime}}\Sigma_{c^{\prime}}^{1 / 2}$ and $F_{1} = \Sigma_{c^{\prime}}^{1 / 2}V_{c^{\prime}}^{T}W_{1}^{\dagger}$ to obtain $W_{2}F_{2}F_{1}W_{1}\approx U_{c^{\prime}}\Sigma_{c^{\prime}}V_{c^{\prime}}^{T}$ , where $\dagger$ means the + +![](images/eb8244987e92b9b976fe78679688273a4f5a673162a5473f5cd5865744bd8cf8.jpg) +(a) Temporal blocks in the original architecture of SVD. + +![](images/b69b5ab12e38f5ffda40308ab75b73a2e7cea6884ce5ad49c307bd40c23fcbb5.jpg) +(b) A zero-one gate multiplier is sampled to each temporal block during training. + +Figure 3. Learned pruning of temporal blocks. (a) Each temporal block in the base SVD model is implemented as a residual block w.r.t. its input $x_{s}$ . The output of temporal layers $r_t$ is summed with the input $x_{s}$ , and after that once again averaged with $x_{s}$ with learnable weight $\alpha$ . By reordering the terms, we derive the effective update rule $\alpha x_{s} + (1 - \alpha)x_{t} = x_{s} + (1 - \alpha)r_{t}$ . (b) During training, we introduce a scalar gate $\hat{z} \in \{0,1\}$ to the residual update rule of each block. We learn importance values $\{q_i\}_i$ of temporal blocks which are transformed to inclusion probabilities $\{p_i\}_i$ at each training step. Zero-one gate multipliers are sampled according to those probabilities. To enable end-to-end training, we use straight-through estimator trick. At inference, only $n$ blocks with highest importance values are used. + +# Moore-Penrose pseudoinverse. + +Training. We apply channel funnels in attention layers where query and key embedding $W_{q}$ and $W_{k}$ are used to compute the similarity map of $XW_{q}(XW_{k})^{T}$ . With funnel matrices $F_{q}$ and $F_{k}$ of size $c_{\mathrm{inner}} \times c'$ , we modify the aforementioned bilinear map as $XW_{q}F_{q}(XW_{k}F_{k})^{T} = XW_{q}F_{q}F_{k}^{T}W_{k}^{T}X^{T}$ . Similarly, funnels are applied to the pair of value and output projection matrices of a self-attention layer. In our ablations we also show the impact of channel funnel on convolutions in residual blocks. Unless specified otherwise, we use fun-factor of 50%. + +# 3.4. Temporal block pruning + +Motivation. The original UNet in the SVD model does not contain 3D convolutions or full spatiotemporal attention layers. Instead, to model motion dynamics, SVD incorporates temporal blocks after each spatial block. The output of such group is a linear combination of the spatial and temporal block outputs, $x_{s}$ and $x_{t}$ respectively, $\alpha x_{s} + (1 - \alpha)x_{t}$ , + +![](images/2a74abee29bf532e7909bddd9332255428ecbc81b1fbfa582b487cf873846d8b.jpg) + +![](images/7033d3d16674b7260cab709b1e4360218868857ca37edadf53f4db86d076eea7.jpg) + +![](images/a0030ea5809bb54da05ecee9400c2f3ecb36d81dd54f14b3a0c2d5605f5a66b0.jpg) +Figure 4. Comparison with recent models. We provide the 1st, 6th, 10th and 14th frames from the videos generated with different models2. For animateLCM [62] and SF-V [72] we downsampled the released high-resolution videos from Zhang et al. [72]. For SVD [2] and our MobileVD model, videos were generated at their native resolution, $1024 \times 576$ and $512 \times 256$ respectively. + +![](images/d9fb6df02ef17b689f8b71f4cd0011f76eef17c368a715d3ea9d702df4c6ee66.jpg) + +![](images/e8063b17087bb1b4f232bae088f544d6bf00a3d3f1f47e0f2c7a657cfe2ba24a.jpg) + +![](images/fbc1c90dce5a0b6563195400b80dc74f886b4c55a4d53b503e4ac68857f348a6.jpg) + +where $\alpha$ is a weight scalar that emphasizes spatial features when higher and temporal features when lower, see Fig. 3a. While this approach leverages image model priors when extending the model to videos, it adds computational cost. Moreover, not all of these blocks are equally important for maintaining quality. Here, we propose a learnable pruning technique to remove less important temporal blocks while minimizing quality degradation. To this end, for each temporal block we define an importance value $q_{i}$ , $0 \leq q_{i} \leq 1$ where $i = 1, \ldots, N$ and $N$ is number of temporal blocks. The values $\{q_{i}\}_{i}$ are trained to identify the blocks that are the most crucial for model performance. At inference time, only $n$ blocks with the highest importance $q_{i}$ are kept where $n$ is the budget chosen in advance. In our experiments we + +found it possible to remove as many as $70\%$ of all temporal blocks which leads to $14\%$ reduction in FLOPS as compared to the model with optimizations from Sec. 3.2 applied. + +Training. At each training iteration, we sample randomly $n$ blocks which participate in the computational graph. To this end, we define the indicator variable $z_{i} \in \{0,1\}$ where $z_{i} = 1$ if $i$ -th block is sampled for participation, and $z_{i} = 0$ otherwise. The sum of all participants should equal to the budget value i.e. $\sum_{i} z_{i} = n$ . Note that $\mathbb{E}\left[\sum_{i} z_{i}\right] = \sum_{i} \mathbb{E}\left[z_{i}\right] = \sum_{i} p_{i} = n$ , where $p_{i}$ is the inclusion probability of the $i$ -th block. We relate $i$ -th importance value $q_{i}$ to the inclusion probability of $p_{i}$ using the constrained optimization problem + +$$ +\min _ {c, \{p _ {i} \} _ {i}} \sum_ {i} (p _ {i} - c q _ {i}) ^ {2}, \quad \mathrm {s . t .} \quad \sum_ {i} p _ {i} = n, 0 \leq p _ {i} \leq 1, c \geq 0. +$$ + +We obtain a closed-form solution of the above optimization with Lagrange multipliers which is differentiable w.r.t. $q_{i}$ . In simple words, we find the proper set of inclusion probabilities $p_{i} \approx c q_{i}$ , with importance values $q_{i}$ and a proportionality coefficient $c$ . After obtaining $\{p_i\}_i$ at each training iteration, we sample $n$ blocks without replacement using Brewer's sampling [4, 60]. As such sampling is non-differentiable, we employ straight-through estimators (STE) [1] to enable end-to-end training. Namely, we define gate $\hat{z}_{i}$ as STE of the probability $p_{i}$ , i.e. $\hat{z}_{i} = p_{i} + \text{stop-gradient}(z_{i} - p_{i})$ . The output of a temporal block is multiplied by this gate as Fig. 3b shows. For practical aspects of training, please refer to SM. + +# 4. Experiments + +In this section, we describe our experimental setup, followed by a qualitative and quantitative evaluation of our model. Finally, we present ablations to justify our choices for the final model deployed on the device. + +# 4.1. Implementation details + +Dataset. For our experiments, we use a collected video dataset. We follow the data curation pipeline from OpenSora [74, V.1.1], selecting videos with motion scores between 4 and 40, and aesthetic scores of at least 4.2. This results in a curated dataset of approximately 31k video files for finetuning. + +Micro-conditioning. UNet used by SVD, has two conditioning parameters called FPS and Motion bucket id. To obtain videos with different FPS, we chose each $k$ -th frame from the video with randomly sampled $k$ , $1 \leq k \leq 4$ , and adjusted the native FPS value of the video accordingly. The notion of motion bucket has not been properly documented at time of the model release. While it is connected with the speed of motion in the video, as described in the original SVD paper, the motion estimator has not been open-sourced. For that reason, we implemented our own definition of the motion bucket using a simple heuristic. For the sampled chunk of 14 frames, we converted them to gray color, spatially downsampled to the resolution of $14 \times 128 \times 64$ , and reshaped to the matrix of size $14 \times (128 \cdot 64)$ . After that, we computed the singular values of that matrix. Note that for a completely static video this matrix has a rank of 1, and therefore the only non-zero singular value. And the less similar frames are, the more singular components are needed to faithfully reconstruct the full video. Based on that observation, we re-defined the motion bucket as the area under the normalized cumulative sum of singular values. + +Training. For training, we begin with the original SVD + +weights, apply all the optimizations (excluding temporal block pruning), and train the resulting UNet with a standard diffusion loss for 100k iterations on 4 A100 GPUs with a total batch size of 8. This UNet serves as the initialization for adversarial finetuning, where a good initialization is crucial for fast convergence. We found that training for 5k iterations on 2 GPUs suffices for the second stage. We implement temporal block pruning in the second stage as we observed that excessive pruning in the first stage hinders model performance. In this case, we train the second stage for 10k steps. Check SM for more details. + +Metrics. We used DeepSpeed library [51, v0.14.2] to measure the number of FLOPs. For GPU latency, NVIDIA® A100 SXM™ 80GB GPU was used. To measure GPU latency, UNet model was compiled using the PyTorch [47, v2.0.1] compiler with default settings. Phone latencies are measured on a Xiaomi-14 Pro that uses Snapdragon® 8 Gen. 3 Mobile Platform with a Qualcomm® Hexagon™ processor. All performance metrics were measured for a single UNet evaluation with batch size of 1. For video quality metric, we follow existing works [2, 72] by using Fréchet Video Distance (FVD) [61] with I3D feature extractor [29]. We use the first frame of UCF-101 dataset [59] as the conditioning image, generating 14-frame clips at the model's native resolution. Unless stated otherwise, we set the FPS, an SVD micro-condition, to 25, matching the UCF-101 frame rate [2]. For motion bucket, for our models we used the median value at the specified frame rate across UCF-101 data. For SVD the default bucket of 127 was used. In addition, we evaluated our model using the recent VBench-I2V toolkit [23, 24]. For that purpose, we generated videos with different speeds to demonstrate the trade-off between motion degree and frame-wise plausibility. + +# 4.2. Results + +MobileVD. In Tab. 2 we compare MobileVD to the baseline model. As the results indicate, each optimization reduces speed of inference on a mobile phone. Optimized cross-attention unlocks on-device execution with a latency of 3.6 seconds. More specifically, temporal downsampling layers in UNet make inference $29\%$ faster. Additionally, temporal blocks pruning reduces phone latency by $13\%$ , and channel funneling further decreases it by $9\%$ . Empirically, we found that a difference of up to 20 FVD units does not significantly affect visual quality and typically falls within the standard deviation when using different random seeds. Based on that, we see that our optimizations reduce on-device inference by $50\%$ while having minimal impact on FVD. As Tab. 3 shows, by changing the motion bucket, we can generate videos with the same dynamic degree as original SVD model. + +SOTA comparison. In Tab. 1 we compare to the recent works that similarly aim for accelerating SVD image-to-video model, namely, AnimateLCM [62], LADD [54], SF- + +
ModelNFEFVD ↓TFLOPs ↓Latency (ms) ↓
25 FPS7 FPSGPUPhone
SVD (finetuned for 512 × 256)501941968.6082OOM
+ optimized cross-attention501941968.24763630
+ adversarial finetuning11331688.24763630
+ temporal multiscaling11391565.42592590
+ temporal block pruning11271504.64472100
+ channel funneling11491714.34451780
+ +Table 2. Effect of our optimizations. We successfully deployed the image-to-video model to a mobile device without significantly sacrificing the visual quality. FLOPs and latency are provided for a single function evaluation with batch size of 1. We call the model in the bottom row Mobile Video Diffusion, or MobileVD. + +
ModelMotion bucketI2V SubjectI2V BackgroundAesth. QualityImag. QualityDynamic Degree
SVD (original)12793.4894.7453.5963.4995.69
SVD (finetuned)2095.7296.3654.9165.1716.26
SVD (finetuned)4095.2496.0454.6265.1665.04
MobileVD2093.6894.3053.6967.1668.21
MobileVD4092.9893.9353.1967.4695.77
+ +V [72], and UFOGen [67]. As all these methods operate on $1024 \times 576$ resolution, for a fair comparison, we also trained a high-resolution version of our model called MobileVDHD. It uses the whole set of our proposed optimizations, and training details are provided in Supplementary. For lower resolution, we observe that MobileVD leads to a comparable FVD to SVD and SF-V but requires significantly less computation. + +Qualitative results. Following previous works [62, 72], we show qualitative results with a commonly used set of conditioning images. Sampled frames from the generated videos are presented in Fig. 4. For this visualization, we generated videos at 7 FPS and with spatial resolution of $512 \times 256$ using our MobileVD. Please refer to the Supplementary for the full videos. We observe that in general our method produces videos with sharp details and consistent motion. + +# 4.3. Ablations + +In this section, we evaluate our design choices through ablation experiments. Unless otherwise specified, we use the SVD checkpoint with low-resolution input, optimized cross-attention, and adversarial finetuning as the reference model, cf. Tab. 2. + +# 4.3.1. Resolution impact in UNet + +In Tab. 4 we compare different latent multiscaling optimizations proposed in Sec. 3.2. Specifically, we investigate the impact of inserting spatial or temporal multiscaling layers after the first UNet block in terms of FLOPs, latency, and FVD. Spatial multiscaling offers better FLOPs and latency than temporal multiscaling and it increases FVD by 12 units + +Table 3. VBenchmark-12V evaluation. By varying the motion bucket, we can generate videos with different dynamic degree. Faster videos generally have slightly worse visual quality, as framewise metrics show. + +
Spatial multiscalingTemporal multiscalingFVD ↓TFLOPs ↓Latency (ms) ↓
GPUPhone
××1338.24763630
×✓1385.42592590
✓×1454.35512280
✓✓1633.3948—
+ +Table 4. Effect of additional multiscaling layers in UNet. We observe that both temporal and spatial multiscaling has good impact on mobile latency without compromising much on FVD, while combining the two increases FVD by a noticeable amount. + +compared to 5 for temporal downsampling. While we typically do not see video degradation with this increase in FVD, we do see clear degradation in video quality when using spatial instead of temporal multiscaling. We hypothesize that this is because the model already enjoys multiple stages of spatial downsampling, while temporal downsampling was originally absent. Based on these results, we have opted for temporal downsampling for our mobile-deployed model. We hold similar conclusions for combining the two multiscaling approaches with spatiotemporal multiscaling. + +# 4.3.2. Funnel finetuning + +Fun-factor and funnel initialization. Reducing the width of affine layers in the model is a form of lossy compression, and overly aggressive fun-factor values will hurt the model performance. In Tab. 5, we observe the impact of the fun-factor. Reducing the fun-factor to 0.25 results in a performance loss of 22 FVD units compared to fun-factor of 1 (i.e., no compression). To avoid performance degradation from stacking multiple optimizations described in Sec. 3, we set the fun-factor to 0.5 for the deployed model. Additionally, the results highlight that the proposed coupled singular initialization (CSI) is essential for optimal funnel behavior, whereas the standard He initialization [18] is suboptimal. + +Funnel merging and low-rank layers. We compare channel funnels with multiple baselines in terms of FLOPs, on-device latency and FVD. All baselines are applied on the same attention layers, unless specified otherwise. The first baseline uses channel funnels but merges funnel and weight matrices during training, hence mimicking behavior at inference time as shown in Fig. 2. We report in Tab. 6 that keeping + +
InitializationFun-factorFVD ↓
Coupled singular init. (CSI)0.25155
Coupled singular init. (CSI)0.50132
Coupled singular init. (CSI)0.75145
Coupled singular init. (CSI)1.00133
He init. [18]0.50332
+ +Table 5. Effect of funnel initialization and fun-factor. Initialization funnels with CSI is crucial to getting good FVD as He initialization [18] obtains roughly 200 FVD units more. Additionally, we see that reducing the fun-factor beyond 0.5 starts to affect the performance. + +
Width reduction methodrFVD ↓TFLOPs ↓Latency (ms) ↓
Original UNet-1338.63630
+ Funnels0.51328.02870
+ Funnels (merge before finetune)0.51388.02870
+ Funnels (convolutions)0.51397.23400
+ Truncated singular decomposition0.51428.63482
+ Truncated singular decomposition0.251308.03345
+ +funnel and weight matrices separate at training performs equally well. The second baseline is applying funnels to convolutions in ResNet blocks instead of attention layers. While we obtain favourable FVD and even greater gain in TFLOPs (7.2 vs 8.6), it does not translate to the latency reduction we see with funnels on attention (3.40 vs 2.87 seconds). We hypothesize that the attention layers play a greater role in reducing latency on device than convolutions for this model. The last baselines employ the standard technique of truncated singular decomposition of individual layers [70]. This decomposition breaks down a weight matrix of a linear layer $W \in \mathbb{R}^{C_{\mathrm{out}} \times c_{\mathrm{in}}}$ into a low-rank product of two matrices $W_1 \in \mathbb{R}^{rC \times C_{\mathrm{in}}}$ and $W_2 \in \mathbb{R}^{C_{\mathrm{out}} \times rC}$ where $r$ is the rank reduction factor, $r < 1$ , and $c = \min(c_{\mathrm{in}}, c_{\mathrm{out}})$ . Note that reduction in the number of parameters and FLOPs is achieved only if $r < 0.5$ , while the size of the feature map after these two matrices remain intact in this approach. While truncated decomposition after finetuning performs well in terms of FVD for both $r = 0.25$ and $r = 0.5$ , it is slower on device compared to channel tunneling (3.35 and 3.48 vs. 2.87 seconds respectively). This difference is attributed to memory transfer overhead from introducing additional layers as well as not decreasing the original feature size, emphasizing the benefit of funnels. + +# 4.3.3. Temporal blocks pruning + +As mentioned in Sec. 3.4, in our experiments we found it possible to reduce up to $70\%$ of all temporal blocks in the UNet. Notably, even with such a high pruning rate the quality is comparable to the original model: it achieves FVD of 127 and requires $14\%$ less FLOPs, while the original model has + +Table 6. Comparison of model width reduction methods. We compare the proposed channel funneling (in grey) with finetuned low-rank approximation of individual attention layers with truncated singular decomposition. We additionally compare to Funnels applied to convolutions instead of attention. The reduction rate (referred to as fun-factor in case of funnels) is highlighted with $r$ . + +
Blocks pruned (%)FVD ↓TFLOPs ↓Latency GPU (ms) ↓
Our method
902014.0642
802454.3544
701274.6447
L1 regularization
702074.6748
531655.1752
+ +Table 7. Impact of temporal blocks pruning. Our pruning outperforms the $L_{1}$ - regularization which does not have explicit control over the number of removed blocks. We use the checkpoint, optimized up to the temporal block pruning stage, as the starting point. + +FVD of 139. However, pruning even further seems far from straightforward. FVD degrades to the values above 200 with a pruning rate of $80\%$ , and visual quality drops drastically. + +Additionally, we compare our method with another pruning baseline. As described in Sec. 3.4, the output of a spatiotemporal block in SVD is a linear combination of the spatial and temporal blocks $x_{s}$ and $x_{t}$ , respectively, $\alpha x_{s} + (1 - \alpha)x_{t}$ , where $\alpha$ is a weight scalar. The baseline aims to minimize the influence of temporal blocks, by adding a loss term during finetuning: $\mathcal{L} = \lambda \sum_{i} (1 - \alpha_{i})$ . After training, blocks with the highest weight scalar $\alpha_{i}$ are pruned. However, this method lacks explicit control over the desired pruning rate, as only weight hyperparameter $\lambda$ can be adjusted. While effective for small pruning rates, this approach did not allow us to remove as many blocks as our method, achieving only a $7\%$ reduction in FLOPs with acceptable FVD level, see Tab. 7. + +# 5. Conclusion + +This paper introduced the first mobile-optimized image-to-video diffusion model, addressing the high computational demands that have limited their use on mobile devices. By optimizing the spatio-temporal UNet from Stable Video Diffusion and employing novel pruning techniques, we significantly reduced memory and computational requirements. Our model, MobileVD, achieves substantial efficiency improvements with minimal quality loss, making video diffusion technology feasible for mobile platforms. + +Limitations. Despite the impressive acceleration, the output is currently limited to 14 frames at a resolution of $256 \times 512$ pixels. The next step involves leveraging more efficient autoencoders to achieve higher spatial and temporal compression rates, enabling the generation of larger and longer videos at the same diffusion latent generation cost. Also, our model inherits the lack of textual control from the released SVD version, which had been finetuned by its authors from a text-to-video to an image-to-video model. We plain to solve this in future either by reverse finetuning, or by switching to another pretrained backbone. + +# References + +[1] Yoshua Bengio, Nicholas Léonard, and Aaron Courville. Estimating or propagating gradients through stochastic neurons for conditional computation, 2013. 6 +[2] Andreas Blattmann, Tim Dockhorn, Sumith Kulal, Daniel Mendelevitch, Maciej Kilian, Dominik Lorenz, Yam Levi, Zion English, Vikram Voleti, Adam Letts, Varun Jampani, and Robin Rombach. 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However, deploying deep learning models on resource-constrained platforms, such as mobile devices, remains challenging due to high computation and memory demands. To address these challenges and facilitate real-time IE on mobile, we introduce an extremely lightweight Convolutional Neural Network (CNN) framework with around 4K parameters. Our approach integrates reparameterization with an Incremental Weight Optimization strategy to ensure efficiency. Additionally, we enhance performance with a Feature Self-Transform module and a Hierarchical Dual-Path Attention mechanism, optimized with a Local Variance-Weighted loss. With this efficient framework, we are the first to achieve real-time IE inference at up to 1,100 frames per second (FPS) while delivering competitive image quality, achieving the best trade-off between speed and performance across multiple IE tasks. The code will be available at https://github.com/AVC2-UESTC/MobileIE.git. + +# 1. Introduction + +Image enhancement (IE) aims to restore images degraded by factors such as camera limitations [86], poor lighting [48], or challenging environments (e.g., underwater [55]). With the growing prevalence of smart devices and embedded systems, real-time image enhancement has become essential in applications like mobile devices. These scenarios require not only high-quality output but also real-time processing, demanding efficient image enhancement within the constraints of limited computational resources [9, 16-18]. + +Recent advancements in Transformer-based [14, 42, 69] and Diffusion-based [79, 84, 96] methods have demonstrated significant progress in image enhancement (IE) tasks. However, their reliance on computationally expensive self-attention mechanisms and iterative diffusion pro + +![](images/08f3f155ebc2fe8157d658b771caab9a29fb1577cee8d91052e0cc30f67c293a.jpg) +Figure 1. Efficiency comparison. MobileIE achieves superior performance in balancing speed, compactness, and accuracy. + +cesses makes them unsuitable for mobile devices. While lightweight models have been developed to reduce computational complexity using parameter compression and lowFLOPs architecture designs [57, 59, 63, 80, 83], these approaches often compromise enhancement quality, making it challenging to achieve high performance across a wide range of degradation scenarios [1]. Furthermore, the increasing demand for high-resolution images [69] exacerbates the computational burdens on mobile platforms. + +Besides facing computational bottlenecks, current IE methods are typically optimized for specific degradation types, restricting their adaptability. Although advanced operators [10, 11] have shown effectiveness in certain tasks, their complexity makes them unsuitable for mobile deployment. Consequently, designing a universal and efficient network capable of real-time IE on resource-constrained devices remains a significant research challenge. + +We believe that mobile-based IE should strike a balance between speed and performance, leveraging general architectures and hardware-friendly operators [66, 88]. To address these challenges, we introduce MobileIE, an efficient method designed for real-time enhancement in resource-constrained environments, optimizing both performance and resource utilization. Although degradation types vary widely, IE tasks share common requirements: global information for structural integrity and local details for accurate + +recovery. This commonality enables the use of universal modules across different tasks. + +Building on this concept, MobileIE employs a streamlined topology and deployable operators to achieve efficient performance on resource-constrained devices. We decouple the training and inference phases, simplifying the feedforward structure for more efficient inference. At the core of our design is MBRCov, a Multi-Branch Reparameterized Convolution, which captures multi-scale features using various convolution sizes. These features are then processed through concatenation, compression, and mapping to achieve the desired output dimensions. Additionally, we introduce a Feature Self-Transform (FST) module, which enhances the feature representation capability of linear convolutions by capturing nonlinear relationships through secondary feature interactions. + +To enhance focus on critical regions, we simplify the attention mechanism and develop a hardware-friendly Hierarchical Dual-Path Attention (HDPA) mechanism, which efficiently fuses global and local features. To overcome training bottlenecks, we introduce an Incremental Weight Optimization (IWO) Strategy and a Local Variance Weighted (LVW) Loss function. The IWO strategy freezes prior knowledge, integrates it into trainable convolutional kernels, and re-parameterizes these into new kernels to boost model performance. Meanwhile, the LVW Loss function enhances accuracy without increasing the number of parameters. Key contributions of this paper include: + +- We introduce MobileIE, a framework designed for real-time image enhancement on mobile devices, featuring compact and efficient modules tailored for resource-constrained environments. +- We propose an Incremental Weight Optimization (IWO) Strategy and a Local Variance Weighted (LVW) Loss to address the challenges of training compact models, enhancing performance without adding complexity. +- We demonstrate that MobileIE achieves state-of-the-art speed and performance across three image enhancement tasks, sustaining over 100 FPS and enabling seamless deployment on mobile devices. + +# 2. Related Works + +# 2.1. Low-Level Vision Tasks + +This section covers three key tasks: Low-Light Enhancement (LLE), Underwater Image Enhancement (UIE), and end-to-end Image Signal Processing (ISP). + +LLE. LLE focuses on mitigating color distortion and noise in degraded images. Retinex-based [5, 46, 78, 81, 85] enhance images by separating illumination and reflectance. Zero-DCE [28] adjusts underexposed images using a luminance enhancement curve, and PairLIE [26] learns enhancement from varying lighting conditions. Transformer + +based [5, 71, 76] and Mamba-based [93] methods have also achieved notable success, while Diffusion-based [39, 85] methods excel at generating accurate images in extremely low-light conditions, even with noise and limited data. + +UIE. Compared to traditional UIE methods [24, 101], CNN-based [38, 52, 53, 61] directly learn feature representations from underwater images. Five $\mathrm{A + }$ [40] proposed a two-stage framework with a pixel attention module for real-time enhancement. Transformer-based [41, 55] and Mamba-based [2, 12] models more effectively handle complex underwater scenes with their global receptive fields. Additionally, Diffusion-based [65, 96] approaches reduce noise and enhance contrast efficiently. + +ISP. Learning-based ISP pipelines replace traditional multi-module systems by employing end-to-end models that directly process RAW input into RGB images. PyNet [35] focuses on mobile ISPs, while MW-ISP [34] and AWNet [20] improve performance using wavelet transforms. LiteISP [95] resolves misalignment between RAW and sRGB images, achieving better results through joint learning. Rawformer [56] eliminates the need for paired datasets with an unsupervised Transformer, and DiffRAW [84] introduces diffusion models into ISP. Several ISP challenge works [34, 36, 37] have also produced notable results. + +# 2.2. Efficient Architectures Design + +Efficient neural networks aim to balance computational complexity and performance. Models like MobileNet [32] and ShuffleNet [91] achieve high performance with fewer FLOPs, while GhostNet [29] and FasterNet [8] generate feature maps through cost-effective operations. StarNet [51] excels in extracting rich representations with star-shaped operations, and VanillaNet [7] demonstrates minimalism's power using only a few convolutions. + +Furthermore, re-parameterization strategies have also proven successful in efficient network design. Models like ACNet [21], DBB [22], and RepVGG [23] use multi-branch topologies to accelerate inference, while RepGhost [23], RepViT [68], and MobileOne [66] adopt similar approaches to enhance performance. Several NTIRE challenge submissions [15, 45, 60] have utilized re-parameterized structures to accelerate inference in efficient IE tasks. + +# 3. Proposed Method + +# 3.1. Overall Pipeline + +We aim to design an efficient IE model that balances parameters, speed, and performance. Following the simplicity principle [88], we adopted a streamlined topology based on basic operations, illustrated in Figure 2. + +The proposed MobileIE, built on Re-parameterization, integrates four key components: shallow feature extraction, deep feature extraction, feature transform, and an attenuated feature extraction. + +![](images/fe6476b3506c06e4a459d5d3395db6a1e9fd10ce61a9530bef883211e51b813f.jpg) +Figure 2. Architecture of the proposed MobileIE includes Multi-Branch Re-param Convolution (MBRConv), Feature Self-Transform (FST), and Hierarchical Dual-Path Attention (HDPA). During inference, MBRConv re-parameterizes into a standard convolution, reducing the model size to 4K parameters while maintaining training performance. The detailed architecture settings are provided in the Appendix. + +tion mechanism. During training, the degraded image first passes through MBRCov5 $\times 5$ and the PReLU activation function to extract shallow features. Two MBRCov3 $\times 3$ and FST modules then process these to learn deeper features. The HDPA mechanism directs the model's focus to important regions, and MBRCov3 $\times 3$ refines the output. To address training performance bottlenecks, we introduce the IWO strategy and LVW loss function. + +In inference, all MBRCov layers are re-parameterized into standard convolutions, reducing parameters while maintaining performance. MobileIE's streamlined structure ensures fast inference and easy deployment on mobile devices. Despite its simplicity, MobileIE surpasses SOTA lightweight IE models, as shown in Figure 1. + +# 3.2. Multi-Branch Re-param Convolution + +Re-parameterization has achieved success in high-level vision tasks [21-23], but yields unsatisfactory results when directly applied to image enhancement [27]. We introduce MBRCConv, specifically designed for image enhancement. + +Figure 3(a) shows MBRConv with multiple convolutional branches of varying kernel sizes, capturing multiscale features that are concatenated and integrated via a Conv $1 \times 1$ ( $conv_{out}$ ). The branches are re-parameterized during inference into a single convolution, reducing computational cost while preserving training performance. Unlike previous Rep methods, MBRConv includes parallel Batch + +Norm (BN) layers in each branch. Although BN is less effective for IE tasks [74, 92], it enhances nonlinearity and cannot be replaced by other activations due to its unique ability to merge into a single convolution. The parallel BN layers retain both smoothed and original features, improving robustness across diverse data distributions. Additional details on MBRCov can be found in the Appendix. + +![](images/4ff0b94bbd8c6cc08b4902cd2547fc7283396442125f97629fe92a96fadd604f.jpg) +Figure 3. Structural of MBRCConv $3 \times 3$ . + +Although multi-branch topologies assist in feature extraction, compact networks still struggle to learn complex features, leading to stagnation in later training stages. Adjusting training hyperparameters often results in marginal improvements. To address this, we propose the Incremental Weight Optimization (IWO) strategy, which combines learnable weights with prior knowledge to enhance the in + +tegration performance of the convout by better capturing relationships between features across layers in MBRCov. + +As shown in Figure 3(b), IWO combines two weight components: frozen weights, $W_{pre}$ , from prior training, and learnable weights, $W_{learn}$ . These are fused as: + +$$ +W _ {\text {f i n a l}} = \operatorname {F r o z e n} \left(W _ {\text {p r e}}\right) + W _ {\text {l e a r n}}, \tag {1} +$$ + +where $W_{pre}$ is the optimal weight from earlier training and remains frozen, and $W_{learn}$ is dynamically updated during subsequent training. The final weight, $W_{final}$ , is applied to the concatenated feature map: + +$$ +y _ {o u t} = F _ {\text {c o n v 1} \times 1} \left(x _ {\text {c o n c a t}}; W _ {\text {f i n a l}}\right) + b _ {\text {c o n v} _ {\text {o u t}}}, \tag {2} +$$ + +where $x_{\text{concat}}$ denotes the concatenated multi-branch features, $F_{\text{conv}}$ represents the convolution. $y_{\text{out}}$ and $b_{\text{conv}_{\text{out}}}$ represent the output feature map and the bias, respectively. $W_{\text{pre}}$ offers a stable initial feature representation, minimizing redundancy. $W_{\text{learn}}$ refines these features, improving task-specific detail capture. IWO combines prior knowledge with learnable parameters, balancing knowledge transfer and feature refinement to improve feature integration. + +# 3.3. Feature Self-Transform + +While MBRConv captures multi-scale features, its linear operations restrict higher-order feature interactions. To address this, we introduce FST, which employs a quadratic interaction mechanism [51] to boost the model's nonlinear expressiveness. In FST, the input features are element-wise multiplied by themselves, scaled by a learnable parameter, Scale, and adjusted by a learnable bias term. + +$$ +\operatorname {F S T} (x) = \operatorname {S c a l e} \cdot (x * x) + \text {b i a s}. \tag {3} +$$ + +This quadratic interaction captures more complex relationships between features, unlike traditional linear combinations. A learnable bias term is also applied channel-wise to fine-tune the output further. FST significantly improves feature representation by capturing higher-order interactions, while the learnable bias enhances adaptability across dimensions. This design balances improved expressiveness with computational efficiency, making FST suitable for lightweight models and real-time inference. + +# 3.4. Hierarchical Dual-Path Attention + +We propose a simple HDPA mechanism to improve feature extraction in IE. HDPA selectively captures both global and local features, integrating spatial and channel interactions to improve feature precision and comprehensiveness. Its dual-path structure optimizes feature selection at each layer through two distinct pathways. HDPA operates in two steps: + +(1) Global Feature Extraction: Global statistics are extracted using adaptive average pooling. Global features are + +processed by an MBRCConv1x1 layer, and Sigmoid activation to generate channel-wise attention weights, modulating the importance of each channel. This step is expressed as: + +$$ +A _ {g} = \operatorname {S i g m o i d} (\operatorname {M B R C o n v} 1 \times 1 (\operatorname {A v g P o o l} (F))), \quad (4) +$$ + +where $A_{g}$ denotes the global attention weights, and $F$ represents the input features. + +(2) Local Feature Enhancement: In the second pathway, local features are extracted using max pooling on globally enhanced features. The input is multiplied by the global weights $W_{g} = F * A_{g}$ , followed by max pooling to capture local information. The local responses are processed by an MBRCov1 × 1, with Sigmoid activation generating the local attention weights. + +$$ +A _ {l} = \operatorname {S i g m o i d} (\operatorname {M B R C o n v} 1 \times 1 (\operatorname {M a x P o o l} (W _ {g}))), \tag {5} +$$ + +where $A_{l}$ represents the local attention weights. + +Finally, the global and local attention weights are combined through element-wise multiplication to produce the final attention feature, which is applied to the input features: + +$$ +\hat {F} = \operatorname {H D P A} (F) = \left(A _ {g} * A _ {l}\right) * F, \tag {6} +$$ + +where $\hat{F}$ donates the output feature after HDPA processing. + +This dual-path hierarchical design balances global context and local feature enhancement, improving both depth and accuracy in feature extraction. Its simplicity reduces the computational cost, making it well-suited for resource-constrained environments. + +# 3.5. Local Variance Weighted Loss + +Compact CNNs, with limited parameters, struggle to capture rich features and are sensitive to extreme pixels that hinder optimization [1, 27]. While $L1$ loss is robust, its equal weighting limits outlier handling; $L2$ emphasizes outliers but may cause imbalance. To address this, we introduce Local Variance Weighted Loss (LVW), which adapts to local variability and mitigates outliers effectively. + +![](images/6668432817441e99e122c442ca759ceadb57ee78b732d05c5945b2d7f4c29a95.jpg) +(a) + +![](images/e50a8d998ddd1d205d67cbda4f24cb765917502e5fce6ce1a4b81ff26705dc64.jpg) +(b) +Figure 4. (a) Effect of Batch Norm on Data Distribution. (b) Comparison of Loss Functions for Pixel Difference Handling. + +Let $\{\mathbf{O},\mathbf{L}\} \in \mathbb{R}^{B\times C\times H\times W}$ denote the predicted output and ground-truth, where $B,C,H$ ,and $W$ denote batch + +
MethodVenue#Params↓(K)Model Size↓(MB)Latency↓(GPU,ms)Latency↓(SoC,ms)FPS↑(600×400)LOLv1 [75]LOLv2-Real [82]
PSNR↑SSIM↑LPIPS↓SCORE↑PSNR↑SSIM↑LPIPS↓SCORE↑
Kind++ [94]IICV'218,280/>500>500<1017.750.7660.198<0.00117.660.7700.217<0.001
DDNet [58]IEEE TITS'245,38920.5632.910>50030.79221.820.8020.1860.20823.020.8380.1731.099
PairLIE [26]CVPR'23341.7671.3011.580>50086.35419.510.7360.2480.02419.880.7780.2340.040
IAT [19]BMVC'2286.8560.336.204202.33161.18623.380.8080.2169.60425.460.8430.182171.690
Zero-DCE [28]CVPR'2079.4160.302.53982.94393.91014.860.5590.335<0.00118.060.5740.3130.015
3DLUT [87]IEEE TPAMI'20593.5002.261.176/850.34017.590.7210.2320.21819.680.6370.2246.000
Zero-DCE++ [44]IEEE TPAMI'2110.5610.041.97457.91506.55814.680.4720.340<0.00117.230.4120.3190.006
SCI [50]CVPR'2210.6710.044.773116.8209.52514.900.5310.341<0.00117.300.5340.3080.003
SGZ [98]WACV'2210.5610.041.97059.27507.66215.280.4730.339<0.00117.340.4090.3220.007
RUAS [46]CVPR'213.4380.014.421109.15226.17516.400.5000.270<0.00115.330.4880.310<0.001
SYELLE [27]ICCV'235.2590.020.9447.731059.73221.030.7940.2192.42821.260.8010.3083.340
Adv-LIE [72]MMM'24238.5600.9114.269>50070.08323.020.8080.2032.53521.950.8440.1920.575
Ours/4.0470.020.8956.721120.58423.620.8120.19892.85525.080.8450.180702.767
+ +Table 1. Performance comparison of different low-light image enhancement models on LOL datasets. SCORE [37] represents a comprehensive measure of model performance and efficiency. The top results are marked: best in red and second in blue. + +size, number of channels, height, and width of the image, respectively. The absolute difference between the predicted output and the ground truth at pixel $(m,n)$ is calculated as: + +$$ +\Delta_ {m, n} = \left\| O _ {m, n} - L _ {m, n} \right\| _ {1}. \tag {7} +$$ + +For each predicted output, we calculate the local mean $\mu_{m,n}$ and variance $\sigma_{m,n}^2$ of $\Delta_{m,n}$ across the spatial dimensions $H$ and $W$ . This can be expressed as follows: + +$$ +\left\{ \begin{array}{l} \mu_ {m, n} = \frac {1}{H \cdot W} \left(\sum_ {m = 1} ^ {H} \sum_ {n = 1} ^ {W} \Delta_ {m, n}\right) \\ \sigma_ {m, n} ^ {2} = \frac {1}{H \cdot W} \left(\sum_ {m = 1} ^ {H} \sum_ {n = 1} ^ {W} \Delta_ {m, n} - \mu_ {m, n}\right) ^ {2} \end{array} \right. \tag {8} +$$ + +To demonstrate the impact of mean and variance on outliers, we applied BN to simulated data with both normal values and outliers (Figure 4(a)). BN balances sample contributions to mean and variance, reducing outliers' influence on the distribution. Based on these local statistics, we compute a weighted factor for each pixel. The weight $W_{\Delta}$ , is normalized by the absolute deviation of the error relative to the local mean and scaled according to the local variance: + +$$ +W _ {\Delta} = \operatorname {T a n h} \left(\frac {\left| \Delta_ {m , n} - \mu_ {m , n} \right|}{\sigma_ {m , n} + \varepsilon}\right), \tag {9} +$$ + +where $\varepsilon$ is a small constant added to prevent division by zero. The Tanh function is applied to ensure the weights remain within a bounded range, facilitating a smooth transition between high-variance and low-variance regions. + +The final loss is calculated by multiplying $\Delta_{m,n}$ with the corresponding local weighted factor: + +$$ +\mathcal {L} _ {L V W} = \frac {1}{H \cdot W} \sum_ {m = 1} ^ {H} \sum_ {n = 1} ^ {W} \left(W _ {\Delta} \cdot \Delta_ {m, n}\right). \tag {10} +$$ + +$\mathcal{L}_{LVW}$ dynamically adjusts each pixel's contribution to the overall loss based on locally computed weights, thereby placing greater emphasis on optimizing anomalous pixels. + +Figure 4(b) illustrates how different loss functions handle pixel differences, emphasizing their handling of prediction errors. $\mathcal{L}_{LVW}$ avoids the steep increase of $L2$ loss for large errors, reducing sensitivity to extreme pixels while preserving enough gradient response for small errors, balancing robustness and detail preservation. + +# 4. Experiments + +# 4.1. Experimental Settings + +Implementation Details. We implemented MobileIE in PyTorch. The model uses the Adam optimizer with a cosine annealing learning rate schedule, starting at 0.001. The learning rate is reset every 50 epochs with gradual decay. A 10-epoch warm-up phase [30] is applied with a fixed learning rate of 1e-6. The model is trained for 2,000 epochs, incorporating an Incremental Weight Optimization Strategy for improved convergence. For the ISP task, input data is preprocessed into a $256 \times 256$ Bayer pattern. + +Dataset and Metrics. For LLE task, the LOLv1 [75] and LOLv2 [82] datasets are used for both training and testing. For UIE and ISP tasks, the UIEB [43] and ZRR [35] datasets are utilized, respectively. + +# 4.2. Quantitative and Visual Comparisons + +In this section, we compare the proposed MobileIE with current lightweight SOTA methods across three IE tasks, focusing on visual comparisons and performance metrics. Specifically, PSNR, SSIM, LPIPS, and SCORE [37] are used as evaluation metrics, while computational complexity is tested on a single NVIDIA 4090 (GPU) and a smartphone with a Snapdragon 8 Gen 3 System on Chip (SoC). + +LLE: The quantitative results on the LOLv1 [75] and LOLv2 [82] datasets are presented in Table 1. MobileIE achieves superior or comparable PSNR and SSIM scores across all metrics, with an inference speed of $0.895\mathrm{ms}$ . Compared to the lightweight SOTA method IAT [19], MobileIE delivers comparable PSNR gains while using only $4.7\%$ of the parameters, with a $6.9\mathrm{x}$ faster inference speed. + +
MethodVenue#Params↓(K)Model Size↓(MB)Latency↓(GPU,ms)Latency↓(SoC,ms)FPS↑(640×480)UIEB [43]
PSNR↑SSIM↑LPIPS↓SCORE↑
FUnIE-GAN [38]IEEE RA-L'207,02026.783.69876.61270.42819.720.8450.2390.101
Shallow-UWNet [53]AAAI'21219.4560.8411.158400.0189.62016.690.7470.365<0.001
PUIE [25]ECCV'221,4015.3424.000>50041.65821.250.8850.1610.130
UIE-WD [52]ICASSP'2213,70452.2810.235386.7297.92020.920.8470.2120.192
U-Shape [55]IEEE TIP'2322,81787.0438.484>50025.98421.250.8450.1980.081
FiveA+ [40]BMVC'238.9740.0311.700423.4390.22422.510.9020.1651.525
Boths [47]IEEE GRSL'236.4470.022.56758.04389.43122.230.9040.1562.173
SFGNet [97]ICASSP'241,2984.95>100>500<1021.660.8710.191<0.001
LiteEnhanceNet [90]ESWA'2413.6880.056.654190.02150.28921.440.9030.1680.608
LSNet [99]Arxiv'247.5340.0359.519>50016.81019.240.8290.2420.003
Ours/4.0470.020.9108.941099.37022.810.9060.15529.711
+ +Table 2. Performance comparison of different underwater image enhancement models on UIEB datasets. SCORE [37] represents a comprehensive measure of model performance and efficiency. The top results are marked: best in red and second in blue. + +Figure 5 shows the visual results, where MobileIE produces higher-quality images, closely resembling the ground truth. + +UIE: The quantitative results in Table 2 show that MobileIE achieves a PSNR of $22.81\mathrm{dB}$ . Remarkably, MobileIE surpasses FiveA+ [40] by 0.3 dB in PSNR while using only $45\%$ of its parameters. Figure 6 provides visual comparisons, highlighting MobileIE's superior color restoration compared to other lightweight methods. + +ISP: On the ZRR [43] dataset, the quantitative results in Table 3 show that MobileIE maintains competitive performance while delivering $3\mathbf{x}$ faster inference than existing lightweight SOTA models. Figure 7 provides the corresponding visual comparisons. + +Mobile Deployment: As shown in Tables 1, 2, and 3, MobileIE's streamlined design (4K parameters and 0.924 GFLOPs) enables seamless deployment on commercial mobile devices, achieving real-time image enhancement at + +![](images/386c2612ff87a14ab3c1cd6d776ea3277ec6ba2f700ca718e037ee8082d7e3ac.jpg) + +![](images/6dc4b2842659fed4e174a83ed611513400b53182808781aff3dd4712aabf51cb.jpg) +(a) Input +(f) PairLIE [26] + +![](images/35f7af3c26b04d74ec30400538c3bfef4ca025e4ca65c7ab7afda7b356833423.jpg) + +![](images/4f6350b724e78bfc9051e23b4bde41778ea06cf595c0b3725de61d61e8dae80c.jpg) +(b) Zero-DCE [28] +(e) SYELLE [27] + +![](images/96f5303fa055ceef56e8cd28f6b0abdf4d750375cb90e51d9ebd4a657e1481af.jpg) + +![](images/5bbd5b6ba16a503a2689f79553bcf869019f344b747d78b0e3a7a76d671d4f30.jpg) +(c) RUAS [46] +(i) Ours + +![](images/a8931990e8bb515b1f194027f6a02e4da92dd918264c5238e79d77bb717ba8bf.jpg) + +![](images/4f4735aab7fc64473908f3bf8c679cc100198710a69a697216fb78095309d012.jpg) +(h) IAT [19] +(j) Ground Truth + +![](images/b08edcd7bd0c7c0d06a03dab000160075ca44f5c0ba18d4e6cefa1fab1267305.jpg) +Figure 5. Visualization comparison of LLE on LOLv1 [75]. + +![](images/702f8cf01925fef2560dd75bf89523e55e386cbd761319e99d61fc543e3e7c15.jpg) +(a) Input +(e) LiteEnhanceNet [90] (f) LSNet [99] +Figure 6. Visualization comparison of UIE on UIEB [43]. + +![](images/1ef9238e1dd2f606b79c889e992c4a2cd49324649902a7e7ed4d1d0099592ac8.jpg) + +![](images/8b6216ef01693f7e8ef004d545913d7b4b1053bcef126f7258788ab90fe4c2e6.jpg) +(b) PUIE [25] + +![](images/fe73026813a20d95529b936e023291f809b49f54cfce6cf0863e737ad0b6fc04.jpg) + +![](images/eff7758992ff9dd466ac167a65c66f4005c4c11d243d0da906b76daf63390f06.jpg) +(c) FivaA+ [40] +(g) Ours + +![](images/91fcc5b54edade8188e5e03121d04e15513955ba2d13e9439f0301d8d1201d51.jpg) + +![](images/54c47a29f9c9419bacb89dbb9f5a6eabf6fe82a641dfdb70e9bb1446f94d6843.jpg) +(d) Boths [47] +(h) Ground Truth + +![](images/87d3cbdc8351bc86a91897eba5a8b66ca8feeb3006f608683daed37a2789a9f3.jpg) + +![](images/68f5325c58a5fad5b9045b409fcc650b80016284b295977f52ea1be22d0f3f6e.jpg) + +![](images/94fcf4051b2eebd9809472ac346efa58828b19d6db6a3deccf52029218de758e.jpg) + +![](images/1678742d0e506da66df89af6018cf2aa5411eebb59b505d284fc56e273786d8a.jpg) + +![](images/c29d333ab127396b97bc6e2c010f481051683c8364c99e2f98356a574f75659d.jpg) +(a) Raw visualized + +![](images/0f7309f58cee93a007721b4ec8b9fe47ca38b58d24ae42e28a4bbaf0e1b0f4ad.jpg) +(b) PyNet [35] +(e) LiteISPNet [95] +(f) SYEISP [27] + +![](images/10377fdbe723a00863dd1c64c109edfac903539b2998bc5ddc7f837c05613ad5.jpg) +(c) AWNet [20] +(d) MW-ISPNet [34] +(g) Ours + +![](images/f7aa6c94bc92a766b08d3210cf528e658d34cc372c571b7a308039743068e0f2.jpg) +(h) Ground Truth + +Figure 7. Visualization comparison of ISP on ZRR [35]. + +
MethodVenue#Params↓(K)Latency↓(GPU,ms)Latency↓(SoC,ms)FPS↑(448×448)ZRR [35]
PSNR↑SSIM↑SCORE↑
PyNet [35]CVPRW'2047,548118.339>500<1021.190.7470.024
AWNet(raw) [20]ECCVW'2045,408102.932>500<1021.420.7480.038
MW-ISP [34]ECCVW'2029,200///21.160.732/
LiteISP [95]ICCV'2111,90046.326>50021.33421.280.7390.070
NAFNet [9]ECCV'227,8443.10878.62321.76021.120.7360.836
SYEISP [27]ICCV'235,6161.15616.47865.24720.840.7281.524
FouriSP [31]AAAI'247,59022.869>50043.73121.650.7550.237
Ours/4.1041.02014.40980.51621.430.7313.913
+ +Table 3. Performance comparison of different image signal processing models on ZRR datasets. SCORE [37] represents a comprehensive measure of model performance and efficiency. The top results are marked: best in red and second in blue. + +over 100 FPS. This efficiency paves the way for real-time UHD images (2K-8K) enhancement on mobile platforms. + +# 4.3. Ablation Studies and Analyses + +We conducted a series of ablation studies to verify the effectiveness of MobileIE's modules. First, MBRConv was compared with other re-parameterization methods [23, 89, 92], and LVW loss was replaced by conventional loss functions. As shown in Table 4, both MBRConv and LVW loss significantly improved the model's performance. Importantly, MBRConv merges into standard convolutions during inference, adding no computational or memory overhead. + +# (1) Why does MBRConv + IWO work? + +IWO enhances the kernel skeletons. To explore the impact of IWO on MBRCnv kernels, we visualized the + +
DatasetsUIEB [43]
MetricsPSNR↑SSIM↑LPIPS↓LOE↓MAE↓
Only inference network21.480.8870.1920.1080.086
L1 loss22.200.9020.1680.0980.078
L2 loss21.740.8940.1750.0950.083
Smooth L1 loss22.270.9040.1640.0970.078
Charbonnier loss22.310.9050.1620.0970.077
Robust loss [4]22.340.9050.1670.0990.077
LVW loss22.570.9060.1600.0970.075
DatasetsLOLv1 [75]+LOLv2-Real [82]
RepVGG [23]22.690.8210.2020.2570.089
RepNAS [89]21.900.8100.2100.2590.099
ECBSR [92]23.960.8160.2040.2400.080
MBRCConv(No BN)23.270.8210.2320.2580.082
MBRCConv(No IWO)24.020.8230.1990.2570.078
Ours24.350.8290.1890.2540.074
+ +weight increments $\Delta W$ in the last convolutional layer of the MobileIE model trained on the UIEB dataset. Here, $\Delta W$ is defined as the difference between the weights trained with IWO $(W_{IWO})$ and those trained without it $(W_{base})$ , i.e., $\Delta W = W_{IWO} - W_{base}$ . As shown in Figure 8, most $\Delta W$ values reinforce the center-row and center-column characteristics of the convolutional kernels, which contributes to improved model performance [6, 21]. + +![](images/e552d241abf4d32e0d624934630da5c0748210cd8ff8235d7cb627b6ef65ae4e.jpg) +Figure 8. Visualization of kernel differences pre- and post-IWO. + +IWO reduces channel redundancy, validated by comparing the last Conv $1 \times 1$ layer of MBRCConv $5 \times 5$ before and after IWO optimization. Channel similarity was measured using Kullback-Leibler (KL) [6, 73, 100] divergence, with higher values indicating lower redundancy. We trained MobileIE on the LOLv1, saving checkpoints at different stages. Applying softmax across channels and calculating KL divergence between channel pairs, we generated KL matrices at different training stages (Figure 9). As training progressed, KL divergence increased, and after IWO, it rose significantly, underscoring MBRCConv's effectiveness in reducing redundancy and improving feature representation. + +Impact of IWO on Training Convergence. Similar to the Pre-training stage, $W_{pre}$ is the well-performing weight obtained after the first 1000 epochs. As shown in the train- + +![](images/b46aab15c6bef42b1b7ad3e3051320b60504702fd2e7ef66c0e5ad3b9d6090e1.jpg) +Figure 9. KL similarity matrix for the last convolutional layer of MBRCov at different training stages. + +ing curves (Figure 10), without IWO, the loss stagnates in the later training stages, whereas with IWO, it continues to decrease. This demonstrates that IWO facilitates further optimization of the weights, enhancing the model's convergence performance. The oscillation is due to cosine decay. + +![](images/62321c3bddbb521f01b090aeb7736e252e649b607202d87c7405ada490e6912c.jpg) +Figure 10. Training loss curves showing the effect of IWO. + +(2) FST can enhance nonlinear feature interaction. The FST uses a nonlinear squaring transformation to enhance high-frequency sensitivity, highlighting image details and edges (Figure 11). In the Fourier spectrum, squaring shows a stronger high-frequency response than ReLU, effectively preserving detail. The learnable parameters, Scale, and bias, further adaptively adjust the feature dynamic range, enhancing restoration performance. + +![](images/ff38fa2e65dd6e4430d215330916f6d63ff69d4e5db7dd00bfa7e84f9adb8299.jpg) +(a) Original Feature: $F$ + +![](images/d4b7d92568f67c63f99a0e5a913f9eaafb63a03f4369ab895485f459fb6f73ea.jpg) +(b) $\operatorname{ReLU}(F)$ + +![](images/8e9da5ab552bc02905bf289b2b32a79135534b332a7511813e329542ad2c39e5.jpg) +(c) $F * F$ +Figure 11. Feature Transformation Fourier Spectrum. + +![](images/cdb31c3fbc7097912fea7503bdf5c35f32cc83b13fa02262e69a91429f7e5fe5.jpg) +(d) $\mathbf{FST}(F)$ + +Figure 12 shows that the FST achieves a faster convergence rate during training compared to other feature transform methods. In the initial epochs, the FST rapidly reduces loss, demonstrating its ability to enhance feature representation early and accelerate convergence. Additionally, the FST's final stabilized loss is lower than other methods, highlighting its robustness and effectiveness in complex tasks. Table 5 further confirms that FST delivers the best feature transform performance on the UIEB [43] dataset. + +Table 4. Performance comparison of Loss and Re-param modules. + +
MethodsPSNR↑SSIM↑LPIPS↓LOE↓MAE↓
Baseline21.120.8840.1990.1010.088
ADD21.500.8960.1780.1070.084
Scale*ADD21.340.8930.1730.1050.087
ADD+Bias21.580.8900.1770.0930.086
CAT21.440.8930.1810.0950.085
MUL21.800.9010.1730.0950.084
MUL+Bias21.840.9010.1680.0920.081
Scale*MUL21.950.9020.1670.0920.081
Ours22.600.9060.1570.0920.075
+ +Table 5. Performance comparison of different feature transform. "Baseline" represents the model without any feature transform. + +(3) Dual-path fusion enables precise feature capture. + +How can one achieve both efficiency and precise capture of local and global feature dependencies? Following + +![](images/f914df98570fb582149618957ed180978ecdfc0ef1ca8d63001f20c7ba6038ed.jpg) +Figure 12. Training loss comparison of different feature transform. + +Occam's Razor principle, HDPA adopts a streamlined design language, utilizing a dual-path structure and adaptive feature interaction to decompose and aggregate features hierarchically, thereby extracting critical information across different scales. This dual-path design also supports mutual optimization during backpropagation. + +![](images/88190fad12cd8ffded1bcbdfaa59b2e7ee653b429d8b27979eac9d96ea0f9911.jpg) +(a) RGB image + +![](images/391c895e1e9805851b474fea969beef2c57b25dad18e0b895891435811182151.jpg) +(b) Input feature + +![](images/ffb14797bff7cf07d29d38e39fab8b68bc3b58a5b1f1bbdede2ca075de79d8a9.jpg) +(c) HDPA heat map ( + +![](images/873dbf022ca71d32426f98a3df145460512868b38879c0af5f1e599eda8ceefd.jpg) +(d) Output feature +Figure 13. Visualization of feature maps at different stages. + +Figure 13 illustrates HDPA's effectiveness. The initial convolution preserves key edges and structures, while the HDPA heatmap highlights important regions, focusing attention on key details. This produces a sharper output feature map, demonstrating how HDPA's attention improves image enhancement by refining key details. + +
Method#Params↓ (K)FLOPs↓ (G)Latency↓ (GPU,ms)Latency↓ (SoC,ms)LOLv1 [35]
PSNR↑SSIM↑LPIPS↓SCORE↑
SE-Net[33]4.1790.9220.9487.4122.270.8040.21717.259
CBAM[77]4.2540.9456.57395.7122.380.7960.2311.556
ECA-Net[70]3.8700.9220.8056.6521.790.7990.2219.886
EA[62]4.4911.0571.23211.4519.930.7790.2600.436
NAM[49]3.8910.9300.9057.0220.100.7610.2520.900
SCA[9]4.0230.9220.7696.3320.820.7860.2502.707
DFCI[64]3.9790.9210.8906.2921.500.8020.2086.992
EMA[54]4.2391.0861.5699.7920.780.7920.2331.656
SPAN[67]5.5111.3081.83510.2419.790.7670.2600.401
CGA[13]6.3301.4861.4379.6222.330.8030.20914.447
LKA[3]5.2471.2361.0828.9619.760.7820.2270.440
Ours4.0350.9240.8866.7223.260.8050.21375.079
+ +Finally, we replaced it with mainstream attention mechanisms and conducted ablation experiments, as shown in Table 6. With minimal added parameters $(+0.168\mathrm{K})$ and FLOPs $(+5.76\mathrm{M})$ , HDPA achieved a PSNR gain of $+3.08$ dB. Tests on mobile devices confirmed HDPA's high performance with minimal latency, underscoring the efficiency of our edge-focused IE design in MobileIE. + +(4) Effectiveness of LVW in Outlier Optimization. We observed that the pixel error histograms follow a Laplace-like distribution, suggesting the model optimizes accurate pixels while neglecting outliers [27]. Based on $L1$ Loss, + +LVW adjusts weights to increase the constraint on outliers. Normalization standardizes errors, bringing the data distribution closer to uniform and ensuring balanced pixel weights. Additionally, we visualized the pixel prediction error histograms for different loss functions, as shown in Figure 14. LVW exhibits lower mean and median pixel errors, improving effectiveness in optimizing challenging regions. + +![](images/481f638439f1a028a867ed676c452215f194c1a5f490abe0c91b2a29f1d05764.jpg) + +![](images/b0dfa10256f9afa65660729554dab7035c53038d1dc780cd429c1b271e50cbc8.jpg) +Figure 14. Visualization of pixel prediction error histograms for various loss functions. + +![](images/5564fef0b1c8c9038dbfcac6b9fce556fe032cdc42884d22b7441d15d4acb23d.jpg) + +![](images/31ed2d60c16efb7c7c15033dbce70ce4d77713b035e20407b459a333bcccbb24.jpg) + +(5) Module-Wise Lightweight Contributions. Table 7 demonstrates that re-parameterization significantly reduces model complexity during inference. IWO and LVW introduce no extra cost, making them suitable for efficient deployment. Re-parameterization combined with cost-free strategies enables efficient and lightweight inference. + +Table 6. Performance comparison of different Attention mechanisms on LOLv1 [75] dataset. SCORE [37] reflects the efficiency. + +
ModelTrainingw/o FSTw/o HDPAInferencew/o FSTw/o HDPAIWOLVW
Params (K)47.21147.21143,9714.0474.0473.867
Model Size (MB)0.180.180.170.020.020.01Cost-Free
FLOPs (G)11.04211.04217.0990.9240.9240.919Optimization
Latency (ms)9.589.528.990.8950.8640.732
+ +Table 7. Ablation on different module efficiency. + +# 5. Conclusion + +In this paper, we introduce MobileIE, a lightweight CNN with only 4K parameters designed for real-time image enhancement on mobile devices. MobileIE combines simplicity with high performance across low-light image enhancement, underwater image enhancement, and image signal processing tasks. Key components such as the MBRCov, Feature Self-Transform module, Hierarchical Dual-Path Attention mechanism, and Local Variance-Weighted loss enable MobileIE to achieve superior results while maintaining an inference time of around $0.9\mathrm{ms}$ . Furthermore, MobileIE can be easily deployed on any commercial mobile device with minimal computational overhead and efficient resource utilization. Future work will explore optimizations to expand MobileIE's application to more different tasks. + +Acknowledgements. 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However, existing video pre-trained models still focus on the common ViT architecture with high latency, and few works attempt to build efficient architecture on mobile devices. This paper bridges this gap by introducing temporal structural reparameterization into an efficient image-text model and training it on a large-scale high-quality video-text dataset, resulting in an efficient video-text model that can run on mobile devices with strong zero-shot classification and retrieval capabilities, termed as MobileViCLIP. In particular, in terms of inference speed on mobile devices, our MobileViCLIP-Small is $55.4 \times$ times faster than InternVideo2-L14 and $6.7 \times$ faster than InternVideo2-S14. In terms of zero-shot retrieval performance, our MobileViCLIP-Small obtains similar performance as InternVideo2-L14 and obtains $6.9\%$ better than InternVideo2-S14 on MSR-VTT. The code is available at https://github.com/MCG-NJU/MobileViCLIP. + +# 1. Introduction + +Large vision-text models [9, 27, 51, 72] have demonstrated excellent zero-shot performance in a wide range of downstream tasks. Learning transferable video-text representations is becoming a fundamental task in video understanding. With the advent of high-quality video-language datasets [2, 8, 42, 64] for large-scale pre-training, several powerful video-text foundation models [28, 63, 65] have emerged. They are typically trained from scratch and have achieved excellent results on various downstream tasks including video-text retrieval and action recognition. However, to ensure performance, most of these works use ViT-L [15] or larger backbones. The model size limits its pos + +![](images/e3c5c1288c4ce429d0caf8440a3d964cb3b4e17260689b29a2ae61d79ec7b53f.jpg) +Figure 1. Comparison of latency and the R@1 scores for zero-shot text-to-video retrieval on video retrieval dataset MSR-VTT [69]. The latency is measured on iPad Air 2020 with iOS 18. MobileViCLIP achieves the best trade-off of recall and latency. + +sibility of deployment on mobile devices with limited storage capability. Also, excessive computing resource requirements (tens of A100 GPUs are required), too long training time (thousands of hours of GPU training time), and a large amount of pre-training datasets (ensemble of datasets larger than 100M) increase the training cost and make these works difficult to reproduce for a university lab. + +Parameter-efficient transfer learning (PETL) [30, 33, 44, 71] is becoming a promising and efficient paradigm for adapting large image-text models for video understanding due to their huge numbers of parameters and the high computational cost of full fine-tuning. These methods have successfully transferred image representations to video recognition tasks and obtained good zero-shot recognition results on several action classification datasets [5, 19, 24, 50]. However, these transfer learning methods often focus on the simple video classification task and fail to directly investigate the visual-textual representations on more complex video-text tasks. We argue that video-text models are expected to be more flexible and can handle a more diverse of downstream video understanding tasks. Furthermore, de + +Despite the extremely small number of trainable parameters in these transfer learning works, their used image-text models are still too large (ViT-B or ViT-L) to be deployed on mobile devices. It still remains a challenge that how to develop an efficient video-text model for mobile devices. + +For image-text models, there have been several works [14, 56, 57, 60, 66, 74] exploring efficient neural network architectures for mobile devices. Most of them adopt a hybrid architecture, by combining ViTs to capture global context through self-attention mechanisms and lightweight CNNs for their parameter efficiency and low latency. With the help of high-quality and large-scale imagedataset datasets [18, 47, 49], these models [12, 41, 58] have achieved good results on multiple image classification and retrieval tasks. However, the domain gap between image and video and the lack of temporal modeling limits their capabilities in video-text understanding. We aim to bridge this gap by adapting these image clip models to enable video understanding on mobile devices. + +Specifically, we design an efficient video-text model that is able to run on a mobile device, coined as MobileViCLIP. The number of parameters in MobileViCLIP is smaller than all of these existing video-text models, which makes it possible to be deployed on mobile devices. In addition, the latency of MobileViCLIP is comparable with other efficient image-text models, which is significantly faster than the existing video-text models. To avoid the complex design and multi-stage training process of previous video-text models [10, 65], we resort to the PETL paradigm by leveraging the image-text understanding capability of an existing model [58] and retraining on the additional high-quality and large-scale video-text datasets [64] to learn powerful and transferable video-text representations. To endow MobileViCLIP with the temporal modeling power, we replace the original block with Spatiotemporal RepMixer and Spatiotemporal Attention to capture both temporal dynamic and spatial representation. We only use 8 NVIDIA GeForce RTX 3090 GPUs to train our MobileViCLIP by fully finetuning the video branch and freezing the text branch. It only takes 2 days for training on the InternVid dataset. As shown in Fig 1, the resulting MobileViCLIP-Small obtains comparable zero-shot text-to-video retrieval results to the ViT-L model from InternVideo2 [65] (coined as InternVideo2-L14) with much lower latency and fewer parameters. In summary, our contributions are as follows: + +- We introduce MobileViCLIP, the first video-text model with efficient structure that is able to be efficiently deployed on mobile devices. Our MobileViCLIP has learned good video-text representations and achieved excellent zero-shot evaluation results on multiple datasets. +- We are the first to present an in-depth analysis on the latency of each basic module in current video-text models on the mobile devices, trying to figure out the key ingredients. + +clients for future design of efficient video-text models. + +- We verify the generalization performance of MobileViCLIP on downstream tasks including text-video retrieval and temporal grounding, demonstrating stronger generalization performance compared to the baseline. + +# 2. Related Work + +Vision-Language Pretraining. By utilizing web-scale paired image-text data for training, CLIP [46] shows robust zero-shot object recognition abilities. Also, some advanced works [9, 11, 52, 53] have explored the upper bound of scaling up contrastive language image pre-training. These models have billions of parameters, requiring billions of pretraining datasets and tens of thousands of hours of GPU training time. These works have achieved results comparable to fully supervised models on widely used recognition and retrieval datasets. The success of contrastive language-image pre-training has also inspired pre-training tasks for other modalities like video and audio. + +Video-Language Pretraining. The success of CLIP inspired the video domain. The study of video-language pretraining is becoming increasingly crucial considering its wide applications. Following the idea of image-text pretraining, several foundation models in the video domain have been born [7, 17, 28, 29, 61, 68, 73]. These works explore the relationship between video modality and other modalities from different perspectives, achieving leading results across various video tasks. Undoubtedly, these works still require huge computing resources and training data, and the number of model parameters is huge. Our MobileViCLIP attempts to propose a foundation model that is mobile-friendly, with faster inference speed, lower latency, and fewer parameters within limited computing resources. + +CLIP-based Action Models. Inspired by the strong representation of the pre-trained image-text CLIP model, many video recognition approaches [6, 21, 30, 34, 43, 44, 48, 62, 71] have been proposed based on CLIP. Although these works successfully transfer knowledge from image to video domain, these models are still far from the foundation models. These models are usually fully fine-tuned [34, 48, 62] on video classification datasets [5, 24, 50], or partially fine-tuned [6, 30, 43, 44, 71] based on a proxy video action classification dataset. These models usually do not have videotext retrieval capability and cannot serve as feature extractors for downstream tasks. Our MobileViCLIP is fine-tuned based on a large-scale pre-training video-text dataset [64], showing excellent generalization on more tasks. + +Efficient CLIP Models. Recently, more and more works [14, 56-58, 60, 74] have realized the importance of deploying CLIP models on mobile devices, and propose a wide range of architectures that have shown great promise for accomplishing vision tasks on resource constraint devices. These architectures can be broadly classified into + +![](images/345197060bc5f34ae9ce5ea7b10bc1c230e9013a023bf1b9b8c05f433368a89f.jpg) +Figure 2. Overview of MobileViCLIP. We fine-tune Mobile-CLIP [58] with minimal changes, which means we only introduce simple module modification to the Repmixer and Attention stage to convert the image encoder into a video encoder. During training, we freeze the text encoder and fully fine-tune the video encoder. We use a simple temporal pooling operation without any trainable parameters to generate the video-level representation for similarity matching with corresponding embeddings. + +purely convolutional [14, 20, 57], transformer based [35, 37] and convolution-transformer hybrids like [56, 60, 74]. However, to take into account low latency on mobile devices, the architectures of these models are generally smaller and their accuracy is much lower than that of conventional CLIP models [52]. To solve this problem, MobileCLIP tried to enhance the dataset [18] with additional information and learned a good image-text representation. Based on it, we add efficient temporal modeling modules in Video TokenMixer and fine-tune it using a large-scale, high-quality video multimodal dataset [64], so that MobileVi-CLIP can still demonstrate excellent zero-shot performance on multiple video-text retrieval and action recognition tasks while maintaining low latency. + +# 3. Method + +# 3.1. MobileCLIP Revisited + +Backbone Baseline. We start with the description of image-text backbone designed by MobileCLIP [58]. We adopt two versions of MobileCLIP: MobileCLIP-S0 and MobileCLIP-S2, and build our MobileViCLIP-Tiny and MobileViCLIP-Small, respectively. For the image backbone, it is an improved hybrid vision transformer called + +MCi based on FastViT [56]. MobileCLIP-S0 adopts MCi0 which has a similar stage configuration as MobileOne [57] while MobileCLIP-S2 adopts MCi2 which is a wider and deeper version of MCi0. For the text encoder, MobileCLIP-S0 uses MCt which is an efficient hybrid text encoder inspired by the reparameterizable convolutional token mixing (RepMixer) in FastViT [56]. MobileCLIP-S2 adopts a 12-layer Transformer similar to that of ViT-B/16-CLIP [46]. + +Structural Reparameterization. Recent works [14, 56] show the benefits of reparameterizing skip connections to lower memory access costs. In our model, we follow the similar design in RepMixer, that is reparameterizable at inference. Specifically, for an input tensor $X$ , the mixing block in the layer can be implemented as: + +$$ +Y = \operatorname {D W C o n v} 2 \mathrm {D} (\mathrm {B N} (X)) + X. +$$ + +And it can be reparameterized at inference time to a single depthwise convolutional layer without non-linear activation function $\sigma$ and Batch Normalization $BN$ as: + +$$ +Y = \operatorname {D W C o n v} 2 \mathrm {D} (X). +$$ + +# 3.2. Overview of MobileViCLIP + +We describe the details of our MobileViCLIP pipeline shown in Fig 2. Given a video sample $V \in R^{T \times H \times W \times 3}$ with T frames and corresponding text description, the video encoder encodes T frames and produces frame-level embeddings $f_{images} \in R^{T \times D}$ . These frame-level embeddings are average-pooled to obtain a video-level representation $f_{video} \in R^{D}$ during inference. We refer to this as temporal pooling as this operation implicitly incorporates temporal learning via aggregation of multiple frames. The CLIP text encoder encodes the text descriptions to produce text embedding $t \in R^{D}$ . Then we adopt video-text contrastive learning (VTC) to learn independent representations for video and text by maximizing the agreement between positive (video, text) pairs while minimizing the agreement between negative pairs. During inference, we only extract features through the video encoder and text encoder, and the pooling operation depends on the task requirements to choose whether to use. + +# 3.2.1. Block Design + +MCi is a hybrid vision transformer architecture that combines convolutional and transformer designed to effectively capture local and global information. However, as an image-text foundation model, it lacks the ability to understand temporal relationships. In this part, we present our block improvement to better understand the spatiotemporal relationships inside the video. + +Spatiotemporal Repmixer. Inspired by [4, 55, 70], introducing a simple temporal modeling block can effectively enhance the model's video understanding capabilities. Specifically, we construct a 1D depthwise convolutional layer to process temporal modeling before the 2D + +![](images/0662fe7df1ee0f9dfd78ac0ebde2a66ca47345252f500b545ddec4cff5e069c3.jpg) +(a) Spatial Repmixer +(b) Spatiotemporal Repmixer + +![](images/55881254091f4b56d2bbe9908f1f7b4612829d39546afcd32f2531a1b5b71a81.jpg) +Figure 3. Spatiotemporal RepMixer. (a) is a spatial RepMixer along with ConvFFN provided by MCi. (b) is the spatiotemporal RepMixer which adds 1D depthwise convolutional layer along with skip-connection and it can also be reparameterized at inference time. The norm layer and nolinarity are omitted for simplicity. +(a) Naive Attention +(b) Spatiotemporal Attention +Figure 4. Spatiotemporal Attention. (a) is a native attention block along with conditional positional embeddings and ConvFFN provided by MCi. In (b) we add learnable temporal positional embeddings (short for TPE) and update the native attention to spatiotemporal attention while maintaining other design elements. The norm layer and nonlinearity are omitted for simplicity. + +depthwise convolutional layer shown in Fig 3. Specifically, for an input tensor $\mathbf{X}$ , the Spatiotemporal RepMixer can be implemented as: + +$$ +X ^ {\prime} = D W C o n v 1 D (B N (X)) + X, +$$ + +$$ +Y = D W C o n v 2 D \left(B N \left(X ^ {\prime}\right)\right) + X ^ {\prime}. +$$ + +where $X'$ needs to be rearranged to align with corresponding operations. It can also be reparameterized at inference time as: + +$$ +X ^ {\prime} = D W C o n v 1 D (X), +$$ + +$$ +Y = D W C o n v 2 D \left(X ^ {\prime}\right). +$$ + +Such design will not affect the subsequent channel mixer ConvFFN [56]. + +Spatiotemporal Attention. Since the attention block in MCI is to learn global image information. Inspired by Vi-CLIP [64], we update the native attention to spatiotemporal attention while maintaining other design elements including conditional positional encodings shown in Fig 4. MCI + +adopts conditional positional encodings (CPE) generated by a depth-wise convolution operator but can only capture spatial relationships. We add a learnable temporal position encoding (TPE) before CPE to provide the model with temporal position information. Specifically, for an input tensor $X$ , the process of adding positional encoding can be described as follows: + +$$ +X ^ {\prime} = X + T P E, +$$ + +$$ +Y = X ^ {\prime} + C P E (X ^ {\prime}). +$$ + +During inference, we follow the structural reparameterization mentioned before: + +$$ +X ^ {\prime} = X + T P E, +$$ + +$$ +Y = C P E \left(X ^ {\prime}\right). +$$ + +In this way, we successfully add spatial and temporal position encoding to the input and send it into the subsequent Spatiotemporal Attention module for global spatiotemporal representation modeling. + +# 3.3. Training + +Settings. For the video input of our MobileViCLIP, we sample 8 frames from the raw videos with an input resolution of $256 \times 256$ . We train both MobileViCLIP-Tiny and MobileViCLIP-Small using AdamW [38] optimizer for 3 epochs with a learning rate of 1e-5, and we set the warm-up epoch to 0.6 with a linear schedule. During training, we use checkpoint technology to reduce the model's memory requirements at the expense of training speed, and then adopt 8 NVIDIA GeForce RTX 3090 GPUs, and the batch size is set to 64 for each GPU. When we fully fine-tune our model on downstream text-to-video retrieval datasets [1, 23, 69], we also set batch size to 64 and adopt 10 epochs with a learning rate of 1e-5 and set the warm-up epoch to 1. Since our MobileViCLIP is sufficiently lightweight and requires less training data compared to other foundation models [9, 28, 65], which is significantly lower than other videotext foundation models. + +Pre-trained Dataset. Our baseline model Mobile-CLIP [58] adopted reinforced DataComp [18] using its multi-modal dataset reinforcement strategy and created DataCompDR-1B by reinforcing DataComp-1B. Such a combination of both real and synthetic captions along with filtered high-quality images enables MobileCLIP to obtain the best zero-shot retrieval and classification performance. Based on the high-quality pretraining stage, we can directly fine-tune the model on the video-text dataset to directly learn video-text representations without designing multi-stage alignment and understanding. As our training dataset, we use InternVid-10M-FLT [64] which includes 10M high-quality YouTube videos spanning 16 scenes with about 6 thousand actions. The fine-grained video captions powered by large language models (LLM) can + +
Training StageDatasetDomainScale
Image-Text learningDataCompDRWeb Image1B
Video-Text learningInternVid-10M-FLTYoutube Video10M
+ +Table 1. Summary of datasets used in MobileViCLIP training. DataCompDR is adopted by MobileCLIP, we fine-tune MobileVi-CLIP on InternVid-10M-FLT based on pre-trained MobileCLIP. + +also ensure accurate descriptions of complex interactions inside these videos. The summary of datasets can be described in Table 1, sufficient training corpus data ensures MobileViCLIP's generalization performance. + +Data Augmentation. We input MobileViCLIP with paired video and text $(v, t)$ . During training, we randomly select 8 frames from the window, then resize and randomly crop the video frames to the resolution of $256 \times 256$ , using bilinear interpolation. Then we horizontally flip the given frame randomly with a given probability 0.5. During inference, we only resize the frame to the resolution of $256 \times 256$ using bilinear interpolation. + +Training Objectives. We use simple video-text contrastive (VTC) loss to maximize the agreement between the paired video and text embeddings. Specifically, it minimizes InfoNCE loss using global video and text features, the video-text contrastive loss $L_{VTC}$ is given as: + +$$ +\begin{array}{l} L _ {V 2 T} = - \sum_ {i = 1} ^ {N} \log \frac {\exp \left(\operatorname {s i m} \left(v _ {i} , t _ {i}\right) / \tau\right)}{\sum_ {j = 1} ^ {N} \exp \left(\operatorname {s i m} \left(v _ {i} , t _ {j}\right) / \tau\right)}, \\ L _ {T 2 V} = - \sum_ {i = 1} ^ {N} \log \frac {\exp \left(\operatorname {s i m} \left(t _ {i} , v _ {i}\right) / \tau\right)}{\sum_ {j = 1} ^ {N} \exp \left(\operatorname {s i m} \left(t _ {i} , v _ {j}\right) / \tau\right)}, \\ L _ {V T C} = \frac {1}{2} (L _ {V 2 T} + L _ {T 2 V}), \\ \end{array} +$$ + +where $v$ and $t$ denote the learned video and text embeddings respectively. $sim()$ computes the cosine similarity between two features. $\tau$ is the learnable temperature. $N$ is the number of samples per batch. + +Evaluation Datasets and Metrics. We used the following three text-to-video retrieval datasets to verify the videotext representation performance and explore the architecture design: MSR-VTT [69], DiDeMo [1], and ActivityNet-Captions [23]. MSRVTT is a widely used text-to-video retrieval dataset containing around 10,000 video clips across various scenes, each accompanied by 20 unique text descriptions. DiDeMo comprises over 10,000 videos, divided into 26,892 five-second video segments, each segment corresponding to multiple descriptions. ActivityNet is a large-scale dataset consisting of 200 categories, and most videos have durations between 5 and 10 minutes. We also test our MobileViCLIP on four widely-used action recognition + +datasets to verify the capability of zero-shot action classification: Kinetics-400 [5], UCF-101 [50], HMDB-51 [24] and Something-Something V2 [19]. Kinetics-400 is a well-established dataset for action recognition, containing 400 different action categories with video clips around 10 seconds in length. UCF-101 includes 13,320 video clips categorized into 101 distinct actions. HMDB-51 consists of 6,766 short video clips divided into 51 unique action categories. Something-Something V2 is an extensive dataset comprising 220,847 videos, capturing a wide variety of actions involving daily object interactions. For Something-Something V2, We transform it into a multiple-choice task, namely SSV2-MC. Each video is paired with 173 descriptions, 172 of which are negative distractors. Models are required to retrieve the single correct description. As our evaluation metric, we only report the Top-1 (Recall@1) text-to-video (T2V) and video-to-text (V2T) retrieval accuracy across these three text-to-video retrieval datasets [1, 23, 69]. We report Top-1 Accuracy (Acc) on these four action classification datasets [5, 19, 24, 50] under zero-shot settings. Specifically, we construct templates for these action categories, such as "a video of action", and verify the model's zero-shot classification capability by evaluating Top-1 V2T. + +# 4. Main Results + +Text-to-Video Retrieval. We compare our MobileVi-CLIP with other models in the video-text retrieval task shown in Table 2 and Table 3. We report R@1 scores for text-to-video (T2V) and video-to-text (V2T) tasks to evaluate retrieval performance. In addition, we also evaluate the model's throughput on GPU, parameters, FLOPs, and latency across various platforms, including Intel Xeon Gold 6248 CPU, V100 GPU, and iPad Air 2020 mobile device. The iPad Air 2020 employs the same A14Bionic SoC as the widely adopted iPhone12ProMax[58]—namely, a six-core CPU, four-core GPU, and 16-core Neural Engine built on the 64-bit ARMv8.5-A architecture—with the only hardware distinction being memory capacity (4GB versus 6GB LPDDR4X, respectively). For iPad latency measurements, we export the models using Core ML Tools (v7.1) with iOS 18. Latency benchmarking batch size is set to 1 as in a real-world scenario and the optimal possible batch size to measure throughput before going out of memory. As shown in Table 2 and Table 3, both versions of MobileViCLIP introduce negligible additional latency during inference while achieving superior performance. For zero-shot text-to-video retrieval, the performance of MobileViCLIP-Small is comparable to InternVideo2-L14 on MSR-VTT [69] (with +0.4/-0.6 T2V/V2T zero-shot R@1 scores) and outperforms InternVideo2-B14 on DiDeMo [1] (with +0.4/+2.0 T2V/V2T zero-shot R@1 scores). Except for long video datasets which consist of several minutes long videos like ActivityNet [23], MobileViCLIP-Small still outper + +
Params RangeMethodGPU Throughput videos/sParams(M) video+textFLOPs(G) video+textLatency(ms)MSR-VTTDiDeMoActivityNet
CPU(video+text)GPU(video+text)Mobile(video+text)T2VV2TT2VV2TT2VV2T
<55MMobileCLIP-S0 [58]114.811.4+42.414.8+1.371.3+7.212.1+5.39.9+2.633.228.631.231.523.822.4
MobileCLIP-S0(10M)114.811.4+42.414.8+1.371.3+7.212.1+5.39.9+2.637.236.933.533.626.026.5
MobileViCLIP-Tiny89.511.5+42.414.9+1.385.5+7.215.4+5.312.4+2.638.738.137.137.029.328.2
55-135MVideoCLIP [68]321.88.4+1109.0+11.342.9+29.114.5+9.54.5+7.210.4-16.6---
MobileCLIP-S2 [58]66.135.8+63.448.4+4.3178.5+15.420.1+8.124.7+4.038.832.835.535.329.627.7
InternVideo-S14 [65]55.523.0+11083.3+11.3488.5+29.123.4+9.5275+7.235.635.933.735.534.523.6
MobileCLIP-S2(10M)66.135.8+63.448.4+4.3178.5+15.420.1+8.124.7+4.041.240.136.939.532.530.8
MobileViCLIP-Small47.936.0+63.449.5+4.3195.7+15.430.9+8.137.8+4.042.543.540.741.135.331.9
135-230MCLIP4CLIP [39]99.687.8+63.437.2+4.384.8+15.411.8+8.118.0+4.032.0-----
Open-VCLIP++(ViT-B/16) [67]21.939.8+11089.6+11.3384.8+29.149.3+9.5175.4+7.234.635.4----
VINDLU [10]27.8121.2+110185.6+11.3775.2+29.138.9+9.5712.5+7.232.0-36.9-30.9-
UMT-B [28]27.8121.2+110185.6+11.3775.2+29.138.9+9.5712.5+7.235.230.341.240.835.532.8
MobileCLIP-B [58]32.086.4+63.4141.8+4.3259.3+15.446.5+8.196.2+4.040.837.836.237.434.431.9
InternVideo-B14 [65]22.189.4+110254.8+11.3992.0+29.157.9+9.5661+7.240.348.540.339.141.538.8
>230MCLIP [46]6.9304+124649+9.71865.5+25.9108.1+9.51875.5+7.030.424.212.718.79.113.2
Open-VCLIP++(ViT-L/14) [67]6.9304+124649+9.71865.5+25.9108.1+9.51875.5+7.039.037.8----
InternVideo-L [63]5.9308.9+124830.7+9.72887.1+25.9174.2+9.52298.7+7.140.739.631.533.530.731.4
ViCLIP [64]5.9308.9+124830.7+9.72887.1+25.9174.2+9.52298.7+7.042.441.338.739.132.131.4
UMT-L [28]4.7429.4+335.1652.2+422672.4+73.1196.1+18.12373.7+20.540.737.148.649.941.939.4
InternVideo2-L14 [65]4.9308.9+335.1830.7+422887.1+73.1178.1+18.12298.7+20.542.144.142.843.243.640.7
+ +Table 2. Results of zero-shot text-video retrieval on MSR-VTT [69], DiDeMo [1] and ActivityNet [23]. T2V and V2T are short for R@1 scores for text-to-video and video-to-text tasks. "video" means the efficient metrics related to video branch in the model, while "text" means the efficient metrics related to text branch in the model. "M" means $10^{6}$ . "G" means $10^{9}$ . "ms" means millisecond. MobileCLIP(10M) is our baseline fine-tuned on InternVid-10M-FLT [64]. + +forms InternVideo2-S14 (with $+0.8/+8.3$ T2V/V2T zero-shot R@1 scores). For fine-tuned text-to-video retrieval, though our MobileViCLIP has a lower upper bound than the video clip model with larger parameters, our MobileViCLIP-Small still achieves a comparable performance with ViCLIP [64]. When we evaluate the efficiency-related metrics of these models, we find that our MobileViCLIP is more efficient than existing video-text models. With a similar number of parameters to InternVideo2-S14, our MobileViCLIP-Small takes only half the amount of FLOPs and is $6.75 \times$ faster than it on mobile devices. However, due to the optimization of transformers on GPUs, MobileViCLIP performs slightly worse than InternVideo2-S14 on GPUs. When compared to other larger-scale video-text models, MobileViCLIP has a significant advantage in these metrics. In summary, our MobileViCLIP shows reliable video text retrieval performance, and its structure based on an efficient image-text understanding model gives it significant advantages over other video CLIPs in terms of latency, FLOP, Params, and throughput. + +Zero-Shot Action Recognition. We further explore the action recognition capability of MobileViCLIP under zero-shot settings. We randomly construct complete description sentences for each action following the prompts provided by [65] and use R@1 scores for video-to-text task to evaluate the top-1 accuracy provided by MobileViCLIP. As shown in Table 4, MobileViCLIP-Small can achieve action recognition capabilities better than InternVideo-S14 with an improvement of +1.0 Top-1 accuracy on Kinetics-400 [5], +2.0 Top-1 accuracy on UCF-101, +1.2 Top-1 on HMDB-51, but -0.3 Top-1 accuracy on Something-Something V2. We also find that MobileViCLIP performs well on the HMDB-51 [24] dataset which is even better than InternVideo2-L14. Although MobileViCLIP is fine-tuned + +on a video-text retrieval dataset, the rich video-text pairs it has learned still enable MobileViCLIP to achieve strong zero-shot action recognition capabilities. + +# 5. Ablation Study + +Effectiveness of Block Design in MobileViCLIP. In this section, we ablate the block design in MobileViCLIP. For a fair comparison, we ablate the following experiments based on MSR-VTT for its sufficient training data and diverse text descriptions and then evaluate these variants based on R@1 scores for text-to-video on the test set of this dataset. Shown in Table 5, both Spatiotemporal RepMixer and Spatiotemporal Attention can achieve higher results. We can also notice that the temporal positional encodings are important to help the model better understand the temporal changes of video. So we accept both of them in our MobileViCLIP. + +Freeze Text Branch or Not. We further ablate on whether to freeze the text branch during training because some works [48] train both vision and text branches simultaneously, while other works [65] freeze the text branch. Shown in Table 6, we find that activating the text branch brings no help to the final video-to-text retrieval results and brings additional training consumption. So we freeze the text branch. + +Validate Video-Text Representation Capability for Video Downstream Tasks. To verify the generalization performance of our MobileViCLIP in other video downstream tasks, we report the results on following video downstream tasks including video temporal grounding, zero-shot temporal action detection and video captioning. Video temporal grounding is to identify specific moments or highlights from a video corresponding to textual descriptions. It relies on excellent video-text pair representation. To validate the video-text representation of our MobileViCLIP, we + +
Params RangeMethodGPU Throughput videos/sParams(M) video+textFLOPs(G) video+textLatency(ms)MSR-VTTDiDeMoActivityNet
CPU(video+text)GPU(video+text)Mobile(video+text)T2VV2TT2VV2TT2VV2T
<55MMobileCLIP-S0(10M)114.811.4+42.414.8+1.371.3+7.212.1+5.39.9+2.643.943.142.841.740.141.2
MobileViCLIP-Tiny89.511.4+42.414.9+1.385.5+7.215.4+5.312.4+2.645.144.944.244.742.743.3
55-135MAll-in-one [61]30.286.2141.0248.427.2102.537.9-32.7-22.4-
VideoCLIP [68]321.88.4+1109.0+11.342.9+29.114.5+9.54.5+7.230.9-----
MobileViCLIP-Small47.936.0+63.449.5+4.3195.7+15.430.9+8.137.8+4.049.350.348.248.547.346.4
135-230MVIOLET [17]29.887.6+11065.6+11.3290.3+29.137.6+9.5-34.5-32.6---
Frozen [33]26.385.8+66.3254.8+3.3652.1+25.741.8+4.7543.8+7.131.0-34.6---
CLIP4CLIP [39]99.687.8+63.437.2+4.384.8+15.411.8+8.118.0+4.045.645.943.043.640.341.6
ALPRO [26]27.1121+110196+11.3324.2+29.140.2+9.51124.9+7.233.9-35.9---
VINDLU [10]27.8121.2+110185.6+11.3775.2+29.138.9+9.5712.5+7.246.5-61.2-55.0-
UMT-B [28]27.8121.2+110185.6+11.3775.2+29.138.9+9.5712.5+7.251.049.061.659.558.356.0
>230MCLIP [46]6.9304+124649+9.71865.5+25.9108.1+9.51875.5+7.038.238.732.233.926.126.9
ViCLIP [64]5.9308.9+124830.7+9.72887.1+25.9174.2+9.52298.7+7.052.551.849.450.249.848.1
VINDLU-L [10]4.7429.4+335.1652.2+422672.4+73.1196.1+18.12373.7+20.548.8-59.8-55.9-
UMT-L [28]4.7429.4+335.1652.2+422672.4+73.1196.1+18.12373.7+20.558.858.670.465.766.864.4
+ +Table 3. Results of fine-tuned text-video retrieval on MSR-VTT [69], DiDeMo [1], and ActivityNet [23]. T2V and V2T are short for R@1 scores for text-to-video and video-to-text tasks. "video" means the efficient metrics related to video branch in the model, while "text" means the efficient metrics related to text branch in the model. "M" means $10^{6}$ . "G" means $10^{9}$ . "ms" means millisecond. MobileCLIP(10M) is our baseline fine-tuned on InternVid-10M-FLT [64]. + +
MethodK400UCF-101HMDB-51SSV2-MC
MobileCLIP-S0 [58]48.667.941.233.2
MobileCLIP-S0(10M)53.073.346.035.5
MobileViCLIP-Tiny56.275.448.839.3
MobileCLIP-S2 [58]57.073.945.741.8
MobileCLIP-S2(10M)60.477.151.844.1
InternVideo2-S14 [65]62.179.049.246.4
MobileViCLIP-Small63.181.053.746.1
MobileCLIP-B [58]61.177.750.144.9
InternVideo2-B14 [65]67.783.452.555.9
CLIP [46]58.468.943.229.6
InternVideo2-L14 [65]70.785.953.259.6
+ +Table 4. Results of zero-shot action recognition. We report top-1 accuracy on Kinetics-400 [5], UCF-101 [50], HMDB-51 [24], and Something-Something V2 [19]. MC is short for "multiple choice". MobileCLIP(10M) is our baseline fine-tuned on InternVid-10M-FLT [64]. + +
ModelMSR-VTT
Baseline38.4
+ Spatiotemporal Repmixer39.5
+ Spatiotemporal Attention w/o TPE39.1
+ Spatiotemporal Attention w/ TPE39.6
+ Spatiotemporal Repmixer + Spatiotemporal Attention w/ TPE40.1
+ +Table 5. Ablation of block designs. Baseline is MobileCLIP finetuned on MSR-VTT. TPE is short for temporal positional encodings as mentioned before. + +
Video BranchText BranchTraining MemoryMSR-VTT
ActivateFreeze24G40.1
ActivateActivate27G39.7
+ +treat MobileViCLIP as the feature extractor for QVHighlights [25] and use CG-DETR [40] as the temporal grounding detector. For a fair comparison, we also finetune the + +Table 6. Freeze branch or not. In order to directly reflect the consumption of training memory, we do not use the checkpoint technology to reduce the consumption of video memory here. We use V100 GPU to do this ablation experiment. + +
BackboneMoment RetrievalHighlight Detection
R1mAP>=Very Good
@0.5@0.70.50.75AvgmAPHIT@1
CLIP [46]66.849.165.844.143.539.364.0
CLIP [46]+SlowFast [16]67.452.165.645.744.940.866.7
MobileCLIP-S0 [58]66.048.064.942.441.839.363.6
MobileCLIP-S0 (10M)67.349.265.944.443.839.864.8
MobileViCLIP-Tiny68.451.766.745.344.940.665.4
MobileViCLIP-Small68.953.367.847.346.341.367.5
+ +Table 7. Performance comparison on QVHighlights [25] validation splits with features from different backbones for CGDETR [40]. We calculate the average mAP score with IoU thresholds ranging from 0.5 to 0.95 in 0.05 intervals. + +
MethodBackbone0.30.40.50.60.7Avg.mAP
T3ALT=0Coca(ViT-L/14)11.46.83.51.70.64.8
MobileViCLIP-Small12.57.43.61.91.25.3
+ +Table 8. Performance comparison on THUMOS14 [22] with features from different backbones for T3AL [31]. We evaluate the average mAP score with IoU thresholds ranging from 0.3 to 0.7 in 0.1 intervals. + +MobileCLIP-S0 with InternVid-10M-FLT and use it as the feature extractor to let MobileCLIP learn video-text representation. As shown in Table 7, MobileViCLIP-Small shows stronger generalization performance on both moment retrieval and highlight detection tasks, even better than the combination of CLIP [46] and SlowFast [16] features which are adopted by many temporal grounding models [36, 40]. Zero-shot temporal action detection seeks to identify and locate actions in untrimmed videos when the action label is unseen. As shown in Table 8, our MobileViCLIP-Small performs slightly better than ViT-L/14 on T3AL [31]. We also evaluate our MobileViCLIP on video captioning task on CLIP4Caption [54] and find that MobileViCLIP-Small performs better than VIT-B/32. + +# 6. Latency Analysis + +As shown in Table 2 and 3, the latency of the ViT model [10, 28, 64, 65] is tens or hundreds of times that of the efficient + +
MethodBackboneBLEU-4ROUGE-LMETEORCIDEr
CLIP4CaptionViT-B/3246.163.730.757.7
Mobile ViCLIP-Small48.966.732.161.5
+ +models [58]. To delve deeper into the reasons, we decompose the convolution and attention modules for further exploration. As shown in Table 10, we use "Conv" to represent our Spatiotemporal RepMixer and "Attn" to represent Spatiotemporal Attention. We also compare the channel mapping layer "ConvFFN" in our MobileViCLIP which is also designed in FastViT [56] and "FFN" adopted in all ViT models as the channel mixer. After that, we also simulate various usage scenarios of the input tensor by trying different input sizes and channel dimensions. We assume that the original input is 8 frames, and the patch size is $14 \times 14$ (ViT-L/14 [63] adopts it), $16 \times 16$ (ViT-B/16 [63] adopts it), $32 \times 32$ (CLIP4CLIP [46] adopts it). For channel dimension, we try 64, 128, 256, 384, 512, 768, and 1024, which are adopted by many models [14, 56, 60, 65, 74]. Among these experiments, we can draw the following conclusions: + +The Latency of Mobile Device is Much Bigger than GPU's under Fair Conditions. As shown in Table 10, we observe that the latency tested on mobile devices is significantly higher than GPU's when the input size and channel dimension are the same. The gap is around 10 times under fair conditions (compare 0.343ms with 3.97ms) and the gap increases when the spatial size is bigger. This indicates that deploying the model on mobile devices requires considering the limited computational power of mobile devices, thus imposing higher requirements on the model. + +The Latency is Positively Correlated with the Input Size. When the input has a larger feature dimension or spatiotemporal size, the latency increases on both mobile devices and GPU shown in Table 10. We also notice that the latency of attention on mobile device is consistent with the computational complexity $O(H^{2}W^{2}C)$ without considering $T$ (from 3.97ms to 60.1ms when width and height are doubled), but GPU latency does not match such complexity. This shows that the GPU has optimizations [13] for attention mechanism operations, while the mobile device does not have. Controlling the size of the input tensor is also an effective measure to reduce latency on mobile device. + +Stacking more Attention Layers Brings Bigger Latency. Table 10 shows that the attention mechanism incurs greater latency than convolution. When we construct more layers for each module shown in Table 11, we can find that building more convolution layers has little effect on latency, but the latency introduced by the attention layers increases dra + +Table 9. Performance comparison on MSR-VTT [69] with features from different backbones for CLIP4Caption [54]. We report the standard captioning metrics, BLEU4 [45], ROUGE-L [32], METEOR [3], CIDEr [59] of CLIP4Caption. + +
ST SizeDimGPU Latency (ms)Mobile Latency (ms)
ConvAttnConvFFNConvAttnConvFFN
8 × 7 × 7640.0660.0700.1910.110.210.33
1280.0670.0950.1980.160.760.57
2560.0700.1320.2090.261.170.80
3840.0710.1980.2140.371.481.01
5120.0730.2370.2250.492.011.22
7680.0750.2750.2361.322.981.75
10240.0780.3430.2951.593.972.56
8 × 14 × 14640.0710.2280.1960.132.480.69
1280.0720.2950.2050.475.010.95
2560.0720.4520.2091.1412.21.42
3840.0740.7620.2201.5518.61.98
5120.0761.0520.2272.0124.72.66
7680.0791.6080.2412.6644.64.37
10240.0822.1680.4023.0860.15.82
8 × 16 × 16640.0700.6910.2280.153.450.83
1280.0710.7660.2360.858.761.27
2560.0730.9740.2491.2518.31.91
3840.0741.5110.2621.7128.12.65
5120.0772.0260.2842.1647.33.46
7680.0813.0710.3253.0370.44.85
10240.0844.1640.4423.8393.56.52
+ +Table 10. Comparison of GPU and Mobile Latency for Different Layers and Input Sizes. "ST" is short for spatiotemporal. We report the 1-layer component's GPU latency by averaging the latency caused by the stacked 30-layer network following the settings in MobileOne [57]. For the mobile latency of each module, we only test a single layer. + +
LayersMobile Latency (ms)
ConvAttnFFNConvFFN
12.0124.71.953.65
102.98296.49.2211.19
203.18543.317.7922.39
303.47783.826.7832.33
+ +Table 11. The impact of the number of layers on the latency of Spatiotemporal RepMixer, Attention layer, FFN, and ConvFFN. The experiments are conducted with a dimension of 512 and an input size of $8 \times 14 \times 14$ . + +matically. Specifically, the latency of attention increases exponentially with the number of stacked layers (from 24.7ms to 296.4ms when stacking 10 layers) on mobile device. This indicates that mobile devices do not have GPU optimizations for attention mechanisms. + +# 7. Conclusion + +We have proposed an efficient video-text model MobileVi-CLIP for mobile devices. Equipped with minor changes inside the spatial modeling block of the efficient imagetext model, our MobileViCLIP shows better spatiotemporal representation understanding capabilities compared to the baseline. MobileViCLIP is suitable for general tasks and yields good performance on several video-text retrieval and action recognition datasets. Furthermore, we comprehensively compare existing video-text models and then analyze reasons that will cause more latency. We hope it will serve as a guideline for future research. + +# References + +[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. In Proceedings of the IEEE international conference on computer vision, pages 5803-5812, 2017. 4, 5, 6, 7 +[2] Max Bain, Arsha Nagrani, Gül Varol, and Andrew Zisserman. Frozen in time: A joint video and image encoder for end-to-end retrieval. In Proceedings of the IEEE/CVF international conference on computer vision, pages 1728-1738, 2021. 1 +[3] Satanjeev Banerjee and Alon Lavie. Meteor: An automatic metric for mt evaluation with improved correlation with human judgments. 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We propose a modularized skill learning framework, ModSkill, which incorporates body-part-level inductive bias for motor skill acquisition. ModSkill decouples full-body motion into skill embeddings for controlling individual body parts. Learned from large-scale motion datasets, these modular skills can be combined to control a simulated character to perform diverse motions, such as the Usain Bolt pose, and seamlessly reused for various downstream tasks. + +# Abstract + +Human motion is highly diverse and dynamic, posing challenges for imitation learning algorithms that aim to generalize motor skills for controlling simulated characters. Prior methods typically rely on a universal full-body controller for tracking reference motion (tracking-based model) or a unified full-body skill embedding space (skill embedding). However, these approaches often struggle to generalize and scale to larger motion datasets. In this work, we introduce a novel skill learning framework, ModSkill, that decouples complex full-body skills into compositional, modular skills for independent body parts, leveraging body structure-inspired inductive bias to enhance skill learning performance. Our framework features a skill modulariza + +tion attention mechanism that processes policy observations into modular skill embeddings that guide low-level controllers for each body part. We further propose Generative Adaptive Sampling for Active Skill Learning, using large motion generation models to adaptively enhance policy learning in challenging tracking scenarios. Results show that this modularized skill learning framework, enhanced by generative sampling, outperforms existing methods in precise full-body motion tracking and enables reusable skill embeddings for diverse goal-driven tasks. + +# 1. Introduction + +Physically simulated characters are widely used in animation [23, 59], VR/AR [36, 62], and robotic tasks [12, 13]. When combined with large-scale human motion capture + +data [38], imitation learning policies allow such characters to perform a wide range of motion skills. [19, 35, 37, 53]. + +Previous approaches to physical character skill learning can be typically classified into two categories. Tracking-based methods train controllers to imitate reference motions by tracking target pose sequences from motion clips. Recently, progressive learning techniques have been utilized to gradually extract more complex full-body motion skills from diverse data into a set of expert controllers [19, 35]. The motor skills learned from this mixture of experts can be distilled into a compact universal motion representation that offers broader coverage of human motion [37]. However, such methods still fall short in addressing scalability challenges with larger datasets, requiring more experts and increasing manual effort for skill extraction. On the other hand, Skill embedding methods employ hierarchical frameworks that pre-train compact skill embedding spaces, which are then repurposed for high-level tasks guided by carefully designed, task-specific rewards [6, 18, 47, 52, 70]. As of yet, the expressivity limitations of these latent skill spaces hinder their ability to capture the diverse range of full-body human motion skills present in larger motion datasets. Moreover, the inherent diversity of human motion poses substantial generalization challenges, making existing methods susceptible to overfitting. + +In this work, we argue that human motion is inherently modular, as evidenced by neuroscience and evolutionary developmental biology [3, 14, 21, 51]. Motivated by this modularity, we pursue Skill Modularization to introduce an inductive bias to the skill learning process that decouples full-body motion for independent control of body parts. Compared to full-body skills, modular skills for individual body parts are not only more compact but also exhibit a compositional quality that can generate highly diverse full-body motion [16, 22]. By emphasizing these compact part-level skill spaces, we can effectively learn discriminative features (Sec. 4.3) that enhance motion skill learning. + +Building on this intuition, we introduce ModSkill, a novel modularized skill learning framework that utilizes body-part inductive bias to effectively decouple full-body motor skills in large-scale motion datasets [38] into reusable, part-specific skills that each guide an independent low-level controller. Our approach incorporates a skill modularization attention mechanism that effectively captures relationships between part-specific observations and produces spherical modular skill embeddings for each controller, guiding the corresponding body parts of the simulated agent. The attention mechanism encourages full-body consistency by enabling information sharing across body parts during data-driven imitation learning. + +Imitation policies trained with DRL methods like PPO [49] often overfit to training samples, limiting generalization. To address this, we further propose a novel + +Active Skill Learning scheme using a Generative Adaptive Sampling strategy. This approach uses pre-trained large motion generation models [54] to generate synthetic samples for challenging motions. Unlike prior efforts [6, 35], where resampled motion clips consistently come from a fixed motion dataset, our method applies a powerful generative model to provide prior-level resampling capabilities, thereby enhancing the skill learning process with more diverse motion samples. We demonstrate the effectiveness of this sampling scheme for skill learning (Sec. 4.4). + +ModSkill, with its modularity and compositionality, effectively learns diverse motor skills that are reusable for various downstream tasks. We conduct extensive experiments to demonstrate that ModSkill achieves state-of-the-art performance both on full-body tracking-based tasks and across a wide range of generative, goal-driven benchmarks, including steering, reaching, striking, and VR tracking. In summary, our contributions are three-fold: + +- We propose a modularized skill learning framework that integrates a body-part level inductive bias, i.e., skill modularization, within an attention mechanism for extracting part-specific skill embeddings that guide independent low-level controllers for each body part. +- We introduce an Active Skill Learning scheme with a Generative Adaptive Sampling strategy using the generative motion prior of large motion generation models that enhances motion imitation performance. +- Our controllers achieve superior performance in precise motion tracking, and the learned part-wise skills are effectively reusable for generative downstream tasks. + +# 2. Related Work + +Physics-based Motion Imitation. Reproducing diverse and realistic human motions with physics-based characters has been a longstanding area of focus [7, 11, 24, 26-29, 41-44, 60, 70]. Given the diversity of human motion, many approaches focus on task-specific scenarios requiring only a subset of motor skills[5, 11, 61, 64, 70]. To generalize motion controllers, adversarial motion priors have been introduced [46]. Mixtures of experts have also been widely used, where each expert can focus on a specific task, bridging the gap between task-specific and generalized motion imitation [34, 35, 45, 56, 63]. However, relying on multiple experts introduces scalability challenges, as adding more experts may require increasing manual effort for progressive skill learning. Furthermore, prior methods predominantly focus on full-body skills, which may limit the expressiveness of the controller. In contrast, we address challenges in motion imitation by decoupling full-body motion into part-specific motor skills, leveraging the inductive bias of modularization to improve skill learning. + +![](images/eb792293b4f83749d5eb778fc4a39134da20cef392a52fdf451c4a1973ca6f05.jpg) +Figure 2. Left: We extract modular skills from a large-scale motion dataset using a motion imitation objective, enabling low-level controllers to control various body parts of a physically simulated character. Active skill learning, through adaptive sampling from an off-the-shelf motion generation model, further enhances policy performance. Right: The learned modular skills can be transferred to downstream tasks by freezing the low-level controllers and training a high-level policy with task-specific rewards. + +![](images/4e05799fda92064c1ff17416157cf77ca693069a2e35d012a783912179e6ad08.jpg) + +Physics-based Skill Embedding. Adversarial learning and motion imitation enable the development of reusable motion skills for diverse downstream tasks. In hierarchical learning settings, adversarial methods have been used to map structured latent embeddings to reusable low-level motor skills [6, 18, 47, 52]. While these skills transfer well to specialized tasks with tailored motion data, they struggle to scale to more diverse motions. On the other hand, efforts have been made to model probabilistic latent spaces that can capture motor skills from larger datasets [25, 40, 65, 74]. Moreover, prior work has shown that precise motion imitation policy networks can be distilled into universal motion representations, enabling coverage of large-scale motion datasets [19, 37, 56]. In contrast, our method focuses on decoupling motor skill learning during motion imitation by emphasizing the formulation of modular, part-level skills, allowing us to achieve effective and reusable skills without the need for additional distillation. + +Kinematics-based Motion Generation. The rich latent space of kinematics-based motion generation models enables the generation of diverse motion patterns from multi-modal conditions [4, 9, 17, 54, 71]. Prior work has shown that synthetic motion data provides valuable supervision for training and refining generative models [2, 8, 66]. Furthermore, when integrated with a physics-based controller, motion generation models can effectively guide task planning and execution [48, 55, 69]. In this work, we propose to leverage the expressive power of large motion generation models to adaptively create synthetic examples of challenging motion imitation scenarios, enhancing policy learning and generalization. + +Part-level Motion Learning. Prior work has shown advantages of body-part-level motion learning in both kinematics- + +based motion generation models [15, 16, 57, 72, 73] and physical controllers [1, 20, 22, 50]. Lee et al. [22] use an assembler module to combine motion signals from different sources before directing a single controller. PMP [42] adapts adversarial motion priors to body parts to extract specialized style rewards from different motion datasets. Similarly, Xu et al. [67] leverage multiple discriminators for training a control policy to imitate body part reference motions from different sources. However, both methods still rely on a single controller for full-body control, limiting motor skill decoupling across body parts. PartwiseMPC [20] takes a step further by decoupling motion planning, enabling planning for both independent body parts and the whole body, improving generalization to unseen environments. In contrast, our approach introduces compact, modularized skill embeddings and low-level controllers for individual body parts, offering reusable modular skills for both precise motion imitation and generative, goal-driven tasks. + +# 3. ModSkill + +In this paper, we present ModSkill, a modularized framework for extracting body-part-level motor skills from large-scale motion datasets through imitation learning. As illustrated in Fig. 2, our policy network consists of two key components for modularized skill learning: 1) a skill modularization attention mechanism (Sec. 3.2) that produces spherical embeddings to capture body-part-specific skills, and 2) a set of low-level skill-conditioned controllers (Sec. 3.3) that control the movement of individual body parts. To further improve policy performance, we introduce a generative adaptive sampling strategy that incorporates synthetic data from motion generation models into policy training (Sec. 3.4). Additionally, we show that the modular skills learned in our framework can be effectively transferred to downstream tasks via a high-level, task-specific policy (Sec. 3.5). + +# 3.1. Preliminaries + +Given a reference motion sequence of $T$ frames, $s_{1:T}^{r}$ , our policy network, denoted as $\pi_{\mathrm{ModSkill}}$ , is tasked to control a SMPL-based simulated humanoid agent [30, 35] to imitate the reference motion. We model the policy network as a Markov Decision Process (MDP), $M = \langle S, A, T, R, \gamma \rangle$ , where $S, A, T, R, \gamma$ represent the state space, action space, transition dynamics, reward function, and discount factor. + +States and Actions. Following prior work [35], the state $s_t$ at time $t$ is composed of the proprioceptive state $s_t^p$ and the reference state $s_t^r$ . Specifically, $s_t^p$ describes the current simulated configuration of the agent and is defined as: + +$$ +s _ {t} ^ {p} := \left(\theta_ {t}, p _ {t}, v _ {t}, \omega_ {t}\right) \tag {1} +$$ + +where $\theta_{t}, p_{t}, v_{t}$ , and $\omega_{t}$ are the simulated joint rotations, positions, velocities, and angular velocities, respectively. The reference state $s_{t}^{r}$ encodes the target joint poses for time step $t + 1$ , and the differences between the target joint poses and velocities of time step $t + 1$ and the corresponding simulated values at the current time step, $t$ : + +$$ +s _ {t} ^ {r} := \left(\hat {\theta} _ {t + 1} \ominus \theta_ {t}, \hat {p} _ {t + 1} - p _ {t}, \hat {v} _ {t + 1} - v _ {t}, \hat {\omega} _ {t + 1} - \omega_ {t}, \hat {\theta} _ {t + 1}, \hat {p} _ {t + 1}\right) \tag {2} +$$ + +where $\ominus$ denotes rotation difference. Here, $\hat{\theta}_{t + 1}$ , $\hat{p}_{t + 1}$ , $\hat{v}_{t + 1}$ , and $\hat{\omega}_{t + 1}$ represent the reference joint rotations, positions, velocities, and angular velocities, respectively. Both $s_t^r$ and $s_t^p$ are canonicalized with respect to the agent's local coordinate frame. PD (proportional-derivative) controllers are used, enabling the agent to follow desired joint angles and velocities based on the reference motion. The action space specifies PD control targets for each actuated joint, without using residual forces [68] or residual control [33]. + +Reward. We define the reward term as the sum of an imitation reward, $r_{\text{imitation}}$ , a full-body discriminator reward, $r_{\text{amp}}$ , to encourage natural and consistent full-body motion from body-part-level motor skills [46], and an energy penalty reward, $r_{\text{energy}}$ , to encourage smoother motion [62]: + +$$ +r := r _ {\text {i m i t a t i o n}} + r _ {\text {a m p}} + r _ {\text {e n e r g y}} \tag {3} +$$ + +Specifically, the imitation reward $r_{\text{imitation}}$ encourages the humanoid agent to imitate the reference motion by minimizing the difference between the translation $(p_t, \hat{p}_t)$ , rotation $(\theta_t, \hat{\theta}_t)$ , linear velocity $(v_t, \hat{v}_t)$ , and angular velocity $(\omega_t, \hat{\omega}_t)$ of the simulated character and the target motion: + +$$ +\begin{array}{l} r _ {\text {i m i t a t i o n}} := w _ {p} e ^ {- \lambda_ {p} \| p _ {t} - \hat {p} _ {t} \|} + w _ {\theta} e ^ {- \lambda_ {\theta} \| \theta_ {t} - \hat {\theta} _ {t} \|} \tag {4} \\ + w _ {v} e ^ {- \lambda_ {v} \| v _ {t} - \hat {v} _ {t} \|} + w _ {\omega} e ^ {- \lambda_ {\omega} \| \omega_ {t} - \hat {\omega} _ {t} \|} \\ \end{array} +$$ + +where $w_{\{\cdot \}}$ $\lambda_{\{\cdot \}}$ denote the corresponding weights. + +# 3.2. Skill Modularization + +To achieve modularized skill learning, we partition the rigid bodies of the simulated agent into $K$ sets, each corresponding to a distinct body part. In this work, we set $K = 5$ , + +![](images/fb071fa30f1e7f63afa55304b3a219ca32cb40b712d97dae2424122dfe6eb5c2.jpg) +Figure 3. Skill Modularization Attention Mechanism: Given partial states for each body part, attention between body parts allows information sharing for producing modular skill embeddings. + +corresponding to the set of body parts, $\mathcal{P} := \{\text{Left Leg (L-Leg)}, \text{Right Leg (R-Leg)}, \text{Left Arm (L-Arm)}, \text{Right Arm (R-Arm)}, \text{Torso}\}$ . Note that the specific partitioning is not restrictive, and can be adapted to suit different use cases or system configurations (see Supplementary). + +Let the state of all joints for body part $k \in \mathcal{P}$ at time $t$ be denoted as $s_t^k$ . Our policy network incorporates an attention mechanism to enable high-level information sharing across body parts for effective skill modularization and encouraging full-body consistency. As shown in Fig. 3, for each body part $k \in \mathcal{P}$ , the corresponding state $s_t^k$ is projected into three vectors: key $\mathbf{K}_t^k$ , query $\mathbf{Q}_t^k$ , and value $\mathbf{V}_t^k$ . The attention scores between the query $\mathbf{Q}_t^k$ of the current body part $k$ and the keys $\mathbf{K}_t^{k'}$ from all body parts $k' \in \mathcal{P}$ are computed by calculating the scaled dot-product between the query and each key, and then passed through a softmax function to obtain the attention weights: + +$$ +\alpha_ {t} ^ {k, k ^ {\prime}} = \operatorname {s o f t m a x} \left(\frac {\mathbf {Q} _ {t} ^ {k} \cdot \mathbf {K} _ {t} ^ {k ^ {\prime}}}{\sqrt {d}}\right) \tag {5} +$$ + +where $d$ is the dimension of the query and key vectors. The attention weights $\alpha_{t}^{k,k^{\prime}}$ indicate the relative importance of the states of different body parts when computing the skill embedding for body part $k$ . The skill embedding $z_{t}^{k}$ for each body part is then obtained by computing a weighted sum of the value vectors $\mathbf{V}_{t}^{k^{\prime}}$ from all body parts, with the attention weights serving as the coefficients: + +$$ +z _ {t} ^ {k} = \sum_ {k ^ {\prime}} \alpha_ {t} ^ {k, k ^ {\prime}} \mathbf {V} _ {t} ^ {k ^ {\prime}} \tag {6} +$$ + +$z_{t}^{k}$ is normalized with respect to $\| z_t^k\|$ to lie on the unit sphere. This normalization ensures that the skill embeddings are constrained within a consistent space, allowing for more stable learning [47]. By sharing information via this attention mechanism, each body part can focus on different aspects of the overall state for modularized skill learning. + +# 3.3. Modular Low-Level Controllers + +To further enhance the flexibility and effectiveness of our policy network, we implement modular low-level con + +![](images/f244e8e7233b04a691613b2cfbd5ee4643a756cc29565f4fff59f500faffd0ac.jpg) +Figure 4. Generative Adaptive Sampling: When the policy struggles to track a challenging motion, such as crawling (left), we adaptively generate new samples (middle) using motion generation models. These generated sequences introduce diverse variations, including changes in motion trajectories and leg usage (highlighted in green), which allow the policy to effectively learn motor skills and successfully track the challenging scenario (right). Motion frames are displayed sequentially from left to right. Red spheres indicate target joint locations. + +![](images/6fce96f6f3aeda6eca6c1d8d69cc0baf74f13a4a6af8328e77e542c2bce3718b.jpg) + +![](images/c1acf80bb53872240714d30b6540e4918274c95a814ffaa92eb8066253697e17.jpg) + +trollers that operate alongside the skill modularization attention mechanism. For each body part $k$ , we designate a low-level controller $\pi^k = \mathcal{N}(\mu (z_t^k),\sigma)$ , which models a Gaussian distribution with fixed diagonal covariance. The skill embeddings, $z_{t}^{k}$ , generated by the attention mechanism serve as the input for these controllers, which process the information to produce targeted actions $a_{t}^{k}$ for the actuated rigid bodies corresponding to body part $k$ . The produced actions for each controller are concatenated to form the full-body PD target, denoted as $a_{t}$ , for controlling the simulated agent. Using the same setup in [46], we incorporate a full-body discriminator $D_{\mathrm{amp}}$ that computes a real/fake value based on the current full-body proprioception of the humanoid. This style signal encourages the formulation of natural full-body motion from modular part-level skills. By decoupling the action prediction into specialized modules, we enhance the flexibility of the network, enabling effective imitation for a wide range of motions. + +# 3.4. Generative Adaptive Sampling + +Active skill learning enables efficient policy training by directing the learning process toward more informative regions of the skill space. Denote $S$ as the skill space and $p_{\theta}$ as the distribution of trajectories produced by the policy network, parameterized by $\theta$ . The objective of skill learning can be defined as maximizing the expected return: $J(\theta) = \mathbb{E}_{\tau \sim p_{\theta}(\tau)}[R(\tau)]$ , where $\tau = \{(s_t, a_t)\}_{t=1}^T$ denotes a sampled trajectory, and $R(\tau)$ represents the cumulative reward. Prior methods [6, 35, 37] adaptively sample motion sequences based on their failure probability. However, this approach operates on a fixed dataset $D_{\mathrm{train}}$ , which may suffer from overfitting to challenging motion sequences. + +Instead of relying solely on the fixed training set, we propose a Generative Adaptive Sampling strategy. For each failed sample $\tau_{\mathrm{fail}}$ , we synthesize $N$ motion sequences $\{\tilde{\tau}_i\}_{i=1}^N$ using an off-the-shelf text-to-motion diffusion model [54], conditioned on the corresponding HumanML3D text descriptions $\mathcal{T}(\tau_{\mathrm{fail}})$ [9]: + +$$ +\tilde {\tau} _ {i} \sim p _ {\phi} (\tau | \mathcal {T} (\tau_ {\text {f a i l}})) \tag {7} +$$ + +where $p_{\phi}(\tau|\mathcal{T})$ denotes the conditional generative distribution of the diffusion model parameterized by $\phi$ . This process ensures that the generated motions maintain semantic consistency with the failed motion while introducing diverse variations. To mitigate the impact of unrealistic motion artifacts from synthetic data, we utilize the adversarial discriminator to filter out "fake" samples: + +$$ +\mathcal {F} \left(\tilde {\tau} _ {i}\right) = \left\{ \begin{array}{l l} \tilde {\tau} _ {i} & \text {i f} D _ {\mathrm {a m p}} \left(\tilde {\tau} _ {i}\right) \geq 0. 5 \\ \emptyset & \text {i f} D _ {\mathrm {a m p}} \left(\tilde {\tau} _ {i}\right) < 0. 5 \end{array} \right. \tag {8} +$$ + +where $\varnothing$ indicates that the sample is discarded. Finally, we integrate the filtered synthetic motion samples into the training process by augmenting the dataset: $\mathcal{D}_{\mathrm{train}}\gets \mathcal{D}_{\mathrm{train}}\cup \{\mathcal{F}(\tilde{\tau}_i)\}_{i = 1}^N$ . Qualitative results in Fig. 4 demonstrate that this expanded dataset provides more balanced and comprehensive motion samples, enabling the policy to generalize better across diverse skill variations. + +# 3.5. Skill Transfer for Downstream Tasks + +After $\pi_{\mathrm{ModSkill}}$ converges, a high-level policy $\pi_{\mathrm{Task}}(z_t^{k_1},\dots,z_t^{k_K}|s_t^p,s_t^g)$ can be trained to apply the learned modular skills to downstream tasks, where $s_t^p$ and $s_t^g$ represent the proprioceptive state and task-specific goal signal, respectively, and $z_t^{k_1},\dots,z_t^{k_K}$ indicate the corresponding spherical skill embeddings for each body part $k_{1},\ldots ,k_{K}\in \mathcal{P}$ . Similar to the low-level controllers, each high-level task policy is modeled as a Gaussian distribution with a fixed diagonal covariance: $\mathcal{N}(\mu_{\mathrm{Task}}(s_t^p,s_t^g),\sigma_{\mathrm{Task}})$ . When training the high-level policy, we freeze the low-level controllers to preserve the learned modular motor skills. In this work, we demonstrate the effectiveness and reusability of our modular part-level skills on a set of generative motion tasks. Details regarding the setup of each task are provided in the supplementary material. + +# 4. Evaluation + +Experiment Settings. Motion Tracking Task: We evaluate ModSkill's performance on the full-body motion tracking task, comparing it against state-of-the-art motion trackers + +![](images/205d4c947c93126384b055be82ec0aba72eb02e76c5c6ad9e90264a708cf8529.jpg) +Figure 5. Qualitative results of motion tracking on AMASS-Test (left) and the corresponding attention maps during skill modularization (right). Red spheres indicate the target joint locations in the simulation. The attention maps reveal that, when extracting skill embeddings, body parts are capable of focusing on their own specific information for precise movements (e.g., hands during clapping) while also attending to holistic information across body parts for full-body consistency (e.g., stabilizing lower body when landing from a jump). + +![](images/936c0b6be4c54e4e2334217ef836336735dfebdc906a01dbaa68f3889ecd22e3.jpg) + +![](images/e253b0e327fad5c982191104dedb605b4c624682a42c5d7136714f1f0a032c29.jpg) + +![](images/3d5bc97e19d18dc5b12f798cdb928bad0ce6111fca1a658233dc6c085e012943.jpg) + +UHC [32], PHC [35], PHC+ and PULSE [37]. Motion Skill Embedding Task: We also highlight the reusability of our modular skill embeddings by applying ModSkill to generative tasks such as reaching, steering, striking, and VR tracking, and comparing its performance with reusable skill representations: PULSE [37] and ASE [47]. Following [37], we adapt ASE to produce per-frame latent skill embeddings for a fair comparison. Notably, while the original ASE uses a full-body adversarial motion prior, we will also compare the impact of partwise adversarial motion priors [1] on learning skill embeddings and high-level tasks (ASE-PMP). We adopt the same body part partition as our framework to formulate ASE-PMP. + +Datasets. For training and testing the full-body and VR tracking policies, we utilize the cleaned AMASS training set and test set, respectively [35]. For the strike and reach tasks, we sample initial states from the AMASS training set. For speed tasks, we follow [59] to use a subset of AMASS of only locomotion for initial state sampling. + +Metrics. For motion imitation and VR tracking, we report the global end-effector mean per-joint position error $(E_{\mathrm{g - mpjpe}})$ and root-relative end-effector mean per-joint position error $(E_{\mathrm{mpjpe}})$ in millimeters. We also compare physics-based metrics, including acceleration error $(E_{\mathrm{acc}})$ in mm/frame² and velocity error $(E_{\mathrm{vel}})$ in mm/frame. Following [35], we define the success rate (Succ) as the percentage of time the average per-joint error remains within 0.5 meters of the reference motion. For VR tracking, the success rate is based on only three body points (Head, Left Hand, Right Hand). For generative tasks (reach, steer, strike), we compare the undiscounted return normalized by + +the maximum possible reward per episode. We also compute the Average Pairwise Distance (APD) [6, 10, 31, 58] to measure the diversity of motion sequences produced for each task, where a larger value indicates higher diversity. + +Implementation Details. All physics simulations are conducted using Isaac Gym [39]. Our policy network is trained with 3072 parallel environments on a single NVIDIA A6000 GPU for approximately 2e9 steps. For PULSE, we use the original model settings. For ModSkill and the ASE baselines, all low-level controller networks are four-layer perceptrons (MLPs) with dimensions [2048, 1536, 1024, 512]. Discriminators and encoders for adversarial skill learning are two-layer MLPs with dimensions [1024, 512]. Each high-level policy for downstream tasks is a three-layer MLP with dimensions [2048, 1024, 512]. The latent dimension of the skill embeddings is 64. The controllers operate at $30\mathrm{Hz}$ , while the simulation runs at $60\mathrm{Hz}$ . Additional details are provided in the supplementary material. + +# 4.1. Motion Tracking + +Tab. 1 and Tab. 2 show the performance of our method on the AMASS train and test sets for the full-body motion tracking task and VR tracking task, respectively. For both tracking tasks, our modular policy network outperforms baselines, reducing tracking errors on both training and test motion sequences. Fig. 5 shows qualitative results of full-body tracking on AMASS test, along with attention maps from skill modularization. Each row of an attention map represents a queried body part, while the columns correspond to other body parts serving as keys. The attention weights reflect how information from each key contributes to the queried part's skill embedding. For precise, localized + +actions such as hand clapping or slow steps, body parts primarily attend to their own features. In contrast, for motions requiring full-body coordination, such as landing or punching from a squat, multiple body parts share information to maintain consistency and stability. Our experiments show that by modularizing skills, a single network can achieve better imitation accuracy and generalization capabilities. + +Table 1. Full-body tracking results on AMASS train and test. + +
AMASS-TrainAMASS-Test
MethodSucc ↑Eg-mjpjeEmpjpe ↓Eacc ↓Evel ↓Succ ↑Eg-mjpjeEmpjpe ↓Eacc ↓Evel ↓
UHC97.0%36.425.14.45.996.4%50.031.29.712.1
PHC98.9%37.526.93.34.997.1%47.540.06.89.1
PULSE99.8%39.235.03.15.297.1%54.143.57.010.3
PHC+100%26.121.12.63.999.2%36.124.16.28.1
Ours99.6%25.520.42.13.499.3%32.222.74.46.3
+ +Table 2. VR tracking results on AMASS train and test. + +
AMASS-TrainAMASS-Test
MethodSucc ↑Eg-mpijeEmpjpeEacc ↓Evel ↓Succ ↑Eg-mpijeEmpjpeEacc ↓Evel ↓
ASE18.6%128.787.940.933.38.0%114.399.257.744.0
ASE-PMP7.2%159.7155.7142.2123.01.5%161.7126.1151.196.4
PULSE99.5%57.851.03.97.193.4%88.667.19.114.9
Ours99.3%52.947.93.76.493.4%83.265.78.813.4
+ +# 4.2. Skill Embedding Downstream Tasks + +As shown in Fig. 6, the modular skills learned by our framework can be effectively applied to downstream tasks. In Tab. 3, we record the normalized return for the downstream tasks, steering, reach and strike, with 0 being the minimum possible return value, and 1 being the maximum. Compared to ASE baselines, our method creates a more expressive skill space, leading to superior normalized returns. Our approach matches PULSE in performance, but, unlike PULSE, our policy network does not require additional distillation from a motion tracking policy to obtain effective skill embeddings. Instead, the learned modular skills can be directly applied to a variety of downstream tasks while preserving accurate motion imitation capabilities. In contrast, PULSE suffers from a significant decrease in motion tracking accuracy compared to the motion tracking policy, $\mathrm{PHC + }$ , used for distillation (see Tab. 1). We further compare the diversity of motion sequences produced by PULSE and ModSkill for each task using the APD score. Specifically, we calculate the mean and standard deviation of this metric over 10 iterations, each sampling 10,000 motion sequences per task. Tab. 4 shows that ModSkill achieves higher motion diversity across the three generative tasks, demonstrating the effectiveness of modular skills. + +# 4.3. Skill Interpolation and Composition + +In Fig. 7, we present the t-SNE visualization of body-part skill embeddings for motions from AMASS-Test. We uniformly sample skill embeddings for each body part every 10 frames, resulting in $\sim 3000$ samples. For clarity, we label a + +Table 3. Normalized returns for steering, reach, and strike. + +
SteeringReachStrike
ASE0.60±0.0010.10±0.0030.12±0.006
ASE-PMP0.31±0.0020.06±0.0020.13±0.004
PULSE0.92±0.0020.77±0.0020.88±0.002
ModSkill0.93±0.0010.79±0.0020.88±0.003
+ +Table 4. APD of motions produced for steering, reach, and strike. + +
SteeringReachStrike
PULSE123.74±0.1387.97±0.1188.94±0.28
ModSkill128.13±0.14116.12±1.6094.86±0.94
+ +![](images/f12fe56459856bc04daf9ff49265b46eca69a488321268e37ba78168d0847928.jpg) + +![](images/a39df22ce7b67e82496ae13a8e0c44838ebe10c6757638207d72bc1f73306479.jpg) + +![](images/de7872fcd3ec43e6af50d3bc02b6b126e435d0617ca6aa14b608043ccb5e7c2b.jpg) + +![](images/e81c941d8e47a604db467683444d550ef93518a1a363cac9ab036ef2b0a54d3c.jpg) +Figure 6. Our modular skill embeddings are flexible and informative, achieving natural human-like behavior in downstream tasks. + +subset of samples for five different types of motions. We observe consistent structures for the same motion across body parts, with symmetric structures emerging for motions with alternating patterns, e.g., walking and jumping. We further demonstrate the structure of modular skill embeddings through interpolation. In Fig. 8, we begin with the sequence of skill embeddings that controls the simulated character to cross both arms in front of its chest, and then gradually interpolate the left-hand skill embeddings towards those corresponding to a left-hand waving motion, while keeping the sequence of skill embeddings for all other body parts unchanged. The resulting motion exhibits a smooth transition, and further analysis of the left hand's linear velocity in the local coordinate frame over simulated time steps confirms this smoothness. Furthermore, due to the modularity of the controllers, our framework allows for flexible integration of new modular components. For example, as shown in Fig. 9, we can combine articulated hand controllers with our pre-trained body part controllers to control a humanoid with dexterous hands to imitate a motion sequence without retraining the entire framework from scratch. + +![](images/34f6643f165166ebe951f894dd63fcbef20e2fb03bb2a55c38ef98c10b690637.jpg) +Figure 7. Modular Skill Embedding t-SNE Visualization on AMASS-Test. + +![](images/56d4637446aa6690475ee8ee4d8142ffa1c36e68f26f13dafd1f3e4c967d8a75.jpg) +Figure 8. Skill Interpolation: Interpolating left-hand skill embeddings from "crossing arms" to "waving" shows a smooth transition in motion (top row) and linear velocity in the local coordinate frame (bottom row) for the left-hand of the humanoid. + +![](images/0f8e82db86769e685f443228ee5296507445172e79da055d44c3f476bcd78b4d.jpg) +Figure 9. ModSkill enables flexible integration of additional modular controllers without needing to retrain from scratch. By combining articulated hand controllers (highlighted in yellow) with our pre-trained body part controllers, we can control a humanoid with dexterous hands. Red spheres represent target joint locations. + +# 4.4. Ablations + +We ablate the effectiveness of each component within our framework with respect to the full-body motion tracking task. In Tab. 5, we present motion tracking results on the AMASS test set with respect to the following configurations: with/without modular controllers for individual body parts, with/without a skill modularization attention mechanism to extract modular skill embeddings, and with/without generative adaptive sampling. We observe that incorporating all components yields the best performance. Notably, even without the attention mechanism, our model outperforms $\mathrm{PHC + }$ in motion tracking on unseen motion sequences, highlighting the effectiveness of modular motor skills. The addition of the attention mechanism not only improves performance but also enables the formulation of + +reusable modular motor skills for applications to downstream tasks. Furthermore, generative adaptive sampling enhances policy performance on unseen motions. + +Table 5. Ablation on components of ModSkill. We evaluate on AMASS-Test for the full-body motion tracking task to demonstrate the effectiveness of each component. Modular: whether to use low-level controllers for each body part, Attention: whether to use a skill modularization attention layer. Generative: whether to use generative adaptive sampling. + +
ModularAttentionGenerativeSucc ↑Eg-mpjpe ↓Empjpe ↓Eacc ↓Evel ↓
×××96.4%41.128.45.47.2
×✓×98.5%37.427.25.17.1
✓××98.6%35.923.84.46.5
✓✓×99.3%32.423.24.56.3
✓✓✓99.3%32.222.74.46.3
+ +# 5. Conclusion + +In this paper, we introduce a novel modularized skill learning framework, ModSkill, which decouples complex full-body skills into compositional, modular skills for independent body parts. The framework incorporates a Skill Modularization Attention layer that transforms policy observations into modular skill embeddings, guiding independent low-level controllers for each body part. Additionally, our Active Skill Learning approach with Generative Adaptive Sampling utilizes large motion generation models to adaptively enhance policy learning in challenging tracking scenarios. Our results demonstrate that this modularized framework, enhanced by generative sampling, outperforms existing methods in achieving precise full-body motion tracking and enables reusable skill embeddings for diverse, goal-driven tasks. + +Limitations. While modularized skill learning offers advantages in creating compact, compositional skill spaces, it introduces an inherent tradeoff in search complexity due to the formulation of multiple modular components. Future work could explore methods for improving the efficiency of modular skill composition. Additionally, incorporating environment-aware interaction priors and strategies for sim-to-real transfer would be promising directions for extending the framework. + +# References + +[1] Jinseok Bae, Jungdam Won, Donggeun Lim, Cheol-Hui Min, and Young Min Kim. Pmp: Learning to physically interact with environments using part-wise motion priors. In ACM SIGGRAPH 2023 Conference Proceedings, New York, NY, USA, 2023. Association for Computing Machinery. 3, 6 +[2] Michael J. Black, Priyanka Patel, Joachim Tesch, and Jinlong Yang. BEDLAM: A synthetic dataset of bodies exhibiting detailed lifelike animated motion. 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Martel $^{1,2}$ + +Sunnybrook Research Institute, Canada + +$^{2}$ University of Toronto, Canada + +3Google Research, USA + +$^{4}$ Independent Researcher + +# Abstract + +Prediction tasks in digital pathology are challenging due to the massive size of whole-slide images (WSIs) and the weak nature of training signals. Advances in computing, data availability, and self-supervised learning (SSL) have paved the way for slide-level foundation models (SLFMs) that can improve prediction tasks in low-data regimes. However, current methods under-utilize shared information between tasks and modalities. To overcome this challenge, we propose ModalTune, a novel fine-tuning framework which introduces the Modal Adapter to integrate new modalities without modifying SLFM weights. Additionally, we use large-language models (LLMs) to encode labels as text, capturing semantic relationships across multiple tasks and cancer types in a single training recipe. ModalTune achieves state-of-the-art (SOTA) results against both unimodal and multi-modal models across four cancer types, jointly improving survival and cancer subtype prediction while remaining competitive in pan-cancer settings. Additionally, we show ModalTune is generalizable to two out-of-distribution (OOD) datasets. To our knowledge, this is the first unified fine-tuning framework for multi-modal, multitask, and pan-cancer modeling in digital pathology. Our code is publicly available at https://github.com/martellab-sri/ModalTune. + +# 1. Introduction + +Prediction tasks in histopathology are challenging due to the massive size and complexity of WSIs, which can contain critical diagnostic information for tumor staging, subtyping, and prognosis assessment. These predictive signals are often at the slide-level, requiring weakly-supervised learn + +![](images/7fe5bcd926aed9906c6cf8d8d772e0d253f792a1cb398bce3899845035badc2b.jpg) +Figure 1. Unlike standard fine-tuning approaches that focus on a single task, modality, and cancer site, our novel fine-tuning framework, ModalTune, leverages shared information across multiple tasks, modalities, and cancer sites to interface with SLFMs. + +ing approaches. Multiple Instance Learning (MIL) has become a key method for WSI analysis, dividing WSIs into patches, extracting features using pre-trained models, and aggregating them into slide-level representations through various pooling methods [9, 28, 54, 59, 61, 79]. With the development of large patch-level foundation models (FMs) [11, 13, 43, 69], feature extraction has improved, thereby enhancing the performance of MIL in slide-level tasks [7]. + +Recent advances in computational resources, data availability, and algorithm efficiency have led to the development of SLFMs, which involve training MIL aggregators ('slide encoders') using SSL techniques. These SSL techniques include masked image modeling [25, 72], contrastive learning with transcriptomics [29, 64], pathology reports [1, 17], and multiple stains [32], marking a shift from patch-level FMs to robust SLFMs. Yet, many domain-specific variations may still not be captured during pre-training, such as differences in tissue preparation across clinical centers, OOD morphological characteristics, and the presence of complex or rare diseases. This makes fine-tuning of SLFMs a more effective strategy for deployment on new datasets. + +Current frameworks for deploying SLFMs are limited to fine-tuning them on a single task and cancer site while taking only WSIs as input (Fig. 1). They fail to fully leverage rich datasets, which may include other modalities like clinical records, reports, and genomics, as well as extensive slide annotations like cancer subtypes, tumor staging, prognosis, and biomarker presence. Existing frameworks face two key limitations when applied in this setting: (1) Existing SLFMs use only WSIs as input during inference, overlooking other modalities. While these models may have incorporated other modalities for training, there are significant benefits to leveraging them during inference to capitalize on multi-modal insights [10, 31]. (2) Current frameworks often emphasize single-task learning, overlooking interconnected multi-task information that could enhance SLFMs' fine-tuning performance and generalization [14]. These challenges result in suboptimally fine-tuned SLFMs. + +To address these limitations, we propose two enhancements that transform SLFMs into multi-modal and multitask learners while preserving their foundational knowledge: (1) We introduce the Modal Adapter. Inspired by recent work in NLP and natural images [12, 51], this module interfaces with slide-encoders in histopathology to integrate information from additional modalities without altering the primary model's weights. (2) We introduce text-based multi-task learning. We convert downstream tasks (e.g. subtype classification, risk prediction) into text and use LLMs to represent them as text vectors in a unified embedding space. We tune our models to predict these text embeddings using a single loss function, regardless of the task type or number, enabling the model to leverage semantic relationships between entities within and across tasks. + +Our overall method called ModalTune is a fine-tuning framework designed to fully leverage the potential of SLFMs and pathology datasets. Our main contributions are: + +- Modal Adapters: We propose Modal Adapters to continually inject multi-modal information into slide encoders without altering their weights. It can interface with any transformer-based slide encoder and dynamically scale to new modalities. +- Multi-Task Learning: We simplify multi-task learning by mapping tasks into a shared embedding space using LLMs, leveraging complementary semantic and intertask relationships. Our formulation optimizes a single loss function regardless of the number or type of tasks. +- Pan-Cancer Fine-Tuning: Our framework integrates multiple cancer sites, resulting in a single resource-efficient, pan-cancer model that generalizes across tasks and sites. We show this approach enables smaller datasets to leverage key insights from larger ones. + +To the best of our knowledge, we propose the first finetuning framework for unified approach for multi-modal, multi-task, and pan-cancer modeling in digital pathology. + +We validate our approach on four TCGA datasets [63]: Breast Invasive Carcinoma (BRCA), Non-small Cell Lung Carcinoma (NSCLC), Glioblastoma Multiforme and Low-Grade Glioma (GBMLGG), and Renal Cell Carcinoma (RCC), covering 4,099 slides and 3,418 patients. Using Prov-Gigapath [72] (referred to as Gigapath) as our SLFM, our model outperforms uni-modal and multi-modal baselines in cancer subtype and survival prediction, achieving higher balanced accuracy and C-indices than the fine-tuned uni-modal Gigapath $(+4.6\%, +9.6\%)$ , its multi-modal counterpart $(+2.8\%, +7.0\%)$ , and the best baseline $(+1.4\%, +1.9\%)$ . We further tested our model on two smaller OOD datasets: Colon and Rectum Adenocarcinoma (COAD-READ) and Bladder Urothelial Carcinoma (BLCA), where it retained generalizability, performed competitively with the supervised baseline and outperformed its fine-tuned counterpart by a large margin $(+25\%, +8.3\%)$ . + +# 2. Related Work + +This section reviews related works on WSI-text alignment, multi-modal and multi-task methods in digital pathology. + +WSI-Text Alignment: Recent vision-language models (e.g. CLIP [52], CoCa [74], Llava [41], and BLIP-2 [38]) have advanced text alignment at the patch-level in digital pathology [43, 44, 80]. More recently, studies have aligned WSIs with slide-level diagnostic reports, with PRISM [57] using attention mechanisms and CoCa [74], and Gigapath [72] leveraging masked autoencoder pre-training [25] and contrastive learning on pathology reports. TITAN [17] enhances WSI-text alignment by first aligning slide embeddings with synthetic region-level captions, then refining them using slide-level pathology reports for improved representation. PathAlign [1] under the BLIP-2 [38] framework integrates slide encoder with frozen LLMs for report generation, WSI classification, and text retrieval. + +While our work shares similarities with contrastive learning-based WSI-text alignment, it introduces key differences. Existing methods rely on large-scale datasets, pathology reports, and large batch sizes, limiting their adaptability. In contrast, our approach aligns more closely with typical MIL frameworks, enabling fine-tuning in a single-batch setting using widely available synoptic data, hence making it adaptable to any dataset. + +Multi-Modal Models: Multiple studies in digital pathology show that integrating WSIs with clinical data—such as RNA transcriptomics [8, 10, 31, 33], copy number alterations (CNA) [10, 16], MRI scans [50], or clinical captions [80]—captures complementary biological and contextual insights, improving prediction over single-modality models. Multi-modal fusion in digital pathology employ various strategies to integrate heterogeneous data. Early fusion combines raw input features before processing, with initial methods using concatenation or pooling [27]. Inspired by + +advances in Visual Question Answering field, recent approaches leverage cross-attention mechanisms [10, 31, 80]. Late fusion aggregates predictions from modality-specific models using methods like concatenation [18, 46], Kronecker products [8], or transformer-based fusion [73]. + +Our Modal Adapters, inspired by ViT Adapters [12], differ by performing cross-attention between modalities at multiple hidden layers, followed by summation-based fusion to generate the final feature representations. + +Multi-Task Learning: Multi-task learning (MTL) optimizes related tasks from the same input by leveraging shared representations, enhancing data efficiency, generalizability, and reducing overfitting [14], making it especially useful in digital pathology which has co-related tasks like cancer subtyping, survival, and biomarker prediction. Early work at the patch level by Li et al. [39] used histopathology patches for breast cancer classification and grading, while Simon et al. [24] proposed a unified model for cell and tissue segmentation and classification. At the WSI-level, Weng et al. [71] introduced MTL for predicting multiple slide-level metadata, Gao et al. [20] developed a framework for cancer region detection and subtyping, and Zhao et al. [78] proposed a multi-task graph transformer for tumor typing and staging. More recently, Shao et al. [58] explored MTL for cancer subtyping, survival prediction, and transcriptomic profiling of gene TP53. + +Unlike prior works that optimize multiple task-specific loss functions, our approach uses LLMs to unify tasks into a single representation, requiring only a single loss function for training. This offers greater simplicity and flexibility, making it easier to adapt to diverse or additional task sets. + +# 3. Method + +We introduce ModalTune, illustrated in Fig. 2, starting with conventional pretrained slide encoder (Sec. 3.1), and feature extraction from additional paired modalities (Sec. 3.2). We then present the Modal Adapter (Sec. 3.3) that injects additional modality features into the slide encoder. Finally, we describe the text embedding process (Sec. 3.4) for unifying tasks and cancer sites into a single embedding space and explain the overall training objective (Sec. 3.5). + +# 3.1. Slide Encoder + +We build on the SLFM Gigapath [72], chosen for its strong performance, computational efficiency, and publicly available pre-trained weights. Gigapath effectively models slide embeddings by leveraging all patches and scales well in scenarios involving multiple slides with a large number of patches, enabling analysis without excessive overhead. This balance of efficiency and coverage makes it a practical choice for our study, even though more recent SLFMs may achieve stronger benchmark performance. Importantly, our framework remains fully adaptable to any transformer- + +based SLFM. For experiments on ModalTune applied to recent SLFM like TITAN [17], please refer to Supp. Sec. 12. + +Slide encoders extract WSI features using a two-step process. First, a WSI $\mathbf{X}_{img}$ is divided into $N_{img}$ patches, and Gigapath's pre-trained patch encoder extracts $D_{img}$ dimensional features, resulting in $\hat{\mathbf{X}}_{img} \in \mathbb{R}^{N_{img} \times D_{img}}$ . The pre-trained Gigapath model, an $L$ -layer LongNet [68], facilitates interactions among patch embeddings. Before further processing, these patch features pass through a linear layer to produce $\mathcal{F}_{img}^0 \in \mathbb{R}^{N_{img} \times D}$ , where $D$ is the LongNet embedding size. For ease of notation in Sec. 3.3, the $L$ LongNet layers are divided into $B$ blocks, each with $L / B$ layers. Following the Gigapath model, we use the frozen pre-trained [CLS] token from the slide encoder to aggregate patch embeddings into a single representation. Thus, after passing through the $i$ -th LongNet block, the patch embeddings are $\mathcal{F}_{img}^i \in \mathbb{R}^{(N_{img} + 1) \times D}$ , for $i \in \{1, 2, \dots, B\}$ . + +# 3.2. Modal Encoders + +Modal encoders are employed to extract features from each additional modality, which will be used to inform the pretrained slide encoder. We define $M$ generic new modalities, denoted as $m_h$ for $h \in \{1, 2, \ldots, M\}$ , with input data $\mathbf{X}_{m_h}$ paired with the WSI $\mathbf{X}_{img}$ . Each modality's input is independently encoded by the modal encoders, producing a feature set $\mathcal{F}_{m_h}^0 \in \mathbb{R}^{N_{m_h} \times D}$ , where $N_{m_h}$ is the token length for each modality. The final multi-modal feature set is formed by concatenating features from all modalities, resulting in $\mathcal{F}_{mm}^0 \in \mathbb{R}^{(N_{m_1} + N_{m_2} + \ldots + N_{m_M}) \times D}$ . + +# 3.2.1. Transcriptomics Encoder + +Bulk transcriptomics data is increasingly available and provides complementary insights on cancer biology to WSIs [8, 10, 31], allowing it to effectively predict patient survival [5, 19]. Thus, we consider it our primary additional modality in this work. Other modalities, such as clinical data (see Supp. Sec. 13), additional "omics," imaging techniques, or domain-specific priors, can in principle be integrated by concatenating their extracted feature tokens. However, further exploration of these extensions is left for future work. + +The transcriptomics encoder compresses bulk transcriptomics data, $\mathbf{X}_t\in \mathbb{R}^{N_g}$ , containing $N_{g}$ genes into a set of tokens. We begin by dividing the genes into $N_{gp}$ gene pathways, which are encoded using a sparse multi-layer perceptron (S-MLP) [19] into pathway features, $\tilde{\mathcal{F}}_{gp}\in \mathbb{R}^{N_{gp}\times D_{gp}}$ , as described in [31]. To merge intra- and interpathway features, we use the MLP-mixer [62], encoding pathway features to produce $\mathcal{F}_{gp}\in \mathbb{R}^{N_{gp}\times D}$ . Finally, a linear projection reduces the number of pathways to $N_{t}$ , enhancing downstream tractability. The encoder finally outputs a compressed set of pathway tokens, $\mathcal{F}_t^0\in \mathbb{R}^{N_t\times D}$ . + +![](images/cd10e5f02eda7a0d3f2237f13315b3d8d18d4defc74f832a356806707192bcd7.jpg) +Figure 2. Overview of ModalTune. Built on a frozen pre-trained slide encoder (a), our Modal Adapter (b) integrates extra-modal features via the Multi-Modal Feature Injector (c) and Extractor (d). A text embedding module (e) unifies multiple tasks and cancer sites, while the enriched image, task, and modal embeddings are fused for training, ensuring a robust multi-modal, multi-task representation. + +# 3.3. Modal Adapter + +To integrate multi-modal features while taking advantage of pre-trained slide encoders, we introduce the Modal Adapter. Our adapter introduces informative cross-modality features into slide encoders, drawing inspiration from the ViT-Adapter [12]. Specifically, it merges compressed pathway features from the transcriptomics encoder with image features from the slide encoder, enriching the network with meaningful multi-modal representations. + +# 3.3.1. Task Prompt + +The Modal Adapter requires distinct feature sets tailored to each downstream task. To facilitate feature interactions and attention operations, we introduce a learnable [task] prompt. This consists of a set of learnable vectors, $\mathcal{F}_{[task]}^{0,j} \in \mathbb{R}^{1 \times D}$ , for each downstream task $j \in \{1,2,\dots,T\}$ , capturing task-specific biases across $T$ tasks. This prompt is concatenated with $N_{t}$ modal tokens derived from compressed pathways in our approach, to create the complete set of multi-modal features: $\mathcal{F}_{mm}^{0,j} \in \mathbb{R}^{(N_t + 1) \times D}$ . + +# 3.3.2. Multi-modal Feature Interaction + +Feature interaction in the Modal Adapter is governed by Multi-modal Feature Injector modules, which inject multimodal features into image features, and Multi-modal Feature Extractor modules, which extract image features to inform the features from extra modalities. + +Multi-Modal Feature Injectors are formulated as standard cross-attention, CrossAttn(·) [65], with query being the WSI features, $\mathcal{F}_{img}^{i,j} \in \mathbb{R}^{(N_{img} + 1) \times D}$ , and key and value + +being the multi-modal features, $\mathcal{F}_{mm}^{i,j}\in \mathbb{R}^{(N_t + 1)\times D}$ . The Injector for the $i$ -th LongNet block and $j$ -th task is given as, + +$$ +\hat {\mathcal {F}} _ {i m g} ^ {i, j} = \mathcal {F} _ {i m g} ^ {i, j} + \gamma^ {i} \operatorname {C r o s s A t t n} \left(\operatorname {L N} \left(\mathcal {F} _ {i m g} ^ {i, j}\right), \operatorname {L N} \left(\mathcal {F} _ {m m} ^ {i, j}\right)\right) (1) +$$ + +where, $\mathrm{LN}(\cdot)$ is LayerNorm [4], and $\gamma^i\in \mathbb{R}^D$ is a learnable vector controlling how the original image features are adjusted by the cross-attention layer. Based on [12], we initialize $\gamma^i$ with 0 to allow multi-modal features to be gradually introduced into the pre-trained slide encoder during training. The image features from the next LongNet block, $\mathcal{F}_{img}^{i + 1,j}$ , are obtained by passing the post-injection image features, $\hat{\mathcal{F}}_{img}^{i,j}$ through the $i$ -th LongNet block. + +Multi-modal Feature Extractors introduce image features back into multi-modal features. It is implemented using cross-attention, followed by an MLP and a self-attention operation SelfAttn(·) to model interactions between different modalities and task tokens. Here, the query is $\mathcal{F}_{m m}^{i,j}$ , and the key and value are the image features after passing through a LongNet block, $\mathcal{F}_{i m g}^{i + 1,j}$ , as shown in Eq. (2) and Eq. (3). + +$$ +\hat {\mathcal {F}} _ {m m} ^ {i, j} = \mathcal {F} _ {m m} ^ {i, j} + \operatorname {C r o s s A t t n} \left(\operatorname {L N} \left(\mathcal {F} _ {m m} ^ {i, j}\right), \operatorname {L N} \left(\mathcal {F} _ {i m g} ^ {i + 1, j}\right)\right) \tag {2} +$$ + +$$ +\mathcal {F} _ {m m} ^ {i + 1, j} = \operatorname {S e l f A t t n} \left(\hat {\mathcal {F}} _ {m m} ^ {i, j} + \operatorname {M L P} \left(\operatorname {L N} \left(\hat {\mathcal {F}} _ {m m} ^ {i, j}\right)\right)\right) \tag {3} +$$ + +# 3.3.3. Output Feature Representation + +We extract the representation from the final LongNet block, $\mathcal{F}_{img}^{B,j}\in \mathbb{R}^{(N_{img} + 1)\times D}$ , using the [CLS] token to get the image feature, $\mathbf{z}_{img}^j\in \mathbb{R}^D$ . We use the final multi-modal + +features $\mathcal{F}_{mm}^{B,j}\in \mathbb{R}^{(N_t + 1)\times D}$ , indexed by the [task] token, to obtain the task-specific vector, $\mathbf{z}_{[task]}^j\in \mathbb{R}^D$ . We also average the multi-modal features across the $N_{t}$ compressed pathway tokens to get a modality-specific feature, $\mathbf{z}_{mm}^{j}$ . Here, $\mathbf{z}_{[task]}^{j}$ encapsulates task-specific information enriched with image and extra-modality features, while $\mathbf{z}_{mm}^{j}$ captures modality-specific information contextualized by image and task features. We average modality features to form $\mathbf{z}_{mm}^{j}$ because the $\mathbf{z}_{[task]}^{j}$ primarily captures enriched task information, making it inadequate to represent modality features independently. Therefore, excluding the modality representation $\mathbf{z}_{mm}^{j}$ would lead to an incomplete feature set. The final output representation, $\mathbf{z}_{comb}^{j}\in \mathbb{R}^{D_{final}}$ combining all features tailored for the $j$ -th task is produced as, + +$$ +\mathbf {z} _ {\text {c o m b}} ^ {j} = \operatorname {M L P} \left(\operatorname {L N} \left(\mathbf {z} _ {\text {i m g}} ^ {j} + \mathbf {z} _ {\text {m m}} ^ {j} + \mathbf {z} _ {[ \text {t a s k} ]} ^ {j}\right)\right) \tag {4} +$$ + +This vector can be used alongside classical machine learning methods on downstream tasks. Importantly, the Modal Adapter does not update the slide encoder weights, taking better advantage of pre-trained SLFMs and reducing the computational cost of our methodology. + +# 3.4. Text Embedding + +We encode tasks using text to unify tasks, datasets, and cancer sites into a single embedding space, eliminating the need for complex loss functions. We generate text embeddings by converting clinical tabular data into text (Fig. 2) and processing it with a pre-trained text encoder. Here, we use the text encoder from CONCH [43], pre-trained on histology captions. Since different tasks require unique feature interactions (Sec. 3.3.1), we create a 'general' task ( $j = 1$ ) text embedding with all clinically relevant information and 'task-specific' ( $j > 1$ ) embeddings tailored to each downstream task. The text for the $j$ -th task is encoded into a vector, $\hat{\mathbf{y}}_{text}^{j} \in \mathbb{R}^{D_{text}}$ , and passed through a fixed, randomly-initialized Projector to produce the final text embedding, $\mathbf{y}_{text}^{j} \in \mathbb{R}^{D_{final}}$ . The Supplementary provides further details on text construction (Sec. 9) and analysis (Sec. 10). + +# 3.5. Training Objective + +We aim to replicate the text embedding distribution to capture both task-specific information and semantic relationships. To achieve this, we use Kullback-Leibler (KL) divergence, following [40], who demonstrated its advantages over CLIP [53] and other distillation losses. ModalTune is optimized to align the multi-modal embedding $\mathbf{z}_{comb}^{j}$ for task $j$ with its corresponding text embedding $\mathbf{y}_{text}^{j}$ . The alignment is achieved by minimizing the KL divergence loss, averaged across all tasks, as shown in Eq. (5), where $\sigma(\cdot)$ denotes softmax function. + +$$ +\mathcal {L} = \frac {1}{T} \sum_ {j = 1} ^ {T} D _ {K L} \left[ \sigma \left(\frac {\mathbf {z} _ {c o m b} ^ {j}}{| | \mathbf {z} _ {c o m b} ^ {j} | | _ {2}}\right) \left| \right| \sigma \left(\frac {\mathbf {y} _ {t e x t} ^ {j}}{| | \mathbf {y} _ {t e x t} ^ {j} | | _ {2}}\right) \right] \tag {5} +$$ + +
BRCAGBMLGGNSCLCRCCCOADREADBLCA
Train cases747401667574273256
Val cases113711001023846
Test cases1881181671706476
# events14620036221985171
# censorship902390572627290207
Rare-set11101030580
Class 0746102378271248312
Class 11914884535106966
Class 2---65--
+ +Table 1. Dataset statistics. Note: 'Rare-set' denotes cancer subtypes not considered for training due to their relative rarity. + +# 4. Experiments and Results + +# 4.1. Datasets + +We utilized four TCGA datasets [63]—BRCA, NSCLC, GBMLGG, and RCC—to train and evaluate ModalTune for cancer subtype and survival prediction, covering 4,099 slides and 3,418 patients. COADREAD and BLCA datasets were used as OOD data to test model generalizability. Data was split at patient-level into $[68\%, 12\%, 20\%]$ for training, validation, and testing, stratified by cancer subtypes (Tab. 1). Transcriptomics data were sourced from the Xena database [23] and preprocessed similar to SurvPath [31], resulting in 331 pathways with 4,987 genes. For subtyping, subtypes were grouped into broader categories based on OncoTree code definitions [37], with rare subtypes ( $< 25$ cases) assigned to a 'Rare-set' used only for training with text embeddings. Baseline models cannot use this class due to insufficient occurrences for effective label-based training. Exact groupings are detailed in the Supp. Sec. 8. For each patient, we extracted $256 \times 256$ patches from WSI foreground regions (via thresholding in HSV colorspace) at $0.5\mu m/pixel$ . Since outputs are generated on a patient-wise basis, patches from multiple WSIs were concatenated into a single bag. Features of size $D_{img} = 1536$ were extracted from each patch using Gigapath's DINOv2 [47] pre-trained feature extractor. + +# 4.2. Baseline Setup + +Baselines are trained in a single-task, single-cancer manner for classification and survival tasks. 'WSI' baselines use only WSIs, including popular models like ABMIL [28] and TransMIL [59]. We also assess the standalone SLFM, Gigapath [72], with full end-to-end tuning. 'Genomics' baselines rely on bulk transcriptomics, including MLP, SNN [35], and S-MLP [19]. We also test ModalTune's transcriptomics encoder, integrating an MLP-mixer [62] with S-MLP. 'Multi-modal' baselines combine image and genomic data, including cross-attention-based early fusion methods like MCAT [10] and SurvPath [31]. We also evaluate late fusion methods, merging image-only baselines with MLP-mixers via concatenation [46] and Kronecker product [8]. + +# 4.3. ModalTune Setup + +We configure ModalTune for $T = 3$ tasks: general, survival, and subtype prediction. Gene pathways are linearly projected to $N_{t} = 64$ dimensions for tractability, and the final output feature dimension is $D_{final} = 256$ . Training runs for 30 epochs with a 0.0001 learning rate and batch size of 1. Additional details are in Supp. Sec. 7. + +After training, we evaluate its feature quality for classification and survival prediction. Using the General $(j = 1)$ task prompt, we extract features from both training and test datasets, selecting the best training epoch based on validation classification performance. For final alignment, we use linear probing (LP), fitting a linear classifier [49] for cancer subtypes and a Cox Proportional Hazards (CPH) model [15] for survival prediction. All ModalTune results are multitask, utilizing a single feature set for both tasks. 'ModalTune' experiments are trained per cancer site and applied to downstream tasks within the same site, while 'ModalTune Pan-Cancer' pools all cancer sites during training and fits separate classifiers or CPH models per site for prediction. + +# 4.4. Generalization Study Setup + +To assess the generalizability of our pipeline, we apply fine-tuned models to unseen TCGA datasets: COADREAD and BLCA. 'ModalTune Pan-Cancer' applies the trained indomain model to extract features on OOD datasets. 'ModalTune' extracts features using the model trained on BRCA. 'Gigapath Surv./Cls. (cat)' applies the respective single-task models directly tuned on BRCA and removes the final prediction layer to extract WSI features. We perform linear probing after feature extraction for all these experiments. The final 'Gigapath Sup. (cat)' experiment uses supervised learning to directly tune the multi-modal Gigapath baseline on both tasks on the train sets of the OOD datasets. + +# 4.5. Quantitative Analysis + +To address class imbalances in subtype classification, we report balanced accuracy, while survival prediction is evaluated using C-indices. Tab. 2 presents subtype classification and survival prediction results, showing the mean and standard deviation across three random seed runs. We report ablation studies on key design choices, including Modal Adapters, text embeddings, text encoders, task prompts, and Projectors in the Supp. Sec. 11. + +Overall Results: On average, we found ModalTune surpassed all other baselines on subtype classification and survival prediction tasks on multiple cancer sites, with $+1.4\%$ and $+1.9\%$ overall improvement, respectively, over the best baseline. ModalTune also greatly improved over the standard image-only SLFM framework, Gigapath (Tuned) $(+4.6\%)$ in subtype, $+9.6\%$ in survival prediction). These large improvements can be partially attributed to the introduction of the additional bulk transcriptomics modal + +ity. However, a fully-tuned Gigapath model with a late fusion of transcriptomics features (Gigapath (cat) and (KP)) still performs $2.8\%$ worse on classification and $7.0\%$ worse on survival prediction compared to ModalTune, indicating the benefits of our overall framework. Though TITAN is a stronger standalone model, applying ModalTune with it yielded similar trends (supp. Sec. 12). + +Importance of Robust Multi-modal Interactions: The best modality for prediction varied by task and cancer site. For instance, WSI-baselines outperformed Genomics-baselines in BRCA subtyping, while the reverse was observed for RCC survival prediction. Combining modalities generally enhanced performance, as seen in GBMLGG, where adding bulk transcriptomics led to near-perfect subtyping in multi-modal models, with a $+7.4\%$ improvement from single to multi-modal Gigapath. Further investigation using a linear classifier on transcriptomics (test balanced accuracy: 0.99) identified four genes—CDC26, IDH1, IL13RA2, and IL8—explaining $97.5\%$ of accuracy, with IDH1 being a well-documented biomarker [66], potentially trivializing classification. Thus, multi-modal results on GBMLGG serve as a “sanity check” for the transcriptomics signal, which fusion models—except MCAT—effectively retained. However, naive fusion of multi-modal features was not always effective, especially for survival prediction, where the best multi-modal TransMIL model (KP) dropped $1.5\%$ compared to Gene Mixer, and Gigapath (cat) dropped $2.5\%$ . These findings emphasize the need for a robust mixing strategy when integrating multi-modal features. + +Generalization Study: As shown in Tab. 3, the fully tuned Gigapath (cat) models severely overfit on BRCA, resulting in poor performance on both subtype and survival prediction tasks. These models fail to extract meaningful features for subtyping, defaulting to predicting the most common class (balanced accuracy of $\sim 0.5$ ). We also observe that ModalTune consistently outperforms Gigapath LP across both tasks and cancer sites. Furthermore, ModalTune PanCancer demonstrated superior generalizability, performing only $2.4\%$ worse than a fully-supervised Gigapath (cat) network in subtype prediction and actually outperforming it by $1.2\%$ in survival prediction. ModalTune's ability to extract highly relevant features without exposure to OOD datasets during fine-tuning underscores its capacity to maintain the generalizability of SLFMs. This result is particularly promising for the downstream application of ModalTune to smaller unseen datasets. + +Pan-Cancer Results: As shown in Tab. 2, training a single ModalTune Pan-Cancer model by merging cancer sites did not outperform training models independently for each site on in-domain datasets, with a decrease of $2.8\%$ in classification and $3.0\%$ in survival prediction. This aligns with findings in [30], where a specialized model outperformed the pan-cancer model for molecular status prediction. How- + +
BRCAGBMLGGNSCLCRCCOverall
Cancer Subtype Prediction
WSIGigapath LP [72]0.6120.9000.8210.8510.796
ABMIL [28]0.853 ± 0.0150.931 ± 0.0400.920 ± 0.0120.921 ± 0.0170.906
TransMIL [59]0.828 ± 0.0110.978 ± 0.0120.934 ± 0.0070.918 ± 0.0160.915
Gigapath (Tuned) [72]0.860 ± 0.0130.931 ± 0.0290.916 ± 0.0120.939 ± 0.0160.912
GenomicsMLP0.752 ± 0.0320.998 ± 0.0020.926 ± 0.0070.883 ± 0.0160.890
SNN [35]0.753 ± 0.0190.991 ± 0.0020.926 ± 0.0010.902 ± 0.0080.893
S-MLP [19]0.839 ± 0.0151.000 ± 0.0000.941 ± 0.0050.890 ± 0.0030.917
Gene Mixer0.840 ± 0.0141.000 ± 0.0000.932 ± 0.0050.898 ± 0.0360.917
Multi-modalMCAT [10]0.875 ± 0.0140.973 ± 0.0050.921 ± 0.0060.933 ± 0.0280.925
SurvPath [31]0.858 ± 0.0280.995 ± 0.0070.932 ± 0.0070.936 ± 0.0300.930
ABMIL (cat) [28]0.861 ± 0.0101.000 ± 0.0000.951 ± 0.0030.937 ± 0.0280.937
ABMIL (KP) [28]0.884 ± 0.0100.998 ± 0.0020.939 ± 0.0050.945 ± 0.0310.941
TransMIL (cat) [59]0.847 ± 0.0271.000 ± 0.0000.950 ± 0.0040.957 ± 0.0200.939
TransMIL (KP) [59]0.868 ± 0.0171.000 ± 0.0000.946 ± 0.0050.930 ± 0.0110.936
Gigapath (cat) [72]0.850 ± 0.0170.998 ± 0.0020.924 ± 0.0110.926 ± 0.0340.925
Gigapath (KP) [72]0.821 ± 0.0201.000 ± 0.0000.963 ± 0.0030.927 ± 0.0180.928
ModalTune (Ours)0.899 ± 0.0261.000 ± 0.0000.956 ± 0.0100.959 ± 0.0030.954
ModalTune Pan-Cancer (Ours)0.858 ± 0.0010.990 ± 0.0090.958 ± 0.0040.902 ± 0.0330.927
Survival Prediction
WSIGigapath LP [72]0.6470.7950.5620.6790.671
ABMIL [28]0.712 ± 0.0040.854 ± 0.0040.582 ± 0.0020.670 ± 0.0040.704
TransMIL [59]0.742 ± 0.0150.868 ± 0.0090.586 ± 0.0110.676 ± 0.0030.718
Gigapath (Tuned) [72]0.680 ± 0.0240.824 ± 0.0170.546 ± 0.0050.685 ± 0.0120.684
GenomicsMLP0.629 ± 0.0390.884 ± 0.0040.542 ± 0.0130.720 ± 0.0020.694
SNN [35]0.519 ± 0.0510.883 ± 0.0100.508 ± 0.0120.723 ± 0.0080.659
S-MLP [19]0.749 ± 0.0300.887 ± 0.0020.571 ± 0.0110.735 ± 0.0030.736
Gene Mixer0.762 ± 0.0490.870 ± 0.0070.556 ± 0.0330.690 ± 0.0090.719
Multi-modalMCAT [10]0.673 ± 0.0440.880 ± 0.0060.592 ± 0.0020.697 ± 0.0040.710
SurvPath [31]0.741 ± 0.0310.895 ± 0.0030.613 ± 0.0100.677 ± 0.0110.732
ABMIL (cat) [28]0.736 ± 0.0070.896 ± 0.0040.605 ± 0.0110.690 ± 0.0040.732
ABMIL (KP) [28]0.685 ± 0.0080.895 ± 0.0020.594 ± 0.0100.699 ± 0.0030.718
TransMIL (cat) [59]0.666 ± 0.0180.872 ± 0.0300.595 ± 0.0030.689 ± 0.0040.705
TransMIL (KP) [59]0.689 ± 0.0140.889 ± 0.0030.541 ± 0.0230.713 ± 0.0030.708
Gigapath (cat) [72]0.678 ± 0.0040.861 ± 0.0230.573 ± 0.0030.693 ± 0.0160.701
Gigapath (KP) [72]0.650 ± 0.0430.865 ± 0.0320.563 ± 0.0050.686 ± 0.0160.691
ModalTune (Ours)0.772 ± 0.0080.879 ± 0.0040.608 ± 0.0230.743 ± 0.0040.750
ModalTune Pan-Cancer (Ours)0.757 ± 0.0390.860 ± 0.0060.586 ± 0.0200.705 ± 0.0070.727
+ +Table 2. Cancer subtype prediction balanced accuracy and survival prediction C-index scores across 4 cancer types. Best model in bold, second best is underlined. Here, LP refers to linear probing, cat refers to concatenation, and KP refers to Kronecker product. + +
COADREADBLCA
Cancer Subtype Prediction
Gigapath LP0.5100.569
Gigapath Sup. (cat)0.581 ± 0.0060.703 ± 0.018
Gigapath Cls. (cat)0.504 ± 0.0300.497 ± 0.005
Gigapath Surv. (cat)0.500 ± 0.0000.497 ± 0.005
ModalTune0.574 ± 0.0240.664 ± 0.025
ModalTune Pan-Cancer0.564 ± 0.0340.689 ± 0.035
Survival Prediction
Gigapath LP0.4820.603
Gigapath Sup. (cat)0.528 ± 0.0230.673 ± 0.020
Gigapath Cls. (cat)0.479 ± 0.0420.610 ± 0.063
Gigapath Surv. (cat)0.512 ± 0.0610.552 ± 0.052
ModalTune0.539 ± 0.0680.629 ± 0.041
ModalTune Pan-Cancer0.543 ± 0.0200.672 ± 0.046
+ +Table 3. Generalization study on OOD datasets using different models, compared with Gigapath Sup. (cat) trained directly on the OOD data. Best OOD model in bold, second best is underlined. + +ever, the Pan-Cancer model is significantly more resource-efficient, requiring only one model instead of one per cancer site. As the number of sites $N_{\text{sites}}$ and tasks $T$ increase, scalability and efficiency benefits become more pronounced, surpassing simple baselines. This highlights a trade-off where the Pan-Cancer model enhances resource efficiency with minor performance compromises. + +We hypothesize the performance drop on in-domain datasets is due to variations in task difficulty across cancer sites. Training standard ModalTune revealed variability in the optimal validation epoch per site—NSCLC reached peak performance 10 epochs earlier than GBMLGG, which required more training to converge. In the pan-cancer model, early stopping optimized for NSCLC led to underfitting for GBMLGG, while extended training overfitted NSCLC. Despite these convergence challenges reducing in-domain performance, exposure to diverse cancer sites in the pan-cancer setup greatly enhances generalizability on OOD datasets (Tab. 3). Thus, we believe the pan-cancer approach is promising and emphasize the need for optimization strategies to recover in-domain performance. + +# 4.6. Qualitative Analysis + +To assess pathway contributions and modality interactions, we analyze two breast cancer cases from high and low-risk categories, as shown in Fig. 3. See Supp. for more qualitative analysis of t-SNE and Kaplan-Meier (Sec. 14). + +Pathway Contributions: We applied Integrated Gradients [60] to analyze pathway contributions as shown in Fig. 3 (e,f). In the high-risk case, incorporating pathway signals + +![](images/c250a5bd677086531830879476b9eb476ddbc174d54c11ab2026559821d4b7f1.jpg) + +![](images/75310efb535a5c5fd460ff3924ba6fc240564d62c069cd195fca42f8b10fffa3.jpg) + +![](images/0c09dfbb8ffe50f1e45c8a6924581d6fc49532e9e2383f53b7e807c2123d6e96.jpg) + +![](images/d81e1310b70b24072e94a4cef78aafe6048683db6fd0b390fb786b384f4e60b9.jpg) +Figure 3. Qualitative analysis of breast cancer cases, highlighting a high-risk (a) and a low-risk case (b). (1) Attention Maps (c,d) depict cross-modal and cross-task interactions, with heatmap colors indicating importance (red: high, blue: low). (2) Integrated Gradients (e,f) shows the top 10 pathways influencing risk, with orange bars indicating pathways increased risk and blue bars indicating pathways decreased risk. The analysis highlights biologically relevant pathways (e.g., G2M checkpoint) and morphologically significant regions. + +![](images/38113dd9280d33279a166275414b7d5d3eac5c4bb4a0cacb7dea50c91eee6ab5.jpg) + +![](images/bb34f0fa9a9044726ed9066dd7e839134507cd1fe95c1aab4856f9fe3e9b6161.jpg) + +raised the risk score from 2.07 to 2.23. Key contributors included mitotic spindle assembly [67], G2M checkpoint regulation [42], and SCF-beta-TrCP Mediated Emi1 degradation [45], consistent with their roles in cell cycle progression and tumor proliferation. In both cases, the inflammatory response [77] lowered risk, reflecting its association with reduced oncogenic activity. Metabolic pathways like alcohol and purine catabolism [70] also reduced risk but require further study. In the low-risk case, the score dropped from 1.09 to 0.75, driven by inflammatory response [77], p53 activation [21], MYC targets [56], and estrogen signaling suppression [48]—aligning with established roles in modulating tumor progression or suppression. Interestingly, myogenesis [36] and apoptosis regulation (BH3-only & BCL-2 interaction, BAK activation, and oligomerization) contributed to increased risk, with myogenesis also linked to risk in SurvPath's analysis [31], warranting further study. Interaction Analysis: We analyzed cross- and self- attention maps to understand different learned interactions, as shown in Fig. 3 (c,d). Specifically, we examined the self-attention of LongNet [CLS] tokens with patch tokens (image-image), averaged cross-attention of pathway tokens with patch tokens (image-transcriptomics), and cross-attention of patch tokens with task prompts (image[task] prompt). Our findings show that image-image self-attention primarily focuses on tumor regions, capturing key pathological features, while image-transcriptomics attention highlights tumor-associated stroma. Differences in attention maps for subtype prediction and survival task + +prompts suggest both shared and distinct feature utilization, with general prompts integrating elements from both. + +# 5. Conclusion + +In this study, we introduced ModalTune, a flexible fine-tuning framework that maximizes dataset usage for SLFMs in histopathology. To our knowledge, ModalTune is the first multi-modal, multi-task and pan-cancer tuning framework. By leveraging inter-modal and inter-task interactions, ModalTune outperformed all single-task baselines while retaining generalizability. Its resource-efficient variant, ModalTune Pan-Cancer, further improves generalization on small OOD datasets, outperforming other fine-tuned models by a large margin while remaining competitive with supervised baselines. This underscores ModalTune's ability to enhance SLFMs' capacity for handling smaller datasets. + +Despite its strengths, ModalTune faces two key challenges. Firstly, because the interaction between multimodal and image features is mediated by cross-attention, it can be computationally expensive. We mitigated this by compressing pathway tokens, but future work may explore cheaper formulations of cross-attention. Secondly, the model may underfit one task while overfitting another due to varying task complexities, as seen in our pan-cancer experiments. Future work will explore strategies to mitigate the pan-cancer convergence issue, and ModalTune's adaptability to other SLFMs. Looking ahead, we also aim to incorporate additional tasks and modalities to ModalTune. + +# 6. Acknowledgments + +This work was supported by funding from the Canadian Institutes of Health Research (CIHR grant #162327), Canada Foundation for Innovation (40206), and the Ontario Research Fund. 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